Advances in Mechanical Design: Proceedings of the 2019 International Conference on Mechanical Design (2019 ICMD) [1st ed. 2020] 978-981-32-9940-5, 978-981-32-9941-2

Focusing on innovation, these proceedings present recent advances in the field of mechanical design in China and offer r

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Advances in Mechanical Design: Proceedings of the 2019 International Conference on Mechanical Design (2019 ICMD) [1st ed. 2020]
 978-981-32-9940-5, 978-981-32-9941-2

Table of contents :
Front Matter ....Pages i-xvi
Multi-hierarchy Carbon Footprint Analysis and Low-Carbon Design Improvement Method (Hong Bao, Sheng Guo, Qing Di Ke)....Pages 1-11
The Design and Dynamics Analysis of Cylindrical Roller Surface Unfolding Mechanism (Yudong Bao, Xiaojian Chen, Chengyi Pan, Yanling Zhao, Liqun He)....Pages 12-27
A Novel Cable-Driven Parallel Robot for Inner Wall Cleaning of the Large Storage Tank (Wanghui Bu, Weiqi Zhou, Laixin Fang, Jing Chen, Xianghua An, Jingkai Huang)....Pages 28-40
A Novel Biomimetic Design Method Based on Biology Texts Under Network (Bowen Chen, Liang Chen, Xiaomin Liu, Hao Dou)....Pages 41-51
Numerical Simulation on Effect of Graphene Doped Morphology on Heat Transfer Efficiency of Anti-/deicing Component (Long Chen, Zhanqiang Liu)....Pages 52-62
Numerical Analysis on Load Sharing Characteristics of Multistage Face Gears in Planetary Transmission (Xingbin Chen, Qingchun Hu, Chune Zhu)....Pages 63-83
Reachable Matrix and Directed Graph – Based Identification Algorithm of Module Change Propagation Path for Product Family (Xianfu Cheng, Liyun Wan, Jian Zhou)....Pages 84-92
6-DOF Industrial Manipulator Motion Planning Based on RRT-Connect Algorithm (Chengren Yuan, Guifeng Liu, Wenqun Zhang)....Pages 93-101
A Precise Identification and Matching Method for Customer Needs Based on Sales Data (Xingpeng Chu, Jian Zhang, Uday Shanker Dixit, Peihua Gu)....Pages 102-112
Optimization Design of the Non-magnetic Drill Rod for Directional Drilling in the Coal Mine (Dayong Tang, Lu Liu)....Pages 113-124
Research on Product Redesign Process Based on Functional Analysis (Yafan Dong, Runhua Tan, Peng Zhang, Wei Liu, Ruiqin Wang)....Pages 125-138
Analysis of Characteristics and Structure Optimization of Anti-rolling Torsion Bar (Yahong Dong, Yuejin Shang)....Pages 139-150
Coupling Mechanism of Errors in the Planetary Roller Screw Mechanism (Chuanming Du, Geng Liu, Junqi Liu, Shangjun Ma)....Pages 151-161
A Novel Tooth Contact Analysis Method Based on Value Iteration (Jinfu Du, Zhengrong Wang, Kai Liu, Yiteng Gao)....Pages 162-169
Rigidity Synthesis and Machining Error Analysis of Machine Tool Chain (Pengyu Hao, Gongxue Zhang, Zijian Pei, Xianming Gao)....Pages 170-188
Thermodynamic Lubrication Performance and Stability for a Deep/Shallow Pocket Hybrid Bearing Considering Bubbly Oil (Hong Guo, Shuai Yang, Ningning Wu, Ruizhen Li)....Pages 189-201
Time Delay Chen System Analysis and Its Application (Hongjun He, Yan Cui, Chenhui Lu, Guan Sun)....Pages 202-213
The Driver-in-the-Loop Simulation on Regenerative Braking Control of Four-Wheel Drive HEVs (Hexu Yang, Xiaopeng Li, Pengxiang Li, Yu Gao)....Pages 214-222
Strength and Modal Analysis of High Speed EMU Gearbox Housing (Haijun Huang, Bichao Yin, Chaowen Wang, Haiyan Zhu)....Pages 223-228
Indirect Adaptive Fuzzy Sliding-Mode Control for Hydraulic Manipulators (Xin Huang, Yi Wan, Yao Sun, Jiarui Hou)....Pages 229-242
Improvement and Research of Tennis Training Machine (Huiqiang Guo, Jianye Pan, Wen Liu, Yiling Yue)....Pages 243-252
Design of Flagstone Transport Device Based on TRIZ Theory (Fan Jiang, Jian Shen, Tao Zhu, Jinfeng Wen)....Pages 253-266
Fault Analysis and Structure Optimization of End Face Seal of Hydraulic Oscillator (Haixiang Jiang)....Pages 267-273
Innovative Design of Leeward Surface of Pin Fin in Flame Arresters Fitted in Explosion Relief Valve (Lanfang Jiang, Shuyou Zhang, Xin Shu, Weina Hao, Yun Ren, Zhiya Chen)....Pages 274-287
Analysis and Optimization of Performance Under Operating Condition of Thrust Aerostatic Bearing with Vacuum Pre-load (Mengyang Li, Qiu Hu, PinKuan Liu, Ming Huang)....Pages 288-301
A Study on Innovative Design of Rotary Pile Foundation Drilling Machine Based on TRIZ Theory (Fuxing Li)....Pages 302-309
Design and Optimization of Focusing X-Ray Telescope Based on Intelligent Algorithm (Liansheng Li, Zhiwu Mei, Jihong Liu, Fuchang Zuo, Jianwu Chen, Hanxiao Zhang et al.)....Pages 310-324
Research of Dormitory Furniture Design Based on Group Interaction (Lin Li, Xupeng Wang, Chunqiang Zhang)....Pages 325-341
Analysis and Extraction of Consumer Information for the Evaluation of Design Requirement Depending on Consumer Involvement (Shipei Li, Dunbing Tang, Qi Wang, Haihua Zhu)....Pages 342-353
Reduction in Aerodynamic Resistance of High-Speed Train Nose Based on Kriging Model and Multi-objective Optimization (Tian Li, Deng Qin, Le Zhang, Jiye Zhang, Weihua Zhang)....Pages 354-370
Research and Simulation on Pilot Configuration in Multi-antenna System Based on Kalman Filter (Ying Li, Lei Cui, Zhe Zhang)....Pages 371-379
Development and Experiment of an XθYθZ Micro-motion Stage Based on a Straight-Beam Three-Quarter Round Type Flexure Hinge (Junlang Liang, Lanyu Zhang, Jian Gao, Gengjun Zhong, Guangtong Zhao, Jindi Zhang)....Pages 380-393
An Improved PC-Kriging Method for Efficient Robust Design Optimization (Qizhang Lin, Chao Chen, Fenfen Xiong, Shishi Chen, Fenggang Wang)....Pages 394-411
Electro-Mechanical Response of a Cracked Piezoelectric Cantilever Beam (Chao Liu, Wenguang Liu, Yaobin Wang)....Pages 412-423
A Time-Variant Reliability Analysis Method Considering Maintenance (Jingfei Liu, Chao Jiang, Xiangyun Long)....Pages 424-446
Research on Tooth Profile Error of Non-circular Gears Based on Complex Surface Theory (Yongping Liu, Fulin Liao, Changbin Dong)....Pages 447-455
Topology Optimization Design of the Monocoque Bus Body Structure (Zhuli Liu, Xiangyu Huo, Hao Zhou, Xiaoguang Wu)....Pages 456-465
Analysis of Wind Vibration Response of Transmission Tower (Zhuli Liu, Beibei Liu, Zhuan You, Mengli Li)....Pages 466-476
Design of a Stabilize Device for Heavy Oil Transportation in Water Ring (Haoran Lu, Fan Jiang, Yuliang Chen, Xiaolong Qi, Zhongmin Xiao)....Pages 477-492
Design of Spatial Lissajous Trajectory Vibrating Screen (Zhipeng Lyu, Sizhu Zhou)....Pages 493-498
Part Retrieval Technology Based on Geometric Shape and Topological Correlation (Ning Ma, Bo Yang, Junzhi Shang)....Pages 499-507
Analysis of Tool Wear and Wear Mechanism in Dry Forming Milling for Rail Milling Train (Chao Pan, Xiaoshan Gu, Mulan Wang, Baosheng Wang)....Pages 508-517
Wear Numerical Simulation and Life Prediction of Microstructure Surface Unfolding Wheel for Steel Ball Inspection (Chengyi Pan, Xia Li, Hepeng Wang, Yanling Zhao, Jingzhong Xiang, Sihai Cui et al.)....Pages 518-530
Design of Passive Gravity Balance Mechanism for Wearable Exoskeleton Suit (Chenxi Qu, Peng Yin, Xiaohua Zhao, Liang Yang)....Pages 531-545
Design and Analysis of Underwater Drag Reduction Property of Biomimetic Surface with Micro-nano Composite Structure (Xuezhuang Ren, Lijun Yang, Chen Li, Guanghua Cheng, Nan Liu)....Pages 546-559
A Method of Parametric Stability Region Determination for Non-linear Gear Transmission System (Dongping Sheng, Xiaozhen Li, Rupeng Zhu)....Pages 560-569
Performance and Parameter Sensitivity Analysis of Finger Seal with Radial Clearance (Hua Su)....Pages 570-591
Calculation and Experimental Study on Comprehensive Stiffness of Angular Contact Ball Bearings (Peng Sun, Weifang Chen, Chuan Su, Yusu Shen)....Pages 592-601
Design of a New Hydraulic Manipulator with Kinematic and Dynamic Analysis (Yao Sun, Yi Wan, Xichang Liang, Xin Huang, Ziruo Liu)....Pages 602-614
Research on Electro-Hydraulic Servo System Based on BP-RBF Neural Network (Tao Chen, Wenqun Zhang, Jianggui Han)....Pages 615-622
Collision Simulation of GQ70 Light Oil Tank Car at the Level Crossing (Maopeng Tian, Ronghua Li, Xiujuan Zhang, Miao Jin)....Pages 623-633
Reason Study of Collision Between Valves and Piston of Diesel Engine Valve Train (Dameng Wang, Xiujuan Zhang, Deyu Yue, Weipeng Fan)....Pages 634-646
Macroscopic Topology Optimization of Fusion Cages Used in TLIF Surgery (Hongwei Wang, Yi Wan, Xinyu Liu, Bing Ren, Zhanqiang Liu, Xiao Zhang et al.)....Pages 647-660
Fuzzy Optimization Design of Disc Brakes Based on Genetic Algorithm (Jianbin Wang, Jishu Yin)....Pages 661-668
Modeling Design and Evaluation of Rotary Tiller Based on Multidisciplinary Optimization (Wang Jianwei, Jianmin Zhang, Qin Yang)....Pages 669-685
Experimental Investigation of Thermal Elasto-Hydrodynamic Lubrication Based on Temperature Control (Shuaihong Yu, Yazhen Wang, Jiacheng Shen, Huihui Yue)....Pages 686-696
Study on Nonlinear Characteristics of Spatial Spreading Mechanism with Multiple Clearance Joints (Wenzhou Lin, Xupeng Wang, Xiaomin Ji, Chunqiang Zhang)....Pages 697-707
A Novel Design of Tapered Sub-array Structure for SSPS-OMEGA (Tong Wu, Yingzhong Tian, Meng Li, Long Li)....Pages 708-718
Research on Multiresponse Robustness Optimization for Unmanned Aerial Vehicle Electrostatic Spray System (Yangdong Wu, Jiajie Lu, Yiquan Wang)....Pages 719-728
Research on Trajectory Optimization of Six-Axis Manipulator Based on Watchcase Polishing (Xiang Wang, Ying Xi, Chao Gu, Mengru Li)....Pages 729-739
Reverse Modeling of the Helix Roller in the Omni-Directional Wheel Based on NURBS (Xie Xia)....Pages 740-748
Research on Automatic Matching Model of Power Battery (Chuanfu Xin, Fengxia Zhao, Yujin Wu, Jianshe Gao)....Pages 749-759
Random Vibration Analysis of Optical Adjustable Frame Based on ANSYS Workbench (Nan Xu, Yuan Wang, Kelin Xu)....Pages 760-768
Analysis of Influence of Eccentricity Error on Transmission Performance of Micro-segment Gears (Rui Xu, Lielong Wang, Peidao Pan, Kang Huang)....Pages 769-784
Research on the Design of Wearable Equipment for Intelligent Emotion Detection for Empty Nester (Yan-min Xue, Chang Ge, Shi-yi Xu, Xu-yang Zhang, Bo-xin Xiao)....Pages 785-794
Narrative Design of Old Brand Image: A Case Study of Demaogong (Yanmin Xue, You Wu, Yihui Zhou, Yang Liu)....Pages 795-803
Study on the Theory and Practice of Mechanical Design (Yunna Xue, Xuehui Shen, Baolin Wang)....Pages 804-810
Simulation Analysis of Pipe Bending Under Multiple Conditions (Guodong Yi, Zhenan Jin, Shaoju Zhang)....Pages 811-822
Simulation Analysis of Sealing Performance of Double-Offset Butterfly Valve (Guodong Yi, Shaoju Zhang, Zhenan Jin)....Pages 823-831
Motion Performance Analysis of the Sawyer Ankle Rehabilitation Robot (Yongfeng Wang, Xiangzhan Kong, Jing Yang, Guoru Zhao)....Pages 832-846
Automated Sustainable Low-Carbon Design of Offshore Platform for Product Life Cycle (Qianyi Yu, Bin He)....Pages 847-863
Comfort of Minors’ Sitting Posture in Learning Based on Motion Capture (Chunqiang Zhang, Xiaomin Ji, Yanmin Xue, Chunmei Zhang)....Pages 864-876
Lightweight Design of Dump Truck Frame Based on Finite Element Method (Gongxue Zhang, Sen Yang, Shanshan Guo, Qichen Niu)....Pages 877-887
Topological Optimization of the Front Beam in Metal Extruders (Xugang Zhang, Peilin Yang, Xiaole Cheng, Yi Hou)....Pages 888-897
Car Radiator Upper Beam Stamping Process Design and Numerical Simulation (Zhiyuan Wan, Yinping Chen)....Pages 898-903
A Fast Tacho-Less Order Tracking Method for Gear Fault Diagnosis Under Large Rotational Speed Variation Conditions Based on Multi-stage Generalized Demodulation (Qi Zhou, Wenjin Liu, Chaoqun Wu)....Pages 904-917
Gear Fault Diagnosis Under the Run-Up Condition Using Fractional Fourier Transform and Hilbert Transform (Qi Zhou, Chaoqun Wu, Qingrong Fan)....Pages 918-943
An Empirical Study of the Effect of the Completeness of Hands-on Training Design Projects on the Preservation of Tacit Knowledge (Yihui Zhou, Wenzhou Lin, Zhi Qiao, Xiaozhou Li)....Pages 944-951
Research on Structural Size Optimization of 3-TPT Parallel Mechanism Based on Stiffness Characteristics (Chunxia Zhu, Chengzhu Hu)....Pages 952-970
Vibration Response Analysis of Gearbox Housing of High Speed Train Under Wheel and Rail Excitation (Haiyan Zhu, Xiao Su, Lei Tao, Qian Xiao)....Pages 971-976
An Intelligent Fatigue Life Prediction Method for Aluminum Welded Joints Based on Fatigue Characteristics Domain (Li Zou, Hongxin Li, Wei Jiang)....Pages 977-989
Optimum Design of Radiation Well Horizontal Drilling Rig Based on TRIZ and Bionics (Chenghao Liu, Changqing Gao, Bo Yang, Zhenghe Xu)....Pages 990-1001
Innovative Design of Reversing Device and Rod Loading Device of Horizontal Drilling Rig Based on TRIZ (Shifeng Sun, Changqing Gao, Bo Yang, Zhenghe Xu)....Pages 1002-1009
AGV Trolley Tray Based on Honeycomb Paper-Based New Material (Jingjing Yang, Xiaoyi Jin, Anran Wang)....Pages 1010-1017
The Study of Electric Field Distribution on Small Holes in Pulse Electrochemical Machining (Zhaolong Li)....Pages 1018-1029
Reliability Optimization Design of New Automatic Tensioning Belt-Gear Transmission (Chengyi Pan, Guanqun Cao, Yuanqi Tong)....Pages 1030-1043
Design and Simulation Analyses of a Five-Wheeled Stair-Climbing Mechanism Based on TRIZ Theory (Chengyi Pan, Yuanqi Tong)....Pages 1044-1053
Extensible Innovation Design of Globoidal Cam Deceleration Mechanism Based on Knowledge (Shengyang Tian, Qingshan Gong, Guangguo Zhang, Mingmao Hu, Yuemin Wu)....Pages 1054-1069
Tension Analysis of Small Motor Stator Winding Tensioning Process (Yanling Zhao, Zhao Zhang, Jingzhong Xiang, Yudong Bao)....Pages 1070-1081
Study on Contact Dynamics of Cylindrical Roller Feeding Mechanism (Yanling Zhao, Xinyue Wang, Yudong Bao)....Pages 1082-1092
Trajectory Planning for Winding Process of Small-Sized Motor Stator Winding Robot (Yanling Zhao, Linqiang Wang, Jingzhong Xiang, Yudong Bao)....Pages 1093-1108
Experimental Study of a Solid-Liquid Mixing and Conveying Pump with Variable Flow and Proportion (Wei Liu, Qian Tang, Wenzhe Cai, Pinghua Liang, Zongmin Liu, Xiaojie Fan)....Pages 1109-1123
Effect of Pore Parameters on Lubrication Performance of Oil-Containing Cage (Tingting Yin, Yuanyuan Li, Ke Yan, Pan Zhang, Yongsheng Zhu, Jun Hong)....Pages 1124-1135
Defects Detection System for Fluorescent Coating of Metal Plate Based on Machine Vision (Yujin Wu, Fengxia Zhao, Chuanfu Xin, Jianshe Gao, Zhigao Chen)....Pages 1136-1149
Back Matter ....Pages 1151-1154

Citation preview

Mechanisms and Machine Science 77

Jianrong Tan Editor

Advances in Mechanical Design Proceedings of the 2019 International Conference on Mechanical Design (2019 ICMD)

Mechanisms and Machine Science Volume 77

Series Editor Marco Ceccarelli, Department of Industrial Engineering, University of Rome Tor Vergata, Roma, Italy Editorial Board Members Alfonso Hernandez, Mechanical Engineering, University of the Basque Country, Bilbao, Vizcaya, Spain Tian Huang, Department of Mechatronical Engineering, Tianjin University, Tianjin, China Yukio Takeda, Mechanical Engineering, Tokyo Institute of Technology, Tokyo, Japan Burkhard Corves, Institute of Mechanism Theory, Machine Dynamics and Robotics, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany Sunil Agrawal, Department of Mechanical Engineering, Columbia University, New York, NY, USA

This book series establishes a well-defined forum for monographs, edited Books, and proceedings on mechanical engineering with particular emphasis on MMS (Mechanism and Machine Science). The final goal is the publication of research that shows the development of mechanical engineering and particularly MMS in all technical aspects, even in very recent assessments. Published works share an approach by which technical details and formulation are discussed, and discuss modern formalisms with the aim to circulate research and technical achievements for use in professional, research, academic, and teaching activities. This technical approach is an essential characteristic of the series. By discussing technical details and formulations in terms of modern formalisms, the possibility is created not only to show technical developments but also to explain achievements for technical teaching and research activity today and for the future. The book series is intended to collect technical views on developments of the broad field of MMS in a unique frame that can be seen in its totality as an Encyclopaedia of MMS but with the additional purpose of archiving and teaching MMS achievements. Therefore, the book series will be of use not only for researchers and teachers in Mechanical Engineering but also for professionals and students for their formation and future work. The series is promoted under the auspices of International Federation for the Promotion of Mechanism and Machine Science (IFToMM). Prospective authors and editors can contact Mr. Pierpaolo Riva (publishing editor, Springer) at: [email protected] Indexed by SCOPUS and Google Scholar.

More information about this series at http://www.springer.com/series/8779

Jianrong Tan Editor

Advances in Mechanical Design Proceedings of the 2019 International Conference on Mechanical Design (2019 ICMD)

123

Editor Jianrong Tan Zhejiang University Hangzhou, China

ISSN 2211-0984 ISSN 2211-0992 (electronic) Mechanisms and Machine Science ISBN 978-981-32-9940-5 ISBN 978-981-32-9941-2 (eBook) https://doi.org/10.1007/978-981-32-9941-2 © Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Since prehistory times, the ancient inhabitants of the earth have made the design as a way to meet needs and increasingly complex. In the days of the great scientist James Watt, who worked on the improvisation of the steam engine, mechanical engineering started developing rapidly and systematically. And nowadays, the design factor has become one of the most important aspects of mechanical engineering. With a detailed design and engineering process, it can always save lots of costs and improve efficiency. China is moving away from a country with a large manufacturing scale to one with strong manufacturing capabilities. In this process, the ability of design is a key to the role translation from a follower to an initiator in the field of manufacturing for China. Every step to realize the goal of manufacturing enhancing national strength strategy needs the improvement of design capabilities. With the development of artificial intelligence, intelligent design becomes possible and provides an excellent opportunity for leaping development for China. Further development requires us to insist on sustainable development as the basic principle. Therefore, green manufacturing will be an inevitable choice for the industry’s development, and it is becoming one of the factors to measure the manufacturing comprehensive strength of a country. In the tide of manufacturing development, it needs us to seize the opportunities and take actions, so that green manufacturing can be developed with the help of intelligent design and the national manufacturing strength will be improved relying on green manufacturing. In order to promote the development and integration of mechanical design-related disciplines, information exchange on the latest developments in the field of mechanical design, and mutual understanding of demands with industry companies. The 2019 International Conference on Mechanical Design (2019 ICMD) has one theme as Intelligent Design Green Manufacturing. The conference is going to be held in Huzhou, China, during October, and it is a leading conference in the field of mechanical design in China and aims to provide an international platform for researchers, scholars, and scientists to present their research advances and exchange their ideas. Based on the annual meeting of Mechanical Design Branch of China Mechanical Engineering Society, the v

vi

Preface

conference is proposed once every two years since 2017 and we hope to establish a brand name of its kind for the development of the mechanical design. With over 148 submissions, the rigorous review process was held with detailed and in-depth comments on each paper. This resulted in the acceptance of 94 papers with an additional period for authors to revise their papers following the reviewers’ comments. We are very pleased with the overwhelming support from authors and from the communities and with the excellent work from the authors and their serious effort to improve and finalize the papers. This book presents a vivid development of mechanical engineering and is a collection of the work in design and development across the disciplines. With the contributions from the authors, this book delivers a lasting impact on the study and development of the mechanical design. In compiling this book, we are pleased to see the variety of the topics, the depth of the study, and the wide range of the applications of innovative design theory. The development of innovative mechanisms is seen in the book contributing to the development of the mechanical design and presents a strong part for advancing the knowledge in the field and for the economical development. We thank all the authors for their contributions and meticulous manner in preparing their manuscripts and thank all the reviewers for their rigorous review and detailed comments to help authors to improve their papers. Further, we thank Jingjun Yu for his dedication and persistence in checking every manuscript and contacting the authors for their revision of the manuscripts and for finalizing this book. We have received immense support from the China Association for Science and Technology (CAST), The National Natural Science Foundation of China (NSFC), the Chinese Mechanical Engineering Society (CMES), and Chinese Academy of engineering. In organizing the 2019 international conference of mechanical design, we are grateful to members of the scientific committee, the program committee, and the chairs/co-chairs for rigorous peer review of papers.

Committees

General Chair Jianrong Tan

Zhejiang University, China

Program Committee Zongquan Deng Yanmin Zhang Feng Gao Peihua Gu Xu Han Zhifeng Liu Stephen Lu Xianmin Zhang Nam P. Suh Moshe Shpitalni Rupeng Zhu Caichao Zhu Renbin Xiao Sami Kara Yimin Zhang Guanghong Duan Yoram Koren Jack Hu Zhenqiang Yao Wei Chen Runhua Tan

Harbin Institute of Technology, China Chinese Mechanical Engineering Society, China Shanghai Jiao Tong University, China Shantou University, China Hebei University of Technology, China Hefei University of Technology, China University of Southern California, USA South China University of Technology, China Massachusetts Institute of Technology, USA Technion - Israel Institute of Technology, Israel Nanjing University of Aeronautics and Astronautics, China Chongqing University, China Huazhong University of Science and Technology, China University of New South Wales, Australia Shenyang University of Chemical Technology, China Tsinghua University, China University of Michigan, USA University of Michigan, USA Shanghai Jiao Tong University, China Northwestern University, USA Hebei University of Technology, China

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Tetsuo Tomiyama Liyang Xie Xilun Ding Hongsheng Ding Guofu Yin Paul Maropoulos Chao Jiang Shuxin Wang Jian S. Dai Yinan Lai Xiangfeng Liu Weizhong Guo Shijing Wu Rainer Stark Hui Liu Jun Hong Xiongping Du Ying Xi Peiqi Ge Zhong You Xiangyang Xin Jingjun Yu Wei Sun Zhongrong Zhou Geng Liu

Committees

Cranfield University, UK Northeastern University, China Beihang University, China Beijing Institute of Technology, China Sichuan University, China Aston University, UK Hunan University, China Tianjin University, China King’s College London, UK National Natural Science Foundation of China, China Tsinghua University, China Shanghai Jiao Tong University, China Wuhan University, China TU Berlin, Germany Beijing Institute of Technology, China Xi’an Jiaotong University, China Missouri University of Science and Technology, USA Tongji University, China Shandong University, China Oxford University, UK Jiangnan University, China Beihang University, China Dalian University of Technology, China Southwest Jiaotong University, China Northwestern Polytechnical University, China

Contents

Multi-hierarchy Carbon Footprint Analysis and Low-Carbon Design Improvement Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hong Bao, Sheng Guo, and Qing Di Ke

1

The Design and Dynamics Analysis of Cylindrical Roller Surface Unfolding Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yudong Bao, Xiaojian Chen, Chengyi Pan, Yanling Zhao, and Liqun He

12

A Novel Cable-Driven Parallel Robot for Inner Wall Cleaning of the Large Storage Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wanghui Bu, Weiqi Zhou, Laixin Fang, Jing Chen, Xianghua An, and Jingkai Huang

28

A Novel Biomimetic Design Method Based on Biology Texts Under Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bowen Chen, Liang Chen, Xiaomin Liu, and Hao Dou

41

Numerical Simulation on Effect of Graphene Doped Morphology on Heat Transfer Efficiency of Anti-/deicing Component . . . . . . . . . . . . Long Chen and Zhanqiang Liu

52

Numerical Analysis on Load Sharing Characteristics of Multistage Face Gears in Planetary Transmission . . . . . . . . . . . . . . . Xingbin Chen, Qingchun Hu, and Chune Zhu

63

Reachable Matrix and Directed Graph – Based Identification Algorithm of Module Change Propagation Path for Product Family . . . Xianfu Cheng, Liyun Wan, and Jian Zhou

84

6-DOF Industrial Manipulator Motion Planning Based on RRT-Connect Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chengren Yuan, Guifeng Liu, and Wenqun Zhang

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Contents

A Precise Identification and Matching Method for Customer Needs Based on Sales Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Xingpeng Chu, Jian Zhang, Uday Shanker Dixit, and Peihua Gu Optimization Design of the Non-magnetic Drill Rod for Directional Drilling in the Coal Mine . . . . . . . . . . . . . . . . . . . . . . . . 113 Dayong Tang and Lu Liu Research on Product Redesign Process Based on Functional Analysis . . . 125 Yafan Dong, Runhua Tan, Peng Zhang, Wei Liu, and Ruiqin Wang Analysis of Characteristics and Structure Optimization of Anti-rolling Torsion Bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Yahong Dong and Yuejin Shang Coupling Mechanism of Errors in the Planetary Roller Screw Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Chuanming Du, Geng Liu, Junqi Liu, and Shangjun Ma A Novel Tooth Contact Analysis Method Based on Value Iteration . . . . 162 Jinfu Du, Zhengrong Wang, Kai Liu, and Yiteng Gao Rigidity Synthesis and Machining Error Analysis of Machine Tool Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Pengyu Hao, Gongxue Zhang, Zijian Pei, and Xianming Gao Thermodynamic Lubrication Performance and Stability for a Deep/Shallow Pocket Hybrid Bearing Considering Bubbly Oil . . . . . . 189 Hong Guo, Shuai Yang, Ningning Wu, and Ruizhen Li Time Delay Chen System Analysis and Its Application . . . . . . . . . . . . . 202 Hongjun He, Yan Cui, Chenhui Lu, and Guan Sun The Driver-in-the-Loop Simulation on Regenerative Braking Control of Four-Wheel Drive HEVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Hexu Yang, Xiaopeng Li, Pengxiang Li, and Yu Gao Strength and Modal Analysis of High Speed EMU Gearbox Housing . . . 223 Haijun Huang, Bichao Yin, Chaowen Wang, and Haiyan Zhu Indirect Adaptive Fuzzy Sliding-Mode Control for Hydraulic Manipulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Xin Huang, Yi Wan, Yao Sun, and Jiarui Hou Improvement and Research of Tennis Training Machine . . . . . . . . . . . . 243 Huiqiang Guo, Jianye Pan, Wen Liu, and Yiling Yue Design of Flagstone Transport Device Based on TRIZ Theory . . . . . . . 253 Fan Jiang, Jian Shen, Tao Zhu, and Jinfeng Wen

Contents

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Fault Analysis and Structure Optimization of End Face Seal of Hydraulic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Haixiang Jiang Innovative Design of Leeward Surface of Pin Fin in Flame Arresters Fitted in Explosion Relief Valve . . . . . . . . . . . . . . . . . . . . . . . 274 Lanfang Jiang, Shuyou Zhang, Xin Shu, Weina Hao, Yun Ren, and Zhiya Chen Analysis and Optimization of Performance Under Operating Condition of Thrust Aerostatic Bearing with Vacuum Pre-load . . . . . . . 288 Mengyang Li, Qiu Hu, PinKuan Liu, and Ming Huang A Study on Innovative Design of Rotary Pile Foundation Drilling Machine Based on TRIZ Theory . . . . . . . . . . . . . . . . . . . . . . . . 302 Fuxing Li Design and Optimization of Focusing X-Ray Telescope Based on Intelligent Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 Liansheng Li, Zhiwu Mei, Jihong Liu, Fuchang Zuo, Jianwu Chen, Hanxiao Zhang, Hao Zhou, and Yingbo He Research of Dormitory Furniture Design Based on Group Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Lin Li, Xupeng Wang, and Chunqiang Zhang Analysis and Extraction of Consumer Information for the Evaluation of Design Requirement Depending on Consumer Involvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Shipei Li, Dunbing Tang, Qi Wang, and Haihua Zhu Reduction in Aerodynamic Resistance of High-Speed Train Nose Based on Kriging Model and Multi-objective Optimization . . . . . . . . . . 354 Tian Li, Deng Qin, Le Zhang, Jiye Zhang, and Weihua Zhang Research and Simulation on Pilot Configuration in Multi-antenna System Based on Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Ying Li, Lei Cui, and Zhe Zhang Development and Experiment of an XhYhZ Micro-motion Stage Based on a Straight-Beam Three-Quarter Round Type Flexure Hinge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 Junlang Liang, Lanyu Zhang, Jian Gao, Gengjun Zhong, Guangtong Zhao, and Jindi Zhang An Improved PC-Kriging Method for Efficient Robust Design Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 Qizhang Lin, Chao Chen, Fenfen Xiong, Shishi Chen, and Fenggang Wang

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Electro-Mechanical Response of a Cracked Piezoelectric Cantilever Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 Chao Liu, Wenguang Liu, and Yaobin Wang A Time-Variant Reliability Analysis Method Considering Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 Jingfei Liu, Chao Jiang, and Xiangyun Long Research on Tooth Profile Error of Non-circular Gears Based on Complex Surface Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 Yongping Liu, Fulin Liao, and Changbin Dong Topology Optimization Design of the Monocoque Bus Body Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 Zhuli Liu, Xiangyu Huo, Hao Zhou, and Xiaoguang Wu Analysis of Wind Vibration Response of Transmission Tower . . . . . . . . 466 Zhuli Liu, Beibei Liu, Zhuan You, and Mengli Li Design of a Stabilize Device for Heavy Oil Transportation in Water Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 Haoran Lu, Fan Jiang, Yuliang Chen, Xiaolong Qi, and Zhongmin Xiao Design of Spatial Lissajous Trajectory Vibrating Screen . . . . . . . . . . . . 493 Zhipeng Lyu and Sizhu Zhou Part Retrieval Technology Based on Geometric Shape and Topological Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 Ning Ma, Bo Yang, and Junzhi Shang Analysis of Tool Wear and Wear Mechanism in Dry Forming Milling for Rail Milling Train . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 Chao Pan, Xiaoshan Gu, Mulan Wang, and Baosheng Wang Wear Numerical Simulation and Life Prediction of Microstructure Surface Unfolding Wheel for Steel Ball Inspection . . . . . . . . . . . . . . . . . 518 Chengyi Pan, Xia Li, Hepeng Wang, Yanling Zhao, Jingzhong Xiang, Sihai Cui, and Yudong Bao Design of Passive Gravity Balance Mechanism for Wearable Exoskeleton Suit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Chenxi Qu, Peng Yin, Xiaohua Zhao, and Liang Yang Design and Analysis of Underwater Drag Reduction Property of Biomimetic Surface with Micro-nano Composite Structure . . . . . . . . 546 Xuezhuang Ren, Lijun Yang, Chen Li, Guanghua Cheng, and Nan Liu A Method of Parametric Stability Region Determination for Non-linear Gear Transmission System . . . . . . . . . . . . . . . . . . . . . . . 560 Dongping Sheng, Xiaozhen Li, and Rupeng Zhu

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Performance and Parameter Sensitivity Analysis of Finger Seal with Radial Clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 Hua Su Calculation and Experimental Study on Comprehensive Stiffness of Angular Contact Ball Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592 Peng Sun, Weifang Chen, Chuan Su, and Yusu Shen Design of a New Hydraulic Manipulator with Kinematic and Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602 Yao Sun, Yi Wan, Xichang Liang, Xin Huang, and Ziruo Liu Research on Electro-Hydraulic Servo System Based on BP-RBF Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Tao Chen, Wenqun Zhang, and Jianggui Han Collision Simulation of GQ70 Light Oil Tank Car at the Level Crossing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 Maopeng Tian, Ronghua Li, Xiujuan Zhang, and Miao Jin Reason Study of Collision Between Valves and Piston of Diesel Engine Valve Train . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 Dameng Wang, Xiujuan Zhang, Deyu Yue, and Weipeng Fan Macroscopic Topology Optimization of Fusion Cages Used in TLIF Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647 Hongwei Wang, Yi Wan, Xinyu Liu, Bing Ren, Zhanqiang Liu, Xiao Zhang, and Mingzhi Yu Fuzzy Optimization Design of Disc Brakes Based on Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661 Jianbin Wang and Jishu Yin Modeling Design and Evaluation of Rotary Tiller Based on Multidisciplinary Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 Wang Jianwei, Jianmin Zhang, and Qin Yang Experimental Investigation of Thermal Elasto-Hydrodynamic Lubrication Based on Temperature Control . . . . . . . . . . . . . . . . . . . . . . 686 Shuaihong Yu, Yazhen Wang, Jiacheng Shen, and Huihui Yue Study on Nonlinear Characteristics of Spatial Spreading Mechanism with Multiple Clearance Joints . . . . . . . . . . . . . . . . . . . . . . 697 Wenzhou Lin, Xupeng Wang, Xiaomin Ji, and Chunqiang Zhang A Novel Design of Tapered Sub-array Structure for SSPS-OMEGA . . . 708 Tong Wu, Yingzhong Tian, Meng Li, and Long Li

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Research on Multiresponse Robustness Optimization for Unmanned Aerial Vehicle Electrostatic Spray System . . . . . . . . . . . . . . . . . . . . . . . 719 Yangdong Wu, Jiajie Lu, and Yiquan Wang Research on Trajectory Optimization of Six-Axis Manipulator Based on Watchcase Polishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729 Xiang Wang, Ying Xi, Chao Gu, and Mengru Li Reverse Modeling of the Helix Roller in the Omni-Directional Wheel Based on NURBS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 740 Xie Xia Research on Automatic Matching Model of Power Battery . . . . . . . . . . 749 Chuanfu Xin, Fengxia Zhao, Yujin Wu, and Jianshe Gao Random Vibration Analysis of Optical Adjustable Frame Based on ANSYS Workbench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760 Nan Xu, Yuan Wang, and Kelin Xu Analysis of Influence of Eccentricity Error on Transmission Performance of Micro-segment Gears . . . . . . . . . . . . . . . . . . . . . . . . . . 769 Rui Xu, Lielong Wang, Peidao Pan, and Kang Huang Research on the Design of Wearable Equipment for Intelligent Emotion Detection for Empty Nester . . . . . . . . . . . . . . . . . . . . . . . . . . . 785 Yan-min Xue, Chang Ge, Shi-yi Xu, Xu-yang Zhang, and Bo-xin Xiao Narrative Design of Old Brand Image: A Case Study of Demaogong . . . 795 Yanmin Xue, You Wu, Yihui Zhou, and Yang Liu Study on the Theory and Practice of Mechanical Design . . . . . . . . . . . . 804 Yunna Xue, Xuehui Shen, and Baolin Wang Simulation Analysis of Pipe Bending Under Multiple Conditions . . . . . . 811 Guodong Yi, Zhenan Jin, and Shaoju Zhang Simulation Analysis of Sealing Performance of Double-Offset Butterfly Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 Guodong Yi, Shaoju Zhang, and Zhenan Jin Motion Performance Analysis of the Sawyer Ankle Rehabilitation Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832 Yongfeng Wang, Xiangzhan Kong, Jing Yang, and Guoru Zhao Automated Sustainable Low-Carbon Design of Offshore Platform for Product Life Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847 Qianyi Yu and Bin He Comfort of Minors’ Sitting Posture in Learning Based on Motion Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 Chunqiang Zhang, Xiaomin Ji, Yanmin Xue, and Chunmei Zhang

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Lightweight Design of Dump Truck Frame Based on Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877 Gongxue Zhang, Sen Yang, Shanshan Guo, and Qichen Niu Topological Optimization of the Front Beam in Metal Extruders . . . . . 888 Xugang Zhang, Peilin Yang, Xiaole Cheng, and Yi Hou Car Radiator Upper Beam Stamping Process Design and Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898 Zhiyuan Wan and Yinping Chen A Fast Tacho-Less Order Tracking Method for Gear Fault Diagnosis Under Large Rotational Speed Variation Conditions Based on Multi-stage Generalized Demodulation . . . . . . . . . . . . . . . . . . 904 Qi Zhou, Wenjin Liu, and Chaoqun Wu Gear Fault Diagnosis Under the Run-Up Condition Using Fractional Fourier Transform and Hilbert Transform . . . . . . . . . . . . . . 918 Qi Zhou, Chaoqun Wu, and Qingrong Fan An Empirical Study of the Effect of the Completeness of Hands-on Training Design Projects on the Preservation of Tacit Knowledge . . . . . 944 Yihui Zhou, Wenzhou Lin, Zhi Qiao, and Xiaozhou Li Research on Structural Size Optimization of 3-TPT Parallel Mechanism Based on Stiffness Characteristics . . . . . . . . . . . . . . . . . . . . 952 Chunxia Zhu and Chengzhu Hu Vibration Response Analysis of Gearbox Housing of High Speed Train Under Wheel and Rail Excitation . . . . . . . . . . . . . . . . . . . . . . . . . 971 Haiyan Zhu, Xiao Su, Lei Tao, and Qian Xiao An Intelligent Fatigue Life Prediction Method for Aluminum Welded Joints Based on Fatigue Characteristics Domain . . . . . . . . . . . . 977 Li Zou, Hongxin Li, and Wei Jiang Optimum Design of Radiation Well Horizontal Drilling Rig Based on TRIZ and Bionics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 990 Chenghao Liu, Changqing Gao, Bo Yang, and Zhenghe Xu Innovative Design of Reversing Device and Rod Loading Device of Horizontal Drilling Rig Based on TRIZ . . . . . . . . . . . . . . . . . . . . . . . 1002 Shifeng Sun, Changqing Gao, Bo Yang, and Zhenghe Xu AGV Trolley Tray Based on Honeycomb Paper-Based New Material . . . 1010 Jingjing Yang, Xiaoyi Jin, and Anran Wang The Study of Electric Field Distribution on Small Holes in Pulse Electrochemical Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1018 Zhaolong Li

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Reliability Optimization Design of New Automatic Tensioning Belt-Gear Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1030 Chengyi Pan, Guanqun Cao, and Yuanqi Tong Design and Simulation Analyses of a Five-Wheeled Stair-Climbing Mechanism Based on TRIZ Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044 Chengyi Pan and Yuanqi Tong Extensible Innovation Design of Globoidal Cam Deceleration Mechanism Based on Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054 Shengyang Tian, Qingshan Gong, Guangguo Zhang, Mingmao Hu, and Yuemin Wu Tension Analysis of Small Motor Stator Winding Tensioning Process . . . 1070 Yanling Zhao, Zhao Zhang, Jingzhong Xiang, and Yudong Bao Study on Contact Dynamics of Cylindrical Roller Feeding Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1082 Yanling Zhao, Xinyue Wang, and Yudong Bao Trajectory Planning for Winding Process of Small-Sized Motor Stator Winding Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093 Yanling Zhao, Linqiang Wang, Jingzhong Xiang, and Yudong Bao Experimental Study of a Solid-Liquid Mixing and Conveying Pump with Variable Flow and Proportion . . . . . . . . . . . . . . . . . . . . . . . 1109 Wei Liu, Qian Tang, Wenzhe Cai, Pinghua Liang, Zongmin Liu, and Xiaojie Fan Effect of Pore Parameters on Lubrication Performance of Oil-Containing Cage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124 Tingting Yin, Yuanyuan Li, Ke Yan, Pan Zhang, Yongsheng Zhu, and Jun Hong Defects Detection System for Fluorescent Coating of Metal Plate Based on Machine Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136 Yujin Wu, Fengxia Zhao, Chuanfu Xin, Jianshe Gao, and Zhigao Chen Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1151

Multi-hierarchy Carbon Footprint Analysis and Low-Carbon Design Improvement Method Hong Bao1,2(&), Sheng Guo1, and Qing Di Ke1 1

HeFei University of Technology, 193 Tunxi Road, Hefei 230009, China [email protected] 2 The State Key Laboratory of Fluid Power and Mechatronic Systems of Zhejiang University, No. 38 Zheda Road, Xihu District, Hangzhou 310027, China

Abstract. Multi-hierarchy carbon footprint analysis for products is proposed to support product low-carbon design. A multi-hierarchy carbon footprint analysis model is established. The analysis model of product carbon footprint is established by analyzing the factors which influence product carbon footprint. Carbon footprint of module unit is calculated and allocated through function-structure mapping. By integrating sensitivity analysis into multi-hierarchy carbon footprint analysis for products, the application of this method in design improvement is discussed. Finally a case study of refrigerator is done to illustrate the feasibility and applicability of this method. Keywords: Multi-hierarchy carbon footprint analysis Function-structure mapping  Low-carbon design  Integrating sensitivity analysis  Design improvement



1 Introduction With the growing tension of the global environment, energy and resource use, technical barriers in the international trade has become increasingly harsh, the green and lowcarbon attributes of products becomes as important as function, performance and quality control. Low carbon design based on product life cycle, which aims to improve the performance of its carbon emissions, has become one of the important trends in the field of product design. On the premise of not reducing the effectiveness of products, low carbon design based on product life cycle considers energy efficiency improvements and resource conservation at the design stage, and minimizes the carbon footprint of products by the key technologies of energy and material saving design, which is of great significance in supporting and guiding the design process of products. The performance analysis of product carbon emission is the basis of low-carbon design based on life cycle. Many scholars have carried on the research. Haapala et al. [1, 2] built an energy consumption prediction model of the product manufacturing process by using basic product information and processing information. By analyzing environmental impact of products, energy and raw material consumption in the life cycle as well as the emissions of waste are reduced. Kainuma et al. [3] predicted the demand for energy services with an indicator of ecological and economic factors by © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1–11, 2020. https://doi.org/10.1007/978-981-32-9941-2_1

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using Asian-pacific integrated model, and made comparisons and decisions on the existing technical data and energy data. Venkatesh et al. [4] built an uncertainty assessment model of the emissions of greenhouse gases in the life cycle of fossil fuel by using the method of process framework and statistical modeling. On the basis of product life cycle energy analysis, Qi [5] built a life cycle energy model, described the dynamic characteristics of energy consumption in product life cycle, and gave the formula of energy consumption. Zhang [6] conducted a life cycle assessment of greenhouse gas emissions in the use process of mechanical products, established the parameters and evaluation boundary for life cycle inventory analysis, and then carried out the inventory calculation and the results comparison. Xu [7] established a cold chain carbon footprint model based on the product life cycle time dimension. By analyzing and calculating the model, the accurate method of quantifying the carbon footprint of cold chain workstation in unit time was given. Zhang [8] proposed a lowcarbon product design information model based on carbon footprint, and a dual progressive carbon footprint feature location method based on product structure tree and detailed design parameters after analyzing the content of low-carbon design decision information. Inakollu [9] proposed a practical life cycle assessment method to realize the carbon footprint calculation of fiber production. Restrepo [10] proposed a life cycle assessment (LCA) method for carbon footprint analysis to analyze carbon emissions from bamboo production. However existing researches are mainly focused on the calculation of carbon emissions of product and the quantitative analysis on the perspective of energy consumption while the research on the mapping between product carbon emissions and design parameters is still not enough, which can not provide a better guide for the designer to improve the low-carbon design. This article builds a product model of multi-hierarchy carbon footprint analysis and proposes a multi-hierarchy carbon footprint analysis method on the basis of the carbon footprint analysis of product layer and module unit layer. It combines the carbon footprint analysis method with sensitivity analysis and discusses its application into low-carbon design improvements, which provides practical analytical tools and application methods for low-carbon design.

2 Multi-hierarchy Carbon Footprint Analysis Model Product carbon footprint is the sum of greenhouse gas emissions generated in all stages of the product life cycle which is used to measure their contribution on global warming in particular system boundaries. Product carbon footprint mainly includes four steps: selection of functional unit; determination of system boundary; data collection and calculation of carbon footprint [11]. On the basis of the acquisition of customer’s demand for products, product layer can be decomposed to the module unit layer according to product function decomposition and function structure mapping. Through the level mapping of carbon emissions of the acquisition of raw materials, manufacturing, using and recycling etc. in each stage of the life cycle emissions, all levels of carbon footprint can be distributed and quantified. On the basis of the acquisition of the product layer and the result of module unit layer carbon footprint analysis, it is necessary to identify the key life cycle

Multi-hierarchy Carbon Footprint Analysis

3

stage and module, research the mapping relationship between key design parameters and carbon emissions based on the sensitivity analysis to support the following low carbon design improvements. Multi-hierarchy carbon footprint analysis model is shown in Fig. 1.

The existing product model

Product layer

Product carbon footprint

Function structure mapping

Carbon footprint map

Module layer

Module unit carbon footprint

BOM

Target definition and scoping Inventory analysis

Impact assessment

Impact assessment Multi-hierarchy carbon footprint analysis

based on the sensitivity analysis of key design parameters and the mapping relationship and improvement direction of the various levels of carbon emissions

Fig. 1. Multi-hierarchy carbon footprint analysis model

3 Multi-hierarchy Carbon Footprint Analysis Method 3.1

Product Carbon Footprint Analysis

Product carbon footprint can be regarded as the superposition of carbon emissions generated in each stage of life cycle, carbon emissions in each stage can be analyzed through decomposing the life cycle. Carbons emissions in life cycle can be divided into direct carbon emissions generated by material flow and indirect carbon emissions caused by energy flow. Here five stages are considered including acquisition of raw materials and energy, manufacturing, distribution, use, end of life. We need to ignore the life cycle stages according to the specific circumstance in the actual calculation process. The product carbon footprint based on the energy flow and material flow is shown in Fig. 2. The quantitative analysis model of product carbon footprint can be expressed as: G  Gm þ Ge þ Gp þ Gd þ Gu þ Gr

ð1Þ

Gi ¼ Gienergy þ Gimaterial

ð2Þ

Where Gm , Ge , Gp , Gd , Gu , Gr respectively represents the carbon emissions in stage of acquisition of raw materials, stage of acquisition of energy, stage of manufacturing, stage of distribution, stage of use, stage of recycling. Gi represents a stage of life cycle,

4

H. Bao et al. Natural resources

Raw materials, energy

Exploitat … … -ion

Manufacturing

Process Smelting

Component assembly

……

Product assembly

*

Transportion

Transport Total carbon emissions

Remanufacturing reuse Materials recovery

Dismantling Energy recovery Scrap use

recycling Carbon emissions generated by energy consumption energy flow

*

Carbon emissions generated by material consumption material flow

Fig. 2. The products processes of carbon footprint based on the energy flow and material flow

Gienergy and Gimaterial respectively represents the direct carbon emissions generated by material flow and indirect carbon emissions caused by energy flow. Carbon emission in each stage of product life cycle is based on the indirect calculation of carbon emission factors. Its quantitative methods of carbon emission and factors which are needed to be considered are introduced as follows. • Acquisition of raw materials and energy: the carbon emission in the stage of acquisition of raw materials mainly depends on the energy consumption and the direct emission of greenhouse gases in the process of material production. The carbon emission generated by the energy consumption mainly depends on the type and physical quantity of energy consumption and the emission factors corresponding to the energy in production activities. The carbon emission caused by the direct emission of greenhouse gases depends on the type and physical quantity of material consumption and the emission factors corresponding to the material in production activities. The carbon emission in the stage of acquisition of energy mainly depends on the type and physical quantity of energy consumption and the emission factors corresponding to the energy in production activities. Here it is confined to production of the primary energy. • Manufacturing: The carbon emissions in this stage mainly depends on the energy consumption and the direct emission of greenhouse gases, which is reflected in the energy consumption of manufacturing of basic component, the direct emissions of greenhouse gases in the process of manufacturing, energy consumption of product assembly and the direct emission of greenhouse gases in the process of assembling. The energy consumption here is confined to the combustion of primary energy and the use of secondary energy. The carbon emission can be calculated by the physical quantity of each kind of energy in production activities multiplied by the sum of emission factors corresponding to the energy production. The carbon emission caused by the emissions of greenhouse gases can be calculated by the physical

Multi-hierarchy Carbon Footprint Analysis

5

quantity of each kind of greenhouse gas in production activities multiplied by the sum of equivalent corresponding to the greenhouse gas. • Distribution: The carbon emission in this stage is generated when basic components are sent to manufacturers; products are distributed to vendors, products are distributed to customers. It mainly depends on the types of distribution, distribution distance, the amount of energy consumption per km and the corresponding energy emission factors. • Use: The carbon emission in this stage mainly depends on the electricity consumption and direct emissions of greenhouse gases. The carbon emissions caused by the electricity consumption on average running time can be calculated by the power consumption measured per day multiplied by average running time and average power emission factor of national grid. The carbon emission caused by emission of greenhouse gases can be calculated by the physical quantity of each kind of greenhouse gases in the stage of using multiplied by the sum of equivalent corresponding to the greenhouse gas. The formula of specific products also varies. Take the refrigerator as an example: The carbon emissions caused by emission of greenhouse gases can be calculated by the weight of refrigerant multiplied by leakage factors in the stage of using and the equivalent of carbon dioxide of the refrigerant. • End of life: The carbon emission in this stage mainly depends on the energy consumption and the direct emissions of greenhouse gases. The carbon emissions caused by the energy consumption can be calculated by the physical quantity of each kind of energy in recycling activities multiplied by the sum of the emission factors corresponding to energy production. The carbon emissions caused by the emissions of greenhouse gases can be calculated out by the leakage of each kind of greenhouse gases in recycling activities multiplied by the sum of equivalent corresponding to the greenhouse gas. 3.2

The Quantitative and Distribution Method of Carbon Footprint of Module Unit Layer

Through product function structure mapping, product family is divided into a number of module units of different functions. According to the conventional and green demand of customers, each module can be derived from a number of instances of module units which have the same function and different carbon footprint through the selection and combination of components inside module unit. The quantitative analysis of carbon footprint of module unit mainly includes the selection of functional unit, the determination of system boundary, data collection, the calculation of carbon footprint and the distribution of product carbon footprint. Functional unit is selected as a modular unit. Component elements are the components inside module unit. System boundary is defined as the acquisition of raw materials, the acquisition of energy, manufacturing, distribution, use and end of life. The quantitative model of carbon footprint of module unit can be expressed as:

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Gkj ¼

m X h¼1

GkjMh

þ GkjEh

þ

n X

! kj EPhi



b þ GkjRh

þ GkjPmaterial þ GkjU þ GkjD

ð3Þ

i¼1

Where: Gkj represents the carbon footprint of j-th instance derived from k-th module unit. GkjMh , GkjEh , GkjRh represents respectively the carbon emissions of the h-th component of j-th instance derived from k-th module unit in the stage of the acquisition of raw materials, the stage of the acquisition of energy and the stage of recycling. kj EPhi , b, GkjPmaterial represents respectively the energy consumption, emission factors and emission of greenhouse gas of the h-th component of j-th instance derived from k-th module unit in the i-th manufacturing process. GkjU , GkjD respectively represents the carbon emissions of the jth instance derived from kth module unit in the stage of use and the stage of distribution. The carbon emission of the module unit instance produced in acquisition of raw materials and energy, manufacturing and recycling stages can be indirectly calculated by using the carbon emission factors according to the product carbon footprint quantitative methods afore mentioned, the carbon emission produced in the distribution stage needs to be identified according to carbon emissions contribution ratio in the entire product system in and the carbon contribution ratio h of this stage can be expressed by the ratio of the weight of the module unit instance to total product weight. Since the function of each module unit are independent, and the influence of carbon emissions in use phase on the entire product system is not the same, the carbon emissions of the module unit instance in use phase mainly from two ways, one is the allocation of indirect carbon emissions resulting from the energy consumption in the operation process of the products, the other is its internal greenhouse gas leak caused by the direct carbon emissions. The allocation ratio of carbon emissions η produced by energy consumption during the use phase of each module unit instance mainly depends on the proportion of its energy consumption during operation of the product in total energy consumption. The energy consumption of each module unit instance can be determined through the energy storage of the system and the coupling and superposition of energy function of all component consumption based on the behavioral modeling of energy [12]. The internal greenhouse gas leak caused by the direct carbon emissions of the module unit instance in use phase can be quantified through calculating the internal containing greenhouse gas leakage. The formula to quantify the carbon emissions of the module unit instance system allocated by the product system can be expressed as: GkjA ¼ gkj  EUenergy  b þ

m X

kj WUi  li  pi þ hkj  GD

ð4Þ

i¼1

Where: GkjA —The allocation of carbon emissions in the j-th instance derived by the k-th module unit of product in the product system;

Multi-hierarchy Carbon Footprint Analysis

7

EUenergy , GD —Represent the energy consumption the use phase and the carbon emissions generated by the distribution phase of the product; gkj , hkj —Represent the indirect carbon emissions produced by power consumption in the use phase of product system in the j-th instance derived by the k-th module unit of product, and the distribution ratio of carbon emissions in the distribution phase; kj , li , pi —Represent the weight, the leakage rate and the carbon dioxide WUi equivalent of i-th class greenhouse gases within the j-th instance derived by the k-th module unit of product.

4 Sensitivity Analysis Based Carbon Design Improvement Multi-hierarchy carbon footprint analysis result can be used to guide low-carbon design improvements of products. Firstly carbon footprint analysis on the product level should been done, if the result is higher than the set target value, the carbon emission performance requirement of product meets the design goal, there is no need for low-carbon design improvements; otherwise, there is necessary for module unit-level carbon footprint analysis. By comparing the carbon footprint quantitative analysis results of each modular unit, we can determine the module unit with higher impact on the carbon footprint of product and its distribution of the carbon emissions in various stages of the life cycle and find a significant life cycle stage. By analyzing the relationship between major changes in structural parameters and direct or indirect carbon emissions change in the significant life-cycle stage of the key module unit, we will find that the structural parameters are sensitive or not to the increase of carbon emissions of module unit, which can provide a direction for life cycle carbon design improvement of products from the aspects of energy efficiency improvement and resource conservation. To calculate the degree of sensitivity, the functions between life-cycle carbon emissions of the module unit and relevant structural parameters must be established, which involve the principle of product and related theories. For example, the function relation between the indirect carbon emissions due to energy consumption in the use phase and the relevant structural parameters of the refrigerator door foam layer is: GUenergy ¼

kDT t1 be x

ð5Þ

Where, k, DT, x, t1 and be —Respectively, the conductivity of the foam layer, the door body temperature difference between both sides, the foam layer thickness, the door body working hours and the electricity emission factors. To obtain the sensitivity of the impact of GUenergy during the changes of the structural parameters, a further mathematical transformation is necessary. For example, in order to find x’s impact on the sensitivity of GUenergy , the mathematical derivation is as follows:

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H. Bao et al.

@GUenergy kDT ¼  2 t1 be x @x

ð6Þ

When the premise of other variables remain constant,, the sensitive degree between indirect carbon emissions and structure parameters x can be gotten by calculating the specific change value of GUenergy after each additional unit of x (0.01). The sensitivity between the other parameters can be gotten by the same method. To guide the lowcarbon design improvements according to the result of sensitivity analysis, the improvement direction of key design parameters can be further defined until the product level carbon footprint is higher than the set target.

5 Examples Demonstration Take a refrigerator which is a low-carbon design product of a company for the example, we verify the methodology of multi-hierarchy carbon footprint analysis. A refrigerator can be divided into six module units through function-structure mapping, which includes door system, cabinet system, refrigeration system, attachment and package. 5.1

Product and Carbon Footprint Analysis of Module Unit

System boundary includes use of raw material, manufacturing, distribution, use, end of life. The major system boundary for the carbon footprint analysis of the refrigerator is shown in Fig. 3. In the process of gaining the raw materials, direct greenhouse gases emissions and indirect emissions which is caused by energy consumption in the production process of steel, iron, copper, plastic, foam, freezing medium and etc. are mainly considered. Cyclopentane is used as foam beater and R134a is used as freezing medium. Obtaining carbon emission factor data of the main materials production, energy consumption and greenhouse gas emissions of the processes in the production stage should be considered, which include the manufacturing of key parts in every system, door pre-installed, cabinet pre-installed, the foaming of door, the foaming of box, the assembly of door, the assembly of cabinet, the packing of refrigerant, phosphate coating and the splice between the processes. Energy source is set to power grid in eastern China and the power consumption is about 12kwh in this stage. The foaming process of carbon leakage is negligible because the GWP value of the used cyclopentane is approximately zero. The GWP value of R134a is 1300, its amount is about 50 g, the leak rate is 0.8% in the packing process, and the leakage of the substance can be calculated as 0.4 g. In the distribution stage, the distribution mode is defined as rail and road, and the average distribution distance is 1000 km. The power consumption of the product in use stage is 0.45 kwh and its life is 10 years. Boundary conditions of the recycling stage include refrigerant recovery, crushing, materials recovery and etc. Refrigerant recovery and the crushing process not only require calculating the indirect carbon emissions caused by energy consumption, but also considering the direct carbon emissions caused by the refrigerant leak. Synthesizing the above analysis, carbon emission in life cycle of this refrigerate can be calculated as

Multi-hierarchy Carbon Footprint Analysis

9

1690.09 kgCO2e by using carbon footprint analysis and allocation method of product and module unit. Carbon emissions in recovery stage is negative, which indicates that the stage counteract the carbon emissions of the entire life-cycle. The result of carbon footprint analysis of product and module unit is shown in Fig. 4.

raw material acquisition

manufacturing

distrbution Foam leakage

steel

side plate door tank

iron

side plate cabinet tank

copper foam

energy

PUR recycle

refrigeration attachment

greenhouse gas emissions Lubricant recycle outsourcing Wind classifi cation

door foaming

cabinet preinstalled

Cabinet foaming

coal oil

energy

bracket bracket

assembly

Oil and gas classificati on Magenetism classification

railway

assembly Coolant leakage

energy

assembly

foam leakage

compressor

Coolant plastic

door preinstalled

Coolant leakage Coolant recycling House shredding

road

energy

Manual disassembly

The use of electricity

energy energy

foam leakage recycling

use

Fig. 3. The major system boundaries of carbon footprint analysis for the refrigerator

Fig. 4. The result of carbon footprint analysis of product and its module unit (kgCO2e)

10

5.2

H. Bao et al.

Low-Carbon Design Improvement Based on Sensitivity Analysis

According to the proportion of carbon emissions of life cycle stages in product carbon footprint, the proportion of carbon emissions in the use phase and the use of raw materials are higher than the other life cycle stages, 86% and 15% respectively, which need our attention. By way of carbon footprint analysis of module units, refrigeration system and door are the module units which have the strongest influence on carbon emissions in the use phase of the refrigerator. The proportion in the total carbon emissions in the use phase are 38% and 34% respectively, which are the key module units to be improved. Taking door system as an example, low-carbon design improvement is applied by sensitivity analysis. According to the steps described in Sect. 3, the sensitivity of the relevant structure parameters with the indirect carbon emissions that are caused by energy consumption in the use phase of the foaming layer, which is shown as Table 1.

Table 1. The sensitivity of the structure parameters with the indirect carbon emissions of the foaming layer Number Change

GUenergy

1 2 3 4

−0.188 −0.036 −0.011 −0.042

x increases 1% DT reduces 1% t1 reduces 1% k reduces 1%

From Table 1, the thickness of the faming layer x is the most sensitive design parameters that influence the indirect carbon emissions caused by energy consumption in the use phase of the foaming layer. If the thickness of the faming layer x increases by 1%, carbon emissions will reduce 0.188 kg. Considering the design constraints, the indirect carbon emissions of the foaming layer caused by energy consumption during the use phase can be reduced significantly by increasing the thickness.

6 Conclusion A multi-hierarchy carbon footprint analysis model for products is established. On the basis of carbon footprint analysis of product and module unit, a multi-hierarchy carbon footprint analysis method is proposed, and the application of sensitivity analysis in low-carbon design improvement is discussed. The case study illustrated this method can identify the key parameters of low-carbon design and support product low-carbon design effectively. The result of carbon footprint analysis is influenced by some factors which include usage modes by consumer, energy types, service life, there is some uncertainty. The process of life cycle is simplified, and some data input items are assumed. The application of this method requires the support of abundant basis data, the accumulation of basis data at the present stage is not enough. Therefore the data accumulation and assumption of input parameters is the important condition before the

Multi-hierarchy Carbon Footprint Analysis

11

application of this method. The range extension of product applied by this method and the development of computer aided design tools will be the research activities in the future. Acknowledgment. This work was financially supported by the National Science Foundation in China (51505119) and the Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems.

References 1. Haapala, K.R., Khadke, K.N., Sutherland, J.W.: Predicting manufacturing waste and energy for sustainable product development via WE-FabSoftware. In: Proceedings Global Conference on Sustainable Product Development and life Cycle Engineering, pp. 243–250 (2004) 2. Haapala, K.R., Sutherland, J.W., Rivera, J.L.: Reducing environmental impacts of steel product manufacturing. Trans. NAMRI/SME 37, 419–426 (2009) 3. Kainuma, M., Matsuoka, Y., Morita, T.: The AIM/end-use model and its application to forecast Japanese carbon dioxide emissions. Eur. J. Oper. Res. 122, 416–425 (2000) 4. Venkatesh, A., Griffin, W.M., Jaramillo, P.: Uncertainty analysis of life cycle greenhouse gas emissions from petroleum-based fuels and impacts on low carbon fuel policies. Environ. Sci. Technol. 45(1), 125–131 (2010) 5. Qi, Y., Huang, H., Liu, G.: Energy analysis method based on dynamic life cycle. Chin. J. Mech. Eng. 43(8), 129–134 (2007). (in Chinese) 6. Zhang, C., Pu, G., Wang, C.: Comparison of life cycle assessment between e-bike and motorbike. Mach. Des. Res. 19(4), 69–71 (2003). (in Chinese) 7. Xu, X., Li, R.W., Wu, X.L., Zhao, Y., Wang, X.Z., Bao, S., Nyberg, T.: Carbon footprint model and calculation of cold chain workstation based on product life cycle time dimension. Comput. Integr. Manuf. Syst. 24(2) (2018) 8. Zhang, Y., Li, W.Q., Li, Y., Ma, J.L.: Product low carbon innovation design based on carbon footprint information model. Chin. J. Eng. Des. 24(2), 141–148 (2017) 9. Inakollu, S., Morin, R., Keefe, R.: Carbon footprint estimation in fiber optics industry: a case study of OFS Fitel, LLC. Sustainability 9(5), 865 (2017) 10. Restrepo, Á., Becerra, R., Tibaquirág, J.E.: Energetic and carbon footprint analysis in manufacturing process of bamboo boards in Colombia. J. Clean. Prod. 126, 563–571 (2016) 11. British Standards Institute (BSI), PAS 2050-Specification for the Assessment of the Life Cycle Greenhouse Gas Emissions of Goods and Services (2008) 12. Zhang, J., Wei, X., Zhang, D.: Principle scheme design of mechanical systems based on energy interaction model. China Mech. Eng. 15(9), 820–823 (2004). (in Chinese)

The Design and Dynamics Analysis of Cylindrical Roller Surface Unfolding Mechanism Yudong Bao(&), Xiaojian Chen, Chengyi Pan, Yanling Zhao, and Liqun He School of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin 150080, China [email protected]

Abstract. In order to design an efficient and stable cylindrical rollers surface unfolding mechanism, and know about the motion of the cylindrical rollers surface during the unfolding process. The surface unfolding model of the cylindrical roller is established. The time taken for roller to achieve the uniform rotation and the rollers vibration on the direction of x-axis are used to evaluate the roller unfolding effect. The factors affecting the roller unfolding efficiency and the unfolding stability are determined. The roller accelerating timeconsuming equation and the deformation equations of the unfolding wheel are established. The dynamics of the surface unfolding model for the cylindrical roller is studied. The simulation of the roller unfolding motion is carried out by the Adams software to the roller which is U32  52 mm. The simulation results are consistent with the theoretical analysis results. In the roller surface unfolding process, the roller accelerates firstly, the vibration of roller is large, and then the uniform rotation is achieved, and the vibration of roller is small. According to the simulation data, the influence of the material of the unfolding wheel, the bottom radius of the unfolding wheel and the minimum distance between the outer edges of the two unrolling wheels on the stability and unfolding efficiency of the roller unfolding motion are determined. It is concluded that the bottom radius of the unfolding wheel is 16 mm, the material is silicone rubber and the minimum distance between the outer edges of the two unfolding wheels is 8 mm, the cylindrical roller has the best unfolding effect. According to the simulation results, the cylindrical roller surface unfolding mechanism is designed to meet the requirements of use, and the rationality of the cylindrical roller surface unfolding model is verified. It provides a theoretical basis for the research of the surface unfolding equipment for the column workpieces. Keywords: Cylindrical roller Vibration

 Surface unfolding model  Dynamics 

This project is supported by Research Special Fund Project of Harbin Science and Technology Innovation Talent (Grant Nos. 2017RAQXJ060, 2016RAXXJ001). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 12–27, 2020. https://doi.org/10.1007/978-981-32-9941-2_2

The Design and Dynamics Analysis of Cylindrical Roller Surface

13

1 Introduction With the development of Chinese rail transportation, the reliability of cylindrical roller bearings has been paid more attention. Cylindrical roller as an important part of the bearing, its surface quality is an important factor affecting the normal operation of the cylindrical roller bearing [1]. In order to get higher detection efficiency, machine vision technology has been applied to defect detection of cylindrical rollers surface widely [2]. The effectively unfolding of the cylindrical rollers surface is the premise to detect cylindrical rollers surface defects by machine vision. Therefore, it is necessary to have a reasonable design and dynamic analysis for the cylindrical rollers surface unfolding mechanism. The cylindrical rollers surface unfolding system has been studied by some scholars. A cylindrical rollers surface unfolding system that relies on rollers gravity to accelerate off the slope and then roll on the horizontal raceway at a constant speed is designed by Wang [3]. A cylindrical rollers surface unfolding system that uses electromagnetic force to fix cylindrical rollers on a turntable is designed by Zhang [4]. A cylindrical work piece surface unfolding system is designed by rotating the wheel to drive the roller [5]. Wu presents a twin-screw transmission scheme for surface unfolding of cylindrical roller [6]. Li from Harbin University of Science and Technology designs a cylindrical rollers dimension measuring system [7], which uses a pusher to push the roller rolling on the horizontal raceway for the surface unfolding of cylindrical roller. Tan et al. designs a battery cylinder surface unfolding system, which working principle is that the battery is rotating on its revolution [8], which provided a reference for the design of cylindrical roller unfolding system. Bo et al. proposes a new method is proposed for developable surface reconstruction [9]. Koukash et al. proposes a new cylindrical roller unfolding method, which the laser beam is focused and cleaned by the spatial filter, the expanded beam is passed through the square wave amplitude grating to form a fringe pattern, which is projected onto the surface of the cylindrical roller to complete the surface unfolding of the cylindrical roller [10]. In this paper, a new cylindrical roller surface unfolding mechanism is designed, and a two-dimensional cylindrical roller surface unfolding model is constructed. The model is used to determine the factors that affecting the roller vibration and acceleration time in the process of the acceleration rotation and uniform rotation. The dynamic characteristic of the cylindrical rollers surface unfolding model is analyzed. The physical prototype is established and the surface unfolding efficiency is verified. The research has provide a reference for the relevant research of cylinder surface defect detection.

2 The Cylindrical Rollers Surface Unfolding Mechanism The cylindrical rollers surface unfolding mechanism consists of stepping motor, gear I, gear II, gear III, bearing assembly, unfolding wheel I, unfolding wheel II and support frame, which is shown in Fig. 1. The unfolding wheel I and the unfolding wheel II are installed on the support frame through the bearing assembly. The gear II is connected to the unfolding wheel I, and the gear III is connected to the unfolding wheel II. The gear I is connected to the output shaft of the stepping motor, and engaging with the gear II and the gear III. When it is working, the cylindrical roller is placed on the middle of

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two unfolding wheels, and the stepping motor is energized. The rotating unfolding wheels drive the cylindrical roller to rotate around its own axis, and unfold the full surface of the cylindrical roller. Unfolding wheel

Gear

Cylindrical roller Gear

Stepping motor

Gear

Unfolding wheel

Bearing

Support frame

Fig. 1. Cylindrical roller unfolding mechanism

3 Establishment and Dynamic Analysis of Surface Unfolding Model of Cylindrical Roller 3.1

Establishment of the Two-Dimensional Model of Cylindrical Rollers Surface Unfolding

In order to understand the dynamic law of the cylindrical rollers surface unfolding process, a two-dimensional model of the cylindrical rollers surface unfolding is established, as shown in Fig. 2.

ylindrical roller nfolding wheel

nfolding wheel

Fig. 2. Two-dimensional model of cylindrical rollers surface unfolding

The Design and Dynamics Analysis of Cylindrical Roller Surface

15

The cylindrical roller, which rotates around its own axis, is driven by the frictional force between the roller and the two unfolding wheels. In order to ensure the stationarity and simpleness of the roller unfolding mechanism, the roller unfolding mechanism should be easy to install and maintain. So the two unfolding wheels have the same material, size and surface roughness, and their axis are placed in the same horizontal plane. Therefore, the cylindrical rollers surface unfolding mechanism could be simplified into a two-dimensional model in the xoy plane. Through analysis of the two-dimensional model, it can be seen that the axis C of the cylindrical roller with the axis A and the axis B of the two unfolding wheels constitute an isosceles triangle in the xoy plane. The point E which is the contact point of the circle C and the circle A is on the straight line CA, as well the point H which is the contact point of the circle C and the circle B is on the straight line CB. h1 is the angle between the line BC and the vertical direction, h2 is the angle between the line AC and the vertical direction, both h1 and h2 is equal to h which could be calculated by the following equation. h ¼ arcsin

  R þ d=2 Rþr

ð1Þ

where R is the bottom radius of the unfolding wheel, and r is the bottom radius of the cylindrical roller, and d is the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II. 3.2

Dynamic Analysis of the Two-Dimensional Model of Cylindrical Rollers Surface Unfolding

3.2.1 The Acceleration Rotation of Cylindrical Roller At the beginning of the cylindrical roller unfolding motion, the cylindrical roller is placed on the two unfolding wheels which rotates at the same angular velocity, and the roller starts to accelerate. The unfolding model is shown in Fig. 3.

θ1 r Δx1 ω2

FAC E FCA

G

R

Δx2 FBC

Ft2 ω2

H

Ft1

A

y o

θ2 MC α C

B

R

d

x

Fig. 3. Unfolding model of the accelerated rotation for cylindrical roller

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At the beginning of the unfolding movement, the cylindrical roller is greatly vibrated when contacted with the two unfolding wheels at an instant. After the roller is fully contacted with the two unfolding wheels, the roller is accelerated. The force of the cylindrical roller satisfies the following equation. G ¼ FAC cos h þ FBC cos h þ Ft2 sin h  Ft1 sin h

ð2Þ

0 ¼ Ft1 cos h þ Ft2 cos h þ FAC sin h  FBC sin h

ð3Þ

MC ¼ Ft1  r þ Ft2  r

ð4Þ

Ft1 ¼ FAC  l

ð5Þ

Ft2 ¼ FBC  l

ð6Þ

where Ft1 is the friction that the unfolding wheel I provides for the cylindrical roller, and Ft2 is the friction that the unfolding wheel II provides for the cylindrical roller, and FAC is the support force to the cylindrical roller which is accelerated rotating, and FBC is the support force to the cylindrical roller, and MC is the cylindrical rollers moment of force, and G is the weight of the cylindrical roller, and l is the friction coefficient between the cylindrical roller and the unfolding wheels. The following relationships could be obtained by the formulas (2) to (6). FAC ¼

Gðtan h  1Þ 2ðl2 þ 1Þ sin h

ð7Þ

FBC ¼

Gðl þ tan hÞ 2ðl2 þ 1Þ sin h

ð8Þ

Glrð2 tan h þ l  1Þ 2ðl2 þ 1Þ sin h

ð9Þ

MC ¼

It can be seen from Eqs. (7) and (8) that the cylindrical roller is subjected to different supporting forces during the accelerated rotation phase, which causes the cylindrical rollers to vibrate greatly on the direction of x-axis and the direction of yaxis. The angular acceleration during the rotation of the roller can be obtained by the following formula. MC ¼ Ja

ð10Þ

mr2 2

ð11Þ



Where a is the angular acceleration of the cylindrical roller, and J is the moment of inertia to the cylindrical roller, and m is the mass of the cylindrical roller.

The Design and Dynamics Analysis of Cylindrical Roller Surface

17

The following relationship can be obtained by the formulas (9) to (11). a¼

glð2 tan h þ l  1Þ rðl2 þ 1Þ sin h

ð12Þ

Where g is the gravitational acceleration. Since the roller does not always accelerate during the unfolding process, when the linear velocity at the contact point of the unfolding wheel and the roller is equal, the angular acceleration of the roller disappears, and the acceleration phase of the roller is completed. The acceleration time of the roller can be calculated by the following formula. Rx2 ¼ rx1 ¼ rat

ð13Þ

Where x1 is the angular velocity of the roller which is rotating at uniform speed, x2 is the angular velocity of the two unfolding wheels, t is the time taken for the roller to accelerate the rotation phase. It can be seen from the Eqs. (12) and (13) that the time t taken for the roller to accelerate the rotation phase can be calculated by the following formula. t¼

x1 rðl2 þ 1Þ sin h glð2 tan h þ l  1Þ

ð14Þ

It can be seen from Eqs. (1) and (14) that if the specification of the roller and the detection speed of the roller are known, the radius of the unfolding wheel, the material of the unfolding wheel, and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II are main factors that affecting the accelerate time to the roller. Through the two-dimensional unfolding model of the cylindrical roller during acceleration, it can be seen that the unfolding wheel I and the unfolding wheelII support the cylindrical roller, and also cause deformation by the reaction force from the roller, the deformation amount can be calculated by the following formula. FAC ¼ FCA ¼ K1 Dx1

ð15Þ

FBC ¼ FCB ¼ K2 Dx2

ð16Þ

Where FCA is the force of the cylindrical roller on the unfolding wheel I, and FCB is the force of the cylindrical roller on the unfolding wheel II, and K1 is the stiffness coefficient of the unfolding wheel I, and K2 is the stiffness coefficient of the unfolding wheel II.

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Since the material, size and surface roughness of the unfolding wheel I and the unfolding wheel II are the same, both K1 and K2 are equal to K. The amount of deformation of the unfolding wheel I and the unfolding whee l II can be obtained by the Eqs. (7), (8), (15), and (16). Dx1 ¼

Gðtan h  1Þ 2Kðl2 þ 1Þ sin h

ð17Þ

Dx2 ¼

Gðl þ tan hÞ 2Kðl2 þ 1Þ sin h

ð18Þ

Where Dx1 and Dx2 are the deformation amount of the unfolding wheel I and II respectively during the roller acceleration rotation phase. It can be seen from the Eqs. (1), (17) and (18) that during the accelerated rotation phase of the cylindrical roller, the deformation amount of the unfolding wheel I and II at the contact of the roller is different, which makes the roller have a serious vibration on the direction of x-axis and the direction of y-axis. If the roller specification is known, the bottom radius of the unfolding wheel, the material of the unfolding wheel and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II are main factors affecting the deformation of the unfolding wheel. 3.2.2 The Uniform Rotation of Cylindrical Roller When the linear velocity at the point of contact between the cylindrical roller and the unfolding wheel is equal, the roller is rotating at uniform speed, and the roller unfolding model during the uniform rotation is as shown in Fig. 2. The forces relationship of the roller unfolding model following these equation. 0 0 G ¼ FAC  cos h þ FBC  cos h

ð19Þ

0 0 0 ¼ FAC  sin h  FBC  sin h

ð20Þ

0 is the support force to the cylindrical roller which is uniformly rotation, Where FAC 0 and FBC is the support force to the cylindrical roller which is uniformly rotation. It is known from the formulas (19) and (20) that the support forces to the roller which is rotating at uniform speed could be calculated by the following formula. 0 0 FAC ¼ FBC ¼

G 2 cos h

ð21Þ

The Design and Dynamics Analysis of Cylindrical Roller Surface

19

It can be seen from the formula (21) that if the roller rotates at a constant speed, the support forces on the roller are equal. It can be known from the Newton’s third law that the reaction force to the unfolding wheel I and II is also equal, so the deformation of the unfolding wheel I and II can be calculated by the following formula. Dx01 ¼ Dx02 ¼

G 2K cos h

ð22Þ

Where Dx01 and Dx02 are the deformation amount of the unfolding wheel I and II respectively, when the roller rotates at a constant speed. It can be seen from the Eqs. (1) and (22) that when the roller rotates at a constant speed, the deformation amount of the unfolding wheel I is equal to deformation amount of the unfolding wheel II, and the roller’s vibration is smaller. If the roller’s specification is known, the bottom radius of unfolding wheel, the material of the unfolding wheel, and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II are main factors that affecting the deformation of the unfolding wheel. According to the above analysis, when the roller rotated acceleratory, the roller rotates unsteadily and vibrates sharply, which is not suitable for image acquisition. When the roller rotates at a constant speed, the roller rotates steadily and the vibrates less, which is suitable for image acquisition. The time taken for the roller to accelerate and the vibration of the roller which is rotating are affected by the material of unfolding wheel, the bottom radius of the unfolding wheel, and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II.

4 The Surface Unfolding Model Simulation and Data Analysis for Cylindrical Roller 4.1

The Design of Orthogonal Experiment for the Surface Unfolding Model of Cylindrical Roller

In order to verify the analysis of the roller surface unfolding model is correctly and know about the influence of various factors on the time taken for roller to accelerate and roller’s vibration, the bottom radius of unfolding wheel, the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II and the material of unfolding wheel were selected as factors A, B and C used to design a three-factor and three-level orthogonal experiment, as shown in Table 1. The cylindrical roller used for orthogonal experiment has a specification of U32  52 mm and it’s material is bearing steel. The stable rotation speed of the roller is required to be 1.2 r/s, and the accuracy of roller surface detection is 0.01 mm. Under the premise of ensuring that the roller reaches the predetermined surface unfolding speed, it is often

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used for prevent the contact deformation between the unfolding wheel and the roller from being too large that the bottom radius of the unfolding wheel is as much as the bottom radius of the roller, so 10 mm, 16 mm and 22 mm are selected as Levels A1, A2 and A3 of the bottom radius for the unfolding wheel. In order to facilitate the installation and transportation of the equipment, the cylindrical rollers surface unfolding mechanism should be as small and light as possible, so the distance of the outer edges between the two deployment wheels should be less than 10 mm, as well as a reliable distance can prevent the two unfolding wheels from crashing caused by installation errors, so the distance of the outer edges between the two unfolding wheels should be greater than 2 mm, therefore, 8 mm, 6 mm and 4 mm are selected as levels B1, B2 and B3 for the outer edges minimum distance between the two unfolding wheels. In order to ensure the unfolding wheel have a good abrasive resistance and low cost, steel, nylon and silicone rubber were selected as the three levels C1, C2 and C3 for the material of unfolding wheel. At the same time, it is necessary to ensure that the two unfolding wheels have the same surface roughness. Table 1. The orthogonal test scheme Experiment number A 1 A1 2 A1 3 A1 4 A2 5 A2 6 A2 7 A3 8 A3 9 A3

B B1 B2 B3 B1 B2 B3 B1 B2 B3

C C1 C2 C3 C3 C1 C2 C2 C3 C1

When the bottom radius of the unfolding wheel is 10 mm, 16 mm and 22 mm respectively, in order to achieve the rotation speed of 1.2 r/s to the roller, the rotation speed of the unfolding wheel should be set at 1.92 r/s, 1.2 r/s and 0.87 r/s respectively. 4.2

The Simulation of Surface Unfolding Model for Cylindrical Roller Based on the Orthogonal Experiment

The orthogonal experiment for the surface unfolding model of cylindrical roller has been designed and based on the analysis above in this paper. It can be known that the friction coefficients of steel, nylon and silicone rubber with the bearing steel are 0.15, 0.5 and 0.85, respectively. The dynamics simulation is carried out in Adams software base on the orthogonal experiment of the surface unfolding model for the roller, and the simulation time is set to 0.15 s and the number of steps is set to 300 steps. The simulation results are shown in Fig. 4.

The Design and Dynamics Analysis of Cylindrical Roller Surface

Fig. 4. The simulation results of the surface unfolding model for the roller

21

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Fig. 4. (continued)

Figure 4 is the line chart showing the displacement of the roller’s center of mass on the direction of x-axis and the direction of y-axis in the process of roller’s rotation. It can be seen from the simulation results in Fig. 4 that two phases are contained in the roller unfolding process. The first phase is the roller rotates acceleratingly phase, the roller and the unfolding wheel just start to contact, resulting in the rotation speed of the roller instability, and the rotation speed of the roller reaches 1.2 r/s gradually. At the same time, the vibration of the roller’s center of mass on the direction of x-axis and

The Design and Dynamics Analysis of Cylindrical Roller Surface

23

y-axis becomes stable gradually. The second phase is the uniform rotation of the roller, the roller’s rotation speed is stable at 1.2 r/s, and the vibration of the roller’s center of mass on the direction of x-axis and y-axis is much smaller than the first phase. The simulation results shown in Fig. 4 are consistent with the analysis results of the roller surface unfolding model. 4.3

The Analysis and Verification of the Simulated Data Based on Roller Surface Unfolding Model

The prerequisite for using machine vision to detect cylindrical roller’s surface defects is having a clear image of the cylindrical roller. When the roller rotates at a constant speed, the time taken for the roller to reach a uniform speed and the vibration on the direction of x-axis are the two main factors affecting the efficiency and sharpness for image capturing. According to the simulation results of the orthogonal experiment, the motion of the cylindrical roller during the unfolding process is known, as well as, it is necessary to assess the effect of the bottom radius of the roller, the material of the roller, and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II on the vibration of the roller’s center of mass and the time taken for roller to rotate acceleratingly by the range analysis and the variance analysis based on the simulated data. According to the orthogonal experiment scheme, the test indicator of time taken for roller to reach a uniform speed is T, and the test indicator of the vibration of the roller’s center of mass on the direction of x-axis when the roller rotates uniformly is D. The time taken for the roller to reach the uniform rotation and the vibration value in the direction of x-axis when the roller is rotated at a constant speed are recorded in Table 2. Table 2. Orthogonal experiment design array L9 for 3 key factors Experiment number A 1 A1 2 A1 3 A1 4 A2 5 A2 6 A2 7 A3 8 A3 9 A3

B B1 B2 B3 B1 B2 B3 B1 B2 B3

C C1 C2 C3 C3 C1 C2 C2 C3 C1

T(s) 0.115 0.0385 0.0355 0.022 0.028 0.0365 0.039 0.0265 0.126

C(mm) 1.29E−05 3.95E−04 2.66E−03 2.68E−04 1.29E−04 2.84E−05 7.54E−06 4.19E−05 2.69E−06

For understanding the effect of factors A, B and C on the test indicators T and D, a range analysis was performed according to the data in Table 2, as shown in Table 3. T1, T2 and T3 in Table 3 indicate the effect of level 1 level 2 and level 3 on the orthogonal experimental results, respectively, and R indicates the effect of the level change on the experimental results. The less time it takes for the roller to reach a uniform speed, the

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Y. Bao et al. Table 3. The range analysis based on the simulation data of the orthogonal experiment Influence T1(T) T2(T) T3(T) R(T) T1(D) T2(D) T3(D) R(D)

A 0.189 0.0865 0.1915 0.105 0.0030679 0.0004254 0.00005213 0.00301577

B 0.176 0.093 0.198 0.105 0.00028844 0.0005659 0.00269109 0.00240265

C T 0.269 T(T) = 0.467 T(D) = 0.003545 0.114 0.084 0.185 0.00014459 0.00043094 0.0029699 0.00282531

higher efficiency of roller unfolding. Therefore, the optimal combination of factors is A2B2C3. The order of influence for the factors on the time taken for the roller to reach a uniform speed is the unfolding wheel’s material, the radius of unfolding wheel, and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II. The smaller vibration on the direction of x-axis when the roller rotates at a constant speed, the more stable for the motion roller unfolding. So the optimal combination of factors is A3B1C1, and the order of influence of various factors on the vibration of the roller on the direction of x-axis when the roller rotates at a constant speed is the bottom radius of unfolding wheel, the material of unfolding wheel and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II. As the bottom radius of the unfolding wheel increasing, the time taken for the roller to reach a uniform speed is reduced firstly and then increased. When the bottom radius of the unfolding wheel is 16 mm, the time taken for the roller to reach a uniform speed is the least. With increasing of the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II, the time taken for the rollers to reach a uniform rotation is reduced firstly and then increased. When the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II is 6 mm, the time taken for the roller to rotate at a constant speed is the least. The greater coefficient of friction between the unfolding wheel and the roller, it takes less time for the roller to reach a uniform speed. With increasing of the bottom radius of the unfolding wheel, the vibration on the direction of x-axis is smaller when the roller rotates at a constant speed. With the reducing of the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II, the vibration on the direction of x-axis is greater when the roller rotates at a uniform speed. With increasing of the rigidity of the unfolding wheel’s material, the vibration on the direction of x-axis is smaller when the roller rotates at a constant speed. According to the range analysis, the order of the influence was determined that the radius of unfolding wheel, the material of unfolding wheel and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II to the time taken for roller to reach a constant speed and the vibration of the roller on the direction of x-axis when the roller rotates at a constant

The Design and Dynamics Analysis of Cylindrical Roller Surface

25

speed. In order to know about the significance that the factors A, B and C affect the vibration of the roller on the direction of x-axis and the time taken for the roller to reach a constant speed, it is necessary to make variance analysis of simulation data based on the orthogonal experiment. As shown in Table 4. Table 4. The analysis of variance based on the simulation data of the orthogonal experiment Factor A

Index T D B T D C T D Error range T D Total T D

Quadratic sum 2.393  10−3 1.802  10−6 2.044  10−3 1.152  10−6 6.572  10−3 1.612  10−6 1.425  10−3 1.360  10−6 3.667  10−2 7.323  10−6

NDOF 2 2 2 2 2 2 2 2 9 9

Mean square 1.197  10−3 9.009  10−7 1.022  10−3 5.759  10−7 3.286  10−3 8.061  10−7 7.13  10−4 6.801  10−7

F 1.679 1.325 1.434 0.847 4.611 1.185

P 0.373 0.430 0.411 0.541 0.178 0.458

The influence of the three factors A, B and C can be determined from Table 4. When the level of significance a = 0.05, the bottom radius of the unfolding wheel has a significant effect on the time taken for the roller to reach a uniform speed (P < 0.05), and it has an effect on the x-axis vibration when the roller rotates at a constant speed (P is close to 0.05). The smallest distance from the outermost point on the unfolding wheelI to the outermost point on the unfolding wheel II has an effect on the time taken for the roller to reach a uniform speed (P is close to 0.05), and have no effect on the vibration of the x-axis when the roller rotates at a constant speed (P > 0.05). The material of unfolding wheel has a significant effect on the time taken for the roller to reach a uniform speed (P < 0.05), and has an effect on the x-axis vibration when the roller rotates at a constant speed (P is close to 0.05). This is consistent with the results of the range analysis based on the simulation data of the orthogonal experiment. The results of simulation and data analysis show that the vibration of the roller on the x-axis is within the required range of detection accuracy, so the scheme with the shortest time for the roller to achieve a uniform speed is selected as the best design scheme. The bottom radius of the unfolding wheel is 16 mm, the outer minimum distance of two unfolding wheels is 8 mm, and the material of the unfolding wheels is silicone rubber, the unfolding efficiency is the highest, and the vibration range of the roller is less than 0.01 mm. So the fourth experiment is chosen as the best design, a set of surface unfolding mechanism of cylindrical roller is designed, as shown in Fig. 5, the mechanism can unfold cylindrical rollers effectively and help linear camera to obtain clear image of the rollers surface.

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Fig. 5. Physical prototype of cylindrical roller surface unfolding mechanism and roller unfolding effect

5 Conclusions (1) The surface unfolding model of two-dimensional cylindrical roller is established and the position relation between the two unfolding wheels and the cylindrical roller is determined. According to the analysis of the model, the influence can be known of the unfolding wheel material, the bottom radius of the unfolding wheel and the minimum distance between the outer edges of the two unfolding wheels on the time taken for the roller to reach a uniform speed and the vibration of the roller. It can be found that in the process of the roller unfolding, the roller accelerates firstly, the vibration of roller is large, and then the uniform rotation is achieved, and the vibration of roller is small. (2) The cylindrical roller with the specification of U32  52 mm and density of 7.9 g/cm3 and bearing steel material is selected as the experiment object. The orthogonal experiment of three factors and three levels is designed according to the unfolding model of cylindrical roller. The experimental data analyses and simulation results show that the optimal bottom radius of the unfolding wheel in the cylindrical roller unfolding mechanism is 16 mm, the material of the unfolding wheel is silicone rubber, and the smallest distance from the outermost point on the unfolding wheel I to the outermost point on the unfolding wheel II is 8 mm.

References 1. Su, J., Zhang, S., Yuan, J., et al.: Research on precision polishing technology of cylindrical roller of bearing. Mech. Electr. Eng. 35(10), 1073–1076+1093 (2018) 2. Li, X., Zhang, Z., Bai, R.: Visual inspection method for surface defects of bearing cylindrical rollers. Autom. Instrum. 35(12), 58–62 (2014)

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3. Wang, H.: Machine vision based cylindrical roller surface defect detection system. Henan University of Science and Technology (2012) 4. Zhang, B.: Research on surface defect detection of bearing roller based on machine vision. Nanchang Hangkong University (2018) 5. Zhang, J., Ye, Y., Xie, Y., et al.: Photoelectric detection of defects in metal cylindrical workpieces. Opt. Precis. Eng. 22(07), 1871–1876 (2014) 6. Wu, J.: Machine vision-based bearing roller surface defect detection system. Zhejiang University (2018) 7. Li, H.: Research on comprehensive measurement method and measurement system of bearing cylindrical roller size. Harbin University of Science and Technology (2018) 8. Tan, W., Wen, Q., Duan, F., et al.: Visual inspection of curved surface defects of cylindrical batteries based on HV&VHS. Control Eng. 26(01), 17–22 (2019) 9. Bo, P., Yuan, Y., Zhang, C.: Automatic reconstruction of developable surfaces. J. Comput. Aided Des. Comput. Graph. 28(09), 1428–1435 (2016) 10. Koukash, M., Hobson, C.A., Lalor, M.J., Atkinson, J.T.: Detection and measurement of surface defects by automatic fringe analysis. Opt. Lasers Eng. 87(07), 125–135 (1986)

A Novel Cable-Driven Parallel Robot for Inner Wall Cleaning of the Large Storage Tank Wanghui Bu1(&), Weiqi Zhou1, Laixin Fang1, Jing Chen2, Xianghua An3, and Jingkai Huang1 1

2

School of Mechanical Engineering, Tongji University, Shanghai 201804, China [email protected] School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China 3 School of Mechanical and Power Engineering, Dalian Ocean University, Dalian 116023, China

Abstract. Large vertical tanks are widely used in the storage of slag and powder in metallurgical industry. For inner wall cleaning of these large storage tanks, traditional working platforms such as hanging baskets and scaffolds have disadvantages of high labor intensity, high danger and low efficiency. Hence, this paper presents a novel cleaning robot working in the large tank based on the cable-driven parallel mechanism. A novel kinematic modeling method based on lifting point coordinates for the cable-driven parallel mechanism is proposed, which need not directly calculate the position and orientation of the center of the moving platform, but just indirectly analyzes the position and orientation of the moving platform through the positions of lifting points. In this way, the kinematic analysis becomes concise, and the workspace of the moving platform is convenient to obtain. For the cleaning robot working in a large storage tank with 50 m high and 18 m diameter, the forward and inverse kinematic solutions of the parallel mechanism with three cables are studied under the kinematic modeling method based on lifting point coordinates. Finally, the specific structure of the cable-driven parallel robot is designed. Keywords: Cable driven Kinematic analysis

 Parallel mechanism  Cleaning robot 

1 Introduction Solid wastes such as dust and mud are inevitably produced in iron and steel production process. These by-products can be used for building materials. Iron and steel mills store all the dust in the large storage tank, which will harden and stick to the tank wall during the long storage process, so it needs to be cleaned regularly. The tank studied in this This work was supported by National Natural Science Foundation of China (Grant Nos. 51475331, 61703127, 51605067), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY17F020026), and Fundamental Research Funds for the Central Universities. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 28–40, 2020. https://doi.org/10.1007/978-981-32-9941-2_3

A Novel Cable-Driven Parallel Robot for Inner Wall Cleaning

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paper is 50 m high and 18 m in diameter. The clearance work in this suspended environment is dangerous. At present, the cleaning of the tank wall is mainly carried out by artificial hanging baskets. The labor intensity, high risk and low efficiency of the workers are urgently needed. Therefore, it is urgent to research a new type of clearance device to meet the large load and sufficient space for activities. The cable-driven parallel mechanism has the advantages of high rigidity and high precision of the rigid parallel mechanism, and also has the advantages of small mass, inertia and large length range of the cable. By controlling the length change of the cable, the cable-driven parallel mechanism has a great working space advantage; Through the synchronous control of multiple ropes, the dynamic platform orientation of the cable parallel mechanism can be flexibly adjusted. And this kind of mechanism mainly uses light weight, high strength and low inertia polymer rope [1], in order to meet the need for high sensitivity occasions. These advantages make the cable-driven parallel mechanism an ideal substitute for rigid link manipulators in many industries or combined with connecting rods to produce light components [2]. Therefore, it is a good application potential and prospect to realize the cleaning operation of large vertical storage tanks by using cable-driven parallel mechanism. The force and motion of the driving unit of a cable-driven parallel robot are transmitted to the moving platform through the cable [3–5], Compared with the rigid link parallel robot, the position and direction of the moving platform are determined by the cable length. However, due to the special characteristics of the cable, it can only bear tension but not pressure, that is to say, the tensile force of each driving cable must be greater than zero [6–8]. Such unilaterality means that the existing analysis and design methods of rigid linkage mechanisms cannot be directly applied to cable-driven parallel robot. This is also a difficult point in the application of cable-driven parallel robots. At present, Diao et al. [9] discussed the singularity analysis of a fully constrained planar cable robot with four or more cables. And based on the rank analysis of Jacobian matrix, a set of Jacobian singularities were proved mathematically. Yang et al. [10] carried out kinematics and singularity analysis of 4-cable 3-DOF cable-driven parallel robot in the plane, and calculated the singularity of robot motion. Carricato and Merlet [11] analyzed the dynamic and static characteristics of under-constrained 3cable parallel robot under crane conditions. Soon afterwards Abbasne and Carricato [12] extended the research to underconstrained n-cable-driven robots and looked for cable tensile force distribution under equilibrium conditions. While Xu et al. [13] analyzed the dynamics and control of a cable-driven hyper-redundant manipulators Barrette et al. [14] introduced a new concept of dynamic workspace to analyze workspace. Merlet [15] establishes a new model and gives a general solution to the inverse solution of 6-cable-driven robot. To perform the static and kinematic analysis, the screw theory with wrenches and twists can be adopted [16–18]. In above papers, the rigid parallel mechanism kinematical modeling method is usually used to establish the kinematics model of the flexible parallel mechanism. The process of modeling and solving is complex and complicated, and the structural characteristics of the flexible mechanism are not utilized. Therefore this paper presents a lifting point coordinate modeling method for kinematics analysis of cable-driven parallel mechanism. This method does not directly calculate the position and orientation of the center of the moving platform, but indirectly analyzes the position and

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orientation of the moving platform through the position of each lifting point of the moving platform. And it has a simple and intuitive kinematics modeling process, which is convenient for analyzing the advantages of the moving platform workspace.

2 Statics of the Cable-Driven Mechanism According to the working conditions in practical application, the stereogram and structure of the 3-cable-driven parallel robot are given at first in Fig. 1. B2

z

B3

B1 O

L2

y

x

L3

L1 P2 P P3 P1

Fig. 1. Structure of the 3-cable-driven parallel robot

Assuming that the mass of the cable is neglected, that is, the weight of the cable is not taken into account and the cable is considered to be straight at rest. As shown in the figure, the global fixed coordinate system (XO, YO, ZO) is established on the stationary platform and the local coordinate system (XP, YP, ZP) is established on the moving platform. B1, B2, and B3 denote the anchor points on the stationary platform; P1, P2, and P3 denote the lifting points on the moving platform. According to the static equilibrium relationship of the moving platform, the following equations can be obtained. 8 3 P > > < ui Ti þ f = 0 i¼1

3 P > > : (R  ri Þ  ui  Ti þ M = 0

ð1Þ

i¼1

where ui denotes the unit vector of the ith cable; Ti denotes the tensile force of the ith cable; ri denotes the vector from the center of moving platform to the anchor point described in the coordinate system P; f and M denote the external force and moment on the moving platform; and R denotes the rotation matrix of the coordinate system P relative to coordinate system O, and

A Novel Cable-Driven Parallel Robot for Inner Wall Cleaning

2

cos b cos c R ¼ 4 cos c sin a sin b þ cos a sin c sin a sin c  cos a cos c sin b

31

3 sin c  cos b sin a 5 cos a cos b

 cos b sin c cos a cos c  sin c sin a sin b cos a sin c þ cos a sin b sin c

where a, b, and c are three Euler angles. Equation (1) can be rewritten in the matrix form: JT ¼ W where  J¼

u1 ðR  r1 Þ  u1

u2 ðR  r2 Þ  u2

T ¼ ð T1

T2

u3 ðR  r3 Þ  u3



T3 ÞT

W¼  (f MÞT In the global coordinate system, the unit vector of the cable is as follows. ui ¼

OBi  OPi jjOBi  OPi jj

3 Kinematical Analysis 3.1

Inverse Kinematic Solution

Inverse kinematic solution refers to the solution of each cable length with the position of the moving platform known. In this paper, a lifting point coordinate modeling method is proposed. This method does not directly calculate the position and orientation of the center of the moving platform, but indirectly analyses the position and orientation of the moving platform through the position of each hanging point of the moving platform. In this way, instead of calculating the transformation between the dynamic and static coordinate systems, only a global coordinate system is needed on the static platform, which reduces the amount of calculation and improves the accuracy of calculation. We know the coordinates of the anchor points Bi of the cable on the stationary platform, and the distribution of the lifting points Pi on the moving platform. In order to calculate the cable length through the center of moving platform P (Px, Py, Pz), the formula of cable length is as follows. Li ¼ OBi  OPi where Li denotes the vector of cable i.

ð2Þ

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Equation (2) shows that li ¼ kOBi  OPi k. Then we requires coordinates of P1, P2 and P3. Because the three-cable parallel mechanism studied in this paper is only affected by gravity of the moving platform, if the gravity is G, then the following equations hold. f ¼ð 0

0

G ÞT

M ¼ f  OP The static equilibrium equations can be obtained by Eq. (1). In order to avoid the influence of direction vectors on the calculation, we express the tensile force of each cable as follows. Ti ¼ ti kOBi  OPi k

ð3Þ

Si ¼ OPi  Li

ð4Þ

Where Ti represents the tensile force, li represents the length. Substituting Li and Si into Eq. (1), the following equation is obtained. 

LT ¼f ST ¼M

ð5Þ

where L ¼ ½ L1 S ¼ ½ S1

L2 L3  S2 S3 

i represent the vector matrix of cable. From Eq. (3), we know ti ¼ kOBiTOP , and ik

T ¼ ½ T1 T2 T3  T . In this way, we avoid the calculation of unit vectors and treat as an unknown number. Since the length of the cable is inversely decomposed by the center coordinate of the platform, and the position of three anchor points of the moving platform is uniformly fixed on the moving platform and the size of the moving platform is known. Hence, the position relation of three points can be mathematically described as follows. 8 > < ðP1x þ P2x þ P3x Þ=3 ¼ Px ðP1y þ P2y þ P3y Þ=3 ¼ Py > : ðP1z þ P2z þ P3z Þ=3 ¼ Pz

ð6Þ

8 2 2 > < kOP1  OP2 k ¼ p12 kOP1  OP3 k 2 ¼ p213 > : kOP2  OP3 k 2 ¼ p223

ð7Þ

and

A Novel Cable-Driven Parallel Robot for Inner Wall Cleaning

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where Pix ; Piy ; Piz denote the x, y, z coordinates of the Pi point, and pij denotes the distance between Pi and Pj. From the previous illustration, it can be seen that there are 9 unknowns from three lifting points, and 3 unknowns ti . Hence, there are totally 12 unknows. By combining Eqs. (5), (6), and (7), a total of 12 scalar equations can be conveniently solved through mathematics software. 3.2

Forward Kinematic Solution

Forward kinematic solution refers to solving the position and orientation parameters of the moving platform with the given length of each cable. For the analysis of the positive kinematics solution of the parallel mechanism, it is often necessary to solve a set of nonlinear equations coupled with position and orientation, which is rather difficult. The Newton-Raphson method may be adopted, where the length of the cable obtained by the inverse solution approximates the target length of the cable and finally obtains the forward kinematic solution. Although this method is effective, the error will always accumulate to a large extent. In this paper, the lifting point coordinate modeling method is established to avoid these problems and simplify the calculation steps. Solving the position and orientation parameters of the moving platform by the cable length, the coordinates of the center point of the platform and the corresponding X-YZ Euler angles need to be obtained. The relationship of cable length has been expressed in Eq. (2). Thus, substituting l1 ; l2 ; l3 ; p12 ; p13 ; p23 into Eqs. (2), (5), and (7), results in the forward position solution. After solving the coordinates of P1 ; P2 ; P3 , the center point can be mathematically expressed from Eq. (6). And the orientation of the moving platform can be obtained through three lifting points. Then the corresponding X-YZ Euler angles of the moving platform can be calculated.

4 Orientation Analysis of the Moving Platform The motion of moving platform is limited by cables. Only when the path of moving platform is planned in the workspace can the required motion be realized. The workspace is to measure the translational and rotational performance of the cable-driven parallel robot, which is defined as the set of all position and posture points of the moving platform satisfying the cable tensile force constraints in space. In traditional research, workspace is usually computed by traversing all required points in a range. But these methods are computationally expensive and inaccurate. In this paper, based on the singular condition that the cable tensile force is zero, assuming one of the three cables has a cable tensile force of 0, that is T1 = 0, the following equations hold.

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82 3 B2x  P2x B3x  P3x   > > > > 4 B2y  P2y B3y  P3y 5 t2 ¼ f > > t3 > > B2z  P2z B3z  P3z > > > < t ½ S2 S3  2 ¼ M t 3 > > > > > kOP1  OP2 k2 ¼ p212 > > > > kOP1  OP3 k2 ¼ p213 > > : kOP2  OP3 k2 ¼ p223

ð8Þ

We take the coordinates of x, y and z of Pi as output, take t1 and t2 as input, and the functional relationship between them is expressed by f. The polynomial expression can be obtained. 

 Pix ; Piy ; Piz ¼ fi ðt2 ; t3 Þ

So that 

 1X f i ðt 2 ; t 3 Þ Px ; Py ; Pz ¼ 3

According to the working conditions of the cable, the tensile force of each cable is positive when the moving platform is subjected to external force ðf M ÞT at any point in the working space. And a minimum positive force is needed to ensure that the cable is not relaxed during the movement. In addition, the maximum tensile force of the cable cannot be infinite, it should be more practical, and the maximum value should be less than the ultimate tensile force of the cable. By combining Eqs. (3) and (4), the range of ti can be obtained. Tmin \tkOBi  OPi k\Tmax According to the range of a singular surface with tensile force of 0 for each cable, the three-sided closed part is the workspace of the three-cable-driven mechanism. On the basis of workspace, there are various paths that can be planned. For the purpose of research, we choose the path as shown in the Fig. 2. This path can be described as rðaÞ ¼ ð 9 sin a

4:5 sin a

a Þ; a 2 ½0; 2p

Set the starting point of motion on point P0(9, 9, 25), the position and orientation of the moving platform can be obtained as shown in Fig. 3.

A Novel Cable-Driven Parallel Robot for Inner Wall Cleaning

35

Fig. 2. The path of moving platform

Fig. 3. The position and orientation of the moving platform

5 Structural Design The main function of the cable-driven parallel robot designed in this paper is to clear the tank. Considering the influence of the workspace of the mechanism, the top view of the cleaning robot is shown in the Fig. 4. The moving platform is driven by three cables. One end of the cable is connected to a guide rail driven by a motor at the top of the tank, and the other end is connected to three fixed joints connected by hooks and rings on the moving platform as shown in the Fig. 5. Four saw blades for cleaning work are installed under the moving platform. The four saw blades are interlaced to ensure that no matter which side of the moving platform moves to the tank wall, they can work normally. In the working state, the dust adhering to the tank wall is cut by high-speed rotating gear. The electric saw is controlled to rotate in the way that the direction of the cutting force acting on the tank wall is upward. Therefore, the direction of the reaction force acting on the moving platform is downward, which is consistent with the gravity direction. Hence, the tensile

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Guide rail and mobile table

Moving platform with saw blade

Fig. 4. The top view of the cleaning robot

forces of three cables, the gravity and the reaction force produced by cutting can ensure the force closure of the moving platform when the electric saw rotates. At this time, fasteners will be subject to greater vertical tensile force, so the bolts between the motor and the installation plate, and the bolts between the installation plate and the moving platform should be fastened.

Fig. 5. The structure of the moving platform

In view of the actual working conditions, this paper proposes a method of installing guide rail along the wall of the tank, which can move the fixed hanging point at the upper end, and make the mechanism clean the wall completely in a limited number of times of movement. Motors are installed on the mobile table and gears are installed under the mobile table. In order to prevent undercutting, the modified gears should be used here. Rollers are installed on the worktable to control the collection and release of

A Novel Cable-Driven Parallel Robot for Inner Wall Cleaning

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cables. The motor drives the gear to rotate. With the movement of the gear, the position of the lifting points on the wall can be changed (Fig. 6).

Fig. 6. The structure of the guide rail and the mobile table

Considering the actual situation, three lifting points of the tank are evenly distributed in a quarter of the circle area, and the center of the moving platform is located in the center of the gravity center vertical line of the isosceles triangle formed by the three lifting points. Overhead view of the overall structure is shown in the Fig. 7.

B2

P2 B3

P3

P1

B1

Fig. 7. The top view sketch

The minimum distance between moving platform and tank wall is as follows. DP ¼ D=2  jjOP3 jj

ð9Þ

Where D denotes the diameter of the tank, The center of the moving platform is the center of gravity of DB1B2B3. By substituting coordinates of three lifting points B1, B2 and B3 of static coordinate into Eq. (6), coordinates P1, P2 and P3 can be obtained, then substituting coordinates B1, B2 and B3 into Eq. (8), we can obtain that DP = 1.21 m. Figure 8 shows the change of the triangle orientation of lifting points on the moving platform. The solid line graph shows the initial distribution position of three lifting

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points on the moving platform, and the dotted line graph shows the distribution of lifting points under the working condition. From calculation we can see that the z-Euler angle of the moving platform is 15°, that is to say, the moving platform rotates 15° around the z-axis. At this time, the center of the moving platform is 1.21 m away from the tank wall and the radius of the moving platform is 1 m. Therefore, in order to ensure that the moving platform keeps close to the horizontal posture, the radius of the saw blade can be designed to be about 0.25 m.

Fig. 8. The position of lifting points on the moving platform

In order to ensure that the orientation angle of the working process is not too large, and the dust can be cleaned smoothly. In practice, we change the cleaning position by moving the mobile station on the guide rail. Starting from the upper boundary of the initial position, the moving platform moves vertically along the tank wall through the extension and shortening of the cable. When the moving platform moves to the lower boundary, a cleaning step is completed. Then the motor drives the moving platform to move a certain distance along the circumferential direction of the tank wall, and the moving platform continues to move vertically. In this way, the whole tank is cleaned up after the moving platform circles the tank.

6 Conclusions In this paper, a cable-driven parallel robot for cleaning large vertical storage tank is proposed. A kinematic model based on lifting point coordinates is established, and the forward and inverse kinematic solutions of the three-cable parallel mechanism are analyzed. Finally, the mathmatica software can be used to quickly calculate the platform posture and cable length corresponding to the position of each moving platform. On the basis of calculation, the workspace constraints of the cable structure are obtained, and the traveling path of the moving platform is planned in the space under the condition of equal lifting points, and shows the changing trend of the position and posture of the moving platform. For storage tanks with a diameter of 18 m and a height of 50 m, a control device using track control motion is designed. Saw blades can be

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used to achieve the action of clearing dust up and down. Saw blade diameter is designed to keep the moving platform close to the horizontal posture, so that the effective working space can cover the whole tank wall that needs to be cleaned by sliding smoothly through the lifting point position. Acknowledgement. This work was supported by National Natural Science Foundation of China (Grant Nos. 51475331, 61703127, 51605067), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY17F020026), and Fundamental Research Funds for the Central Universities.

References 1. Schmidt, V., Pott, A.: Increase of position accuracy for cable-driven parallel robots using a model for elongation of plastic fiber ropes. In: New Trends in Mechanism and Machine Science. Springer, Cham (2017) 2. Li, C., Rahn, C.D.: Design of continuous backbone, cable driven robots. J. Mech. Des. 124 (2), 265–271 (2002) 3. Tang, X.: An overview of the development for cable-driven parallel manipulator. Adv. Mech. Eng. 6, 823028 (2015) 4. Gouttefarde, M., Collard, J.F., Riehl, N., et al.: Geometry selection of a redundantly actuated cable-suspended parallel robot. IEEE Trans. Robot. 31(2), 501–510 (2017) 5. Lin, Y., Ban, W., Hai, H., et al.: An adaptive mechanism for space tetherreel. J. Astronaut. 35(12), 1379–1387 (2014). (in Chinese) 6. Yu, L., Qiu, Y., Yu, S.: Dynamic workspace of a high-speed cable-driven camera robot. Eng. Mech. 30(11), 245–250 (2013). (in Chinese) 7. Bo, O., Shang, W.: Efficient computation method of force-closure workspace for 6-DOF cable-driven parallel manipulators. J. Mech. Eng. 49(15), 34–41 (2013). (in Chinese) 8. Wei, Y., Deng, Z., Li, Q., et al.: Analysis of dynamic response of tethered space solar power station. J. Astronaut. 37(9), 1041–1048 (2016). (in Chinese) 9. Diao, X., Ma, O., Lu, Q.: Singularity analysis of planar cable-driven parallel robots. In: IEEE Conference on Robotics. IEEE (2008) 10. Yang, G., Yeo, S.H., Pham, C.B.: Kinematics and singularity analysis of a planar cabledriven parallel manipulator. In: Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, (IROS 2004). IEEE (2004) 11. Carricato, M., Merlet, J.P.: Direct geometrico-static problem of underconstrained cabledriven parallel robots with three cables. In: IEEE International Conference on Robotics & Automation. IEEE (2011) 12. Abbasnejad, G., Carricato, M.: Direct Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots with Five Cables. Computational Kinematics. Springer, Dordrecht (2014) 13. Xu, W., Liu, T., Li, Y.: Kinematics, dynamics and control of a cable-driven hyper-redundant manipulator. IEEE/ASME Trans. Mechatron. 23, 1693–1704 (2018) 14. Barrette, G., Gosselin, C.M.: Determination of the dynamic workspace of cable-driven planar parallel mechanisms. J. Mech. Des. 127(2), 242 (2005) 15. Merlet, J.P.: A new generic approach for the inverse kinematics of cable-driven parallel robot with 6 deformable cables. In: Springer Proceedings in Advanced Robotics: Advances in Robot Kinematics (2018)

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A Novel Biomimetic Design Method Based on Biology Texts Under Network Bowen Chen, Liang Chen(&), Xiaomin Liu, and Hao Dou Institute of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China [email protected], [email protected], [email protected], [email protected]

Abstract. Most of works on biomimetic design methods are devoted to provide an artificially built biological information database and make engineering design depending on inspiring. Though using these approaches can improve work efficiency on biomimetic design, it sometimes limits the scope of thinking. Here we provide an approach that using natural language text of biological from network to expand design ideas. In addition, a new biomimetic design mode is proposed by building tree model of engineering object. This paper descript how to retrieve biological texts from network and make text processing, then introduce a text matching algorithm combining with TRIZ to map engineering design problems to biological texts. After obtaining biological texts by using match algorithm, a novel method to guide product design with these texts is proposed. At the end of this paper, an example of dust collector design is used to explain the whole process. Keywords: Biomimicry  Biologically inspired design  Natural language processing  Text processing  Design theory Innovation  Computer aided design

 TRIZ 

1 Introduction Biologically inspired design was first proposed on the late of last century (French 1997). It refers to a method of combining exploration and practice with reference to organisms in nature. A series of innovators were created that inspired from nature creatures. Dating back to 2002, foreign scholar proposed the idea of introducing TRIZ [1] to realize the technical transformation from biological to engineering system and proposed a PRIZM matrix for comparing the similarity between engineering problems and biological examples [2]. A mapping between the functions of biology and engineering was established by making an engineering-biological dictionary method [3, 4]. Combining the traditional TRIZ method with the functional basis is a research hotspot in recent years. A bio-inspired design software was developed, which combine semantic relationship dictionary among various functional keywords, then stored in the ontology database [5]. By abstracting engineering and biology information into functional ontology, a bionic design website was schemed, through searching the ontology database by inputting key statements in a specific format then got relative biological © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 41–51, 2020. https://doi.org/10.1007/978-981-32-9941-2_4

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prototypes [6]. Receiving revelation by information engineering, material flow, information flow, and energy flow was combined as the functional relationship, the 39 engineering parameters in TRIZ are re-divided, and then FB-TRIZ was proposed [7]. The contradiction matrix with the 40 invention principles of TRIZ was combined and the genetic algorithms in the ParaGen framework to implement a mapping based on the design process [8]. The relationship between TRIZ innovation principle and biological case was combined, and then a system optimization strategy for the design of product service system been proposed [9]. In the last few parts, we will introduce an innovative approach, which using biology texts scrawling from Internet and other sources like biological authority books, using information extract from these texts to guide us on engineering design. At first, several concepts and theories are proposed to introduce the working process of this novel biomimetic design method. Second, we explain the core theories behind the whole processing. Then, based on the workflow illustrated, corresponding code and Graphical User Interface (GUI) is written and debugged. After that, we give an example of optimization of cyclone dust collector to show the practicality of this biomimetic design method. Finally, a conclusion is proposed to summarize our current research on biology inspired design and our future plan of work on it.

2 Overall Approaches The whole processing of the biomimetic design could be separated as three parts, been sorted as engineering field, biological field and intermediate, as shown in Fig. 1. Designer get design object based on a specific mission plan or customer request at the beginning. To complete the first step on design, as a concept design, successfully, a tree-like model based on TRIZ has to be constructed, which serves as a part of our design method, will be illustrated in detail on Sect. 3. After construct the initial model, we get one or several pairs of contradiction and map them into principle keywords of expanded TRIZ based on intermediate. Searching on the local biological database with principle keywords and customize keywords, which are decided by designer’s own experiential knowledge, several biological texts in database are matched. Based on corresponding algorithm, which introduce in Sect. 3, designer could get operators to modified current engineering model. Repeat this whole process continuously until model satisfied designer’s intention, and then get a feasible solution on this stage.

Fig. 1. Whole processing of biomimetic design

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To make this process work successfully, some preparations in the early stage should be done, including crawling raw texts data and restore them normally in the local database; expanding traditional TRIZ 40 principle keywords to make retrieving database in a large range. Meanwhile, what algorithm based on search database and how to build the engineering model and translate biological texts into operators to modified model are also parts of question. All of them would immediately explained in Sect. 3.

3 Core Theories 3.1

Biological Data

The method presented in this paper using normalized biologically texts from network. First, we need to scrawl raw texts from websites about biological in a certain scale; and then, after filter the stop words and stem each word, we embedding words in documents into a vector space [10], then, a bi-LSTM layer and a CRF layer is used to construct part of speech tagging neural network model [11], trained with Conll2000 corpus. The documents are represented via a bag of words (BOW) encoding technique, which is regarded as x, and the output is the part of speech tags, which is regarded as y. As Fig. 2 shows, totally 2033198 parameters are need to be trained. After hours of training and parameter tuning, the model could be used to extract nouns and verbs in sentences of each text and deposit into the database. The specific steps is described in Fig. 3.

Fig. 2. Neural network model

Fig. 3. Normalizing raw texts based on neural network

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Engineering Model

To map engineer problems to biological texts and then translate the information from biological text to product design again, a specific corresponded model based on TRIZ is introduced. The engineering model is separated into four parts as function, principle, behavior and structure. When we get a certain design object at the beginning, we use certain words as nodes and add them onto this tree-like model, inclusion relationships could be expressed as layers of model. The number of nodes in each branch determined by actual situation and designer’s own experience. The more nodes, the lower the design freedom, on the contrary, the fewer nodes, the higher the design freedom. After construct our design object properly, designer should consider the contradiction of every leaf nodes and determine the principle keywords based on TRIZ contradict matrix. The initialized engineering model then been constructed. The kind of tree model structure is shown in Fig. 4.

Fig. 4. A tree model structure

3.3

TRIZ Principle Words Expand

On the other side, we expand the traditional 40 principle words into 40 principle sets, based on pre-trained 300 dimensions Word2Vec [10], which is a popular words embedding model, calculating the words distance in embedding vector space and extract nearest 10 words of each principle word into one set. The aim of expanding words is explained in Sect. 3.4. 3.4

Searching Method and Algorithm

After determine the certain principle words, we search the database with using a list of principle words and a list of custom words defined by designer for each contradiction. Figure 5 shows the keywords to be searched on a specific contradiction. When input principle words, we actually input sets of words expanded before potentially. After designer set weight for each pair of word list, Term Frequency-Inverse Document Frequency (TF-IDF) algorithm [12] is used to calculate scores for texts in database and count score for each texts and return texts sorted by score.

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Fig. 5. The keywords to be searched for contradiction i

3.5

Modifying Engineering Model by Texts

Before we get close to strategy in detail, we firstly define “operators”: (1) Add: add a child node from current node; (2) Delete: delete current node and its child node; (3) Change: change the word in current node; (4) Merge: delete all child nodes from parent of current node; (5) Split: add a child node from parent of current node; (6) Connect: connect current node with other node; (7) Disconnect: disconnect current node with other node. We extract the most high score text from return result to modify current engineering model. The strategy used here is to map noun into node in engineering model, and map verb into operator to define how to modify the model. The steps in detail is to get sentences in text, then get the verbs and nouns in each sentence. Based on Word2Vec model, the distance of nouns in sentence and node in engineering model are calculated, and return the most nearest word pair, which are regarded as operating node. Meanwhile, the distance of verbs in sentence and operators are calculated, return the nearest operator and operate on matched node to modify the engineering model. The process is shown in Fig. 6. Because the matching mechanism not always return the correct way to modify the model, designer plays an important part in selecting right node and operator, this depends on the experience of designer. If designer concerned the text cannot meet the design needs, the second high score of text can be selected and analyze.

Fig. 6. Use biological texts to modify engineering model

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After each time of modifying model, we may get new contradictions, search the database with new principle and custom keywords, and modify model again, loop this process until the model satisfied specific needs, then the feasible solution is got.

4 Software Develop Based on core theories introduced in Sect. 3, relative software is developed, the main user interface is shown in Fig. 7. The interface is obviously separated into two parts, the left side is for constructing and modifying engineering model, the principle keyword sets of model is automatically given while designer input related contradict parameters for leaf nodes.

Fig. 7. Interface of software

At the beginning of design, the graphic on left side is set with “function”, “principle”, “behavior” and “structure” initially. Based on specific application situation, the graphic is updatable when user set an operator and input the correct format of string, after we generate pairs of contradictions, we can input a list of custom keywords, and set the weight of custom keywords for each pair of contradiction. Waiting for few seconds, the corresponding biological texts with verbs and nouns would generate automatically for each contradiction. As introduced in Sect. 3, repeating this process until a feasible solution is got.

5 Case Study In order to verify the validity of this method and explain the processing more specifically, the case of the cyclone dust collector design is used to illustrate. 5.1

Physical Model of Cyclone Dust Collector

Cyclone dust collector is used to enhance the quality of air released by collecting dust and other impurities from air or gas. We depart the cyclone dust collector model into nodes of

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four dimensions. For the dimension of “function”, we only consider the direct function to avoid limiting freedom of design, thus the only one node “dust collect” is added as a child node of “function”. Cyclone dust collector separates air and dust by centrifugal force, and it generates by inertia, a node names “centrifugal force” under “principle”, and derivative a node names “inertia” as a child node of “centrifugal force”. The act of cyclone dust collector during operating is to keep inner rotate to divide air and dust, dust been separated is sink and fill into the collector, and air is risen and pollute outside of dust collector, so the node “rotate” is added under “behavior”, “sink” and “rise” is generated as child nodes under “rotate”. The main parts of cyclone dust collector are entrance aisle, main body, exit aisle. And reference the traditional structure [13], we add “entrance”, “body”, “exit” under node “structure”, add “area” under “entrance”, add “wall” and “tilt” under “body”, add “area” under “exit”, add “diameter” and “height” under “wall”. After the model is initialized, analyzing the current model, “loss of substance” and “use of energy” are as a pair of contradiction generated by “dust collect”, “force” and “area of moving object” are as a pair of contradiction under “inertia”, “speed” and “area of stationary object” are as a pair of contradiction under “diameter”. After analyzing the function, principle, behavior and structure of a traditional cyclone dust collector, the initial engineering model and three contradictions appear, three lists of custom keywords are all set with weights 0.5. The user interface with initial model we build shown as Figs. 8 and 9 shows the keywords and potential word sets we used to search.

Fig. 8. Initial model and keywords to search

Fig. 9. Workflow of keywords used to search

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Modify Engineering Model

After a few second, several texts of biological species are obtained. Considering that the nouns and verbs extracted may not always relate to texts, spending time on filter invalid words should be done. The operator and operating nodes to be selected depends on designer. At that, two operators are used to modify engineering model, which is shown in red boxes in Fig. 10. The operation “add” structure “diameter” and “split” behavior “rise”. We conceive design plan at the text of species spike trisetum and heartleaved foamflower, the picture of their images are shown in Fig. 11. For the current engineering model, we could make different plans of the design of the dust collector.

Fig. 10. Select nodes and operators

Fig. 11. Spike trisetum and heartleaved foamflower

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After modifying model, we concern the mean contradiction in model is eliminated, the current engineering model satisfied preliminary requirements, then we get a feasible solution. Because the map from biology text to engineering product based on intrinsic association of word similarity, the relationship between them can not be expressed intuitively. 5.3

Physical Product Modeling

Based on parameters of a practical dust collector [13] and the engineering model modify of product, we could come up with many options to adjust our plan to practical dust collector. Inspired by the modifying of engineering model, we consider two types of dust collector as example. (1) By operator “add”, we add nodes “upper diameter” and “lower diameter” as child nodes of “diameter”; and by operator “split”, we split the node “rise” into nodes “elevate” and “uplift”. The inlet of cyclone dust collector are designed with a tilt angle to increase the uplift of gas to be filtered. Consider of more centrifugal force we need to separate the gas and impurities and innovate by added nodes “upper diameter” and “lower diameter”, the diameter closed to exit is expanded. The product model of biological inspired cyclone dust collector at the conceptual design stage is built. (2) By operator “add”, we add nodes “changeable diameter” as child nodes of “diameter”; and by operator “split”, we split the node “rise” into nodes “elevate” and “uplift”. On the inner wall of cyclone dust collector, the tilt shape also assist to make a separation between gas and dust, combining with the idea of adding diameter of inner wall, we could also we sacrifice some performance of centrifugal force to increase the tilt of wall. As the part of nodes “elevate” and “uplift”, we also use a tilt angle of inlet to increase the uplift of gas to be filtered.

Fig. 12. Biological inspired cyclone dust collector

The kinds and amounts of product design results is different among designers because of various ideas and experiences. The design of the dust collector on the step of concept design is shown in Fig. 12. Now we have completed the preliminary

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physical design step, designer could regard it as a basic model for further optimization such as performance and service life. 5.4

Design Comparison

Comparing with traditional design structure, the two models above using biomimetic design methods are difference on aspect of air inlet and the shape of inner wall. Although deep analysis like simulation should be done after numerical optimization, we could theoretically analysis the feasibility of the new designs. Air with dust enter the filter body of cyclone dust collector from inlet. Traditional cyclone dust collector only provides horizontal tangential speed for inner air and dust, as the innovative cyclone dust collector, the tilt angle is used for providing an axial speed for air and dust, and reduces the influence of gravity, to thus increase the rotate time of air and dust in the body, and to more completely distinct dust. Two different kinds of inner wall are used in the innovative design. One of the plans, diameter of the lower part of the straight cylinder is reduced, to make the downer part of cylinder providing more centrifugal force while the upper part of body could not depart the dust from air. Another plan is to replace the cylinder to a whole cone, although it would increase the friction between air and wall, it provides an axial force above from inner side, and meanwhile increase the centrifugal force at lower part.

6 Conclusions Traditional biologically inspired design methods focus on product designers to drive the processing and these is no doubt that using these methods may accomplish tasks of biomimetic design well, but it usually wasting lots of times to get the appropriate way on design. As is shown in Sect. 5, with a computer aided method could improve the efficiency of engineering design at a certain extent, on other hand, the texts information could be from network or arthritic books, which means that it provides a broader range of biomimetic design and prevent directional thinking of designer. The source of data could continuously added into database and the process of raw texts processing is fast because of the trained neural network model, making the software easy to maintenance and adjustment. On the case of dust collector optimize design, the method works well on mapping engineering problems to biological texts, but works a little worse while modifying engineering model using operators, which is translated from texts. The software at the current stage requires the designer using own experience of product designing on selecting reasonable verb-operator and noun-node pairs, huge difference of model modification among designers, the advance of the method is that respecting subjective of different designers, but sometimes the uniform standard is hard to be given. Future work will focus on providing a second way to guide designers to make biological inspired design with more automated operation pipeline, and different training model is considered to be integrated in the current neural network model for extracting nouns and verbs more accurately.

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References 1. Altshuller, G.S.: Creativity as an Exact Science: The Theory of the Solution of Inventive Problems. Gordon and Breach, Amsterdam (1984) 2. Vincent, J.F.V., Mann, D.L.: Systematic technology transfer from biology to engineering. Philos. Trans. Roy. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 360(1791), 159–173 (2002) 3. Nagel, J.K.S., Stone, R.B., McAdams, D.A.: An engineering-to-biology thesaurus for engineering design. In: ASME 2010, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 117–128. American Society of Mechanical Engineers (2010) 4. Nagel, J.K.S., Nagel, R.L., Stone, R.B.: Abstracting biology for engineering design. Int. J. Des. Eng. 4(1), 23–40 (2011) 5. Trotta, M.G.: Bio-inspired design methodology. Int. J. Inf. Sci. 1(1), 1–11 (2011) 6. Kozaki, K., Mizoguchi, R.: A keyword exploration for retrieval from biomimetics databases. In: Joint International Semantic Technology Conference, pp. 361–377. Springer, Cham (2014) 7. Nix, A.A., Sherrett, B., Stone, R.B.: A function based approach to TRIZ. In: ASME 2011, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 285–295. American Society of Mechanical Engineers (2011) 8. Khodadadi, A.: Synergy of a genetic algorithm and TRIZ in conceptual design. In: Proceedings of IASS Annual Symposia, no. 2, pp. 1–8. International Association for Shell and Spatial Structures (IASS) (2018) 9. Chen, J.L., Hung, S.C.: Eco-innovation by TRIZ and biomimetics design. In: 2017 International Conference on Applied System Innovation (ICASI), pp. 40–43. IEEE (2017) 10. Mikolov, T., Sutskever, I., Chen, K., et al.: Distributed representations of words and phrases and their compositionality. Im: Advances in Neural Information Processing Systems, pp. 3111–3119 (2013) 11. Xu, K., Zhou, Z., Hao, T., et al.: A bidirectional LSTM and conditional random fields approach to medical named entity recognition. In: International Conference on Advanced Intelligent Systems and Informatics, pp. 355–365. Springer, Cham (2017) 12. Salton, G., Buckley, C.: Term-weighting approaches in automatic text retrieval. Inf. Process. Manag. 24(5), 513–523 (1988) 13. Chi, Y., Huo, H., Dai, Y.: Cyclone dust collector optimization design and CFD numerical verification. Mech. Des. Manuf. 2018(8), 33–35, 40 (2018)

Numerical Simulation on Effect of Graphene Doped Morphology on Heat Transfer Efficiency of Anti-/deicing Component Long Chen1,2(&) and Zhanqiang Liu1,2 1

2

Key Laboratory of High Efficiency and Clean Manufacturing, Shandong University, Jinan 250061, China {chenlong,melius}@sdu.edu.cn School of Mechanical Engineering, Shandong University, Jinan 250061, China

Abstract. Graphene doping can effectively improve the heat transfer capacity and anti-/deicing efficiency of anti-/deicing component. The main factors that affecting the improvement of heat transfer efficiency of graphene-doped anti-/ deicing component are the graphene-doped morphology, which including the distribution and location in the composites and the size and shape of the graphene sheet. In this paper, the heat transfer characteristics of graphene-doped anti-/deicing component were studied by numerical simulation. By establishing the heat transfer mathematical model of graphene-doped anti-/deicing component, the cross-scale heat transfer numerical simulation with different graphenedoped forms was proposed to solve the temperature field distribution of graphene-doped anti-/deicing component. Finally, based on the results of temperature field calculation of graphene-doped anti-/deicing component, the effect of graphene doping morphology on the heat transfer efficiency of anti-/deicing component was studied, which were beneficial to heat transfer of anti-/deicing component. By employing the proposed cross-scale heat transfer model for graphene doping of composite materials, the heat transfer characteristics of graphene doping was qualitatively described, and it is shown that the doping of graphene can optimize the heat transfer of the composite anti-/deicing component. Keywords: Graphene doping  Numerical simulation Anti-/deicing component  Composites



1 Introduction With the continuous prominence of engineering safety problems, more and more engineering safety technologies have been developed and studied extensively. Wind turbine blades and aircraft will ice under extreme conditions, which causing serious safety accidents. Icing will affect the power supply efficiency of wind turbine blades, This project is supported by Fundamental Research Funds of Shandong University (Grant No. 2018GN034), State Key Laboratory of Mechanical System and Vibration (Grant No. MSV2019-13), and 13th Five-Year Plan Equipment Pre-Research Fund (Grant No. 61402060404). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 52–62, 2020. https://doi.org/10.1007/978-981-32-9941-2_5

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especially the flight control and flight safety of aircraft. At present, the research on improving heat transfer of composite materials is more extensive: Wang et al. [1] proposed a composite porous wick with spherical-dendritic powders. Two evaporative heat transfer modes are observed through political and legal experiments, which can improve the heat transfer characteristics. Buffone [2] proposed a paradigm shift in improving the heat transfer rate between the surface of the radiator and the surrounding fluid by a new design method of composite radiator. This approach consists in using high thermally conductive coatings on top of the finned substrate in order to increase the local temperature along the fin washed surface. Lei et al. [3] proposed a decomposition algorithm which using a composite cylindrical surface source solution to deal with the composite heat conduction along the radius and a coil line source solution to deal with the heat conduction between tube loops in depth direction. Two computationally efficient and accurate solution methods for heat transfer analysis in composite metal cylindrical vessel subjected to internal thermal load are presented by Masumi [4]. The methods were verified by numerical simulation, which are more accurate. In Krysko’s work, the topological optimization of composite structures is widely used while tailoring materials to achieve the required engineering physical properties [5]. Considering the competitive mechanics and thermal properties of the composites, the materials with the maximum effective bulk modulus and thermal conductivity were constructed. Wang et al. [6] developed a grille-sphere composite structured packed bed (GSCSPB). The new structure aims to overcome the shortcomings of random packed bed and traditional packed bed. The pressure drop and heat transfer in GSCSPB were measured by naphthalene sublimation experiment, and the comprehensive heat transfer performance of GSCSPB with random packed bed and structured packed bed was evaluated. Aadmi et al. [7] studied the thermo-physical properties and melting process of phase change material composites numerically and experimentally based on epoxy resin paraffin. The above research optimizes and improves the heat transfer of composite materials through numerical simulation, experimental verification and theoretical derivation, which providing research methodological guidance and research reference for improving anti-/deicing efficiency and solving icing problems. In recent years, graphene, as a new multifunctional material, has shown excellent performance in heat conduction and conduction [8–11]. In terms of thermal conductivity, graphene-related studies show that graphene can improve the thermal conductivity of composites and metal-based materials, which also has toughening effect on mechanical properties. Hussien et al. [12] studied the forced convective heat transfer of water-borne Al2O3 nanofluids mixed with graphene nanofluids. They selected volumetric concentrations of Al2O3/water nanofluids, and graphene nanofluids were compared. Liao et al. [13] theoretically investigated near-field heat transfer between graphene–SiC–graphene–metamaterial (GSGM) multilayer structures. The results show that heat transfer between GSGM structures is significantly larger than that between SiC-coated metamaterials when the chemical potential of graphene is not very high. Anhua et al. [14] established a coupled thermo-mechanical model of graphene film and obtained an accurate analytical solution of the thermoacoustic radiation of graphene film. By comparing with the experimental results, the correctness of the

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theoretical model is verified. Zhou et al. [15] studied the heat transfer performance of graphene nanoplate (GNP) fluid oscillating heat pipe (OHPS). The results showed that GNP nanofluid as a working fluid could improve the heat transfer performance of OHP compared with deionized water (DW). Bharadwaj et al. [16] studied the application of mixed nanofluids in radiators to improve their heat transfer performance. Because graphene has high thermal conductivity, carboxyl graphene and graphene oxide nanoparticles were selected as doping particles of nanofluids. The results show that heat transfer efficiency and cooling rate are improved. In summary, the above researches show that graphene has a significant effect on improving the heat transfer efficiency. In this paper, graphene is doped in composite materials to improve the heat transfer efficiency of composite anti-icing module, and the heat transfer effect of graphene doping is studied by numerical simulation. In this research, the graphene doping technology is used to modify the composite anti-/deicing component in order to improve the heat transfer efficiency of the composite anti-/deicing component and reduce the heat loss in the composite during the heat transfer process. Through cross-scale modeling of graphene-doped composites, multi-field coupling simulation was used to solve the problem, and different morphologies of graphene-doped composites were analyzed and studied. The temperature field distribution of graphene-doped composites was predicted by numerical simulation. Using the advantage of numerical simulation for reference, the number of experiments can be reduced effectively, and the research and result prediction of graphene-doped composites can be improved. The relationship between the temperature field distribution and the graphene doping morphology was established. The effect of graphene doping morphology on the heat transfer characteristics of composites was revealed, which provided a theoretical basis for the optimization and control of graphene doping process.

2 Numerical Simulation Process The micro-morphology of composite anti-/deicing component doped with graphene is shown in Fig. 1. Graphene is distributed in the gap between epoxy resin and glass fiber in lamellar form and is evenly dispersed in epoxy resin. However, within the graphenedoped composites, the graphene lamellae within the unit structure were found to be randomly distributed by scanning electron microscopy. The mathematical model of micro graphene doped composites was established by cross-scale modeling method, and the temperature field of the model was solved by numerical simulation. The temperature field distribution of graphene-doped composites under the coupling of flow field, temperature field and thermal stress field was analyzed by solving the multi-field coupled finite element model. Intelligent meshing technology is used to mesh graphene-doped composites. The partitioned grid satisfies the condition of multi-field coupling and improves the accuracy of numerical simulation.

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Fig. 1. Schematic of cross-scale modeling process for graphene doped composites

In the graphene-doped composites model, the size of graphene sheet length is 300– 600 lm, and the dispersion form is random distribution. Therefore, the three-dimensional model of graphene doping is established according to the microstructure of the composites. The bottom of the simulation unit is a glass fiber paving structure. The glass fiber is preimpregnated in epoxy resin, and the space between epoxy resin and glass fiber is doped with graphene sheets. After the three-dimensional model of graphene doping is established, the geometric model of graphene-doped composites was meshed (as shown in Fig. 2) and imported in the commercial finite element software ANSYS Workbench.

Fig. 2. Schematic of cross-scale modeling meshing

In the process of numerical simulation, micro-scale cross-scale modeling of composite anti-/deicing component with different graphene doping morphology was carried out. The heat transfer effect of composites with different graphene doping morphology was analyzed under the equivalent thermal boundary condition, and the anti-icing efficiency of composite anti-/deicing component was analyzed. Then the influence of graphene doping on the heat transfer effect of composite anti-/deicing component was expounded. Graphene doping morphology includes graphene doping content and graphene distribution. The heat transfer characteristics of composite anti-icing module under different doping conditions were studied by simulating different graphene doping morphologies. The steps of numerical simulation are as follows: • Step 1: Firstly, the geometric model of graphene-doped composites is established. • Step 2: Then the multi-field coupling boundary conditions of graphene-doped composites are determined.

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• Step 3: Solving flow field distribution of graphene-doped composites and applying the results on geometric model as initial boundary conditions of thermal module. • Step 4: Thus the temperature distribution of graphene-doped composites is solved. • Step 5: Using the temperature field results as initial conditions to solute of thermal stress field distribution. • Step 6: Solving thermal stress field distribution of graphene-doped composites. • Step 7: Finally, the temperature and stress fields of graphene-doped composites are solved by coupling method.

3 Calculation of Effective Thermal Conductivity According to the law of thermal resistance and the equivalent thermal conductivity, a series-parallel heat transfer model of graphene doped composites was established. The integral composite anti-/deicing component was considered to consist of a large number of square elements. An arbitrary element is selected from the composite graphene doped anti-/deicing component (see Fig. 3). The equivalent thermal resistance of the whole structure is established by calculating the equivalent thermal conductivity of the layered structure in the unit.

Fig. 3. Schematic of unit and equivalent thermal resistance

Through the analysis of heat transfer unit, the composite graphene doped anti-/ deicing component is composed of glass fiber and epoxy resin matrix. kb and kf are set as the thermal conductivity of epoxy resin matrix and glass fiber respectively. According to Fourier’s law, the thermal resistance is as follows: R¼

d kA

ð1Þ

Where d is the unit thickness, and A is the cross-sectional area of the unit. The equivalent thermal resistance model of Fig. 3 is analyzed. The model divides the unit into model 1, model 2 and model 3. Due to the randomness of the shape and content of graphene doping between glass fiber and epoxy resin, it is approximately considered that the graphene sheet doped in the space formed by glass fiber and epoxy resin are uniformly distributed. Therefore, the equivalent thermal resistance of

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graphene in epoxy resin is set as Rg , and the equivalent thermal resistances of the corresponding models are R1 , R2 , and R3 respectively. Then the equivalent thermal resistance model of the element body is a parallel model, and the equivalent thermal resistance Re of the element body can be expressed as: 1 1 1 1 ¼ þ þ Re R1 þ Rg R2 þ Rg R3 þ Rg

ð2Þ

Therefore, based on the equivalent thermal resistance model in Ref. [17], considering the influence of graphene equivalent thermal resistance on each model, the equivalent thermal resistance model of model 1, model 2 and model 3 are deduced as follows: 2 kb D " #9 8 > > 2kf 3kb > > > a tan 1 > > > < 2 2 = 2k k 3k ð f b bÞ 1 2 R2 ¼ þ  1 2kb D D2 > > > 2kf kb  3k2b 2 > > > > > ; : R1 ¼ ¼

" #9 8 > > 2k 3k f b > > > a tan 1 > > > < 2 2 = ð2kf kb 3kb Þ 8 R3 ¼ 2  1 D > > > 2kf kb  3k2b 2 > > > > > ; :

ð3Þ

ð4Þ

ð5Þ

Equation (2) is sorted out and the equivalent thermal resistance model of the unit body Re is deduced as follows: Re ¼

ðR1 þ Rg ÞðR2 þ Rg ÞðR3 þ Rg Þ R1 R2 þ R1 R3 þ R3 R2 þ Rg ðR1 þ R2 þ R3 þ 3Rg Þ

ð6Þ

R1 R2 R3 R1 R2 þ R1 R3 þ R2 R3

ð7Þ

R0e ¼

Equation (6) is compared with Eq. (7) by division, and Eq. (8) is obtained:   Rg ðR1 þ R3 þ R2 þ 3Rg Þ Re R1 R2 R3  1 þ ¼ R1 R2 þ R1 R3 þ R2 R3 R0e ðR1 þ Rg ÞðR2 þ Rg ÞðR3 þ Rg Þ

ð8Þ

Based on the above deduced equivalent thermal resistance model, the doping heat transfer of graphene in composite materials was analyzed theoretically. The expression can be used to analyze that, because the thermal resistance of graphene Rg \ R1 ; R2 ; and R3 , thus, the ratio of Eq. (8) is less than 1. The above formula shows

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that the equivalent thermal resistance of the whole unit doped with graphene composite anti-/deicing component is less than that of the composite anti-/deicing component unit without graphene.

4 Results and Discussion The heat transfer of composite graphene doped anti-/deicing component was solved by establishing a mathematical model of cross-scale graphene doping heat transfer. The heat transfer solutions of graphene-doped anti-/deicing component were compared with that temperature distribution of undoped graphene. Table 1 shows the relevant thermophysical parameters of composite anti-/deicing component. According to the relevant parameters in the table, the mathematical model of heat transfer of composite graphene-doped anti-/deicing component is solved. The influence of graphene doping on heat transfer characteristics of composite anti-/deicing component is analyzed, and the effect of graphene sheet on heat transfer characteristics is expounded.

Table 1. Material thermal physical parameters

2700

Thermal conductivity (W/m K) 1.46

Coefficient of thermal expansion (1/K) 2.7e−6

2300

0.21

5.6e−7

1760

5300

−3e−5

Layer

Density (Kg/m3)

Glass fiber Epoxy resin Graphene

The heat transfer of composite graphene doped anti-/deicing component was solved by establishing a mathematical model of cross-scale graphene doping heat transfer. The heat transfer solutions of graphene-doped anti-/deicing component were compared with that undoped graphene. Graphene doping played a significant role in promoting the temperature field of composite anti-/deicing component. The numerical results show that graphene doping has a significant effect on the homogenization of temperature field of composite anti-/deicing component. As shown in Fig. 4, by comparing the temperature distribution of graphene-doped anti-/deicing component under the same thermal boundary conditions, the temperature field of nondoped graphene composite anti-/deicing component forms a large area of low temperature region, while that of doped graphene anti-/deicing component is smaller, which shows that the heat transfer effect of doped graphene composite anti-/deicing component is optimized.

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Fig. 4. Temperature field distribution of composite anti-/deicing component: (a) graphene doped; (b) graphene undoped.

As shown in Fig. 5, by analyzing the temperature field of graphene-doped composite anti-/deicing component, the area where the surface temperature of composite anti-/deicing component meets the anti-icing temperature requirement (the surface temperature is above 2 °C) is shown in the following figure. From the distribution of temperature field, it can be found that the areas are the zone where graphene sheets are densely distributed. The results indicate that graphene doping plays a positive role in heat transfer of composites.

Fig. 5. Anti-icing area distribution of graphene doped anti-/deicing component

The heat flux of graphene-doped composites anti-/deicing component was analyzed (as shown in Fig. 6). The numerical simulation results of graphene-doped composites show that the graphene layer doped in the composites has a significant effect on the heat flux in the local area. It shows that the heat transfer characteristics of graphene layer have promoted the heat transfer performance of the entire composites. The numerical simulation results show that the heat flux at the agglomeration of graphene sheet is significantly higher than that in the space region composed of epoxy resin and glass fiber.

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Fig. 6. Heat flux distribution of graphene doping model

The heating efficiency curve as shown in Fig. 7 is drawn by collecting the surface heating area of the composite graphene doping anti-/deicing component and without doping. It can be found from the curve that the proportion of the area where the surface temperature of graphene-doped anti-/deicing component reaches the anti-icing temperature increases with the heating time. The increasing speed of graphene-doped anti-/ deicing component is higher than that of the non-doped graphene, which indirectly verifies that the anti-icing ability of graphene-doped composite anti-/deicing component has been improved.

Fig. 7. The heating efficiency curve of composite anti-/deicing component

5 Conclusions 1. By establishing a cross-scale heat transfer model of graphene doping in composite materials, the numerical simulation of graphene doping was carried out to reveal the effect of graphene doping on heat transfer of composite materials. The proposed

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cross-scale heat transfer model for graphene doping of composite materials can qualitatively describe the heat transfer characteristics of graphene doping. 2. Based on the assumption of uniform distribution of graphene sheets, the equivalent thermal resistance of graphene doped glass fiber and epoxy resin matrix was deduced. The expression of equivalent thermal resistance of graphene doped composites was obtained. 3. The numerical model of graphene doping is solved by multi-field coupling numerical solution method, and the temperature field distribution of graphene doping numerical simulation is obtained. By comparing the temperature distribution of the components of the composite anti-/deicing component with that of the undoped graphene, it is shown that the doping of graphene can optimize the heat transfer of the composite anti-/deicing component. 4. The numerical simulation results show that graphene doping can improve the local surface temperature and heat flux of composite anti-/deicing component, which effectively increase the surface temperature of composite anti-/deicing component. The anti-icing surface area ratio of composite anti-/deicing component was also increased by graphene doping. Through graphene doping, the surface heating speed of composite anti-/deicing component was increased, and the anti-icing efficiency can be improved, which promoting the anti-icing reaction rate of anti-/deicing component.

References 1. Wang, D., Wang, J., Bao, X., et al.: Evaporation heat transfer characteristics of composite porous wick with spherical-dendritic powders. Appl. Therm. Eng. 152, 825–834 (2019) 2. Buffone, C.: A novel approach for heat transfer enhancement in composite fins. Int. J. Heat Mass Transf. 130, 650–659 (2019) 3. Lei, F., Hu, P., Huang, X.P.: Hybrid analytical model for composite heat transfer in a spiral pile ground heat exchanger. Appl. Therm. Eng. 137, 555–566 (2018) 4. Masumi, A.A., Rahimi, G.H., Liaghat, G.H.: The use of the layerwise theory in heat transfer analysis of metal composite vessel by DQM. Int. J. Therm. Sci. 132, 14–25 (2018) 5. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., et al.: Topological optimization of thermoelastic composites with maximized stiffness and heat transfer. Compos. B Eng. 158, 319–327 (2019) 6. Wang, J., Yang, J., Cheng, Z., et al.: Experimental and numerical study on pressure drop and heat transfer performance of grille-sphere composite structured packed bed. Appl. Energy 227, 719–730 (2017). S0306261917310152 7. Aadmi, M., Karkri, M., El, H.M.: Heat transfer characteristics of thermal energy storage of a composite phase change materials: Numerical and experimental investigations. Energy 72, 381–392 (2014) 8. Tan, Y.W., Zhang, Y., Bolotin, K., et al.: Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 99, 246803 (2007) 9. Kim, H., Miura, Y., Macosko, C.W.: Graphene/polyurethane nanocomposites for improved gas barrier and electrical conductivity. Chem. Mater. 22(11), 3441–3450 (2010) 10. Esfahani, M.R., Languri, E.M.: Exergy analysis of a shell-and-tube heat exchanger using graphene oxide nanofluids. Exp. Therm. Fluid Sci. 83(Complete), 100–106 (2017)

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11. Tian, L., Wang, Y., Li, Z., et al.: The thermal conductivity-dependant drag reduction mechanism of water droplets controlled by graphene/silicone rubber composites. Exp. Therm. Fluid Sci. 85, 363–369 (2017) 12. Hussien, A.A., Yusop, N.M., Moh’d, A.A.N., et al.: Numerical study of heat transfer enhancement using Al2O3–graphene/water hybrid nanofluid flow in mini tubes. Iran. J. Sci. Technol. Trans. A: Sci. 1–12 (2019) 13. Liao, Y.F., Wang, G.Y.: Active control of near-field radiative heat transfer via multiple coupling of surface waves with graphene plasmon. Eur. Phys. J. B: Condens. Matter Complex Syst. 92, 65 (2019) 14. Anhua, B., Shuang, L.I., Qianhe, X., et al.: Thermoacoustic theory of graphene films considering heat transfer of substrate materials. Chin. J. Acoust. 42(2), 755–761 (2018) 15. Zhou, Y., Cui, X., Weng, J., et al.: Experimental investigation of the heat transfer performance of an oscillating heat pipe with graphene nanofluids. Powder Technol. 332, 371–380 (2018). S003259101830175X 16. Bharadwaj, B.R., Sanketh, M.K., Manjunath, D.M., et al.: CFD analysis of heat transfer performance of graphene based hybrid nanofluid in radiators. In: IOP Conference Series: Materials Science and Engineering, vol. 346, p. 012084 (2018) 17. Long, C., Yidu, Z., Qiong, W.: Heat transfer optimization and experimental validation of anti-icing component for helicopter rotor. Appl. Therm. Eng. 127, 662–670 (2017)

Numerical Analysis on Load Sharing Characteristics of Multistage Face Gears in Planetary Transmission Xingbin Chen1(&), Qingchun Hu1, and Chune Zhu2 1 School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China [email protected] 2 Institute for Biomedical and Pharmaceutical Sciences, Guangdong University of Technology, Guangzhou 510006, China

Abstract. Planetary transmission devices that use multistage face gears comprise structural components such as bevel gears, cylindrical gears, and face gears. Because of the novel structure and innovative operating principle of variable speed transmissions, inevitably, there are some problems such as manufacturing, installation errors and need for geometric parameter optimization. Therefore, it is necessary to study the static and dynamic load sharing characteristics of the planetary system to improve the transmission reliability under variable speed conditions. In this study, the calculating methods of the static and dynamic load sharing coefficients are studied by constructing the dynamic structure model and moment equilibrium equation. The influences of the manufacturing and installation errors on the load sharing coefficient among the various stages of the transmission system are analyzed. The influences of various component errors on the dynamic load sharing characteristics under the conditions of different stages with various speeds are studied by the dynamic response analysis. The influence of working condition, physical, and geometric parameters on the load sharing characteristics are analyzed. The results are beneficial in reducing the vibration and noise of the planetary transmission caused by uneven load distribution. They also provide a theoretical basis for improving the stability and loading capacity. Keywords: Multistage face gears  Load sharing Dynamic characteristics  Planetary gears

 Variable speed 

1 Introduction The load sharing characteristics of planetary gears reflect the uniformity of the transmission power of each branch, which is directly related to the design rationality of the system and the reliability of the transmission. In order to study the dynamic performance of planetary gears more deeply, many domestic and foreign scholars have This work was supported by the National Natural Science Foundation of China under Grant No. 51575191. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 63–83, 2020. https://doi.org/10.1007/978-981-32-9941-2_6

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analyzed the load sharing characteristics of planetary gears from the static and dynamic perspectives respectively. Shuai et al. studied the three split static load sharing characteristics of the two-stage external meshing planetary transmission system of an aeroengine, and obtained the load sharing coefficient under manufacturing and installation error conditions [1]. Kahraman et al. analyzed the load sharing performance of planetary gears, and proposed to characterize the load sharing effect with static load sharing coefficient, dynamic load sharing coefficient and dynamic load coefficient [2]. Hu et al. established a static load-sharing calculation model for the aeronautical twostage five-branch planetary gear train, and introduced loaded tooth contact analysis method. Combined with the coordination condition of torsion angle deformation, the torque of each gear pair is obtained. The load-sharing coefficient of the system is further calculated [3, 4]. Viadero et al., studied the quasi-static characteristics of threeplanet gear transmission system by numerical definition and finite element modeling, and analyzed the influence of planetary radial mounting errors on the load sharing characteristics under different pressure angles [5, 6]. Yi et al. analyzed the initial position’s influence on the load sharing of transmission system to provide a theoretical basis of load sharing control [7]. Zhu R.P. et al. established a coupled dynamic analysis model considering the time-varying meshing stiffness, mesh errors and mesh damping to obtain the distribution law of the sensitivities of load sharing coefficient for the split torque transmission system of the traditional epicyclic gear transmission of the helicopter [8–10]. Li et al. established a model to predict the reliability of helicopter planetary gear train under the condition of partial load. The bad influence of unequal load sharing on planetary gear train is shown by prediction result and the reliability model is verified through a statistical analysis method of random censored data [11]. Du et al. proposed a load sharing analysis methodology for a new type of power split spiral bevel gearing system based on the closed-loop characteristic of the power flow. A general formula for calculating the simplified engineering load distribution is derived. An experiment is designed to demonstrate the feasibility of this method [12]. In addition, Zhang [13], and Huang et al. established the equilibrium equations of the corresponding planetary gear system from factors such as the planetary gear eccentricity error, number of planets and gear clearance, and calculated the non-load-sharing coefficient of planetary transmission system [14]. Singh [15], Shu [16], Gu [17], Chaari et al. studied the load sharing characteristics of planetary gear systems from different aspects, such as positional deviation of the gear, tooth frequency error, tooth profile error, meshing stiffness of gear pair, support stiffness and floating quantity of each component [18, 19]. Presently available results pertain mainly to single-stage planetary gear systems, and there are significant differences among the various models, so it is difficult to use each other. The paper studies a planetary multistage face gears train, which has provision for multiple stages to allow for variable speeds. Static and dynamic load sharing models are established to analyze the influence of working conditions, geometry and corresponding physical parameters on the load sharing characteristics, which can provide a theoretical basis for improving the stability and load carrying capacity of the system. It also has considerable practical significance for the optimization of planetary multistage face gears devices.

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2 Model of the Multispeed Transmission Device In the previous research, a novel multistage transmission was proposed that with face gears introduced into the planetary multistage transmission for the first time and the novel multistage transmission was constructed by the structural advantages of the face gear transmission, as shown in Fig. 1A. Compared to an ordinary multistage system, the novel transmission mode can reduce the complexity and irregularity of the mechanism which has the features of stable transmission, high transmission efficiency, flexible space layout and simple structure, as shown in Fig. 1B. The motion is input from driving bevel gear (splined joint), and then split into four branches by driven bevel gears which are connected with the cylindrical gears by spline shafts, the cylindrical gear meshes with the multistage face gears at the same time. Among that, the number of the driving bevel gear is 36, the driven bevel gear is 19, the cylindrical gear is 17, the face gears are temporarily set to three stages, and the numbers of teeth are 56, 68 and 80 respectively. The teeth in the axial direction of the face gears are reserved for meshing with the shifting brake mechanism. If one stage of face gears is braked, the cylindrical gears revolve around the face gear corresponding to this stage, causing the driven bevel gears to rotate and revolve with the cylindrical gears through the spline shaft. If no brake is applied, face gears all freely idling, power transmission does not take place. Under the action of the spline shaft, the planets drive the output shaft to rotate. In summary, it is the revolution confluence of four planetary axes. The input stage of the system is the splitting transmission of face gear. Considering the meshing characteristics of the face gear transmission, the synchronous meshing request of the input gear can be satisfied as long as the teeth numbers of all stages face gears are the multiple of the number of meshing gears in the split-twist configuration of the face gear transmission system.

Fig. 1. A: Structure schematic diagram of multistage face gears planetary transmission B: Assembly diagram of key core structure of planetary multistage face gears (1. Input shaft; 2. Driving bevel gear; 3. Driven bevel gear; 4. Planetary gear; 5. Planetary shaft; 6-8. Face gears; 9. Output shaft)

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3 Analysis of the Load Sharing Mechanism According to the structural principle of the planetary multistage face gears transmission device (MFGTD), the swing arm is an output component, and it must be assumed that the driving bevel gear and face gear are combined as input component. The speed of the driving bevel gear is constant, while the speed of the face gear is adjustable (0  njmax ), the direction of the rotation speed is unchanged, and the distribution coefficient is 0  K  1. Then the speed of the face gear can be expressed as K  njmax at any time. P1 T1 n1 T1 n1 ¼ ¼ Pj Tj nj Tj  K  njmax n1 1 R ¼ ¼ ¼ i3j i27  K  njmax K  w K

ð1Þ

i i Kn

In this equation, w ¼  3j 27 n1 jmax is speed regulation magnitude and R ¼ w1 is the differential ratio. According to the power equilibrium equation: (

P1 ¼  R þR K PH Pj ¼ P3 ¼  R þK K PH

ð2Þ

The magnitude of the distribution coefficient varies with the speed of the face gear, and is an important factor affecting the power ratio. If the working speed is different, the power ratio of two input components is also different. But the truly decisive factors are the speed regulation magnitude w and the differential ratio R. w is larger, R is smaller, the power transmitted by the face gear consumes a greater proportion of the total input power, and vice versa. Similarly, if the face gear is assumed to have a constant speed and the driving bevel gear as shifting, the results so obtained are consistent. 3.1

Transmission Ratio Analysis

As the planetary gear is a moving shaft transmission, the transmission ratio cannot be calculated simply by the equation of fixed axis driving, but usually by the fixed planetary carrier method, graphic method, vector method and moment method, etc. For studying simplification, the planetary MFGTD can be considered as a differential planetary gear mechanism conforming to a 2 K-H (NW) type. Among that, face gears are composed of multiple circular rings, which can be unlimited in number theoretically, however, considering the loading capacity and general gear box dimension, this paper sets the face gears combination j to level 3 with a, b and c, as shown in Figs. 2 and 3.

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The transmission ratio of the transfer mechanism is obtained according to the general equation of a fixed planetary carrier: (

j ¼ 1  iH i1H 1j ZZ

j 7 iH 1j ¼ ðn1  nH Þ=ðnj  nH Þ ¼  Z3 Z2

Fig. 2. Kinematic relationship schematic about planetary transmission system

Fig. 3. Structure schematic of transmission ratio

ð3Þ

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j In this equation, i1H is the transmission ratio of the input shaft 1 and the tumbler H rotating relative to the face gears j. iH 1j is the transmission ratio of the input shaft 1 and the face gears j rotating relative to the tumbler H. n1 is the speed of the input shaft 1. nH is the speed of the tumbler H. nj is the speed of the face gears j. Zj represents the teeth number of the face gear. Z7 represents the teeth number of the driven bevel gear. Z3 represents the teeth number of the cylindrical gear. Z2 represents the teeth number of the driving bevel gear. So: j i1H ¼ 1þ

Zj Z7 Z3 Z2

ð4Þ

Defining the speed ratio relations of the gear pairs as i27 ¼ Z7 =Z2 , i3j ¼ Zj =Z3 , the corresponding kinematic relation of each component are: 8 ZZ ZZ > n1 ¼  Z3j Z72 nj þ ð1  Z3j Z72 ÞnH ¼ i3j i27 nj þ ð1  i3j i27 ÞnH > > < ZZ i i Z2 nH ¼ Z3 ZZ23Z n1 þ Z3 Z2jZ7 j Z7 nj ¼ 1i13j i27 n1 þ 1i3j 3j27i27 nj j Z7 > > > : n ¼ Z3 Z2 Zj Z7 n  Z3 Z2 n ¼ ði i  1Þn  1 n j H 3j 27 H i3j i27 1 Zj Z7 Zj Z7 1

ð5Þ

When selecting the relevant tooth numbers to determine the transmission ratio, the corresponding concentric condition, assembly condition, adjacency condition and other additional conditions should be considered. For example, the teeth number on every stage of the face gears should be an integral multiple of the number of planetary gears. uan qan ¼ 2p=Z ¼n 2

j i1H Z2 np

¼ Znj Z2 Z3 np Z2 Z7 ¼ N; ðN ¼ 1; 2;   Þ

ð6Þ

In this equation, qan is the ratio between the installation angle and the corresponding center angle a of two teeth with the adjacent center gear. uan ðn ¼ 1; 2;   Þ is the angle turned to match the installation angle of corresponding planetary gear. np is the number of planetary gears. n cannot be a multiple of np . N is an integral multiple of the number. If the numbers of driving and driven bevel gears are Z2 ¼ 36 and Z7 ¼ 19, based on the above conditions, the relationship between the teeth numbers of cylindrical gears and face gears and the planetary system transmission ratio is shown in Table 1. Table 1. Relationship about tooth numbers of cylindrical gears, face gears and transmission ratios of planetary system Z3 multipleofthenumberofplanetary 44 56 68 80 17 2.3660 2.7386 3.1111 3.4837 19 2.2222 2.5556 2.8889 3.2222 21 2.1058 2.4074 2.7090 3.0106

92 3.8562 3.5556 3.3122

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3.2

69

Force Analysis

In order to study the relationship between the distribution of power flow and the structural parameters in the system, it is necessary to analyze the forces in each component to determine the magnitude of the load torque. Dynamic meshing force equation: Fn ðtÞ ¼ km ðtÞfb ðxÞ þ cm ðtÞ_eðtÞ

ð7Þ

Normalize the meshing force of differential gears train and planetary gears train: (

Fbi ðtÞ ¼ kmb ðtÞDbR Fcfi ðtÞ ¼ kmcf ðtÞDcfR

ð8Þ

In this equation, kmb ðtÞ, kmcf ðtÞ are the time-varying mesh stiffness. DbR , DcfR are the relative displacements of ideal meshing line containing the integrated errors. Among that: 8 bi i cosðwb t þ ubi Þ k ðtÞ ¼ kbs þ kbs > > > m > > < kcfi ðtÞ ¼ kcfs þ ki cosðwc t þ ucfi Þ m cfs > Dbi > R ¼ f ðdb Þ þ Db > > > : cfi DR ¼ f ðdcf Þ þ Dcf

ð9Þ

In this equation, kbs , kcfs are the average meshing stiffness of the bevel gear pair and i i the cylinder-face gear pair respectively. kbs , kcfs are the transient meshing stiffness fluctuation amplitude of the bevel gear pair and the cylinder-face gear pair respectively. db , dcf are the clearance functions of the bevel gear pair and the cylinder-face gear pair respectively. f ðdb Þ, f ðdcf Þ are the integrated error displacement of the bevel gear pair and the cylinder-face gear pair respectively. Db , Dcf are the integrated error of the bevel gear pair and the cylinder-face gear pair respectively. xb ¼ 2pnb Zb =60, xc ¼ 2pnc Zc =60 are the meshing Angle frequency of the bevel gear pair and the cylinderface gear pair respectively. ubi ¼ ði  1Þ 2pi , ucfi ¼ ði  1Þ 2pi are the initial installation angles of each bevel gear in the bevel gear pair and each cylindrical gear in the cylinder-face gear pair respectively. 3.3

Torque and Power Analysis

Before analyzing the power flow of each component, it is necessary to clarify the rules for determining the input and output power: (1) When the torque direction is consistent with the motion direction, the power of the component can be defined as the input power. (2) When the torque direction is opposite to motion direction, the power of the component can be defined as the output power. (3) When the torque or speed is zero, the component does not transmit power.

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Based on the structural of the planetary MFGTD, it is assumed that the friction loss is neglected in the torque equilibrium equation: T 1 þ Tj þ T H ¼ 0

ð10Þ

In this equation, T1 is the torque of the driving bevel gear (sun gear). Tj is the torque of the face gear (gear ring). TH is the torque of the swing arm (planetary carrier). The power equilibrium equation is: T1 n1 þ Tj nj þ TH nH ¼ 0

ð11Þ

The torque relationships of the components obtained from the Eqs. 10 and 11 are: T1 ¼ ð1 þ i3j i27 ÞTH ¼ 

1 Tj i3j i27

ð12Þ

Then the corresponding power ratio relationship is given by: 8P i 1 ¼ TT1j nn1j ¼  i3j1ji27 > > < Pj P1 T1 n 1 PH ¼ TH nH ¼ ð1 þ i3j i27 Þi1H > > : Pj Tj n j PH ¼ TH nH ¼ ð1 þ i3j i27 Þi3j i27 ijH

ð13Þ

In this equation, P1 is the power delivered by the driving bevel gear. Pj is the power delivered by the face gear. PH is the power delivered by the swing arm. When the driving bevel gear 1 and the face gear j are all input components, the power transmitted by both can be categorized as input power, if P1 =Pj [ 0, then, i1j \0, indicating that the driving speed of the driving bevel gear is opposite to that of the face gear. Assuming that the face gear rotates in the positive direction, according to Eq. 5, both the swing arm and the driving bevel gear are in the negative direction. Therefore, it should be ensured that the motion direction of the driving bevel gear is opposite to that of the face gear, so as to ensure the output power converging of the planetary gear. When the driving bevel gear 1 and the swing arm H are all input components, the power transmitted by both are can be categorized as input power, if P1 =PH [ 0, then, i1H [ 0, indicating that the driving speed of the driving bevel gear is the same as that of the swing arm. Assuming that the driving bevel gear rotates in the positive direction, according to Eq. 3, the swing arm moves in the positive direction, but the motion of the face gear is in the negative direction. Therefore, it should be ensured that the motion direction of the driving bevel gear is the same as that of the swing arm, so as to ensure the output power converging of the planetary gear. When the face gear j and the swing arm H are all input components and the power transmitted by both can be categorized as input power, if Pj =PH [ 0, then, ijH \ 0, indicating that the driving speed of the face gear is opposite to that of the swing arm. Assuming that the swing arm moves in the positive direction, according to Eq. 3, the driving bevel gear rotates in the positive direction, but the face gear rotates in the

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negative direction. Therefore, it should be ensured that the motion direction of the face gear is opposite to that of the swing arm, so as to ensure the output power converging of the planetary gear. The relationship between the input powers of the system and each branch when ignoring the meshing power loss is given by: P1 ¼ P21 þ P22 þ P23 þ P24

ð14Þ

The relationship between the powers of the each branch and output power of system when ignoring the meshing power loss: P31 þ P32 þ P33 þ P34 ¼ PH

ð15Þ

On the planet carrier, the driven bevel gear and cylindrical gear are fixed by a spline shaft, which can be considered: P21 ¼ P31 ; P22 ¼ P32 ; P23 ¼ P33 ; P24 ¼ P34

ð16Þ

Define the meshing efficiencies of the four bevel gear pairs as a1 , a2 , a3 and a4 , the meshing efficiencies of four pairs with cylindrical gears and different stage face gears as b1j , b2j , b3j and b4j (j corresponds to the first, second, and third stage), when considering the meshing power loss, the relationship between the input power of the system and the power of each branch is given by: P1 ¼ a1 P21 þ a2 P22 þ a3 P23 þ a4 P24

ð17Þ

When considering the meshing power loss, the relationship between the power of each branch and the output power of the system is given by: b1j P31 þ b2j P32 þ b3j P33 þ b4j P34 ¼ PH

ð18Þ

4 Calculation of Static Load Sharing Characteristics Since there are inevitably different errors in design, manufacture and installation of each individual gear, the uniformity of load distribution among the planet gears directly affects the stability, reliability, load capacity and service life of the transmission system. Therefore, it is great significance to study on the load sharing characteristics of the planetary MFGTD. The load sharing characteristics of each train of the planetary system can be characterized by the corresponding load sharing coefficient. The socalled load sharing coefficient can be defined as the ratio between the maximum load experienced by a differential gear/planetary gear and the average load experienced by

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all the gears in each component when the load distribution of the differential gear/planetary gear component is not uniform. The load sharing coefficients can be obtained by solving the static equilibrium equation:   8 < Xbi ¼ Fbi ðNrbbi Þ  1 þ 1  T1  ð19Þ : Xcfi ¼ Fcfi ðNrbcfi Þ  1 þ 1 T3 In this equation, Xbi is the load sharing coefficient of the i driven bevel gear. Fbi is the meshing force of the i driven bevel gear. N is the number of planetary gears or differential gears. rbbi is the base radius of the i driven bevel gear. Xcfi is the load sharing coefficient of the i cylindrical gear. Fcfi is meshing force of the i cylindrical gear. rbcfi is the number of the i cylindrical gear. The static load sharing coefficient is the maximum value of the load sharing coefficient among all the tooth frequencies in each gear component, which is given by: 

Xb ¼ maxðXb1 ; Xb2 ;    ; XbN Þ Xcf ¼ maxðXcf 1 ; Xcf 2 ;    ; XcfN Þ

ð20Þ

According to the relevant dynamic model, several main structural parameters of the planetary system are extracted to study the influence on the static load characteristics, such as the number of differential gears, number of planetary gears, teeth number, interstage load sharing characteristics and input torque. 4.1

Influence of the Number of Differential/Planetary Gears on Static Load Sharing Characteristics

Based on the structural principle and design parameters of the optimized planetary system, it is assumed that the input torque of the driving bevel gear is 100 Nm, the modulus of the driving and driven bevel gears are 3, the teeth number of the driving bevel gear is 36, and the teeth number of the driven bevel gear is 19. The modulus of the cylindrical-face gears pairs are 2, the teeth number of the cylindrical gear is 17, the second stage of the face gear is selected for the study, and the teeth number is 68. The corresponding discrete value curves of the static load sharing characteristics are shown in Figs. 4 and 5. From Figs. 4 and 5, no matter in the differential gear train or the planetary gear train, as the numbers of related gears increase, the static load sharing characteristics are first decreased and then increased, when the number of bevel gears is selected as 3 or that of cylindrical gears as 2, the load sharing characteristics are the smallest. However, considering the loading capacity, transmission stability, and variable speed smoothness, the numbers of the bevel gears and cylindrical gears are still arranged in four.

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Fig. 4. Influence of static load sharing characteristics about the driven bevel gears numbers

Fig. 5. Influence of static load sharing characteristics about the cylindrical gears numbers

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Influence of the Teeth Numbers on the Static Load Characteristics

It is assumed that the input torque of the driving bevel gear is still 100 Nm, the modulus of bevel gears pair are 3, the teeth numbers of the driving bevel gears are all 36, the teeth numbers of driven bevel gears are 17–25. The modulus of the cylindricalface gears pairs are 2, the teeth numbers of the cylindrical gears are 17–25, the face gears would be selected 3 stages for study and the teeth numbers are 56, 68, and 80 respectively. The corresponding discrete values curves of the static load sharing characteristics are shown in Figs. 6 and 7. From Figs. 6 and 7, in the differential gear train, as the teeth numbers of the bevel gears increase, the load sharing characteristic also increases. As the teeth numbers of cylindrical gears increase, the load sharing characteristic decreases. When switching through stages, the larger the teeth number of the face gear, the larger the load sharing characteristic.

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Fig. 6. Influence of static load sharing characteristics about the driven gears tooth numbers

Fig. 7. Influence of static load sharing characteristics about the cylindrical gears tooth numbers

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Influence of Input Torque on Static Load Sharing Characteristics

The other parameters remain unchanged, and the input torque is varied in the range 100 Nm–3000 Nm. The corresponding discrete values curves of the static load sharing characteristics are shown in Figs. 8 and 9. From Figs. 8 and 9, regardless of the differential or planetary gear train, the load sharing coefficient does not change as the input torque changes. Otherwise, since static analysis does not consider the influence of acceleration or damping, the main static load excitation parameters of support stiffness and friction damping have only insignificant influence on the static load sharing characteristics, therefore, this study does not make further analysis.

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Fig. 8. Static load sharing characteristics of driven bevel gears with different input torque

Fig. 9. Static load sharing characteristics of cylindrical gears with different input torque

5 Analysis of Dynamic Load Sharing Characteristics In the process of dynamic meshing transmission, the planetary system is affected not only by design, manufacturing, and installation errors, but also by contact deformation, meshing abrasion, and inter-stage coupling. In the analysis of static load sharing characteristics, the influence of acceleration and deceleration, friction damping and time-varying meshing stiffness in transient meshing that arise from these errors are not considered, which cannot completely reflect the actual load sharing state of the transmission system. Consequently, this section tries to solve the dynamic meshing force linearly, and establish the corresponding dynamic load sharing coefficient equation in order to analysis the influences of system parameters or excitation factors such as the error, stiffness, friction, and working conditions on the dynamic load sharing characteristics.

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Calculation of Dynamic Load Coefficient Analysis of Transmission System

The load sharing coefficient of the single tooth frequency of each gear can be defined as the ratio between the maximum load of this gear and the mean load of all the planet gears in the planetary component: 8 N P > D > < Xbi ¼ N  ðFbi ðtÞÞmax = ðFbi ðtÞÞmax i¼1

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Influence of Arrangement Number or Installation Angle of Differential Gears/Planetary Gears

According to the structural device scheme of the universal planetary gear, in order to guarantee transmission stability, high load capacity and variable speed smooth, when the structure is arranged with three or four differential/planetary gears respectively, it is necessary to arrange them symmetrically around the periphery at intervals of 90° or 120°, the corresponding dynamic load sharing characteristics are shown in Figs. 10, 11, 12 and 13.

Fig. 10. Dynamics load sharing characteristics of three driven bevel gears with different layout angles

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Fig. 11. Dynamics load sharing characteristics of three cylindrical gears with different layout angles

Fig. 12. Dynamics load sharing characteristics of four driven bevel gears with different layout angles

Fig. 13. Dynamics load sharing characteristics of four cylindrical gears with different layout angles

By comparing Figs. 10, 11, 12 and 13, it can be seen that in the differential gear train or the planetary gear train, as the number of gears increase and the arrangement angle decreases, the load sharing coefficient increases, but the fluctuation periods remain unchanged. Similarly, the behavior of the gear train corresponding to different arranged numbers of the cylindrical gears also has a similar trend. In addition, comparing the fluctuation characteristics of the dynamic load sharing coefficient of each bevel gear in the differential gear train, the load sharing coefficient of each cylindrical gear in the planetary gear train is more even and stable as the face gears meshing with the cylindrical gears are used for braking and have static motion characteristics.

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Influence of Integrated Error

The design error present in the system mainly arises from the difference between the meshing curve of the double crown face gear and the ideal conjugate curve. The bevel gear is a standard gear with straight tooth structure, the design error is assumed in the ideal state without deviation. Manufacturing errors include crown machining deviation, radix-node error, tooth pitch error, radial run-out error of gear ring, and tooth flank spacing. Installation errors mainly include offset error, and shaft angle error, etc. In order to simplify the analysis, three kinds of errors can be combined to introduce a comprehensive error sensitivity function represented by: 

Db ¼ db ð1 þ 2 sin ab Þ=mb Dcf ¼ dcf ð1 þ 2 sin acf Þ=m

ð23Þ

In this equation, db and dcf are the linear distance between the theoretical contact point and the actual contact point of the bevel gear pair or the cylindrical-face gear pair (which also can be further simplified to the maximum deformation) respectively. ab and acf are the angles between the axis and the dedendum line of the bevel gear pair or the cylindrical-face gear pair respectively. mb and m are the modulus at the midpoints of tooth width of the bevel gear pair and the cylindrical-face gear pair respectively. Assuming that the input torque is 300 Nm and rotational speed is 300 r/min, based on the simulation results of the dynamic model by the finite element method, which are computed that the average meshing stiffness of the bevel gear pair is 2.7747e+8 N/m, the fluctuation amplitude of the meshing stiffness is 1.414e+9 N/m; and the average meshing stiffness of the cylindrical-face gear pair is 5.3825e+8 N/m, the fluctuation amplitude of the meshing stiffness is 0.6145e+9 N/m. Considering a bevel gear and a cylindrical gear connected by a planetary spline shaft, it is assumed that the meshing deviation values in the integrated error are 0.01 mm, 0.06 mm and 0.11 mm respectively, and the offset angles are respectively 1°, 6° and 11°, so the dynamic load sharing characteristics are shown in Figs. 14 and 15.

Fig. 14. Dynamics load sharing characteristics of driven bevel gears with different integrated errors

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Fig. 15. Dynamics load sharing characteristics of cylindrical gears with different integrated errors

The integrated error fluctuates with the rotation of the gear shaft, which has significant periodic characteristics. For the same differential or planetary gear, when considering different errors values, the difference in dynamic load characteristics are not obvious, but as the integrated error values increase, the load sharing characteristics also increase. 5.4

Influence of Meshing Stiffness

Considering a bevel gear and a cylindrical gear connected by a planetary spline shaft, it is computed that the average meshing stiffness of the driven bevel gears are 0.9497e+8, 2.7747e+8, 4.1471e+8 and 5.9883e+8 N/m respectively, the fluctuation amplitudes of transient stiffness are 0.4223e+9, 1.4140e+9, 2.4803e+9 and 5.3165e+9 N/m respectively. Besides, it is also computed that the average meshing stiffness of the cylindrical gears are 3.1887e+8, 5.3825e+8, 5.6359e+8 and 5.2064e+8 N/m respectively, the fluctuation amplitudes of transient stiffness are 0.1835e+9, 0.6145e+9, 1.0778e+9 and 2.3104e+9 N/m respectively, so the dynamic load sharing characteristics are shown in Figs. 16 and 17.

Fig. 16. Dynamics load sharing characteristics of driven bevel gears with different meshing stiffness

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Fig. 17. Dynamics load sharing characteristics of cylindrical gears with different meshing stiffness

For the same stage of a differential gear and planetary gear, the dynamic load sharing coefficient increases with the increase in meshing stiffness, which indicates that the load sharing capacity optimizing the system load transmission through the meshing axis of the differential gear/planetary gear is reduced. Since there is effect of decelerating and torque increasing on the system, the loading capacity of driven gear in the differential gear train is smaller than that of cylindrical gear in the planetary gear train. Therefore, in comparison with the differential gear train, the load distribution in the planetary gear train is smoother and the dynamic load sharing coefficient is much smaller. 5.5

Influence of Input Speed

Other parameters remaining the same, it is assumed that the input speeds are 100, 300, 500 and 1000 r/min respectively. Considering a bevel gear and cylindrical gear connected by a planetary spline shaft, the dynamic load sharing characteristics are shown in Figs. 18 and 19.

Fig. 18. Dynamics load sharing characteristics of driven bevel gears with different input speed

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Fig. 19. Dynamics load sharing characteristics of cylindrical gears with different input speed

For the same stage of a differential and planetary gear, the dynamic load sharing coefficient increases with the increase in the input speed, and there is a notable periodicity to the characteristic plots. When the rotation speed is low, the variation amplitude of the load sharing coefficient is gentler and less affected by the errors. For the load sharing characteristics of the cylindrical gear, when the speed is 300 r/min, the change trend of the load sharing coefficient is close to the standard fluctuation curve, which indicates that the transmission stability is better at this speed.

6 Conclusion This study has examined the calculation methods of static load sharing coefficient and dynamic load sharing coefficient of the system, analyzing the influence of key structural parameters on the load sharing coefficient between stages of the transmission system, in order to quantify the influence of the key system parameters on the load sharing characteristic, which provides a theoretical basis for improving the stability and loading capacity of the transmission. (1) In order to maximize the transmission efficiency and optimize the transmission performance of the planetary transmission system under different loads or working conditions, the transmission mechanism and transmission characteristics of a planetary MFGTD are studied from the aspects of speed ratio selection and load sharing or splitting. (2) The mechanism, size and property of the dynamic excitation of the transmission system are studied through the dynamic meshing force of the gear teeth, to determine the dynamic load and dynamic load coefficients of the gear teeth and thereby improve the loading capacity of the transmission system. (3) The effects of working condition parameters (input speed, input torque), as well as physical and geometric parameters (central components support stiffness, numbers of planet gears, tooth surface friction) on the load sharing characteristics of the system stages are studied. The vibration and noise caused by the uneven load distribution in planetary gear transmission are reduced to improve the stability and reliability of the device. This work analyzes the feasibility of a planetary MFGTD. The results are beneficial to mitigate unfavorable phenomenon, such as gear wear and damage, transmission

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discontinuity and jerky motion caused by the uneven load distribution. It is also helpful to understand the influence of the dynamic excitation mechanism, size, and properties on transmission efficiency to provide a reference for the dynamic design and structural optimization of the transmission system. Acknowledgements. The authors would like to thank Miss Tiancui Xu and Dr. Ding Yao for free help in professional writing. The authors would also like to thank editor and reviewers for their helpful comments and suggestions to improve the manuscript. Conflicts of Interest. The authors declare that there are no conflicts of interest regarding the publication of this paper.

References 1. Shuai, M., Yidu, Z., Qiong, W.: Research on multiple-split load sharing of two-stage star gearing system in consideration of displacement compatibility. Mech. Mach. Theory 88, 1– 15 (2015) 2. Hong, J., Talbot, D., Kahraman, A.: A generalized semi-analytical load distribution model for clearance-fit, major-fit, minor-fit, and mismatched splines. Proc. Inst. Mech. Eng. C-J. Mech. 230(7–8), 1126–1138 (2016) 3. Dong, H., Liu, Z.Y., Duan, L.L., Hu, Y.H.: Research on the sliding friction associated spurface gear meshing efficiency based on the loaded tooth contact analysis. PloS ONE 13(6), e0198677 (2018) 4. Hao, D., Fang, Z.D., Hu, Y.H.: Study on the load-sharing characteristics of an aeronautical II-stage five-branching planets gear train based on the loaded tooth contact analysis. Math. Probl. Eng., 1–18 (2018). https://doi.org/10.1155/2018/5368294 5. Iglesias, M., del Rincon, A.F., de-Juan, A., Garcia, P., Diez-Ibarbia, A., Viadero, F.: Planetary transmission load sharing: manufacturing errors and system configuration study. Mech. Mach. Theory 111, 21–38 (2017) 6. Iglesias, M., Del Rincon, A.F., De-Juan, A.M., Garcia, P., Diez, A., Viadero, F.: Planetary gear profile modification design based on load sharing modelling. Chin. J. Mech. Eng. 28(4), 810–820 (2015) 7. Yi, P.X., Zhang, C., Guo, L.J., et al.: Dynamic modeling and analysis of load sharing characteristics of wind turbine gearbox. Adv. Mech. Eng. 7(3), 1–16 (2015). https://doi.org/ 10.1177/1687814015575960 8. Jin, G.H., Xiong, Y.P., Gui, Y.F., Zhu, R.P.: Sensitive parameter and its influence law on load sharing performance of double input split torque transmission system. J. Vibr. Eng. Technol. 5(6), 583–595 (2017) 9. Sheng, D.P., Zhu, R.P., Jin, G.H., Lu, F.X., Bao, H.Y.: Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances. J. Cent. South Univ. 22(7), 2521–2532 (2015) 10. Sheng, D.P., Zhu, R.P., Jin, G.H., Lu, F.X., Bao, H.Y.: Dynamic load sharing characteristics and sun gear radial orbits of double-row planetary gear train. J. Cent. South Univ. 22(10), 3806–3816 (2015) 11. Li, M., Xie, L.Y., Ding, L.J.: Load sharing analysis and reliability prediction for planetary gear train of helicopter. Mech. Mach. Theory 115, 97–113 (2017) 12. Du, J.F., Mao, J., Cui, Y.H., Liu, K., Zhao, G.R.: Theoretical and experimental study on load sharing of a novel power split spiral bevel gear transmission. Adv. Mech. Eng. 10(6) (2018)

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13. Jing, L.B., Zhang, T., Lin, Y., Cheng, J.: Design, analysis, and realization of a magnetic force transmission PM brushless motor. IEEJ Trans. Electr. Electron. Eng. 13(5), 791–798 (2018) 14. Huang, C.H., Tsai, S.J.: A study on loaded tooth contact analysis of a cycloid planetary gear reducer considering friction and bearing roller stiffness. J. Adv. Mech. Des. Syst. 11(6) (2017) 15. Singh, A.: Epicyclic load sharing map - development and validation. Mech. Mach. Theory 46(5), 632–646 (2011) 16. Shu, R.Z., Liu, Z.J., Liu, C.Z., Lin, X.Y., Qin, D.T.: Load sharing characteristic analysis of short driving system in the long-wall shearer. J. Vibroeng. 17(7), 3572–3585 (2015) 17. Gu, X., Velex, P.: A dynamic model to study the influence of planet position errors in planetary gears. J. Sound Vibr. 331(20), 4554–4574 (2012) 18. Hammami, A., Del Rincon, A.F., Chaari, F., Santamaria, M.I., Rueda, F.V., Haddar, M.: Effects of variable loading conditions on the dynamic behaviour of planetary gear with power recirculation. Measurement 94, 306–315 (2016) 19. Hammami, A., Del Rincon, A.F., Chaari, F., Rueda, F.V., Haddar, M.: Dynamic behaviour of back to back planetary gear in run up and run down transient regimes. J. Mech. 31(4), 481–491 (2015)

Reachable Matrix and Directed Graph – Based Identification Algorithm of Module Change Propagation Path for Product Family Xianfu Cheng(&), Liyun Wan, and Jian Zhou School of Mechatronics and Vehicle Engineering, East China Jiaotong University, Nanchang 33001, China [email protected]

Abstract. Product family design is the core of mass customization and has been identified as an effective tool to quickly respond to the customers’ demands, and achieve the proliferation of product variants by diverse market niches. There are often coupling dependence relationships between modules, which will increase the difficulty of product design. For this reason, an identification algorithm of change propagation path for modular product family. Instigating component and affected component between association modules are determined, and the latter is regarded as feeding component inside the module. Applying reachable matrix, the target components influenced by affected component can be confirmed. Then the directed graph combined, the search process of change propagation path is presented. Keywords: Product family Identification algorithm

 Module change  Change propagation path 

1 Introduction Product family design is a complex task. There is not only a contradiction between commonality and diversity, but also often exist association relationship between modules, which bring about the coupling of product family design and increases the difficulty of product design. In view of engineering change, design change in modular product considers mainly the increase, deletion or replacement of module, as well as the change of characteristic parameter or assembly constraints of the component in modules, which is called module change. The increase, deletion or replacement of module belong to module overall change, which causes the change of components in other modules through the change module level parameters, thus a new modular product is acquired. Therefore, the problem on module change can be transformed into that of change propagation between components. Change propagation paths are analyzed and change influence degree is measured, which can provide methodological guidance for reducing iteration of modular product family design. Clarkson et al. [1] used likelihood and impact of change to predict the risk of change propagation, traced potential propagation paths among components base on DSM, and outlined the methods to compute the risk of direct and indirect change © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 84–92, 2020. https://doi.org/10.1007/978-981-32-9941-2_7

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propagation. Tang et al. [2] proposed the concrete method for analyzing direct and indirect engineering change impacts based on design structure matrix, and presented mathematical model to predict the comprehensive impact of engineering change. Yang and Tang [3] analyzed the propagation of change from characteristic linkage perspective and categorized the characteristic relations were into two types. They discussed propagation features and proposed the process model of change propagation. Qiao et al. [4] applied graph theory to develop an adjacency matrix to describe the relevance between different parameters, organized changing paths and related information into structured storage files to improve the extendibility of the changing paths and their related information, and then integrated the structured information and fully constrained module to develop the self-adaption module. Koh et al. [5] presented a method matrix-based to assess the effects of engineering change propagation, which set up the HoQ and the CPM to model the effects of potential change propagation caused by different change options. Yang and Duan [6] constructed a product model from the parameter linkage perspective, and discussed propagation mechanism of change prediction. Then they proposed a searching method of change propagation paths. Ullah et al. [7] proposed a change propagation mathematical model in a product family design, and progressive change propagation algorithm, which was viewed as a modified breadth first search method, to find the shortest possible route between the reachable nodes. Cheng et al. [8] discussed the coupling in product family design, identified coupling incidence path between modules, and calculated correlation impact degree. For simple modular product, if the size of modular product is small, change propagation path between modules can be intuitively analyzed. However, with the increase of the size of module and the coupling between modules, identifying the indirectly related information will become more and more difficult. For this reason, it is necessary to develop an identification algorithm of change propagation path, in order to compute effectively the change influence degree between modules.

2 Determining Target Components of Change Propagation Before analyzing the change propagation path, firstly, the instigating component and affected component of the two interaction modules should be determined. Assume there exists an interaction between module Mp and Mq, and Ci in Mp has impact on Cj in Mq, then Ci is called instigating component of Mp affecting Mq (denoted as Mp! Mq), and Cj is called affected component. For the module in which affected component is located, if there is a relationship between other components and affected component, then the affected component will have a change propagation effect on other components. In order to search for all coupling correlation paths within the module, the affected component should be used as the starting point, and identify all components affected by change propagation. According to the characteristics of this task, searching can be done by means of reachable matrix, because the reachable matrix is a matrix to describe the reachability between nodes in a directed graph, and other components within module are determined that are reachable by above-mentioned affected component through calculating reachable matrix corresponding to a module of the product

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family, which are the target components affected by change propagation. Since this method is universal, therefore, a module with less design components and simpler coupling correlation is illustrated as an example, and its form is shown in Fig. 1. C

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In order to calculate the reachable matrix corresponding to the module, the corresponding adjacency matrix should be derived according to its change propagation directed graph. Suppose C4 is the affected component of the module for other modules, when analyzing the impact of other modules on the propagation of changes to this module, C4 can be regarded as feeding component inside the module. As can be seen intuitively from Fig. 1, change in C4 can directly affect C1, C2 and C3, and does not directly affect C5, C6 and C7. Whereas change of C3 can directly affect C7, therefore, the change of C4 can affect C7 indirectly. According to this method, the directed graph of change propagation path between components can be drawn, as shown in Fig. 2.

Fig. 2. The directed graph of change propagation path

From the knowledge of graph theory, directed graph D can be represented by a binary array , i.e., D = . In this formula, V = {v1, v2, ……, vn}, it is a set of non-empty numbers, called the vertex set of directed graph D, the elements in V are all vertices of directed graph D (or known as node), and n is the number of vertices.

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E = {}, it is a multiple subset of Cartesian product, the elements in E are called directed edges of directed graph D (can be abbreviated as edge). denotes directed edges with vertex vi and vertex vj as starting and ending points respectively. The adjacency matrix A corresponding to directed graph D can be expressed as A = {aij}. It is an n-order Boolean matrix. When there is a directed edge between vertex vi and vertex vj, then aij = 1; When there is no directed edge between vertex vi and vertex vj or i = j, then aij = 0. Therefore, the adjacency matrix A corresponding to the directed graph of the change propagation path shown in Fig. 2 can be obtained, and its form is shown in Fig. 3. No.

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Comparing the form of Figs. 1 and 3, it can be seen that the adjacency matrix is actually derived from the variant of the original design incidence matrix, that is, the diagonal values in original matrix are all changed to 0, the non-zero values in the nondiagonal elements are all changed to 1, and the zero values in the non-diagonal element remains unchanged. Therefore, when there are many components in the module and the coupling relationship between components is complex, the adjacency matrix can be obtained without drawing the directed graph of the change propagation path. The reachable matrix P corresponding to the module shown in Fig. 1 can be represented as P = {pij}. It is also an n-order Boolean matrix. When vertex vi is reachable to vertex vj, pij = 1. When vertex vi is not reachable to vertex vj, pij = 0. Because the reachable matrix P is a Boolean matrix, it can not be obtained directly by calculation. The precursor matrix M of adjacent matrix A should be calculated firstly, and then the reachable matrix P is obtained by the variant of the precursor matrix M. The precursor matrix M can be expressed by the following formula: M ¼ I þ A þ A2 þ . . .. . . þ An ¼ ðI þ AÞn

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The elements in the precursor matrix M represent the degree of accessibility between components in the module. Non-zero elements represent reachability, while 0 elements represent inaccessibility. According to the value rule of the row and column elements pij in the reachable matrix, all non-zero elements in M are modified to 1, while 0 elements remain unchanged. Thus the obtained matrix is the reachable matrix P, and its form is shown in Fig. 4.

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As can be seen from the reachable matrix shown in Fig. 4, changes in C4 propagated to C1, C2, C3 and C7, so these components are the target components affected by change propagation. However, the reachable matrix can only represent the reachability between components, and can not be used to judge the nodes and the length of the corresponding change propagation path. That is to say, it is impossible to identify the direct or indirect coupling relationship between components.

3 Identification Algorithm of Change Propagation Path In the reachable matrix, if there is a zero element in the column in which the affected component is located, it means that the component corresponding to the row with 0 element will not appear in the change propagation path. These components can be removed from the single module to which they belong, that is to say, it is not considered when searching for changing propagation path, so as to simplify the reachable

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matrix. Here, the matrix obtained by this way is called reduced dimension reachable matrix. For instance, in the reachable matrix shown in Fig. 4, there are two zero elements in the column where C4 is located, their rows correspond to C5 and C6 respectively, that is to say, the change of C4 will not affect C5 and C6, at this time, the reachable matrix can be reduced in dimension. When analyzing all possible paths of change propagation in C4, C5 and C6 can be ignored. The corresponding form of reduced dimension reachable matrix is shown in Fig. 5. The larger the size of the module and the higher the position of the components in the module, the wider the scope of the impact of change propagation and the more complex the propagation path. There are two ways of change propagation for components, one is that one component propagates directly to another component, the other is that one component propagates to another component through at least one intermediate component, that is, indirect change propagation. Different correlations among components will make change propagation diffuse in different directions and form multiple change propagation routes. Different propagation routes are connected according to the relationship between components in the module and the propagation behavior characteristics, which will form a change propagation tree, as shown in Fig. 6.

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Assume a module is composed of m components, and has n components through dimension reduction, where Cj is a feeding component. The DSM of change impact is denoted with B. How to determine change propagation paths of Cj? This section addresses a search algorithm of change propagation path based on design incidence matrix and directed graph. In the presented algorithm, a vertex denotes a product component. The feeding component is deemed as start vertex V0 of directed graph, the adjacent vertex directly related to V0 are visited. They will be taken as new vertices, and the vertices directly related to them are continuously visited. Repeat the procedure until access traverses all vertices. Suppose the feeding component Cj is regarded as start vertex V0 of directed graph, the target component of change propagation Ck is regarded as target vertex Vtarget, the number of the level of change propagation tree is n-1, initial propagation level t = 0, initial number of propagation paths S = 0, change impact degree of each propagation path P = 0, as well as change impact degree of each level of change propagation tree L = 0. The procedure of searching algorithm is as follows: Step 1: input matrix B, set queue Q = 0. Step 2: search adjacent vertex directly related to V0, record its direct change impact degree ri;j ; L ri;j ; If there exists Vtarget (i.e. i = k) in all adjacent vertices, S S þ 1, PðSÞ rk;j , t t þ 1, then these adjacent vertices will be placed in the queue Q(t). Step 3: Take out a vertex that is not Vtarget from queue Q(t) as the current vertex in turn, search its adjacent vertex that is not visited in propagation path, and record its direct change impact degree rp;I , L L  rp;I ; If adjacent vertex is Vtarget, S S þ 1, PðSÞ L Step 4: t t þ 1, above adjacent vertices will be continuously placed in the queue Q(t). If Q(t) is empty, the search ends. Step 5: If t  n  1, the algorithm terminates. Otherwise, go to step 3. The search process of change propagation path from one feeding component to one target component is shown as Fig. 7 and the procedure of the searching method is illustrated in Fig. 8. rk,i ri,j Cj

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4 Conclusion Product family design is a complex task. There is not only a contradiction between commonality and diversity, but also often exist association relationship between modules, which bring about the coupling of product family design and increases the

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difficulty of product design. For simple modular product, if the size of modular product is small, change propagation path between modules can be analyzed intuitively. However, with the increase of the size of module and the coupling between modules, identifying the indirectly related information will become more and more difficult. This paper proposed reachable matrix and directed graph – based identification algorithm of module change propagation path for product family. We utilized dimension reduction reachable matrix to determine the target components of change propagation. The search process of change propagation path was built on change propagation tree. It can provide methodological guidance for reducing iteration of modular product family design. Acknowledgements. This project was supported by the National Natural Science Foundation of China (Grant No. 51765019 and No. 71462007).

References 1. Clarkson, P.J., Simons, C., Eckert, C.: Predicting change propagation in complex design. J. Mech. Des. 126(5), 788–797 (2004) 2. Tang, D.B., Xu, R.H., Tang, J.C., et al.: Analysis of engineering change impacts based on design structure matrix. J. Mech. Eng. 46(1), 154–161 (2010). (in Chinese) 3. Yang, F., Tang, X.Q.: Propagation of engineering change based on characteristic linkage perspective. J. Beijing Univ. Aeronaut. Astronaut. 38(8), 1032–1039 (2012). (in Chinese) 4. Qiao, H., Mo, R., Xiang, Y.: Adaptive module modeling by predicting change path. J. Comput.-Aided Des. Comput. Graph. 12, 2358–2366 (2015). (in Chinese) 5. Koh, E.C.Y., Caldwell, N.H.M., Clarkson, P.J.: A method to assess the effects of engineering change propagation. Res. Eng. Des. 23(4), 329–351 (2012) 6. Yang, F., Duan, G.J.: Developing a parameter linkage-based method for searching change propagation paths. Res. Eng. Des. 23(4), 353–372 (2012) 7. Ullah, I., Tang, D., Wang, Q., et al.: Exploring effective change propagation in a product family design. J. Mech. Des. 139(12), 1–13 (2017) 8. Cheng, X., Xiao, R., Wang, H.: A method for coupling analysis of association modules in product family design. J. Eng. Des. 29(6), 327–352 (2018)

6-DOF Industrial Manipulator Motion Planning Based on RRT-Connect Algorithm Chengren Yuan1, Guifeng Liu2, and Wenqun Zhang1(&) 1

Power Engineering Department, Naval University of Engineering, Wuhan 430033, China [email protected], [email protected] 2 Office of Educational Administration, Naval University of Engineering, Wuhan 430033, China [email protected]

Abstract. The motion planning and obstacle avoidance of industrial manipulator are researched in the V-REP platform. Virtual motion control and motion simulation of PUMA-560 manipulator are realized in the simulation environment. The manipulator STL file drawn by Solidworks is imported into the VREP platform. The embedded thread script of the LUA language uses OMPL as a plug-in to provide motion planning functions, enabling more flexible implementation of robot motion planning. The RRT-Connect algorithm called by the motion planning library in the embedded script form API is implemented in the simulation environment. The algorithm gets fast convergence in motion planning and maintains good accuracy and rapid response. But the simulation trajectory is random and blind. For the defects of simulation, this paper gives the direction of future work to realize trajectory optimization. Keywords: Industrial manipulators  RRT-Connect algorithm Fast convergence  Motion planning



1 Introduction Motion planning is an important topic in robotics, especially in the study of the manipulator. The purpose in motion planning is that the manipulator can search a collision-free path to operate in a three-dimensional space under certain constraints [1] from the start-state to goal-state. For the manipulator motion planning problem, it can be divided into the method of graph search, the method of artificial potential field, the method of random sampling and the method of intelligent optimization. The motion planning of the random sampling method has obvious advantages over other methods. In Cartesian space where the manipulator is located, the collision-free path is obtained by randomly sampling the unknown space and then forming the connection graph from the sampling points. However, Probabilistic Roadmap Methods (PRM) and Rapidly-exploring Random Tree (RRT), which first proposed by LaValle [2], are two most successful planning methods based on random sampling method.

© Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 93–101, 2020. https://doi.org/10.1007/978-981-32-9941-2_8

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In order to improve the search speed, many improved RRT algorithms have proposed. The RRT algorithm was improved the adaptiveness of random tree expansion by Melchior et al. introduced Particle Filter [3]. AlDahak et al. proposed the KD tree concept and improved the search efficiency [4]. Yershova et al. added extended feedback information to suppress extended point range [5]. Burns et al. proposed a dynamic RRT algorithm based on predictive models, which reduced planning time [6]. Kuffner et al. improve search efficiency and response speed by increase the connection tree [7]. The performance of the improved algorithm in path planning has been significantly improved. Especially, the performance of the RRT-Connect algorithm is outstanding. The RRT-Connect algorithm can effectively avoid falling into local optimum. It can also improve the efficiency of trajectory planning. In this paper, the PUMA-560 robot arm is selected as the simulation object. The simulation environment is built in V-REP, and the RRT-Connect algorithm is used to realize motion planning. In particular, V-REP is a flexible robot simulator. And not widely use in domestic, only the official manual can be referred. At the same time, the reliability of the simulation process was verified.

2 Manipulator and Simulation Platform 2.1

PUMA-560 Manipulator

PUMA-560 industrial manipulator is used as a case, which structures is shown in the Fig. 1. PUMA-560 is an articulated manipulator that has 6 rotating joints. The first three joints determine the position of the wrist reference point, and the last three joints determine the orientation of the wrist. The axis of the joint 1 is in the vertical direction, and the axes of the joint 2 and the joint 3 are horizontal and parallel by a2 . The axes of joint 1 and joint 2 intersect perpendicularly, and the axes of joint 3 and joint 4 are vertically staggered with a distance of a3 . The distance between the joints 1 and 2 in the x-axis direction is d2 , and the distance between the joints 3 and 4 in the x-axis direction is d4 [8].

Fig. 1. Schematic diagram of the PUMA-560 industrial manipulator.

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Virtual Robot Experiment Platform (V-REP) is an experimental platform for robot motion simulation. It supports six programming methods such as embedded scripts, and six programming languages such as C/C++, Python and Lua. In addition, simulations support path planning, shortest distance calculation, and collision detection etc. V-REP uses the Open Motion Planning Library (OMPL) as a plug-in to replace the previous method for motion planning by calling the API. This approach can solve motion planning problems more flexibly and conveniently. When developed offline programming software that integrates programming and simulation, V-REP can be selected to embed into as a separate simulation environment [9]. To realize the simulation of the motion planning, setting up the simulation environment in V-REP requires the following steps: (1) Set up the simulation environment; (2) Import the standard CAD format of the manipulator into the simulation environment; (3) Add kinematic and dynamic properties to the manipulator; (4) Add dummy, including the start and goal position of the motion planning point (dummy_start and dummy_goal) and the handle position of the end of manipulator (dummy_handel); (5) Write control script code and communication interface to model. There are usually some constraints (obstacles) in the motion planning process of the manipulator. After setting up the simulation environment, the STL format of the manipulator is imported into the created environment, as shown in Fig. 2. It should be noted that the introduced manipulator has no kinematics and dynamics. So, in the next process, the properties of kinematics and dynamics need to be set. Finally, determine the starting point and end point of the motion planning, and add dummy to the end of the arm, as shown in Fig. 3. In this way, the manipulator can achieve the accuracy position of motion planning.

Fig. 2. V-REP simulation environment layout.

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Lua and Simulation Experiment

V-REP supports 6 programming languages. This article uses embedded thread scripts in Lua. The advantage is that it can be executed cyclically and can continue to accept external commands during the run. V-REP uses OMPL as a plug-in to provide motion planning functions, enabling more flexible implementation of robot motion planning. In this paper, the RRT-Connect algorithm is called by the motion planning library in the embedded script form API, which is implemented in the simulation environment. Writing programs mainly includes: create tasks, select appropriate algorithms, create state space and create a state space for each joint, set state space, set collision pairs, set start and target states, calculate appropriate paths, and so on. In the programming process, the official manual can be referred [10]. In addition, this paper involves seven rotating joints, six of which are used to drive the simulated motion of the manipulator. The last one is set at the end of the manipulator. The end handle is used to accurate the position between the start-point and the goal-point, as shown in Fig. 3.

Fig. 3. Simulation result.

3 RRT-Connect Algorithm Traditional path planning algorithms include artificial potential field method [11], fuzzy rule method [12], genetic algorithm [13], neural network [14], simulated annealing algorithm [15], ant colony optimization algorithm [16]. However, these methods need to model the obstacles in a certain space. The computational complexity is exponential with the degree of freedom of manipulator. It is not suitable for solving the multidegree-of-freedom manipulator in complex environments [17]. The planning principle of the RRT algorithm is to perform collision detection on sampling points in the state space. Furthermore, the modeling of space is avoided, and the path planning problem of high-dimensional space with complex constraints can be

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effectively solved. RRT algorithm is suitable for motion planning of multi-degree-offreedom robots in complex environments. Compared with the RRT algorithm, the branch of RRT-Connect expansion method is improved. The basic idea is to make the distance of the single step expansion as far as possible. The RRT-Connect algorithm improves the basic one-step extension to a greedy multi-step extension that ends an extended iteration until it encounters an obstacle or reaches the target point. This method can effectively avoid the possibility of falling into a local optimum, and can quickly expand to the unexplored area in a relatively open zone. The result can greatly improve the efficiency of the spanning tree. There are Figs. 4 and 5 of the RRT and RRT-Connect algorithms.

Fig. 4. The way of RRT path planner.

Fig. 5. The way of RRT-Connect path planner

The RRT-Connect planner is designed specifically or path planning problems that involve no differential constraints. The method is based on two ideas: the connect heuristic that attempts to move over a longer distance, and the growth of RRTs from both qstart and q goal [16]. qnew is a random point, and qrand is a random invalid point. The RRT-Connect algorithm initializes two trees Ta and Tb respectively. Ta and Tb alternately expand toward each other in the C space, iterating over and over until the two trees meet, and successfully find a path from the initial state to the final state. If the number of iterations is still not met, the pathfinding fails. For each iteration, first select a random point for T1 and select a point on T that is closest to the random point as the growth point. Then select one of all the inputs to make the new pose point closest to the

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random point as the best input, and use this input to multi-step expansion until the new generation point is no closer to the random point, then the latest generated point. As a random point of Ta , Tb grows in the same manner. Then judge whether the latest node distance of the two trees meets the error requirement, that is, whether they meet. When encountering, record the shortest path length; if they do not meet, exchange Ta and Tb sequentially into the next iteration. Once again, judge whether you meet. When the encounter meets, the path length is calculated and compared with the previous path to retain the shortest path. After the number of iterations, the output path is reached: if the number of encounters is still not met, the exit is failed [7].

4 Results and Discussion Since the RRT-Connect algorithm has a certain degree of blindness and randomness, the motion planning trajectory generated for each time is different. Figure 3 shows a simulation process from the start-point to the goal-point. The corresponding graphic in the simulation process were drawn in Figs. 6, 7, 8 and 9. As shown in Fig. 6, the end of manipulator was represented the movement of three curves in X-axis, Y-axis, and Z-axis. It can be seen that the manipulator is moving slowly without violent shaking.

Fig. 6. Manipulator tip track in three axes.

Angular velocity and angular acceleration of manipulator joints were described in Figs. 7 and 8. As shown as Fig. 7, the joints of the manipulator are slow in motion which cost about 20 s. In this period, there is no large speed change. In Fig. 7, the overall movement of the manipulator is relatively gentle. But at the start and near the goal-point has a large speed change, which is caused by the blindness and randomness of the RRT-Connect algorithm.

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Fig. 7. Joint angular velocity of each arm.

Fig. 8. Joint angular acceleration of each arm.

As shown in Fig. 9, the joint rotation speed of manipulator is generally stable, also the rotation amplitude is small. It is indicating that RRT-Connect algorithm gets fast convergence in motion planning and maintains good accuracy and rapid response.

Fig. 9. Joint rotation speed of each arm.

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5 Conclusions In this paper, the virtual simulation of the PUMA-560 manipulate is carried out in VREP software. RRT-Connect algorithm is used to realize the motion planning problem of the manipulate. The properties of the manipulator in motion planning under such conditions are analyzed. The existed problems and future work prospects are raised. As we can see, the motion planning is well solved. The key of motion planning, convergence speed and accuracy, can be obtained from the simulation. The RRTConnect algorithm converges quickly and manipulator find target in the specific motion planning. But the algorithm has certain blindness and randomness, each search path is different from the ideal path. It can also be seen from the figure that the generated motion trajectory has inflection points. There are also large variations in angular velocity and acceleration figure. Reflected in the actual problem, it is easy to produce a certain impact and energy loss on the manipulator itself. For future work, Artificial Neural Networks can be integrated with the RRT-Connect algorithm to increase the manipulator motion planning to achieve the ideal state and trajectory optimization.

References 1. Liu, G., Xie, H., Li, C.: Method of MOBILE robot path planing in dynamic environment based on genetic algorithm (2003) 2. LaValle, S.M., Kuffner Jr., J.J.: Rapidly-exploring random trees: progress and prospects (2000) 3. Melchior, N.A., Simmons, R.: Particle RRT for path planning with uncertainty. In: Proceedings 2007 IEEE International Conference on Robotics and Automation, pp. 1617– 1624. IEEE (2007) 4. AlDahak, A., Elnagar, A.: A practical pursuit-evasion algorithm: detection and tracking. In: Proceedings 2007 IEEE International Conference on Robotics and Automation, pp. 343– 348. IEEE (2007) 5. Yershova, A., Jaillet, L., Siméon, T., et al.: Dynamic-domain RRTs: efficient exploration by controlling the sampling domain. In: 2005 IEEE International Conference on Robotics and Automation, pp. 3856–3861. IEEE (2005) 6. Burns, B., Brock, O.: Single-query motion planning with utility-guided random trees. In: Proceedings 2007 IEEE International Conference on Robotics and Automation, pp. 3307– 3312. IEEE (2007) 7. Kuffner Jr., J.J., LaValle, S.M.: RRT-connect: an efficient approach to single-query path planning, p. 2. ICRA (2000) 8. Cai, Z.: Robotics (2000) 9. Zhao, H., Qian, W., Sun, F.: Research of articulated robot motion simulation based on VREP. Electron. Sci. Technol. 30(4), 53–55 (2017) 10. http://www.coppeliarobotics.com/helpFiles/index.html 11. Chen, Y., Luo, G., Mei, Y., et al.: UAV path planning using artificial potential field method updated by optimal control theory. Int. J. Syst. Sci. 47(6), 1407–1420 (2016) 12. Mohanty, P.K., Parhi, D.R.: A new intelligent motion planning for mobile robot navigation using multiple adaptive neuro-fuzzy inference system. Appl. Math. Inf. Sci. 8(5), 2527 (2014)

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13. Asadi, H., Mohamed, S., Rahim Zadeh, D., et al.: Optimisation of nonlinear motion cueing algorithm based on genetic algorithm. Veh. Syst. Dyn. 53(4), 526–545 (2015) 14. Singh, B., Marks, T.K., Jones, M., et al.: A multi-stream bi-directional recurrent neural network for fine-grained action detection. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1961–1970 (2016) 15. Dowsland, K.A., Thompson, J.M.: Simulated annealing. In: Handbook of Natural Computing, pp. 1623–1655 (2012) 16. Lazarowska, A.: Ship’s trajectory planning for collision avoidance at sea based on ant colony optimisation. J. Navig. 68(2), 291–307 (2015) 17. Feng, L., Jia, J.: Improved algorithm of RRT path planning based on comparison optimization. Comput. Eng. Appl. 47(3), 210–213 (2011)

A Precise Identification and Matching Method for Customer Needs Based on Sales Data Xingpeng Chu1, Jian Zhang1(&), Uday Shanker Dixit2, and Peihua Gu3 1

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Department of Mechatronics Engineering, Shantou University, Shantou 515063, China {17xpchu,jianzhang}@stu.edu.cn 2 Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India [email protected] College of Mechanical Engineering, Tianjin University, Tianjin 300072, China [email protected]

Abstract. In the stage of product design, it is very helpful to understand customer needs accurately to improve product performance. The current customer needs identification scheme cannot meet the dynamic and precise characteristics of customer needs. A precise identification architecture of customer demand based on online sales data and probability theory is proposed. Online sales data provide potential customer demand information, the data is used to build the relationship between customer satisfaction and product function. Vector similarity is used to match user needs and product functions. At the same time, a ranking method of product satisfaction recommended to users is proposed by using the concepts of probability and statistics. The characteristic of this method is that it can feedback user’s needs in real time. The customer eventually gets a product that meets the demand and the customer is most satisfied with the product. Finally, this paper demonstrates the implementation process of this method by taking the multi-functional desk as an example. Keywords: Customer requirements  Product design  Customer satisfaction  K nearest neighbor

1 Introduction In modern society, product design is facing challenges like shortening production cycle and rapid iteration. This requires designers to identify customers’ demands as accurately as possible during the early stage of design. On the other hand, with the rapid development of e-commerce, a rich supply of product information and sales records can be quickly and easily obtained from the Internet (especially e-commercial websites)

This project is supported by National Natural Science Foundation of China (No: 51505269), the National Key R&D Program of China (No: 2018YFB1701701). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 102–112, 2020. https://doi.org/10.1007/978-981-32-9941-2_9

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using data mining techniques. These lay a foundation for the research of customer needs using online purchasing data. The motivation of this paper is the following problems present in customer needs identification. On the one hand, customers and designers have different understandings of products. Customers’ descriptions of needs and Designers’ descriptions of needs are different. Using traditional tools such as Quality Function Deployment (QFD) for modeling and analysis requires a high skill from designers. On the other hand, in the process of requirement definition, problems such as inaccurate content, omission, ambiguity and inconsistency of description occur very often. On these basis, the objective of this paper is to implement a method of customer needs identification. This method builds up a real-time system utilizing online sales data and probability theory to accurately identify customers’ requirements and match the corresponding product feature combinations. The structure of this paper is arranged as follows. The following part in this section introduces the related work on customer needs identification. The second section introduces the basic process of this method, including building up the relationship between customer satisfaction and product characteristics by using the existing product data, analyzing the user’s needs and forecast using vector similarity search, and improving the prediction by receiving customers’ feedback. The third section is the case study of this proposed method, taking students’ multi-functional desk as an example, to verify the practicability of the scheme. The fourth section gives a conclusion and some future works. In the process of acquisition, analysis, and identification of customer needs (CNs), relevant research has given a lot of inspiration in the study of data sources for user needs. Wang et al. [1] developed a high-end equipment customer requirement analysis method based on online reviews. Ireland [2] used online product reviews to identify a series of customer needs. Haug [3] developed a conceptual framework based on 10 industrial designers’ interviews and studies on reference projects. Many attempts have been made on how to process the collected user data. Ni et al. [4] used extended quality function deployment (QFD) and data-mining (DM) techniques to develop a supplier selection methodology. Wang and Chin [5] proposed a linear goal programming (LGP) approach to evaluate the relative weight of customer requirements (CRs) in QFD. Juang et al. [6] use fuzzy reasoning and expert systems to propose and develop a customer requirement information system (CRIS) in the machine tool industry. Guo et al. [7], based on the fuzzy set theory and Euclidean space distance, puts forward a method for customer requirement weight calculation called Euclidean space distances weighting ranking method. Chan et al. [8] used the genetic programming to generate accurate nonlinear models in QFD systems to relate the CR and the engineering characteristics. For the constraints of product characteristics on customer needs, Xie et al. [9] proposed a constraint model as an extension to constraint satisfaction problems (CSPs) with the independent and dependent variables, Sheng et al. [10] studied the customer requirement modeling and its mapping to a numerical control machine design. Shiau [11] considered the finite resource constraint to the rapid changing CRs.

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Ma et al. [12] gives out a new method for obtaining and describing the common understanding of CRs and more importantly transferring them into a detailed and accurate product design specifications (PDS) to interact with different team members effectively. At present, the related research mainly focuses on the classification of user reviews or questionnaires QFD method and expert system, and the establishment of the relationship between customer needs and product feature functions. Little consideration is given to the impact of product feature combination on product performance. At the same time, due to the lack of user participation in the demonstration process, relevant research cannot guarantee to eliminate the impact of user demand changes on product performance. The method introduced in this paper solves the uncertainty caused by the change of user’s demand or repeated results prediction by real-time user participation. This method can accurately identify user needs. Users can get the product feature combination of their needs in real time.

2 The Proposed Method 2.1

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The implementation of this method can be divided into offline and online stage. The offline stage is set up because collecting and processing products’ data takes a long time. It can save time by collecting in advance. By setting the online stage, customers can feedback the product feature combination in real-time, and determine the convergence condition of the user demand by each input after the user accepts the feedback. Offline stage: common needs of customer could be presented by the statistical results of network sales data. By collecting historical sales data of a certain product through e-commercial websites, including the collection of product information and sales information, the relationship between product characteristics and customer satisfaction can be constructed to facilitate product retrieval in the offline part. Online stage: The user’s understanding of the product is usually vague and incomplete. Therefore, the customer needs usually do not completely and accurately represent the product of the customers’ real needs. A set of programs is set up, which can compare the similarity between the customer demand information proposed by the user and the actual product characteristics in real time and obtain some results most similar to the features currently proposed by the user. At the same time, by establishing a feedback mechanism, the process of obtaining a satisfactory product for the user is as short as possible (Fig. 1).

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2.2.1 Online Shopping Data Collection The e-commerce website has rich product information including sales-related attributes and product-related attributes, such as product’s price, sales volume, cumulative evaluation, style, weight, etc. Using web crawling techniques, product information can be obtained from the e-commerce website in large-scale batches. The raw data of the obtained information is generally in the presence of duplicates, vacancies, over definitions, and the like. By using data cleaning techniques, an XML document containing all the information about a product is obtained. The constructed product feature can describe a product in the form of a column vector Pi, as is shown in Eq. 1. Each item of the vector Si represents a feature of the product, and the feature is described by the value Vi of the feature. After the feature is extracted and transformed, the product is converted into a vector in the n-dimensional vector space; here n represents number of the product’s specification. Thus, the customer’s needs can be represented by a vector containing the feature values of the following form:

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Pi ¼ ½ S1 V1

S2 V1

S3 V1 . . . Sn V1 

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2.2.2 Building Up Feature Library The behavior of predicting the products that the user may need can be converted into a problem of comparing the similarity between user requirements and product features, i.e. product specification combinations. Following Sect. 2.2.1, any product Pi can be represented by a point in the vector space D, as is shown in Eq. 2. The product information library collected offline in this paper can be regarded as a M-Dimensional vector set in the vector space D: D ¼ ½ P1

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Limited by the collection conditions, the collected product data does not fully cover all the forms of the product’s feature performance. At this time, the performance of each feature of the product is arranged and combined. By setting feature-related constraints and excluding feature combinations that are not physically feasible, a vector space of all product specification combinations can be obtained. 2.3

Building Up Relationship Between Product Specifications and Customer Satisfaction Index

In this step, Customers satisfaction index (CSI) is used for the quantification of customer’ satisfaction on a specific product [13]. Product sales number is used to indicate Customer satisfaction index. Since CSI and product feature library has been obtained, the relationship between specification combinations and CSI is established using machine learning (ML) models. 2.4

Matching Customer Needs and Product Features

2.4.1 Distance Measurement Customers initial need could be described as a vector lower than the dimension of the product’s full specification combination. It is possible that the customer’s need P0x does not include all the specifications. The user’s request P0x could be expressed as P0x ¼ ½ Si Vi

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Before the comparison, the user’s initial requirement P’x is expand to the same dimension as the vector in the product feature library, those specifications that the customer does not mention is added to 0. Then it is compared with the product feature library. By comparing vectors of the same dimension, the distance between two vectors can be used to describe the degree of similarity.

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2.4.2 Type of Query For different application fields, the query mode of multidimensional database is mainly divided into two types: range query and k-nearest neighbor query. Given the query point and query distance threshold, according to the distance measurement method, the range query will query all the points with less distance from the point [14]. In K nearest neighbor query, we select K points closest to the query point from the database as the result set [15]. For range queries, if the size of the feature library cannot be determined in advance, a user cannot determine how many query results can be obtained after defining the query distance. In this case, it is possible to get no results, or to get most points in the database. In this case, the k-nearest neighbor query method greatly reduces the amount of computation because it defines the number of query results in advance. It is selected as the method used to query similar requirements in this method. The selection of K depends on the number of samples in the feature library. 2.5

Result Ranking and Customer Feedback

After getting K nearest product specification combinations, the CSI of each combination could be obtained from Sect. 2.3. Thus, these specification combinations are sort out by referring to their CSI. Customers see each of the specification combination with its CSI and similarity with their own needs and give their feedback in forms of a new set of needs. By calculating the distances between optimal results for each iteration, a threshold is set to detect convergence. The threshold is set on the basis of the minimum distance between specification combinations

3 Case Study In this paper, the multi-functional desks for school students are selected because the needs of customers for the desks can be intuitively transformed into the form of physical components. Therefore, this product is selected as an example to verify the implementation process of this method. 3.1

Data Acquisition and Preprocessing

The data used in this article is derived from data publicly available on the China Ecommerce website (Taobao). Using the keyword “desk, students, multi-function” to get a list of products that meet the search criteria and using the crawler software to customize the rules. Sales information and product information on the target product page can be obtained in batches. A sample data is shown in Table 1.

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Value 2149 6500 42728 4900 154179 …

Product specification Lifting mode Facing material Target users Furniture structure Assembled or not …

Value Hand-held Fireproof board Children scaffold structure Assembled …

The obtained product information is organized in the form of matrix, and the original data is 80 groups. The original data obtained by the crawler may have some problems, such as missing data, vague description, misleading data and so on. It is necessary to use data cleaning techniques in data science field to process the original data. The evaluation criteria for a set of qualified data is as follows. A set of data corresponds to a product independently, and each feature information of the product is fully represented by the data. After cleaning up the original data, a set of product feature information database is obtained. Each group of data has 15 features, including price, monthly sales, whether to support customization and so on. Due to the limitation of acquisition conditions, 80 sets of data collected cannot fully represent the whole feature combination of this product. All the eigenvalues of each feature should be reassembled to obtain a complete feature information base of 1474560 combinations. However, the constraints between product features make not all feature combinations satisfy the requirements of product feasibility. It is assumed here that after feature constraints, only 80 sets of product feature combinations can meet the requirements of product feasibility. After users put forward their requirements, the recommended similar product portfolio will be given from the collected 80 sets of data. 3.2

Establishing the Relationship Between Product Customer Satisfaction and Product Feature Portfolio

After cleaning, the data contains 80 groups of data, each group of data has 15 characteristics. Firstly, the customer satisfaction index (CSI) of each group of data is constructed. Then, the regression model is established by using the neural network technique. Finally, all features are rearranged. The relationship between feature combination and customer satisfaction is obtained. In this case, the ANN Fit Neural Network Model of Mathematical Modeling Software MATLAB is used to construct the model. The model uses 10 hidden layers, and the activation function uses Bayesian model. The results are validated by using all product feature combinations in mentioned in Sect. 3.1, as shown in Fig. 2. It can be seen that some feature combinations have higher customer satisfaction than other feature combinations.

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Fig. 2. Product specification combinations and their CSI

3.3

Costumer Real-Time Feedback

A random customer who is willing to buy a multi-functional student desk is chosen to utilize this method. Accurate identification of user requirements is carried out according to the process described in Sect. 2. Customer present initial needs, as is shown in Table 2. Customer feedback is shown in Table 3. Table 2. Customer initial needs Assembled or not (1: yes, 2: no) 1 Is it customizable (1: yes, 2: no) 2 Is it taxi transportable (1: yes, 2: no) 1 Lift mode (1: pneumatic, 2: no lift, 3: hand pull, 4: hand held) 4 Style orientation (1: economic type, 2: luxury quality type, 3: artistic style type) 2 Furniture structure (1: scaffold structure, 2: frame structure) 1 Expansion - computer table (1: support, 2: not support) 1

Table 3. Customer feedback Assembled or not (1: yes, 2: no) Is it customizable (1: yes, 2: no) Is it taxi transportable (1: yes, 2: no) Lift mode (1: pneumatic, 2: no lift, 3: hand pull, 4: hand held) Style orientation (1: economic type, 2: luxury quality type, 3: artistic style type) Furniture structure (1: scaffold structure, 2: frame structure) Decoration materials (1: PVC, 2: wood-based panels, 3: other, 4: fire-proof panels, 5: none) Expansion - Computer Table (1: Yes, 2: No)

1 2 1 1 2 1 2 1

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The user requirements are organized according to the form in the product feature library, and the vector representing the initial customer needs is obtained as Px1 ¼ ½ 0 0 1 2 1 4 0 0 2 1 0 0 1 0 

ð4Þ

According to the size of the data set (80), we set K = 3, closest product feature vectors. The K-nearest neighbor search algorithm is programmed and three closest product feature combinations are obtained as is shown in Table 4. Table 4. Matching results Product specifications Price Gross weight Assembled or not (1: yes, 2: no) Is it customizable (1: yes, 2: no) Is it taxi transportable (1: yes, 2: no) Lift mode (1: pneumatic, 2: no lift, 3: hand pull, 4: hand held) Style orientation (1: economic type, 2: luxury quality type, 3: artistic style type) Decoration materials (1: PVC, 2: wood-based panels, 3: other, 4: fire-proof panels, 5: none) Style orientation (1: economic type, 2: luxury quality type, 3: artistic style type) Furniture structure (1: scaffold structure, 2: frame structure) Main material (1: solid wood, 2: wood-based panels, 3: metal, 4: other) Expansion - bookshelf (1: yes, 2: no) Expansion - computer table (1: yes, 2: no) Expansion - division plate (1: yes, 2: no) CSI Similarity

First round matching results >5000 2000– 1000– 3000 2000 20–30 20–30 >40 1 1 1 1 2 1 1 1 1 1 1 1

Second round matching results >5000 2000– < 440  x  760; y ¼ 370 fA ðx; y; zÞ ¼ ; 12  z  80 ð27Þ 50  y  370; x ¼ 440 > > : 50  y  370; x ¼ 760

Fig. 10. Process error analysis of milling square façade

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The A side is the milling process, and the corresponding cutting force calculation model is:

F ðx; y; zÞ

8 > > > > > > > < > > > > > > > :

Fx ¼

x

y

u

CF apF fz F ae F z kFc q d0 F nwF

d a

x

n

 0d0 p  CFx  apFx  f yFx  vc Fx  KFx sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  x y u xF nF C a Ff Fa Fz 0:5d0 ap Fy ¼ F2dp qFznwFe kFc 1  0:5d  CFy  ap y  f yFy  vc y  KFy ð28Þ 0 0 Mc ¼

Fz ¼ 0 x y u CF apF fz F ae F zkFc d0 q 3d F nwF 0

210

Where d0 –Milling cutter outer diameter ðmmÞ; n–Milling cutter revolution ðr=minÞ; fz –Milling cutter movement distance per tooth table, that is, feed per tooth ðmm=zÞ; z–Number of milling cutter teeth; ae –Milling width ðmmÞ; ap –Milling depth ðmmÞ; kFc –Cutting force correction factor when cutting conditions are changed; The other characteristics and the cutting loads corresponding to the features are sequentially modeled according to the above formula. Due to space limitations, this article will not repeat them. 4.3

Standard Parts Error Analysis

For the same machining feature, the machining error is mainly due to the difference in machine tool rigidity at different positions on the machined surface, which in turn causes machining errors on the machined surface, and the machining error is inversely proportional to the rigidity. The machining error caused by the static rigidity of the machine tool mainly includes roundness error, straightness error, flatness error, contour error, and other shape errors. The above shape error produces a position error with a plurality of processing surfaces, and mainly includes positioning errors such as parallelism error, verticality error, and inclination error. The cylindricity error is primarily due to the weak rigidity of the machine tool’s corner direction. Under the action of the cutting force, the angle of the tool changes, and the cylindricity error is caused by the oblique feed. The errors such as straightness and flatness are mainly due to the rigidity of the machined surface. The field is uneven, and the rigidity field mentioned here is the axial rigidity, and the direction is the normal direction of the machined surface (Fig. 11).

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Fig. 11. Main error analysis results of standard test pieces

Error modeling all the working surfaces of the whole standard test piece, introducing the processing parameters, and completing the error analysis of the surface of the part. The results of the XYZ analysis are shown below. From the analysis results, when the part is processed, when the tool is from Y direction When it is thought to increase, the machining error increases and the accuracy decreases. At the same time, the amount of error of the part on the X-axis during the machining of the section is small, which is mainly due to the symmetrical structure design of the machine tool to enhance the rigidity of the X-direction. According to the analysis of machining error between parts, it can be known that this type of machine tool should ensure the lateral feed machining of the tool when arranging the machining process. For the too high longitudinal parts, it can be processed horizontally, thus avoiding the error-sensitive direction and improving the machining precision (Fig. 12).

Fig. 12. X-direction error results of the square façade

Taking the square façade of the standard test piece as an example, the influence of the static rigidity of the machine tool on the machining error is analyzed. According to the requirements of the national standard accuracy inspection manual, the primary detection accuracy of the square façade is the straightness of the side. Comparing the

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analysis results of the whole standard test piece, the deformation of the square façade in the Y direction is quite different. Therefore, the straightness of the square YZ façade is analyzed, and the X-direction machining error analysis result is extracted. As shown in the figure, the plane is in the Y direction. There is a significant straightness error, the straightness error is 0.004, and the tolerance is 0.010, so the straightness error meets the design requirements. Since ANSYS cannot achieve the above-mentioned continuous analysis of part feature error, to verify the accuracy of the error analysis of this method, 6 points are selected on the surface of the part, and the error analysis is performed point by point using ANSYS to extract the Z-direction deformation in the analysis result. Analysis results and calculation efficiency and accuracy of the error analysis model (Fig. 13 and Table 2).

Fig. 13. Comparative analysis points

Table 2. Z-direction error analysis comparison Operation time P1 (650, 50, 50) P2 (650, 114, 50) P3 (650, 178, 50) P4 (650, 242, 50) P5 (650, 306, 50) P6 (650, 370, 50)

Error synthesis model ANSYS 0.83 (s) 137(s) 8.29 lm 7.83 lm 9.10 lm 8.75 lm 9.85 lm 9.55 lm 10.56 lm 10.30 lm 11.22 lm 11.03 lm 11.83 lm 11.73 lm

Comparing the calculation results of the two, the accuracy of the error synthesis model is consistent with the results of the finite element analysis. Comparing the operation time of this model with ANSYS, the time taken to calculate 6 points simultaneously in this model is 0.83 s, and only the finite analysis time of single point after ANSYS meshing is 137 s. At the same time, in the ANSYS analysis, the analysis

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of another point requires adjustment of the component position in the model phase, remeshing, and then finite element error analysis. Therefore, the computational efficiency of the method far exceeds that of ANSYS, and the technique is not limited to the processing characteristics and processing technology of the parts and has broad applicability (Fig. 14).

Fig. 14. Z-direction comparison analysis results

5 Conclusions Through the establishment of the chain-spinning synthesis model of the machine tool, the reasonable characterization of the space rigidity field of the machine tool was realized. The spatial rigidity field characterization model of the machine tool with integrated rigidity chain could directly describe the 6-direction rigidity variation in the sufficient machining space of the machine tool. At the same time, the model had realized the 6-direction machining error prediction of the parts through the processing technology of the associated components. The rigidity synthesis model could solve the machining error under any proportional load process, thus an effective prediction of the machining error of the machine tool integrating multiple machining processes was realized. By comparing the results of ANSYS analysis, the method greatly had improved the analysis efficiency on the basis of ensuring accuracy. Finally, the space rigidity field was established with the precision coordinate boring machine as the object. Furthermore, the machining error of the standard profile test piece was analyzed. The analysis showed that the machining accuracy of the machine tool had met the design requirements. The method greatly improved the analysis efficiency on the basis of ensuring the accuracy, and had wide applicability. It provided a good performance reference for the process design of the machine tool and the design of the machine tool structure was based on the machining process.

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References 1. Lu, B.: Technical Basis of Machinery Manufacturing. Machinery Industry Press, Beijing (2007) 2. Schellekens, P., Rosielle, N., Vermeulen, H., et al.: Design for precision: current status and trends. CIRP Ann. 1998-Manuf. Technol. 47(2), 557–586 (1998). Annals of the international institution for production engineering research 3. Huang, T., Lee, J.: On obtaining machine tool rigidity by CAE techniques. Int. J. Mach. Tools Manuf. 41, 1149–1163 (2001) 4. Wang, J., Wang, L., Li, T., et al.: Study on the rigidity of a 5-DOF hybrid machine tool with actuation redundancy. Mech. Mach. Theory 44(2), 289–305 (2009) 5. Gosselin, C.: Rigidity mapping for parallel manipulators. IEEE Trans. Robot. Autom. 6(3), 377–382 (1990) 6. Yan, R., Chen, W., Peng, F., Lin, S., Li, B.: Modeling and stiffness performance analysis of closed-chain stiffness field for multi-axis machining system. J. Mech. Eng. 48(1), 177–184 (2012) 7. Salgado, M.A., Lo pez de Lacalle, L.N., et al.: Evaluation of the rigidity chain on the deflection of end-mills under cutting forces. Int. J. Mach. Tools Manuf. 45, 727–739 (2005) 8. Lo pez de Lacalle, L.N., Lamikiz, A.: Machine Tools for High Performance Machining. Springer, London (2009) 9. Chanal, H., Duc, E., Ray, P.: A study of the impact of machine tool structure on machining processes. Int. J. Mach. Tools Manuf 46(2), 98–106 (2006) 10. Zhao, Y., Lin, Z., Wang, H.: Operational performance analysis of heavy forging operator. J. Mach. Tool Mech. Eng. (6), 69–75 (2010) 11. Liu, Q., Zhang, Y., Lin, J., Li, H., Zhao, F.: Series stiffness field of CNC machine tools and its application. Manuf. Technol. Mach. Tools (2), 29–32 (2011) 12. Liu, H., Zhao, W.: Dynamic characteristics analysis of machine tools based on the concept of generalized processing space. J. Mech. Eng. 46(21), 54–60 (2010)

Thermodynamic Lubrication Performance and Stability for a Deep/Shallow Pocket Hybrid Bearing Considering Bubbly Oil Hong Guo, Shuai Yang(&), Ningning Wu, and Ruizhen Li School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China {gghhletter,lrzh}@zzu.edu.cn, [email protected], [email protected]

Abstract. In order to research on the influence of thermal effect and bubbly lubricant oil on the bearing performance and rotor system stability. A hybrid bearing with deep and shallow pockets was selected as a study object, and its thermodynamic models including Reynolds equation, energy equation, viscosity-bubble volume fraction equation and temperature-viscosity equation were established. The pressure distribution, temperature and viscosity distribution were calculated considering the influence of the bubble using the classical numerical method, and the lubricant characteristics were analyzed. The motion model was derived for a single mass flexible rotor supported in two hybrid bearings, the system thermal instability was simulated and discussed further when the bubble volume fraction is lower than 5.0%. The results show that there exists an obvious non-uniformed temperature distribution in the lubricant film, and the bearing lubrication parameters are climbing with the rising of the bubble volume fraction, and the thermal effect weakens the bearing load capacity and friction loss, whereas it increases the flow volume rate. The stability parameters drop when the thermal effect is considered, and they would be improved with the consideration of bubble within the limited bubble proportion range. Keywords: Hybrid bearing  Thermodynamic lubrication Thermal instability  Bubbly lubricant oil



1 Introduction The sliding bearings are widely used in high-speed and high-accurate rotational machineries due to their high stability and lower friction [1–3]. The hybrid bearings as a type of bearings which combine the advantages of the hydrodynamic bearing and hydrostatic bearing are paid attention to increasingly [4, 5]. With the development of research, the influence of the thermodynamic (THD) behaviors on the bearing characteristics have become a hot issue, and there have been a large number of related work. Yuansheng et al. [6], used the Newton-Raphson method to solve the bearing This project is supported by National Natural Science Foundation of China (Grant No. 51575498). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 189–201, 2020. https://doi.org/10.1007/978-981-32-9941-2_16

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pressure and temperature, and analyzed the thermal dynamic performance. Lu, et al. [7], aimed to ceramic water-lubricated bearing to simulate the thermal expansion and verify the thermal boundary conditions in their theoretical studies through experiments. Jintai and Yonggang [8] gave a comprehensive THD analysis about a dynamically rolling piston loaded bearing, and they further compared the bearing eccentricity and axis orbits between the isothermal model and THD model. Donghyun et al. [9], associated the increasing temperature with the lubrication failure mechanism including the minimum film thickness and load capacity for a tilting pad journal bearing. Shi et al. [10], calculated the temperature rise of the floating ring bearing and the impact of operating conditions on the lubrication performance of the turbochargers. Besides these, Lin et al. [11], took account the surface texture into the slide bearing THD analysis. During the accelerating of shaft, lubricant film would appear some gas bubbles due to the surround air vibration and oil vaporization. It would change the properties of the lubricant oil to affect some important performance parameters of bearing. The scholars made many researches about this. Nikolajsen [12, 13] studied the impact of bubble on the lubricant density and viscosity considering bubble surface tension, and analyzed how the bubbly oil affect the load capacity of bearing. Rust [14] explained the mechanism of bubble deformation, and deigned the experiments to measure the specific impact of bubble on the viscosity of corn syrup. Zebin et al. [15], researched the relationship between the bubble proportion and dynamic viscosity of the lubricant oil through the experiment. The models of two-phase fluid including gas and oil were applied to the lubricant simulation of the bearing in these existing studies. Hekmat and Biukpour [16] predicted the effect of the shaft speed and external load on the instability mechanism of the bearing lubricant film under the influence of the cavitation. Lili and Qingliang et al. [17], focused on the specific boundary conditions affecting the cavitation behaviors for a three oil wedges bearing based on the computational fluid dynamics software. Above all, there are rare studies about coupling the bubbly oil and thermal effect on bearing characteristics and stabilities. In this research, a THD model and bearing-rotor system motion model are established considering the bubble in the lubricant film for a hybrid bearing with deep/shallow pockets. The finite element method and finite difference method are used to solve the THD models, and to simulate the temperature distribution in the lubricant film. It is discussed that the influence of the thermal effect and bubble content on the lubrication performance involving load capacity, friction loss and volume and stability for this bearing. This research provides a reference for lubrication theory modelling and sliding bearing design.

2 The Basic Simulating Models The hybrid bearing structure is presented in Fig. 1. The lubricant oil from the external pump to the bearing interior through the deep pocket which shows the static effect. The shallow pocket and bearing land show the strong hydrodynamic effect when journal begin rotating under the external load.

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External load Shallow pocket Deep pocket

Φ

Bearing shell Lubricant film

θ Ω

Journal

Fig. 1. Configuration of the hybrid bearing with the deep/shallow pockets

2.1

Reynolds Equation

The lubricant film is assumed to be the laminar and Newtonian flow, and the journal misalignment and bearing shell elastic deformation are ignored. The U represents the clockwise circular direction and the k represents the axial direction. The dimensionless Reynolds equation which governing the lubricant film pressure can be expressed as follow: !   ! 3 3 @ h @p d 2 @ h @p 3 @h þA þ ¼ BM @U l @U l @k l @k 2 @U

ð1Þ

p ¼ pps ; h ¼ hc ; e0 ¼ ec0 ; u ¼ U  h; BM ¼ lp0 ds c2X ; 2

  A ¼ 3BM cos u þ e0 h_ sin u where d is the bearing diameter, l is the bearing axial length, c is the bearing clearance, h is lubricant film thickness, X is the journal angular speed, p is the pressure distribution of the lubricant film, and ps is the external supply pressure. 2.2

Thermodynamic Governing Equations

2.2.1 Energy Equation The quantities of heat convection is dominant comparing with heat conduct in the lubricant film, the heat conduct is neglected. So, the simplified dimensionless energy equation which describes the temperature distribution along the bearing circular and axial directions is presented [18]:   3 d 2 2 h3 @p @T 2l 2 h @p @T h  3BM l @U @U  l 3BM l @k @k ¼ h þ   2 3 d 2 @p2 @p 8 h þ l @U @k 3BM 2 l T¼

T l ;l¼ T0 l0

ð2Þ

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where T and l is the temperature distribution and viscosity distribution of the lubricant film, respectively. The T0 is the bearing inlet temperature and l0 is the dynamic viscosity at this temperature. 2.2.2 Isothermal Model In order to simplify the complex thermal analysis process, the lubricant film temperature distribution is assumed to be uniformed. Therefore, the bearing outlet temperature is regarded to be equal to the effective temperature of the whole lubricant film. This effective temperature model is expressed as follow: DT ¼

Hf cv qQ

ð3Þ

Teff ¼ T0 þ DT

ð4Þ

where the Hf is the fiction power loss, Q is the lubricant oil leakage from the bearing ends, cv is the lubricant specific heat, q is the lubricant density. The D T and Teff are the average temperature rise and effective temperature of the whole lubricant film, respectively. 2.2.3 Viscosity Equation The lubricant viscosity is affected by the bubble existing in the lubricant film, and the impact of bubble on the density is ignored, so the dependent relationship equation between the viscosity and bubble volume fraction equation is [15]: lb ¼ 1 þ j/2

ð5Þ

where the / is the bubble volume fraction, and the j is the viscosity-bubble volume fraction coefficient. The Reynolds temperature-viscosity equation is used to express the influence of the temperature on viscosity: l ¼ eaðTT 0 Þ

ð6Þ

where the a is the temperature-viscosity dependence coefficient. The isothermal model cannot describe the real non-uniformed temperature distribution, so the THD models analyze the bearing lubrication parameters relating the thermal effect more accurately. 2.3

Lubricant Film Thickness 8 < 1 þ e cosðU  hÞ h ¼ 1 þ e cosðU  hÞ þ hd : 1 þ e cosðU  hÞ þ hs

Bearing land Deep pocket Shallow pocket

ð7Þ

where hd ¼ hcd , hs ¼ hcs , hd is the deep pocket depth, and hs is the shallow pocket depth.

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Boundary Conditions

As the Fig. 2 is shown, the deep pocket has the internal feedback restrictor which shows the static effect, so the hybrid bearing pressure distribution have to obey the Reynolds boundary condition and restrictor flow equations simultaneously.

Fig. 2. Boundary conditions

The pressure conditions expression is 8 j 2 C1 > < pj ¼ 0; pj ¼ prm ; j 2 C2 > : p ¼ 0; @pj ¼ 0; j 2 C3 j @Uj

ð8Þ

where 1  prm ¼ ðqout  qin þ qcout þ qcout Þm Rrm  3 R k  2  3 h @p qin ¼ k23 dl BMh  2 l @U U¼U dk  2 3 R k3  l 2  3 @p qout ¼ k2 d 2 BMh  hl @U dk U¼U3 R U3 h3 @p qcout ¼  U2 l @k dU k¼k2

The temperature in the deep pocket is regarded to be the inlet temperature, so the temperature condition is (

T j ¼ T 0;

j 2 C2

@T j @Uj

j 2 C3

¼ 0;

ð9Þ

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Lubrication Characteristic Parameters

The lubricant characteristic parameters can be obtained through the lubricant film pressure integration: Dimensionless load capacity: 8 Z Z l 2p 1 > > > F ¼  p sin UdkdU < x d 0 1 Z Z > l 2p 1 > > p cos UdkdU : Fy ¼  d 0 1

ð10Þ

Dimensionless friction power loss: Z Hf ¼

2p

Z

0

1



 l h @p BM þ dkdU 2 @U 4h

1

ð11Þ

Dimensionless flow volume rate: Z

2p

Q¼ 0

3

h @p l @k

! dU

ð12Þ

k¼1

3 Stability Modelling The Fig. 3 presents a flexible symmetric rotor supported in two hybrid bearings, the rotor mass is 2mr, and the shaft flexural stiffness is ks.

Fig. 3. Flexible symmetric bearing-rotor system

The stiffness coefficients and damping coefficients are kmn and bmn (m, n = x, y), respectively. The lubricant film can be seen as the springs and dampers. The motion equation of the bearing-rotor system is established as follow:

Thermodynamic Lubrication Performance and Stability

8 ks  n ¼ DFx > > < ks  g ¼ DFy DFx ¼ kxx x þ kxy y þ bxx x_ þ bxy y_ > > : DFy ¼ kyx x þ kyy y þ byx x_ þ byy y_

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ð13Þ

where DFx and DFy are the lubricant film force increment, x and y are the displacement of the shaft away from the mass center, n and g are the displacement of the rotor away from the shaft center. The general solution form of the Eq. (13) is: x ¼ x0 em t , y ¼ y0 em t , n ¼ n0 em t , g ¼ g0 em t , so the Eq. (13) is transferred as follow:



   keq  ixbxx  kxx x0  ixbxy þ kxy y0 ¼ 0  ixbyx þ kyx x0 þ keq  ixbyy  kyy y0 ¼ 0

ð14Þ

The system remains stable when both of the real and image parts of the Eq. (14) solution are 0, so the rotor dimensionless critical mass Mst can be obtained as follows: Mst ¼

keq c2st

ð15Þ

where the system effective stiffness coefficient k eq is keq ¼

kxx byy þ kyy bxx  k xy byx  kyx bxy bxx þ byy

ð16Þ

The system instability whirl frequency cst is 

c2st

  keq  kxx k eq  kyy  k xy k yx ¼ bxx byy  bxy byx

ð17Þ

The rotor system produce oil whirl/oscillation when the dimensionless rotor mass exceeds the Mst. The viscosity is variable at the different spots in the lubricant film, so the threshold speed has to be calculated though iteration using Routh-Hurwitz method rather than above stability analysis method [19, 20].

4 Results and Discussion The finite element is used to solve the Reynolds equation and the finite difference method is used to solve the energy equation. Table 1 gives the main parameters during the simulation process.

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4.1

Value 4 70 80 10/10 15 55 0.25 0.022 0.035 2.5 40 4.475 1800 889 0.03568 269.1

Temperature Distribution

Figure 4 presents the 3-D temperature distributions of the lubricant film under different bubble volume when the rotational speed is 12000 rpm and the eccentric ratio is 0.3. The lubricant temperature is climbing from the deep pocket end to the bearing land along the clockwise circular direction. Because the cold oil in the deep pocket cool the lubricant film, and the temperature is dropped dramatically after its peaks along this direction. In the axial direction, the heat is transferred from the pocket center to the bearing ends with lubricant leakage. The difference between temperature peak in the pocket center and temperature at the bearing end is about 7–12 °C. The bubble increases the inner shear fore of the lubricant film, so it is seen clearly that temperature is increasing due to the increment of bubble volume fraction.

(a) φ = 0.0%

(b) φ = 5.0%

Fig. 4. The temperature distribution of the lubricant film

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Lubrication Characteristics

The Figs. 5, 6 and 7 describe the influence of the thermal effect and bubbly oil on the bearing lubrication performance parameters when the shaft rotational speed is 12000 rpm. The load capacity is increasing while the eccentric ratio gets climbing. The thermal effect is considered, the load capacity is diminished due to the reduction of lubricant viscosity. For example, when / = 0 and e = 0.2, the dimensionless load capacity is 1.318 with isothermal model, and it goes to 1.165 with THD model which drops by 11.5%. While the bubble volume fraction gets increasing, and the capacity gets larger. So the bubbly oil is beneficial to improve the load capacity and alleviate the bad influence of viscous dissipation.

Dimensionless load capacity Fr

9

THD model, Isothermal model, THD model, Isothermal model, THD model, Isothermal model,

8 7 6 5 4 3 2 1 0

0.1

0.2

0.3 0.4 Eccentric ratio ε

0.5

0.6

Fig. 5. The dimensionless load capacity F r

The dimensionless friction power loss goes up with the increasing of the shaft rotational speed rapidly, however, there is almost stable trend to the eccentric ratio except the high eccentric ratio situations. The bubble increase the friction loss, with the isothermal model, when e = 0.1 and / = 0, the dimensionless friction loss is 21.89, and it goes up to 36.74 dramatically which climbs by 67.8% while / = 5.0 at the same operation. Therefore, the influence of the bubble on the bearing friction should not be ignored. While thermal effect of the lubricant film is considered, the friction loss gets lower.

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Fig. 6. The dimensionless power loss H f

Considering the influence of thermal effect, it is easier to flow out from the bearing for the lubricant film. Especially at the high bubble fraction relatively, the difference between the THD model and Isothermal model reaches about 30%. Moreover, the lubricant volume flow rate rises with the bubble fraction is climbing, and the impact of the bubble in the oil has exceeded the influence of the eccentricity on the fluid volume flow rate while the rotational speed of the shaft remains constant.

 Fig. 7. The dimensionless volume flow rate Q

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For the general slide bearings, the system would be more stable if the keq is larger and the c2st is smaller. From the Figs. 8 and 9, it can be found that keq growing with the increment of the bearing eccentricity. When the thermal effect is considered, k eq is fallen, and this tendency is obvious increasingly while the growth of the eccentric ratio and bubble fraction. The c2st with THD model shows an growth than isothermal model. Therefore, the temperature rise of the lubricant film would suffer the system stability. Additionally, it can be seen obviously that the keq increase rapidly when the bubble fraction is rising from 0.0% to 5.0% using THD and isothermal models. But the c2st dose not change significantly with the variation of bubble fraction.

Fig. 8. The dimensionless effective stiffness keq

Fig. 9. Instability whirl frequent square c2st

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The Fig. 10 illustrates the variation of rotor dimensionless critical mass Mst under different operating conditions when the rotational speed of the shaft is 12000 rpm. It is showed that the hybrid bearing-rotor system has an excellent stability at high eccentricities. Below the threshold speed, when the thermal effect is considered, the Mst drops comparing with the isothermal assumption, especially at the high eccentricities and bubble fraction. As bubble increase the lubricant viscosity which could improve the stiffness effect and the lubricant film resistance on external vibration and shock, the increment of the bubble fraction would increase the Mst within the given range.

Fig. 10. The dimensionless critical mass Mst

5 Conclusions (1) There are consecutive temperature peaks in the lubricant film along the fluid main flow direction for the hybrid bearing, the temperature at bearing ends is higher than pocket center. The non-uniformed temperature distribution should not be neglected at high rotational speeds and eccentricities, and the maximum temperature is increasing while the bubble volume fraction is going up. (2) With the considering of the thermal effect on the lubricant film, the load capacity and friction loss are fallen, and the flow volume rate gets larger. And they become increasing with the increment of bubble volume fraction particularly at high eccentricities. (3) The parameters relating to the stability including the effective stiffness, whirl frequency and critical mass are dropped due to the reduction of the lubricant viscosity caused by temperature rise. However, the bubble existing in the lubricant could improve the system stability when the bubble volume fraction is lower than 5.0%.

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References 1. Abali, E., Uckan, E.: Parametric analysis of liquid storage tanks base isolated by curved surface sliding bearings. Soil Dyn. Earthq. Eng. 30(1-2), 21–31 (2010) 2. Amamou, A., Chouchane, M.: Nonlinear stability analysis of long hydrodynamic journal bearings using numerical continuation. Mech. Mach. Theory 72, 17–24 (2014) 3. Zhang, K., Zhao, X., Feng, K., et al.: Thermohydrodynamic analysis and thermal management of hybrid bump-metal mesh foil bearings: experimental tests and theoretical predictions. Int. J. Therm. Sci. 127, 91–104 (2018) 4. Linjamaa, A., Lehtovaara, A., Larsson, R., et al.: Modelling and analysis of elastic and thermal deformations of a hybrid journal bearing. Tribol. Int. 118, 451–457 (2018) 5. Jianbin, Z., Changqing, C.: Analysis of thermal effects in shallow pocket-step hydrostatic and hydrodynamic oil bearings. J. Beijing Univ. Aeronaut. Astronaut. 23(3), 390–394 (1997) 6. Yuansheng, L., Ming, Y., Liangbo, A., et al.: Thermohydrodynamic lubrication analysis on equilibrium position and dynamic coefficient of journal bearing. Trans. Nanjing Univ. Aeronaut. Astronaut. 29(3), 227–236 (2012) 7. Lu, D., Kejia, K., Wanhua, Z., et al.: Thermal characteristics of water-lubricated ceramic hydrostatic hydrodynamic hybrid bearings[J]. Tribol. Lett. 63(2), 23 (2016) 8. Jintai, M., Yonggang, M.: THD analysis of rolling piston and journal bearings in rotary compressors. Tribol. Trans. 59(2), 195–207 (2016) 9. Donghyun, L., Kyung, H., Byungock, K.: Thermal behavior of a worn tilting pad journal bearing: thermohydrodynamic analysis and pad temperature measurement. Tribol. Trans. 61 (6), 1074–1083 (2018) 10. Shi, Z., Kang, Y., Wang, J., et al.: An investigation on static lubricating characteristics of floating ring bearing considering thermal effects. Lubr. Eng. 44(1), 36–41 (2019). (in Chinese) 11. Lin, W., Zhanhai, H., Guoding, C., et al.: Thermo-hydrodynamic analysis of largeeccentricity hydrodynamic bearings with texture on journal surface. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. 232(19), 3564–3569 (2018) 12. Nikolajsen, J.L.: The effect of aerated oil on the load capacity of a plain journal bearing. Tribol. Trans. 42(1), 58–62 (1999) 13. Nikolajsen, J.L.: Viscosity and density models for aerated oil in fluid-film bearings. Tribol. Trans. 42(1), 186–191 (1999) 14. Rust, A.C., Manga, M.: Effects of bubble deformation on the viscosity of dilute suspensions. J. Non-Newton. Fluid Mech. 104(1), 53–63 (2002) 15. Zebin, Z., Yong, L., Rognshang, C., et al.: Effect of void fraction on viscosity of lubricating oil. J. Henan Univ. Sci. Technol.: Nat. Sci. 2, 23–27 (2019). (in Chinese) 16. Hekmat, M.H., Biukpour, G.A.: Numerical study of the oil whirl phenomenon in a hydrodynamic journal bearing. J. Braz. Soc. Mech. Sci. Eng. 41(5), 218 (2019) 17. Lili, W., Qingliang, Z., Changhou, L., et al.: A numerical analysis and experimental investigation of three oil grooves sleeve bearing performance. Ind. Lubr. Tribol. 71(2), 181– 187 (2019) 18. Laraqi, N., Rashidi, M.M., Garcia, J.M., et al.: Analytical model for the thermohydrodynamic behaviour of a thin lubricant film. Lubr. Int. 44(9), 1083–1086 (2011) 19. Hong, G., Zhiming, Z., Shaolin, Z., et al.: Multi stable regions of hydrodynamic floating ring journal bearing-rotor system. J. Vib. Shock 35(2), 168–172 (2016). (in Chinese) 20. Zhiming, Z.: Fluid Hydrodynamic Lubrication Theory. Higher Education Press, Beijing, pp. 90–120 (1986). (in Chinese)

Time Delay Chen System Analysis and Its Application Hongjun He, Yan Cui(&), Chenhui Lu, and Guan Sun Shanghai University of Engineering Science, Shanghai 201620, China [email protected]

Abstract. This paper analyzes the stability of Chen system equilibrium point and Hopf bifurcation parameter with a time delay term. According to routhhurwitz criterion, the asymptotic stability of the system near the zero equilibrium point is determined. The distribution of characteristic roots of the system is calculated, and the time delay parameters of Hopf bifurcation are calculated by using the distribution results. Based on the calculation results, the path of the wireless robot with the Chen system with added parameter terms as the navigation equation is solved, and the path map is drawn. The actual operation results show that the time delay parameters determined by this method can increase the coverage rate of robot travel path from 60% to more than 80%. Keywords: Time delay

 Chen system  Hopf bifurcation  Wireless robot

1 Introduction Chaos theory points out the initial value sensitivity, ergodicity and long-term unpredictability of nonlinear systems, which makes the nonlinear systems have been concerned by the academic community. Since lorenz modeled and proposed the first chaotic system [1] in 1963, chaotic systems have been applied in various fields [2–4], such as memristor circuit [5–7], chaotic synchronization [8–10], secure communication [11], industrial robots [12–15] and so on. In recent years, applying chaos theory to robot research has become a new research direction. In 2012, Volos et al. [16] designed a random signal generator using a chaotic system with double vortex-attractors to control the humanoid robot. Experimental results show that the bit sequence generated by chaos generator can be converted into four or eight motion steps, and the robot has good stability. In the same year, Ni et al. [17] proposed a new chaos algorithm (FCGA) for target search in the unknown environment of robots. When there is no target information or the information density around the robot is the same, the algorithm can avoid the disordered motion of the robot and greatly reduce the searching time. Experiments show that the chaotic genetic algorithm enables the robot to find the target effectively. There are also many robots that use chaotic systems as navigation equations, such as sweeping robot [18] and fire robot [19, 20]. In 2016, Sambas et al. [21] took the sweeping robot as the prototype, This project is supported by National Natural Science Foundation of China (Grant No.11604205). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 202–213, 2020. https://doi.org/10.1007/978-981-32-9941-2_17

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established the kinematics model of robot motion, and successfully realized the line control. Combined with a new network system of three-dimensional impulse circuit, the driving strategy of mobile robot is studied to produce the most unpredictable trajectory, but the coverage rate is low. In 2017, they changed the wire control to wireless control [22] on the basis of the previous one, and increased the track coverage to 67% at the same time. The research shows that the Hopf bifurcation characteristic of time-delay Chen system as a navigation equation can improve the coverage of mobile robot. In this paper, according to the existing research literature [23–25], Hopf bifurcation condition of Chen system with time delay was analyzed, time delay parameters were calculated and its dynamic characteristics were verified by Matlab simulation. Based on the analysis results, the time-delay parameters were determined and the navigation equation was established. Based on the experimental model used in literature [21], the mobile robot was controlled and its real coverage was tested.

2 Time Delay Chen System Analysis The state equation of the single time delay class Chen system studied in this report is as follows: 8 < x_ ðtÞ ¼ aðyðtÞ  xðtÞÞ y_ ðtÞ ¼ ðc  aÞxðt  sÞ  xðtÞzðtÞ þ cyðtÞ ð1Þ : z_ ðtÞ ¼ xðtÞyðtÞ  bzðtÞ Where [x, y, z]T is the parameter of system (1), a; b and c are the parameters of system (1). By Ref. [20] know when a [ 2c, system (1) has a unique equilibrium for Að0; 0; 0Þ and when a\2c there are pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi bð2c  aÞ; bð2c  aÞ; bð2c  aÞÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cð bð2c  aÞ;  bð2c  aÞ; 2c  aÞ Bð

and the equilibrium B and C are symmetric about the Z axis. 2.1

Stability Analysis

Firstly, the equilibrium point Að0; 0; 0Þ is analyzed. According to the method proposed by the canonical lemma and Ref. [15], the system (1) can be expressed as after linearization at that point. 8 < x_ ðtÞ ¼ aðyðtÞ  xðtÞÞ y_ ðtÞ ¼ ðc  aÞxðt  sÞ þ cyðtÞ : z_ ðtÞ ¼ bzðtÞ

ð2Þ

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Corresponding jacobian matrix of the system   a  JðAÞ ¼  ðc  aÞekt  0

(2) is: a c 0

 0  0  b 

The corresponding characteristic equation of the jacobian matrix is: k3 þ p1 k2 þ p2 k  p3  ðp4 k þ p5 Þeks ¼ 0

ð3Þ

Where the parameter is: p1 ¼ a þ b  c; p2 ¼ ab  a  b; p3 ¼ ab p4 ¼ aðc  aÞ; p5 ¼ abðc  aÞ Lemma 1. The system (1) is asymptotically stable at the equilibrium point Að0; 0; 0Þ. Prove: When the time delay is equal to 0, we can get from Eq. (3) that k3 þ p1 k2 þ ðp2  p4 Þk  p3  p5 ¼ 0 According to the routh-hurwitz criterion, Eq. (3) has a negative real part of all characteristic roots, which should satisfy the following conditions: p1 [ 0; p3 þ p5 \0; p1 ðp2  p4 Þ þ p3 þ p5 [ 0 The corresponding parameters are taken into the equation. The system is stable at the equilibrium point a when a > 2c. So at that time, when the delay was equal to 0, the system (1) was stable at equilibrium A. 2.2

Hopf Bifurcation Analysis

Let the s [ 0, k ¼ ixðx [ 0Þ is a pair of pure virtual roots of the characteristic equation. Bring it into Eq. (3): ix3  p1 x2 þ p2 xi  p3  ðp4 xi þ p5 Þðcos xs  i sin xsÞ ¼ 0

ð4Þ

After simplifying Eq. (4), the following equations can be obtained: 

p1 x2 þ p3 þ p5 cos xs þ p4 x sin xs ¼ 0 x3 þ p2 x  p4 x cos xs þ p5 sin xs ¼ 0

ð5Þ

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First square the two sides of Eq. (5), and then add the following six-member parametric equation for x:     x6 þ p21  2p2 x4 þ p22 þ 2p1 p3  p24 x2  p25 þ p23 ¼ 0

ð6Þ

Lemma 2. Equation 6 contains at least one positive real root Prove: Let x ¼ x2 , then Eq. (6) can be converted into the following form     x3 þ p21  2p2 x2 þ p22 þ 2p1 p3  p24 x  p25 þ p23 ¼ 0 Of the above equation is changed as follows:     gð xÞ ¼ x3 þ p21  2p2 x2 þ p22 þ 2p1 p3  p24 x  p25 þ p23

ð7Þ

The problem of the root of the equation is then transformed into a positive zero in Eq. (7). Perform the following transformation on Eq. (7): gð x Þ ¼

    1 þ p21  2p2 1x þ p22 þ 2p1 p3  p24 x12  p25 x13 þ p23 x13 1 x3

Obviously there is: gð0Þ ¼ p25 þ p23 ; lim gð xÞ ¼ þ 1 [ 0 x! þ 1

For gð0Þ ¼ p25 þ p23 ¼ ðp3  p5 Þðp3 þ p5 Þ, according to condition 1 p3 þ p5 \0, then gð0Þ\0. Therefore, gð xÞ must have a little x0 on ð0; þ 1Þ so that gðx0 Þ ¼ 0 is established and it is verified. Based on the above verification, we set x0 to be a positive real root of the equation, then we get according to Eq. (5) cos xs ¼

p2 p4 x2  p1 p5 x2  p3 p5  p4 x4 p25 þ p24 x2

We can available the time-delay parameter s is: s¼

1 p2 p4 x2  p1 p5 x2  p3 p5  p4 x4 2np cos1 þ ðn ¼ 0; 1; 2. . .Þ x0 x0 p25 þ p24 x2

ð8Þ

According to Eq. (8), the solution of Eq. (3) is ðx0 ; sn Þ, k ¼ ix0 (x0 > 0) is a pair of pure imaginary roots of the characteristic equation. Take the time-delay parameter s ¼ s0 , which is the minimum time-delay parameter. The following gives a bifurcation condition for the hopf bifurcation of the system at this point. Let the characteristic root of the equation be ks ¼ aðsÞ þ ixðsÞ.

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    ð sÞ Lemma 3. If g0 x20 ¼ 3x4 þ 2 p21  2p2 x2 þ p22 þ 2p1 p3  p24 [ 0, then dRek [ 0. ds Prove: Finding the derivative of the delay s on both sides of (3) is available:  2  dk ¼ kðp4 k þ p5 Þeks 3k þ 2p1 k þ p2  p4 eks  sðp4 k þ p5 Þeks ds

ð9Þ

The following equation is obtained from Eq. (3): ðp4 k þ p5 Þeks ¼ k3 þ p1 k2 þ p2 k  p3 Bring it into Eq. (9): 1 dk 3k2 þ 2p1 k þ p2 p4 s þ  ¼  3 ds kð p4 k þ p5 Þ k k k þ p1 k2 þ p2 k  p3 Bringing its characteristic root k ¼ ix0 into the equation above: "

# dk 1 Re js ¼ s n ¼ ds

"

# 3k2 þ 2p1 k þ p2 p4 þ Re  3 js ¼ sn kð p4 k þ p5 Þ k k þ p1 k2 þ p2 k  p3 p2  3x2 þ 2p1 xi p4 ¼ Re 4 þ Re x  p2 x2  ðp1 x3 þ p3 xÞi p4 x2 þ p5 xi 2 2 3 ðx  p2 Þðp2  3x Þ þ 2p1 ðp1 x þ p3 xÞ p24 ¼  p24 x2 þ p25 ðx2  p2 Þ2 x2 þ ðp1 x3 þ p3 xÞ2 ð10Þ

Bringing its eigenvalue k ¼ ix0 into the characteristic equation yields the following equation: x3 i  p1 x2 þ p2 xi  p3  ðp4 xi þ p5 Þeixs ¼ 0 Because eixs ¼ cos xs  i sin xs and jeixs j ¼ 1, so we take the absolute value of both sides of the equation:  3  x i  p1 x2 þ p2 xi  p3  ¼ jp4 xi þ p5 j According to Eqs. (10) and (11), the following equation can be obtained: "

# dk 1 gð x Þ Re [0 j s ¼ sn ¼ 2 2 ds p4 x þ p25

ð11Þ

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Since Re

h  dk 1 ds

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i    js ¼ sn and Re dk ds js ¼ sn have the same sign, Lemma 3 holds.

Combining Hopf’s bifurcation lemma, the following conclusion can be drawn: if   g0 x20 [ 0, then: (a) When s 2 ½0; s0 , system (1) is asymptotically stable at point Að0; 0; 0Þ. (b) When s [ s0 system (1) is unstable at Að0; 0; 0Þ. (c) When s ¼ sn , system (1) generates Hopf bifurcation at Að0; 0; 0Þ and generates a limit cycle.

3 Numerical Simulation In this section, we use matlab to simulate the system (1) with time-delay term to verify the correctness of the theoretical analysis results in the previous section. According to the previous analysis, the system parameters a ¼ 5; b ¼ 1; c ¼ 1, the system (1) is as follows: 8 < x_ ðtÞ ¼ 5ðyðtÞ  xðtÞÞ y_ ðtÞ ¼ 4xðt  sÞ  xðtÞzðtÞ þ yðtÞ : z_ ðtÞ ¼ xðtÞyðtÞ  zðtÞ

ð12Þ

According to Eq. (6) we can get the equation about x: x6 þ 27x4  349x2  375 ¼ 0 this equation yields the only positive root x ¼ 3:213 and  Solving  2 g x0 ¼ 527:78 [ 0. According to the conclusion (8), the time-delay coefficient s ¼ 0:2176 can be calculated. The above conclusion is translated into: When the system parameter a ¼ 5; b ¼ 1; c ¼ 1 (b) When s  0:2176 þ 0:6225npðn ¼ 0; 1; 2. . .Þ, system (1) generates Hopf bifurcation at Að0; 0; 0Þ and generates a limit cycle. Combining the above conclusions, using matlab simulation software, the numerical value is brought into the system for simulation, and the state phase diagram of the system under different time-delay terms is given to verify the correctness of the conclusion. Figure 1 below shows the time-series diagram of the system when the lag coefficient s ¼ 0:21. It can be observed from the figure that only about 70 integration times have elapsed from the integration starting point ð1; 1; 1Þ to stabilization, and finally it is stable. Balance point ð0; 0; 0Þ, this result shows that the conclusion (a) is correct. 0

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Fig. 1. System time series with lag coefficient s = 0.21

Figure 2 below shows the system time-series diagram when the lag coefficient s ¼ 0:22. Since the time-delay coefficient has passed the bifurcation point s ¼ 0:2176, according to the conclusion (b), the limit cycle has already been generated. It is also not difficult to observe from the graph that starting from the starting point of the integration ð1; 1; 1Þ, about 5 integration times have entered a stable oscillation, that is, a limit cycle has been generated and continues to stabilize in this state. Conclusion (b) Get a preliminary verification.

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In order to more intuitively observe the actual state of the system under various time-delay coefficients, the projections of the system phase diagrams in the xy plane with three different time-delay coefficients are also given in Fig. 3, and are distinguished by different colors. From Fig. 3, it can be observed that when the time lag coefficient s ¼ 0:21, the system phase diagram is projected to be red, and the system gradually approaches the equilibrium point ð0; 0; 0Þ from the iterative starting point ð1; 1; 1Þ and eventually stabilizes. Balance point. When the lag coefficient s ¼ 0:22, the phase diagram of the system is projected to be blue, and the system does not move closer to the equilibrium point from the iterative starting point ð1; 1; 1Þ. Instead, the system generates a limit cycle, enters the oscillating state, and finally stabilizes. On the limit ring. When the lag coefficient s ¼ 0:25, the phase diagram of the system is projected to be green. At this time, the process experienced by the system is similar to

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s ¼ 0:22. The only difference is that the resulting limit cycles have different amplitudes. After repeated experiments, it was verified that when s  0:2176, the system generates limit cycles and the stability is good, which further verifies the correctness of the conclusion (b). 5 4 3 2 1 0 -1 -2

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4 Application in Wireless Mobile Robot 4.1

The Mathematical Model of a Wheeled Robot

In recent years, many scholars have successfully applied chaotic systems to mobile robots. In 2015, M.J.M et al. [19] successfully developed a chaotic fire fighting robot. There are many other applications, such as cleaning robots [18], mobile robot patrols [20] and so on. The robot’s wire control was successfully implemented in [21]. Soon after, their team implemented wireless control of the robot in reference [22], making the design more practical. However, the simulated trajectories of robots in the existing References all show that the coverage is generally low. Our team is working hard to improve the report on robots in this report. In addition, we also added an infrared obstacle avoidance module to the robot so that the robot can avoid obstacles in actual motion. The world recognized three-wheeled mobile robot navigation equation is [21]: 8 < X_ ¼ vðtÞ cos hðtÞ ð13Þ Y_ ¼ vðtÞ sin hðtÞ : h_ ¼ wðtÞ Where vðtÞ ¼ 12 ðvr ðtÞ þ vl ðtÞÞ in the above Eq. (13), vr ðtÞ is the speed of the left

l ðt Þ wheel and vl ðtÞ is the speed of the right wheel, wðtÞ ¼ vr ðtÞv is angular velocity, L is L the direct distance between two active wheels. The principle of navigation using chaotic system is to replace the left and right wheel linear velocity in the navigation equation with two state quantities in the chaotic equation. The navigation equation and chaotic system are combined into a 6dimensional system, and the motion trajectory of the robot is solved by the fourth-order runge-kutta method. In this report, vr ðtÞ is replaced by xðtÞ, vl ðtÞ by yðtÞ, and the navigation equation is changed into the following equation:

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(

vðtÞ ¼ 12 ðxðtÞ þ yðtÞÞ ðtÞ wðtÞ ¼ xðtÞy L

ð14Þ

In order to better demonstrate the characteristics of the path, we simply transform the Chen system into the following form: 8 < x_ ðtÞ ¼ ayðtÞ  bxðtÞÞ y_ ðtÞ ¼ dxðtÞ  xðtÞzðtÞ þ cyðtÞ ð15Þ : z_ ðtÞ ¼ xðtÞyðtÞ  ezðtÞ By combining Chen’s Eqs. (15) and (14), we can get the following equation: 8 x_ ðtÞ ¼ ayðtÞ  bxðtÞÞ > > > > _ ðtÞ ¼ dxðtÞ  xðtÞzðtÞ þ cyðtÞ y > > < z_ ðtÞ ¼ xðtÞyðtÞ  ezðtÞ X_ ¼ vðtÞ cos hðtÞ > > > > Y_ ¼ vðtÞ sin hðtÞ > > :_ h ¼ wðtÞ

ð16Þ

The above equation describes the navigation of the robot about the Chen system. The motion trajectory image of the robot can be obtained by solving the above equation with matlab. In the previous References, the selected chaotic equation is in the state of chaos, and the coverage rate of robot is very low. In this paper, it is found that the chaotic system in Hopf bifurcation state can also cause the chaotic trajectory of the robot. While the chaotic trajectory is ensured, the motion coverage of the robot is also improved, which is about 80%. In previous experiments, the trajectory of the robot was scattered, while when the system was in the Hopf bifurcation state, the trajectory of the robot was in the center attachment. The trajectory of the robot is similar to that of a chaotic attractor, moving at a certain point. Figure 4 shows the motion trajectory of the simulated robot. 8

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In the above equation a ¼ 35; b ¼ 25; c ¼ 20; d ¼ 8; e ¼ 3. The starting point of the iteration is ðx; y; zÞ ¼ ð0:2; 0:2; 0:1Þ and ðX0 ; Y0 ; h0 Þ ¼ ð0; 0; 0Þ. 4.2

Control Circuit Design

The path simulation results in the previous section are used to control the robot. First, the computer establishes a Bluetooth connection with the robot, and then sends the path data to the Bluetooth module of the robot through the Bluetooth serial port assistant. The microprocessor controls the left and right wheels after receiving the data. The path coverage shown in Fig. 4 is around 82%. This coverage is higher than in previous Ref. Through multiple experiments, we found that when other systems are in Hopf bifurcation state, they can still maintain a high coverage rate. The communication methods used in this report are those in Ref. [25]. We use an external bluetooth to sent chaos signal to wireless mobile robot. After receiving the path signal from the bluetooth module, arduino sends the path data to the left and right wheels in the form of PWM. The control loop selects the existing loop in [22]. First establish a connection between the PC and the HC05 Bluetooth module, use the Bluetooth management software to establish a serial port with the HC05, and send the prepared path data to the HC05 through the serial debugging assistant. The preprogrammed Arduino program on the mainboard will be in sequence. The data is read, then the left and right wheels are turned with the PWM pulse of 0–255, and the above operation is repeated until the drawing of all paths is completed. Due to the measurement error of the vehicle’s track distance L, the trajectory of the vehicle will be different from the numerical simulation during the experiment. The following Fig. 5 shows the experimental results.

Fig. 5. Navigation experiment results of mobile robot

5 Conclusion This paper analyzes the stability of Chen system equilibrium point and Hopf bifurcation parameter with a time delay term. From the theoretical analysis, Hopf bifurcation still occurs in the case of parameters with time-delay. The specific bifurcation parameters are listed in the text, and the dynamics simulation of the bifurcation shows that the theoretical analysis is correct. The combination of chaos theory and mobile robot navigation is currently less studied, mainly because its motion trajectory is not

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predictable. The previous research has successfully realized the wireless control of mobile robots. This paper successfully improves the robot’s motion coverage by changing the navigation equation. From the experimental results, the coverage of the motion trajectory is significantly improved compared with the previous study. The theoretical coverage rate in Matlab simulation is 80%. Due to experimental errors and other factors, the actual coverage may decrease, and it needs to be improved in future research. The nonlinear system with time-delay term has very rich dynamic characteristics, mainly in the high concentration of its attraction domain, which is conducive to navigation research. At present, nonlinear systems have been successfully applied to military UAV navigation, path planning for sweeping robots, etc. I believe that this technology will have better development in the future due to its particularity.

References 1. Lorenz, E.N.: The mechanic of vacillation. J. Atmos. Sci. 20(5), 448–465 (1963) 2. Vaidyanathan, S., Volos, C.: Advances and Applications in Chaotic Systems. Springer, Heidelberg (2016) 3. Azar, A.T., Vaidyanathan, S.: Advances in Chaos Theory and Intelligent Control. Springer, Heidelberg (2016) 4. Vaidyanathan, S., Volos, C.: Advances and Applications in Nonlinear Control Systems. Springer, Heidelberg (2016) 5. Azar, A.T., Vaidyanathan, S., Ouannas, A.: Fractional Order Control and Synchronization of Chaotic Systems. Studies in Computational Intelligence, vol. 688 (2017) 6. Li, J.: Dynamic analysis and sliding mode control of fractional-order memristor chaotic circuits. Anhui University (2017) 7. Min, F., Wang, Z., Cao, G.: Analysis of multi-steady state characteristics of chaotic circuit of bimemristor based on hyperbolic function. Acta Electronica Sinica 46(2), 486–494 (2018) 8. Liang, L.I., Qingbin, L.I., Beixing, M.: Chaos synchronization for fractional-order synchronous motor systems. Henan Sci. (2017) 9. Jingbo, C., Ping, F., Hong, T., et al.: Chaos secure communication research based on feedback regulating function projective synchronization. Comput. Digit. Eng. (2017) 10. Lu, L., Li, Y., Wei, L.: Chaos synchronization of regular network based on sliding mode control. Acta Physica Sinica 61(12), 120504 (2012) 11. Lin, S., Jiang, L., Wang, C.: A three-dimensional encryption orthogonal frequency division multiplexing passive optical network based on dynamic chaos-iteration. Acta Physica Sinica 67(2), 282–290 (2018) 12. Dongsheng, X., Yongtao, L.: Study on application of chaotic dynamic behavior in multi degree of freedom robot. Comput. Measur. Control 25(1), 70–73 (2017) 13. Li, J.X., Meng, R.: Global positioning method of intelligent warehousing robot. Ind. Control Comput. 29(9), 85–86 (2016) 14. Ren, J., Yu, Q., Yao, J.: Study on nonlinear dynamic characteristics of multi-stage planetary gear train of shield tunneling machine. Mech. Drive (9), 45–50 (2017) 15. Zhang, C.: Path planning for robot based on chaotic artificial potential field method. Sci. Technol. Eng. 317(1), 012056 (2011) 16. Volos, C., Kyprianidis, I.M., Stouboulos, I.N.: Motion control of robots using a chaotic truly random bits generator. J. Eng. Sci. Technol. Rev. 5(2), 6–11 (2012)

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17. Ni, J., Yang, S.X.: A fuzzy-logic based chaos ga for cooperative foraging of multi-robots in unknown environments. Int. J. Robot. Autom. 27(1), 15–30 (2012) 18. Palacin, J., Salse, J.A., Valganon, I., Clua, X.: Building a mobile robot for a floor cleaning operation in domestic environments. IEEE Trans. Instrum. Meas. 53, 1418–1424 (2004) 19. Tavera, M.J.M., Dutra, M.S., Diaz, E.Y.V., Lengerke, O.: Implementation of chaotic behaviour on a fire fighting robot. In: Proceedings of the 20th International Congress of Mechanical Engineering, Gramado, Brazil, November 2015 20. Tavera, M.J.M., Lengerke, O., Dutra, M.S.: Implementation of chaotic behavior on a fire fighting robot. In: Mechatronics Series. Intelligent Transportation Vehicles (2012) 21. Sambas, A., Vaidyanathan, S., Mamat, M.: A 3D novel jerk chaotic system and its application in secure communication system and mobile robot navigation. Studies in Computational Intelligence, vol. 636, pp. 283–310 (2016) 22. Sundarapandian, V., Aceng, S., Mustafa, M.: A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot. Arch. Control Sci. 27(4), 541–554 (2017) 23. Li, D., Lian, Y.: Hopf bifurcation analysis of the delayed Lorenz-like system. J. Math. 30(3), 7–11 (2015) 24. Wenjuan, L., Xiaomeng, N., Xvchao, L., et al.: Hopf bifurcation analysis of the disturbed Lorenz-like System with the delayed. Pure Appl. Math. 33(5), 475–485 (2017) 25. Chen, G., Lv, J.: Dynamic Analysis, Control and Synchronization of Lorenz System Family. Science Press, Beijing (2003)

The Driver-in-the-Loop Simulation on Regenerative Braking Control of Four-Wheel Drive HEVs Hexu Yang1,2(&), Xiaopeng Li1, Pengxiang Li2, and Yu Gao2 1

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China [email protected], [email protected] 2 School of Mechanical Engineering, Ningxia Institute of Science and Technology, Shizuishan 753000, China

Abstract. Nowadays, the environmental problem is becoming more and more serious, attracting the attention of most people. Automobiles emission pollution has a great influence on environment, so the development of vehicles requires more efficient and cleaner. Regenerative braking is an effective method for hybrid electric vehicle (HEV) to improve fuel efficient. In this paper, firstly, the dynamics of the target vehicle was verified according to the selected parameters, including acceleration and climbing conditions. Then, a control strategy based on the parallel hybrid electric vehicle was proposed. Finally, in order to verify the control strategy’s effectiveness and real-time performance, a driver-in-theloop real-time simulation platform for HEVs was built up based on the Development to Production (D2P) product-level controller, which can reduce development costs and is easy to implement. The results show that the proposed regenerative brake control strategy has good real-time performance. Keywords: Hybrid electric vehicle Driver in the loop simulation

 Control strategy  D2P 

1 Introduction The problems of environmental pollution and energy crisis are becoming more and more serious. Environmental issues require the development of the vehicle must be toward to the direction of low pollution and high efficiency [1]. Including hybrid electric vehicle, pure electric vehicle, and fuel cell electric vehicle, when the vehicle is braking, compared to conventional cars, these types of electrified vehicles can be recharged by generators and stored in the batteries. Thereby, these types of electrified are an effective way for the vehicle to extend the mileage compared with traditional automobile [2].

This project is supported by National Natural Science Foundation of China (Grant No. 51875092), The Fundamental Research Funds for the Central Universities (N170302001) © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 214–222, 2020. https://doi.org/10.1007/978-981-32-9941-2_18

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Nowadays, regenerative braking technologies is widely used in electrified vehicles, in order to improve the efficiency of this technology, more and more scholar study about regenerative braking. HAN etc. proposed an adaptation regenerative brake torque optimization method using under-steer index to recover optimal braking energy for front wheel drive HEV, and by CARSIM software to verify the effects [3]. Maia etc. proposed a fuzzy logic model of regenerative braking to distribute the ratio of regenerative braking force [4]. Xu etc. proposed a braking system using only electric motors/generators as the actuators with a hierarchical control structure [5]. Kim etc. aimed at a four-wheel-drive hybrid electric vehicle using rear motor driving as the research object and proposed a stability enhancement control algorithm, using ADAMS and MATLAB Simulink simulations [6]. All of the above papers are off-line simulation. Using off-line simulation can short the development cycle and reduce costs. But it can’t reflected the real-time of the control strategy and ignore the driver’s impact on the vehicle. Based on the issue discussed in the article, the proposed effect of regenerative braking is accurately studied. This paper takes a four-wheel hybrid vehicle as the research object. In the study, author carried out the-driver-in-the-loop simulation for HEV using rear motor control. This paper mainly studies the of the control usage strategy of the parallel hybrid electric vehicle. A driver-in-the-loop real-time simulation platform for HEVs was built up based on the development to Production (D2P) of product-level controller. And the regenerative brake control strategy is proposed and simulated under acceleration and climbing conditions. Compared with offline simulation, the driver-in-the-loop real-time simulation can verify the real-time effect. Therefore, it is of great importance to study this kind of model in the loop simulation. The remainder of this paper is organized as follows: the analysis of vehicle dynamics is described in Sect. 2. The braking force distribution strategy and driver in the loop real time simulation system are proposed in Sect. 3. Simulation results and analysis are carried out in Sect. 4, and conclusions are given in Sect. 5.

2 Analysis of Vehicle Dynamics In this paper, the target model is different from the conventional parallel hybrid electric vehicle. The electric motor and the engine drive the front and rear wheels respectively, and the torque is coupled by the ground. This structure simplifies the torque coupling structure and that can achieve four-wheel drive under certain conditions. Figure 1 shows the structure of a hybrid electric vehicle with rear axle electric drive vehicle that is proposed in this study. In this section, firstly, according to the driving equation of vehicle, the selected parameters of the vehicle were shown on the Table 1. Then, in order to verify the selected parameters meeting the performance requirements of vehicle, we passed through simulation on the different road conditions in this paper. The results were shown in the Figs. 2 and 3.

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Charge

Transimission

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Fig. 1. The structure of rear axle electric drive vehicle Table 1. Key parameters of target vehicle Name Maximum engine power Electric motor power Battery capacity Vehicle loaded mass Gearbox Air resistance coefficient Windward area Number of batteries Rolling resistance coefficient Wheel radius

Value 40 KW 49 KW 45 Ah 1400 kg 3.52, 2.04, 1.40, 1 0.301 2.05 m2 25 0.012 0.315 m

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Fig. 3. Climbing map of rear axle electric drive vehicle

Figure 2 is an acceleration diagram of a rear axle hybrid electric vehicle on different road surfaces with varying coefficients of adhesion. From the experimental data, it can be seen that the acceleration value of rear-wheel drive electric vehicle increases with time in 0–60 s when the vehicle is on the road with good adhesion. This changing trend is related to the size of the adhesion coefficient. The larger the adhesion coefficient, the more obvious the acceleration increase value. The slope of change trend decreases obviously after 60–80 s, and gradually reaches the critical value. After the 80 s, the critical value of acceleration remains constant, and the higher the adhesion coefficient, the higher the critical value of acceleration. The blue line shown in Fig. 2 shows that the vehicle has high acceleration, and the maximum speed can reach 200 km/h. Even if the road surface does not have good adhesion conditions, such as the adhesion coefficient shown by the red line is only 0.3, the maximum speed can reach 150 km/h. Therefore, we can conclude that the selected parameters can meet the acceleration requirements of the vehicle. Figure 3 is a climbing map of the target vehicle on different slopes of the road. The climbing ability of rear wheel drive electric vehicle is related to the gradient of the road surface. The smaller the gradient of the road surface, the stronger the climbing ability, the larger the gradient of the road surface, the weaker the climbing ability of the vehicle. As can be seen from Fig. 3, when the gradient of the road surface is 9°, the climbing ability of the vehicle is strong, and the maximum speed can reach 100 km/h. When the gradient of the road surface increases to 16°, the climbing ability of the vehicle is slightly weaker, but the maximum speed can also reach 60 km/h. Therefore, the matching parameters can meet the climbing requirements of the vehicle. From what has been discussed above, we can get the conclusion that the target model can get better power when the road conditions are poor or the torque requirements are large. Therefore, the study of this type of vehicle is very necessary.

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3 Regenerative Braking Control Strategy In this paper, development of control strategy must ensure the braking safety as much as possible on the recovery of braking energy. The specific process is shown in Fig. 4. When the vehicle is braking, the Electronic Control Unit (ECU) calculates the required braking force through the change of the brake pedal travel. Then, brake force distribution between front and rear axles is determined by the braking strength z. The braking force of the front wheels is supplied by mechanical brake system braking, and the braking force of the rear wheels is supplied by regenerative braking force and mechanical braking force. The size of the regenerative brake force is determined by many factors such as motor maximum braking power and maximum charge power of the battery. Start Total braking force F b Distribution strategy of braking force

> ϕ



G ϕ (a − ϕ × hg) L Fbf = Fb − Fbr

G (a − Z × hg) L Fbf = Fb − Fbr

Fbr = GZ

Fbr =

Fbr = Z

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Limiting factor Motor maximum braking power Pmotor

Maximum charge power of the battery Pbat

SoC fs  Pv > fs  Ps > Pv  Ps > Ps > Pv. Relation diagram of effective curves is shown in Fig. 6. It can be seen that if interaction effect is not considered, stiffness volatility is optimal when fs values level 3, Pv values level 4 and Ps values level 2. Namely, stiffness volatility has a minimum value of 4.272 N/lm when area ratio values 30%, vacuity values −50 kPa, and positive pressure values 0.4 MPa. This value is better than any of the cases calculated above. It means that we do obtain a relatively optimization.

100 90 80

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12345 12345 12345 12345 12345 12345 factor level

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Optimization of Average Stiffness Under Operating Conditon

Change of average stiffness is analyzed below. Average (Ki) and extreme difference (R) of each level are shown in Table 5.  Table 5. Visual analysis of results of K

K1 K2 K3 K4 K5 R

Factor ns 304.1 275.9 328.4 333.3 251.5 81.8

Pv 218.4 279.7 281.1 343.1 371 152.6

ns  Pv 340.7 301.1 255.9 292.4 303.2 84.7

Ps 204.7 287.4 323.1 342.1 336 137.5

ns  Ps 311.1 294.3 320.8 290.5 276.6 44.2

Pv  Ps 320.2 301.8 319.5 268.4 283.3 51.8

Extreme difference of vacuity Pv and positive pressure Ps are significantly larger than other factors. That means that these two factors have more influence on average stiffness. Degree of effect ranks like this: Pv > Ps > fs  Pv > fs > Pv  Ps > fs  Ps. Relation diagram of effective curves is shown in Fig. 7. It can be seen that if interaction effect is not considered, average stiffness is optimal when fs values level 4, Pv values level 5 and Ps values levels 4. Maximum of average stiffness is 499 N/lm when area ratio values 35%, vacuity values −60 kPa, and positive pressure values 0.6 MPa. This value is also better than any of the cases calculated above. 380 360 340

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Synthesis Optimization

Optimization of the two performance objects are been obtained respectively in previous analysis (summarized in Table 6). It shows that there are different choices of parameter combination when pursuing different requirements. Too large stiffness is not necessary in some applications. Conversely, a small performance difference of stiffness under different operating condition is required to make equipment predictable and stable. In this situation, we choose the first optimization in Table 6 which has little stiffness volatility. If we need sufficient stiffness, the second optimization is better. Table 6. Optimum scheme of the VPL pad N Optimization object Parameter combination Results  (N/lm) Pv (KPa) Ps (MPa) Sv fs K 30% −50 0.4 4.272 334.07 1 Sv  2 K 35% −60 0.6 23.64 499.17

5 Conclusions In this paper, a new index is defined to express performance of VPL pad under operating condition. A better static performance is obtained by orthogonal method. The findings are summarized as below. (1) Stiffness volatility is considerable while parameters of VPL pad are incongruous. (2) Vacuity, area ratio and positive pressure distinctly influence performance of VPL pad. Stiffness volatility grows when value of parameters is relatively small or large. (3) Orthogonal method is effective to optimize performance of VPL pads with multiply parameters. Computing quantity is reduced obviously. (4) Extreme value of average value and stiffness volatility infrequently emerge together. Selection of optimization of performance object is based on actual application.

References 1. Raparelli, T., Viktorov, V., Colombo, F., et al.: Aerostatic thrust bearings active compensation: critical review. Precis. Eng. 44, 1–12 (2016) 2. Chen, C.H., Tsai, T.H., Yang, D.W., et al.: The comparison in stability of rotor-aerostatic bearing system compensated by orifices and inherences. Tribol. Int. 43(8), 1360–1373 (2010) 3. Miyatake, M., Yoshimoto, S.: Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed holes. Tribol. Int. 43(8), 1353–1359 (2010) 4. Zhao, G., Belyaev, A., Wolters, C.H., et al.: Stabilizing a substrate using a vacuum preload air bearing chuck: US, US7607647, 27 October 2009

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5. Yandayan, T., Akgoz, S.-A., Asar, M.: Calibration of high-resolution electronic autocollimators with demanded low uncertainties using single reading head angle encoders. Measur. Sci. Technol. 25(1), 303–309 (2014) 6. White, J.: Air bearing slider-disk interface for single-sided high speed recording on a metal foil disk. J. Tribol. 129(3), 562 (2007) 7. Schenk, C., Buschmann, S., Risse, S., et al.: Comparison between flat aerostatic gas-bearing pads with orifice and porous feedings at high-vacuum conditions. Precis. Eng. 32(4), 319– 328 (2008) 8. Zhu, H., Li, Y., Lin, Y., et al.: CFD investigation on the performance of aerostatic thrust bearing with exhaust slots used in low-vacuum condition. Mems-12 (2012) 9. Liu, S.-S., Chen, H., Chen, X.-D.: Experimental investigation of static characteristics of a vacuum preloaded aerostatic bearing. Adv. Mater. Res. 311–313, 1012–1016 (2011) 10. Huang, M., Xu, Q., Li, M., et al.: A calculation method on the performance analysis of the thrust aerostatic bearing with vacuum pre-load. Tribol. Int. 110(Suppl. C), 125–130 (2017) 11. Wang, N., Kong, P.-H.: A simulated air bearing analysis by design of experiments and its applications in optimization. Tribol. Trans. 44(4), 597–602 (2001) 12. Shinde, A.B., Pawar, P.M.: Multi-objective optimization of surface textured journal bearing by Taguchi based grey relational analysis. Tribol. Int. 114, 349–357 (2017) 13. Jia, X., Guo, F., Huang, L., et al.: Parameter analysis of the radial lip seal by orthogonal array method. Tribol. Int. 64(3), 96–102 (2013) 14. Wang, N., Tsai, C.M., Cha, K.C.: Optimum design of externally pressurized air bearing using cluster Openmp. Tribol. Int. 42(8), 1180–1186 (2009) 15. Wang, N., Cha, K.C.: Multi-objective optimization of air bearings using hypercube-dividing method. Tribol. Int. 43(9), 1631–1638 (2010)

A Study on Innovative Design of Rotary Pile Foundation Drilling Machine Based on TRIZ Theory Fuxing Li(&) Qilu University of Technology (Shandong Academy of Sciences), Jinan, China [email protected]

Abstract. Whereas such problems as small borehole diameter and low efficiency occur in the operation process of rotary pile foundation drilling machine, this paper puts forward an innovative design method based on the TRIZ theory and comes up with the detailed solution to the conflicts, through the use of the contradiction conflict solution matrix comprised by 39 engineering parameters and 40 pieces of inventive principles pertaining to TRIZ, in the aspects of borehole diameter enlargement and operation efficiency improvement. Furthermore, this paper has manifested the feasibility to conduct TRIZ-theory-based innovative design in the field of engineering machinery, thus providing important theoretical tools for design ideas in the field of traditional engineering innovation. Keywords: TRIZ theory  Rotary pile foundation drilling machine Technical conflict  Innovative theory  Conflict solution matrix



1 Introduction As is well-known to all, prior to the constructions of house, high tower or bridge, etc., pile foundation should be constructed using drilling machine. Rotary-digging pile foundation drilling machine is one of the most frequently-used machines. However, due to the limitation of drill’s diameter, it’s hard to carry out project with largediameter drill hole. Besides, during drilling work, drill at the defined position first, and then elevate the drill to the outside of hole to unload the clump, and finally move the drill back to the hole to continue the drilling process. Repeat the preceding working process until the drill reaches the scheduled depth. In the whole process, to align the “original hole” consumes too much time and seriously lowers the drilling efficiency. To this end, this paper aims to carry out innovative design of rotary drilling rig based on TRIZ theory, so as to enhance its working capacity.

2 TRIZ Theory Summary TRIZ, the Russian abbreviation for “Teoriya Resheniya Izobreatatelskikh Zadatch” (which means Theory of Inventive Problem Solving in English), is the theory system formed through the analysis of nearly 2.5 million high-level patents for invention © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 302–309, 2020. https://doi.org/10.1007/978-981-32-9941-2_26

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worldwide and integration of the theories and rules of multi-disciplinary fields, which was made by the research institution with a former Soviet Union expert named Altshuller as the leader. 2.1

Constitution of TRIZ Theory System

With dialectics, system theory and epistemology as philosophical guidance, the analytic research results of natural science, system science and noetic science as the foundation, and technical system evolution rule as the theoretical basic and core concept, TRIZ theory system includes all kinds of analytic methods, solution tools and algorithm flow that are needed for solving engineering conflict problems and complicated inventive problems [1], as seen in Fig. 1. The application of TRIZ theory can expedite the process of creation and invention to get high-quality innovative products. As regards the innovation design of rotary-digging pile foundation drilling machine, the contents of TRIZ theory, including 39 general engineering parameters, 40 pieces of inventive principles, 39  39 conflict solution matrix, etc., will be used.

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Fig. 1. TRIZ theory system

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Determination of Technical Conflict and Its Solution Procedure

StyFunction is a kind of understanding of product from the angle of technical realization and a kind of abstract description of the changes to parameter or condition when product inputs or outputs under given conditions [2]. Product innovation design starts

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from product function first, and through the analysis of function, points out the ideal function and disadvantageous function, so as to determine the technical conflict. The so-called function: it means an action can result in both advantageous and disadvantageous results at the same time [3], and the results can be solved by utilizing the contradiction solution matrix of TRIZ theory. TRIZ believes the product evolution process is to find out and solve the conflicts constantly so as to boost the product to develop ideally [4]. Therefore, the TRIZtheory-based design process will center upon how to analyze the problem and solve the conflict. TRIZ theory serves to solve the complicated inventive problems which are characterized by technical conflict and physical contradiction, and, via the systemic problem-solving process, shows the designers the most effective solution [5]. Figure 2 shows the product design flow by applying the conflict solution principle of TRIZ theory: firstly, analyze the product function, find out the ideal function and disadvantageous function, and determine its technical conflict; then, use the 39 engineering parameters of TRIZ theory to describe the pre-determined technical conflict; finally, obtain the related inventive principle by querying the conflict solution matrix [6], and conduct the innovation design of product scheme with the inventive principle as the guiding ideology.

Fig. 2. Design process model for TRIZ theory

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3 TRIZ Theory Based Innovation Design Example 3.1

Analysis of Problems in Rotary-Digging Pile Foundation Drilling Machine

Rotary-digging pile foundation drilling machine crushes the rock-soil by rotating the bucket drill which has a valve at the bottom. Put it directly into the drill bucket, and then use the hoisting unit and bumper sub to lift the drill bucket up to unload the clump. Repeat the process to load clump first and then unload it. When the hole has reached the scheduled depth, cast concrete and then a pile is built. In drilling work, the process goes as follows: drill a hole ! lift the drill to unload ! return to the original hole ! drill again. However, it really consumes too much time and energy to pinpoint the original hole, thus severely reducing the work efficiency. In addition, the rotary-digging drilling machine relies on lifting the drill bucket for dislodging. So when the drilling depth is too deep, the drill pipe has to be enlarged, and then time spent on drilling in the hold will be much less than that on lifting the drill and unloading the clump, which will reduce work efficiency. Then, to improve the work efficiency, the drill pipe has to be shortened, while innovative design should be made to the structure of rotary-digging drilling machine to guarantee the drill effect. As a result, the whole set of drilling equipment will be much more complicated. Besides, to enlarge the diameter of drill hole, the diameters of drill pipe and drill bucket should be enlarged as well, i.e., the cross sectional area will be enlarged, which will undoubtedly add to its weight and thus require larger momentum. 3.2

Determination of Technical Conflict

In the working process of rotary drilling rig, the cross section area of drill pipe and its weight constitute technical conflict, while the improvement of drilling efficiency and the complexity of the whole set of drilling equipment also constitute technical conflict. Then, turn the technical conflicts into the 39 engineering parameters, namely: Area of No. 5 moving object: it refers to the geometric measure inside or outside of the moving object, which may be the area in plane profile and also that in threedimensional surface. In this example, it refers to the cross section area of drill and belongs to the improved parameter. Weight of No. 1 moving object: it refers to the force acted by the moving object in gravitational field on the support that prevents the former from free falling. In this example, it refers to the deteriorated parameter [7]. Production rate of No. 39 unit: it refers to the functions performed or quantity operated by the system in unit time; or it refers to the time to complete a function or an operation, which should be the improved parameter. Complexity of No. 36 unit: it refers to the number and diversity of system element and its mutual relationship, which belongs to the deteriorated parameter [8].

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Determination of Inventive Principle

As regards the technical conflict produced during the working process of rotary-digging pile foundation drilling machine, the corresponding inventive principle can be obtained via querying the contradiction solution matrix provided in TRIZ theory, as seen in Table 1.

Table 1. Conflict solution matrix Improved general Deteriorated general engineering parameter engineering 1 Weight of 2 Weight 3 Size of … 36 parameter moving of static moving Complexity object object object of unit 1 Weight of – – 15, 8, 38, … 26, 30, 36, moving object 34 34 2 Weight of static – – – … 1, 10, 26, 39 object 3 Size of moving 8, 15, 29, – – … 1, 19, 26, 24 object 34 4 Size of static – 35, 28, 40, – … 1, 26 object 29 5 Area of moving 2, 17, 29, 4 – 14, 15, 18, … 14, 1, 13 object 4 … … … … … … 39 Productivity of 35, 26, 24, 28, 27, 15, 18, 4, 28, … 12, 17, 28, unit 37 3 38 24

… 39 Productivity of unit … 35, 3, 24, 37 … 1, 28, 15, 35 … 14, 4, 28, 29 … 30, 14, 7, 26 … 10, 26, 34, 2 … … … –

As regards the conflict constituted by “area of moving object” and “weight of moving object”, the 2th, 17th, 29th and 4th inventive principles can be selected. The specific explanations for each inventive principle can be seen in Table 2.

Table 2. Inventive principle and explanation (one) Serial number 2 4 17

29

Principle name

Explanation

Separation principle Asymmetric Dimensional change

Select or separate the key parts of the object

Pneumatic and hydrodynamic

Change the object shape from symmetric to asymmetric Turn the moving or static object in one-dimensional space into that in two-dimensional space, and change the object in two-dimensional space to that in three-dimensional space The solid parts of object can be replaced with pneumatic or hydrodynamic parts, with gas or liquid used for expansion or damping

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As regards the conflict constituted by “productivity” and “complexity of unit”, the 12th, 17th, 28th and 24th inventive principles can be selected. The specific explanations for each inventive principle can be seen in Table 3. Table 3. Inventive principle and explanation (two) Serial number 12

Principle name

Explanation

Equipment principle

24

Mediator principle

28

Replacement of mechanical system

Change the work condition so that the object doesn’t need to be raised or lowered ① Use mediator to transmit certain object or certain medium process; ② Integrate one easily-removable object with another one temporarily Use the electric field, magnetic field or electromagnetic fields that have interaction with the object

With regards the to-be-solved problems in rotary digging rig, screen out the inventive principles and then the 2th, 17th, 24th, 29th inventive principles are selected, which will be the guiding ideology for innovation design of rotary digging rig. No. 29 pneumatic and hydrodynamic structure principle: use the pressure difference produced from power plant, suck in the drilled rock-soil to unload to the outside of drill hole so that the drill hole and soil unloading can work at the same time to improve the efficiency of drill work; No. 17 dimensional change principle: the drill can rotate in the vertical direction and revolve in the horizontal direction, so as to enlarge the diameter of drill hole; No. 2 separation principle: place the dislodging passage outside of the pile foundation drilling machine to separate it from engine body par, so as to facilitate the elimination of muck and control the muck; No. 24 mediator principle: use the support frame to put up the drilling machine and wind-power unit, so as to leave work space for drill bit and suction headpiece and other units and enable the whole set of equipment to go down along with the increase of drilling depth.

4 Design Scheme for Ultra-large Diameter Pile Foundation Drilling Machine To use the ultra-large diameter pile foundation drilling machine, fix the position of cement caisson circle (18) first on the ground, place the track frame (9) and rotary support frame (4) sequentially on cement caisson circle (18), adjust the earthling positions of drill bit (17) and sucker (10); then, unlock the adjustable-speed motor (3) and wind motor (8), via the driving gear (12), the adjustable-speed motor (3) can drive the input gear (13) and drill spindle (2) to rotate; at the same time, via the carrier gear (1), the input gear (13) can drive the running gear (15) to rotate, so as to rotate and revolve around the central axis at the same time; wind motor (8) can drive the wind wheel (6) to rotate and form the high negative pressure, which sucks the drilled rocksoil into the air conveying pipe (5) and thus exhausts the soil outside of the pipe; when

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the drill hole reaches a certain depth, new cement caisson circle (18) can be added, however, the second cement caisson circle (18) should leave the support part of track frame (9) empty so that the drill rig can dig deep repeatedly. When the scheduled depth is reached, use the hoist to dismantle the drill rig step by step, as seen in Fig. 3. The ultra-large diameter pile foundation drilling machine principle is relatively novel, which changes the traditional drilling principle and can finish projects with ultra-large diameter. However, the whole set of pile foundation drilling machine is bulky, while its structure is not compact. Therefore, more improvements will be made.

Fig. 3. Ultra-large diameter pile foundation drilling machine structure principle

5 Conclusions By applying the conflict solution principle of TRIZ theory, conduct innovation design on traditional rotary-digging pile foundation drilling machine to enable the drill to rotate in the vertical direction and meanwhile revolve in the horizontal direction of the center axis of rotary table, so as to enlarge the diameter of drill hole; use wind power installation to discharge the drilled rock-soil directly, thus reducing the time spent on repetitive soil-casting. Besides, adjust the activity range of drill and suction headpiece on the pile foundation drilling machine so as to meet with the requirement for diameter in actual working condition and thus make it the orientation for improvement. The application of TRIZ theory to conduct innovation design on rotary-digging pile

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foundation drilling machine verifies the feasibility to use this theory to conduct innovation design in the field of engineering machinery, so as to provide a new theoretical tool for the development and design of related product.

References 1. Ren, G.: Research the effect of industrial design to product maturity based on TRIZ. Mach. Des. Manuf. 3, 264–265 (2009) 2. Lu, X.: Product innovation design based on the theory of TRIZ and functional analysis. Mach. Des. Manuf. 12, 255–257 (2010) 3. Zhang, J.: Innovation design of products based on TRIZ theory. J. Mach. Des. 2, 35–37 (2009) 4. Fu, M.: Reviews on integrated innovation methods for TRIZ-based product design. Chin. J. Constr. Mach. 2, 170–174 (2013) 5. Hou, L.: Optimal design for dry filter clip based on TRIZ theory. Mach. Des. Manuf. 7, 240– 242 (2011) 6. Chen, S.: Innovative design of new wire-saw winding equipment based on TRIZ theory. Mach. Des. Manuf. 1, 4–6 (2013) 7. Tan, R.: Study on the conceptual design process based on QFD and TRIZ. J. Mach. Des. 9, 1– 4 (2002) 8. Li, F.: Innovation design of road roller based on the conflict solving principle of the TRIZ. J. Mach. Des. 98–111 (2014)

Design and Optimization of Focusing X-Ray Telescope Based on Intelligent Algorithm Liansheng Li1(&), Zhiwu Mei1, Jihong Liu2, Fuchang Zuo1, Jianwu Chen1, Hanxiao Zhang1, Hao Zhou1, and Yingbo He1 1

2

Beijing Institute of Control Engineering, Beijing 100191, China [email protected] School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

Abstract. Focusing X-ray telescope (FoXT) is widely used in space science detection, pulsar navigation and timing, space X-ray communication, etc. In order to improve the performance and reduce the weight of FoXT, this paper proposes a FoXT design and optimization method based on intelligent algorithm. Firstly, based on the X-ray total reflection theory, a multi-objective optimization model with maximum effective area and light weight is formulated. The Pareto non-inferior solution set of the product is obtained using the nondominated sorting genetic algorithm (NSGA-II). With data mining methods such as cluster analysis and association analysis, the implicit correlation characteristics and variation rules between design parameters and optimized solution sets are studied. The influence of parameters such as X-ray optic length, optical aperture and nested layer on effective area is revealed. The distribution of focal length and optical aperture ratio, effective collection area and weight ratio are implemented with statistical analysis. Finally, five sets of design optimization solutions are selected according to practical engineering development capability and cost, which provides theoretical basis for design and optimization of FoXT. Keywords: Focusing X-ray telescope Intelligent algorithm

 Multi-objective optimization 

1 Introduction With the advantages of high angle resolution, low background noise, and large collecting areas, the focusing grazing incidence X-ray telescope (FoXT) gained more and more attentions. Especially, due to recent advancements in fabrication technology, multilayer mirrors open a wide range of possibilities in the field of X-ray astronomical telescope, X-ray pulsar navigation and timing [1], space scientific exploring, and deep space exploration, etc. [2]. As an X-ray astronomical instrument, how to improve the inherent characteristics and performances is a very import thing. With the actual demand for aerospace This project is supported by National Natural Science Foundation of China (Grant no. 51175019), The National Key Research and Development Program of China (Grant No. 2017YFB0503300). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 310–324, 2020. https://doi.org/10.1007/978-981-32-9941-2_27

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engineering, this requires an instrument with the large effective area, high sensitivity and the lowest possible weight, volume, and power. Actually, the focusing grazing incidence X-ray telescope is a typical complex space product which involves coupled structure, optics, thermal, electrics etc. In addition, the enhancement of effective collecting area that means the telescope has longer focal, bigger optical aperture and more multi-layer nested mirrors. As a result, the weight of FoXT will increase dramatically with the improvement of efficient collecting area. Obviously, the optimization of FoXT is a multi-objective optimization problem (MOOP) due to conflicting nature of effective collecting area and weight. Currently, researches of focusing X-ray telescope are mainly focus on the optimization of optical performance or other single objective. A figure-of merit that accounts for the coating response over a specified range of energies and off-axis angles is developed by Mao et al. [3], which presents a deep understand of optical performance and coating thickness. Take the reflectivity of X-ray mirrors as an optimization objective, an extensive numerical method is used by Biskach et al. [4] to obtain the optical solutions based on analytical method with oversimplified analytical and semiempirical formulation. A ray-tracing simulation method is proposed by Mitsuishi [5] to investigate the optical performance of ultra-lightweight X-ray optics prepared for the future Jupiter exploration mission. Conconi et al. [6] employs a weighted merit function method to carry out the multi-objective optimization of wide field X-ray telescope, considering the angular resolution and effective area simultaneously. To improve focusing performance of large X-ray observatory, the size optimization of mirror segments for X-ray optics has been implemented by Zhao et al. [7]. With the method of ray tracing and finite element analysis considering the thickness, axial length, azimuthal span and mass density. Obviously, conventional single-objective optimization methods are always employed to optimization the grazing incidence X-ray telescope, which may obtain a local or a subjective optimal result that far from the engineering tradeoff solutions. In engineering design, for a designer, it is important to know a number of optimal solutions that gives lot of insight into the design thereby providing lot of feasible and useful design solutions. Over the past decades, a number of multi-objective evolutionary algorithms (MOEAs) have been suggested [8]. The NSGA-II is adopted in this paper to implement multi-objective optimization of the focused X-ray telescope. Meanwhile, the influence of multivariate on the effective collection area is analyzed based on data mining method. Using mathematical statistics to analyze the distribution characteristics of focal length optical aperture ratio and effective collecting weight ratio, this is expected to summarize the theoretical basis for similar design optimization. Finally, five sets of optimization solutions were selected considering the development cost and capability, and then the correctness of the optimization results was verified by simulation.

2 Focusing X-Ray Telescope FoXT is a complex product involving multiple disciplines such as opto-mechanical, electronics and thermal, which includes Wolter-I optical system, detector, electronics and structure, as shown in Fig. 1. Based on the total reflection theory, the Wolter-I

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optics reflect and focus the X-ray photons onto a small detector. The high efficiency of FoXT and the small size of the detector’s size help to minimize background radiation, allowing for a relatively high signal-to-noise readout.

Fig. 1. Focusing grazing incidence X-ray telescope

(1) Focusing X-ray optics. The focusing X-ray optics is made up of concentric foil mirrors. The mirrors concentrate X-rays onto a small detector area using a single bounce, in contrast to typical imaging X-ray optics that require two bounces and thus incur a significant efficiency penalty to achieve quality imaging. Unlike the typical Wolter-I, the FoXT is not imaging optics, X-rays undergo a single reflection. The absence of secondary mirrors increases efficiency and decreases weight and assembly complexity. (2) Detector. The silicon drift detector is employed in this paper, which has very high quantum efficiency over the photon energy range of interest. Due to the fact that the detector is read out by dual-channel electronics chains, therefore, both high time resolution (100 ns) and excellent spectral resolution (150eV) with very low dead time. In addition, the SDD include integrated thermoelectric coolers (TECs) and thermal/optical-blocking filters. SDDs offer energy resolutions typical of silicon-based detectors, approaching the Fano limit. (3) Electronics subsystem. The electronics subsystem includes the detector readout, slow and fast shaper, peak detect, event logic and power electro circuit, which aims at obtaining high signal-to-noise ratio in dealing with the faint X-rays radiated from pulsars. (4) Mechanical structures. The mechanical structures of FoXT are composed of mirror structures, optical bench and flange, which holds the optical and detector systems in a compact, co-aligned assembly, providing mechanical rigidity, thermal stability.

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3 Multiobjective Optimization Model 3.1

Design Variables and Parameters

Large effective collecting area can be achieved by nesting multiple co-aligned, co-axial grazing-incidence mirror pairs in order to optimize the available aperture. Consequently, large-effective-area X-ray telescopes must use thin, lightweight mirrors to achieve a high degree of nesting and acceptably low weight. In addition, the focal length and weight should be considered during the design and development simultaneously due to the some exhibitions of the rocket. As a result, both minimum of reciprocal of area (f1) and weight (f2) are chosen as the optimization objectives. The design variables and parameters are shown in Tables 1 and 2. Table 1. Design variables of FoXT w t h n L* Rd [120, 150] [3, 5] [0.3, 0.5] [2, 4] [1.0, 1.5] [5, 30] *L: Length of mirrors (mm) Rd: Radius of detector (mm) w: Thickness of mirrors (mm) t: Thickness of tube (mm) h: Grazing incidence angle (°) n: number of multilayer mirrors

Table 2. Design parameters of FoXT qtube FOV* h qm 0.125° 0.6 [0.3, 0.5] [2, 4] *FOV: Field of view h: Reflectivity (mm) qm: Density of Ni qs: Density of Al

3.2

Optimization Model

In order to formulate the multi-objective function, we give the schematic of multi-layer nested Wolter-I mirrors that arranged from inner to outer in Fig. 2. The ri1 denotes the inner radius of the ith bottom layer, whereas the ri2 represents the inner radius of the ith upper layer.

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r12 r22

L

w

r21=r12-w r11

w

Fig. 2. The schematic of multi-layer nested X-ray mirrors

3.2.1 Effective Aera All the income X-ray photons from the FOV of FoXT should be focused on the small detector after reflected by the Wolter-I mirrors. Therefore, the focal length of FoXT can be calculated by the Eq. (1) when both the radius of detector and FOV are known. f ¼

Rd tanðxÞ

ð1Þ

The focusing X-ray mirrors is a single reflection focusing mirror, because it is used to collect the number of focused X-ray photons only, but not imaging. As a result, the X-ray mirrors includes a parabola mirror, the surface formula of which can be depicted by Eq. (2). y ¼

1 rci  x2  2rci 2

ð2Þ

where, rci is the curvature radius of each nested mirror, i denotes the number of nested layer. Generally, the surface formula of parabola can be simplified as Eq. (3) in engineering design, because the curvature radius are always tiny. y ¼

x2 2rci

ð3Þ

When x equals to ri1, the function value of Eq. (3) is just the focal length. ri1 ¼

pffiffiffiffiffiffiffiffiffi 2rci f

ð4Þ

And also, the ri2 can be derived when the length of mirror (L) is known, which can be expressed as following.

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ri2 ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2rci ðf  LÞ

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ð5Þ

Obviously, there is a recursive relationship between ri1 and ri2, shown in Eq. (6). ri2

sffiffiffiffiffiffiffiffiffiffiffiffiffi L ¼ ri1 1  f

ð6Þ

Meanwhile, the FOV of FoXT should not be obscured by the nested mirrors. We can derive the following relationship between any two layered nested mirrors. rði þ 1Þ;2 ¼ rðiÞ;1  w

ð7Þ

As a result, the total effective collecting area of FoXT which has n layered nested mirrors can be represented by Eq. (8). 8 n < Aeff ¼ h P pr 2  r 2  i1 i2 i¼1 :f ¼ 1 1

ð8Þ

Aeff

3.2.2 Weight In this paper, only the weight of mirrors and structures are considered.   f2 ¼ Min Woptics þ Wtube

ð9Þ

where, f2 is the weight of FoXT, Woptics is the weight of multi-layer nested mirrors, Wtube denotes the weight of optical tube. According to [9], the ratio of effective area and weight of nickel (twice reflected Xray optics) is about 10. Since the single reflection of X ray optics is adopted in this paper, the ratio of effective area and weight of which can be viewed equal to 33.3, which the reflectivity of X-ray optics is 0.6. So, the total weight of X-ray optics can be calculated by the following Eq. (10). Woptics ¼

n  2  3 X 2 g p ri1  ri2 100 i¼1

ð10Þ

The mirror structure is a cylinder minus a circular truncated cone, the weight of which can be derived by Eq. (11). h i Wtube ¼ pf qtube ðRto þ tÞ2  R2to

ð11Þ

Where, Rto is the inner radius of mirror structure, t is the thickness of tube. As a result, the multi-objective optimization model of FoXT can be formulated as Eq. (12).

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Min : ðf1 ; f2 Þ 8 1 f1 ¼ P > n > > h p < ðr2 r2 Þ i1

> > > : f2 ¼

i¼1

3 100 h

i2

h

n  2  P 2 p ri1  ri2 þ pf qtube ðRto þ tÞ2  R2to

i

ð12Þ

i¼1

4 Nondominated Sorting Genetic Algorithm II 4.1

Main Idea

With the aim of minimizing the weight and reciprocal effective area of FoXT, the Nondominated sorting genetic algorithm-II (NSGA-II) is adopted to obtain the Pareto frontier. With the elitist strategy, the NSGA-II sorts the set of solutions according to their fitness (or objective values) and then selects the best solutions as parents for the next generation in every generation. Non-dominated Pareto frontier at each generation are found. The main characteristic of NSGA-II includes: (1) the computational complexity is reduce dramatically with the adoption of ranging strategy-based fast non-dominated sorting method. (2) the elitist preserve strategy is adopted to make sure the paternal progeny population have competition capability, and thus avoid of losing the non-dominated solution. (3) using a module of multi-dimensional vector to avoid local minima. 4.2

Procedures

The procedure of NSGA-II is shown in Fig. 3.

Initialization of DV Setting Pareto MOOP parameters

Create/Update current Pareto frontier

Stopping criteria is met? Yes

No

Create new population by genetic manipulation

Output the final Pareto frontier End

Fig. 3. The procedures of NSGA-II

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The steps of procedures are as followings: Step1: Initialization. Setting the design parameters of FoXT. Step2: Pareto optimization. Setting the parameters of population type, number of population, iterations, cross function, Pareto front coefficient, and then implementing the global optimization. Step2.1: Select the reasonable fitness of individual distribution, facilitating the continuation of optimization and near to the Pareto front gradually. Assign the fitness for each individual and thus they have individual replication probability. The calculation of fitness can be expressed as Eq. (13). Fitn V ð pÞ ¼ 2  ps þ 2ðps  1Þ

p1 Mc  1

ð13Þ

where ps is a selecting coefficient, which has the range of values [1, 2], p is the position of individual in the ranking population, FitnV(p) is the fitness of the individual at the p position, Mc represents the number of individual in the population. Step2.2: Elitist preserve strategy. Select Nc individuals that ranked ahead of the elitist storage library according to the ranking result of Step2.1. After the genetic manipulation of the residual populations, the new produced elitist will be combined with the selected Nc individuals, which are viewed as the new populations that to be implemented with the genetic algorithm. Step2.3: To improve the efficiency of genetic algorithm, it must try to generate as diverse a population as possible in order to avoid local minima. The modified NSGA II uses a module of multi-dimensional vector, the individual fitness value of which is viewed as the wash out rule. The individual fitness value can be expressed as Eq. (14). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fit V ðYi Þ ¼ kfi k ¼ ðfi1 ð xÞÞ2 þ ðfi2 ð xÞÞ2 þ    þ ðfin ð xÞÞ2

ð14Þ

where i and j are two different individuals, when there are lots of objectives have the same ranking number, the minimum distance among them should be calculate accordingly through Eq. (13). The individual will be washed out if the individual fitness value of which less than the given value. This method resolves the problem that when lots of individuals have the same fitness value and ranking order, in which it is difficult to evaluate how to wash out individual according to the fitness value only. Namely, when any two individuals in the same ranking and also the distance between them is smaller enough than the given value, the fitness of each module of multi-dimensional vector can be viewed as the evaluation criterion. Step2.4: Setting the NSGA-II optimization parameters, in which includes the population, selection, reproduction, mutation, crossover, migration and generations. The Pareto solutions can be obtained after implementing the NSGA-II. Step3: End.

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5 Optimization and Data Mining 5.1

Multiobjective Optimization

The design variables and parameters are shown in Tables 1 and 2. The optimization parameters of NSGA-II are as follows: Population (200), iterations number (300), the scattered is employed in crossover function, the Pareto front population fraction is 0.7, and selecting coefficient is 1.5. The Pareto solution of FoXT is shown in Fig. 4. Totally, there are about 350 arrays solutions. 12

Weight W/kg

10 8 6 4 2 0

0.005

0.01 0.015 0.02 1/Effective Aera (1/cm2)

0.025

0.03

Fig. 4. Pareto solutions of FoXT

It is can be seen from Fig. 4, both the weight and the reciprocal of effective area are conflicted optimization objectives. 210 Pareto solutions have been obtained from this optimization, some of which are shown in Table 3. Obviously, both of the two optimization objectives have order of magnitude difference, which provide more chances for designers and engineers to select personal preference solution. Table 3. Pareto frontier L/mm 149.9998 120.0015 147.8684 149.9906 149.9753 149.9755 149.9918 147.8679 149.9995 149.9991 149.9997 144.1223

Rd/mm 3.0000 3.0119 3.0059 3.0083 4.6033 3.3675 3.7808 3.1861 4.1387 3.0009 3.4827 3.0000

w/mm 0.3001 0.3001 0.3157 0.3028 0.3000 0.3001 0.3001 0.3000 0.3000 0.3000 0.3000 0.3001

t/mm 2.0002 2.0000 2.0000 2.0065 2.0000 2.0001 2.000 2.0000 2.0000 2.0237 2.0000 2.0000

h/° 1.4059 1.2000 1.2036 1.2970 1.4941 1.4903 1.4910 1.4915 1.4999 1.4687 1.4999 1.2000

n 29 18 18 24 30 30 29 29 30 18 29 5

A/cm2 125.4304 77.9245 84.2729 104.4371 315.9749 176.8945 220.0687 158.6052 263.1243 126.3477 191.0850 43.453

W/kg 4.1976 3.4570 3.5433 3.8764 9.9467 5.5165 6.8612 4.9591 8.1779 4.2532 5.9132 3.1758

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Data Mining and Analysis

Cluster analysis, correlation analysis are adopted in this paper to mining the optimization results. The statistical characteristics of focal, diameter of X-ray optics, ratio of effective area and weight, and the law of influence some design variables exerted on the multi-objective have been researched. 5.2.1 The Influence Design Variables on Effective Area According to Eq. (8), the effective area of FoXT is closely related to the aperture and length of X-ray optics, number of nested layers. (1) Length of X-ray optics The Pareto solution that have the approximately same values are selected to implement the data analysis, and with the hope of finding some law of influences. The function shown in Fig. 5 can be fitted according to the optimization solutions. The maximum error, minimum error and mean square error of fitting errors are 0.0203 mm, 0.01887 mm and 0.009151 respectively. yAeff ¼ 0:0024x2L þ 0:9352xL þ 87:2141

ð15Þ

Effective Aera of X-ray Optics (A/cm2)

174 172 170 168 166 164 120

125

140 145 130 135 Length of X-ray Optics (L/mm)

150

Fig. 5. Length of X-ray optics and effective area

(2) Diameter of X-ray optics Through statistical analysis of optimized data, we can see that, the aperture of the X-ray optics is proportional to the product of the detector radius and the tangent value of grazing incidence angle. The law of change is shown in Fig. 6. The larger the effective area of each layer corresponding to the large diameter, and the larger the aperture of the optical system, the more the number of nesting layers. If the lengths of the mirrors are the same, the effective collecting area is larger.

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250 225 200 175 150 125 100 1.5 1.45

1.4 1.35

1.3 1.25

1.2 1.15

Grazing incidence angle (°)

1.1

3

3.25

3.5

3.75 4

4.25 4.5

4.75 5

Radius of detector (mm)

Fig. 6. Influence of detector radius and grazing incidence angle on optical aperture

Number of nesting layers: set the other parameters to be the same, the optical aperture selects the maximum and minimum values of the optimized solution are 240.2038 mm, and 115.2672 mm. The variation of effective collecting area from nesting layer from 5 to 30 layers is shown in Fig. 7. There is a common law between the optical effective area and the number of nested layers, which is the effective area gradually increases with the number of nested layers, and the increasingly rate is becoming from faster to slower, and gradually becomes gentle. This is mainly because the outermost optical aperture is large, and the effective collecting area of each layer contributes greatly, and as the optical aperture from the outside is gradually reduced, the effective area of the single layer is increasingly reduced. In the case of the same number of nesting layers, as the optical aperture increases, the effective area increases sequentially, with increases of 50.34%, 50.92%, 53.27%, 57.22%, 60.46%, 63.21%, and 65.19%, respectively.

Effective Aera of X-ray Optics

400 350 300 250

D=240.2mm D=219.3mm D=195.8mm D=173.0mm D=152.2mm D=130.2mm D=115.3mm

200 150 100 50 0 0

4

8 12 16 20 Cases of Pareto Frontiers

24

28

Fig. 7. The influence of the number of nesting layers on the effective area

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5.2.2 Ratio of Focal Length and Effective Area According to the statistical analysis of 210 sets of disaggregation, the ratio of focal length to optical aperture is statistically significant and the distribution is significant, mainly distributed in the following three intervals (as shown in Fig. 8). (1) 9  Df  10 : 174 (2) 10  Df  11 : 10 (3) Df  11 : 26

12

Focal/Diameter of X-ray optics

11 10 9 8 7 6 5 4 3 2 1 0 0

30

60

90 120 Pareto frontier

150

180

210

Fig. 8. Distribution of focal length to optical aperture ratio

It can be seen that before designing the focused X-ray telescope, the focal length of FoXT can be determined according to the launch rocket envelope or the spacecraft system, and the focal length and optical aperture of the telescope can be initially determined, and the selection can be basically between 9 and 11. In addition, by defining other parameters, statistical analysis shows that the ratio has a reciprocal relationship with the grazing incidence angle. Therefore, in the design of the scheme, the reflectance angle of the different X-ray energy segments can be determined according to the requirements, and the focal length and optical are determined. 5.2.3 Ratio of Effective Area and Weight According to the Pareto optimization results, there are differences in the magnitude of the effective area and weight optimization values. In the field of optical telescope design, the performance of the product is often measured by the aspect ratio. To this end, the ratio of the effective detection area to the weight is analyzed as a statistic, and the statistical result is shown in Fig. 9.

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Effective Aera/ Weight

30 25 20 15 10 5 0 0

30

60

90 120 150 Pareto Frontiers

180

210

Fig. 9. Effective area and weight ratio distribution

As can be seen, the corresponding effective area and weight ratio is the largest when f/D belong to [9 10], the minimum value is 31.0266, the maximum value is 32.3156, and the average value is 32.0322. When f/D becomes to greater or equal to 11, the minimum value is 18.2538, the maximum value is 23.7834, and the average value is 20.2247. Through in-depth analysis, it can be seen that the X-ray mirror length and the grazing incidence angle corresponding to the design scheme with relatively large surface weight basically reach the maximum value of the design interval, and the number of Pareto optimization solutions conforming to this type of distribution is 174 groups. 5.3

Decision-Making

How to select the design program that meets the requirements of engineering development from the above three types of Pareto frontier solutions is the key. It is well known that X-ray optical reflection efficiency is directly related to the grazing incidence angle. Generally, the grazing incidence angle when the product of the surface reflectance and the grazing incidence angle is maximum is the optimum average grazing incidence angle. Therefore, the optimal average grazing incidence angle of the X-ray optical system of the 0.2 keV–12 keV energy section is about 1.25° [9]. According to the analysis of 210 sets of optimization solutions, there are 26 sets of solutions satisfying the grazing incidence angle constraint, that is, the Pareto optimal solution corresponding to f/D  11, the focal length is basically between 1370 mm– 1380 mm, and the optical aperture range is 115 mm–125 mm. From the perspective of engineering development, the design scheme with relatively large surface weight has certain advantages. Therefore, this paper selects 5 competitive design schemes in 26 sets of optimization solutions, as shown in Table 4.

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Table 4. Selected five Pareto results Pareto frontiers h(°) Num. Aeff(cm2) 1 1.20 5 37.46 2 1.23 7 59.20 3 1.26 24 98.19 4 1.26 18 94.01 5 1.29 24 104.43

Weight(kg) 3.14 3.37 3.74 3.69 3.83

L(mm) 120.00 149.96 149.99 149.99 149.99

D(mm) 115.27 118.41 121.23 121.66 124.94

f(mm) 1375.10 1376.83 1375.18 1377.00 1378.89

Considering the difficulty and cost of engineering development (ultra-precision manufacturing and assembly), the design is carried out with the fourth group of optimization solutions. Table 5 shows the large and small port diameters of the nested 18-layer system and their parabolic curvature radius. Figure 10 is a simulation of optimized FoXT. Table 5. Optical Aperture Pareto frontier (i = 1, 2, 3…18) ni 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ri1/mm 60.8255 57.1168 53.6161 50.3115 47.1921 44.2475 41.4679 38.8441 36.3673 34.0293 31.8224 29.7391 27.7726 25.9162 24.1639 22.5098 20.9484 19.4745

ri2/mm 57.4167 53.9161 50.6115 47.4921 44.5476 41.7679 39.1441 36.6674 34.3294 32.1224 30.0391 28.0726 26.2162 24.4639 22.8098 21.2483 19.7744 18.3831

Fig. 10. Simulation of optimized FoXT

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6 Conclusions (1) A multi-objective optimization method based on intelligent algorithm for FoXT is proposed. Based on X-ray total reflection theory, a multi-objective optimization model of FoXT is constructed. The non-dominated sorting genetic algorithm (NSGA-II) is used to obtain Pareto solutions. (2) Data mining methods such as cluster analysis and association analysis are used to explore the implicit correlation characteristics and variation laws between design parameters and optimization solutions. The effects of optical lens length, optical aperture, nesting layer and other parameters on the effective area are revealed. The distribution characteristics of focal length and optical aperture ratio and surface weight ratio are statistically analyzed. It is concluded that the optical aperture is proportional to the product of the detector radius and the grazing incidence angle. (3) According to the data mining and analysis results, five sets of optimization schemes with design competitiveness were selected, and one of them was designed and implemented. The number of nesting layers was 18, the aperture was 121.65 mm, the focal length was 1377 mm, and the effective area and weight were 94.01 cm2 and 3.69 kg respectively.

References 1. Sheikh, S.I., Pines, D.: Spacecraft navigation using X-ray pulsar. J. Guid. Control Dyn. 29(1), 49–63 (2006) 2. Li, L.S., Mei, Z.W., Lv, Z.X., et al.: Grazing incidence focusing X-ray pulsar telescope and analysis of in-orbit observation data. J. Ordnance Equip. Eng. 38(12), 175–179 (2017). (in Chinese) 3. Mao, P.H., Bellan, L.M., Harrison, F.A., et al.: Evaluation and optimization of multilayer design for astronomical X-ray telescope using a field-of-view and energy-dependent figure of merit. In: Proceedings of the International symposium on Optical Science and Technology, Xray Optics, Instruments and Missions IV, pp. 126–133 (2000) 4. Biskach, M.P., Mcclelland, R.S., Saha, T., et al.: Size optimization for mirror segments for Xray optics. In: International Society for Optics and Photonics, pp. 814711–814711-9 (2011) 5. Mitsuishi, I., Ogawa, T., Sato, M., et al.: Ray-tracing simulations for the ultra-lightweight Xray optics towards a future Jupiter exploration mission. Adv. Space Res. 57(1), 320–328 (2016) 6. Zhao, D.C., Chen, B., Liu, P., et al.: Image quality evaluation of Wolter X-ray nested telescope. Acta Optica Sinca 36(3), 84–90 (2016). (in Chinese) 7. Conconi, P., Pareschi, G., Campana, S., et al.: Design optimization and trade-off study of WFXT optics. In: Proceedings of the SPIE-the International Society for Optical Engineering, Optics for EUV, X-Ray, and Gamma-Ray Astronomy IV, San Diego, pp. 1–10 (2009) 8. Kalyanmoy, D., Amerit, P., Sameer, A., et al.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002) 9. Li, L.S., Deng, L.L., Mei, Z.W., et al.: Pareto-based multi-objective optimization of focusing X-Ray pulsar telescope and multi-physics coupling analysis. J. Mech. Eng. 54(23), 174–184 (2018). (in Chinese)

Research of Dormitory Furniture Design Based on Group Interaction Lin Li(&), Xupeng Wang, and Chunqiang Zhang Department of Industrial Design, Xi’an University of Technology, Xi’an 710054, China {lilin15158,wangxupeng}@xaut.edu.cn, [email protected]

Abstract. In order to improve Chinese university students’ life and learning quality through the design and layout of dormitory furniture in a limited space, a dormitory furniture design concept for university students based on group interaction is researched in this paper. Firstly, the current relevant data in China of student dormitory furniture arrangement collected based on field visits, online surveys, and conducts scientific analysis in order to summarize both the main problems of living environment and dormitory furniture, as well as the main factors that affect the needs of group communication in the dormitory. Secondly, a design concept for college dormitory furniture is introduced to meet the needs of group communication. Finally, two dormitory furniture design schemes are used as example to validate the design concept proposed in this paper. Keywords: Dormitory furniture design  Spatial function region Group interaction  Communication space  Design concept



1 Introduction As an important place for college students to study and live, the dormitory has important application significance and theoretical value. The choice of accommodation for foreign college students is diversified because except student residences, many students choose to rent out of school. And the number of student living in the dormitory is small, the living environment is relatively relaxed and comfortable, so students have higher satisfaction with dormitory furniture. Foreign scholars’ research on these area mainly refer to: (1) Research on classroom desks and chairs based on anthropometric analysis and ergonomics [1–3]. (2) Dormitory space design based on indoor physical environment of dormitory (such as indoor temperature, humidity, illumination, etc.) and interpersonal relationship [4]. (3) Renovation of old dormitory space that takes advantages and controls disadvantages [5]. (4) Evaluation of dormitory facilities from a technical and functional perspective to promote the improvement of dormitory facilities [6].

This project is supported by MOE (Ministry of Education in China). Project of Humanities Social Sciences (Project NO. 14YJCZH199). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 325–341, 2020. https://doi.org/10.1007/978-981-32-9941-2_28

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In China, student dormitory is almost the only accommodation choice for college students. The ratio of student number and dormitory area is large, and the per capita accommodation area is small. Therefore, how to improve college students’ life and learning quality through the design and layout of dormitory furniture in a limited space is particularly important and urgent. At present, the domestic scholars’ research on dormitory furniture is mainly to solve the problems of living and storage. The structure, function, man-machine size and storage space of the furniture were discussed [7–9], and some design methods of dormitory furniture were put forward. From the research of Yu, it can be concluded that according to the students’ behavioral habits in the dormitory and the anthropometric analysis, the function of furniture is refined, design details are concerned, and the humanized design idea is embodied [7]. Yang studied the relationship between furniture and space, and concluded that the variability and applicability of the dormitory function is improved by the combination of different furniture, or the space separation by the soft materials for home decoration [8]. Through the analysis of the human status data when using furniture, the ideal humanmachine size is obtained, which is applied to design practice [9]. The satisfaction of individual psychological needs in dormitory has an important influence on the students’ personal emotions, interpersonal communication with roommates, as well as construction of the dormitory culture. At present, personal privacy requirements have been paid more attention to the study of dormitory furniture design [10], and the author has explored a design concept of dormitory furniture based on privacy requirements [11]. The satisfaction of the group interaction needs is based on the communication space in the dormitory, and the research on the communication space is mainly from the perspective of dormitory space planning and design [12–14]. Although dormitory furniture is an important way to realize the dormitory space planning, there is almost no relevant literature published refers to the relationship between dormitory furniture and communication space. The paper intends to explore a design concept of college dormitory furniture, which meets the group interaction and communication needs. The research framework is as follows. In Sect. 2, the current situation of dormitory environment and dormitory furniture are comprehensive understood by field survey and network investigation. The main problems in the living environment, dormitory furniture and the main factors affecting the group interaction needs in the dormitory are determined by questionnaire research. In Sect. 3, the design concept of dormitory furniture based on the needs of group interaction and communication is summarized. Two dormitory furniture design cases are put forward to verify the effectiveness of the research process in Sect. 4. Finally, the conclusion of this study is drawn in Sect. 5.

2 Investigation of University Dormitory Environment and Dormitory Furniture in China The investigation consists of two parts: (1) The current situation of dormitory environment and dormitory furniture are comprehensive understood by field survey and network investigation. According to the regional distribution, 32 colleges and universities in China were selected for survey research. The research team found that many

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students are dissatisfied with the dormitory living environment, and the insufficient function of dormitory furniture is very prominent. (2) According to the previous survey research, the online questionnaire survey was used to further clarify the main problems of dormitory furniture, as well as the main factors affecting group communication in the dormitory. 2.1

Questionnaire Design

Dormitory space, dormitory furniture, and furniture users are closely connected and interact with each other. Therefore, the dormitory furniture design questionnaire is carried out in three aspects: living environment, status of dormitory furniture and the effect of dormitory furniture on group interaction in the dormitory. The questionnaire has five parts, and a total of 18 questions as depicts in Table 1. Table 1. Questionnaire content Number of questions Part 1 3 Part 2 5

Questionnaire content

Basic information of questionnaire respondents Dormitory living environment, dormitory life satisfaction, dormitory function effectiveness Part 3 3 Dormitory furniture type, dormitory furniture satisfaction, concrete problems of dormitory furniture Part 4 5 Demand degree on group interaction and communication, factors affecting the interaction between roommates, forming elements of communication space Part 5 2 (open questions) In-depth information on the insufficiency of dormitory furniture, ideal dormitory life

2.2

Data Collection

A questionnaire was sent out on the questionnaire website, and a total of 265 questionnaires were retrieved, of which 257 were valid ones. The basic information of the sample is shown in Table 2.

Table 2. Sample basic information (N = 257) Variable Option Frequency Proportion Gender Male 85 33.2% Female 172 66.8% Grade Freshman 57 22.27% Sophomore 64 24.61% Junior 57 22.27% Senior 62 24.22% Master student 17 6.64%

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Samples from all over the country, as shown in Fig. 1.

Fig. 1. Sample source basic information

2.3

Data Analysis

2.3.1 Reliability Analysis The Cronbach’s coefficient method [15] was adopted for the reliability analysis, which is calculated as follows: P 2 k s a¼ ð1  2 i Þ k1 sx

ð1Þ

where, k is the number of test questions, s2i indicates the variance of the test results on a certain scale, and s2x indicates the total variance of all test results. Quantifying 257 questionnaires and using them as sample data into SPSS software for reliability analysis, the results can be obtained as following: Table 3. Reliability statistics Cronbach’s Alpha Cronbach’s Alpha based on Standardized item 0.675 0.675

It is clear as shown in Table 3 that the Cronbach’s Alpha is 0.675, which is close to 0.7, it means that the questionnaire has high internal consistency, high reliability, and the results are credible and effective. 2.3.2 Validity Analysis The validity analysis was carried out by the KMO sample measurement method and the Bartlett spherical test method [15]. The results are as follows: Table 4. Inspection of KMO and Bartlett Kaiser-Meyer-Olkin metric Sampling enough Bartlett’s sphericity test Approximate chi square Approximate chi square Approximate chi square

0.724 2375.7177 780 780

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As depicts in Table 4, the KMO value is 0.724, and the significant level value of the chi-square statistical value of the Bartlett spherical test is 0.000 < 0.01. Both of them have reached the test standard of factor analysis, indicating that the sample data selected in this study is more suitable for factor analysis. 2.4

Analysis of the Relationship Between Dormitory Furniture and Student Dormitory Life Satisfaction

In this paper, H0 represents no significant impact on dormitory furniture and student dormitory satisfaction, and H1 represents a significant impact on dormitory furniture and student dormitory satisfaction. The statistic formula is: F ¼

SA =s  1  Fðs  1; n  sÞ SE =n  s

ð2Þ

where, SA is the sum of the squares of the regression, SE is the sum of squared errors. The specific analysis is as follows: Table 5. Analysis of furniture type and dormitory life satisfaction Furniture type

Number of cases

Average value

Standard Standard deviation error

95% confidence Minimum interval for the value mean Lower Upper limit limit

Maximum value

Bunk beds, tables and cabinets are independent Upper bed, lower table, cabinet, integral Beds, tables, cabinets are independent Other Total

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3.80

.886

.077

3.65

3.95

1

5

84

3.02

.776

.085

2.86

3.19

1

5

16

3.56

.727

.182

3.17

3.95

2

4

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4.04 3.55

.690 .905

.141 .056

3.75 3.44

4.33 3.66

3 1

5 5

As depicts in Table 5, 1 indicates that it is very satisfied, 2 expressed satisfaction, 3 indicates basic satisfaction, 4 indicates dissatisfaction, and 5 indicates that it is very dissatisfied. It can be seen from Table 6 that the significance level is 0.279, which is greater than 0.05. Therefore, the assumption of the homogeneity test of variance is established, and the results of one-way ANOVA (Analysis of Variance) are valid and credible.

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From Table 7, it can be seen that the significance level is 0.000, less than 0.05, rejecting H0, accepting H1, which indicates that the improvement of dormitory furniture design plays an important role in improving student dormitory life satisfaction. Table 7. One-way ANOVA Satisfaction Sum of square Degree of freedom Mean square F Significance Between groups 37.174 3 12.391 18.188 0 Within groups 172.367 253 0.681 Total 209.541 256

2.5

Investigation and Analysis of College Dormitory Environment and Dormitory Furniture

From Figs. 2 and 3, it can be concluded that the problems existing in the current dormitory of Chinese universities are mainly concentrated in the following four aspects: (1) The dormitory space is small, the living environment is crowded, and the storage space is insufficient, as well as the items are piled up and messy. (2) Dormitory space planning focuses on the realization of living functions, while social functions are neglected, which is not conducive to promoting the development of dormitory community activities. (3) The lack of dormitory furniture, insufficient variability and combination of furniture are difficult to meet the multi-level needs of dormitory members. (4) Dormitory furniture is old-fashioned and monotonous in color, which cannot meet the aesthetic needs of young people, nor can it adapt to the pace of modern campus construction. Crowded 200 150 Other shortcomings

100

Unreasonable spatial planning

50 0

Disordered item storage

Roommates don't get along well

Simple dormitory facilities

Fig. 2. Problems in the dormitory environment

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Few types of furniture 200 150

Other shortcomings

Lack of functional diversity

100 50 0 Insufficient storage space

Inappropriate size of furniture

Monotonous color

Outdated shape

Fig. 3. Problems with dormitory furniture

The above problems have seriously affected the achievement and satisfaction of the function for dormitory furniture. Especially the spatial planning and furniture configuration are mainly focused on the realization of daily living functions, and neglect the needs of group communication in the dormitory. 2.6

Main Factors Affecting the Needs of Group Communication in the Dormitory

As illustrated in Figs. 4 and 5, the main factors which affect the development of group communication activities in the dormitory are the following four aspects: (1) Dormitory space planning is mainly based on sleeping space, learning space and storage space, but social space is not included in the planning system. (2) Dormitory furniture is configured to achieve daily living functions, whereas, casual furniture that meets the needs of group communication rarely appears. (3) Dormitory furniture is used in a single way, and the correlation between furniture is weak, which limits the expansion of dormitory functions. (4) Insufficient storage space, messy living environment and dull dormitory atmosphere are not conducive to promote good interpersonal interaction for dormitory members.

Lack of communication space

150

other problems

100

Lack of leisure furniture

50 0 Different hobbies

Unharmonious roommate relationship

Single use of furniture

Dormitory atmosphere is dull

Fig. 4. Factors affecting the interaction between roommates

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100 50

Multifunctional furniture

0 Furniture accessories and decorations

Modular furniture

Dividing function space with color

Fig. 5. Construction method of the communication space

From Figs. 6 and 7, it can be concluded that the warm, harmonious, clean and orderly dormitory life is the yearning for students, and the dormitory furniture based on group interaction helps to promote good interpersonal interaction in the dormitory, as well as create a harmonious and orderly dormitory environment.

Fig. 6. Word cloud diagram of the deepening of dormitory furniture design

Fig. 7. Word cloud diagram of ideal dormitory life

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3 Dormitory Furniture Design Concept Based on Group Interaction and Communication Needs According to the research conclusions above, the activity of group interaction among roommates is influenced not only by psychological factors such as personal personality, hobbies et al., but also the dormitory environment. And effect of the dormitory environment on the group interaction activities in the dormitory is mainly reflected in the two aspects as follow, the one is the facility allocation, and the other is space atmosphere. It need to be highlighted that facility allocation includes communication space, leisure furniture et al., which provide a basic guarantee for the dormitory members’ group interaction and communication activities. The space atmosphere includes the cleanliness, aesthetics, comfort and other elements of the dormitory environment, which enhance the enthusiasm and the harmony of communication between the roommates. It is clear that dormitory furniture plays an important role on the layout of dormitory space, the realization of dormitory functions, the beautification of indoor environment and the comfortability of residence. It can be concluded that in order to improve the enthusiasm and initiative of communication, and interaction among roommates, the aspects of dormitory facility allocation and space atmosphere should be considered seriously in design concept of dormitory furniture. 3.1

Design Concept of Dormitory Furniture Based on Living Environment and Usage Requirements

The dormitory leisure furniture design should suitable for the living environment and usage requirements. According to the previous investigation and research, it can be concluded as follow. (1) Living environment and usage requirements should be considered in the design of dormitory leisure furniture. And the dormitory leisure furniture should be small and simple, the structure should not be complicated, and the size should not be too large, as well as the number should be limited. (2) In order to provide the facilities for the group interaction activities, dormitory furniture design can be combined with other functions to bring more convenience to dormitory life. (3) The flexible usage expands the function of dormitory furniture, and creates a multifunctional space for both living and leisure in a limited space. It need to be noted that there is a small population and relatively large space in postgraduate dormitory, so the group interaction needs can be considered by setting up the social space and equipping the leisure furniture. Contrary to postgraduate dormitory, the undergraduate dormitory has small living space but large population. Therefore, it is useful to fully expand the usage of dormitory furniture of undergraduate through design methods, such as multi-functional design and modular combination, to meet the diverse living needs.

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Design Concept of Dormitory Furniture to Create Clean Environment and Harmonious Atmosphere

(1) Expanding the storage space and optimizing the storage method to create a clean and bright living environment. The dormitory storage space should be planned based on the user’s storage needs, and the type of items to be stored. While providing storage furniture with sufficient storage space, it becomes possible to expand the storage space with high-altitude space and multi-functional storage furniture. (2) Furniture accessories, decorations and other items can emphasize the casual atmosphere of the interaction and communication space. Appropriate furniture accessories can expand the functional scope of the main furniture. Wall or space decoration can beautify the environment and enhance the harmonious atmosphere of the dormitory which is conducive to the development of personal mental health. (3) Appropriate form design, reasonable structure, and good color design can create a warm and comfortable dormitory atmosphere, which can promote the positive interaction between roommates It need to be highlighted that Chinese college dormitory furniture is mainly made of wood, with a simple shape and natural color. However, this style of furniture has been used for many years, lacking visual attraction and becoming difficult to be recognized by young people. The indoor environment affects people’s emotional changes, and dormitory furniture plays an important role in shaping the dormitory environment. The fashionable style and pleasant color matching can meet the aesthetic needs of young people, and enhance the desire for communication between roommates.

4 Dormitory Furniture Design Examples Based on Group Communication Needs According to the design concept of dormitory furniture based on the group communication needs, two design examples are presented as follow. 4.1

Example 1: The Fusion of Movement and Static

According to the questionnaire survey, most students hope that the number of people living in a dormitory is less than four, and the dormitory space is spacious and bright. This example sets the dormitory area to 25 m2 and the number of residents is three. The design results not only provide reasonable solutions for daily dormitory life, but also meet the needs of group interaction among roommates. The style and color of the scheme should match the aesthetic needs of young people. 4.1.1 Dormitory Furniture Design In Figs. 8, 9, 10, 11, 12 and 13, the design contents of college dormitory furniture are shown based on the needs of group communication.

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Fig. 8. Dormitory furniture

Fig. 9. Top view of dormitory furniture

Fig. 10. Bed, desk and bookcase

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Fig. 11. Leisure table, lounge chair, shared bookshelf, wardrobe and shoe cabinet

Fig. 12. Leisure exchange area

Fig. 13. Rotating table and rack

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Design Features

(1) The spatial planning of “moving and quiet” is the basis for realizing the multilevel functional requirements of the dormitory. The dormitory space is divided into a static space area and a dynamic space area (as shown in Figs. 8 and 9). The static space satisfies the needs of individual activities, such as learning and rest, in which mainly places furniture such as beds, desks, and personal bookcases are placed. The dynamic space satisfies the collective communication and storage needs, mainly including leisure stools, leisure tables, shared bookshelves, wardrobes, shoe cabinets and other furniture. (2) The leisure furniture structure is simple and exquisite, economical and practical. The structures of lounge chair, small table and bookshelves are simple and delicate which not only provides convenience for interaction between students,but also can save costs and space (as shown in Fig. 11). (3) Small furniture accessories enhance the character of the space and create a relaxed and welcoming dormitory atmosphere. The design details reflect human care and enhance the quality of life in the dormitory. Two lounge chairs with storage functions, a small table, a TV set, and a row of shared bookshelves form a small and comfortable space for casual interaction (Fig. 12). The rotatable tabletop mounted on the side of the bed provides convenience for students to read or write in the bed (as illustrates in Fig. 13). (4) Reasonable storage forms a clean and orderly dormitory environment. The storage space of the dormitory furniture adopts a box structure, and the articles are stored inside the cabinet without being directly exposed to the external environment, thereby solving the problem of disordered personal items and making the dormitory environment orderly. The desk design of the foldable tabletop improves the space utilization and further improves the cleanliness of the dormitory environment (as depicts in Fig. 10). (5) The multi-functional storage furniture effectively utilizes the structural space of the furniture, expands the functional scope of the furniture, and expands the storage space. The four storage compartments arranged vertically on the side of the desk, which can store personal small items and can also be used as bed ladders (as depicts in Fig. 10). The combination of the leisure chair and the shoe cabinet in the leisure exchange area has both practicality and aesthetics while saving space (as shown in Fig. 12). 4.2

Example 2: Beating Melody

According to the survey and analysis, two styles of dormitory environment are yearn for by students, which are the fashionable and novel dormitory space, the warm and harmonious dormitory atmosphere. This example sets the dormitory area to 30 m2 and the number of students is four. The design scheme is novel and lively, and it can create a warm feeling of “home”. The usage of furniture should be flexible and varied to meet different needs.

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4.2.1 Dormitory Furniture Design In Figs. 14, 15, 16, 17, 18 and 19, the design contents of college student dormitory furniture are shown based on the needs of group communication.

Fig. 14. Combo desk

Fig. 15. Vertical cabinet

Fig. 16. Desk usage scenarios for group activities

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Fig. 17. Desk usage scenarios for personal events

Fig. 18. Overall environment of the dormitory

Fig. 19. Foldable bunk

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4.2.2

Design Features

(1) The new and lively style creates a comfortable and inviting living environment. The whole set of dormitory furniture uses circular shape as a modeling element in order to create a fashionable and modern space style. The combinable curved desk, the semi-transparent cabinet, and the simple and exquisite wall cabinet are all blended with the circular elements, which make people feel refreshed (as illustrates in Fig. 18), creating a relaxed and pleasant “home” atmosphere. (2) Functional variability provides a flexible and versatile way to use furniture. The combinable personal desk features an arc shape as shown in Fig. 14, which can be placed for different usage needs. When the desk is placed in a line, the users are staggered in position, which reduces mutual interference and facilitates the development of personal activities (as illustrates in Fig. 17). The four desks can also be combined into a large round table to provide a discussion and chat area for roommates (as depicts in Fig. 16). (3) The foldable bunk bed can be transferred into a sofa which creates a small leisure space in the dormitory with limited space. The upper bunk bed is foldable and the lower mattress is a pillow top mattress. When the upper bunk is folded up, the double bottom mattress of the lower bunk is unfolded, and the lower bunk becomes a simple and comfortable leisure sofa (as see in Fig. 19). (4) The semi-transparent cabinet separates the bed, but maintains the visibility between roommates which is convenient for communication. A hollow design method is used for the vertical cabinet between the two sets of beds (as illustrates in Fig. 15). The cabinet separates the beds on both sides, creating a relatively independent personal sleeping space. As one of the favorite ways of communication, dormitory symposiums are an indispensable part of college life in China. The hollow structure maintains the permeability of sight on both sides of the bed, which is conducive to bedtime communication between roommates.

5 Conclusions Based on the social function of the dormitory and the needs of group communication, a design concept and specific methods of dormitory furniture have been presented and discussed in this paper, and two design examples are used to validate the design concept. The main conclusions can be obtained as follows: (1) Through extensive investigation and research, the main factors that influence the living environment and dormitory furniture, as well as the community interaction in the dormitory have be summarized as follow: rare consideration of social space in dormitory space planning, less leisure furniture, weak correlation between furniture and insufficient storage space for items. (2) The design concept of college dormitory furniture that meets the needs of group communication is proposed, which mainly includes five aspects as follow: rationally planning the functional division of dormitory space, strengthening the

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association and variability of furniture, increasing furniture accessories, and expanding storage space, as well as optimizing modeling and color design. (3) Based on the design concept proposed in this paper, two dormitory furniture design schemes “the fusion of movement and static” and “the melody of beating” are given, which show that the reasonable dormitory furniture design can not only promote the communication between roommates, but also improve other functions of the dormitory. It is need to be highlighted that, this paper puts forward the design concept of dormitory furniture from the perspective of psychological needs, but does not study the use comfort, durability, production process and cost of dormitory furniture. The sample data of the questionnaire is mainly based on Shaanxi Province, and the data of other provinces is relatively small. So the extensiveness of samples is relatively insufficient. So these will be researched seriously in our future researches.

References 1. Asif, S., Qutubuddin, S.M., Hebbal, S.S.: Anthropometric analysis of classroom furniture used in colleges. Int. J. Eng. Res. Dev. 3, 1–7 (2012) 2. Qutubuddin, S.M., Hebbal, S.S., Kumar, C.S.: Anthropometric consideration for designing students desks in engineering colleges. Int. J. Curr. Eng. Technol. 3, 1179–1185 (2013) 3. Odunaiya, N.A., Owonuwa, D.D., Oguntibeju, O.O.: Ergonomic suitability of educational furniture and possible health implications in a university setting. Adv. Med. Educ. Pract. 5, 1–14 (2014) 4. Kılıcaslan, H.: Design of living spaces in dormitories. Procedia-Soc. Behav. Sci. 92, 445– 451 (2013) 5. Khajehzadeh, I., Vale, B.: Shared student residential space: a post occupancy evaluation. J. Facil. Manag. 14, 102–124 (2016) 6. Hassanain, M.A.: On the performance evaluation of sustainable student housing facilities. J. Facil. Manag. 6, 212–225 (2008) 7. Yu, L.: Humanized design of college dormitory furniture-A case study of Tsinghua university. Decoration 5, 96–99 (2018) 8. Yang, C.: Overall furniture design of college dormitory with outstanding space reconstruction. Art J. 6, 116–120 (2014) 9. Ma, G., Wang, M.: Research on man-machine scale of modular multi-functional furniture in college apartment. J. Shenyang Constr. Univ. (Nat. Sci.) 4, 734–740 (2014) 10. Li, M., Chen, S.: Research on humanistic design creativity of college student dormitory furniture. Packag. Eng. 22, 115–122 (2013) 11. Li, L.: Research on dormitory furniture design based on personal privacy requirements. Decoration 2, 136–137 (2018) 12. Wei, W., Liu, Y.: Interaction space design of college student dormitories. J. Anhui Inst. Archit. Technol. (Nat. Sci. Ed.) 4, 94–96 (2008) 13. Sun, Z., Wang, H.: Talking about the design of college student dormitories from the perspective of space communication. Shanxi Archit. 24, 37–38 (2006) 14. Cronbach, L.J.: Coefficient alpha and the internal structure of tests. Psychometrika 16(3), 297–334 (1951) 15. Li, H., Jiang, H.: SPSS Data Analysis Course, pp. 251–252. The Posts and Telecommunications Press, Beijing (2012). (in Chinese)

Analysis and Extraction of Consumer Information for the Evaluation of Design Requirement Depending on Consumer Involvement Shipei Li, Dunbing Tang(&), Qi Wang, and Haihua Zhu College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China [email protected], [email protected], [email protected]

Abstract. In the product design, identification of critical design requirements (DRs) is essential to the success of the product. Usually, DRs are rated according to CRs for allocating resources reasonably as well as improving consumer satisfaction. With the popularization of the Internet, consumers can involve in open design (OD) and describe their requirements freely. It is a challenge to rate DRs due to a great quantity of CRs that are expressed as free text in OD. In existing approaches, CRs are collected by the method of survey or questionnaire in the market, and it cannot amply reflect the CRs in OD. To this end, this paper focuses on analyzing CRs for rating DRs in OD. The CRs are captured and rated in OD by a group-organization approach and a fuzzy Delphi method. Based on the importance weight of CR, a machine learning approach and a fuzzy QFD method are proposed to rate DRs according to the expression of CRs in OD. A case study is presented to demonstrate the effectiveness of the method. Keywords: Open design  Consumer requirement Group-organization  Fuzzy QFD

 Design requirement 

1 Introduction As market competition increases and product life-cycles decrease significantly, companies have been forced to develop new products for meeting the highly varied and rapidly changing consumer requirements (CRs). It can be argued that the products can be developed successfully by the full understanding of CRs [1]. Based on the sale network and market survey of the company, Li et al. [2] integrated analytical hierarchy process (AHP), Kano’s model, rough set theory, and scale method for evaluating the importance weight of CR. Considering both consumer preference and consumer satisfaction, Nahm et al. [3] proposed two sets of evaluating methods to analyze the This work was supported by National Natural Science Foundation of China (Grant Nos. 51575264, 51805253); Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 2018K017C); and Qinglan Project of Jiangsu Province of China. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 342–353, 2020. https://doi.org/10.1007/978-981-32-9941-2_29

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importance and competitive advantage of CRs. Zheng et al. [4] put forward a weighted interval rough number method for rating CRs while the importance weights of consumers are considered. Dou et al. [5] obtained CRs using a fuzzy Kano model and benchmarking theory to enhance the consumer satisfaction of each product attribute. In these methods, interview and questionnaire were used to collect CRs. With the development of the Internet, consumers can participate in the product design process and express their requirements freely in open design (OD) [6]. The number of CRs is increasing as consumers continuously to involve in OD. The ability of identifying crucial CRs is considered as a significant element in the product design process [7]. Traditionally, the methods of collecting and analyzing CRs are survey or questionnaire in the market, and they are inappropriate for dealing with a great quantity of CRs that are expressed freely [8]. In the product design process, it is essential to estimate the final priority ratings of design requirements (DRs). The importance weights of DRs can be rated based on the weights of CRs and the relation intensity between CRs and DRs. Quality Function Deployment (QFD) is a widely used planning methodology for interpreting CRs into DRs. Normally, human subjective judgments are used as the inputs of QFD [9]. Owing to the vagueness and uncertainty of human judgment, the fuzzy evaluation method was widely used in rating DRs in QFD [10]. Chen, Fung, and Tang [11] applied a fuzzy weighted average method with fuzzy expected value operator to rate DRs in fuzzy QFD. Chen and Weng [12] used the fuzzy goal programming models to deduce the different fulfill levels of DRs considering the fuzzy coefficients in QFD. Wang and Chin [13] applied a pair of nonlinear programming models and two equivalent pairs of linear programming models to evaluate the importance weights of DRs in fuzzy QFD. Wang [14] utilized a fuzzy-normalisation-based group decision-making approach to evaluate DRs, and their technical importance was aggregated in fuzzy QFD. Miao et al. [15] applied two uncertain chance-constrained programming models to determine the importance of DRs in QFD with the condition of minimizing the design cost and maximizing consumer satisfaction. In these methods, CRs were collected by survey or questionnaire, and it cannot understand CRs sufficiently from the consumer’s perspective. Additionally, the relationship between CR and DR was assumed or evaluated by designers manually, and it is hard to rate the DRs exactly using these methods due to a great quantity of CRs that are expressed freely in OD. Although there have been many methods for collecting and analyzing CRs, they are not suitable for dealing with a great quantity of CRs. In addition, most fuzzy evaluation methods are difficult to rate the DRs exactly according to the CRs that are expressed freely in OD. In this paper, to evaluate DRs in QFD, CRs are collected and analyzed in OD by a group-organization approach and a fuzzy Delphi method. Then a machine learning approach and a fuzzy QFD method are proposed to rate DRs on the basis of the expression of CRs in OD.

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2 Process Model With the development of Internet technology, product design patterns are being challenged as consumers can involve in the process of OD. In OD, consumers can participate in product design process and describe their requirements freely. As more and more consumers involved in OD, an increasing number of CRs can be captured. Precise information about CRs is helpful to rate DRs accurately. Designers can distribute resources properly according to the importance weights of DRs in the product design process. To rate DRs, CRs are collected depending on consumers involvement in OD. The framework of the analyzing CRs for the evaluation of DRs is shown in Fig. 1. Initially, an OD platform is established by the Internet. Consumers can involve in product design to describe their requirements and evaluate CRs through the OD platform. Then, a group-organization approach is put forward to eliminate the evaluation values of CRs that are very different from others. Based on the processed evaluation data, a fuzzy Delphi method is used to rate CRs. Meanwhile, the relation intensity between CR and DR is identified by a machine learning approach. Finally, the importance weights of DRs are evaluated based on the weights of CRs and the relation intensity between DRs and CRs in fuzzy QFD.

Fig. 1. The framework of analyzing CRs for the evaluation of DRs in OD

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3 Processing Consumer Requirements in OD The consumer who participants in OD can describe the requirements freely and interact with others. As participants can exchange their opinions about the CRs with each other in OD, their initial requirements may change. Consumers who participant in OD expect to get their ideal product, and it is similar to the economic issues in negotiations. Nash equilibrium is widely used for dealing with the collective beneficial relationship among participants [16]. The dynamic CRs in OD can also be analyzed using the Nash Equilibrium. Because consumers involve in OD to get their desired product, the similar CRs will tend to reach the common expectation with the increasing of their communication. 3.1

Collecting Consumer Requirement in OD

Though Internet, OD platform can be constructed for collecting CRs. Consumers with different age or background can describe requirements and communicate with each other in the OD platform. Because consumers are given the freedom to involve in OD, there will be a large number of CRs. The qualitative method is more suitable for extracting the most important information of CRs. Usually, the importance of CRs can be rated by consumers using numerical values. In OD, consumers can evaluate the CRs that they are interested in. As anyone who participates in OD can evaluate CRs, there may be someone who evaluates CRs maliciously. Therefore, a filtering method is proposed for eliminating the abnormal values of the evaluation data. 3.2

Analyzing Consumer Requirement

Through OD platform, consumer can evaluate the CRs by using numerical values. The evaluation value of a requirement that is evaluated by the ith consumer is denoted as xi . To eliminate the abnormal values of the evaluation data, a group-organization approach (GOA) is proposed in this section. The evaluation values of CRs in OD can be organized into different groups on the basis of time series. The outliers of each group are filtered by the GOA. In GOA, based on the similarity analysis approach given by  Yang and Wu [17], the similarity relation S xi ; xj can be expressed as follows: 

S xi ; xj



   xi  xj  ¼ a exp  b

ð1Þ

where a is the influence factor, and the normalized term b is expressed as:  Pn  x j¼1 xj   b ¼ n

Pn where x ¼

j¼1 xj

n

ð2Þ

where n is the number of CRs in each group. To improve the performance for filtering the outliers of groups, the similarity of xi to the other evaluations in the group is denoted as AðSi Þ, and it is presented as:

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AðSi Þ ¼

n X j¼1

   xi  xj  a exp  ; i ¼ 1; . . .; n b

ð3Þ

Based on the values of similarity evaluation, the outliers of CR evaluations in each group can be filtered according to the Pauta criterion [18]. For the vagueness of human language, it is more appropriate to rate CRs using fuzzy numbers. Fuzzy Delphi method is a widely used method for the group decision. In fuzzy Delphi method, the expert team may be invited to evaluate the CRs many times for achieving the consensus condition. The fuzzy Delphi method proposed by Wang and Chen [19] is used to evaluate the importance weight of CR. Consumers involve in OD for capturing their desired product, and the CRs and its evaluation values that are collected in OD tend to stabilization with the communications among consumers. As the number of consumers who involve in OD is increasing, an opening degree needs to be defined to determine the degree of consumer involvement. Consumers who involve in OD are organized into different groups on the basis of time series. The opening degree is calculated according to the mean value of the CRs in each group. The deviation between the average of two adjacent groups and the expected mean value of the group are applied to determine the opening degree in OD.

4 Evaluating the Design Requirement in OD In the product design process, it is crucial to identify critical DRs according to CRs for maximizing consumer satisfaction. Fuzzy QFD has been widely applied for converting CRs into DRs. To evaluate DRs, the importance weight of CR and the relation intensity between CR and DR are considered as the inputs of fuzzy QFD [20]. Although many previous studies have been proposed for rating DRs, they cannot deal with an excessive number of CRs and evaluate DRs on the basis of the language information of CRs in OD. Therefore, a machine learning approach based on fuzzy QFD is proposed for evaluating DRs in OD. 4.1

Using a Machine Learning Approach to Identify the Relationship Between CRs and DRs

For rating DRs, the relationship between DR and CR need to be identified by a machine learning approach. To improve the efficiency of identifying the relationship between CR and DR in OD, it is necessary to preprocess the context of CRs. Stop words removal and word stemming methods can be applied to preprocess the language expression of CRs in OD. In addition, the keywords of DRs are applied for identifying the relation intensity between CRs and DRs. According to the words on different sides of the keyword, the relationship between CR and DR can be identified. Normally the words on both sides of the keyword have various effects on identification of the relationship between the words and keyword. Consequently, it is assumed that Wk represents the keyword and Wc is the word of the sentence. The left and right words of Wk are denoted by Wl and Wr respectively. The keywords of DR and the preprocessed

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CR are applied for identifying the relationship between DR and CR. The probability that the ith left word Wli is related to DRk is denoted as: P0 ðWli ; Dk Þ ¼

CðWli ; Dk Þ C ðDk Þ

ð4Þ

where CðWli ; Dk Þ is the number of CRs that include Wli and relate to DRk simultaneously, CðDk Þ is the number of CRs related to DRk . Obviously, if CðWli ; Dk Þ equals zero, P0 ðWli ; Dk Þ is zero and it will cause the model inapplicable. To address this problem, Dirichlet Priors smoothing method can be used in the process of identifying the probability that the ith left word Wli is related to DRk , and it is defined as: PðWli ; Dk Þ ¼

CðWli ; Dk Þ þ lPðWli ; C Þ C ðD k Þ þ l

ð5Þ

where l is a constant that can be used to adjust the smoothing item, PðWli ; CÞ represents the occurrence probability of Wli in training corpus C. According to Eq. (5), the probability that the left word Wl is related to DRk is denoted as: PðWl ; Dk Þ ¼

Nl 1X PðWli ; Dk Þ Nl li¼1

ð6Þ

where Nl is the number of the words that are on the left of the keyword. The probability that the right word Wr is related to DRk can be obtained with the same method. The probability that CRi is related to DRk on the basis of the Nik th keyword is expressed as: Pik ¼

 1 1  10Nikn 2 Nikn h    i 1 X N N þ P Wl ; Dk ikj þ P Wr ; Dk ikj 4Nikn Nikj ¼1

ð7Þ

N

where DNk ik is the Nik th keyword that is related to CRi , Nikj is the sequence of Dkki in N CRi , Nikn represents the number of Dkki in CRi . When there is no keyword in CR, the word with the maximum probability for relating to a CR is defined as the keyword. Based on Eq. (7), a threshold d is suggested to identify the relationship between CRi and DRk . Then the relation intensity between each keyword and DR needs to be defined by designers. According to the value of probability and the relation intensity between the keyword and DR, the relation intensity between CR and DR can be identified on the basis of the language expression of CR. 4.2

Evaluating the Design Requirement in Fuzzy QFD

Based on the importance weight of CR and the relation intensity between DR and CR, the importance weight of the DR can be evaluated in QFD. In practice, DRs are not independent with each other, and therefore the relation intensity among DRs should be

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considered in the process of evaluating DRs. Let Rij be the relationship between CRi and DRj , and cij represents the relationship between DRi and DRj . Based on previous study [19], the relation intensity between CRi and DRj that has been normalized by considering the relationship among DRs is expressed as: 1þ R0ij

¼ Rs ¼

P k6¼j

! ckj Rij ; ckj 2 ½0; 1

Rs Xn Xm i¼1

j¼1



X k6¼j

where !

ckj Rij

ð8Þ

where n is the number of CRs and m is the number of DRs. The importance weights of DRs can be obtained as: WjDR ¼ WiCR R0ij

ð9Þ

where WiCR is the importance weight of CRi . For the fuzziness of human thought as well as language, fuzzy evaluation method is more appropriate to rate DRs in QFD. Triangular fuzzy number (TFN) has been widely used in the fuzzy evaluation method. In this section, TFN is applied to represent the language expression (see Table 1). Supposing A is a TFN and it is denoted as A ¼ ða; b; cÞ, where a  b  c. To deal with fuzzy numbers, Rs ¼ ðRs a; Rs b; Rs cÞ in Eq. (8) is defined as Rs ¼ Rs a þ Rs3 b þ Rs c. lA ð xÞ represents the membership function of A, and it can be expressed as:

Table 1. Linguistic expression and fuzzy number Linguistic expression Very weak relationship Weak relationship Medium relationship Strong relationship Very strong relationship

Symbol VW W M S VS

8 < ðx  aÞ=ðb  aÞ; l A ð xÞ ¼ ðc  xÞ=ðc  bÞ; : 0

Fuzzy number (0, 0.1, 0.2) (0.2, 0.3, 0.4) (0.4, 0.5, 0.6) (0.6, 0.7, 0.8) (0.8, 0.9, 1)

a  x\b bxc otherwise

ð10Þ

  Some algebraic operations of Ai ¼ ðai ; bi ; ci Þ and Aj ¼ aj ; bj ; cj can be defined as follows [20]:

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  Ai þ Aj ¼ ai þ aj ; bi þ bj ; ci þ cj   Ai  Aj ¼ ai  aj ; bi  bj ; ci  cj

349

ð11Þ ð12Þ

  Ai  Aj ¼ ai  aj ; bi  bj ; ci  cj

ð13Þ

  Ai Aj ¼ ai aj ; bi bj ; ci cj

ð14Þ

kAi ¼ ðkai ; kbi ; kci Þ

ð15Þ

Based on QFD, the fuzzy importance weights of DRs can be obtained via Eq. (9) and algebraic operations. To determine the importance priority of DRs, the fuzzy numbers need to be converted to the crisp value. Then the defuzzification for a TFN can be expressed as follows: Rc xlA ð xÞ xð AÞ ¼ Rac a lA ð xÞ

ð16Þ

5 Case Study In this section, a case study of analyzing the CRs for evaluating the DRs of a smartphone in OD is proposed for demonstrating the effectiveness of the proposed method. Based on the Internet, consumers who are interested in the product are able to involve in OD. 5.1

Collecting and Analyzing CRs in OD

To capture CRs, an OD platform is constructed for collecting CRs and their evaluations. Consumers can publish CRs and evaluate CRs by using fuzzy numbers. Due to the fact that there will be a large number of evaluation data in OD, the evaluation data is divided into different groups and filtered using the GOA. For example, a requirement CR0 can be evaluated by any consumer who involves in OD. In this study, the scale 1– 9 is used for rating CRs. The numbers 1 and 9 represent unimportant and very important respectively, and number 5 represents important. The evaluation values of CR0 are divided into different groups and the outliers are filtered using GOA, and it is shown in Fig. 2. The evaluations of CRs are divided into 4 groups, and each group includes 50 values. Based on the Pauta criterion, the deviation values that are greater than 0 are defined as outliers. Then the evaluation values are used to evaluate the importance weights of CRs according to fuzzy Delphi method, and the importance weight of CR0 is 7.7198 using the proposed method.

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Fig. 2. The analysis of CRs using GOM in OD

5.2

Evaluating Design Requirements

The importance weight of CR and the relationship between DR and CR are applied as the inputs of QFD for evaluating DR. The relationship between CR and DR can be identified according to the text language of CRs using the machine learning approach. In this section, six CRs (see Fig. 2) of a smartphone are selected as an example. Based on the machine learning approach and the formulation of Table 1, the relationship between CR and DR can be identified. For example, “running memory” is the keyword of CR1 and it corresponds to the DR “random access memory”. The language expression of CR1 is preprocessed using stop words removal and word stemming methods. Based on the preprocessed CR1 and Eq. (7), the relationship between CR1 and the DR “running memory” is identified as VS. The relationship between other CR and DR is identified with the same way (see Table 2). The relationship among DRs are evaluated by designers using fuzzy Delphi method according to Table 1. The fuzzy relationship matrix for a smartphone can be identified (see Fig. 3). In OD, designers can select the CRs according to their importance weights. Based on the importance weights of CRs and the relation intensity between DRs and CRs, the fuzzy importance weights of DRs can be evaluated by using Eqs. (8) and (9). Then according to Eq. (16), the crisp value of the importance weights of DRs can be obtained, and it is shown in Table 3. It can be seen that DR1 has the maximum importance weight (2.0622), and DR2 has the minimum importance weight (0.9157). Therefore, designers should pay more attention to DR1 than to DR2 . Based on the importance weights of DRs, the resources can be distributed efficiently in the process of product design.

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Table 2. The relationship between CRs and DRs CR

Expression

Keyword

DR

CR1 I suggest improving the running memory of the mobile phone

Running memory

CR2 I can’t hear what the other person is saying while I’m on the phone. It will be better if the phone has the function of noise reduction CR3 I also suggest increasing the service life of battery. It is better to reduce the battery charging time CR4 I hope that the camera function of mobile phone is more professional CR5 I hope that the smart phone has multiple operating modes. For example, it can be set up to receive only one person’s phone CR6 I would like the screen size to be 6.0inch

Hear, Noise

Random access memory Call quality

Relation Weight intensity VS 8.9522

VS

8.8047

Battery

Battery capability

VS

8.7096

Camera, Photos Operating modes

Photography VS

8.4972

System

M

7.9634

Screen size

Screen size

VS

7.7198

Fig. 3. The fuzzy QFD relationship matrix for a smartphone

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S. Li et al. Table 3. The importance weight of DR Design requirements Fuzzy value Crisp value (1.6553, 2.0483, 2.4833) 2.0622 DR1 DR2 (0.8144, 0.9157, 1.0178) 0.9157 DR3 (1.4493, 1.8116, 2.2140) 1.8251 DR4 (1.0995, 1.3256, 1.5711) 1.3322 (0.7366, 1.0121, 1.3251) 1.0246 DR5 DR6 (0.9989, 1.2043, 1.4274) 1.2103

Rank 1 6 2 3 5 4

6 Conclusions The analysis of consumer information is critical in the product design process. The importance of DRs can be evaluated according to CRs. Along with the popularization of Internet, consumers can involve in product design process and express their requirements freely. Since the product design is open to all the consumers, there will be a large amount of information about the product. It is difficult for designers to rate DRs on the basis of these CRs. Therefore, this paper aims to rate DRs by analyzing consumer information depending on consumer involvement in OD. To rate DRs in OD, firstly, an OD platform is constructed for prompting consumer participation in product design. An SFM is proposed to analyze the CRs and a fuzzy Delphi method is used to rate the importance weights of CRs. Secondly, a machine learning approach is proposed to determine the relationship between DRs and CRs in OD. The importance weights of DRs are evaluated according to the weights of CRs and the relation intensity between DRs and CRs in fuzzy QFD. Finally, an example of a smartphone design was provided to illustrate the application of the method. For future research, the number of the words and the distance between the word and the keyword will be considered in the process of analyzing DRs in OD.

References 1. Wang, C.H., Hsueh, O.Z.: A novel approach to incorporate customer preference and perception into product configuration: a case study on smart pads. Comput. Stand. Interfaces 35(5), 549–556 (2013) 2. Li, Y., Tang, J., Luo, X., Xu, J.: An integrated method of rough set, Kano’s model and AHP for rating customer requirements’ final importance. Exp. Syst. Appl. 36(3), 7045–7053 (2009) 3. Nahm, Y.E., Ishikawa, H., Inoue, M.: New rating methods to prioritize customer requirements in QFD with incomplete customer preferences. Int. J. Adv. Manuf. Technol. 65(9–12), 1587–1604 (2013) 4. Zheng, P., Xu, X., Xie, S.Q.: A weighted interval rough number based method to determine relative importance ratings of customer requirements in QFD product planning. J. Intell. Manuf. 30(1), 3–16 (2019) 5. Dou, R., Li, W., Nan, G.: An integrated approach for dynamic customer requirement identification for product development. Enterp. Inf. Syst. 13(4), 448–466 (2019)

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6. Tan, L., Tang, D., Wang, Q., Yang, J.: Open design pattern, method, and its selforganization mechanism. Procedia CIRP 56, 34–39 (2016) 7. Lettl, C.: Learning from users for radical innovation. Int. J. Technol. Manag. 33(1), 25–45 (2004) 8. Song, W., Ming, X., Han, Y., Wu, Z.: A rough set approach for evaluating vague customer requirement of industrial product-service system. Int. J. Prod. Res. 51(22), 6681–6701 (2013) 9. Liu, A., Hu, H., Zhang, X., Lei, D.: Novel two-phase approach for process optimization of customer collaborative design based on fuzzy-QFD and DSM. IEEE Trans. Eng. Manag. 64 (2), 193–207 (2017) 10. Vanegas, L.V., Labib, A.W.: A fuzzy quality function deployment (FQFD) model for deriving optimum targets. Int. J. Prod. Res. 39(1), 99–120 (2001) 11. Chen, Y., Fung, R.Y., Tang, J.: Rating technical attributes in fuzzy QFD by integrating fuzzy weighted average method and fuzzy expected value operator. Eur. J. Oper. Res. 174(3), 1553–1566 (2006) 12. Chen, L.H., Weng, M.C.: An evaluation approach to engineering design in QFD processes using fuzzy goal programming models. Eur. J. Oper. Res. 172(1), 230–248 (2006) 13. Wang, Y.M., Chin, K.S.: Technical importance ratings in fuzzy QFD by integrating fuzzy normalization and fuzzy weighted average. Comput. Math Appl. 62(11), 4207–4221 (2011) 14. Wang, Y.M.: A fuzzy-normalisation-based group decision-making approach for prioritising engineering design requirements in QFD under uncertainty. Int. J. Prod. Res. 50(23), 6963– 6977 (2012) 15. Miao, Y., Liu, Y., Chen, Y., Zhou, J., Ji, P.: Two uncertain chance-constrained programming models to setting target levels of design attributes in quality function deployment. Inf. Sci. 415, 156–170 (2017) 16. Baldwin, C.Y., Clark, K.B.: The architecture of participation: does code architecture mitigate free riding in the open source development model? Manag. Sci. 52(7), 1116–1127 (2006) 17. Yang, M.S., Wu, K.L.: A similarity-based robust clustering method. IEEE Trans. Pattern Anal. Mach. Intell. 26(4), 434–448 (2004) 18. Shen, C., Bao, X., Tan, J., Liu, S., Liu, Z.: Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint. Opt. Express 25(14), 16235–16249 (2017) 19. Wang, C.H., Chen, J.N.: Using quality function deployment for collaborative product design and optimal selection of module mix. Comput. Ind. Eng. 63(4), 1030–1037 (2012) 20. Liu, H.T.: The extension of fuzzy QFD: from product planning to part deployment. Exp. Syst. Appl. 36(8), 11131–11144 (2009)

Reduction in Aerodynamic Resistance of High-Speed Train Nose Based on Kriging Model and Multi-objective Optimization Tian Li(&), Deng Qin, Le Zhang, Jiye Zhang, and Weihua Zhang State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China {litian2008,jyzhang,tpl}@home.swjtu.edu.cn, [email protected], [email protected]

Abstract. In order to minimum the aerodynamic resistance of both the head and tail cars, an approach for aerodynamic design of a high-speed train nose based on Kriging model and multi-objective optimization is proposed. The aerodynamic resistances of the head and tail cars are chosen the dependent variables. 5 independent variables are related to 5 typical curves, which are the vertical outline of the front nose, vertical outline of the window, lateral outline of the nose, the first auxiliary outline and the second auxiliary outline. Optimal Latin-hypercube design (OLHD) is used to generate the design matrix of the independent variables of the train nose. The dependent variables for every set of independent variables are obtained using computational fluid dynamics. The multi-objective optimization is solved by Non-dominated Sorting genetic algorithm II (NSGA-II). Compared to the initial value which is calculated using the original train model, the aerodynamic resistance of the head car decreased by about 6.5%, and the resistance of the tail car decreased by 5.0%. The magnitude of the decrease in the resistance of the head car is larger than that of the tail one. The vertical outline of the window is the most sensitive to aerodynamic resistance for both head and tail cars. The first auxiliary outline has a contradictory effect on the aerodynamic resistance of the head and tail car. Keywords: Kriging model  Multi-objective optimization Aerodynamic resistance  Train aerodynamics



1 Introduction As known to all, high-speed train has been developed rapidly all over the world, especially in China. As a major breakthrough in the construction of an innovative country and the iconic achievement of independent innovation, high-speed railway has become China’s new “diplomatic business card” and “image representative.”

This project is supported by National Natural Science Foundation of China (Grant No. 51605397), Sichuan Science and Technology Program (No. 2019YJ0227) and Self-determined Project of State Key Laboratory of Traction Power (2019TPL_T02). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 354–370, 2020. https://doi.org/10.1007/978-981-32-9941-2_30

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The increase of train aerodynamic drag seriously restricts the increase of train running speed and affects the economics of train operation. In recent years, the multi-objective aerodynamic optimization design of the train nose has been attracted more and more attention in order to improve the operation economy and running safety of trains. Kwon [1] used the response surface method to optimize the high-speed train head shape, and studied the influence of the train head shape on the tunnel pressure wave. Lee [2] aimed to reduce the micro-pressure wave generated when the train entered the tunnel. The Kriging model and the improved support vector machine technology were used to generate the approximate model, and the high-speed train head type was optimized. Krajnovic [3] proposed an optimization design method for train aerodynamic characteristics based on response surface method. The results show that the combination optimization is the best. Vytla et al. [4] based on the hybrid method of genetic algorithm and particle swarm optimization, combined with the Kriging approximation model, optimized the longitudinal two-dimensional contour of the high-speed train head to reduce the aerodynamic drag and aerodynamic noise of the train. Munoz-Paniagua et al. [5] optimized the aerodynamic drag and maximum pressure gradient when the high-speed train entered the tunnel, combined with genetic algorithm and perceptron neural network method, and carried out threedimensional head shape optimization design. Sun et al. [6] carried out a singleobjective optimization design on the nose shape of the CRH3 train and the height of the upper wall of the driver’s cab. The aerodynamic drag was used as a single optimization target to solve the optimization goal. Yao et al. [7] simplified the train model for the three groups of CRH380A, established a three-dimensional parametric model of the train head by local function method, and established the optimization target and optimization design variables based on Kriging method. Yao et al. [8] selected train aerodynamic drag and tail car aerodynamic lift as optimization targets, and optimized the high-speed train head shape based on particle swarm optimization. Li et al. [9] parameterized the three-dimensional head shape of high-speed train based on free-form deformation technology, combined with genetic algorithm and Kriging approximation model to optimize multi-objective design of high-speed train head shape to reduce the aerodynamic drag of high-speed trains. Yu et al. [10] and Zhang et al. [11] established an optimized design flow for high-speed train head shape, with the aerodynamic drag of the train running in the open air and the maximum wheel load shedding rate of the first car or the aerodynamic lift of the tail car as the optimization goal, through genetics. The algorithm optimizes the design of high-speed train heads. Zhang et al. [12] established a parametric model of the high-speed train including the bogie area, based on the Kriging approximation model and combined Multi-objective aerodynamic optimization design of high-speed train head shape based on genetic algorithm. The above researches concerned about the aerodynamic drag force of the train, for example, the aerodynamic drag of the head car or the whole train. Few work studied the effect of train nose on the aerodynamic drag force of the tail car. Moreover, the train nose affects the aerodynamic drag force of both head and tail cars. The design in train nose could be more complex if the contradiction for drag force of head and tail cars. In this research, the aerodynamic resistances of the head and tail cars are chosen as the dependent variables, an approach for aerodynamic design of a high-speed train nose based on Kriging model and multi-objective optimization is proposed to minimum the

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aerodynamic resistance of both the head and tail cars. Section 2 describes the numerical approach, and results are shown in Sect. 3, followed by conclusions.

2 Numerical Approaches The flow chart for the aerodynamic design of a train nose based on Kriging model and multi-objective optimization in this study can be described as follows. STEP1. According to the concerned objective variables and the parameterized train nose, choose the design variables including the dependent variables (also referred to as response variables or output variables) and independent variables (also referred to as input variables or predictor variables). And also the lower and upper values of the independent variables should be given. STEP2. Obtain the design matrix for the independent variables using Optimal Latin-hypercube design (OLHD). STEP3. Based on the parameterized train nose and every set of the independent variables, generate the train geometry using software CATIA. Establish the numerical simulation model for the aerodynamic including generating the mesh, numerical iteration and the result analysis. Obtain the dependent variables for every set of independent variables. STEP4. Establish Kriging model based on the above samples. STEP5. Perform the multi-objective optimization of the train nose based on the Non-dominated Sorting genetic algorithm II (NSGA-II) and the above Kriging model. The pareto results are obtained. The above procedures are illustrated in Fig. 1.

Determine the design variables

Concerned objective variables

Obtain the design matrix using OLHD

Design of Experiment

Generate the train geometry using CATIA

Parameterized train nose

Obtain the dependent variables

Computational Fluid Dynamics

Establish Kriging model

Multi-objective optimization using NSGA-II

Fig. 1. Configuration of the exoskeleton arm system

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2.1

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Design Variables and Parameterized Train Nose

The aerodynamic resistance of a train is one of the most important factors for the shape design of a high-speed train. Therefore, the aerodynamic resistances of the head and tail cars are chosen the dependent variables. Figure 2 shows the nose of a conceptual high-speed train, which is made up of several characteristic curves. Five typical curves are the vertical outline of the front nose C1, vertical outline of the window C2, lateral outline of the nose C3, the first auxiliary outline C4 and the second auxiliary outline C5.

C2

C1

C5 C4 C3 Fig. 2. Train nose and characteristic lines

All curves are B-spline ones generated by several key points, and then B-spline surfaces are generated by the above curves. The shape of the train nose is composited of several B-spline surfaces. The independent variables correspond to the characteristic curves, which are d1, d2, d3, s4, s5, respectively. Variables d1, d2, d3 are the maximum distance for the deformation of the corresponding curve. Variables s4 and s5 are the scale size for the deformation of the corresponding curve. The parametric method of the train nose is similar to the one used by Zhang et al. [12]. Table 1 gives the lower and upper values of design variables. Table 1. Lower and upper values of design variables d1/mm d2/mm d3/mm s4 s5 Lower value −100 −200 −30 −0.1 −0.15 Upper value 200 400 50 0.15 0.4

Figure 3 shows the variations of lower and upper values of design variables. For the upper value of variables d1 and d2, the height of the nose and the window increase as shown in Fig. 3(a). In the original model, the first and second auxiliary outlines are

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slightly concave (Fig. 3(e)), and they are concave at a certain for the upper value of variables s4 and s5 (Fig. 3(f)), whereas, they are convex when variables s4 and s5 are at lower value as shown in Fig. 3(d).

(a) Upper value of d1 and d2

(b) Initial value of d1 and d2

(c) Lower value of d1 and d2

(d) Upper value of s4 and s5

(e) Initial value of s4 and s5

(f) Lower value of s4 and s5

Fig. 3. Variations of independent variables

2.2

Design of Experiment (DOE)

The design of experiments (DOE) for the train nose is a design that aims to describe or explain the variation of independent variables under certain conditions that are hypothesized to reflect the variation. Optimal Latin-hypercube design (OLHD) was

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proposed by Park [13] to minimize the integrated mean squared error or maximize entropy. In this paper, OLHD is used to generate the design matrix of the independent variables of the train nose. In order to ensure the regression accuracy and the calculation efficiency, the number of designs is chosen as 301. The design matrix of independent variables is given in Table 2. The number 0 in Table 2 represents the original train model. Table 2. Design matrix of variables d1/mm 0 −97.00 −34.00 28.00 81.00 −47.00 … 29.00 9.00 114.00

0 1 2 3 4 5 … 299 300 301

2.3

d2/mm 0 272.00 −154.00 82.00 −138.00 342.00 … 358.00 158.00 28.00

d3/mm 0 −14.27 20.40 −5.73 19.07 44.67 … 2.00 32.40 −0.93

s4 0 −0.04 −0.05 −0.09 −0.08 0.12 … 0.12 0.03 −0.02

s5 0 −0.03 0.38 0.07 0.33 0.06 … 0.14 0.07 0.02

Numerical Model for Aerodynamics

The computational domain is shown in Fig. 4. The characteristic length H, which is based on the train height, is about 3.6 m. The computational domain has a length of 65H, width of 30H and height of 15H. A uniform velocity u = (83.33 m/s, 0, 0) is specified at the inlet boundary. A traction-free condition is prescribed at the outlet boundary, a symmetry condition is specified at the top boundary and 2 side boundaries, and a non-slip condition is specified all walls and train surface. The boundary conditions are shown in Fig. 4.

Symmetry Outlet

15H

Symmetry

Inlet

30 H

y x z

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50H

15H

Fig. 4. Computational domain and boundary conditions

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The commercial software FLUENT is used to obtain the aerodynamic characteristics of the train model. The Finite Volume Method (FVM) is adopted for the discretization of the Navier-Stokes equations. The Semi-Implicit Method for PressureLinked Equations (SIMPLE) algorithm is chosen to obtain the pressure and flow field. The SST k-w model and the Second Order spatial discretization schemes are chosen in this study [14, 15]. The mesh with about 15 million cells is generated using ANSYS ICEM. A boundary layer is considered in the mesh, which make the y+ on the surface of the train around 30–150. The number of iterations is 4000 and the average value over the latest 1000 iterations is calculated and chosen as the dependent variables. 2.4

Kriging Model

Kriging model is a type of interpolation technique. It is extremely flexible due to the wide range of correlation functions. It provides a minimum error-variance estimate of any un-sampled value, and it tends to smooth out the details and extreme values of the original data set. Matlab Kriging Tool box DACE is adopted to establish the Kriging model for the aerodynamic forces calculated using different independent variables. The usage of the tool box DACE is to construct a kriging approximation model based on the independent variables and corresponding dependent variables. In this paper, the second order polynomial is chosen for the regression model, and the Gaussian is chosen for the correlation model. 2.5

Multi-objective Optimization

Multi-objective optimization is an area of multiple criterion design making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics. Non-dominated Sorting genetic algorithm II (NSGA-II) is a solid multi-objective algorithm, widely used in many real-world applications. While today it can be considered as an outdated approach, NSGA-II has still a great value, if not as a solid benchmark to test against. NSGA-II generates off springs using a specific type of crossover and mutation and then selects the next generation according to nondominated-sorting and crowding distance comparison.

3 Results According to numerical approaches described in Sect. 2, the aerodynamic design of a high-speed train nose based on Kriging model and NSGA-II is studied in this section. The results include the train aerodynamics, Kriging model and the multi-objective optimization.

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Train Aerodynamics

The aerodynamic resistances of trains given in Table 3 are monitored during the iteration for every design. Symbols Fdh, Fdm, and Fdt are the aerodynamic resistances of the head, middle and tail cars, respectively. Meanwhile, F is the total aerodynamic resistance of the train. It can be seen that the resistance of the head car is larger than that of the tail car. Among all cases, the resistance of the head car is smallest for case 162, and also the resistance of the whole train is. Compared to the original model, the resistance of the head car for case 162 decreased by about 8.87%, and the resistance of the train decreased by 4.47%. Case 164 has the smallest resistance of the tail car, which decreased by 5.01% with comparison to that of the original tail car. The magnitude of the decrease in the resistance of the head car is larger than that of the tail one.

Table 3. Aerodynamic resistances 0 1 2 3 4 … 162 163 164 … 299 300 301

Fdh 6473.2 5998.4 6307.5 6184.5 6246.2 … 5899.2 6246.5 6132.3 … 6157.8 6375.1 6099.1

Fdm 4082.2 4045.0 4166.9 4110.9 4102.7 … 4062.4 4028.6 4114.0 … 4027.7 4146.4 4099.5

Fdt 5298.7 5131.3 5190.2 5154.4 5213.4 … 5184.0 5225.2 5033.4 … 5269.6 5183.0 5077.9

F 15854.1 15174.7 15664.6 15449.8 15562.3 … 15145.6 15500.3 15279.7 … 15455.1 15704.5 15276.5

In order to discriminate the difference in the aerodynamic forces, the pressure distribution on the head car and tail car are shown in Figs. 5 and 6, respectively. Three train models are chosen including the original one, case 162 with a minimum resistance of the head car and case 164 with a minimum resistance of the tail car. For the head car, the pressure on the head car is basically positive. The maximum pressure is located at the nose tip. Compared to the original head car, the pressure on the coupling cover is smaller for both cases 162 and 164. Meanwhile, the pressure on the window for case 162 is smaller than that on the corresponding position for case 164. Therefore, case 162 has the minimum aerodynamic resistance of the head car. For the tail car, the pressure on the tail car is basically negative except for the region of the front nose. Compared to the original tail car, the positive pressure on the

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(a) The original model

(b) Case 162

(c) Case 164 Fig. 5. Pressure distribution on the nose of the head car (Pa)

front nose is larger for both cases 162 and 164. Meanwhile, the area of the positive pressure for case 162 is smaller than that on that for case 164. Therefore, case 162 has the minimum aerodynamic resistance of the tail car.

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(a) The original model

(b) Case 162

(c) Case 164 Fig. 6. Pressure distribution on the nose of the tail car (Pa)

3.2

Approximation Model

There are 302 sets of independent variables and corresponding dependent variables including the original train model. Among them, 15 random sets of samples are chosen randomly as the validation samples, and the others are used to establish the Kriging model. Figure 7 shows the error in the drag forces of head and tail cars between predicted and numerical results. The maximum error in the drag force of the head car is almost less than 2% and the average error is 0.97%. For the tail car, the maximum and average

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errors are 1.85% and 0.73%, respectively. Results show that the Kriging model has a great ability to predict the aerodynamic drag forces for both head and tail cars, especially for the tail car.

(a) head car

(b) tail car Fig. 7. Error between predicted and numerical results

3.3

Multi-objective Optimization

The optimization process of the NSGA-II includes selection, crossover, and mutation. The manners of crossover and mutation of the NSGA-II are the same as those of the standard genetic operations. In present study, the population size is set to be 60, the evolution generation is set to be 40 and the crossover probability is 0.9.

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(a) independent variable d1

(b) independent variable d2

(c) independent variable d3

(d) independent variable s4

(e) independent variable s5

Fig. 8. Convergence history of five independent variables

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Figure 8 shows the convergence history of five independent variables during the process of the multi-objective optimization. The pentagrams in the Fig. 8 are the optimal results. Variable d1 is converged to be −100 mm, which means that the lower of the vertical outline of the front nose C1, the better aerodynamic forces are. The variations of d2 and s5 are similar to that of d1. It has lower aerodynamic force if the vertical outline of the window C2 is lower, the first auxiliary outline C4 is convex and the second auxiliary outline C5 is concave. While the variable s4 is in the middle range, it has a better performance. Moreover, the convergence of the variables d1, d2, and s5, is better than that of d3 and s4. Figure 9 shows the convergence history of aerodynamic drag force of the head and tail cars during the process of the multi-objective optimization. The red pentagrams in the figure represent the optimal results. Compared to the initial value which is calculated using the original train model, the aerodynamic resistance of the head car decreased by about 6.5%, and the resistance of the tail car decreased by 5.0%. The magnitude of the decrease in the resistance of the head car is larger than that of the tail one.

Fig. 9. Optimal results of multi-objective optimization

The main effect of all independent variables on the aerodynamic resistances of the head and tail cars is shown in Fig. 10. The main effect graph shows the effect of the independent variable on the dependent variable by plotting the relationship as determined by regression analysis of the data set. For the head car, the aerodynamic resistance increase with the incremental of variables d1, d2, and s5 and decrement of variable s4. Whereas the aerodynamic resistance of the tail car almost increase with the incremental of all independent variables.

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(a) head car

(b) tail car Fig. 10. Main effect of independent variables on the aerodynamic resistances of the head and tail cars

Pareto plot for the aerodynamic resistance of the head and tail cars is shown in Fig. 11. The pareto plot is similar to the main effect. For the head car, variables d1, d2 and s5 have positive effects on the aerodynamic resistance, and variables d3 and s4 give negative effects. Meanwhile, all independent variables have positive effects on the aerodynamic resistance of the tail car.

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(a) Head car

(b) Tail car Fig. 11. Pareto plot for the aerodynamic resistance of the head and tail cars

4 Conclusions (1) The approach of the reduction in the aerodynamic resistance of a high-speed train nose based on Kriging model and multi-objective optimization is proposed. (2) Compared to the original model, the resistance of the head car for case 162 decreased by about 8.87%, and the resistance of the train decreased by 4.47%. Case 164 has the smallest resistance of the tail car, which decreased by 5.01% with comparison to that of the original tail car. The magnitude of the decrease in the resistance of the head car is larger than that of the tail one. (3) The Kriging model has a great ability to predict the aerodynamic drag forces for both head and tail cars, especially for the tail car. (4) Compared to the initial value which is calculated using the original train model, the aerodynamic resistance of the head car decreased by about 6.5%, and the resistance of the tail car decreased by 5.0%. The magnitude of the decrease in the resistance of the head car is larger than that of the tail one.

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(5) Variables d1, d2 and s5 have positive effects on the aerodynamic resistance. The vertical outline of the window C2 is the most sensitive to aerodynamic resistance for both head and tail cars. The first auxiliary outline C4 has contradict effect on the aerodynamic resistance of the head and tail car.

Appendix Appendix and supplement both mean material added at the end of a book. An appendix gives useful additional information, but even without it the rest of the book is complete: In the appendix are forty detailed charts. A supplement, bound in the book or published separately, is given for comparison, as an enhancement, to provide corrections, to present later information, and the like: A yearly supplement is issue.

References 1. Kwon, H.B., Jang, K.H., Kim, Y.S., et al.: Nose shape optimization of high-speed train for minimization of tunnel sonic boom. JSME Int. J. Ser. C 44(3), 890–899 (2001) 2. Lee, J., Kim, J.: Kriging-based approximate optimization of high-speed train nose shape for reducing micropressure wave. Proc. Inst. Mech. Eng. Part F: J. Rail and Rapid Transit 221 (2), 263–270 (2007) 3. Krajnovic, S.: Shape optimization of high-speed trains for improved aerodynamic performance. Proc. Inst. Mech. Eng. Part F: J. Rail Rapid Transit 223(5), 439–452 (2009) 4. Vytla, V.V., Huang, P.G., Penmetsa, R.C.: Mufti objective aerodynamic shape optimization of high speed train nose using adaptive surrogate model. In: 25th AIAA Applied Aerodynamics Conference, Chicago, USA (2010) 5. Munoz-Paniagua, J., Garcia, J., Crespo, A.: Genetically aerodynamic optimization of the nose shape of a high-speed train entering a tunnel. J. Wind Eng. Ind. Aerodyn. 130, 48–61 (2014) 6. Sun, Z.X., Song, J.J., An, Y.R.: Optimization of the head shape of the CRH3 high speed train. Sci. China-Technol. Sci. 53(12), 3356–3364 (2010) 7. Yao, S.B., Guo, D.L., Yang, G.W.: Three-dimensional aerodynamic optimization design of high-speed train nose based on GA-GRNN. Sci. China-Technol. Sci. 55(11), 3118–3134 (2012) 8. Yao, S.B., Guo, D.L., Sun, Z.X., et al.: Parametric design and optimization of high speed train nose. Optim. Eng. 17(3), 605–630 (2016) 9. Li, R., Xu, P., Peng, Y., et al.: Multi-objective optimization of a high-speed train head based on the FFD method. J. Wind Eng. Ind. Aerodyn. 152, 41–49 (2016) 10. Yu, M.G., Zhang, J.Y., Zhang, W.H.: Multi-objective optimization design method of the high-speed train head. J. Zhejiang Univ.: Sci. A 14(9), 631–641 (2013) 11. Zhang, L., Zhang, J.Y., Li, T., et al.: Multi-objective aerodynamic optimization design of high-speed train head shape. J. Zhejiang Univ.: Sci. A (Appl. Phys. Eng.) 18(11), 841–854 (2017) 12. Zhang, L., Zhang, J.Y., Li, T., et al.: A multi-objective aerodynamic optimization design of a high-speed train head under crosswinds. J. Rail Rapid Transit 232(3), 895–912 (2018)

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13. Park, J.-S.: Optimal Latin-hypercube designs for computer experiments. J. Stat. Plan. Infer. 39(1), 95–111 (1994) 14. Li, T., Hemida, H., Zhang, J.Y., et al.: Comparisons of shear stress transport and detached eddy simulations of the flow around trains. J. Fluids Eng. 140(11), 111108–111112 (2018) 15. Li, T., Zhang, J.Y., Rashidi, M., et al.: On the Reynolds-averaged Navier-Stokes modelling of the flow around a simplified train in crosswinds. J. Appl. Fluid Mech. 12(2), 551–563 (2019)

Research and Simulation on Pilot Configuration in Multi-antenna System Based on Kalman Filter Ying Li1(&), Lei Cui2, and Zhe Zhang1,3 1

2

Department of Electronics and Information Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China [email protected], [email protected] Department of Society, Gansu Academy of Mechanical Sciences CO. LTD., Lanzhou 730030, China [email protected] 3 Gansu Provincial Key Laboratory of Wearable Computing, School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China

Abstract. CRH has become a distinctive business card in the transportation industry around the world. However, transmitted signals suffer multi-path effect in wireless channels. Especially, server Doppler shift causes energy loss to received signals, and the wireless communication quality declines. In this paper, architecture of a joint Kalman Filter and multi-antenna system is designed, based on Ricean fading channels. A comparative analysis of channel performance estimation is given between the estimator designed by Ref. [5] and that of our architecture by simulations. For the same velocity of the train and Ricean factor, DFO estimation error is less than the estimator mentioned before for the same number of received antennas. Then, we compare DFO estimation with pilots decreased by 10 in a frame according to previous assumptions of 50, simulation results show that, before the pilot number drops to 20, DFO estimation error has no obvious growth, when equals to 20, error increases significantly, that is, the estimation performance referred in this paper gets worse. Another important contribution for this paper is that the framework we have established provides a method and basis for the pilot configuration in a multiantenna system to a receiver. Keywords: High Speed Railway Multi-antenna  Kalman filter

 DFO  Ricean fading channel  Pilot 

1 Introduction The construction of China Railway High-Speed (CRH) is the longest in the world, which has become a distinctive business card of contemporary China [1–3]. By the end of 2018, the operational mileage of CRH exceeded 29000 km, two-thirds of the total This project is supported by National Natural Science Foundation of China (No. 61841202)Scientific Research Projects of Universities in Gansu province of China (2017A-1022017A-106). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 371–379, 2020. https://doi.org/10.1007/978-981-32-9941-2_31

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mileage of the High Speed Railway (HSR) in the world [4]. However, transmitting signals experience reflection, refraction and scattered paths multiple times to receivers in wireless channels, leading to signal degradation. For instance, the modulated signals transmit in high mobility situations suffer severe multi-path fading caused by Line-ofsight (LOS) propagation, and penetration loss caused by signals pass through the train body. Furthermore, Additive White Gaussian Noise (AWGN) and random phase shift can also lead to signal energy loss. Besides, the most challenge in the HSR channel is the serious Doppler shift, due to fast movement of HSR [5]. All problems above result in the decline of wireless communication quality, and the passengers’ communication requirements cannot be met as well. Regarding the problems mentioned before, many researchers focused on HSR channel estimations and compensations to improve wireless communication quality. For the penetration loss, a two-hop channel model was proposed by a bunch of literatures [6–8], in the uplink of the model, passengers’ data transmit firstly to antennas installed outside the carriage, then, the gathered data is transferred to the base station, and the opposite function for the downlink transmission process. The advantage of this model is the direct information exchange can be avoided, problems of penetration loss and energy loss can be solved as well. So, this model is applied in our paper. For multipath problem, MIMO technology significantly improves the reliability of the channel and reduces the transmission error rate, and the problem of the multi-path fading has also been solved [9]. [10–14] studied some methods to estimate the channel performance in MIMO system. [15, 16] discussed pilot designing in massive MIMO networks. In this paper, we present architecture for Doppler shift estimation based on Kalman filtering in multi-antenna system, estimation results can be given in simulation work based on the architecture we have noted before. Main contributions for this paper are: (1) the transmit channel model of joint Kalman Filter and multi-antenna system is proposed to estimate channel performance. (2) Comparisons of channel estimation based on Rice fading model with that of the estimator proposed in [5] are also studied by simulations. (3) Simulation works of pilot configuration in data frames are shown and illustrated, by estimating channel character. (4) The framework can offer a way and basis for pilots’ configuration in a cooperative antenna system to a receiver. The rest of the paper is organized as follows, in Sect. 2, we describe the system model and channel model. Then, comparisons of channel character estimation for those two estimators are shown, and pilots’ configuration for our architecture is also shown in Sect. 3 by simulations. Conclusions are given in Sect. 4.

2 System Model 2.1

System Model

A two-hop model is shown in Fig. 1, passengers’ communications to the base station are done through antennas installed on the carriages, instead of communicating to the base station directly. Suppose there’s one antenna fixed in one carriage, if we know the distance from the first antenna to the origin, the distance from the origin to all antennas

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can be calculated, because the length of carriage is a fixed value, typically 10 m. The train usually has 16 carriages, so the train length can also be calculated. Besides, the distance from base station to the origin is also known for 50 m [5].

Fig. 1. A two-hop model

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Channel Model

We consider a transmission channel model shown in Fig. 2. It shows clearly that after estimating all parameters, received signals will be decoded, and then the information is sent to user terminals after demodulation.

Fig. 2. A transmission channel model

In Fig. 2, there is a multi-antenna system with N antennas over a high speed train. Each antenna receives signals transmitted from the base station, and it also transmits signals to the base stations. Received signals suffer an Additive White Gaussian Noise W with a variance of 2d2 . Small-Scale Fading causes server Doppler shift and multipath effect in channel. In addition, Large-Scale Fading causes Shadow-fading and path loss, etc. Therefore, we let l to be the Large-Scale fading factor for simulations. Then, the channel model is given by Y ¼ HX þ W

ð1Þ

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Where N is antenna number, R is received symbols in a frame.Y 2 SNR is the received signals vector, and H denotes Ricean channel fading with Ricean factor k, which indicates the intensity of the direct component relative to the multipath component. By Eq. (1), received signals can be rewritten as yn ¼

R1 X

hnr xnr þ wn ; n ¼ 1; 2; . . .N

ð2Þ

r¼0

The average received SNR for each antenna can be given as n o n o RE jhnr j2 E jxr j2 n o SNR ¼ E jwn j2

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Pilots and Kalman Filter Configuration

It was reported that Kalman approach is of the superiority in improving estimation accuracy in time-varying linear systems [17]. For high mobility of HSR, channel estimation became very difficult, especially for limited pilots. Therefore, we introduce Kalman filtering into multi-antenna system for better DFO estimations. Suppose there are B symbols in a data frame, while we choose C of them for pilots, that is, there are (C-B) symbols after each pilot. Estimation accuracy increases at the expense of transmission efficiency and estimation complexity. In our architecture, we use limited pilots less than C for estimation, so we replace the removed pilots with Kalman filtering. If the channel performance estimation results are similar to that without Kalman filtering, it can be proved that the architecture proposed in this paper is reasonable, especially, pilots can be saved effectively. Pilot and Kalman filter configuration is shown in Fig. 3. The probability Density Function (PDF) can be given by Ref. [5] f ðx; v; hÞ ¼

N [ C [

f ðxnr ; v; hnr Þ

ð4Þ

n¼0 c¼1

The coherent time T can be calculated by T = c/fv, if the train velocity and carrier frequency are given. Suppose v = 150 m/s, f = 1.8 GHz, then coherent time T  1.1 ms, the frame interval can be set to 1 ms in simulations in Sect. 3, while the sampling time is 0.25 ls.

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Fig. 3. Pilots and Kalman filter configuration

3 Simulation Ref. [5] derives the channel parameter estimation performance such as path loss, velocity random phase, and DFO estimation error by the Theoretical Rao bound (CRB). Besides, theoretical symbol error rate function is also derived. In this section, first, we compare the DFO estimation error of the architecture proposed in this paper with that of the estimator designed in Ref. [5], for good estimation performance results in Ref. [5]. Second, we compare the channel performance estimations for different number of pilots by simulations. Finally, theoretical comparison and analysis are summarized. For comparison purposes, we choose the 9th received antenna, the same as Ref. [5], Assume the distance from the base station to the first antenna is within 100 m [18], we stipulate the estimation error is set no more than 1%, if not, error range can exceed 5%. In addition, it should be noted that, when calculating the DFO estimation error, there will be some deviation, because the receiver is moving constantly but the frequency offset estimation is only once. 3.1

Estimation Performance Compared with Ref. [5]

The channel estimation performance compared with that in Ref. [5] by simulations shown in Fig. 4, let v = 100 m/s, while the average of k is about 8.25 [18]. The sampling time TS = 0.25 ls, symbols in a frame B = 4000 and pilots C = 50, the Ricean factor k = 5 for Doppler shift estimation. From Fig. 4, we can conclude that (1) Simulation results of DFO estimation error performance are basically consistent with the theoretical performance with the same v and k, which can prove the correctness of simulation results. (2) The estimation error increase as a increases, especially for a > 100 m. (3) Comparison of simulated results show that estimation performance proposed in this paper is better than the estimator in Ref. [5].

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Fig. 4. Error performance of DFO estimation for the 9th received antenna, when v = 100 m/s, k = 5, C = 50

We know that Doppler shift increases as the train speed increases, Fig. 5 shows simulations on DFO estimation error performance when the velocity v = 150 m/s.

Fig. 5. Error performance of DFO estimation for the 9th received antenna, when v = 150 m/s, k = 5, C = 50

We conclude from Fig. 5 that DFO estimation error has no obvious growth under the condition of the train speed increase. Simulation results show that the estimation performance is stable for the framework proposed by us.

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Estimation Performance Compared Different Pilot Configuration

We choose the average value of Ricean factor k = 8.25 for simulation in this section. The previous simulations are under the condition of C = 50. In this section, we reduce the number of pilots in a frame, then, DFO estimation error performance is given in Fig. 6.

Fig. 6. Comparisons of estimation performance for the 9th received antenna, when v = 150 m/s, k = 8.25, with different pilot configuration

We conclude that, in the situation of C = 40 and C = 30, the DFO estimation error performance is close to that of C = 50, nevertheless, when C drops to 20, the performance begins to be worse. Simulation results demonstrate that, the estimation accuracy of our framework is relatively stable when k is reduced to a certain extent, which means the number of pilots for estimation can be saved effectively. 3.3

Comparisons of BER Performance for Different Ricean Channels

Figure 7 shows the comparisons of bit error rate (BER) performance for different Ricean channels by 16QAM. When k = ∞, means the interference of AWGN is added, we can conclude that, (1) The bit error still exists for both framework, the nonlinear communication system for high mobility channel is one reason, another is the estimation method needs to be further improved. (2) For the same SNR, BER performance applying our framework is better than the estimators’ in Ref. [5]. The estimation framework proposed by us is more efficient. (3) When k varies to 8.25, BER performance becomes better obviously, because channel fading drops. The increase of Ricean factor k reduces the noise and the channel fading, and the estimation accuracy is improved.

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Fig. 7. Comparisons of BER performance for different Ricean channels, when k = ∞, k = 8.25

(4) The larger the SNR, the better the bit error rate performance. Especially, when BER is 10−4, SNR performance for both estimators’ is less than 1 dB.

4 Conclusion In this paper, an architecture for DOF and channel performance estimation is devised, which consists a multi-antenna system installed outside the train carriages, and Kalman filtering is also included. A comparative analysis of channel performance estimation is given between the estimator in [5] and that of our architecture in Ricean fading channel by simulations. Simulation results show that, (1) The theoretical DFO estimation error performance is basically the same as the simulation performance with the same velocity and Ricean factor k. (2) The estimation error increase as a increases, especially for a > 100 m, a denotes the distance from the base station to the first antenna. (3) Estimation performance proposed in this paper is better than that of the estimator in Ref. [5]. (4) DFO estimation error has no obvious growth as the train speed increases. (5) The number of pilots for estimation can be saved effectively by our framework. The framework we have established provides a method and basis for the pilot configuration in a multi-antenna system to a receiver. (6) Simulation results prove the efficiency of estimation method. Simulations on BER performance show there are still some bit errors in system, we need to improve the estimation algorithm and framework to increase the estimation accuracy in our future work.

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References 1. Cao, J., Liu, X.C., Wang, Y., Li, Q.: Accessibility impacts of China’s high-speed rail network. J. Transp. Geogr. 28, 12–21 (2013) 2. Shaw, S.-L., Fang, Z., Shiwei, L., Tao, R.: Impacts of high speed rail on railroad network accessibility in China. J. Transp. Geogr. 40, 112–122 (2014) 3. Lvhua, W., Yongxue, L., Liang, M., Sun, C.: Potential impacts of China 2030 high-speed rail network on ground transportation accessibility. Sustainability 10, 1–16 (2018) 4. January 2019. http://society.people.com.cn/n1/2019/0104/c1008-30502584.html 5. Yaoqing, Y.A.N.G., Pingyi, F.A.N.: Doppler frequency offset estimation and diversity reception scheme of high-speed railway with multiple antennas on separated carriage. IEEE J. Mod. Transp. 20(4), 227–233 (2012) 6. Zhang, C., Fan, P., Dong, Y., Xiong, K.: Service-based high-speed railway base station arrangement. Wirel. Commun. Mob. Comput. 15(13), 1681–1694 (2015) 7. Dong, Y., Fan, P., Letaief, K.B.: High speed railway wireless communications: efficiency versus fairness. IEEE Trans. Veh. Technol. 63, 925–930 (2014) 8. Li, Y., Zhang, C.: Analytic comparisons of the high-speed railway base station arrangement strategy in fading channels, Beijing, pp. 187–191, November 2014 9. Oestges, C., Clerckx, B.: MIMO Wireless Communications: From Real-World Propagation to Space-Time Code Design, vol. 312. China Machine Press, Beijing (2010) 10. Shen, L., Yao, Y.-D., Wang, H., Wang, H.: ICA based semi-blind decoding method for a multicell multiuser massive MIMO uplink system in Rician/Rayleigh fading channels. IEEE Trans. Wirel. Commun. 16(11), 7501–7511 (2017) 11. Yapıcı, Y., Güvenç, I., Kakishima, Y.: A MAP-based layered detection algorithm and outage analysis over MIMO channels. IEEE Trans. Wirel. Commun. 1–29 (2017) 12. Li, T., Wang, X., Fan, P., Riihonen, T.: Position-aided large-scale MIMO channel estimation for high-speed railway communication systems. IEEE Trans. Veh. Technol. 66(10), 8964– 8978 (2017) 13. Lu, J., Chen, Z., Fan, P., Letaief, K.B.: Subcarrier grouping for MIMO-OFDM systems over correlated double-selective fading channels. Wirel. Commun. Mob. Comput. 1–30 (2015) 14. Kim, H.K., Byun, Y.S., Lee, Y.H.: Estimation of MIMO channel with imperfect channel correlation information. Wirel. Pers. Commun. 95(3), 3377–3389 (2017) 15. Akbar, N., Yan, S., Yang, N., Yuan, J.: Mitigating pilot contamination through locationaware pilot assignment in massive MIMO networks. In: 2016 IEEE Globecom Workshops, Washington, DC USA, December 2016 16. Noh, S., Zoltowski, M.D., Sung, Y., Love, D.J.: Pilot beam pattern design for channel estimation in massive MIMO systems. IEEE J. Sel. Top. Sig. Process. 8(5), 1–15 (2013) 17. Komninakis, C., Fragouli, C., Sayed, A.H., Wesel, R.D.: Multi-input multi-output fading channel tracking and equalization using Kalman estimation. IEEE Trans. Sig. Process. 50(5), 1065–1075 (2010) 18. Liu, L., Tao, C., Qiu, J.H., Yu, L.: Position-based modeling for wireless channel on highspeed railway under a viaduct at 2.35 GHz. IEEE J. Sel. Areas Commun. 30(4), 834–845 (2012)

Development and Experiment of an XhYhZ Micro-motion Stage Based on a Straight-Beam Three-Quarter Round Type Flexure Hinge Junlang Liang1, Lanyu Zhang1,2(&), Jian Gao1,2, Gengjun Zhong1, Guangtong Zhao1, and Jindi Zhang1 1

Laboratory of Electronic Precision Manufacturing Equipment and Technology of Ministry of Education, Guangdong University of Technology, Guangzhou 510006, China [email protected] 2 State Key Laboratory of Precision Electronic Manufacturing Technology and Equipment, Guangdong University of Technology, Guangzhou 510006, China

Abstract. This paper proposes a type of straight-beam three-quater round type (STR) flexure hinge for a micro-actuation motion stage in the field of precision micro-operation manufacturing. Based on the hinge, a three degree-of-freedom precision parallel micro-motion stage is designed. Firstly, the rigid and flexure structural design of the STR flexure hinge is presented, and theoretical analysis and simulation performance verification are carried out. Based on the elastic statics and calculus theory, the flexibility expression of the flexure hinge is derived under different stresses. The flexibility of the hinge is verified by ANSYS software. The results show that the designed flexure hinge can effectively achieve complaisant deflection and rigid support with high stress. Moreover, a XhYhZ micro-motion stage based on the STR hinge is established, and the dynamic performance of the stage is simulated and verified by Matlab/Simulink. Finally, the experimental stage is set up. The experimental results are compared with the simulation results, and the stage can achieve about 3.7 times micro-actuation amplification ratio and 68 lm displacement stroke. Keywords: Micro-motion stage Precision micromotion operation

 Flexure hinge  Parallel mechanism 

1 Introduction With the rapid development of MENS technology, the precision micro-motion stage based on flexure hinge has been widely used in many precision manufacturing and operation fields because the stage has the characteristics of no mechanical friction, no gap, high motion sensitivity and good stability, etc. It has an vital position in many

This work is supported in part by the National Natural Science Foundation under Grant 51675106, and 51905108, and in part by the Guangdong Provincial R&D Key Projects under Grant 2015A030312008, 2016A030308016 and 17ZK0091. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 380–393, 2020. https://doi.org/10.1007/978-981-32-9941-2_32

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precision equipment and devices, such as microelectronic precision manufacturing, micro-positioning robots, ultra-precision processing equipment, etc. Scholars from all over the world have carried out extensive researches on the micro-motion stage flexure hinge [1]. Wu et al. proposed an concise compliance and accurate flexure hinge formula for achieving a rapid analysis [2]. Lobontiu et al. derived the calculation formula of the flexibility of the angular straight beam type flexure hinge by Cartesian second comparison. The results showed that the precision performance of straight-circular flexure hinges can realize better performance in the common hinge types [3]. At present, the straight beam flexure hinge is widely used because its advantages of high precision motion and stable rigidity. However, its stroke range is still limited, which generally has lower degree of flexibility. The flexibility degree of arc flexure hinge is higher than common hinges, which can obtain a large deflection by comparing with the straight beam type hinge. But, its precision stability is lower than the straight beam type [4]. Therefore, in order to improve the precision and deflection performance of the flexure hinge, this paper proposes a straight-beam three-quater round type (STR) flexure hinge by combining of the straight beam characteristics and the arc beam. The proposed hinge is symmetrically arranged based on the central point with a short wide straight beam in the middle, and round edges are designed around the wide straight beam. The flexibility calculation is derived by elastic statics and calculus theory, and the performance of the hinge is verified by ANSYS software (Fig. 1).

Fig. 1. Model diagram of the hinge and parameter sketch

For the precision micro-manipulation motion stage, the stage must have the characteristics of high precision output [5–7]. Now, the piezoelectric (PZT) element is widely used as the actuation element in the micro-motion stage with the characteristics of high-precision, high-speed response, large thrust, etc. But the stroke of PZT is limited, which is usually used with a displacement flexure hinge amplification mechanism in the micro-motion stage to realize a large-stroke high-precision micro-motion [8, 9]. In this paper, the STR flexure hinge is used as the rotating link in a designed two-stage amplification mechanism, and the spatial position of the amplifying mechanism is analyzed. The natural frequency of the stage is analyzed by dynamic theoretical analysis, which is verified with simulation software. Based on the set up of the experimental stage, the performance of the stage is verified with experiments.

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2 STR Flexure Analysis 2.1

Flexibility Analysis of the STR Hinge

The designed STR flexure hinge can be divided into two parts. The first part is the equivalent two round edges of the hinge; the second part is the straight beam width at the middle of the hinge. Figure 2 is a dimensional sketch of the Part 1 of the hinge, where r is the inscribed radius of the circle; t is the minimum thickness of hinge; H is the width of the X-axis symmetry; h is the central angle of the inscribed cylindrical surface. Figure 3 is a schematic diagram of a micro-element parallel to the Y-axis direction including a height dx, a length d, and a width b.

Fig. 2. Dimensional sketch of Part 1 of the hinge

Fig. 3. Micro-element diagram parallel to the Y-axis direction

To study the compliance characteristics of the hinge, the upper end is assumed as a fixed end, the lower end is assumed as a free end (Fig. 2). Six-dimensional generalized force act on point O, relatively, which are displaced in six degrees of the freedom point O. According to the Euler-Bernoulli beam theory and small deformation hypothesis,  T the setting six-dimensional generalized force are Qo ¼ Fx ; Fy ; Fz ; Mx ; My ; Mz ; the  T deformation is uo ¼ Dx; Dy; Dz; ax ; ay ; az : uo ¼ ½C Qo

ð1Þ

In the equation, the symmetric matrix C is set to measure the relationship between the load and the deformation. The I represents deformation, j represents the load, and the compliance element is Cij. The designed STR flexure hinge is composed of two identical T-type bodies. Firstly, the flexibility properties characteristics of the T-type bodies are studied. We set the elastic modulus parameter of the material is E, the shear modulus parameter is G,

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and I(x) is the moment of inertia of the cross section for the micro-element dx facing the central axis. In the O-xyz coordinate system, the hinge is divided into two regions, such as shown in Fig. 4. Then the area of this hinge section can be calculated.

Fig. 4. Schematic diagram of the partition of the T-shaped section

1. For the I section, the section area can be obtained when p=2  h  p=2: a1 ¼ 2r þ t  2r cos h; dx1 ¼ d ðr sin hÞ ¼ r cos hdh

ð2Þ

2. For the II section, the section area can be obtained when p=2  h  p: a ¼ 2r þ p þ r cos h dx2 ¼ d ðr sin hÞ ¼ r cos dh

ð3Þ

At the same time, when make s ¼ r=t; m ¼ r=p, the first intermediate variable h(h) and the second intermediate variable g(h) can be obtained:

2.2

hðhÞ ¼ s þ 1=2  s cos h

ð4Þ

gðhÞ ¼ m þ 1=2 þ m cos h

ð5Þ

Compliance Formula

This section studies the rotational stiffness performance of the STR flexure hinge around the Z-axis. It is an important performance indicator for flexure. The moment Mz is expressed the lead to a deflection angle around the Z-axis. az ¼ CaMz  Mz

ð6Þ

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The flexure of the angular deformation az can be expressed as: Cðaz Mz Þ ¼ az=Mz Z r ¼ ðMz dxÞ=ðEIz ð xÞÞ ðr Þ

Z ¼

ðp=2Þ

ðp=2Þ Z p ðp=2Þ

r cos hdh=ð2t  hðhÞÞ3 þ

ð7Þ

r cos hdh=ð2p  gðhÞÞ3

  ¼ 3r=2Eb f1 =t3 þ f2 =p3 Among them, the intermediate variables are: Z f1 ¼

ðp=2Þ

Z f2 ¼

ðp=2Þ

ðp=2Þ

ðp=2Þ

  cos h= h3 ðhÞ dh

ð8Þ

  cos h= g3 ðhÞ dh

ð9Þ

The flexibility of the hinge (Fig. 5) around the Z-axis compliance equation can be obtained according to the mechanics of materials: C 0 a M ¼ az =Mz ð ðzÞ z Þ Z ðh=2Þ ¼ ðMz dxÞ=ðEIz ð xÞÞ ðh=2Þ

  ¼ 12= Ebð2r þ tÞ3

Fig. 5. Schematic diagram of the second hinge around the Z axis direction

ð10Þ

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385

Calculation of Overall Rotational Stiffness of Flexure Hinge

The total flexibility of the flexure hinge about the Z-axis can be obtained from the superposition formula of compliance: Cz ¼ CðaðzÞ Mz Þ þ Cð0 a M Þ ðzÞ z    3  ¼ 3r=Eb f1 =t þ f2 =p3 þ 12h= Ebð2r þ tÞ3

2.4

ð11Þ

Finite Element Verification and Comparison

Through the ANSYS software, the calculated formula of the overall stiffness/flexure hinge is verified (Figs. 6 and 7). The material of the STR hinge is aerospace aluminum 7075, and the corresponding flexibility is calculated. By comparing the theoretical solution with FEA, the error between the simulation and the theoretical analysis is less than 5%.

Fig. 6. Flexure hinge finite element model

Fig. 7. Finite element deformation of flexure hinge

In order to further verify the performance of the designed STR flexure hinge, the flexibility performance of the STR hinge is compared with the straight circular flexure hinge which is widely used in many motion stages. The simulation results are shown in

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Table 1. The results show that the STR hinge has better mobility in terms of compliance performance. Under the size parameters of r = 1.75; b = 12; t = 1.25; p = 1.5; h = 1.5, the flexure movement of the STR hinge is 6.4410−4 (better than the 6.0410−4 of the biaxial straight circular flexure hinge).

3 XhYhZ Micro-motion Stage Based on the STR Hinge 3.1

Structural Composition

In the field of micro-motion precision manufacturing, there is a high requirement for the linear precision motion performance of the micro-motion stage [10, 11]. For achieving a high precision position adjustment micro-driving, the PZT is used as the driving component. A lever-type amplification mechanism is designed, and the center of mass is designed by the two-lever alignment method. The proposed STR hinge is used in the amplification mechanism. Finally, a XhYhZ micro-motion stage is established with three amplification mechanisms. The specific structure is shown in Fig. 8.

Fig. 8. XhYhZ Micro-motion stage structure Table 1. Geometric parameters and flexibility comparison 组别 r/mm b/mm t/mm p/mm h/mm The straight circular compliance FEA 1 2 3 4 5 6

0.75 1 1.5 1.75 2 2.25

7 10 10 12 12 14

1 1 1.25 1.25 2 2.5

1 1 1.5 1.5 2 2.5

0.5 1 1.25 1.25 1.5 2

7.25 10−4 6.0410−4 2.1110−4 1.5510−4 0.8910−4 0.5710−4

The proposed STR hinge compliance Theoretical solution 7.7310−4 6.2710−4 2.7610−4 1.6510−4 0.9810−4 0.7110−4

FEA 7.3210−4 6.4410−4 2.2710−4 1.6910−4 0.9610−4 0.6810−4

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Analysis of Kinetic Theory

The structural features of micro-motion dynamics model (Fig. 9) can be represented with Newton’s second law kinematics, and the motion dynamics differential equations can be expressed as follows: 8 < F1  k1 x1 þ k2 ðx3  x1 Þ  Cx01 þ k2 ðx2  x1 Þ ¼ m1 x001 F2  k1 x2 þ k2 ðx3  x1 Þ  Cx02  k2 ðx2  x1 Þ ¼ m2 x002 : F3  k1 x3  k2 ðx3  x1 Þ  Cx03  k2 ðx2  x1 Þ ¼ m3 x003

ð12Þ

Where k1 is the stiffness of the spring element in the micro-dynamic structure; k2 is the stiffness of the precision motion stage; C is the damping coefficient of the piezoelectric ceramic; m1, m2, m3 are the equivalent masses of the three enlarged structures respectively; F1, F2, F3 represents the driving force of the drive piezoelectric micromotion stage. x1, x2, x3 are the output displacements, respectively.

Fig. 9. Micro-motion dynamic theoretical model

In order to analyze the dynamic performance of the stage, the kinetic equations are expressed in matrix form: MX 00 þ CX 0 þ KX ¼ f

ð13Þ

2

3 m1 0 0 Here, M ¼ 4 0 m2 0 5 is the equivalent mass matrix; K ¼ 0 0 m3 2 3 k1 þ 2k2 k2 k2 4 k2 k1 þ 2k2 k2 5 is the equivalent stiffness matrix for the kinetic k2 k2 k1 þ 2k2 2 3 0 1 C 0 0 x1 model; C ¼ 4 0 C 0 5 is the damping matrix for the dynamic model; X ¼ @ x2 A 0 0 C x3 0

1 0 00 1 x01 x1 is a displacement vector; X 0 ¼ @ x02 A is the speed vector; X 00 ¼ @ x002 A is the x03 x003

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2

3 0 F1 0 acceleration vector; f ¼ 4 0 F2 0 5 is the equivalent force matrix acting on the 0 0 F3 micro-motion process. Accordingly, the general displacement solution of the system can be expressed as: x ¼ A sinðxt þ hÞ

ð14Þ

Similarly, the velocity equation can be expressed as: x0 ¼ Ax cosðxt þ hÞ

ð15Þ

x00 ¼ Ax2 sinðxt þ hÞ

ð16Þ

The acceleration equation is:

0

1 A1 Here, A ¼ @ A2 A is the amplitude coefficient of the system, x is the angular A3 frequency, h is the phase angle. The free vibration equation of the system can be obtained by using the displacement and acceleration equations in the above equation:   K  x2 M X ¼ 0

ð17Þ

For this equation, the characteristic equations of the system can be obtained by solving the characteristic equations:   K  x2 M  ¼ 0

ð18Þ

The solves of the above characteristic equations are: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 ðmk1 Þ=m < x1 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi mðk1 þ 3k2 ÞÞ=mffi x2 ¼ pðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : x3 ¼ ðmðk1 þ 3k2 ÞÞ=m

ð19Þ

The natural frequency of the stage can be obtained based on the kinetic model parameters of Table 2. 8 < x1 ¼ 149:35 Hz x ¼ 216:43 Hz ð20Þ : 2 x3 ¼ 216:43 Hz

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Table 2. Related parameters of the dynamic model Parameter M (kg) K1 (N/m) K2 (N/m) Value 0.269 6000 2200

3.3

Natural Frequency Simulation Analysis

In order to verify the correctness of the dynamics theoretical analysis, the natural frequency analysis of the object is performed by the ANSYS/model simulation.

Fig. 10. Finite element model of the micro-motion stage

(a) First-order mode

(b) Second-order mode

(c)Third-order mode Fig. 11. Vibration pattern analysis

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J. Liang et al. Table 3. ANSYS natural frequency values x2 x3 Inherent frequency x1 (Hz) (Hz) (Hz) Value 141.34 229.05 229.09

Figure 10 is a finite element model of the micro-motion stage, and the model is meshed firstly. Moreover, by setting the model parameters, the amplitude of the stage is analyzed, and the analysis result is shown in Fig. 11. Table 3 is the simulation results of the natural frequency. Based on the theoretical solution and the natural frequency obtained by ANSYS, it can be seen that the error of theoretical analysis and simulation analysis is less than 5%, which proves the correctness of the dynamic analysis of the stage. 3.4

Dynamics Simulation Analysis

In order to observe dynamic performance of the stage, the rapid motion positioning, positioning overshoot, and the positioning accuracy performance of the stage are tested with MATLAB/Simulink simulation. The results are shown in Fig. 12. It can be seen that the stage designed in this paper can effectively meet the high-precision performance requirements of precision motion operating on its motion stage.

Fig. 12. Dynamic simulation result of the micro-motion stage

4 Experimental Analysis The experimental stage is shown in Fig. 13. The micro-motion stage is set under the laser precision manufacturing device from Han’s Laser Ltd. A laser interferometer is used to verify the position performance of the stage.

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Fig. 13. Experimental setup of the designed micro-motion stage

4.1

Natural Frequency Experiment Verification

In the experiments, the stage is mounted on a vibration isolation platform, and the natural frequency of the stage is measured. The experimental result is shown in Fig. 14. By using the Fourier analysis, a natural frequency 115.32 Hz is obtained, which is has a 10% error with the theoretical analysis because the testing viewfinder on the stage increases the stage quality.

Fig. 14. Laser interferometer amplitude map

4.2

Motion Positioning Experiment Verification

To test the stage displacement point positioning accuracy performance, different stage strokes are test in the experiments. By inputting the different strokes to the PZT, the output of the stage can be obtained. The results are shown in Figs. 15 and 16. It can be seen that the stage can reach stable 3.7 times magnification effect, while the displacement distance was 68 lm. Moreover, the output close-loop precision of the stage is stable. The average positioning accuracy of the stage is about 30 nm with different output strokes from 10 lm to 68 lm.

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Fig. 15. Input and output diagram

Fig. 16. Scale enlargement

5 Conclusion This paper proposed a STR flexure hinge and applied it to a designed XhYhZ three degree-of-freedom micro-motion stage. Firstly, by using the elastic static formula and the calculus theory, the flexibility formula of the flexure hinge was derived. Based on the ANSYS simulation, the flexibility of theoretical analysis was verified. At the same time, by comparing the STR flexure hinge with the ordinary two-axis straight circular flexure hinge, the rigidity of the STR flexure hinge was verified, and the results showed that the proposed STR hinge can achieve high compliance deformation performance, which can be effectively applied into the bending action of the precision motion stage. Moreover, based on the designed STR hinge mechanism, a XhYhZ micro-motion stage is designed. The dynamic analysis of the stage was carried out, and the theoretical natural frequency of the stage was verified by the ANSYS simulation. The error between the simulation and the theoretical analysis is less than 2%. Based on the dynamic simulation, the results showed that the stage can achieve a short response time, small overshoot, and high precision position performance. Finally, the experimental stage was set up and the experimental analysis was carried out. The results showed that the stage can be achieved 3.7 times amplification ratio, 68 lm displacement stroke, and about 30 nm positioning accuracy.

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References 1. Paros, J.M., Weisbord, L.: How to design flexure hinges. Mach. Des. 37(27), 151–156 (1965) 2. Wu, Y.F., Zhou, Z.Y.: Design calculation for flexure hinges. Rev. Sci. Instrum. 73(8), 3103– 3106 (2002) 3. Lobontiu, N., Paine, J.S.N., Garcia, E., et al.: Corner-filleted flexure hinges. J. Mech. Des. 123(3), 346–352 (2001) 4. Nishiwaki, S., et al.: Topology optimization of compliant mechanisms using the homogenization method. Int. J. Numer. Methods Eng. 42(3), 535–559 (1998) 5. Wu, Z.H., Huang, N.E.: Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv. Adapt. Data Anal. 1(1), 1–41 (2009) 6. Ma, Z.Q., Li, Y.C., Liu, Z., et al.: Rolling bearing fault feature extraction based on variational mode decomposition and Teager energy operator. J. Vib. Shock 35(13), 134–139 (2016) 7. Wang, Y., Markert, R., Xiang, J., et al.: Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system. Mech. Syst. Sig. Process 60 (61), 243–251 (2015) 8. Itagaki, H., Tsutsumi, M.: Design method for high-gain control of linear motor feed drive systems using virtual linear friction. Procedia CIRP 1, 244–249 (2012) 9. Lee, T.H., Tan, K.K.: Intelligent control of precision linear actuators. Eng. Appl. Artif. Intell. 13, 671–684 (2000) 10. Sharon, A., Hogan, N, Hardt, D.E.: High bandwidth force regulation and inertia reduction using a macro/micro manipulator system. In: Proceedings of the IEEE International Conference on Robotics and Automation, Philadelphia, PA, USA, pp. 126–132 (1985) 11. Yang, Y.: Development status of micromanipulator technology for biomedical application. Chin. J. Mech. Eng. 23, 1–13 (2011)

An Improved PC-Kriging Method for Efficient Robust Design Optimization Qizhang Lin1, Chao Chen2, Fenfen Xiong1(&), Shishi Chen3, and Fenggang Wang1 1

3

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China [email protected] 2 Science and Technology on Complex Aviation Systems Simulation Laboratory, Beijing 100076, China Beijing Electromechanical Engineering Institute, Beijing 100074, China

Abstract. The polynomial-chaos-kriging (PC-Kriging) method has been derived as a new uncertainty propagation approach and widely used for robust design optimization in a straightforward manner, of which the statistical moments would be estimated through directly conducting Monte Carlo simulation (MCS) on the PC-Kriging model. However, the computational cost still cannot be negligible because thousands of statistical moment estimations might be performed during robust optimization, especially for highly nonlinear and complicated engineering problems. An analytical statistical moment estimation method is derived for PC-Kriging in this work to reduce the computational cost rather than referring to MCS. Meanwhile, a sequential sampling strategy is applied for PC-Kriging model construction, in which the sample points are not generated all at once, but sequentially allocated in the region with the largest prediction uncertainty to improve the accuracy of PC-Kriging model as much as possible. Through testing on three mathematical examples and an airfoil robust optimization design problem, it is noticed that the improved PC-Kriging method with analytical statistical moment estimation and sequential sampling strategy is more efficient than the traditional ones, demonstrating its effectiveness and advantage. Nomenclature

D F Ma N P PC PCK p RðÞ R a b

= = = = = = = = = = = =

dimension of random variables information matrix in PC model mach number of flight flow field number of sample points number of coefficients in PC model polynomial chaos polynomial chaos kriging order of PC model auto-correlation function lift-to-drag ratio flight angle of attack coefficient of PC model

© Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 394–411, 2020. https://doi.org/10.1007/978-981-32-9941-2_33

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r2 uðÞ

395

= prior variance of the gaussian random process = multi-dimensional orthogonal polynomial

1 Introduction Robust design optimization aims at optimizing the product performance while minimizing the sensitivity of performance to uncertainties, which has been widely applied to engineering design problems, such as aerospace engineering [1], automobile engineering [2], civil engineering [3]. As is well known, a key component of robust design optimization is to estimate the mean and variance of the output response, given the uncertainty information of inputs [4]. For practical engineering design problem, it often involves complex and time-consuming high-fidelity simulation analysis models, such as finite element analysis (FEA) for structural analysis and computational fluid dynamics (CFD) for aerodynamic analysis. Compared to the design optimization based on traditional empirical formula, the application of these high-fidelity simulation analyses significantly improves the design accuracy, which however greatly increases the computational cost. Therefore, it is of great importance to increase the efficiency of statistical moment estimation (mean and variance) to perform robust design optimization for real engineering applications. Literature has seen many approaches about statistical moment calculation, among which the polynomial chaos (PC) method has been widely studied as it has a solid mathematical foundation and fast convergence rate [5]. With PC, a random variable can be represented as a stochastic metamodel, i.e., a weighted summation of some orthogonal polynomials, based on which the mean and variance of the random variable can be analytically obtained. Therefore, the PC method is popularly applied to robust design optimization in different fields, such as aerodynamic optimization [6], ship optimization [7], structure shape optimization [8], and trajectory optimization in flight dynamics [9–11]. To further improve the accuracy of PC, Schobi et al. proposed to combine the PC method with the classic Kriging technique to construct the so-called PC-Kriging method (hereinafter referred to as PCK for short) [12], within which a PC model is employed to describe the global trend of the original random response, and a Gaussian random process is used to capture its local characteristics. Many works have demonstrated that PCK is more accurate than both PC and Kriging [13, 14]. The PCK method can be considered as a generalized Kriging model, and the difference is that PCK is constructed in the stochastic domain, while the classic Kriging is done in the deterministic one. Once the PCK model is constructed, the mean and variance of the random output response can be conveniently obtained by conducting Monte Carlo simulation (MCS) on the PCK model, and the computational cost taken by one uncertainty analysis is almost negligible compared to the original time-consuming response function evaluation. However, when it is applied to the practical robust design optimization problems, especially those involving coupled multidisciplinary system that may require hundreds of thousands of uncertainty analyses, the computational cost

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taken here cannot be ignored. The PC-based analytical statistical moment estimation [15, 16] has been derived and widely applied, which however is not applicable for PCK as the Gaussian random process is added on the basis of PC model. Therefore, the analytical formulae of statistical moments (mean and variance) calculation for PCK are derived in this work to improve the efficiency of PCK-based robust design optimization. On the other hand, a certain number of sample points are required to estimate the unknown metamodel parameters (aka hyper-parameters) for both PC and PCK. Therefore, the sampling strategy has a great influence on the accuracy and efficiency of uncertainty analysis [17]. Till now, researches on the sampling strategy for PC and PCK generally focus on the comparative study of various sampling approaches [18, 19], such as random sampling, Latin hypercube sampling, Hemmasy sampling, Gaussian quadrature sampling, in which the sample points are basically generated altogether at one time according to the order of PC term and the dimensionality of uncertain inputs. However, just as the construction of metamodel in the deterministic field, the characteristics of the response function cannot be considered during the sampling process for the one-stage sampling scheme, which probably causes the waste of limited computational resource. Therefore, the sequential sampling strategy is further introduced into the construction of PCK model in this paper. Considering that the uncertainty of metamodel can be conveniently quantified as the Gaussian process theory is employed in PCK [20, 21], the sample point is sequentially generated in the region with the largest uncertainty to update the PCK model and improve its accuracy as far as possible. As the sample points are adaptively generated with the sequential sampling strategy, the computational cost of the uncertainty analysis can be reduced to some extent. The remainder of this paper is organized as follows. In Sect. 2, the PCK method is briefly reviewed at first. In Sect. 3, the proposed improved PCK method with analytical statistical moment estimation and sequential sampling is presented in detail, followed by numerical examples in Sect. 4 to test the effectiveness of the two proposed strategies. In Sect. 5, the improved PCK method is applied to an airfoil robust design optimization problem to further verify its effectiveness and applicability. Conclusions are drawn in the last section.

2 Review of PC-Kriging Method As a generalized Kriging model constructed in the probabilistic space, the PCK method employs a weighted sum of a series of orthogonal polynomials (i.e., PC model) to represent the global trend of the random response, and a Gaussian random process to capture its local variation characteristics. With PCK, the random response y ¼ cðxÞ; ðx ¼ ½x1 ; . . .; xd Þ can be expressed as: y  M ðPCKÞ ðxÞ ¼

P X i¼0

bi ui ðxðnÞÞ þ r2 Z ðxÞ

ð1Þ

An Improved PC-Kriging Method for Efficient Robust Design Optimization

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where ui ðxðnÞÞ represents the multi-dimensional orthogonal polynomial obtained by conducting tensor product on one-dimensional orthogonal polynomials; M ðPCKÞ is PCK model; n is a standard random vector transformed from the random vector x in the original stochastic space; b ¼ ½b0 ; b1 ; . . .; bp  and r2 denote the PC coefficient vector and the prior variance of the Gaussian random process, respectively. The number of orthogonal polynomials in the PC model is P þ 1 ¼ ðp þ d Þ!=ðd!p!Þ, where p is the order of the model. ZðxÞ is a static Gaussian random process with zero mean and unit variance, which depends on the auto-correlation function between the existing sample points Rðx; x0 Þ ¼ Rðjx  x0 j; hÞ. h is the hyper-parameter vector to be estimated by the maximum likelihood estimation (MLE) method or the cross-validation method (CV) as below.   ^hMLE ¼ arg min 1 ðy  FbÞT R1 ðy  FbÞðdet RÞN1 N h h i   ^hCV ¼ arg min yT R1 diag R1 2 R1 y h

ð2Þ ð3Þ

where N is the number of sample points; y ¼ ½y1 ; . . .; yN T is the output response vector at the sample points; R the autocorrelation matrix composed of the autocorrelation functions with element as Rij ¼ RðjxðiÞ  xðjÞ j; hÞ; F the information matrix with ele  ment as Fij ¼ ui xðjÞ ðnÞ . Once h is estimated, b and r2 can be expressed as:  1 bðhÞ ¼ FT R1 F FR1 y r2 ðhÞ ¼

1 ðy  FbÞT R1 ðy  FbÞ N

ð4Þ ð5Þ

Once the PCK model is constructed, the predicted output response at any point x can be expressed as yðPCKÞ ðxÞ ¼

P X

bi ui ðxðnÞÞ þ rðxÞT R1 ðy  FbÞ

ð6Þ

i¼0

where rðxÞT is the correlated vector composed of the correlation function values between the predicted point x and all the existing sample points. Based on Eq. (6), the mean and variance of the output response y can be obtained using MCS.

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3 The Proposed Improved PCK Method 3.1

Analytical Statistical Moment Estimation

In order to save the computational cost of statistical moment estimation by using MCS directly on the PCK model, the analytical statistical moment estimation formulae are derived. It can be seen from Eq. (1) that the PCK model can be regarded as the sum of the PC term (denoted as gðxðnÞÞ) and the Gaussian random process (denoted as f(x)). y  M ðPCKÞ ðxÞ ¼

P X

bi ui ðxðnÞÞ þ r2 Z ðxÞ ¼ gðxðnÞÞ þ f ðxÞ

ð7Þ

i¼0

Thus, the mean ly and variance r2y of the random output response y can be obtained by the following two equations.   ly ¼ E M ðPCKÞ ¼ EðgðxðnÞÞÞ þ Eðf ðxÞÞ

ð8Þ

  r2y ¼ var M ðPCKÞ ¼ varðgðxðnÞÞÞ þ varðf ðxÞÞ þ 2covðgðxðnÞÞ; f ðxÞÞ

ð9Þ

In practical implementation, it is found that the value of the covariance term covðgðxðnÞÞ; f ðxÞÞ is insignificant compared to the value of the variance terms in Eq. (9), and thus the covariance term is assumed to be neglected here, which will be verified in the subsequent example tests. (a) Calculating EðgðxðnÞÞÞ and varðgðxðnÞÞÞ To calculate Eqs. (8) and (9), the mean and variance of gðxðnÞÞ and f ðxÞ should be firstly calculated. According to the orthogonality of orthogonal polynomials in PC, one has Eðg12...N Þ ¼

P X

bi Eðui ðxðnÞÞÞ ¼ 0

ð10Þ

i¼1

Then, EðgðxðnÞÞÞ can be calculated as EðgðxðnÞÞÞ ¼ Eðg0 Þ þ Eðg12...N Þ ¼ Eðg0 Þ ¼ b0

ð11Þ

In Eqs. (10) and (11), gi (i = 0, 1, …, P) corresponds to each item bi ui ðxðnÞÞ of PC model in sequence. For varðgðxðnÞÞÞ, one has varðg0 Þ ¼ 0 varðg12...N Þ ¼

P X i¼1

ðbi Þ2 varðui ðxðnÞÞÞ

ð12Þ ð13Þ

An Improved PC-Kriging Method for Efficient Robust Design Optimization

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Clearly, one has     varðui ðxðnÞÞÞ ¼ E ðui ðxðnÞÞÞ2  ðEðui ðxðnÞÞÞÞ2 ¼ E ðui ðxðnÞÞÞ2

ð14Þ

Through substituting Eqs. (14) into (13), var ðgðxðnÞÞÞ can be computed as varðgðxðnÞÞÞ ¼ varðg12...N Þ ¼

P X

  ðbi Þ2 E ðui ðxðnÞÞÞ2

ð15Þ

i¼1

(b) Calculating Eðf ðxÞÞ and varðf ðxÞÞ f ðxÞ is a Gaussian random process, which can be expressed as below. f ðxÞ ¼ r2 Z ðxÞ ¼ rð xÞT R1 ðy  FbÞ ¼

N X

ri ð xÞci

ð16Þ

i¼1

where ri is the i-th element of vector r and ci is the i-th element of vector c. c ¼ R1 ðy  FbÞ

ð17Þ

  As the Gaussian exponential model Rðjx  x0 j; hÞ ¼ exp hjx  x0 j2 is simple, and has good smoothness and wide scope of application, it is employed as the autocorrelation functions in this work. Then, f ðxÞ can be written as: f ð xÞ ¼

N X

ci

i¼1



xj  mj r2 P exp  j 2n2j d

2 !!

 2 ! ! pffiffiffiffiffiffi 1 xj  m j ¼r ci P nj 2p pffiffiffiffiffiffi exp  j 2n2j nj 2p i¼1 N   X d d d ¼ r2 ð2pÞ2 P nj ci P PN xj jmj ; n2j 2

N X

d

j

¼k

N X i¼1

d

i¼1

ð18Þ

j

  d ci P PN xj jmj ; n2j j

d

where k ¼ r2 ð2pÞ2 P nj , d is the dimensionality of random input variables x, N is the j

number of sample points, mj and nj are respectively the mean and standard deviation of the j-th random input variables xj, PN ðÞ denotes the probability density function (PDF) of the normal distribution.

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Eðf ðxÞÞ can be expressed as: Eðf ðxÞÞ ¼ k

Z N    

X d ci P PN xj jmj ; n2j PXj xj dxj

ð19Þ

j

i¼1

  where PXj xj is the PDF of random input variable xj . In this work, it is assumed that all random variables are subject to uniform distribution for the simplification of computation, and thus 0 1 xuj Z N   X Bd C 1 Eðf ðxÞÞ ¼ k ci B PN xj jmj ; n2j dxj C @P A u l j x x j j i¼1 xlj ð20Þ " !#!

N X d xuj  mj xlj  mj 1 ¼ ci P u U  U j x  xl nj nj j j i¼1 where UðÞ is the cumulative distribution function (CDF) of the standard normal distribution; xuj and xlj represent the upper and lower limits of the distribution for xj. It is noteworthy that if the random input variable does not follow the uniform distribution, it can be firstly transformed into a uniform distribution by the transformation approach [22]. According to the relationship between variance and expectation, one has varðf ðxÞÞ ¼ var k

N X

ci P PN

¼E

k

¼E k

d

ci P PN

i¼1 2



j

i¼1 N X

d

N X N X i1 ¼1 i2 ¼1

j



xj jmj ; n2j

xj jmj ; n2j





!

! k

N X

d

c i P PN j

i¼1 d

ci1 ci2 P PN j



xj jmj ; n2j



 PN



xj jmj ; n2j

xj jmj ; n2j





!!  ðE ðf ðx ÞÞÞ2

!  ðEðf ðxÞÞÞ2

ð21Þ where  PN

xj jmj ; n2j



 PN

xj jmj ; n2j



!2  2 !  2 ! xj  mj xj  mj 1 pffiffiffiffiffiffi exp  ¼ exp  2n2j 2n2j nj 2p !2 !  2  2 xj  mj x j  mj 1 pffiffiffiffiffiffi exp  ¼  2n2j 2n2j nj 2p ! ! n2j 1 pffiffiffi pffiffiffiffiffiffi ¼ PN xj jmj ; 2 2nj 2p

ð22Þ

An Improved PC-Kriging Method for Efficient Robust Design Optimization

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By substituting Eq. (22) into Eq. (21), one has ! !! n2j 1 pffiffiffi pffiffiffiffiffiffi varðf ðxÞÞ ¼ E k ci1 ci2 P PN xj jmj ;  ðEðf ðxÞÞÞ2 j 2 2nj 2p i1 ¼1 i2 ¼1 ! !Z N X N X d   n2j 1 PXj xj dxj  ðEðf ðxÞÞÞ2 ¼ k2 ci1 ci2 P PN pffiffiffi pffiffiffiffiffiffi PN xj jmj ; j 2 2p 2 n j i1 ¼1 i2 ¼1 2

N X N X

d

ð23Þ Similarly, it is assumed that the random variables are subject to uniform distribution, and one has varðf ðxÞÞ ¼k 2

N X N X i1 ¼1 i2 ¼1

¼k

2

N X N X i1 ¼1 i2 ¼1

d

ci1 ci2 P PN j

u ! ! Zxj n2j 1 1 pffiffiffi pffiffiffiffiffiffi u PN xj jmj ; dxj  ðEðf ðxÞÞÞ2 2 2nj 2p xj  xlj

!

d

ci1 ci2 P PN j

xlj

"

xuj  mj 1 1 pffiffiffi pffiffiffiffiffiffi u U n l pjffiffi 2nj 2p xj  xj 2

!

xlj  mj U n pjffiffi

!#  ðEðf ðxÞÞÞ2

2

ð24Þ

(c) Calculating ly and r2y Based on Eqs. (8), (9), (11), (20), (16) and (24), one has N X

ly ¼ g 0 þ

ci

i¼1

r2y ¼

P X

ð25Þ

  ðbi Þ2 E ðui ðxðnÞÞÞ2

i¼1

þk

" !#!

xuj  mj xlj  mj 1 P u U U j x  xl nj nj j j d

2

N X N X i1 ¼1 i2 ¼1

d

ci1 ci2 P PN j

! " ! !# xuj  mj xlj  mj 1 1 pffiffiffi pffiffiffiffiffiffi u U  ðEðf ðxÞÞÞ2 U n n pjffiffi pjffiffi 2nj 2p xj  xlj 2 2

ð26Þ Once the PCK model is constructed, the mean and variance of the output response y can be obtained according to Eqs. (25) and (26). It should be pointed out that the random input variables are assumed to follow uniform distribution to make the analytical calculation of integrals possible and convenient. Of course, the random input variables do not necessarily obey the uniform distribution in practice. When they follow other distribution types (such as normal and exponential distributions, etc.), the transformation approach can be applied to convert them into uniform distributed variables once the PCK model is built, based on which Eqs. (25) and (26) are applied.

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Q. Lin et al.

Sequential Sampling

Considering that the PCK model is actually a generalized Kriging model, the variance of the response prediction can be expressed as follows [23]. VyðPCK Þ ðxÞ ¼ r

2



1  uðxðnÞÞ

T

 0 r ð xÞ F T

FT R

1 

uðxðnÞÞ rðxÞ

! ð27Þ

where uðxðnÞÞ ¼ ½u0 ðxðnÞÞ; u1 ðxðnÞÞ; . . .; uP ðxðnÞÞT . The response variance shown in Eq. (27) represents the confidence level of predicted response value at the predicted point for the PCK model. The larger the value is, the greater the uncertainty of the predicted response value at this point is. Taking advantage of the response variance, a sequential sampling strategy is developed to improve the accuracy of the PCK model by sequentially generating sample points in the region with the largest prediction uncertainty. A step-by-step description of the proposed sequential PCK method for uncertainty analysis is presented as follows. Step 1: Generate N0 initial sample points X ¼ ½x1 ; . . .. . .; xN0 T according to the distribution information of the random input variables at certain design point, and calculate the corresponding output response values Y ¼ ½y1 ; . . .. . .; yN0 T of y ¼ cðxÞ. Step 2: Based on the current sample points X and Y, construct a PCK model according to Eqs. (1)–(6), and perform uncertainty analysis based on the PCK model to obtain uncertainty information of the output response y, such as mean and variance. Step 3: According to the distribution information of random input variables at certain design point, generate a large number of input sample points, and calculate the prediction variance at each sample point using Eq. (27). Select the input position x* with the largest prediction variance, which is added into the existing sample points, i.e. X ¼ ½X; x ,Y ¼ ½Y; cðx Þ. Then, update the PCK model using the extended sample points, based on which uncertainty analysis is conducted. Step 4: Repeat Step 3 till the variation of mean (ly ) and variance (r2y ) of the output response function y with respect to the previously obtained values are less than the specified value e or the total number of sample points reaches the limit Nmax.

4 Mathematical Examples In this section, three mathematical examples (see Table 1) are employed to test the effectiveness of the proposed analytical statistical moment estimation (denoted as PCKAE) and the sequential sampling (denoted as SPCK) strategies for PCK. Considering the compromise between accuracy and efficiency, the order of the PC term in the PCK model is set as p = 4. The simulation is done on a personal computer with i5-4590 CPU and 8.00 GB memory.

An Improved PC-Kriging Method for Efficient Robust Design Optimization

403

Table 1. Mathematical examples for test No. Function Distribution   2 xi  U ð0; 1Þ 2 2 1 cðxÞ ¼ 100 x2  x1 þ ð1  x1 Þ       0:5ðx2 þ x3 Þ 2 x1  N 55:29; 0:07932 ; x2  N 22:86; 0:00432 cðxÞ ¼ arccos xx14 þ 0:5ðx2 þ x3 Þ     x3  N 22:86; 0:00432 ; x4  N 101:60; 0:07932 3 cðxÞ ¼ x1 þ x22 þ x33 þ x44 þ x55 þ x66 xi  U ð0; 1Þ

4.1

Test of the Statistical Moment Estimation Strategy

The proposed analytical statistical moment estimation based PCK method (PCK-AE) is compared to the existing PCK approach that employs MCS (106 runs) on the PCK model for statistical moment estimation (denoted as PCK-MCS). The results of direct MCS on the original response model (106 runs) are used as benchmark to verify the effectiveness of PCK-AE and PCK-MCS. Table 2 shows the results of the three functions, in which N represents the number of function evaluations and T the calculation time of moment estimation. It can be seen that the proposed PCK-AE method can produce results that are very close to those of the existing PCK-MCS, and both results show great agreements to those of the direct MCS. Meanwhile, the calculation time for one uncertainty analysis of PCK-AE is clearly shorter than that of PCK-MCS. These results demonstrate the effectiveness and efficiency of the proposed analytical statistical moment estimation strategy. Table 2. Results of statistical moment estimation Function 1 ly r2y

T(s)

N

Function 2 ly r2y

T(s)

N

Function 3 ly r2y

T(s)

N

PCK- 465.667 375915.330 1.963 16 0.1222 0.0001377 1.468 71 1.5338 0.4723 3.207 211 AE PCK- 465.661 375911.287 6.009 16 0.1221 0.0001384 6.801 71 1.5381 0.4701 25.742 211 MCS 106 1.5969 0.4417 / 106 MCS 454.469 366451.284 / 106 0.1219 0.0001408 /

4.2

Test of the Sequential Sampling Strategy

In order to verify the effectiveness and advantage of the proposed SPCK method for uncertainty analysis, the three examples in Table 1 are tested with the same PC order. The existing PCK with one-stage sampling strategy is also tested for comparison. The results obtained by direct MCS (106 runs) are used as benchmark to verify the effectiveness of the proposed method. Figures 1, 2 and 3 show the relative errors (%) of the mean and variance of output response compared to MCS with the increase of the number of sample points. It is observed that with the increase of sample points, the errors of the existing PCK with one-stage sampling strategy are slightly decreased, while they are significantly reduced

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2.5

2.6

Relative error of variance/%

Relative error of mean/%

2.5 2

1.5

1

PCK sequential PCK 0.5 16

17

2.4 2.3 2.2 2.1 2 1.9

PCK sequential PCK

1.8 18

Number of sample points

19

20

1.7 16

17

18

19

20

73

74

75

213

214

215

Number of sample points

Fig. 1. Test results of Function 1

2.5

Relative error of variance/%

Relative error of mean/%

0.25

0.2

0.15

PCK sequential PCK 0.1 71

72

73

Number of sample points

74

75

2

1.5

1

PCK sequential PCK 0.5 71

72

Number of sample points

4

7

3.5

6

Relative error of variance/%

Relative error of mean/%

Fig. 2. Test results of Function 2

3 2.5 2 1.5 1 0.5 0 211

PCK sequential PCK 212

213

214

Number of sample points

215

5 4 3 2 1 0 211

PCK sequential PCK

212

Fig. 3. Test results of Function 3

Number of sample points

An Improved PC-Kriging Method for Efficient Robust Design Optimization

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for the proposed SPCK method. The interpretation is that the sample points generated by the SPCK method can more effectively improve the accuracy of the PCK model. Meanwhile, with the same number of sample points, the results of the SPCK method are more accurate than the existing one-stage PCK method. That is to say, in order to achieve the same accuracy of statistical moment estimation, the SPCK method requires fewer sample points. Such reduction of sample points will greatly improve the efficiency of robust design optimization, which will be verified in the application of the engineering example in the next section.

5 Application to Airfoil Robust Optimization 5.1

Problem Description

The airfoil optimization problem adopted from Ref. [24] aims to maximize the lift-todrag ratio (R) of the airfoil by designing the geometry of the airfoil subject to its constraint of the maximum thickness tmax . The flight states considered here are a = 1.55° and Ma = 0.7. As the main component for providing the lift, the wing suffers from many uncertainties during the flight process, such as the Mach number (Ma) of the incoming flow. In this example, Ma is considered to be uncertain and follow normal distribution Ma* N ð0:7; 0:0152 Þ. The mathematical model for airfoil robust optimization is: min F ðyÞ ¼(lR þ krR subject to :

tmax  0:1

ð28Þ

yi 2 ½0:006; 0:006

where y is the design variable vector, i.e. the vertical locations of the control points after the parametric modeling of the airfoil; and k is the weight set as k = 3 in this example. Due to the good local control property and differentiability, the B-spline curve [25] with 10 control points is employed for the geometry parametrization of the airfoil, where the horizontal locations of the 10 control points are fixed as x = [0.1 0.3 0.5 0.7 0.9 0.9 0.7 0.5 0.3 0.1] and the vertical locations y are free to move for optimization, as shown in Fig. 4. The corresponding vertical locations of the 10 control points of the original airfoil are y = [0.04698, 0.06000, 0.05216, 0.03667, 0.01450, −0.01450, −0.03667, −0.05216, −0.06000, −0.04698].

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Q. Lin et al. 0.1 NACA0012 Control points

0.08 0.06

2

3

1

4

0.04

y

0.02

5

0

6

-0.02

7

-0.04 -0.06

10

8

9

-0.08 -0.1 0

0.1

0.2

0.3

0.4

0.5

x

0.6

0.7

0.8

0.9

1

Fig. 4. Schematic diagram of parametric model of airfoil with B-spline curve

During the optimization, the computational fluid dynamics (CFD) analysis using Fluent17.0 is performed to obtain the aerodynamic data, with the k-omega two-path turbulence model. The steady-state density solver with Roe-FDS is employed. Figure 5 shows the mesh grids used in the CFD analysis. The number of nodes in the remote field of the grid is 100 and the number in the airfoil boundary is 300. The genetic algorithm based on the Pareto strategy [26, 27] is selected as the optimization algorithm, with the population size as 40 and the evolutionary generation as 25.

Fig. 5. Grids used in CFD analysis

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5.2

407

Optimal Results and Analysis

The proposed analytical statistical moment estimation based PCK method (PCK-AE) and sequential PCK-AE with both analytical statistical moment estimation and sequential sampling strategies (SPCK-AE), PCK-MCS using one-stage sampling, and PCK-MCS with sequential sampling (SPCK-MCS) are all employed to calculate the statistical moments at each iteration design point during the airfoil robust optimization. The PC order is set as p = 2, the number of runs of MCS is set as 100,000, and the number of initial sample points used to construct the sequential PCK model is set as 4. Meanwhile, the deterministic optimization (DO) without considering any uncertainty is also done. Once the optimization is completed, the confirmed mean and standard deviation of the lift-to-drag ratio are calculated using MCS through respectively substituting the optimal design variables obtained by robust optimizations with the four statistical moment estimation schemes as well as the deterministic optimization, and the NACA0012 original airfoil parameters into the CFD analysis model, with the consideration of uncertainty in Ma. Table 3 shows the confirmed results, the total number of CFD calls required during the optimization, and the optimization time cost. Table 3. Comparison of the confirmed results SPCK-AE 26.3258 lR rR 2.7318 # of CFD runs 1627 Time (h) 81

PCK-AE 26.2661 2.9501 2237 112

SPCK-MCS 26.3277 2.7410 1620 94

PCK-MCS 26.2658 2.9760 2270 132

DO 29.4807 4.7264 328 17

NACA0012 23.8161 4.9224 / /

Several observations can be made from Table 3. Firstly, it is found that the deterministic optimization significantly increases the mean of airfoil lift-to-drag ratio lR , while the decrease in the corresponding standard deviation rR relative to the original airfoil NACA0012 is small, which is clearly larger than that of robust optimization. For all the robust optimizations using the four statistical moment estimation schemes, the mean of airfoil lift-to-drag ratio is clearly increased, and the standard deviation is significantly reduced as well, which evidently improves the robustness of the airfoil design. Secondly, by comparing the results in Table 3 (SPCK-AE vs. SPCKMCS, PCK-AE vs. PCK-MCS), it is found that the proposed analytical statistical moment estimation strategy can clearly reduce the computational time of robust optimization compared to the MCS-based PCK methods (with about 15% reduction in time). Thirdly, by comparing the results in Table 3 (SPCK-AE vs. PCK-AE, SPCKMCS vs. PCK-MCS), it is noticed that the proposed sequential sampling strategy can significantly reduce the number of CFD calls compared to the one-stage PCK, resulting in about 28% reduction of optimization time. These results further demonstrate the effectiveness and advantages of the proposed improved PCK method with analytical statistical moment estimation and sequential sampling. Figure 6 shows the optimized airfoils by the SPCK-AE based robust optimization and the deterministic optimization, and the original NACA0012 airfoil. Considering

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that the optimal results of robust optimizations using the four statistical moment estimation schemes (SPCK-AE, PCK-AE, SPCK-MCS and PCK-MCS) are very close, only the results of robust optimization using SPCK-AE are shown here. It is noticed that compared to the original NACA0012 airfoil, the upper surface leading edge thickness and curvature of the airfoil for both the deterministic optimization and robust optimization are reduced, resulting in the increase of lift. This is the main reason for the increase of lift-to-drag ratio.

0.1

NACA0012 DO SPCK-AE

0.08 0.06 0.04

y

0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

Fig. 6. Comparison of airfoils before and after optimization

Figure 7 shows the diagrams of the static pressure cloud of the three airfoils shown in Fig. 6 with Ma = 0.7, from which it is observed that the regions in dark blue on the upper surface of the airfoil for both deterministic optimization and robust optimization are larger than that of the original one, and the region in dark blue of the deterministic optimization is larger than that of robust optimization. It indicates that both deterministic optimization and robust optimization can reduce the static pressure of upper surface compared to that of the original airfoil, and deterministic optimization can reduce more than robust optimization. Meanwhile, the regions in green on the lower surface for both deterministic optimization and robust optimization are larger than that of the original airfoil, and it is larger for deterministic optimization. This indicates that both deterministic optimization and robust optimization can increase the static pressure of the lower surface of the airfoil, and the deterministic optimization can increase more. In summary, the lift of optimized airfoil is increased, and the deterministic optimization improves more than that of the robust optimization. Therefore, the lift-to-drag ratio is increased after optimization, which is more obvious for the deterministic optimization. These results show great agreement to those displayed in Table 3.

An Improved PC-Kriging Method for Efficient Robust Design Optimization

(a) SPCK-AE

(b) DO

409

(c) NACA0012

Fig. 7. Comparison of static pressure cloud diagram

In order to illustrate the robustness of the robust design optimization, the lift-todrag ratio of the optimized (both robust and deterministic) and original airfoils corresponding to Ma = [0.64, 0.66, 0.68, 0.70, 0.72, 0.74, 0.76, 0.78] are respectively calculated, of which the curves are shown in Fig. 8.

34 32 30 28

Cl/Cd

26 24 22 20 18 16 14 0.64

NACA0012 DO SPCK-AE 0.66

0.68

0.7

0.72

0.74

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Fig. 8. Variation of lift-to-drag ratio at different Mach numbers

It can be seen from Fig. 8 that in the region with Ma > 0.72, the airfoil lift-to-drag ratio obtained by the robust optimization changes more gently with the variation of Ma compared to the deterministic optimization. Although the deterministic optimization can improve the performance of lift-to-drag ratio, it may vary greatly under uncertainty during certain flight condition, which shows the necessity and significance to perform robust design optimization to reduce the sensitivity of airfoil to uncertainty.

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6 Conclusions The existing PC-Kriging method employs the Monte Carlo simulation directly on the PC-Kriging model to obtain the statistical moments during robust optimization, which certainly would take lots of computational time especially for highly nonlinear complex design problem requiring a large number of statistical moment estimations. Therefore, an analytical statistical moment estimation strategy is proposed for PC-Kriging in this work. Meanwhile, a sequential sampling strategy is established to further reduce the computational cost, with which the sample point in the region with the greatest prediction uncertainty is sequentially allocated to update the PC-Kriging model. The effectiveness and advantages of the proposed two strategies are tested and verified by three mathematical examples. The application on the NACA0012 airfoil robust design optimization problem further demonstrates the effectiveness and applicability of the improved PC-Kriging method with analytical statistical moment estimation and sequential sampling strategy in solving practical engineering problems. Acknowledgement. The grant support from Science Challenge Project (No. TZ2018001) and Hongjian Innovation Foundation (No. BQ203-HYJJ-Q2018002) is greatly acknowledged.

References 1. Cook, L.W., Jarrett, J.P.: Robust airfoil optimization and the importance of appropriately representing uncertainty. AIAA J. 55(11), 1–15 (2017). https://doi.org/10.2514/1.j055459 2. Zhang, Y., Zhu, P., Chen, G.L.: Lightweight design of automotive front side rail based on robust optimization. Thin-Walled Struct. 45(7), 670–676 (2007). https://doi.org/10.1016/j. tws.2007.05.007 3. Cheng, Q., Wang, S.W., Yan, C.C.: Robust optimal design of chilled water systems in buildings with quantified uncertainty and reliability for minimized life-cycle cost. Energy Build. 126(15), 159–169 (2016). https://doi.org/10.1016/j.enbuild.2016.05.032 4. Ben-Tal, A., Nemirovski, A.: Robust optimization – methodology and applications. Math. Program. 92(3), 453–480 (2002). https://doi.org/10.1007/s101070100286 5. Xiu, D.B., Karniadakis, G.E.M.: The Wiener-askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2), 619–644 (2002). https://doi.org/10.1137/ s1064827501387826 6. Dodson, M., Parks, G.T.: Robust aerodynamic design optimization using polynomial chaos. J. Aircr. 46(2), 635–646 (2015). https://doi.org/10.2514/1.39419 7. Wei, X., Feng, B.W., Liu, Z.Y.: Ship uncertainty optimization design based on multidimensional polynomial chaos expansion method. Ship Eng. 1(40), 42–47 (2018) 8. Kim, N.H., Wang, H., Queipo, N.V.: Efficient shape optimization under uncertainty using polynomial chaos expansions and local sensitivities. AIAA J. 44(5), 1112–1116 (2006). https://doi.org/10.2514/1.13011 9. Fisher, J., Bhattacharya, R.: Linear quadratic regulation of systems with stochastic parameter uncertainties. Automatica 45(12), 2831–2841 (2009). https://doi.org/10.1016/j.automatica. 2009.10.001 10. Prabhakar, A., Fisher, J., Bhattacharya, R.: Polynomial chaos based analysis of probabilistic uncertainty in hypersonic flight dynamics. J. Guid. Control Dyn. 33(1), 222–234 (2010). https://doi.org/10.2514/1.41551

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11. Wang, F.G., Xiong, F.F., Jiang, H., Song, J.M.: An enhanced data-driven polynomial chaos method for uncertainty propagation. Eng. Optim. 50(2), 1–20 (2017). https://doi.org/10. 1080/0305215x.2017.1323890 12. Schobi, R., Sudret, B., Wiart, J.: Polynomial-chaos-based Kriging. Statistics 5(2), 55–63 (2015). https://doi.org/10.1615/int.j.uncertaintyquantification.2015012467 13. Kersaudy, P., Sudret, B., Varsier, N., Wiart, J.: A new surrogate modeling technique combining Kriging and polynomial chaos expansions application to uncertainty analysis in computational dosimetry. J. Comput. Phys. 286(14), 103–117 (2015). https://doi.org/10. 1016/j.jcp.2015.01.034 14. Schobi, R., Sudret, B.: Imprecise structural reliability analysis using PC-Kriging. In: 25th European Safety and Reliability Conference (2015). https://doi.org/10.1201/b19094-549 15. Xiong, F.F., Yang, S.X., Liu, Y., Chen, S.S.: Analysis Method of Engineering Probability Uncertainty. Science Press, Beijing (2015) 16. Sepahvand, K., Marburg, S., Hardtke, H.J.: Uncertainty quantification in stochastic systems using polynomial chaos expansion. Int. J. Appl. Mech. 2(2), 305–353 (2010). https://doi.org/ 10.1142/s1758825110000524 17. Xiong, F.F.: Weighted stochastic response surface method considering sample weights. Struct. Multidiscip. Optim. 43(6), 837–849 (2011). https://doi.org/10.1007/s00158-0110621-3 18. Hosder, S., Walters, R.W., Balch, M.: Efficient sampling for non-intrusive polynomial chaos applications with multiple uncertain input variables. In: AIAA Non-Deterministic Approaches Conference (2007). https://doi.org/10.2514/6.2007-1939 19. Hampton, J., Doostan, A.: Compressive sampling of polynomial chaos expansions: convergence analysis and sampling strategies. J. Comput. Phys. 280(12), 363–386 (2015). https://doi.org/10.1016/j.jcp.2014.09.019 20. An, D., Choi, J.H.: Efficient reliability analysis based on Bayesian framework under input variable and metamodel uncertainties. Struct. Multidiscip. Optim. 46(4), 533–547 (2012). https://doi.org/10.1007/s00158-012-0776-6 21. Xiong, F.F.: Robust design optimization considering metamodel uncertainty. J. Mech. Eng. 50(19), 136–143 (2014, in Chinese). https://doi.org/10.3901/jme.2014.19.136 22. Miller, F.P., Vandome, A.F., Mcbrewster, J.: Inverse Transform Sampling. Alphascript Publishing, German (2010) 23. Lockwood, B.A., Anitescu, M.: Gradient-enhanced universal Kriging for uncertainty propagation. Nucl. Sci. Eng. 170(2), 168–195 (2012). https://doi.org/10.13182/nse10-86 24. Ganesh Ram, R.K., Cooper, Y.N., Bhatia, V.: Design optimization and analysis of NACA0012 airfoil using computational fluid dynamics and genetic algorithm. Appl. Mech. Mater. 664(22) 111–116 (2014). https://www.scientific.net/AMM.664.111 25. Liang, Y., Cheng, X.Q., Li, Z.N., Xiang, J.W.: Multi-objective robust airfoil optimization based on non-uniform rational B-spline (NURBS) representation. Sci. China Ser. E: Technol. Sci. 53(10), 2708–2717 (2010). https://doi.org/10.1007/s11431-010-4075-4 26. Chen, X., Agarwal, R.K.: Optimization of wind turbine blade airfoils using a multi-objective genetic algorithm. J. Aircr. 50(2), 519–527 (2013). https://doi.org/10.2514/1.c031910 27. Cheng, F.Y., Li, D.: Multiobjective optimization design with Pareto genetic algorithm. J. Struct. Eng. 123(9), 1252–1261 (1997). https://doi.org/10.1061/(asce)0733-9445(1997) 123:9(1252)

Electro-Mechanical Response of a Cracked Piezoelectric Cantilever Beam Chao Liu, Wenguang Liu(&), and Yaobin Wang School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China [email protected], [email protected], [email protected]

Abstract. Piezoelectric ceramics are of importance to the field of aerospace, electric and electronic. However, crack often happens on the surface of piezoelectric ceramics due to harsh working environment. The purpose of this article is to study the impacts of crack on the electro-mechanical response of a piezoelectric beam. Firstly, a finite element model of the piezoelectric cantilever beam was set up by using the software of ABAQUS. And subsequently, the mechanic and electric induced response of the cantilever beam was discussed. Thereafter, a cracked piezoelectric cantilever beam was developed. The effects of crack on the electro-mechanical response of a cantilever beam were studied. Results indicate that the electro-mechanical response is proportional to the input force and the input voltage. As crack propagates, the variation rule of the electro-mechanical response depends on the crack size. This conclusion is helpful to the prediction of crack size, and to provide a new idea for the prediction of the piezoelectrical structure life. Keywords: Piezoelectric ceramic

 Crack  Electro-mechanical response

1 Introduction Piezoelectric ceramic is a kind of material that has unique mechanical properties and electro-mechanical coupling properties. Its positive and converse piezoelectric effects is widely used in the field of energy-transducing. However, the piezoelectric ceramic is brittle. It is prone to failure or damage under the action of external loads for the piezoelectric ceramic with the initial defects. This characteristic is easy to affect the performance and reliability of the piezoelectric structure. Thus, it is of importance to study the fracture problem of a piezoelectric structure under the positive and converse piezoelectric effect of piezoelectric ceramic. The piezoelectric effect was first discovered in 1880 by the brothers of P. Curie and J. Curie [1]. In the process of utilizing the mechanic-electric conversion characteristics of piezoelectric ceramics, piezoelectric energy harvesters and ultrasonic motors are of the most representative. Among them, the piezoelectric energy harvester is a device that This project is supported by National Natural Science Foundation of China (Grant No. 51565039), the Jiangxi Provincial Nautral Science Foundation (Grant No. 20181BAB206023). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 412–423, 2020. https://doi.org/10.1007/978-981-32-9941-2_34

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converts mechanical energy into electrical energy by using the positive piezoelectric effect, and is widely used as a sensor in the aerospace equipment. The piezoelectric cantilever beam is a typical model for the piezoelectric energy harvesters. But it has a drawback of collecting the vibrational energy from only one direction of the ceramic. The vibrations in the actual environment may come from any directions in the threedimensional space. An accurate and detailed analysis of an efficient piezoelectric energy harvester has attracted the attention of many researchers. F or example, Fan et al. [2, 3] proposed a cantilever-type two-dimensional vibration energy harvesting system in 2014, which was superior to the linear piezoelectric energy harvesting device. Chen et al. [4] presented a kind of multi-dimensional energy harvesting device likes a dandelion structure, which can effectively collect multi-directional vibration. A three-dimensional vibration energy harvesting device was designed by Su et al. [5, 6] in 2013, which can realize energy collection in three-dimensional direction and adapt to the vibration response of actual broadband. The converse piezoelectric effect of piezoelectric ceramics is used by ultrasonic motors to convert electrical energy into mechanical energy. The research on piezoelectric theory represented by ultrasonic motors is also widely focused. Since Williams et al. [7] invented the first piezoelectric actuator in the world, the achievement of piezoelectric driving studied by researchers at the forefront all the time. In 2015, Tan [8] applied piezoelectric actuators designed by himself to medical procedures, and designed the composite controller to drive the ultrasonic motor for precise driving. In the same year, a French scientist Sofiane Ghenna invented a multi-modal ultrasonic motor [9] to enable the motor to run smoothly in the case of interference. In 2016, Canadian scientists Tavallaei et al. [10] studied the influences of temperature and other uncertain factors on the accuracy and stability of piezoelectric actuator operation, and gave a new situation to study the operational stability of ultrasonic motor. By analyzing the reliability of ultrasonic motor in detail, a second-order model traveling wave was proposed by Kuhne et al. [11] in 2018. It has been shown that the application of ultrasonic motor is more widely promoted. However, the characteristic of piezoelectric ceramics is brittleness, and their fracture toughness is usually only about 1 MPa. In the process of manufacturing piezoelectric material which is subjected to various initial defects, such as cracks, holes and inclusions, are inevitably generated. These initial defects are prone to growth under external loads, resulting in failure of the structure [12, 13]. Therefore, it is of great significance to analyze the fracture behaviour which was focused by a lot of people [14]. In order to solve this problem, numerous research results and literatures are employed to analyze these fracture problems. For example, a T-shaped crack in a ceramic material was successfully observed by Kida et al. [15] and they investigated the thermo-electro-mechanical fracture behavior of an infinite piezoelectric material which also was subjected to T-shaped crack under thermo-electro-mechanical loadings [16]. Kwon et al. [17] used the method of integral transformation to transform the

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moving anti-plane crack problem in a strip-shaped piezoelectric material into Fredholm integral equation solved, and the results were the same as those of Hou et al. [18]. In order to solve crack problems, complex analysis method is also employed to obtain the analytical results [19, 20]. Above studies shown that many researches on the piezoelectric characteristics and fracture mechanics of piezoelectric ceramic materials have been carried out by the workers. So far, most of them used the theoretical or experimental ways to study the problems about piezoelectric ceramics. However, due to the coupling relationship of the piezoelectric structure and the complexity of the structural parameters, theoretical modeling is extremely difficult to derive, which leads to a large difference between the experimental design and the theoretical value. At the same time, considering the lack of research on the life prediction of the reliability of ultrasonic motor and energy harvester. The purpose of this article is to use the ABAQUS finite element software to establish a numerical model of piezoelectric beam, and to study the effects of crack on the output response of the piezoelectric ceramic cantilever beam with two kinds of working modes, such as positive piezoelectric effect and converse piezoelectric effect. It is of great significance for the further study of the response relationship between the crack and the resonant frequency. And it is also helpful to predict the residual life of the cracked piezoelectric cantilever beam.

2 The Modeling of Piezoelectric Ceramic Beam 2.1

Description of Piezoelectric Ceramic

Most of the common piezoelectric materials, particularly piezoelectric ceramics, are mainly divided into transversely isotropic piezoelectric ceramics and orthogonal anisotropy piezoelectric ceramics. And a transversely isotropic piezoelectric materials is named as the 6 mm crystal system with its consisting of 10 independent material constants, among which the elastic constant is 5, the piezoelectric constant is 3, and the dielectric constant is 2. An orthogonal anisotropy piezoelectric material is named as the 2 mm crystal system with 17 independent material constants, having 9 elastic constants, 5 piezoelectric constants and 3 dielectric constants. In this article, the 6 mm crystal piezoelectric ceramic (PZT-5H) is employed as the research object. And the isotropic plane is assumed to be perpendicular to the direction of polarization and make the z-axis as its direction of polarization. Since there are four kinds of boundary conditions of crystals, the corresponding piezoelectric constitutive equations are also four ways. Piezoelectric ceramics (PZT-5H) adopts the second type of piezoelectric equation with strain and electric field intensity as independent variables, and the piezoelectric equation can be simplified as following.

Electro-Mechanical Response of a Cracked Piezoelectric Cantilever Beam

3 2 s11 S1 6 S2 7 6 s12 6 7 6 6 S3 7 6 s13 7 6 S¼6 6 S4 7 ¼ 6 0 6 7 6 4 S5 5 4 0 0 S6 2

s12 s22 s23 0 0 0

s13 s23 s33 0 0 0

0 0 0 s44 0 0

0 0 0 0 s55 0

32 3 2 T1 0 0 6 T2 7 6 0 0 7 76 7 6 6 7 6 0 7 76 T3 7 þ 6 0 6 7 6 0 7 76 T4 7 6 0 5 0 4 T5 5 4 d15 s66 0 T6

0 0 0 d24 0 0

415

3 d31 2 3 d32 7 7 E1 d 33 7 74 E2 5 0 7 7 E 0 5 3 0 ð1Þ

2

2

3

2

D1 0 D ¼ 4 D2 5 ¼ 4 0 d31 D3

0 0 d32

0 0 d33

0 d24 0

d15 0 0

3

T1 36 T2 7 2 7 e11 0 6 6 T3 7 6 4 0 5 þ 0 6 7 T4 7 7 0 0 6 4 T5 5 T6

0 e22 0

32 3 E1 0 0 54 E2 5 e33 E3 ð2Þ

In the Eqs. (1) and (2), the subscript 1 denotes the direction along the x-axis and 2 denotes the y direction and 3 denotes the z direction. 2.2

Finite Element Model of Piezoelectric Cantilever Beam

A piezoelectric cantilever beam is considered in the present study. The geometry and the dimension of the beam, where one end is clamped and a piezoelectric ceramic sheet is also attached at the fixed end, shown as Fig. 1. It is assumed that L and l are the length of cantilever beam and piezoelectric ceramic sheet, hp and hs are the thickness of piezoelectric ceramic sheet and cantilever, bp are the width of cantilever and piezoelectric ceramic sheet. As mentioned above, the parameters of the using piezoelectric ceramic is assumed to be shown in Table 1.

Fig. 1. Finite element model

The finite element model of the piezoelectric cantilever beam is developed by using the software of ABAQUS. Due to the anisotropic characteristics of piezoelectric materials, when using ABAQUS finite element software to simulate, the input of material parameters must correspond to the constitutive relationship.

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Parameters

Ceramic material (PZT-5H)

Length (mm) Width (mm) Thickness (mm) Density (kg/m3) Elastic modulous (Gpa) Poisson’s ration Dielectric constant Stiffness coefficient (Gpa)

20 10 0.5 7500 – – k11 = 1.505; k33 = 1.301; (10−8) C11 = 126, C12 = 79.5, C13 = 84.1, C33 = 117, C44 = 23, C66 = 0.5(C11 − C12) e31 = − 6.5, e15 = 17, e33 = 23.3

Piezoelectric constant (c/m2)

Phosphor bronze base 60 10 2.5 8900 117 0.373 – – –

3 Effects of Center Crack on the Mechanic Induced Response 3.1

Finite Element Model of the Cracked Piezoelectric Cantilever Beam

In order to analyze the relationship of crack size and mechanical response, a finite element model of a cantilever piezoelectric beam with central crack was developed. It is assumed that the crack length is 0.2 mm and its width is 0.1 mm and it is in the center of the piezoelectric sheet. Figure 2 shows the finite element model. The mesh at the crack tip is refined for considering the calculation accuracy of the model. Due to the stress singularity generally occurs at the crack tip during the vibration process, the first node of the second circle at the crack tip is selected as the stress observation point as shown in Fig. 3.

Fig. 2. Finite element Model with Cracks

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Fig. 3. Schematic of stress observation points

3.2

Effects of Crack Size on the Mechanical Response

In order to investigate the effect of crack size on the mechanical response, the impact of the occurrence of cracks and the length of center crack on the output response is discussed. Since the 0.2 mm crack is designed ahead of time, this is the initial state of the crack under actual working conditions, which has practical research significance. A kind of sinusoidal excitation force with a size of 1 N is selected by we to study the output response and the length of center crack growth from 0.2 mm, each step increases by 0.2. By comparing the output response of the piezoelectric cantilever beam with the central crack under different sinusoidal excitation forces and different crack lengths, the output responses of displacement, stress and the voltage are obtained. The output response of the cracked piezoelectric cantilever beam is analyzed as shown in Fig. 4. It can be seen from Fig. 4(a) that the initial size of 0.2 mm crack with increasing sinusoidal excitation force has little effect on the displacement of output response. However, when the sinusoidal excitation force is fixed, the end midpoint displacement increases with the size of center crack becoming longer. The variation of displacement changes in the form of exponential function. Figure 4(b) shows the stress output response in PZT-5H under different excitation forces and different length of central cracks. The value of output stress with crack-free beam is greater than that stress with 0.2 mm crack and the difference of output stress is increased with the increasing of excitation force. The effect of the propagation of the central crack on the crack tip stress is approximately linear. Figure 4(c) shows the variation of piezoelectric ceramic output voltage subjected to different excitation forces is similar to the displacement response. The behavior of output voltage under excitation force is opposite of those output voltage under different length of central cracks. The value of output voltage is decreased by increasing the length of central crack. As expected, Fig. 5 shows the increase of central crack length leads to the decrease of the first-order resonant frequency of the piezoelectric cantilever. The decreasing slope of the output voltage in longer length is greater than those in shorter length.

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Fig. 4. Effects of crack on mechanical response of piezoelectric cantilever beam

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Fig. 5. 1st modal frequency

4 Effect of Crack on Electrical Induced Response The driving stator of ultrasonic motor is essentially a piezoelectric cantilever structure, and the actuator is driven by deformation under converse piezoelectric effect. Due to the harsh working environment of ultrasonic motors, the physical characteristics of piezoelectric ceramic materials varies and it is are prone to fracture and failure during work. Moreover, ultrasonic motors are widely used in scenes with high safety levels such as artificial satellites and aerospace devices. A large amount of data shows that the cracks of the piezoelectric material are generally generated in the center, and extended to both sides. Thus, the relationship between the central crack and the electrical responses of the piezoelectric cantilever beam is studied. So as to clarify the mechanism of structural damage and to provide a theoretical guidance for the application and promotion of ultrasonic motor. In order to further analyze the effect of crack on the electrical response of piezoelectric cantilever beam, the output response of the piezoelectric cantilever beam with the central crack under a sinusoidal alternating voltage with 14th frequency of 29586.3 Hz and different crack lengths is analyzed. On the one hand, a sinusoidal alternating voltage with 14th frequency of 29586.3 Hz is applied to the upper surface of the piezoelectric sheet, on the other hand, an initial crack of 0.2 mm at the center of the piezoelectric sheet was set, and then, the effect of increasing crack length of the piezoelectric cantilever beam subjected to fixed alternating voltage of 250 V on the surface with 14th frequency of 29586.3 Hz was studied. The output response of the piezoelectric cantilever is shown in Fig. 6. It can be seen from Fig. 6(a) that the displacement response is completely different to certain extent. When a 0.2 mm small crack occurs on the piezoelectric cantilever piezoelectric sheet, with the increasing of external excitation voltage, the difference of crack on displacement response becomes larger and larger. Under the alternating voltage of 250 V, the displacement response of the end midpoint decreases all the time until the propagation of central crack to 0.6 mm, then the value of displacement

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Fig. 6. Effects of crack on electrical response of piezoelectric cantilever beam

increases with central crack length less than 1.3 mm, and decreases with the central crack length more than 1.3 mm. Figure 6(b) shows that the effect of different excitation voltages on the stress response is little. Under the fixed alternating voltage of 250 V, the stress at the crack tip of the piezoelectric sheet increases with the propagation of the crack, and its variation trend can be regarded as linear relationship approximately. The effect with a 0.2 mm crack for the displacement response and stress response is obvious different. To more clearly describe this change, the rate of decline of output response is defined as follows: the rate of decline ¼

crack  free response  cracked response crack  free response

ð3Þ

The relationship between the excitation voltage and the rate of decline in the output response is shown in Fig. 7.

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Fig. 7. Relationship between excitation voltage and the rate of decline in the output response

The Fig. 8. shows that the 0.2 mm small crack has a relatively large influence on the displacement response of the piezoelectric cantilever beam, and when the value of excitation voltage is reached to a certain extent, keeping the rate of decline trend in the output response unchanged.

Fig. 8. Relationship between crack length and the 14th modal frequency

This trend indicates that the resonant frequency of the piezoelectric cantilever beam has changed when the crack propagates, which affects the magnitude of the resonant amplitude, resulting in unstable output response. Therefore, crack propagation has a significant influence on the resonant frequency of the piezoelectric cantilever beam.

5 Conclusions From the analysis of the electro-mechanical response of a cracked piezoelectric cantilever beam, some conclusions are as follows: (1) The electro-mechanical response is proportional to the input force and the input voltage.

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(2) As crack propagates, the variation rule of the electro-mechanical response depends on the crack size. This conclusion is helpful to the prediction of crack size, and to provide a new idea for the prediction of the piezoelectrical structure life.

References 1. Zhao, C.S.: Ultrasonic Motors Technologies and Applications, pp. 128–129. Science Press, Beijing (2007). (in Chinese) 2. Fan, K.Q., Chao, F.B., Zhang, J.G., et al.: Design and experimental verification of a bidirectional nonlinear piezoelectric energy harvester. Energy Convers. Manag. 86(10), 561– 567 (2014) 3. Fan, K.Q., Chang, J.W., Pedrycz, W., et al.: A nonlinear piezoelectric energy harvest for various mechanical motions. Appl. Phys. Lett. 106(22), 223902 (2015) 4. Chen, R.W., Ren, L., Xia, H.K., et al.: Energy harvesting performance of a dandelion-like multi-directional piezoelectric vibration energy harvest. Sens. Actuators: Phys. 230, 1–8 (2015) 5. Su, W.J., Zu, J.: An innovative tri-directional broadband piezoelectric energy harvester. Appl. Phys. Lett. 103(20), 203901–203901-4 (2013) 6. Su, W.J., Zu, J.W.: Design and development of a novel bi-directional piezoelectric energy harvester. Smart Mater. Struct. 23(9), 095012 (2014) 7. Kurosawa, M., Kodaira, O., Tsuchitoi, Y., et al.: Transducer for high speed and large thrust ultrasonic linear motor using two sandwich-type vibrators. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45(5), 1188–1195 (1998) 8. Tan, K., Liang, W.Y., Huang, S.N., et al.: Precision control of piezoelectric ultrasonic motor for myringotomy with tube insertion. J. Dyn. Syst. Meas. Control 137(6), 064504-2– 064504-4 (2015) 9. Ghenna, S., Amberg, M., Giraud-Audine, C., et al.: Modelling and control of a travelling wave in a finite beam, using multi-modal approach and vector control method. In: Joint Conference of the IEEE International Frequency Control Symposium and the European Frequency and Time Forum, villeneuve-d’ascq, franch (2015) 10. Tavallaei, M., Atashzar, S., Drangova, M.: Robust motion control of ultrasonic motors under temperature disturbance. IEEE Trans. Ind. Electron. 63(4), 2360–2368 (2016) 11. Kuhne, M., Rochin, R., Santiesteban, R., et al.: Modeling and two-input sliding mode control of rotary traveling wave ultrasonic motors. IEEE Trans. Ind. Electron. 65(9), 7149– 7159 (2018) 12. Jamia, N., El-Borgi, S., Rekik, M., et al.: Investigation of the behavior of a mixed-mode crack in a functionally graded magneto-electro-elastic material by use of the non-local theory. Theor. Appl. Fract. Mech. 74, 126–142 (2014) 13. Herrmann, K., Loboda, V., Khodanen, T.: An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial. Arch. Appl. Mech. 80(6), 651–670 (2010) 14. Li, Y.D., Xiong, T., Cai, Q.G.: Coupled interfacial imperfections and their effects on the fracture behavior of a layered multiferroic cylinder. Acta Mech. 226(4), 1183–1199 (2015) 15. Kida, K., Saito, M., Kitamura, K.: Flaking failure originating from a single surface crack in silicon nitride under rolling contact fatigue. Fatigue Fract. Eng. Mater. Struct. 28(12), 1087– 1097 (2005)

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16. Ueda, S., Hatano, H.: T-shaped crack in a piezoelectric material thermo-electro-mechanical loadings. J. Therm. Stress. 35(1–3), 12–29 (2012) 17. Kwon, J., Lee, K., Kwon, S.: Moving crack in a piezoelectric ceramic strip under anti-plane shear loading. Mech. Res. Commun. 27(3), 327–332 (2000) 18. Hou, M.S., Qian, X.Q., Bian, W.F.: Energy release rate and bifurcation angers of piezoelectric materials with antiplane moving crack. Int. J. Fract. 107(14), 297–306 (2001) 19. Jangid, K., Bhargava, R.: Complex variable-based analysis for two semi-permeable collinear cracks in a piezoelectro-magnetic media. Mech. Adv. Mater. Struct. 24(12), 1007–1016 (2017) 20. Wan, Y.P., Yue, Y.P., Zhong, Z.: A mode III crack crossing the magnetoelectroelastic bimaterial interface under concentrated magnetoelectromechanical loads. Int. J. Solids Struct. 49(21), 3008–3021 (2012)

A Time-Variant Reliability Analysis Method Considering Maintenance Jingfei Liu, Chao Jiang(&), and Xiangyun Long State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, People’s Republic of China {liujingfei,jiangc,longxy}@hnu.edu.cn

Abstract. A time-variant reliability analysis method taking into account the maintenance is proposed in this paper. The effects of maintenance on structural resistance and resistance decay function are first quantified by repair functions. A new time-variant reliability model that are capable of considering maintenance is then established by integrating the repair functions. A solution strategy based on stochastic process discretization is then formulated to calculate the time-variant reliability. A reliability-based optimization approach for designing maintenance strategy is further presented. Finally, three numerical examples are investigated to verify the validity of the proposed method. Keywords: Time-variant reliability  Maintenance  Stochastic process discretization  Reliability-based optimization

1 Introduction Due to material degeneration, random dynamic loads or other time-variant uncertain factors, the reliability of many engineering structures will generally degenerate with time, leading to the so-called time-variant reliability problem. The time-variant reliability analysis computes the probability that a system or component fulfills its intended function over a time interval of interest without failures. It is very important for the full lifecycle design of structures. Therefore, the time-variant reliability analysis problem has received widespread attention in recent years. The main research methods to solve the time-variant reliability problem include the outcrossing rate method, the extremum method and the stochastic process discretization-based method. Among the above-mentioned methods, the most dominating one is the outcrossing rate method, in which the outcrossing rate of performance function at each moment in the design cycle need to be computed to calculate the reliability index under the assumption of Poisson process, Markov process or their improved models. Rice [1, 2] studied the issue of crossings between a dynamic This work is supported by the National Science Fund for Distinguished Young Scholars (51725502), the National Key Research and Development Project of China (2016YFD0701105), and the Science Challenge Project (TZ2018007). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 424–446, 2020. https://doi.org/10.1007/978-981-32-9941-2_35

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response and an allowable threshold and proposed the well-known first-passage formula, which established the foundation for dynamic reliability analysis. Engelund et al. [3], proposed approximations of first-passage times for differentiable processes based on higher-order threshold crossings. Schall et al. [4], and Rackwitz et al. [5], deal with the reliability problem with time-variant load through the outcrossing rate method. Li and Kiureghian [6–8] investigated the reliability problems involving nonlinear dynamics and inelastic space-variant finite element analysis. Andrieu-Renaud et al. [9], proposed the PHI2 method, which simplifies the evaluation of outcrossing rate. Hu and Du [10] employed the First Order Reliability Method (FORM) [11–13] for the estimation of outcrossing rate and then proposed the JUR/FORM method. In addition to the above-mentioned outcrossing rate methods, there seems to be a trend to develop some more effective and conceptually simple methods to deal with time-variant reliability problems without using outcrossing rate. Jiang et al. [14], proposed a timevariant reliability analysis method based on stochastic process discretization (TRPD). Wang and Wang [15], and Hu and Du [16] developed several extremum methods where the extreme value distribution of the performance function was modeled first and then transformed into the time-variant reliability. Singh et al. [17], analyzed the timevariant reliability of random dynamic systems using the importance sampling approach. Hu and Du [18] combined the equivalent Gaussian process and the stochastic process simulation, thereby proposed a first order reliability method for time-variant problems. Besides, various surrogate model-based methods have been proposed to solve the timevariant problems [19–23]. Although the above-mentioned reliability analysis methods have been applied in the engineering successfully, they did not consider the practical maintenance for the structures during its life cycle. However, for many important equipment or structures (e.g. airplanes, automobiles and bridges etc.), regular inspections are usually employed to monitor their health status, and corresponding maintenance strategies are adopted to repair them [25–27]. Since maintenance can change the resistance [28] and the resistance decay function [29], the reliability of the repaired structure will increase [30–32]. Without considering the maintenance, the initial design of the structure will be quite conservative to satisfy the reliability requirement during the whole life cycle, which will cause the waste of resources. Therefore, it is essential to take the maintenance into the consideration of time-variant reliability analysis and optimization design. A time-variant reliability analysis method considering maintenance is developed in this paper. The impact of maintenance on structural reliability can be quantified, and the maintenance strategy can be optimized to ensure the safety and reliability of structure. The remainder of this paper is organized as follows: Sect. 2 provides the problem statement; Sect. 3 details the specific formulation for time-variant reliability analysis method considering maintenance; Sect. 4 proposes an optimization design approach for maintenance strategy. Section 5 discusses several numerical examples; And Sect. 6 gives the conclusion of this study.

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2 Brief Introduction of Time-Variant Reliability Analysis Structural time-variant reliability refers to the probability that a structure can complete its intended function within a specific time frame under specific conditions while experiencing the effects of time-variant uncertainty. The reliability of a structure within a time interval ½0; T  can be expressed as [9]: Ps ðT Þ ¼ PfgðXðtÞ; Y; tÞ [ 0; 8t 2 ½0; Tg

ð1Þ

in which Pfg stands for the probability calculation, gðÞ is the performance function, XðtÞ ¼ ðX1 ðtÞ; X2 ðtÞ; . . .; Xm ðtÞÞ is an m-dimensional stochastic process vector, and Y ¼ ðY1 ; Y2 ; . . .; Yn Þ is an n-dimensional random vector. The outcrossing rate method [5, 9] is currently the most important method to solve time-variant reliability problem. It first calculates the outcrossing rate, which is the mean number of crossings of the performance function from safe state to unsafe state in unit time. The structural reliability or failure probability can then be derived from the outcrossing rate. Therefore, the calculation of outcrossing rate is the core of this type of methods. The outcrossing rate m þ ðtÞ can be defined as [33]: m þ ðt Þ ¼

PfN þ ðt; t þ DtÞ ¼ 1g Dt!0;Dt [ 0 Dt lim

ð2Þ

where N þ ðt; t þ DtÞ stands for the number of crossings of performance function from safe state to unsafe state within the time interval ½t; t þ Dt. Because the numerator of Eq. (2) stands for the probability that the performance function crosses only one time during the interval ½t; t þ Dt, the outcrossing rate can also be given as follows [34]: T PfgðXðtÞ; Y; tÞ [ 0 gðXðt þ DtÞ; Y; t þ DtÞ  0g m þ ðt Þ ¼ ð3Þ lim Dt!0;Dt [ 0 Dt If the outcrossing events are rare and independent, the outcrossing events can be considered to obey Poisson distribution. Therefore, Eq. (1) can be approximated by the following formula [35]:  Z Ps ðT Þ ¼ 1  Ps ð0Þ exp 

T

m þ ðtÞdt

 ð4Þ

0

in which Ps ð0Þ stands for the initial reliability of structure. However, when the outcrossing events are strongly dependent, evaluating time-variant reliability by Eq. (4) may lead to a large error, thus some approaches [10, 35] have been proposed to better model the outcrossing events considering their dependence under different model assumptions, which improves the accuracy.

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3 Time-Variant Reliability Modeling and Analysis Considering Maintenance Though the time-variant reliability analysis methods have made great progress, most of them have not taken the influence of practical maintenance into account. However, maintenance is widespread in practical structures and have important impact on the structural reliability. Taking maintenance into the analysis of time-variant reliability can avoid the conservative initial design, thus to further reduce the waste of resources. It is necessary to develop a method that can quantify the impact of maintenance on the structural reliability and solve the time-variant reliability problem considering maintenance. Therefore, in this paper, for quantifying the impact of maintenance on structural reliability, a time-variant reliability model considering maintenance is first proposed. The impacts of maintenance on structural resistance and resistance decay function are expressed by repair functions explicitly, and those repair functions are integrated into the performance function to further express the impact of maintenance on the structural reliability. Finally, an efficient time-variant reliability analysis method iTRPD is employed to solve the model. 3.1

Reliability Modeling

According to the time-variant reliability analysis model [9, 10], the structural performance function before maintenance can be given by: gðtÞ ¼ gðXðtÞ; Y; tÞ

ð5Þ

Assume that XðtÞ¼½Xr ðtÞ; Xs ðtÞ, Xr ðtÞ ¼ ðX1 ðtÞ; X2 ðtÞ; . . .; Xa ðtÞÞ is a stochastic process vector representing the structural resistance, and Xs ðtÞ ¼ ðXa þ 1 ðtÞ; Xa þ 2 ðtÞ . . .; Xm ðtÞÞ is a stochastic process vector representing the structural load; Y¼½Yr ; Ys , Yr ¼ ðY1 ; Y2 ; . . .; Yb Þ is the random vector representing the structural resistance, and Ys ¼ ðYb þ 1 ; Yb þ 2 . . .; Yn Þ is the random vector representing the structural load. When the maintenance is considered, the performance function Eq. (5) can be further given as follows [36–39]: 8 < gðtÞ ¼ gðRðtÞ; SðtÞ; tÞ RðtÞ ¼ R0 uðXr ðtÞ; Yr ; tÞ ð6Þ : SðtÞ ¼ SðXs ðtÞ; Ys ; tÞ where RðtÞ represents the structural resistance, SðtÞ represents the structural load, R0 is the initial resistance of structure, and uðXr ðtÞ; Yr ; tÞ is the structural resistance decay function, whose specific forms are determined by material properties, service environment and other factors [39].

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Since maintenance generally has no effect on the external load, the structural load after i-th maintenance is assumed to be not changed. Therefore, the performance function of structure after i-th (i = 1, 2, …, n) maintenance is defined as follows:   gi ðt; si Þ ¼ gi Ri ðt; si Þ; Sðt; si Þ; t

ð7Þ

where gi ðÞ and Ri ðt; si Þ are the performance function and structural resistance after i-th maintenance, respectively, and si represents the time to take i-th maintenance. The effects of maintenance on structural resistance includes the effect on structural resistance [28] and the effect on structural resistance decay function [29]. Combining the specific maintenance strategy [25–27, 30–32], the structural resistance after i-th maintenance can be expressed as follows: Ri ðt; si Þ ¼ Ri0 ðR0 ; si Þui ðXr ðtÞ; Yr ; t; si Þ

ð8Þ

where Ri0 ðR0 ; si Þ ¼ R0 As eBs si and ui ðXr ðtÞ; Yr ; t; si Þ ¼ u0 ðXr ðtÞ; Yr ; tÞCs eDs si represent the structural resistance and resistance decay function after i-th maintenance, respectively, where As and Bs represent the maintenance control parameters of structural resistance, Cs and Ds represent the maintenance control parameters of structural resistance decay function. In this paper, the control parameters including As , Bs , Cs , Ds are employed to establish the repair functions, which are determined by practical maintenance strategy that includes maintenance time, means, etc. Different maintenance strategies will cause different impacts on the structure, and different impacts will be further represented by different control parameters. Actually, many structures need to be repaired in their design cycle according to their health statuses. If we can obtain those maintenance data, including the maintenance strategies and the corresponding impacts of maintenance on structures, then regression analysis or maximum likelihood estimation can be utilized to calculate the control parameters. Therefore, the impacts of maintenance on structural resistance and resistance decay function can be expressed by the repair functions explicitly. In turn, we can optimize the maintenance strategy by tuning those control parameters. For simplicity, a piecewise performance function is employed to represent the effect of maintenance on the structure during its design cycle. The piecewise performance function can be given as follows: 8 0 g ðRðtÞ; SðtÞ; tÞ; t 2 ½0; s1 Þ > > > < g1 ðR1 ðt; s1 Þ; Sðt; s1 Þ; t; s1 Þ; t 2 ½s1 ; s2 Þ GðXðtÞ; Y; tÞ ¼ .. > > . > : i i g ðR ðt; si Þ; Sðt; si Þ; t; si Þ; t 2 ½si ; T

ð9Þ

where g0 ðÞ stands for the performance function without maintenance, gi ðÞ is the performance function after i-th maintenance.

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Combining Eqs. (1) and (9), the reliability of the structure with i times maintenance during its design cycle ½0; T can be expressed as follows:   Pis ð0; T Þ ¼ P g0 ðRðtÞ; SðtÞ; tÞ [ 0; 8t 2 ½0; s1  \ . . .     \ g1 R1 ðtÞ; S1 ðtÞ; t; s1 [ 0; 8t 2 ½s1 ; s2  \ . . .     \ gi Ri ðtÞ; Si ðtÞ; t; si [ 0; 8t 2 ½si ; T

ð10Þ

The time-variant reliability considering maintenance can be further calculated by solving the model in Eq. (10). 3.2

Reliability Solution

In order to calculate the overall safe probability of the structure with i times maintenance during its whole lifecycle ½0; T, the recently proposed improved time-variant reliability analysis method based on stochastic process discretization (iTRPD) [24] is introduced to solve this problem. The primary schedule of iTRPD can be summarized as follows. Firstly, discretize the time-variant performance function into a certain number of time-invariant performance function, thus the time-variant reliability problem is transformed into a timeinvariant system reliability problem. Secondly, perform time-invariant reliability analysis for the discretized performance functions at all the time points by FORM to calculate the reliability index vector, and a corresponding approach is further given to calculate the correlation coefficient matrix q of all the components’ performance functions. Finally, the time-variant reliability can be approximately calculated based on the reliability index vector and the correlation coefficient matrix. iTRPD avoids the calculation of outcrossing rate, greatly simplifying the process of solving time-variant reliability problems. Combining Eqs. (7–9), a time-variant performance function with i times maintenance GðXðtÞ; Y; tÞ is discretized over ½0; T at a certain number p of nodes with a time step Dt ¼ T=p, the time-variant reliability problem is changed to an a p-component time-invariant series system reliability problem, whose performance functions can be      expressed as G Xj ðtÞ; Y; tj ; tj ¼ j  12 Dt; Xj ¼ Xr;j ; Xs;j ; j ¼ 1; 2; . . .; p, where tj represents the midpoint of the j-th discretization length. Hence, the reliability of the problem over the whole design cycle can be expressed as: (

Pis ð0; T Þ

 

p  \   1 T ¼P G Xj ; Y; tj [ 0; tj ¼ j  Dt; Dt ¼ 2 p j¼1

ð11Þ

As the time is fixed at tj , the stochastic processes XðtÞ degrade into random parameters Xj whose mean values and variances are determined by the mean value and

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covariance functions of the stochastic processes. Employing the Nataf transformation [40] to transform Xj and Y into standard Gaussian vectors X0j and Y0 , respectively: (

  X0i ; COV X0i ¼ Nataf ðXi ; COV ðXi ÞÞ ðY0 ; COV ðY0 ÞÞ ¼ Nataf ðY; COV ðYÞÞ

ð12Þ

in which Nataf ðÞ represents the Nataf transformation. X0j and Y0 can be further transformed into standard independent Gaussian vectors by orthogonal transformation, respectively: (

U ¼ ATx X0j

ð13Þ

V ¼ ATy Y0

where ATx and ATy represent orthogonal transformation matrix of X0j and Y0 , after the above transformation, Eq. (11) can be represented as follows: (

Pis ð0; T Þ

 

p  \ 1 T 0 ¼P G ðUj ; V; tj Þ; tj ¼ j  Dt; Dt ¼ 2 p i¼1

ð14Þ

Therefore, the reliability index bj and MPP for each discretized performance function G0 ðUj ; V; tj Þ; j ¼ 1; 2; . . .; p can be calculated by FORM [11–13]. By linearizing G0 ðUj ; V; tj Þ; j ¼ 1; 2; . . .; p at their MPPs, Eq. (14) can be approximately expressed as: ( Pis ð0; T Þ

¼P

p \

) bj þ aU;j UTj

þ aV;j V [ 0 T

ð15Þ

i¼1

  in which aU;j ; aV;j represents the unit gradient vector of the j-th performance   function with respect to U; Vp at the MPP. Let Lj ¼ bj þ aU;j UTj þ aV;j VT , Eq. (15) can be written as: ( Pis ðT Þ

¼P

p \

) Lj [ 0

ð16Þ

j

Obviously, keeping the structure safe during the whole design cycle, every component corresponds to the time-invariant performance function G0 ðUj ; V; tj Þ; j ¼ 1; 2; . . .; p at arbitrary time tj needs to be positive. According to the first-order method for series system reliability [32], Eq. (16) can be calculated by: Pis ð0; T Þ ¼ Up ðb; qÞ

ð17Þ

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where Up represents the p-dimensional standard Gaussian cumulative distribution function, b ¼ ðb1 ; b2 ; . . .; bp Þ represents the reliability index vector and q represents the correlation coefficient matrix of the linearized performance functions. Assume all the stochastic processes in XðtÞ and random parameters in Y are mutually independent for simplicity. Each component of q, qj;k ; j 2 1; 2; . . .; p, is the correlation coefficient of Lj and Lk : qj;k ¼

m X

  au;j;l au;j;l q Uj;l ; Uk;l þ aTV;j aV;k

ð18Þ

l¼1

The calculation details of q can be referred to [24, 48]. Besides, the calculation of multi-dimensional Gaussian distribution can be referred to Refs. [35, 40–44]. The framework of the newly proposed method is summarized in Fig. 1.

Reliability modeling considering the maintenance

Discrete the stochastic process into p segments

Implement Nataf transformation and orthogonal transformation

Calculate the time invariant reliability index by FORM

Calculate the autocorrelation and intercorrelation of stochastic processes

The time variant reliability is obtained by calculating a multi-dimensional Gaussian integral

Fig. 1. Framework of the proposed method

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4 Optimization of the Maintenance Strategy Structural time-variant reliability refers to the probability that a structure can complete its intended function within a specific time frame under specific conditions while experiencing the effects of time-variant uncertainty. Thus, the time-variant reliability of a structure within a time interval ½ta ; tb  can be expressed as: Ps ðta ; tb Þ ¼ PfgðXðtÞ; Y; tÞ [ 0; 8t 2 ½ta ; tb g

ð19Þ

The reliability indexes corresponding to the above time-variant reliability can be calculated as follows: bðta ; tb Þ ¼ U1 ðPs ðta ; tb ÞÞ

ð20Þ

Accumulative Reliability index

For better understanding of the impact of different maintenance strategies on structural reliability, a schematic diagram is given in Fig. 2. As shown in Fig. 2, bi ð0; si Þ represents the reliability index of structure within the time interval ½0; si , bH represents the structural reliability index during the whole design cycle ½0; T without maintenance, b1H and b2H correspond to the reliability indexes during the whole design cycle ½0; T with once and twice maintenance, respectively, and bt is the structural target reliability within the design cycle. As is seen from Fig. 2, when bH is smaller than bt , it indicates that the structure is not safe enough to satisfy the reliability requirement without maintenance during its design cycle. After being repaired once at time s1 , bH is increased to b1H , thus the repaired structure can satisfy the reliability requirement. Furthermore, if the second maintenance is employed at time s2 , then b1H is increased to b2H . Since different maintenance strategies will cause different influences on the structural reliability, it is essential to develop an optimization model for maintenance strategy, by which the optimal maintenance strategy can be obtained and the reliability of the structure can be ensured.

β 1 (0,τ 1 )

β 2 (0,τ 2 )

β H2 β H1

βt

βH

τ1

τ2

Design lifetime

Fig. 2. Schematic diagram of structural reliability index curve

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In the optimization of the maintenance strategy, the maintenance parameters and maintenance time are taken as design variables, and the objective is to maximize the structural time-variant reliability during its design cycle. Thus, the optimization model of the maintenance strategy can be expressed as follows: max

As ;Bs ;Cs ; Ds ;i;si s:t: biH  bt

Pis ð0; T Þ

As ; Bs ; Cs ; Ds 2 X 0  i  n; 0  si  T

ð21Þ

where biH corresponds to the reliability index during the design cycle ½0; T with i ¼ 1; 2; . . .; n times maintenance, bt is the structural target reliability index within the whole design cycle, As , Bs , Cs , Ds are the parameters determined by maintenance strategy [25–27]. All of those parameters are collectively called maintenance strategy optimization parameters in the rest of this paper. In order to solve the optimization model in Eq. (21), the adaptive response surface method (ARSM) [49] is employed in this paper. ARSM first uses some initial points to construct an initial response surface, which is then utilized to adaptively choose the next experimental points to update the response surface. This sequential procedure terminates when the convergence criterion is satisfied. Then, this easy to call response surface is optimized to obtain the optimal result. Combining Eq. (21) and Eqs. (11– 20), the optimal maintenance strategy can be easily obtained by ARSM.

5 Numerical Examples and Discussions In this section, three numerical examples are used to demonstrate the effectiveness of the proposed method. In all examples, the time-variant reliability analysis considering maintenance of the structure and the maintenance strategy optimization are both performed. Besides, only the maintenance time is optimized while the other maintenance strategy optimization parameters are given in each example. 5.1

A Ten-Bar Truss

In this example, a ten-bar truss [45] as shown in Fig. 3 is investigated. The length L of the horizontal and vertical bars is 9.1 m. Ai ; i ¼ 1; 2; . . .; 10 denote the cross-sectional areas of the bars. The Young’s modulus E of the truss is 68948 Mpa, and the density q is 2768 kg/m3. Joint 4 is subjected to a vertical load F1 , and joint 2 is subjected to a vertical load F2 and a horizontal load F3 ðtÞ. The vertical displacement dy ðtÞ at joint 2 is required to be no larger than the allowable displacement d ðtÞ ¼ d0 ð1  0:02tÞ, where d0 is the initial value of d ðtÞ. All of the involved random parameters are listed in

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Table 1, and the maintenance strategy optimization parameters are listed in Table 2. The performance function with and without maintenance are given as follows: 8 ðtÞ  dy ðtÞ; t 2 ½0; T < gðtÞ ¼ d 6 0 10 0 pffiffiffi P P Ni ðtÞNi ðtÞ Ni ðtÞNi ðtÞ L d ð t Þ ¼ þ 2 : y E Ai Ai i¼1

ð22Þ

i¼7

8 < d ðtÞ  dy ðtÞ; t 2 ½0; s1 Þ GðXðtÞ; Y; tÞ ¼ d 1 ðtÞ  dy ðtÞ; t 2 ½s1 ; s2 Þ : 2 d ðtÞ  dy ðtÞ; t 2 ½s2 ; T

ð23Þ

Where 8 i < d ðt; si Þ ¼ d0 As eBs si ð1  0:02tÞCs eDs si 6 0 10 0 pffiffiffi P P Ni ðtÞNi ðtÞ Ni ðtÞNi ðtÞ L þ 2 : dy ðt; si Þ ¼ E Ai Ai i¼1

ð24Þ

i¼7

pffiffiffi pffiffiffi ¼ F ðtÞ  2 2N8 ; N2 ¼  2 2N10 pffiffiffi ¼ F1  2F ðtÞ þ F2  2 2N8 pffiffiffi ¼ F ðtÞ þ F2  2 2N10 pffiffiffi pffiffiffi 2 2N10 5 ¼ F ðt Þ  2 2N8  pffiffiffi N ¼  2 2N 6 10 > pffiffiffi > > > N ¼ 2 ð F þ F ðtÞÞ þ N8 > 7 1 > > > N ¼ ða b  a b2 Þ=ða11 a22  a12 a21 Þ > 8 22 1 12 pffiffiffi > > > N ¼ 2 F ð t Þ þ N > 9 10 : N10 ¼ ða11 b2  a21 b1 Þ=ða11 a22  a12 a21 Þ

ð25Þ

pffiffiffi   8 a11 ¼a22 ¼ 3=X1 þ 4 2 X2 L=ð2EðtÞÞ > > < a12 ¼a21 ¼ L=ð2X1 EðtÞÞ pffiffiffi pffiffiffi b ¼  ð F þ F ð t Þ Þ=X  2 2 ð F þ F ð t Þ Þ X2 2L=ð2EðtÞÞ > 1 1 1 1 > pffiffiffi  : b2 ¼ 2ðF2  2F ðtÞÞ X1  4F ðtÞ=X2 L=ð2EðtÞÞ

ð26Þ

8 N1 > > > > > N 3 > > > > N4 > > > >

< BðtÞ  rmax ðqðtÞ; E; q; tÞ; t 2 ½0; s1 Þ em As eBs s1 e0:01t Cs eDs s1  eðq; E; QðtÞÞ; t 2 ½0; s1 Þ > : em As eBs s2 e0:01t Cs eDs s2  eðq; E; QðtÞÞ; t 2 ½s2 ; T

ð35Þ

In this automobile frame example, the condition for structural reliability is that the limit strain satisfy the design requirement in the design cycle. The above-mentioned distributions of all the random variables and random process are listed in Table 13 and the maintenance strategy optimization parameters are listed in Table 14. The optimization model for automobile frame is given as: max Pis ð0; T Þ si

s:t:biH  bt As ¼ 1; Bs ¼ 0:015 Cs ¼ 1; Ds ¼ 0:02 i¼f2g; 0  si  T

ð36Þ

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Fig. 8. An automobile frame structure [48]

Table 13. Distributions of the random parameters for the automobile frame Parameter

Type of distribution Limit strain Type I extreme Young’s Modulus E Normal Density q Lognormal Load QðtÞ Gaussian process

Mean

Coefficient of variation (%) 4.0 10 206.86 MPa 10 7700 kg/m3 10 500000 N 10

Autocorrelation coefficient function NA NA NA exp½ð3s2 Þ

Table 14. Values of the maintenance strategy optimization parameters for the automobile frame Parameter As Bs Cs Ds bt Value 1 −0.015 1 0.02 1.8

In this example, we consider twice maintenance during the design cycle of the automobile frame. The reliability indexes of the automobile frame without maintenance are listed in Table 15. The optimal maintenance time is listed in Table 16, and the corresponding reliability indexes are shown in Table 17. It is clear from the tables that the automobile frame cannot satisfy the reliability requirement bt ¼ 2:0 in the whole

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design cycle without maintenance, and the reliability index b1H is increased by 16.92% after the automobile frame is repaired at time s1 ¼ 3:14 and s2 ¼ 6:05. The results for the automobile frame with twice maintenance are shown in Fig. 9. Table 15. The reliability indexes for the automobile frame without maintenance t (Years) b t (Years) b

1 2.59 6 2.03

2 2.34 7 1.97

3 2.26 8 1.92

4 2.17 9 1.87

5 2.09 10 1.83

Table 16. The optimal time for twice maintenance of the automobile frame s2

s1

maxb1H DbH ð%Þ

3.14 6.05 2.05

+16.92

Table 17. The reliability indexes for the automobile frame with twice optimal maintenance t (Years) b t (Years) b

2.7

1 2.56 6 2.13

2 2.32 7 2.11

3 2.15 8 2.10

4 2.21 9 2.08

5 2.17 10 2.05

No maintenance Once maintenance Best maintenance

2.6

Accumulative reliability index

2.5 2.4 2.3 2.2 2.1 2

1.9

βt

1.8 1.7 1

2

3

4 5 6 7 Design lifetime(years)

8

9

10

Fig. 9. The curves indicating the reliability indexes for the automobile frame with twice optimal maintenance

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6 Conclusions In this paper, a time-variant reliability method considering maintenance is proposed, which provides an effective tool for the problem of time-variant maintenance reliability analysis. A new reliability model is first presented, by which the impact of maintenance on structural reliability can be quantified. Besides, an optimization model is also developed to determine the optimal maintenance strategy. Several numerical examples illustrated the effectiveness of the proposed method, the results of which indicate that maintenance can influence structural reliability, and reasonable maintenance strategy is necessary for structure to satisfy the reliability requirement during its design cycle. Thus, it is essential to take maintenance into account during the process of reliability analysis. In the future, this method can be extended to reliability-based multi-objective design optimization. Acknowledgements. This work is supported by the National Science Fund for Distinguished Young Scholars (51725502), the National Key Research and Development Project of China (2016YFD0701105), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (51621004).

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12. Hasofer, A.M., Lind, N.C.: Exact and invariant second-moment code format. J. Eng. Mech. Div. 100(1), 111–121 (1974) 13. Hohenbichler, M., Rackwitz, R.: Non-normal dependent vectors in structural safety. J. Eng. Mech. Div. 107(6), 1227–1238 (1981) 14. Jiang, C., Huang, X., Han, X., et al.: A time-variant reliability analysis method based on stochastic process discretization. J. Mech. Des. 136(9), 091009 (2014) 15. Wang, Z., Wang, P.: A nested extreme response surface approach for time-dependent reliability-based design optimization. J. Mech. Des. 134(12), 121007 (2012) 16. Hu, Z., Du, X.: A sampling approach to extreme value distribution for time-dependent reliability analysis. J. Mech. Des. 135(7), 071003 (2013) 17. Singh, A., Mourelatos, Z., Nikolaidis, E.: Time-dependent reliability of random dynamic systems using time-series modeling and importance sampling. Int. J. Mater. 4(1), 929–946 (2011) 18. Hu, Z., Du, X.: First order reliability method for time-variant problems using series expansions. Struct. Multidiscip. Optim. 51(1), 1–21 (2015) 19. Zhu, Z., Du, X.: Extreme value metamodeling for system reliability with time-dependent functions. In: Proceedings of the ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers. Boston, 2–5 August 2015 (2015) 20. Wang, Z., Chen, W.: Time-variant reliability assessment through equivalent stochastic process transformation. Reliab. Eng. Syst. Saf. 152, 166–175 (2016) 21. Drignei, D., Baseski, I., Mourelatos, Z.P., et al.: A random process metamodel approach for time-dependent reliability. J. Mech. Des. 138(1), 011403 (2016) 22. Hu, Z., Mahadevan, S.: A single-loop kriging surrogate modeling for time-dependent reliability analysis. J. Mech. Des. 138(6), 061406 (2016) 23. Wang, Z., Chen, W.: Confidence-based adaptive extreme response surface for time-variant reliability analysis under random excitation. Struct. Saf. 64, 76–86 (2017) 24. Jiang, C., Wei, X., Wu, B., et al.: An improved TRPD method for time variant reliability analysis. Struct. Multidiscip. Optim., 1–12 (2018) 25. Kong, J.S., Frangopol, D.M.: Life-cycle reliability-based maintenance cost optimization of deteriorating structures with emphasis on bridges. J. Struct. Eng. 129(6), 818–828 (2003) 26. Frangopol, D.M., Lin, K.-Y., Estes, A.C.: Life-cycle cost design of deteriorating structures. J. Struct. Eng. 123(10), 1390–1401 (1997) 27. Frangopol, D.M., Kong, J.S., Gharaibeh, E.S.: Reliability-based life-cycle management of highway bridges. J. Comput. Civ. Eng. 15(1), 27–34 (2001) 28. Mori, Y., Ellingwood, B.R.: Maintaining reliability of concrete structures. I: role of inspection/repair. J. Struct. Eng. 120(3), 824–845 (1994) 29. Mori, Y., Ellingwood, B.R.: Maintaining reliability of concrete structures. II: optimum inspection/repair. J. Struct. Eng. 120(3), 846–862 (1994) 30. Frangopol, D.M., Dong, Y., Sabatino, S.: Bridge life-cycle performance and cost: analysis, prediction, optimisation and decision-making. Struct. Infrastruct. Eng.: Maint. 13(10), 1239– 1257 (2017) 31. Frangopol, D.M.: Life-cycle performance, management, and optimisation of structural systems under uncertainty: accomplishments and challenges. Struct. Infrastruct. Eng.: Maint. 7(6), 389–413 (2011) 32. Frangopol, D.M., Liu, M.: Maintenance and management of civil infrastructure based on condition, safety, optimization, and life-cycle cost. Struct. Infrastruct. Eng. 3(1), 29–41 (2007) 33. Melchers, R.E., Beck, A.T.: Structural Reliability Analysis and Prediction. Wiley, Chichester (1999)

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Research on Tooth Profile Error of Non-circular Gears Based on Complex Surface Theory Yongping Liu, Fulin Liao, and Changbin Dong(&) School of Mechanical and Electronical Engineering, Lanzhou University of Technology, Lanzhou 730050, China [email protected], [email protected], [email protected]

Abstract. In view of the complex shape and structure of non-circular gears, it is difficult to measure the machining errors of non-circular gears, and the complex surface theory is proposed to measure the errors. Firstly, the Euclidean transformation matrix is used to establish the error evaluation function, and the scanner is used to digitally scan the non-circular gears, collect the coordinates of the data points on the tooth surface. Then, the non-uniform rational B-spline function is used to accurately describe the tooth surface and reconstruct the tooth surface. Finally, the theoretical data are matched with the reconstructed tooth surface by coordinate transformation to calculate the tooth surface error. The feasibility of the proposed algorithm is proved by a calculation example, which provides a reference for further accurate detection of the non-circular gear tooth surface error. Keywords: Non-circular gear  Tooth surface error Reconstruct tooth surface  Match



1 Introduction The non-circular gears is a gear mechanism with variable transmission ratio, which has the advantages of large transmission power range, high transmission efficiency, accurate transmission ratio, long service life, strong carrying capacity and reliable operation [1]. At present, with the improvement of the transmission accuracy of non-circular gears, higher requirements are put forward for the processing accuracy and processing accuracy detection of non-circular gears. However, due to the complex shape and structure of non-circular gears, a wide variety of types, and many measurement parameters, so far, there is little research on their geometric accuracy, and there is a lack of effective measurement means [2]. To solve this problem, many scholars have done a lot of research. Among them, Wang mentioned the influence of NC hobbing processing

This project is supported by National Natural Science Foundation of China (Grant No. 51765032). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 447–455, 2020. https://doi.org/10.1007/978-981-32-9941-2_36

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errors and process errors on the accuracy of non-circular gears, and studied the errors of non-circular gears through interpolation algorithm and error compensation [3]. Lu and Wang put forward the use of polar coordinate method to measure the individual errors of eccentric circular gears in CNC gear measuring center [4]. Lin et al. proposed measuring and evaluating the tooth profile error of super large gear based on NURBS surface fitting [5]. Xie et al. put forward the method of NURBS model reconstruction and two-step matching to evaluate the surface error of non-bevel gears in variable ratio differential [6]. On the basis of the above research, aiming at the fact that the left and right sides of each tooth profile of non-circular gear are different and the detection is difficult, and in order to obtain accurate tooth surface error and make the transmission of gear pair more stable, this paper proposes to study the tooth profile error of non-circular gear by using complex surface theory.

2 Mathematical Model for Evaluating Tooth Surface Error Before evaluating the tooth profile error, it is necessary to reconstruct the tooth surface with actual data, and match the reconstructed tooth surface with the theoretical data point. As a rigid body, the reconstructed tooth surface is equivalent to the theoretical data of the tooth surface. The coordinate transformation makes the reconstructed tooth surface contain the theoretical data as much as possible, and minimizes the distance error between the theoretical data and the tooth surface [7]. So the key of matching is to solve the Euclidean transformation matrix. M, and ensure the theoretical data Pi ¼ ðxi ; yi ; zi Þði ¼ 0; 1; 2; . . .; nÞ were contained as much as possible by the recon0 0 0 0 structed tooth surface. Assume transformed data is Pi ¼ ðxi ; yi ; zi Þ, the relative between the theoretical data and the transformed data as follows: 0

0

0

ðxi ; yi ; zi ; 1Þ ¼ ðxi ; yi ; zi ; 1Þ  Mði ¼ 0; 1; 2; . . .; nÞ  M¼

R T

0 1

ð1Þ

 ð2Þ

Where T ¼ ½ T x T y T z , Note that T is displacement matrix of theoretical data relative to reconstructed tooth surface, and T x , T y , T z is displacement vector that theoretical data along the x, y, and z axes of the coordinate axis respectively, and R is the rotation matrix of theoretical data relative to the reconstructed tooth surface, R as follows:

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  R ¼ rij 33

449

ð3Þ

8 < r11 ¼ cos a cos b r ¼ cos b sin c : 12 r13 ¼  sin b

ð4Þ

8 < r21 ¼ sin a sin b cos c  cos a sin c r ¼ sin a sin b sin c  cos a cos c : 22 r23 ¼ sin a cos b

ð5Þ

8 < r31 ¼ cos a sin b cos c þ sin a sin c r ¼ cos a sin b sin c  sin a cos c : 32 r33 ¼ cos a cos b

ð6Þ

Note that a, b, c is the rotation angle of theoretical data rotate around the x, y, and z axes respectively. According to the principle of least squares, the evaluation functions follows: F¼

n  X  P0  Qi 2 i

ð7Þ

i¼1 0

Note that the closest point of point Pi is the point Qi on CAD tooth surface model.

3 Data Acquisition of Non-circular Gear Tooth Surface The purpose of data acquisition is to obtain the three-dimensional point cloud of noncircular gears, which is the process of digitizing the shape of gears. At present, there are two main methods to obtain three-dimensional point cloud data of gears: stereo vision method and laser scanning measurement method. According to the geometric characteristics of the selected research object, a non-contact active laser ranging system is used to obtain the three-dimensional point cloud of the gear. Creaform Metrascan scanner is selected to digitize non-circular gears. Figure 1 is the scanning process, and Fig. 2 is the computer interface of the scanning process

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Fig. 1. The process of scanning

Fig. 2. Computer interface for scanning process.

In order to collect the actual and theoretical 3D coordinates of non-circular gears, the 3D point cloud and non-circular gear CAD model are imported into reverse engineering software. The command [analysis/point coordinates] is selected to collect the actual 3D coordinates of the point cloud, and the command [analysis/creation annotations] is selected to collect the 3D coordinates of the theoretical tooth surface of non-circular gear CAD model. In order to study the tooth surface errors of different teeth, the actual and theoretical three-dimensional coordinates of the teeth No. 1, No. 7, No. 14, No. 20, No. 27, and No. 33 are collected respectively. Table 1 shows the actual three-dimensional coordinates of the left tooth surface of No. 1.

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Table 1. The actual 3D coordinates of left tooth surface of the 1st tooth. Number 3D coordinates x y 1 63.906 −3.362 2 62.733 −2.705 3 61.416 −2.143 4 59.987 −1.706 5 63.860 −3.324 6 62.839 −2.761 … … … 59 61.326 −2.184 60 60.089 −1.837 61 63.953 −3.443 62 62.974 −2.879 63 61.327 −2.169 64 59.997 −1.777

z 1.722 1.688 1.705 1.669 3.003 2.948 … 22.180 22.254 23.771 23.717 23.830 23.823

4 Tooth Surface Reconstruction In order to calculate the distance between the theoretical data points and the reconstructed tooth surface, the Non-Uniform Rational B-Spline curve method was used to accurately describe the reconstructed tooth surface [8]. The rational form of p  q times NURBS tooth surface as follows: m P n P

Sðu; vÞ ¼

xi; j Pi; j Ni;p ðuÞNj;q ðvÞ

i¼0 j¼0 m P n P

xi; j Ni;p ðuÞNj;q ðvÞ

ð8Þ

i¼0 j¼0

Note that Pi; j is control grid in direction of u and v, 0  u, v  1, xi; j is weight factor, Ni;p ðuÞ and Nj;q ðvÞ is Non-Uniform Rational B-Spline basis function, which was defined on node vector U and V respectively. The node vector as follows: 9 8 8 > > > = < > > > > U ¼ 0;    ; 0 ; u ;    ; u ; 1;    ; 1 > p þ 1 rp1 > |fflfflfflffl{zfflfflfflffl} > > > ; :|fflfflfflffl{zfflfflfflffl} < pþ1 pþ1 9 8 ð9Þ > > > > = < > > > > V ¼ 0;    ; 0; vq þ 1 ;    ; vsq1 ; 1;    ; 1 > > |fflfflfflffl{zfflfflfflffl} > > : ; :|fflfflfflffl{zfflfflfflffl} qþ1

Where r ¼ n þ p þ 1,s ¼ m þ q þ 1.

qþ1

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The actual 3D coordinates of the collected tooth surface are imported into the numerical calculation software, and the reconstructed tooth surface can be obtained by fitting and interpolating the above method. Figure 3 shows the reconstructed left and right tooth surfaces of No. 1 tooth.

-1.5 30 -2

z/mm

20 -2.5

10 0 59

-3 60

61

y/mm

62

63

-3.5

64

x/mm

65

(a) Left tooth surface of No. 1 tooth

30

-6.8

z/mm

20 -7 10 -7.2 0 58

-7.4 59

60

61

x/mm

y/mm 62

63

-7.6

(b) Right tooth surface of No. 1tooth Fig. 3. The reconstructed tooth surface of the No. 1 tooth.

5 Matching of Theoretical Data with Reconstructed Tooth Surface Matching is a process of making theoretical 3D coordinates and reconstructed tooth surface in the same coordinate system by coordinate transformation. Firstly, select 3 corner points Pi ði ¼ 0; 1; 2Þ from theoretical 3D coordinates, and select 3 corresponding corner points Qi ði ¼ 0; 1; 2Þ from reconstructed tooth surface, and then construct two sets of unit vectors with corner points from theoretical 3D coordinates and reconstructed tooth surface respectively, two sets of unit vectors as follows:

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8 P1 P0 > < e1 ¼ jP1 P0 j e2 ¼ e3  e1 > : e3 ¼ e1  P2 P0 jP2 P0 j

ð10Þ

8 0 > e ¼ Q1 Q0 > < 1 jQ1 Q0 j 0 0 0 e2 ¼ e3  e1 > > : e0 ¼ e0  Q2 Q0 3 1 jQ2 Q0 j

ð11Þ

And construct two local coordinate systems through taking point P0 and point Q0 as coordinate respectively, and take unit vector group ½ e1 e2 e3  and unit vector  0 origin 0 0  group e1 e2 e3 as axes respectively. Assume the two local coordinate systems are completely coincident through coordinate transformation of Eq (1). Therefore, the relation between the two local coordinates as follows: 

0

e1

0

e2

0

e3

T

¼ ½ e1

e2

e3 T

ð12Þ

  R ¼ rij 33

ð13Þ

The rotation angle of theoretical 3D coordinates around the x, y, and z axes were obtained by consisting of Eqs. (12) and (13), the rotation angle around the x, y, and z axes respectively as follows: 8 a ¼ arctan rr23 > 33 > < r13 b ¼ arctan pffiffiffiffiffiffiffiffiffiffiffiffi 2 þ r2 r23 33 > > : c ¼ arctan r12 r11

ð14Þ

The translation vector T x , T y , T z in the translation matrix T were determined by T, T as follows: T ¼ ½P0  Q0 R

ð15Þ

According to the three-order non-circular gears studied and collected 3D coordinate of tooth surface, the Euclidean transformation matrix M is solved by the above method. Now the transformation matrix M of left tooth surface of 1st tooth was calculated by substituting 3D coordinate into Eqs. (10)–(15), the transformation matrix M of left tooth surface of 1st tooth as follows: 2

0:8256 0:0095 6 0:0767 0:0032 M¼6 4 0:2131 0:0802 0:06235 0:8326

0:0026 0:0003 0:0413 0:5325

3 0 07 7 05 1

ð16Þ

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6 Example Calculation Taking the third-order non-circular gear as an example, the specific parameters are shown in Table 2. The collected tooth data is calculated by the above method, and the calculation result is drawn into a graph. Figure 4 shows the tooth surface error of the left and right tooth faces of each tooth. Table 2. Experimental gear parameters Modulus m Number of teeth Z Center distance a Addendum coefficient h*a Top clearance coefficient C* Tooth width B Eccentricity e Pitch curve equation r

3 39 135 1 0.25 30 0.0773 57:5544 r ¼ 10:0773 cos 3u

Fig. 4. Error of tooth surface

It can be obtained from Fig. 4 that the tooth surface error of No. 1, No. 7, No. 14, No. 20, No. 27, and No. 33 is small, the error of six tooth surface is close, and the error of the left and right tooth surfaces of each tooth is close, and the phase difference is small.

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7 Conclusion From the above analysis, the following conclusions are drawn: (1) The error of tooth surface of No. 1, No. 7, No. 14, No. 20, No. 27, and No. 33 tooth is small and no more than 0.06 mm. In addition, error of 6 teeth surface and error of left and right tooth surface of every tooth are very close. (2) The error evaluation function constructed in this paper, the method of tooth surface reconstruction and the matching of theoretical data and reconstructed teeth surface are effective and feasible. (3) This paper finds a new way to measure the tooth surface error of non-circular gears.

References 1. Dooner, D.B.: Function generation utilizing an eight-link mechanism and optimized noncircular gear elements with application to automotive steering. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 13(215), 847–856 (1995) 2. Litvin, F.L., Gonzalez-Perez, I., Fuentes, A., et al.: Tandem design of mechanisms for function generation and output speed variation. Comput. Methods Appl. Mech. Eng. 198(5), 860–876 (2009) 3. Wang, Y.Z.: Study on Errors Analyse of CNC Hobbing Non-Circular Gears. Lanzhou University of Technology, Lanzhou (2013) 4. Lu, C.X., Wang, J.H.: Measuring technique for non-circular gears. J. Xi’an Inst. Technol. 1 (19), 58–61 (1999) 5. Lin, J.C., Shi, Z.Y., Pan, C.G., et al.: Profile error evaluation of large gears based on NURBS surface fitting. J. Instrum. 3(37), 533–539 (2016) 6. Xie, X., Zhang, X.B., Jia, J.M.: Surface error evaluation of non-circular bevel gear of variable ratio differential. Mech. Transm. 4(41), 48–52 (2017) 7. Liu, Y.P., Liu, J.X., Zhang, L.Y., et al.: Research on point cloud to the complex surface best fitting. China Mech. Eng. 12(16), 1080–1082 (2005) 8. He, G.Y., Liu, X., Liu, P.P., et al.: Evaluating of complex surface profile error based on subdivision and sphere approximation method. Comput. Integr. Manuf. Syst. 3(19), 474–479 (2013)

Topology Optimization Design of the Monocoque Bus Body Structure Zhuli Liu1(&), Xiangyu Huo1, Hao Zhou1, and Xiaoguang Wu2 1

2

School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China [email protected], [email protected], [email protected] Zhengzhou Yutong Bus Co., Ltd., Zhengzhou 450016, China

Abstract. Utilizing the monocoque bus body structure of low floor bus as the research object and the stress as constraint conditions, this paper developed the topology optimization model with the objective function of minimum structural mass under the horizontal bending conditions. Based on the results of topology optimization, a new bus body structure has been designed. This paper makes the finite element static analysis on the new body structure, which shows that its strength and stiffness meet the design requirements and that the topology is feasible. Further optimization of the body’s specific parameters can be put into effect to achieve the goal of the optimization in the design stage. Keywords: Monocoque body structure SIMP  RAMP  OptiStruct

 Topology optimization design 

1 Introduction With the Monocoque bus body structure is composed of profile steel, the whole body structure plays a role in carrying. It is obviously better than separate frame construction with the advantages of structural safety, stability, ride comfort, energy efficiency and environmental protection. For this reason, the Monocoque bus body structure is the mainstream form of high-class coach [1]. Due to the complexity of the monocoque body structure, the traditional design method is to modify the basic model based on design requirements of the new model. This method not only requires design experience, but also has a certain blindness, and the final design may not be reasonable enough. This paper takes the minimum mass of the monocoque bus body structure as the objective function, the strength and stiffness of body as constraint, and adopts the topology optimization to optimize the body structure, in order to find the force transferring path, to realize the conceptual design of the body structure, and to provide reference for subsequent design.

This project is supported by National Key R&D Program of China (Grant No. 2018YFB0106204-03). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 456–465, 2020. https://doi.org/10.1007/978-981-32-9941-2_37

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2 Topology Optimization Theory and Mathematical Optimization Model of Body Topology optimization is an innovative technology in structural optimization. Within the given design space, material is distributed according to the force transferring path of the structure, while the mechanical properties of the structure and lightweight can be considered in the conceptual design phase. Topological optimization can be divided into topology optimization of discrete structure (truss, steel frame, etc.) and topology optimization of continuum structure (2d shell, 3d solid, etc.). Discrete topology optimization originated from the truss theory, which was proposed by Michell in 1904. The ground structure method of Dorn, Gomory and Greenberg, and Schmit’s transformation of structural problems into mathematical programming lay the foundation for the topology optimization of discrete structure. After Bendsoe and Kikuchi proposed the homogenization method to solve the structural topology optimization in 1988, the continuum topology optimization has been developed rapidly in theory. At present, the main methods of continuum topology optimization are homogenization method, variable density method, variable thickness method and topological function description method, of which homogenization method and variable density method are the most representative [2–4]. Homogenization method has strict mechanics and mathematics theory foundation, but it has many design variables, long solution time, and the calculation result is prone to checkerboard phenomenon. Therefore, it is usually used in topology optimization theory research. The variable density method assumes that the material density is variable, taking the element relative density as the design variable. In the calculation, when the element relative density is 0, the material in the element can be removed; when the element relative density is 1, the element reserves. There are two kinds of common interpolation models in variable density method: Solid isotropic material with penalization (SIMP) and Rational approximation of material properties (RAMP) [5, 6]. Variable density method has high computational efficiency, simple program implementation and wide applied range. In the conceptual design, the basic topological form of the structure can be determined only by the constraints and the loads of the structure. SIMP and RAMP are as follows: Ee Ee

SIMP

RAMP

¼

¼ ðxe Þp E0

xe E0 1 þ pð1  xe Þ

ð1Þ ð2Þ

In the formula, xe is element relative density, xe ¼ qe =q0 , qe is hypothetical element density, q0 is the real density of materials, Ee is hypothetical elasticity modulus of element, E0 is material elasticity modulus, p is penalty factor.

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SIMP and RAMP are shown in Figs. 1 and 2, SIMP has two drawbacks: SIMP cannot ensure that the penalty function is a concave function and cannot obtain the global optimal solution; when the value of p is greater than a certain value, the result is completely misleading. By contrast, the above situation does not occur in RAMP, so RAMP is more stable than SIMP [7].

Fig. 1. SIMP

Fig. 2. RAMP

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With the structural stress and displacement of finite element as the constraint condition, the body mass can be transformed into material volume based on the assumption that the body frame uses the same material. The topology optimization mathematical model with the minimum volume as the objective function is as follows: N X

ve

ð3Þ

s:t KU ¼ F

ð4Þ

ðre ÞVM  xpe r

ð5Þ

min

e¼1

0 \ xmin  xe  1

e ¼ 1;   ; N

ð6Þ

In the formula, ve is element volume; K is stiffness matrix; U is displacement matrix; F is load; xe is element relative density; ðre ÞVM is the equivalent stress of the element; r is stress requirements under working conditions; p is penalty factor; xmin is the lower limit of element relative density.

3 Topology Optimization of Body Structure The general topology optimization software mainly includes TOSCA (Germany), OptiShape (Japan), OptiStruct (USA) and Genesis (USA) [8]. In this paper, the OptiStruct of HyperWorks software is used to optimize the structure of the body. 3.1

Determine the Topology Optimization Space

According to low-entry hybrid bus of yutong, the basic parameters of monocoque bus body structure are shown in Table 1.

Table 1. The basic design parameters Name Bus overall length Bus overall height Bus overall width Wheelbase Front/rear overhang Front/rear tread Front suspension Rear suspension

Parameter/mm 12000 3150 2550 6100 2670/3220 2096/1836 Airbag Bearing spring

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Topology optimization space is the largest area of material distribution. According to the basic parameters of the model, the topology optimization space for the bus can be determined, in which the front and middle parts of the bus adapt single floor, and the rear part adopts a double floor to store the battery and engine. The topology optimization space is shown in Fig. 3.

Fig. 3. Design space of topology optimization

Body material is Q345, elasticity modulus is 2.1E5 MPa, the Poisson’s ratio is 0.3, the density is 7.8E-9 T/mm3, the element type is shell element. Since the topology optimization design is a conceptual design, in order to reduce the calculation time, the element size is taken as 25 mm, and free meshing is performed in the hypermesh, and 203,728 elements are finally obtained. 3.2

Apply Constraints and Loads

Refer to Yutong bus, the fulcrum of rear overhang is connected to the body by bolts, and the airbag is connected to the front wheel house. In the topology optimization, the rigid region is selected in the connection position between the overhang and the body, and the RBE2 rigid node is used to replace the overhang fulcrum, so as to establish the coupling relationship between the RBE2 rigid node and the rigid region node. The simulation of rear overhang and front overhang fulcrum are shown in Figs. 4 and 5.

Fig. 4. Simulation of rear overhang

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Fig. 5. Simulation of front overhang

The constraints and loads are as follows in horizontal bending condition: Constrain the Y direction of the fulcrum of right airbag, the Y, Z directions of the left airbag, the X, Z directions of the fulcrum of right suspension, and the X, Y, Z directions of the left suspension; The X, Y, Z directions represent the direction of bus overall length, bus overall height and bus overall width. Body accessories such as passengers, engine, gearbox, clutch, air-conditioner are loaded at the corresponding positions according to the quality point. Due to the large difference between the design space and the actual material distribution space, the quality of the design space is not considered in the topology optimization design stage in order to avoid affecting the body structure 3.3

Topology Optimization Analysis

The design variable for topology optimization is element relative density. Considering strength safety requirement, the maximum stress in the design area is not more than 250 MPa, and the objective function is minimum volume. After 72 iterations, the density threshold is set to 0.09, which means that when the material density value is less than 0.09, the material at that location can be removed. The results of the topology optimization of body structure are shown in Fig. 6, and the reserved material shows the force transferring path of body structure under horizontal bending. In this circumstance, the convergence curve of the objective function value with the iteration number is shown in Fig. 7, the convergence is good.

Fig. 6. Results of topology optimization

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Fig. 7. Convergence curve of objective function

3.4

Topology Optimization Results

Figure 6 shows that the topology optimization result is an irregular pattern, which is different from the actual model and profile shape. According to the manufacturing process and profile selection, the body structure is mostly welded by rectangular steel pipe. Topology optimization results are interpreted as follows: (1) The red area in Fig. 6 is the main force transferring path, which has a large load, and material must be distributed on the path. (2) Considering the design of the body structure (such as structural symmetry, ensuring the closed loop structure after welding) and the bus operating conditions, increase the necessary distribution of materials. (3) Align the side wall pillar with the roof beam and floor beam. (4) In order to improve the anti-rollover ability of bus, the body shape should be square. (5) Take the lightweight design of the body as the criterion to minimize the distribution of materials. The force transferring paths and material distribution of the main structure such as the lower floor, upper floor, the connection of the left and right body side and floor are shown in Fig. 8. With the optimization results of the left body side as an example to make a brief description, it can be seen from Fig. 8(c) that the middle and front parts are the main transferring paths, and the side wall pillars are preferred. The path of the upper part of the body side is triangular, and the oblique brace is added at the upper waist beam. Similarly, oblique brace is added at the middle part of the body side and the lower waist beam. The right side is referred to the left side, which can be taken as symmetrical structure.

Topology Optimization Design of the Monocoque Bus Body Structure

(a) Lower floor result

(b) Upper floor result

(c) Left side result

(d) Floor connection result Fig. 8. Results of main structural topology optimization interpretation

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4 Verification of Finite Element Analysis According to the topological optimization results and the cross-section size of the body frame, the new body structure is welded by Q345 steel pipe with cross-section size of 50  50  3 mm. The body frame is analyzed under horizontal bending condition. Stress and body displacement clouds are shown in Figs. 9 and 10. The maximum displacement is 8.6 mm, which occurs in the upper roof and lower floor of the middle part of the body. The maximum stress is 111 MPa, mainly located at the floor beam and the connection of upper/lower floor. The strength and stiffness of the body meet the design requirements.

Fig. 9. The displacement diagram of bus

Fig. 10. The stress diagram of bus

5 Conclusions Based on the variable density method, the topology optimization of the monocoque bus body is carried out, the load transferring path is clarified, materials are distributed on the load transferring path, and a body frame is redesigned. The static analysis of the new body structure is carried out under bending condition, and the strength and stiffness of the body structure meet the design requirements, which shows that the topology optimization structure is feasible. In the future, based on the topology

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optimization results, the section size of rectangular steel pipe can be optimized, the specific parameters of body structure can be determined, and the optimization objective can be achieved in the design stage.

References 1. Liu, K.: Bus Body Design, pp. 24–27. Mechanical Industry Press, Beijing (2012). (in Chinese) 2. Zuo, K.: Research of Theory and Application about Topology Optimization of Continuum Structure. Huazhong University of Science and Technology (2004). (in Chinese) 3. Bendsoe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using homogenization method. Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988) 4. Sigmund, O., Maute, K.: Topology Optimization Approaches, pp. 1031–1055. Springer, Berlin (2013) 5. Kongtian, Z., Liping, C., Fangyi, Z.: New theory and algorithm research about topology optimization based on artificial material density. Chin. J. Mech. Eng. 4(12), 31–37 (2004). (in Chinese) 6. Qiao, Z., Weihong, Z., Jihong, Z.: Topology optimization of structures under dynamic response constriants. Chin. J. Mech. Eng. 46(15), 45–50 (2010). (in Chinese) 7. Xiang, C., Xinjun, L.: Solving topology optimization problems based on RAMP method combined with guide-weight method. Chin. J. Mech. Eng. 48(1), 135–140 (2012). (in Chinese) 8. Weihong, Z., Min, W.: Applications of topology optimization in the automobilc industry. J. Kunming Univ. Sci. Technol. (Sci. Technol.) 3, 77–81 (2005). (in Chinese)

Analysis of Wind Vibration Response of Transmission Tower Zhuli Liu1(&), Beibei Liu1, Zhuan You1, and Mengli Li2 1

School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China [email protected], [email protected], [email protected] 2 Henan EPRI Gaoke Group Co. Ltd., Zhengzhou 450052, China [email protected]

Abstract. Angular tension-resistant transmission tower is taken as research object in this paper. The Davenport pulsating-wind speed spectrum was used to simulate wind speed time series and the wind power spectrum at different height nodes of transmission tower in MATLAB with the help of the linear filtering method (AR). The reliability of the fluctuating wind speed time series simulation was confirmed by comparing the wind power spectrum with Davenport power spectrum. Refined finite element model of the tower was established by APDL in ANSYS. The wind-load was calculated by the simulation of wind speed time series, and the wind-load time-history curve was generated at the same time. Finally, the dynamic characteristics and the wind-induced dynamic response of transmission tower in hurricane ware studied. The results show that the top of the tower was prone to large deformation and acceleration under strong wind excitation. In other words, there was a significant whipping effect. The research results will prove a useful reference for designing transmission tower and safeguarding the operation of transmission lines. Keywords: Transmission tower  Pulsating wind simulation Dynamic characteristics  Wind-induced dynamic response



1 Introduction The High-voltage transmission tower-line system is a key link of transmission line. If it fails, the entire line will not operate properly. Therefore, it’s great significance to ensure it to operate safely. Generally, the high-voltage transmission tower-line system has a large span, and the tower body is flexible and tall. Hence, it has strong nonlinear characteristics and its mechanical properties is complex. When there are strong winds, it’s easy to cause complex vibration and collapse the tower [1]. In order to ensure the stability of tower in the strong wind, the dynamic characteristics and wind-induced dynamic response of transmission tower were studied in this paper.

This project is supported by state grid henan power company (Grant No. 5217021350HQ). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 466–476, 2020. https://doi.org/10.1007/978-981-32-9941-2_38

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2 Wind-Load Theory and Wind Speed Simulation 2.1

Wind-Load Theory and Characteristics

Air horizontal pressure gradient force is the cause of wind formation. According to the statistical data of wind speed, wind can be divided into mean wind and fluctuating wind [2]. (1) Mean wind. The mean wind is invariable for a certain period and it will not cause structural vibration. The mean wind can be treated as static force in mechanical analysis. The mean wind speed varies with height within a certain range of height. We can calculate it according to the exponential law [3] from Load code for the design of building structure [4]: 

vðzÞ vðzr Þ

 ¼

 a z zr

ð1Þ

Where VðZr Þ denotes the average wind speed at the reference height of Zr, a denotes the ground roughness index, V(z) denotes the mean wind speed at any height. (2) Fluctuating wind Davenport pulsating-wind speed spectrum [5] has been used widely to reach pulsating wind by domestic and foreign scholars and it is also the wind speed spectrum used in the relevant design specifications of China. The formula is as follows: Sv ðnÞ ¼ 4Kv210



X2 f ð1 þ X 2 Þ4=3

1200 f v10

ð2Þ

ð3Þ

Where f donates the pulse frequency (Hz), V10 donates the mean wind speed at 10 m (m/s); K is the surface roughness coefficient, taken as 0.005. Wind speed can be regarded as the superposition of mean wind and fluctuating wind, expressed as:  þ vðx; y; z; tÞ Vðx; y; z; tÞ ¼ VðzÞ

ð4Þ

Where V(z) is the mean wind speed at height z; V is the fluctuating wind speed at height Z; t denotes time.

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The Simulation of Tower’s Wind Speed Time Series

The tension-resistant transmission tower in a certain area is selected as the object of study. Selection of Class B Ground Roughness Types (suburbs, towns with sparse fields and houses, villages, jungles, hills and houses), the corresponding a = 0.16; the design mean wind speed V(zr) is 30 m/s at the reference height 10 m. The transmission tower is divided into 10 sections. Select the wind speed simulation points in each section (in Fig. 1). The mean wind speed V(z) of the wind speed simulation point at the height Z which is calculated by Eq. 1 was listed in Table 1.

Fig. 1. Location of the wind speed simulation points

Table 1. Mean wind speed at each point Note 1 2 3 4 5 6 7 8 9 10

Height (m) Area (m2) 9.0 4.856 12.0 1.520 17.0 2.527 22.0 3.490 28.0 1.952 30.0 1.921 36.1 2.146 38.1 2.974 42.1 0.880 44.1 1.274

Mean wind speed (m/s) 29.50 30.89 32.66 34.03 35.37 35.77 36.84 37.16 37.76 38.04

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Linear filtering method (AR) is widely used to simulate wind speed of time-history, because of its fast calculation speed and small amount of calculation. In this method, the response values of the present time are represented by the linear combination of the response values of the past time and the white noise [6]. The mathematical expression of AR method as follows: V ðX; Y; Z; tÞ ¼

p X

uk V ðX; Y; Z; t  kDtÞ þ N ðtÞ

ð5Þ

k¼1

Where uk denotes the autoregressive coefficient matrix; P denotes the order of the model; N(t) denotes the independent random process vector; Dt denotes the time step of wind speed time series. The mean wind speed at simulated points of wind speed in each section is superimposed with the fluctuating wind speed obtained by the linear filtering method. The wind speed time series of each point is simulated in MATLAB, the simulation time is 180 s. The wind speed time series curves of four simulation points are listed in Fig. 2.

Fig. 2. Wind speed time-history curve of simulated points

Wind power spectrum at 22 m and 38.1 m nodes are compared with Davenport power spectrum. The results are shown in Fig. 3. The simulated wind power spectrum

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at two selected nodes fluctuates around Davenport power spectrum, and the two power spectra have high fitting degree. It proves the feasibility of using AR method to simulate fluctuating wind.

Fig. 3. Comparison diagram of power-spectrum

2.3

Numerical Calculation of Wind Load

Wind loads on transmission towers can be calculated by the following formulas [7]: Ftower ¼ us Af V 2 =1:6

ð6Þ

Where us denotes the shape coefficient of transmission tower, according to Technical Regulation of Design for Tower and Pole Structures of Overhead Transmission Line us = 2.5; V denotes the node wind speed time series; Af denotes the wind-pressure projection area in simulated area. Equation 6 can convert the wind speed time series into the wind load time-history of a certain area at the simulation point. It can provide load conditions for subsequent analysis of wind-induced vibration response of tower.

3 Analysis of Dynamic Characteristics of Transmission Towers 3.1

Establishment of Finite Element Model of Transmission Towers

With the geometric center of the tower leg as the origin, the extension direction of the cross-arm as the X-axis, the vertical direction as the Z-axis, and the transmission traverse direction as the Y-axis, in ANSYS. BEAM188 element is selected to simulate the various poles in the tower by endowing the beam element with different crosssection shapes and parameters and accurately setting the orientation of the angle iron. The refined beam-frame finite element model of the angular tension-resistant transmission tower is completed (as Fig. 4 shows).

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Fig. 4. Finite element model of tensile tower

3.2

Analysis of Dynamic Characteristics of Transition Towers

Block Lanczos method [8] is used for modal analysis of the tower in ANSYS. The natural frequencies and modes of each mode are obtained. The frequencies and modes of ten are listed in Table 2. Table 2. Natural frequency and vibration mode of tower Order 1 2 3 4 5 6 7 8 9 10

Frequency (Hz) Mode of vibration 2.4642 Swing along the Y axis 3.2359 Swing along the X axis 3.3292 Torsion around Z-axis 5.2201 Local deformation 5.6687 Swing along the Y axis & Torsion around Z-axis 5.8947 Swing along the X axis & Torsion around Z-axis 6.0398 Torsion around Z-axis & Local deformation 7.1057 Swing along the X axis & Torsion around Z-axis 7.1069 Local deformation 7.9560 Local deformation

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According to Table 2 and Fig. 5, the top ten natural frequencies of the tower are densely distributed, and the vibration modes are complex, it including lateral and longitudinal oscillation and torsion. At the same time, there are many local modes and spatial coupling modes. The local mode shapes appear many times at the legs and crossbars of the tower in the mode diagram (Fig. 5). It indicates that this part is the weak part of the tower structure which needs to be strengthened, and ensure the stability of the structure.

(a)First-order mode shape

(c)Third-order mode shape

(b)Second-order mode shape

(d)Fourth-order mode shape

Fig. 5. Primary vibration mode of tower

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4 Analysis of Wind Vibration Response of Transmission Tower 4.1

Time Domain Analysis Based on Newmark-b Method

Vibration of transmission tower under wind load belongs to forced vibration of damped structure, and its motion equation can be expressed as follows: ½Mf€ug þ [C]fu_ g þ [K]fug ¼ fFðtÞg

ð7Þ

Where [M] donates the mass matrix; [C] donates the damping matrix; [K] donates _ donates the velocity array; the stiffness matrix; {u} donates the displacement array; {u} {ü} donates the acceleration array; {F(t)} donates the wind load on the transmission tower. Newmark-b method is used to solve the forced vibration response of structures, and the integral solution of Eq. 7 can be solved directly. 4.2

Determining the Structural Damping of the Tower

Damping is an inherent property of structural dynamic characteristics. It is related to material and friction coefficient of structure, and it’s an effective means to weaken vibration. The accuracy of simulation results can be ensured by correct calculation of damping. Since the accurate damping matrix needs to be further studied, the simplified actual damping matrix is used in this paper. The Rayleigh damping hypothesis [9] is used to assist the calculation. ½ C  ¼ a ½ M  þ b½ K 

ð8Þ

Where [M] donates the mass matrix; [C] donates the damping matrix; [K] donates the stiffness matrix; a donates the mass damping coefficient; b donates the stiffness damping coefficient. a and b can be obtained by the following formula:     2wi wj ni wj  nj wi 2 nj wj  ni wi b¼ a¼ w2j  w2i w2j  w2i

ð9Þ

Where wi and wj represent the i-th and j-th vibration frequencies. They are usually taken for the first and second order vibration frequencies; ni and nj represent the corresponding damping ratios of the i-th and j-th modes. For steel structures, they range from 0.01 to 0.02. 4.3

Generating Wind Load Time-History Curve

Based on the wind load numerical calculation method of tower described in Sect. 2.3, the wind load time-history of representative nodes of transmission tower can be

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calculated according to its geometric parameters and the simulation results of wind speed time series in Sect. 2.2 (as Fig. 6 shows).

Fig. 6. Time-history curve of wind-load at classic nodes

4.4

Analysis of Wind Vibration Response of Transmission Tower

The node displacement of transmission tower under strong wind is mainly affected by the wind load on the tower [10]. According to the wind speed time history simulation calculation method, the wind speed time history was transformed into the wind load time history at each node. The wind load was added to the tower model by APDL cyclic command flow, and then the wind vibration response was analyzed. Finally, the time-history curves of displacement, velocity and acceleration at the top and bottom of the tower were extracted (in Fig. 7). According to the extracted response curves of displacement, velocity and acceleration of tower at bottom and top, and combined with Table 3 found that: the displacement, velocity and acceleration increase with the increase of height of tower. The response peaks of displacement, velocity and acceleration at the top tower is 33.9 mm, 0.168 m/s and 3.89 m/s2 respectively. It was found that the top of the tower was prone to large deformation and acceleration under strong wind excitation. That is to say, there was a significant whipping effect.

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Fig. 7. Response curves of displacement, velocity and acceleration at the bottom and top of tower Table 3. The maximum displacement, velocity and acceleration of the tower at the bottom and top Node Bottom 74 Top 518

Maximum displacement (mm) 1.81

Maximum velocity (m/s) 0.0034

Maximum acceleration (m/s2) 0.115

33.90

0.1680

3.890

5 Conclusions In this paper, a refined finite element model of transmission tower was built based on the research object of the turret type tension-resistant tower. The dynamic characteristics of the tower model were analyzed. The tower model was loaded with simulated wind load, and the wind-induced time-history response was analyzed. The conclusions are as follows: (1) The most widely used Davenport wind speed spectrum is adopted to simulate the wind speed time history of transmission tower by using the linear filtering method, and the simulated power spectrum is compared with Davenport power spectrum to verify the accuracy and applicability of the simulated spectrum.

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(2) The modal analysis of the tower model shows that the natural frequencies and mode shapes of each order clearly show that the weak parts of the transmission tower structure are the tower legs and the transverse arms prone to local deformation. (3) The wind-induced vibration response of the tower was analyzed, and the timehistory curves of displacement, velocity and acceleration at the representative nodes were extracted. It was found that for the single tower model, the displacement, velocity and acceleration also increased with the increase of height, and large deformation and acceleration occurred near the tower top, namely whipping effect. Based on the above conclusions, the structural strength of the weak parts, such as the tower leg and the cross arm, which are prone to local deformation, should be fully guaranteed to ensure the stability of the structure. For the high-rise transmission tower structure, the stiffness at the top should be increased to limit its wind-induced vibration response and prevent the occurrence of large displacement and acceleration at the top. The research results in this paper have important reference value for the subsequent design and structural improvement of the transmission tower.

References 1. Chen, J.: Research of Wind-Induced Vibration of Tower-Line System of Power Transmission Tower. Guangxi University, Nanning (2013). (in Chinese) 2. Wang, G., Zhao, P.: Analysis of Anti-overturning of a telecommunication tower under strong wind. J. Zhengzhou Univ. (Eng. Sci.) 33(02), 76–80 (2012). (in Chinese) 3. Ministry of housing and urban-rural development of the People’s Republic of China; General administration of quality supervision, inspection and quarantine of the People’s Republic of China. GB50009—2012 Load code for the design of building structures. China Building Industry Press, Beijing (2012). (in Chinese) 4. Walker, E.K.: The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum, effects of environment and complex load history on fatigue life, ASTM, 1970. STP462, 1–14 (1970) 5. Davenport, A.G.: Gust loading factors. J. Struct. Div. ASCE 93, 11–34 (1967) 6. He, W.: Studies on wind-induced dynamic response of high-rise lattice tower. Hunan University, Changsha (2009). (in Chinese) 7. Zhang, L.: Research on wind stochastic field and dynamic reliability for high-rise building with wind loading. Tongji University, Shanghai (2006). (in Chinese) 8. Li, T., Sun, Y.: Analysis of the dynamic properties of smoke desulphurization absorber tower structure. J. Zhengzhou Univ. (Eng. Sci.) 02, 64–67 (2007). (in Chinese) 9. Wang, Z., Ma, R., et al.: Tower Structure. Science Press, Beijing (2004). (in Chinese) 10. Holmes, J.D.: Along-wind response of lattice tower: derivation of expressions for gust response factors. Eng. Struct. 16(4), 287–292 (1994)

Design of a Stabilize Device for Heavy Oil Transportation in Water Ring Haoran Lu, Fan Jiang(&), Yuliang Chen, Xiaolong Qi, and Zhongmin Xiao School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510000, China [email protected]

Abstract. During the long distance transportation of heavy oil by water ring, instability will occur under the action of gravity. In order to meet the demand of stable transportation of water-ring heavy oil, an innovative design method integrating TRIZ and Extenics is proposed. By analyzing the contradictions in innovative design and implementing effective extension transformation, a waterring heavy oil transportation stabilize device is designed. According to the principle of divergence analysis of a characteristic multi-value, two schemes are designed, in which the bottom liquid outlet is located at the entrance or exit of the stabilizing device. The N-S equation and the turbulence model have been used to describe the fluid flow. Taking the V0F model and the CSF model to track the oil-water interface, the numerical equation and analytical model have been established. The simulation results show that when the bottom liquid outlet is set at the entrance section of the stabilize device, the pipeline can better form the shape of heavy oil wrapped by water ring. Keywords: Core-annular flow  Heavy oil transportation  TRIZ  Extenics Stabilize device  Numerical simulation



1 Introduction The world’s heavy oil resources are abundant. With the large-scale exploitation of conventional crude oil on land, people have turned more attention to heavy oil. The viscosity of the heavy oil is too large, and the shear stress of the oil and the pipe wall is too large to be transported. The use of low-viscosity fluids to encircle the oil phase in a ring-shaped manner (forming an annular flow) for oil transport will greatly reduce the energy consumption of heavy oil transportation, and is one of the effective modes for heavy oil pipeline transportation. Many scholars have studied and discussed the theory of heavy oil-water core-annular flow viscosity, annular flow pattern and unstable surface tension of annular flow [1–5]. Pan et al. [6], first proposed in the patent to use water to lubricate pipelines for viscous fluid transportation. This method can effectively This project is supported by Natural Science Foundation of Guangdong Province (Grant No. 2016A030313653); Science and Technology Program of Guangzhou (Grant No. 201504291436202). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 477–492, 2020. https://doi.org/10.1007/978-981-32-9941-2_39

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reduce friction loss and is suitable for pipeline transportation of high viscous crude oil. In 1994, Ho and Li [7] prepared a oil-in-water emulsion according to the water-oil ratio of 7–11, and successfully applied water film transport. The thicker the oil, the greater the viscosity, the more suitable for liquid ring transport. Li et al. [8], studied the stability of the water ring through local distortion of the pipeline, hydrophilization of the pipe wall and gel adsorption layer on the i walnnerl of the pipe. China’s Shell Oil Company and Shengli Oilfield Qinghe Oil Production Zone also adopted oil-water annular flow technology [9]. The main problem of water ring transportation technology at present: with the increase of transportation distance, the annular water film of lowviscosity fluid (water) wrapped around high-viscosity fluid (heavy oil) will gradually disappear, that is, water ring instability. Jiang et al. [10], designed a new type of water ring generator, which can effectively improve the stable length of water ring and reduce transportation energy consumption, but there are still unstable problems. Aiming at the current problem, a design of water ring heavy oil transportation stabilize device based on TRIZ and extension is proposed, and a set of stabilize device is added for each distance to realize long-distance transportation of water ring.

2 Invention Design of Stabilize Device 2.1

Product Innovation Optimization Design Method Based on TRIZ and Extenics

2.1.1 TRIZ Theory and Extenics TRIZ theory was created by the Soviet scientist Genrich S. Altshuler in the middle of the 20th century. It is literally translated as the “inventive problem solving theory” and is an innovative problem-solving theory. Its main purpose is to study human beings inventing and the scientific principles and rules followed in the process of solving technical problems. The theory has been widely used in various engineering fields [11– 13]. Extenics is an original transversal subject put forward by Chinese scholar Cai Wen in 1983. It uses a formal model to explore the possibilities of things expansion and open up new laws and methods, and to solve contradictions. The basic theory of extenics is extension theory, which consists of three parts: elementary theory, extension set theory and extension logic. In innovation application, it mainly through extension modeling, expansion, transformation, and goodness evaluation to get ideas [14]. At present, extenics has entered some research areas and achieved a series of results. 2.1.2 Product Innovation Optimization Design Method Based on TRIZ and Extenics Innovative design will encounter many problems. The combination of TRIZ theory and extension innovation method will reduce the difficulty of solving. The key point is contradiction recognition and contradiction solving. Here, the TRIZ tool and the extension innovation method are integrated, and the innovative method is established as shown in Fig. 1.

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Need innovative products

No

Conflicts that hinder product

TRIZ theory

Method evaluation

Extenics

Method selection

Practice test

mechanism

Solved?

No

Adjust the crossover idea

Evaluation of program excellence

Fig. 1. The cross fusion model of TRIZ and extenics

2.2

Stabilize Device Innovation Based on TRIZ and Extenics

2.2.1 Problem Recognition Based on Primitive Model Transportation of heavy oil by water-ring heavy oil can greatly improve transportation efficiency and reduce energy consumption. However, the density of heavy oil is smaller than that of water. With the increase of transportation distance, the stratification of heavy oil and water will occur under the action of gravity. The upper layer is heavy oil and the lower layer is water. The contact between heavy oil and pipe wall in the upper layer produces greater friction resistance, which leads to the decrease of heavy oil transportation speed and efficiency, and also requires a large amount of energy consumption. Through these existing phenomena, the main identification problem is the stratification of oil and water.

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2.2.2 Problem Analysis Based on Primitive Model According to the formal description of Extenics, the ultimate goal G of establishing the water ring heavy oil conveying and stabilizing device, and the target event element is  G¼

recovery

Control object requirements

Oil and water phases Water ring heavy oil



After long distance transportation, the stratification of oil and water occurs. According to the formal description of extenics, the current conditional matter element L is 2 L¼4

Oil and waterphases

form flowstate

3 Upper and lower stratification of oilphase and waterphase 5 Slowoilspeed

Obviously, this constitutes an incompatibility problem: to improve efficiency requires the realization of water ring heavy oil, water ring heavy oil needs to be added again, the water content in the pipe increases, and the transportation efficiency is reduced. which is P ¼ G  L. According to the incompatibility problem model, the expansion analysis is carried out to extract a contradiction: to improve the transport efficiency, it is necessary to improve the flow speed of heavy oil, and to improve the speed, the annular flow of oil and water should be formed. The formation of water ring needs to add water again, and the water content in the pipeline increases, so the transport efficiency decreases. The application of standard engineering technical parameters is described in Table 1. Table 1. Standardized description Improving parameter Deteriorating parameter

Contradiction Circular flow pattern

Standardized description of contradiction Parameter 12—shape

Increase energy consumption

Parameter 19—energy consumption of a moving object

2.2.3 Feasibility Solution Prediction Based on TRIZ Innovation Principle Looking for the contradiction matrix under the known technical parameters, getting the four kinds of recommended inventive principles [15], the corresponding serial number is: 02, 06, 14, 34, those are as follows: Principle 02 is extraction: (1) extracting negatively affected parts or attributes from an object; (2) extracting necessary parts from objects. Principle 06 is multi-purpose: (1) to make an object have multiple functions; (2) if the function of an object is replaced, the object can be cut. Principle 14 is curved surface: (1) from straight line to curve, from plane to sphere, from regular hexahedron to spherical structure; (2) using rod, sphere and helix; (3) from straight line to rotary motion, using centrifugal force. Principle 34 is abandonment and repair: (1) the use of dissolution, evaporation and other means to abandon the completed function of parts,

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or directly modify them in the process of system operation; (2) in the process of work quickly supplement system or object in the part of consumption. According to the above principles, it can be seen that the extraction principle, the multi-purpose principle and the curved surface principle are not suitable for fluid pipeline transportation, and they are not considered for the time being. At the same time, we hope that the annular flow pattern can be restored without increasing the water content. According to the suggestion of abandonment principle and repair principle, the original water phase in the pipeline can be abandoned by the replacement transformation in the basic extension transformation method, and new water phase can be added again to replace the initial water phase, so as to realize the recovery of the form of water-ring heavy oil. 2.2.4 Element Transformation of Feasible Solution According to the solution of TRIZ principle, it is necessary to remove part of the water accumulated at the bottom of the pipeline. Firstly, transform T1 so that T1 L1 ¼ L1  L11 . Among them, 2 T1 ¼ 4 2 L11 ¼ 4

Add

3 Actuator object L1 Dominant object L11 5 Transformation result L1  L11

Water phase outlet of pipeline

Shape Number Position

3 Rectangle 5 1 Bottom

At the same time, the location characteristics of the outlet at the bottom of the pipeline can be refined and diverged. The divergence of matter elements (one eigenmultiple value) has L11 jfL111 ; L112 g. Among them, 2

L111

Water phase 6 outlet of pipeline ¼6 4 2

L112

Water phase 6 outlet of pipeline ¼6 4

Shape Number Position

Rectangle

3

7 7 5 1 Pipeline entrance section

Shape

Rectangle

Number Position

1 Pipeline outlet section

3 7 7 5

In order to restore the oil-water annular flow pattern of the fluid in the pipeline, so it is necessary to transform t so that T2 L1 ¼ L1  L12 . Among them,

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2 T2 ¼ 4

Add

3 Actuator object L1 5 Dominant object L12 Transformation result L1  L12

2

L12

Water phase 6 entrance of pipeline 6 ¼6 6 4

Shape

Rectangle

Number Position

3 Circumferential uniform distribution

3 7 7 7 7 5

Meanwhile, the characteristics of water phase inflow direction in pipeline can be refined and diverged. The divergence of matter elements (one eigenmultiple value) has L12 jfL121 ; L122 g. Among them, 2

L121

Water phase 6 entrance of pipeline 6 ¼6 6 4 2

L122

2.3

Water phase 6 entrance of pipeline 6 ¼6 6 4

Inflow direction Number Position

Inflow direction Number Position

Vertical pipeline axis

3

7 7 7 3 7 5 Circumferential uniform distribution 3 Adherent spiral 7 encirclement 7 7 3 7 5 Circumferential uniform distribution

Final Program Objectives

According to the principle of divergence analysis of “one characteristic multi-value” [16]. According to the divergence analysis of the expansion type of the pipeline entrance, two schemes are obtained: (1) when water enters the pipeline, the flow direction is perpendicular to the pipeline axis; (2) when water enters the pipeline, there is an angle between the flow direction and the pipeline axis, that is, the flow enters the pipeline spirally. Comparing comprehensively, the water flow enters in the form of helix, which can better adhere to the inner wall of the pipeline under the action of centrifugal force. According to the divergence analysis of the pipeline outlet expansion type, the following two schemes are obtained: (1) the bottom liquid outlet is located at the inlet section of the pipeline of the stabilization device; (2) the bottom liquid outlet is located at the outlet section of the pipeline of the stabilization device. The final scheme selection needs to be analyzed by simulation results. The overall design of the stabilizing device is innovative in the common conveying pipeline. Its main feature is to add a new water phase inlet and a water phase outlet, and replace the water phase of the inlet and outlet to restore the shape of the oil-water annular flow. Specifically, after the two-phase flow enters the stabilizing device, the water phase sinking at the bottom can flow into the liquid storage tank through the

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bottom outlet recovery pipe for storage, and the transfer pump continuously pumps water into the pipe body, and the water enters the pipe under the guidance of the connecting pipe. In the body, at this time, the water entering the pipe body is conveyed forward along the spiral groove around the inner body of the pipe body under the condition that the conveying pump is pressurized, thereby forming a water ring heavy oil in the pipe body; The water in the tank can be recycled to achieve recycling of the unit. As shown in Fig. 2;

1 flange, 2 pipe body, 3 spiral grooves, 4 connecting pipes, 5 recovery pipes, 6 conveyor pumps, 7 fixing plates, 8 storage tanks

Fig. 2. Transport stabilize device

3 Numerical Simulation of Stabilize Device 3.1

Control Equation

The two-phase fluid obeys the law of mass and momentum conservation. The standard k  e model is chosen for turbulence model, and the continuous surface force CSF model is used for oil-water interaction. The continuity equation is: @q þ r  ð~ vqÞ ¼ 0 @t

ð1Þ

q ¼ ao qo þ ð1  ao Þqw

ð2Þ

Formula: q is fluid density; t is time; r is divergence symbol; ~ v is fluid velocity; qo is oil phase density; ao is volume fraction of oil phase; qw is density of water phase. The momentum conservation equation is: @ ðq~ vÞ þ r  ðq~ v~ vÞ ¼ rp þ rs þ q~ gþ~ F @t

ð3Þ

2 s ¼ l½ðr~ v þ r~ vT Þ  r  ð~ vIÞ 3

ð4Þ

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Formula: p is the pressure, s is the shear stress tensor, g is the acceleration of gravity, ~ F is the external volume force, l is the fluid viscosity, I is the unit tensor. The standard k  e model is: @ðqkÞ @ðqk~ vÞ @ þ ¼ @t @xi @xj @ðqeÞ @t

@ðqe~ vÞ @xi 2 C2e q ek

þ

   l @k lþ t þ Gk  qe rk @xj

¼ @x@ j þ

h  i @e C1e ke Gk l þ rlet @x j

lt ¼ qCl

k2 e

ð5Þ

ð6Þ

ð7Þ

Formula: k is the turbulent kinetic energy, e is the dissipation rate, Gk is the turbulent kinetic energy generation term caused by the average velocity gradient, C1e ; C2e ; Cl is the constant, and its values are 1.44, 1.92 and 0.09, respectively; rk is the turbulent Plante number of turbulent kinetic energy k and its value is 1.0; re is the turbulent Plante number of dissipation rate e and its value is 1.3; xi is the i coordinate direction; xj T is the j coordinate direction; lt is the turbulent viscosity. The surface tension model of CSF is: Fr ¼ row

ao qo jraw þ aw qw jrao 0:5ðqo þ qw Þ   n j¼r j nj n ¼ rao

ð8Þ ð9Þ ð10Þ

Formula: Fr is the oil-water interfacial tension, which can be substituted by external volume force (3); row is the oil-water interfacial tension coefficient; qo ; qw is the density of oil phase and water phase; ao ; aw is the volume fraction of oil phase and water phase; j is the curvature of interface; n is the unit normal direction of the volume fraction of oil phase. 3.2

Computational Model

The internal structure of the transport stabilize device is simplified, and the threedimensional model of the transport stabilizate device runner is created by using Solidworks software. The diameter of the runner is 20 mm, the length of the inlet pipeline is 10 mm, the length of the stabilizate device is 120 mm, the length of the outlet pipeline is 70 mm, the depth of the spiral depression of the inner wall of the pipeline is 1 mm, and the ratio of water to oil inlet area is about 2:8 [10]. The water phase is in the lower layer, the oil phase is in the upper layer, and the flow area model is shown in Fig. 3. The model is divided by using the mesh module in ANSYS

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Workbench. The maximum distortion of the mesh is 0.79, and the minimum orthogonal mass is 0.32, which meets the requirements of numerical simulation.

Fig. 3. Flow area model

The physical parameters of the fluids are shown in Table 2. The boundary conditions are set as follows: the inlet is a velocity inlet, the oil phase velocity is 1.2 m/s, the water phase velocity in the pipe is 1.02 m/s, the water phase velocity in the spiral inlet is 1.5 m/s, the outlet is a pressure outlet, and the rest are wall surfaces. Because the Reynolds number exceeds the critical value, turbulence occurs in the flow region. The standard turbulence model is adopted. SIMPLE algorithm is used to solve the flow equation. The second-order upwind scheme is chosen for all the discrete schemes in the equation, and the two-precision solution is obtained. Table 2. Physical properties of various fluids Name Density (kg m−3) Viscosity (ps s) Surface tension (N m−1) Oil 960.0 0.220000 0.039 Water 998.2 0.001003 –

4 The Analysis and Discussion of the Results 4.1

Scheme Simulation and Comparison

According to the thinking method of characteristic multi-value, we set the bottom liquid outlet at the entrance and exit of the pipeline of the conveying and stabilizing device respectively, and analyze it through numerical simulation. Comparing Figs. 4 and 5 (red area indicates that the area is full of oil, blue area indicates that the area is full of water, and other colors indicate oil-water mixing), when the bottom liquid outlet is set at the entrance section, there is no oil phase on the wall of the whole pipeline, all of them are water phase, and a good oil-water annular flow pattern is formed at the outlet of the pipeline, and the oil phase is wrapped uniformly by the water phase. When the bottom liquid outlet is set at the exit section, some oil phases will appear on the wall of the pipeline, and a better oil-water annular flow pattern has not been formed at the outlet of the pipeline, and the distribution of oil and water phases is not uniform. The main reason is that the water phase of the lower layer flows out from the bottom outlet and the oil level drops. At this time, the liquid of the spiral pipeline has entered the stabilize device pipeline. The oil phase and the water phase leaving the spiral pipeline can not form a good wrapping form. Under the impact of the water phase from the spiral pipeline, the oil phase adheres to the wall.

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Fig. 4. The volume fraction contours of oil phase when the bottom outlet is set at the entrance of pipeline

Fig. 5. The volume fraction contours of oil phase when the bottom outlet is set at the exit of pipeline

Comparing Figs. 6 and 7 synthetically, when observing the volume fraction contours of oil phase in each section, the two schemes have something in common: when the lower water phase passes through the spiral pipeline, a part of the water phase will be wrapped in the oil phase, and the two phases will move forward in a spiral way. At the same time, the water phase wrapped in the oil phase will gradually migrate to the pipeline wall, with the trend of leaving the oil phase wrapped. The difference is that when the bottom outlet is set at the entrance section of the pipeline, the stabilize device can form a good oil-water annular flow pattern; when the bottom outlet is set at the exit section of the pipeline, the intact flow pattern can not be formed. Therefore, the flow pattern in the pipeline varies with the location of the bottom liquid outlet, and the volume fraction of the oil phase varies with the cross-section. The specific relationship values are shown in Fig. 8. The volume fraction of oil phase decreases first and then increases. The main reason is that there is a large amount of water flowing into the pipeline through the spiral pipeline, which leads to the decrease of the volume fraction of oil phase. After a long distance transportation, the two-phase flow is stable, and the volume fraction of oil phase increases gradually when the velocity of water phase is less than the velocity of oil phase, and finally approaches the volume fraction at the entrance. Comparatively, the recovery effect of oil-water annular flow with bottom outlet at the entrance of pipeline is higher than that with bottom outlet at the outlet of pipeline.

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Fig. 6. The volume fraction contours of oil phase of each section when the bottom outlet is set at the entrance section of the pipeline.

Fig. 7. The volume fraction contours of oil phase of each section when the bottom outlet is set at the exit section of the pipeline.

Fig. 8. Oil volume fraction comparison for different locations at the bottom

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The Formation of Two Phase Flow and Its Flow Field Analysis

As shown in Fig. 9 at the initial moment (0–0.06 s), the oil has a downward movement trend. The main reason is that the bottom liquid outlet is set at the entrance section of the pipeline of the transport stabilize device. At this time, part of the water is discharged from the pipeline, and the oil begins to move downward under the action of gravity. In the mid-term moment (0.06–0.12 s), some water enters the stabilize device through the spiral pipeline. At this time, the velocity and direction of the new fluid entering the pipeline are different from that of the original one, so some turbulent phenomena will occur in the contact area. At the same time, the new liquid fills the gap of the pipeline, and the liquid entering the spiral pipeline is better to contact the wall under the action of centrifugal force, thus blocking the oil phase and the wall contact. At the later stage (0.12–0.18 s), the oil is obviously wrapped in the middle, and there is obvious annular flow at the outlet of the pipeline. The water in the upper layer is slightly more than that in the lower layer, which is more conducive to maintaining the stability of the annular flow. At the later moment (0.12–0.18 s), the oil is obviously wrapped in the middle, and there is obvious annular flow at the outlet of the pipeline. The water in the upper layer is slightly more than that in the lower layer, which is more conducive to maintaining the stability of the annular flow. At the end moment (0.18– 0.8 s), it is obvious that a stable annular flow pattern has been formed in the pipeline. At this time, there is a water phase vortex in the middle of the pipeline, mainly because at the outlet of the spiral pipeline, the jets produced by the three pipelines converge to produce the vortex, which has no effect on the stability of the later transportation of the annular flow. As shown in Fig. 10, the flow velocity in the middle of the whole pipeline is faster than that near the pipe wall. The main reason is the influence of the liquid sticky wall to reduce the flow velocity. During pipeline transportation, there are two peaks of velocity increase along the central axis of the channel as shown in Fig. 11. The first wave peak occurs at the end of the entrance of the spiral pipe. The reason is that there is a large amount of water flowing into the spiral pipe, and the high-speed flow around the center of the water squeezes the fluid to increase the flow velocity. The second wave peak occurs at the end of the helical pipe. The main reason is that the cross section of the main channel decreases. The fluid needs to leave the helical wall and enter the pipe. According to Bernoulli equation, the flow velocity increases with the decrease of the area through which the fluid flows, and then the flow velocity tends to be stable. As shown in Figs. 12 and 13, the total pressure between the inlet of the pipeline and the inlet of the helical pipeline increases slightly, and reaches the maximum at the inlet of the helical pipeline. Then the total pressure from this position to the outlet shows a significant downward trend, and the pressure in the center of the pipeline is stronger than that on the wall of the pipeline. The main reason is that the fluid is squeezed at the entrance of the spiral pipe with the newly added fluid, therefore, the total pressure will rise, and then the fluid movement will be balanced, and the squeeze in the center will gradually decrease. However, the central extrusion strength is still greater than the extrusion strength of the fluid on the pipe wall, therefore, the total pressure in the middle of the channel decreases gradually but is still higher than that on the wall of the pipeline.

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0.02s

0.04s

0.06s

0.08s

0.1s

0.12s

0.14s

0.16s

0.18s

0.4s

0.6s

0.8s

Fig. 9. Contours of volume fraction between heavy oil and water at different time

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Fig. 10. The velocity contours of stabilize device

Fig. 11. The velocity plot in the direction of an axis

Fig. 12. The total pressure contours of stabilize device

Fig. 13. The total pressure plot in the direction of an axis

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Evaluation of Program Excellence

According to the feasibility solution analysis of TRIZ innovation principle, we choose the combination of abandonment principle and repair principle. Through the replacement transformation of extension transformation method, we adopt the new method of adding water phase to replace the initial water phase. There is a certain angle between the direction of water phase and the axis of pipeline, that is, the water flow enters the channel in a spiral way. We have designed two different schemes for the initial water phase discharge. Through numerical simulation analysis, it can be concluded that both schemes have a certain degree of recovery effect. By comparing the volume fraction of oil phase and the recovery of water-ring heavy oil, we can find that the effect of the bottom liquid outlet at the entrance section of the pipeline of the stabilization device is better than that of the bottom liquid outlet at the stable installation. The outlet section of the pipeline is located, so the bottom liquid outlet is selected for the inlet section of the pipeline of the stabilization device.

5 Conclusions and Recommendations (1) Innovative design approach combining TRIZ and extenics. Firstly, the contradiction problem in the innovative design is analyzed by using the extenics contradiction method, then the contradictory parameters are standardized, the TRIZ contradiction matrix is searched, the combination of abandonment principle and repair principle is selected to establish the feasible solution, implements the replacement transformation in extenics, and the innovative design scheme is obtained. (2) According to the principle of divergence analysis of a characteristic multi-value, two schemes are designed, in which the bottom liquid outlet is located at the entrance or exit of the stabilizing device. Through numerical simulation, according to the goodness evaluation method, the scheme of setting the bottom liquid outlet at the entrance section of the pipeline of the transport stabilize device is optimized. (3) Spiral pipeline is the core part of the whole stabilize device. The helical elevation angle, the number of helical coils and the wall thickness of the helical pipeline need to be further studied and discussed.

References 1. Cavicchio, C.A.M., Biazussi, J.L., De Castro, M.S., et al.: Experimental study of viscosity effects on heavy crude oil-water core-annular flow pattern. Exp. Therm. Fluid Sci. 92(270– 285), S0894177717303825 (2017) 2. Bhadraiah, V., Mahesh, V.P., Alparslan, O., et al.: Combined buoyancy and viscous effects in liquid–liquid flows in a vertical pipe. Acta Mech. 210(1–2), 1–12 (2010) 3. Dipin, S.P., Dinesh, B., Sundararajan, T., et al.: A viscous potential flow model for coreannular flow. Appl. Math. Model. 40(7–8), 5044–5062 (2016)

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4. Jiang, F., Wang, K., Skote, M., et al.: Simulation of non-Newtonian oil-water core annular flow through return bends. Heat Mass Transf. 54, 37–48 (2017) 5. Jiang, F., Wang, Y., Ou, J.J., et al.: Numerical simulation of oil-water core annular flow in a U-bend based on the Eulerian model. Chem. Eng. Technol. 37(4), 659–666 (2014) 6. Pan, D.L., Tu, D.Y.: Experimental study on high viscosity crude oil transported by liquid loop. Oil Gas Storage Transp. 1(5), 1–8 (1982) 7. Ho, W.S., Li, N.N.: Core-annular flow of liquid membrane emulsion. AIChE J. 40(12), 1961–1968 (1994) 8. Li, J.Y., Liang, C.Q., Zhang, D.M., et al.: Stability of oil-water annular flow transport. Oil Gas Storage Transp. 7(6), 22–29 (1988) 9. Zhao, H.Y., Jing, J.Q.: Research status and progress of annular flow. Petrochem. Technol. 2, 124–126 (2015) 10. Jiang, W.M., Du, S.L., Liu, Y., et al.: Study on stability characteristics and structural optimization of a new type of core-annular flow generator with high viscosity oil. J. Hunan Univ. (Nat. Sci.) (8), 86–90 (2018) 11. Jiang, F., Sun, H., Hu, Y.D., et al.: The plan research on the mechanical foundation Innovative experiment Teaching system combined with TRIZ theory. Equip. Manuf. Technol. 2010(2), 190–192 (2010) 12. Jiang, F., Chen, W.P., Wang, Y.J., et al.: Collection Mode optimization of casting dust based on TRIZ. Adv. Mater. Res. 97–101, 2695–2698 (2010) 13. Robles, G.C., Negny, S., Lann, J.M.L.: Case-based reasoning and TRIZ: a coupling for innovative conception in chemical engineering. Chem. Eng. Process. Process. Intensif. 48 (1), 239–249 (2009) 14. Yang, C.Y., Cai, W.: Generating creative ideas for production based on extenics. J. Guangdong Univ. Technol. 33(1), 12–16 (2016) 15. Jiang, F., Li, S.J.: Did You Innovate Today – TRIZ Innovation Story. Intellectual Property Press, Beijing (2017) 16. Du, Y.S., Liu, Y.P.: The variation of features based on extenics. J. Guangdong Univ. Technol. 34(6), 9–14 (2017)

Design of Spatial Lissajous Trajectory Vibrating Screen Zhipeng Lyu(&) and Sizhu Zhou School of Mechanical Engineering, Yangtze University, Jingzhou 434023, China {Lvzhp,zhsz}@yangtzeu.edu.cn

Abstract. According to the formation principle of two-dimensional Lissajous curve, it is determined that the rotational speed of two linear exciting vibration motors is twice of the rotational speed of circular exciting vibration motors, the spatial Lissajous vibration trajectory can be realized. The relevant vibration equation is established and solved. At last, this paper innovatively divides the conventional single sieve box into two parallel symmetrical arrangements, and put forward a parallel double sieve box structure, then the spatial Lissajous trajectory vibrating screen is designed. Keywords: Lissajous spatial trajectory

 Vibrating screen  Design

1 Introduction Vibrating screen is the key equipment for material separation and is widely used in construction, mining, agriculture and petroleum [1]. For the planar motion of multibody dual-motor and multi-motor elemental-body vibrating screen, scholars have already conducted in-depth research and formed a certain theoretical basis [2–4]. At present, the vibrating trajectory of vibrating screen used in the field is generally in the form of a circle, a straight line and a moving ellipse [5–8]. This paper proposes a new spatial Lissajous vibration trajectory which allows the surface of the screen to move in the X, Y and Z directions, making the solid-phase particles subjected to more uniform forces and this contributes to relieve the screen paste problem.

2 Formation Principle of Two-Dimensional Lissajous Curve The motion synthesized by two simple harmonic vibrations which are perpendicular and have different frequencies is complicated. However, when the frequency of the two partial vibrations is a simple integer ratio, a regular, stable, closed trajectory, the Lissajous curve, can be obtained. Jules Antoine Lissajous conducted a detailed research on this family of curves in 1857 [8]. Set the two simple harmonic vibration equations along the x and y directions as follows: This project is supported by the financial support from the Hubei Provincial Department of education in China (Grant No. D20171303). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 493–498, 2020. https://doi.org/10.1007/978-981-32-9941-2_40

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(

x ¼ A1 cosðx1 t þ u1 Þ y ¼ A2 cosðx2 t þ u2 Þ

ð1Þ

Then, when the vibration frequency ratio x1:x2 is 2 and 3 and the initial phase difference x1:x2 is 0 and p/2, the two-dimensional Lissajous curve family is shown in Fig. 1.

Fig. 1. Two-dimensional Lissajous curves

Fig. 2. Spatial Lissajous trajectory

3 Formation Method of Spatial Lissajous Vibration Trajectory 3.1

Theoretical Equation for Spatial Lissajous Vibration Trajectory

The synthetic trajectory of three mutually perpendicular harmonic vibrations when the frequency of the partial vibration is a simple integer ratio is discussed. Set the expressions of the simple harmonic vibration parameter equations along the x, y and z directions as follows: 8 > < x ¼ A1 sinðx1 t þ u1 Þ y ¼ A2 cosðx2 t þ u2 Þ > : z ¼ A1 cosðx1 t þ u1 Þ

ð2Þ

It can be seen from analytical formula (2) that the synthetic trajectory is circular in the xz plane, and the trajectory is a reciprocating straight line in the y direction. When x1:x2 = 2, a stable and closed spatial vibration trajectory curve can be obtained, as shown in Fig. 2. This curve is similar to one of the two-dimensional Lissajous curves, which is referred as the spatial Lissajous trajectory in this paper.

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Fig. 3. The realization principle diagram of spatial Lissajous vibrating trajectory

3.2

Realization Principle of Spatial Lissajous Vibration Trajectory

The screen box, excitation motor and spring structure are simplified and the corresponding coordinate system is established, as shown in Fig. 3. According to the balance principle [9], if the object is to maintain the translational state, the vibration direction of the reciprocating straight line needs to be directed to its center of mass. Assuming that there is no phase difference between the two linear vibration motors, according to the Darren Bell principle, the equation of motion of the screen box along x, y and z direction is: 8 2 > < M€x þ 4kx x ¼ mc rc xc sin xc t M€y þ 4ky y ¼ 2ml rl x2l cos xl t > : M€z þ 4kz z ¼ mc rc x2c cos xc t

ð3Þ

In the formula: M - Screen box quality (including screen frame, vibration motor, drilling fluid and the reduced mass of rock debris), kg; mc - the quality of the eccentric block of the circular vibration motor, kg; ml - the quality of the eccentric block of the linear vibration motor, kg;

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rc - eccentric distance of the eccentric block of the circular vibration motor, m; rl - eccentric distance of the eccentric block of the linear vibration motor, m; kx, ky, kz - the stiffness equivalent of a single support spring in the x, y and z directions, N/m; xc - circular vibration motor speed, rad/s; xl - linear vibration motor speed, rad/s. According to the solution method of the ternary quadratic differential equation, the steady-state solution of Eq. (3) can be expressed as: 8 > < x ¼ Ax sinðxc tÞ y ¼ Ay cosðxl tÞ > : z ¼ Az cosðxc tÞ

ð4Þ

Equation (4) is the vibration trajectory equation of the model shown in Fig. 3 and Ax, Ay, Az is the amplitude along x, y and z directions, which are 8 mc rc x2c > > > Ax ¼ > > 4kx  Mx2c > > > < 2ml rl x2l Ay ¼ > 4ky  Mx2l > > > > > mc rc x2c > > : Az ¼ 4kz  Mx2c

ð5Þ

Assume kx = kz, then Ax = Az. Formula (4) can be transformed into 8 > < x ¼ Ax sinðxc tÞ y ¼ Ay cosðxl tÞ > : z ¼ Ax cosðxc tÞ

ð6Þ

Comparing formulas (6) and (2), as long as xl = 2xc, a spatial Lissajous vibration trajectory shown in Fig. 2 can be realized. 3.3

Realization Principle of Spatial Lissajous Vibration Trajectory

In order to meet the specific installation requirements of the three motors to realize the spatial Lissajous trajectory, this paper innovatively divides the conventional single sieve box into two parallel symmetrical arrangements, and designs a parallel double sieve box structure, as shown in Fig. 4.

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Fig. 4. Parallel double screen box structure

4 Conclusions (1) According to the formation principle of two-dimensional Lissajous curve, it is determined that the rotational speed of two linear exciting vibration motors is twice of the rotational speed of circular exciting vibration motors, the spatial Lissajous vibration trajectory can be realized. (2) A parallel double sieve box structure can meet the requirements to realize the spatial Lissajous trajectory vibrating screen.

References 1. Jiang, H.S., Zhao, Y.M., Duan, C.L., Yang, X.L., Liu, C.S., Qiao, J.P., Diao, H.R.: Kinematics of variable-amplitude screen and analysis of particle behavior during the process of coal screening. Powder Technol. 306, 88–95 (2017) 2. Yin, Z.J., Zhang, H., Han, T.: Simulation of particle flow on an elliptical vibrating screen using the discrete element method. Powder Technol. 332, 432–454 (2016) 3. Liu, C.S., Wang, H., Zhao, Y.M., Zhao, L.L., DEM Dong, H.L.: Simulation of particle flow on a single deck banana screen. Int. J. Min. Sci. Technol. 23, 273–277 (2013) 4. Kichkar, I.Y.: Analysis of an assigned oscillatory trajectory of a vibratory drilling screen. Chem. Pet. Eng. 46(1–2), 69–71 (2010) 5. Kichkar, I.Y.: Positioning of shale-shaker drive with an assigned vibration trajectory. Chem. Pet. Eng. 46(3–4), 137–141 (2010) 6. Wang, Z.M., Wang, R.H., Xiao, W.S.: Screening mechanism of balanced elliptical motion shale shaker excited by backward elliptical vibrating forces. J. China Univ. Pet. 32(2), 104– 109 (2010)

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7. Wang, Z.M., Wang, R.H., Shi, L., Huang, D.H.: Development and application of a selfsynchronization and balanced elliptical motion shale shaker excited by backward elliptical vibrating forces. Oil Drill. Prod. Technol. 32(2), 89–92 (2010) 8. Taylor, C.A.: The Art and Science of Lecture Demonstration, pp. 50–54. CRC Press, Boca Raton (1988) 9. Zhao, C.Y., Wen, B.C., Zhang, X.L.: Synchronization of the four identical unbalanced rotors in a vibrating system of plane motion. Sci. China Technol. Sci. 53(2), 405–422 (2010)

Part Retrieval Technology Based on Geometric Shape and Topological Correlation Ning Ma, Bo Yang(&), and Junzhi Shang School of Mechanical Engineering, University of Jinan, Jinan 250022, China [email protected], [email protected], [email protected]

Abstract. Part retrieval technology plays an important role in the product structure reconstruction design. Because the basic functional and structural information of the part is represented by the shape and topological association of the geometric elements. A part retrieval technology based on geometric shape and topological correlation is proposed in this paper. The part retrieval method is constructed from the two aspects, the semantic level and the geometric topological correlation. Firstly, at the semantic level, the fuzzy query of the transplanted parts is realized by characterizing the key semantic description of the transplanted parts. Then, at the level of geometric topological relationship, the similarity calculation is performed on the geometric shape information and the topological feature information in the variant parts library and transplanted parts library. Through the similarity retrieval algorithm and the setting of the retrieval threshold, the transplanted parts which similar to the variant parts are retrieved. Finally, the feasibility of the technology is verified by an example. Keywords: Transplanted parts retrieval  Similarity calculation Description semantics  Geometric shape correlation  Topological feature correlation



1 Introduction In the product design process, more than 75% of the engineering design is by improving the existing similar parts [1]. It can shorten the designing period and improve the efficiency. Therefore, the 3D CAD part retrieval technology plays an important role in the product structure reconstruction design and has become a research hot-spot in recent years. At present, the retrieval methods of 3D models mainly include: (1) Content-based retrieval methods. The method mainly uses the geometry of the extracted model or the topological association to describe the model. Based on this, the similarity between geometry and topology is calculated to complete the model retrieval [2]. For example, Gao et al. proposed a mechanical part retrieval method based on typical surface matching. They extract the geometrical topological information and estimate the

This project is supported by National Natural Science Foundation of China (Grant No. 51775239, 50975124). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 499–507, 2020. https://doi.org/10.1007/978-981-32-9941-2_41

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discriminant degree of the surface, finally apply the greedy algorithm to realize the part retrieval [3]. Zhu et al. proposed a 3D model retrieval method of mechanical parts based on skeleton tree [4]. (2) A retrieval method based on high-level semantics. The method defines the characteristics of model as semantic information that meets the user’s needs and extracts the semantic information to achieve similarity retrieval. For example, Xu et al. realized the region segmentation of the 3D model of the part by defining the edge classification specification and used the region structure code to retrieve the similar structural parts [5]. The above methods effectively solved some basic problems of three-dimensional retrieval, but failed to realize the organic combination of global retrieval and local retrieval. Therefore, based on the above methods, this paper proposed a part retrieval method based on geometric shape and topological correlation. The method firstly performed a fuzzy query by characterizing the key semantics of the transplanted part. Then extracted the variant parts information and calculated the similarity between them and the geometric topology information of the transplanted parts. Finally, the transplanted parts similar to the variant parts are retrieved by setting the similarity retrieval algorithm and the retrieval threshold. This method achieved the unification of local retrieval and global retrieval and made 3D retrieval more efficient and accurate.

2 Fuzzy Retrieval Method Based on Part Description Semantics The method of part retrieval based on descriptive semantics is to use the descriptive semantics of the geometric model as the condition for geometric model retrieval. Then the data based fuzzy query method is used to retrieve the transplanted parts. 2.1

The Type of Describe Semantics

Geometric model descriptive semantics includes two aspects: functional descriptive semantics and physical attribute descriptive semantics. Functional descriptive semantics includes support unit, connection unit, transfer motion unit; physical attribute descriptive semantics including part name, part number, part type (classifying feature units: block part, cylinder part, cone parts, sphere parts, boss parts, etc.), geometric matching surface types (plane, cylindrical surface, spherical surface, regular surface, etc.) [6]. 2.2

Fuzzy Retrieval Process Based on Semantic

The 3D model retrieval technology based on descriptive semantics mainly includes the following process: (l) extracting and storing descriptive semantics; (2) matching descriptive semantics; (3) querying model matching; (4) outputting display query results. The process is shown in Fig. 1.

Part Retrieval Technology Based on Geometric Shape Descriptive semantics

Porting feature library

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off line on line Query input Search User interface Visualization result

Descriptive semantics

Matching semantic

Search result

Matching geometric model

Fig. 1. Basic process of transplant unit retrieval based on descriptive semantics

With the descriptive semantics of physical attributes as the query keywords, the query high-level description semantics are divided into three levels: The first level is the type of lap surface; The second level is target matching surface; The third level is plane. In the first level semantics, the lap joints are divided into plane lap joints, cylindrical lap joints and other regular lap joints according to the different lap surfaces. In the second level semantics, the target matching surface is the geometric matching surface on the external transplanted part that needs to be associated with geometric constraints. Then, in the third level query semantics, the plane is taken as the target matching surface and finally the parts are found in the transplanted part library. The final query results are shown in Fig. 2.

Input First level query semantics Query conditions

Mating type Input

Second level query semantics

Target matching surface Input

Third level query semantics

Plane

Query result

Target geometry matching plane - plane

Fig. 2. Part query based on geometric matching face type description semantics

3 Similarity Calculation and Part Retrieval Based on Geometric Shape and Topological Information In order to obtain the transplanted parts similar to the shape and topology of the variation model, the part retrieval method based on geometric model shape and topological information is selected. The retrieval of the transplanted features and the

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variation design of the parts can be realized quickly and effectively by setting the shape weight factor, topology weight factor and retrieval threshold. 3.1

Information Description Based on B-Rep

The B-Rep data structure records the geometric information of all geometric elements and their interconnected topological relations according to the level of “body-surfaceloop-edge-point” [7]. The transplanted structure is a B-Rep data structure and its topology elements include: point, edge, coedge, wire, loop, surface, sub-shell, shell, lump and body. The B-Rep information is extracted from the part model and the CAD part model is convert into the form of a geometric element adjacency graph. The CAD entity model is shown in Fig. 3(a), and its corresponding geometric elements attribute adjacent graph is shown in Fig. 3(b). F8

F4 F3

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e2

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(b) Attribute adjacency graph Fig. 3. CAD model and geometric elements attribute adjacent graph

A mathematical model of the geometric element attribute adjacency graph of the CAD solid model is created: g = [v, e], where v = [v1, v2, …, vi] represents the set of points in the geometric element attribute adjacent graph and vi represents the i-th

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surface in the B-Rep model; e = [e1, e2, …, ei] represents the set of edges and ei represents the i-th edge. The boundary expression method (B-Rep) can perform various geometric operations and judgments based on the surface and edge normal vectors for the dimensional geometric information G. The two adjacent faces are found by using the B-Rep information and the geometric relationship between the dimensional geometry information and the normal vector of the surface is judged, then to transform it into the correct surface [8]. The size conversion idea based on B-Rep is shown in the Fig. 4.

C onv ersion al gorit hm B-R ep inform ati on

Edge a dj ac ent inform ati on Siz e inform ati on mode l

Geo met ric rel ati onshi p Dime nsion informat ion

Dime nsion informa ti on

Fig. 4. The size conversion idea based on B-Rep

3.2

Similarity Calculation

The geometric shape information and the topological feature information values of the unit model are extracted. The similarity calculation is performed on the shape information description set of the two part models and similar part geometric models are retrieved. 3.2.1 Similarity Calculation of Geometric Shapes The geometric shape feature information includes six attribute values, which are stored in the initialized feature vector gi[k]. Where i = 1, 2, …… represents the number of the unit geometric model; k = 0, 1, 2, …, 5 represents the surface area, volume, body length, face length, shape ratio, and compact ratio of the unit geometry model i. The similarity degree of the two geometric models is calculated by the following formula: 5 P

similarityDegreeðg1 ; g2 Þ ¼

SimilarityDegreeðg1 ½i; g2 ½iÞ

0

ð1Þ

6

Where, ( SimilarityDegreeðg1 ½i; g2 ½iÞ ¼

0

jg1 ½ig2 ½ij maxfjg1 ½i;g2 ½ij;jg1 ½ig2 ½ijg

jg1 ½i  g2 ½ij ¼ 0 jg1 ½i  g2 ½ij 6¼ 0

ð2Þ

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The similarity value of the two elements models is calculated as: SimilarityValuegeomtry ¼

1:0 1:0 þ SimilarityDegreeðg1 ; g2 Þ

ð3Þ

3.2.2 Similarity Calculation of Topological Features The topological feature information includes 12 feature attribute values, which are stored in the initialized feature vector ti[k]. Where i = 1, 2, …… represents the number of the unit geometric model; k = 0, 1, 2, …, 11 represents the number of faces, the number of sides, the number of vertices, the number of loops, the number of features, the number of planes, the number of cylinders, the number of cone faces, the number of spheres, the number of inner loops, and the number of outer loops of the unit geometric model i. The similarity degree of the two element geometric models is calculated by the following formula: 11 P

SimilarityDegreeðt1 ; t2 Þ ¼

SimilarityDegreeðt1 ½i; t2 ½iÞ

0

ð4Þ

12

Where, ( SimilarityDegreeðt1 ½i; t2 ½iÞ ¼

0

jt1 ½it2 ½ij maxfjt1 ½i;t2 ½ij;jt1 ½it2 ½ijg

jt1 ½i  t2 ½ij ¼ 0 jt1 ½i  t2 ½ij 6¼ 0

ð5Þ

The topological similarity value of the two element models is calculated as: SimilarityValuetopology ¼

1:0 1:0 þ SimilarityDegreeðt1 ; t2 Þ

ð6Þ

3.2.3 Similarity Calculation of the Overall Model The overall similarity calculation values of the two element geometric models include two parts: the geometric similarity calculation value and the topological similarity calculation value. The overall similarity calculation value is: SimilarityValuemodel ¼

w1 SimilarityValuegeomtry þ w2 SimilarityValuetopolopy w1 þ w2

ð7Þ

Where, w1 þ w2 ¼ 1:0, w1 , w2 respectively represents the weight values of the similarity and topological structure of the unit model. When the user has higher requirements on the shape similarity, the value of w1 is larger. When the user has higher requirements on the topology similarity, the value of w2 is larger.

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Transplant Part Retrieval Process Based on Geometry and Topology Information

The 3D model retrieval technology based on geometric shape and topology information mainly includes the following parts: (l) extracting and storing the description information of shape and topology; (2) calculating model similarity; (3) matching model; (4) outputting query result. The basic process of part retrieval is as follows: The description information of shape and topology is extracted which stored in the transplanted parts library. And then the information set is stored as a field in the database table. Before the retrieval, the shape and topology description information of the variant part are extracted. And then the model information similarity calculation is performed on the description information of the variant part and each model in the transplant part library. The similarity calculation value is obtained by setting the shape weighting factor, the topological weighting factor and the retrieval threshold. The basic process of retrieval is shown in the Fig. 5. Porting library Off-line

extract

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save

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Set weight value User

extract

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Fig. 5. Basic process of part retrieval based on shape and topology information

4 Example As shown in the Fig. 6, the hinge holder is taken as a geometric model of the reference parts. Then the transplanted part model similar to its geometry and topology structure is retrieved in the transplanted part library. Reference geometry model

Target geometry model

1.00

0.9147

0.9618

0.8977

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0.8035

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Firstly, shape description information and topology description information of the reference model are extracted. Then their similarity is calculated with the shape and topology description information of all part models in the transplanted part library. In this process, w1 is the geometric weight value, w2 is the topology weight value, the weight value is set: w1 ¼ 0:6, w2 ¼ 0:4 and the similarity value range is greater than or equal to 0.5. The search result is shown in the Fig. 6. w1 ¼ 0:7, w2 ¼ 0:3 and the similarity value range is greater than or equal to 0.5. The search result is shown in the Fig. 7.

Reference geometry model

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Fig. 7. Search results of the geometric model 2

5 Conclusions (1) In order to realize the organic combination of global retrieval and local retrieval, this paper proposes a part retrieval technology based on geometric shape and topological relationship. (2) The method performs fuzzy query retrieval on the parts by characterizing the key semantics of the transplanted parts. (3) The similarity between the geometrical and topological relationships of the mutated part and the transplanted part is calculated. (4) The transplanted parts similar to the variant parts are retrieved through the similarity search algorithm and the search threshold setting. The method can greatly shorten the designing period and improve product design efficiency.

References 1. Liu, Y.Y., Zhang, X., Yang, D.: Three-dimensional model retrieval of machine parts based on distance transformation. Agric. Equipment Veh. Eng. 56(05), 65–68 (2018) 2. Zhou, C., Yang, B., Yao, K., et al.: Research on generalized axis similarity retrieval method. Mech. Eng. 06, 4–8 (2016)

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3. Gao, Y., Wang, B., Hu, K.M., et al.: Mechanical parts retrieval based on typical face matching. J. Comput.-Aided Des. Comput. Graph. 23(04), 640–648 + 655 (2011) 4. Zhu, W.B., Geng, G.Q., Liu, Y.Y., et al.: 3D model retrieval method of mechanical parts based on skeleton tree. J. Mech. Eng. 52(13), 204–212 (2016) 5. Xu, J., Dong, Y.: 3D part model retrieval method based on surface region decomposition. J. Comput.-Aided Des. Comput. Graph. 29(05), 929–938 (2017) 6. Yao, K.: Research on the Rapid Variant Design Based on the Transplantation of the Unit. University of Jinan (2014) 7. Xu, J.H.: Variation Design Oriented Technology of Transplantation Element Retrieval and Fusion Process Evolution. Zhejiang University (2009) 8. Chen, Z.N., Lin, J., Xu, T.M.: Creation of dimension information model for three-dimensional machining process planning system. Mod. Manuf. Eng. 01, 33–38 (2016)

Analysis of Tool Wear and Wear Mechanism in Dry Forming Milling for Rail Milling Train Chao Pan1(&), Xiaoshan Gu1, Mulan Wang2,3, and Baosheng Wang2,3 1

China Railway Shanghai Administration Group Nanjing EMU Department, Nanjing 210012, China [email protected], [email protected] 2 Jiangsu Key Laboratory of Advanced Numerical Control Technology, Nanjing 211167, Jiangsu, China [email protected], [email protected] 3 Jiangsu Provincial Engineering Laboratory of Intelligent Manufacturing Equipment, Nanjing 211167, China

Abstract. Milling tools of the rail milling train have to face severe weariness due to the uneven surface hardness, inconsistent cutting rate and uncertain status of the rail itself as well as the vibration caused by the suspension system of the rail milling train and its characteristic hunting motion. This study performed a milling tool wearing status analysis and conducted relative research on wearing mechanisms with electron scanning microscope based on the typical milling tools and specific working conditions of rail milling train. Results indicate that the wearing status of rail milling train consists mainly of crater wear, notch wear, cutting edge chipping, surface exfoliation, milling sintering and tool break. The tool wearing conditions of rail milling train, compared with ordinary milling process, are significantly severe, and associated with multiple types of wearing status of which certain relevance exists. The research is of great significance for the improvement of the milling tool, the optimization of the process and the improvement of the mobile milling quality of the rail. Keywords: Rail

 Forming dry milling  Tool wear  Wear mechanism

1 Introduction At present, there are mainly two mobile rail repairing methods, namely, rail grinding and rail milling. The method of rail grinding fixes grinding materials such as motordriven grinding wheels at different points of railhead to grind surface metal through the rotation, translation or rolling motions of grinding materials, aiming at recovering the cross section and longitudinal profile of the rail. Rail milling is a kind of new mobile rail maintenance technology, which makes rail maintenance more efficient and more cost-effective. Rail milling train is a new-type and efficient mobile maintenance This project is supported by National Natural Science Foundation of China (Grant No. 51405210), University Science Research Project of Jiangsu Province, China (Grant No. 18KJA460004). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 508–517, 2020. https://doi.org/10.1007/978-981-32-9941-2_42

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equipment of rail, it has milling and grinding as its two procedures during its operation process. Milling procedure mainly adopts peripheral milling technology. The milling cutter on the whirling head mills top surface of rail, gauge corner and gauge line by rotating whirling head around the longitudinal axis perpendicular to the rail. Rail milling train can be applied to most cases of track maintenance. The rail maintenance technology of rail milling train can reduce roughness on the rail surface, remove railhead surface defects, and mills railhead profile into a targeted one. It has advantages of improving wheel-rail relation, reducing vibration and noises, elevating running stability of train and comfort of passengers and extending service life of rail [1–4]. Since rail should be made from difficult-to-cut material, it is normally made from hot-rolled or quenched high-carbon steel and low carbon microalloyed steel. At present, the 60 kg rail materials in China are mainly PD3, U71Mn and BNbRE with harness between 280–320 HB. The surface of rail may be harded unevenly after repeated rolling of wheels. During mobile milling, in order to avoid influence of cutting fluid on environment and training running, dry milling is generally adopted, but the temperature at milling area may rise rapidly and cause cutter wearing [5]; besides, as there are both straight line and curve line milling demand, and there might be abnormal cases of uneven rail, surface defects and large rail verge which would directly affect the quality of rail processing and service life of cutters; compared with traditional machinery processing method, rail milling train has hunting motion and vibration of suspension system during working on rail, thus equipment status and processing object are always changing, and localization datum is also in constant change, and the stability of equipment and processing object may directly influence service life of cutters. Besides, tool wear is different in milling complicated profile of rail compared with traditional processing method. Therefore, studying milling tool wear forms and tool wear mechanism may be significant to optimization of procedure, improving tool and rail processing quality of rail milling train.

2 Mobile Rail Milling Technology The SF03-FFS rail milling train produced by Linsinger Company in Austria weighs 120 tons. It has two sets of procedures: milling and grinding. The train is fixed with 2 milling units and 1 grinding unit per side. The milling cutters are used for cutting rail, grinding plate is used to improve the smoothness of rail surface. The milling procedure mainly adopts peripheral milling technology. The milling cutter on the whirling head mills rail top surface, gauge corner and gauge line by rotating whirling head around the longitudinal axis perpendicular to the rail and remove the damages on rail surface. Different from rail grinding train which needs many grinding wheels to finish rail milling, rail milling train adopts peripheral milling technology and grinds rail top surface by circumference surface of grinding plate and completely remove the minor concaves made by milling and improve the smoothness of railhead [6]. The milling cutter of rail milling train is mainly made up of blades, milling cutters and fixed bolts. The working status of milling cutter is shown in Fig. 1. The diameter of disk milling cutter is 600 mm and made by wholistic processing. The blades were fixed on the circumference surface of disk milling cutter in the radial direction, with two

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blade groups arranged laterally, each blade group containing eight blades. Moreover, the blades in each group are arranged in dislocation mode in the peripheral direction, forming an integral cutting edge with the same targeted profile of the rail along the axle direction. Rail forming milling cutter is only adopted at gauge corner, where radius of curvature is small. The curve of concave circular of the forming milling cutter matches with that of gauge corner, and other blades have straight cutting edges. The appropriate blade pattern can mill rail into targeted profile. Blades are made from hard alloy, coated with TiAlN on the surface. They can mill to a depth of 0.1–3 mm, and maximum depth of 5 mm at gauge corner. Their working speed can reach up to 420–1200 m/h. Milling range starts from the milling angle of 70° and 14 mm below rail surface of acting side to 40° outside the railhead. Rail section accuracy can reach 0.3 mm, and Accuracy of longitudinal profiles within the measuring range of 300 mm can reach 0.03 mm [7].

Fig. 1. Milling cutter of rail milling train

3 Analysis of Tool Wear in Forming Milling of Rail In order to study the tool wear status and mechanism of the rail milling train, after initial analysis, this study studied three typical blades after wearing, as is shown in Fig. 2. In the three blades, blades 1 and 2 have straight cutting edge, used for finish milling and rough milling of rail profile respectively, blade 3 is in arc-shape, used for the forming cutting of rail gauge corner. Electron scanning microscope was applied to observe the front and rear face of the cutters and to analyze the wearing status and wearing mechanism.

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Fig. 2. Milling blades of rail milling train

Blade 1 as is shown in Fig. 3 is mainly used for finish milling of rail milling train. The blade is an indexable blade with four straight-line cutting edges. It is used for milling the circular arc of the rail profile. The front face of the cutters shows that, crater wear is one of the main wear status. With expanding area of crater wear, there will be exfoliation on surface on the blade. In addition, cutting edge chipping also appears on all blades. With higher degree of wearing, milling sintering may emerge on the blade material.

1-1

1-3

1-2

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Fig. 3. Wearing status of blade 1

Blade 2 as is show in Fig. 4 is mainly used for rough milling of rail. The wear status of front and rear faces of the blades showed that, the notch wear on rear face of blade 2 was more serious than traditional milling processing with larger wear area and greater depth, besides, in terms of milling depth, the wear on rear face was in the shape of triangle, with serious wear near the cutting edge, less wear area with increase of distance from the cutting edge. The front face of blades also had obvious crater wear.

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2-1 2-1

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Fig. 4. Wearing status of blade 2

Blade 3 is the key cutter in mobile forming milling. It mainly mills the small radius arc surface at gauge corner. The precision and performance of the blade directly influence the processing quality of gauge corner. Figure 5 shows that, the wear status of blade 3 has crater wear, notch wear at the rear face and milling sintering, as well as more serious cutting edge chipping, damages and surface exfoliation.

3-1

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Fig. 5. Wearing status of blade 3

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4 Analysis of Wear Mechanism in Forming Milling of Rail An analysis on wear mechanism was done by considering the wear status of milling cutters. (1) Crater wear: crater wear at the front face of cutter is one of the main wear types for blades in rail milling train. Because of fierce thermal shocks and mechanical shocks on the rail milling train during operation, only the method of dry milling should be adopted to avoid the influences by cutting fluid on the friction coefficient of train wheels. In order to study the mechanism of crater wears on the front face of cutters, rail milling process was simulated by the software AdvantEdge FEM and the tool temperature and pressure distribution were analyzed. The parameters in milling process simulation and milling procedure are shown in Tables 1 and 2, and simulation results are shown in Fig. 6. Figure 6 shows that, in the process of milling, cutting heat takes place mainly at the contact area between front face of blades and metal chips, and the temperature rises sharply by friction at the contact area. Heat accumulates at the front surface of blades near the cutting edge, and there was fierce frictions generated by constant contacts between front surface and metal chips. Affected by diffusion and bond-friction between front surface of blades and metal chips, the chips brought away the tool materials of the front surface of blades, thus resulting in crater wears on the front surface [8–11]. Table 1. Parameters of blades Material Hard alloy Surface coating TiAlN Thickness of surface coating l 5 Diameter, mm 60 Teeth number 2 Rake angle, deg 11 Relief angle, deg 1 Edge Radius, mm 0.02

Table 2. Parameters of milling process simulation Milling method Down milling Rotating speed of principal axis r/min 4000 Feed per tooth mm 2 Milling depth mm 3 Initial temperature °C 20

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(1) Temperature distribution

(2) Pressure distribution Fig. 6. Milling temperature and pressure results of simulation

(2) Milling sintering: in the milling process, wear and crumbling on cutting edges made the surface coating fall off and the cutting edge become round. To study the reasons for milling sintering, the milling process was simulated. The corner radius of cutting edge increased to 0.2 mm and there was no surface coating on the tool surface, simulation results are shown in Fig. 7. During the process of milling, milling cutters had fierce frictions with metal chips, the corner radius of the cutting edge increased, and simulation temperature increased from 983 °C under normal conditions to 1042 °C, with evident increase in high-temperature area near the round corner of the cutting edge. Over-temperature brought about oxidizing reaction in the hard alloy and generated soft oxides. This is the phenomenon of milling sintering of the cutter materials [12]. In addition, one milling unit of the rail milling train were fixed with 88 blades. When a blade breaks or chipped during milling and can’t be replaced with a new one immediately, continuous operation may aggravate milling sintering.

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(1) Temperature distribution

(2) Pressure distribution Fig. 7. Temperature and pressure distribution after increase of corner radius

(3) Notch wear: in terms of wear status, the blades of rail milling train has more serious notch wear than traditional milling with larger wear area and greater wear depth, moreover, the notch wear was in the shape of triangle at the rear surface of the blades in the depth direction of milling, and the wear near the concave circular near the cutting edge had the most serious wear. With increased distance from the cutting edge, the notch wear became less serious. In traditional milling, the wear on rear surface of blades is mainly elastic deformation of materials because of low back engagement and fierce friction between the cutting surface and rear surface of the blades. During the mobile milling process, because of suspended rail bottom and the total elasticity of rail, the rail will have elastic bending under pressure and cutter relieving may occur during milling. After rotation of cutting edge, the rail recovers its height and has fierce friction with rear surface of the blades and produces serious notch wear at the rear surface. In addition, since the rail profile is arc-shaped, and the cutting edge of milling cutter is straight, there is friction between a flat surface and an arc surface, resulting deep friction depth at rear surface of the blades in the shape of triangle. (4) Cutting edge chipping: the breakage on milling cutter in mobile milling is mainly caused by chipping of cutting edge. As interrupted milling on the cutter fierce shocks on rail, and high temperature at milling area reduces the strength of hard alloyed cutter, especially the strength of the area near cutting edge after wears produced on the front and rear surface of the blades, resulting in collapse of cutting edge under violent shocks. By studying the working conditions of forming

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milling, it can be found that, the cutting edge contacts the arc-shaped processing surface at a point, which enlarges constantly to a larger area, thus the shocks normally take place at one point which is the most vulnerable point in tool wear, therefore, cutting edge chipping may take place on blades 1 and 2. Blade 3 has arc-shaped cutting edge which milling the gauge corner of rail. Under the same feed conditions, blade 3 has higher cutting amount than blades 1 and 2 and makes the most serious deformation on this part of rail, thus the shocks on blade 3 was more serious and had most serious cutting edge chipping on blade 3. (5) Surface exfoliation: compared with tool steel and high-speed steel, the hard alloy has higher hardness and heat resistance, thus the blade is not easily bent. However, with lower tenacity and uneven organizational structure, surface exfoliation may easily occur in face of unstable processing equipment and fierce shocks on the surface of cutters. (6) Fracture of cutter: because of the characteristics of hard alloy and its inner defects, under very bad processing conditions, the shocks may exceed the bearing capacity of the cutters and fracture the cutters.

5 Conclusions (1) The rail milling train have to face severe weariness due to the uneven surface hardness, inconsistent cutting rate and uncertain status of the rail itself as well as the vibration caused by the suspension system of the rail milling train and its characteristic hunting motion. (2) The wearing status of rail milling train consists mainly of crater wear, notch wear at the rear face of cutter, cutting edge chipping, surface exfoliation, milling sintering and tool break. There are multiple types of wearing status of which certain relevance exists. (3) Serious notch wear on rear surface of blades is caused because of suspended rail bottom and the total elasticity of rail and a triangle area of wearing is formed.

References 1. Liu, Y., Li, J., Cai, Y., et al.: Current state and development trend of rail grinding technology. Chin. Railway Sci. 35(4), 29–37 (2014). (in Chinese) 2. Jin, X., Du, X., Guo, J., et al.: States of arts of research on rail grinding. J. Southwest Jiaotong Univ. 45(1), 1–11 (2010). (in Chinese) 3. Zhou, Q., Tian, C., Zhang, Y., et al.: Research on key rail grinding technology of high-speed railway. Chin. Railway Sci. 33(2), 66–70 (2012). (in Chinese) 4. Liu, Z., Hu, J., Wang, Q., et al.: Research on the internal model control of the constant milling force of the rail milling train. J. Railway Sci. Eng. 10(1), 118–122 (2013). (in Chinese) 5. Yu, J., Lin, Y., Lin, H.: Review of tool wear in high-speed milling. Tool Eng. 49(8), 3–6 (2015). (in Chinese)

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6. Hu, J., Jiang, Y., Fang, J., et al.: Generalized predictive control of the grinding force of rail milling train. Chin. Railway Sci. 35(6), 84–90 (2014). (in Chinese) 7. Lima, F.F., Sales, W.F., Costa, E.S., et al.: Application of online rail maintenance technology for rail surface defects. Urban Mass Trans. 43(1), 677–685 (2017). (in Chinese) 8. Correa, J.G., Schroeter, R.B., Machado, A.R.: Tool life and wear mechanism analysis of carbide tools used in the machining of martensitic and supermartensitic stainless steels. Tribol. Int. 105, 102–117 (2017) 9. Maruda, R.W., Krolczykb, G.M., Nieslony, P., et al.: The influence of the cooling conditions on the cutting tool wear and the chip formation mechanism. J. Manuf. Process. 24, 107–115 (2016) 10. Sartori, S., Moro, L., Ghiotti, A., Bruschi, S.: On the tool wear mechanisms in dry and cryogenic turning additive manufactured titanium alloys. Tribol. Int. 105, 264–273 (2017) 11. Malakizadi, A., Gruber, H., Sadik, I., Nyborg, L.: An FEM-based approach for tool wear estimation in machining. Wear 368–369, 10–24 (2016) 12. Lima, F.F., Sales, W.F., Costa, E.S., et al.: Wear of ceramic tools when machining Inconel 751 using argon and oxygen as lubri-cooling atmospheres. Ceremics Int. 43, 677–685 (2017)

Wear Numerical Simulation and Life Prediction of Microstructure Surface Unfolding Wheel for Steel Ball Inspection Chengyi Pan(&), Xia Li, Hepeng Wang, Yanling Zhao, Jingzhong Xiang, Sihai Cui, and Yudong Bao Harbin University of Science and Technology, Harbin 150080, China [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]

Abstract. Wear is the main failure form of unfolding wheel for bearing steel ball. When the wheel wear reaches a certain level, the unfolding effect to the surface of the steel ball is invalid. Aiming at the life prediction problem for the unfolding wheel, according to analysis the wear profile and wear mechanism of the unfolding wheel drive surface, the main wear type of the unfolding wheel drive surface is determined as adhesive wear. A discrete Archard adhesion wear model is established based on the classical Archard adhesion wear model combined with the finite element method. Using the ANSYS software to simulate the wear of smooth surface unfolding wheel and microstructure surface unfolding wheel respectively, obtaining the relationship between wear depth and number of wear. Then establish the critical failure condition of the unfolding wheel according to the unfolding wheel structure and the unfolding principle. And based on the above theory, establish the wear life prediction model of the unfolding wheel. Finally, the effectiveness of the life prediction model is verified by an example. It is also found that the wear life of the microstructure surface unfolding wheel is about 10% higher than that of the smooth surface unfolding wheel. It provides a theoretical basis for the practical application of the surface microstructure of the unfolding wheel for steel ball inspection. Keywords: Steel ball unfolding wheel  Wear type  Wear model  Microstructure  Finite element  Numerical simulation  Life prediction

1 Introduction The unfolding wheel is the core component of the wheel type unfolding mechanism using for steel ball inspection. As shown in Fig. 1, the steel ball rotates under the movement of the driving wheel and is supported by the supporting wheel. A certain

This project is supported by Heilongjiang Provincial Natural Science Foundation of China (Grant No. E2017052). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 518–530, 2020. https://doi.org/10.1007/978-981-32-9941-2_43

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angle of deflection occurs under the friction of the unfolding wheel’s asymmetrical conical surface, thereby realizing the spiral unfolding of the steel ball [1].

Unfolding wheel Steel ball Support wheel

Drive wheel

Fig. 1. Contact state diagram of various parts of steel ball unfolding mechanism

However, the problem is that the slipping in the process of unfolding the steel ball is objective, it reduce the efficiency of steel ball detection. Moreover, the unfolding wheel is easy to fail due to wear. The unfolding wheel need to be replaced every 50000 times steel ball test [2], it increase the cost of steel ball detection. So it’s necessarily to conduct the analysis of the wear characteristics and life prediction for the unfolding wheel. In recent years, the microstructure surface technology combined with bionics provides a new research idea for improving the wear life of materials. German scholar Feldman [3] applies the microstructure surface to the cylinder surface and tested it on the AVL F528 engine, the results show that the wear of the cylinder and piston ring is reduced by 50%. Otero Nerea [4] applies the microstructure surface to tool surfaces, the surface-textured micro-processed sample was 10 times longer than the untreated sample in the life test. Since the 1970s, with the introduction of finite element theory and the rapid development of computer science, numerical simulation technology has played an increasingly important role in the study of friction and wear. Sun [5] used ANSYS software to model and simulate the non-smooth surface brake disc system, and obtained the wear amount and friction coefficient through friction and wear test. Contrast test and numerical simulation results, it verified the credibility of numerical simulation results. Bortoleto [6] used ABAQUS software to numerically simulate the friction and wear test of the pin-plate under unlubricated conditions, Obtained stress field distribution and surface topography change of wear trajectory. Compared with the wear test, the results were verify the consistency of the numerical simulation results under slight wear. Therefore, the author uses the wear numerical simulation method to study unfolding wheel microstructure drive surface increase friction and reduce wear characteristics, and microstructure surface unfolding wheel conduct the wear life prediction.

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2 Analysis of Unfolding Wheel Drive Surface Wear Type and Establishment of Discrete Archard Adhesive Wear Model 2.1

Analysis of Unfolding Wheel Drive Surface Wear Type

According to the mechanism and characteristics of friction surface damage, wear can be divided into abrasive wear, adhesive wear, fatigue wear and corrosion wear. In general, Wear failure of mechanical equipment components is the result of a combination of multiple wear type, but not all wear type dominate the wear process. For specific research objects, the type of wear that has less impact on the entire wear process can be ignored in order to study the wear mechanism more deeply and establish the wear model as well as predict the wear life. As shown in Table 1, the friction surface wear profile characteristics of different wear types are different. Observing the deployed wheel with an ultra depth microscope, the wear profile of the unfolding wheel drive surface after magnifying 200 times is shown in Fig. 2. Table 1. Friction surface wear profile characteristics of different wear types Wear type Abrasive wear Adhesive wear Fatigue wear Corrosion wear

Wear profile characteristics Scratches, grooves Pits, scratches, grooves Crack, peeling, Pits Reactant

a) Pits, scratches, grooves

b) Pits, scratches

Fig. 2. Wear profile of the unfolding wheel drive surface after magnifying 200 times

From the analysis of the unfolding wheel drive surface wear profile, the unfolding wheel drive surface has clear pits distribution and the scratches are also very obvious, there are many small pitting points. It can be roughly judged that the main type of wear is adhesive wear.

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From the analysis of the unfolding wheel drive surface wear mechanism, there is no chemical or electrochemical reaction occur during the process of unfolding the steel ball, and there are also no obvious alternating load, so corrosion wear and fatigue wear can be clearly excluded. For abrasive wear, the surface of the unfolding wheel and the steel ball has small roughness, and it is not easy to produce two-body wear. There is no abrasive grains between the unfolding wheel and the steel ball at the initial stage of wear, so there is no produce three-body wear. Although the drive surface material may fall off and formed the abrasive grains as the wear progresses, however, three-body wear is not the primary type of wear during the initial wear of the wheel drive surface. Adhesive wear is caused by friction surfaces in contact with each other due to shearing and metal adhesion. The reason why the steel ball can be spiral unfolded is the steel ball generating a certain angle of deflection while rotates, and the deflection of the steel ball is caused by the asymmetric conical surface on both sides drive the steel ball by friction. Therefore, the wear of the unfolding wheel drive surface is in line with the wear mechanism of the adhesive wear. In summary, from the two aspects of the unfolding wheel drive surface profile characteristics and the wear mechanism, the main wear type of the unfolding wheel drive surface is adhesive wear. 2.2

Discrete Archard Adhesive Wear Model Based on Finite Element

The general formula for the classic Archard adhesive wear model is expressed as [7]: WV ¼ Km

PL H

ð1Þ

Among them, WV is the wear volume, P is the normal load, L is the slip distance, H is the Brinell hardness, and Km is the wear coefficient. The differential of Eq. (1) can be expressed as: dWV ¼ Km

dP  dL H

ð2Þ

The differential of the wear volume WV, the normal load P, and the slip distance L can be expressed as: 8 < dWV ¼ dh  dA dP ¼ r  dA : dL ¼ v  dt

ð3Þ

Among them, h is the wear depth, A is the wear area, r is the contact stress of the friction pair contact point, v is the relative sliding speed between the two objects, and t is the wear time.

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The expression for the wear depth per unit time obtained by Eqs. (2) and (3) is: dh ¼ Km

vr dt H

ð4Þ

Select a contact node j on the unfolding wheel surface, assuming that the wear depth of the node in a very short period of time Dti is Dhi,j, where i represents the number of wear and j represents the node number, then: Dhi;j ¼ Km

vr Dti H

ð5Þ

For this junction, the wear depth of n wears is: hn;j ¼

n X i¼1

Dhi;j ¼

n X i¼1

km

vr Dti H

ð6Þ

Equation (6) is the wear depth of the j node after n wears in the whole time history. It is a discretized Archard adhesion wear model based on finite element numerical simulation. It is also the basis for the subsequent wear life prediction model.

3 Wear Numerical Simulation of the Micro-structure Unfolding Wheel First select the unfolding wheel drive surface microstructure type is pit type, the shape is diamond shape [8], the depth is 0.05 mm. The geometric parameters are shown in Fig. 3. Then simplify the steel ball wheel type unfolding mechanism and build the numerical simulation model of the steel ball-unfolding wheel.

Fig. 3. Unfolding wheel diamond surface microstructure geometric parameter map

The most effective way to reduce the numerical simulation calculation time and improve the numerical simulation accuracy is to reduce the number of meshes and improve the mesh quality. Before the meshing, the suppression function of the ANSYS

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Workbench drawing tool Design Modeler was used to suppress a part of the model, this part did not participate in the numerical simulation calculation. The model after suppression and meshing is shown in Fig. 4.

Fig. 4. Steel ball-unfolding wheel finite element mesh model

The boundary conditions are set using the relevant experimental data of the research group [2, 9]. The wear finite element numerical simulation belongs to the contact nonlinear analysis, and the calculation process is complicated and the result is not easy to converge. Therefore, it is unrealistic to simulate the entire life cycle of the unfolding wheel from the beginning of work to the wear failure by numerical simulation. Therefore, a short period of time is taken to repeatedly wear the same position of the unfolding wheel drive surface. The micro-segment time of the interception process is 0.02 s, and the wear process of the whole micro-segment is divided into four load steps. In order to ensure the final convergence of the iterative calculation, the corresponding number of substeps can be set in each load step. In theory, the more substeps, the more iterative operations, the easier the operation to converge; However, the more substeps, the larger the amount of computation, and the longer the numerical simulation consumes. After repeated attempts, set the maximum number of substeps of the four load steps to 100. The minimum number of substeps is set to 10, The initial substeps are set to 10. Turn on the Auto time stepping option. The unfolding wheel drive surface experienced one wear during the 0.02 s period, and repeated 9-time wear numerical simulation at the same position of the unfolding wheel drive surface. Use ANSYS APDL to read the cumulative wear depth after each wear, the wear depth of the smooth surface unfolding wheel drive surface is shown in Fig. 5. The wear depth of the microstructure surface unfolding wheel drive surface is shown in Fig. 6, and the wear depth unit is mm.

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Fig. 5. Smooth surface unfolding wheel drive surface wear depth map

The maximum wear depth accumulated after 1 to 9 times wear numerical simulations was read from Figs. 5 and 6. The relationship between wear depth and the number of wear of the unfolding wheel is shown in Table 2. Fit the data in the Table 2 with software MATLAB, Obtained the relationship equation of smooth surface unfolding wheel wear depth h1 and number of wear n1 is: h1 ¼ 2:8212  107 n1  0:21345  107

ð7Þ

The relationship equation of microstructure surface unfolding wheel wear depth h2 and number of wear n2 is: h2 ¼ 2:5492  107 n2  0:22618  107

ð8Þ

It can be seen from the Eqs. (7) and (8) that the relationship between the wear depth and number of wear is approximately linear. The relationship equation of the unfolding wheel wear depth and number of wear obtained by the wear numerical simulation and provides a mathematical model basis for the establishment of the subsequent unfolding wheel wear life model.

Wear Numerical Simulation and Life Prediction

Fig. 6. Microstructure surface unfolding wheel drive surface wear depth map Table 2. Cumulative wear depth and number of wear of the unfolding wheel mm Number of Smooth surface wear n unfolding wheel Wear depth 1 2:93  107 2 5:56  107 3 8:23  107 4 1:08  106 5 1:38  106 6 1:59  106 7 1:86  106 8 2:31  106 9 2:59  106

Microstructure surface unfolding wheel Wear depth 2:72  107 5:21  107 7:09  107 9:33  107 1:21  106 1:48  106 1:72  106 2:07  106 2:32  106

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4 Establishment of Critical Failure Condition and Wear Life Model of Unfolding Wheel 4.1

Establishment of Unfolding Wheel Critical Failure Condition

As shown in Fig. 7, The deviation of the asymmetrical conical surface on both sides of the wheel is e, usually e take 1°. If unfolding wheel asymmetrical cone surface create wear, it will cause the deviation e decrease. When the e decrease to 0°, unfolding wheel asymmetric conical surface will lose the ability to provide deflection friction to steel ball. The steel ball will not be able to unfold along the spiral, and the wear depth at this time is the maximum wear depth hmax. As shown in Fig. 7, using the unfolding wheel axis as the x-axis, The perpendicular goes through the ball’s center and perpendicular to the x-axis as the y-axis. O is the origin of the coordinates. Build the Cartesian coordinate system. Q1 point is the intersection of the conical axis of the unfolding wheel and the horizontal rotary shaft. A1 is the contact point between the contour of the unfolding wheel and the steel ball at a certain moment. A2 is the intersection of the vertical line of the A1 point and the contour line below the unfolding wheel. M2 is the vertex of the conical surface on the side of the unfolding wheel. Pass M2 build the vertical line of A1A2, and the foot is M1, M1M2 is parallel to the horizontal rotation axis of the unfolding wheel. O1 is steel ball center, M2A1 is tangent to the steel ball, O1A1 is perpendicular to M2A1. According to the geometric principle knowledge, ∠Q1M2M is also e. Known by the unfolding wheel structure, ∠A1M2Q1 is 45°, ∠A1M2A2 is 90°

Fig. 7. Unfolding wheel wear failure geometry diagram

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Based on the above known geometric conditions, the lengths of line A1N1 and M1M2 can be deduced as: 

lA1 N1 ¼ lM1 M2 ¼ r  sinð45 þ eÞ

ð9Þ

According to the triangular function relation, obtained: 

lM1 A2 ¼ lM1 M2 tanð45  eÞ 



¼ r  sinð45 þ eÞ  tanð45  eÞ lA1 M2 lM 1 M 2 ¼   sinð45 þ eÞ sinð45 þ eÞ sinð45  eÞ  r sinð45 þ eÞ r ¼ ¼   sinð45 þ eÞ sinð45  eÞ sinð45  eÞ

ð10Þ

lA1 A2 ¼

ð11Þ

According to the unfolding principle of the unfolding wheel, when e = 0°, the unfolding wheel can not provide asymmetric friction to make the steel ball unfold. The maximum wear depth is: hmax ¼ lA1 A2  2lM1 A2 r    2r  sinð45 þ eÞ  tanð45  eÞ ¼  sinð45  eÞ

ð12Þ

Equation (12) is the critical failure condition for the steel ball to detect the unfolding wheel wear. When the wear depth reaches or exceeds hmax, the unfolding wheel fails. 4.2

Unfolding Wheel Life Prediction Model

For a node j of the unfolding wheel drive surface, the total time that the steel ball rubs against it is Tj, then: Tj ¼

n X

Dti

ð13Þ

i¼1

According to Eqs. (6) and (13), the relationship between the maximum wear depth and wear time of a node can be obtained: hmax ¼ Km

vr Tmax H

ð14Þ

Where Tmax represents the wear time corresponding to the maximum wear depth, which is wear life.

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Convert Eq. (14) into the relationship between wear time and wear depth: Tmax ¼

H hmax vrKm

ð15Þ

In a very small period of time, the steel ball wear number to a node of the unfolding wheel drive surface is recorded as one time. For a node of the unfolding wheel drive surface, using number of wear as a measure of wear life is more convenient in practical calculations, so the relationship between the number of wear and the wear depth can be expressed as: Nmax ¼

H hmax þ B vrKm

ð16Þ

Where Nmax represents the maximum number of wear corresponding to the maximum wear depth, which is wear life; B is the linear compensation value. H Set Ks ¼ vrK , then the wear life of unfolding wheel can be expressed as: m Nmax ¼ Ks hmax þ B

ð17Þ

5 Example of Unfolding Wheel Life Prediction Take the bearing steel ball with a diameter of 16.6688 mm and the unfolding wheel matched with it as an example. The radius of the steel ball is r = 8.3344 mm, Take the unfolding angle of the unfolding cone as e = 1, take into Eq. (12), obtained the maximum wear depth of unfolding wheel failure hmax = 0.41872 mm. 5.1

Example of Smooth Surface Unfolding Wheel Life Prediction

For the smooth surface unfolding wheel, according to the Eq. (7), the relationship between the maximum wear depth and the maximum number of wear can be expressed as: hmax ¼ 2:8212  107 Nmax1  0:21345  107

ð18Þ

According to Eq. (17), the Eq. (18) is converted to the wear life prediction model as: Nmax1 ¼ 3:5446  106 hmax þ 0:07566

ð19Þ

Take hmax = 0.41872 mm into the Eq. (19), take the integer value, obtained Nmaxl = 1484195. Usually, every time a steel ball is tested, the steel ball needs to be turned 30 times on the unfolding wheel [10]. For a node of the unfolding wheel, it is

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rubbing 30 times. Therefore, the unfolding wheel wear life can be expressed by the total number of steel balls tested: 0 Nmax1 ¼

Nmax1 30

ð20Þ

0 Take the integer value, Nmax1 ¼ 49473, this means the unfolding wheel detection 54752 steel ball wills cause failure. This result is consistent with the fact that every 50,000 steel balls test will cause unfolding wheel fail due to wear and need to be replaced. It prove the effectiveness of the unfolding wheel life prediction model.

5.2

Example of Microstructure Surface Unfolding Wheel Life Prediction

For the microstructure surface unfolding wheel, according to the Eq. (8), the relationship between the maximum wear depth and the maximum number of wear can expressed as: hmax ¼ 2:5492  107 Nmax2  0:22618  107

ð21Þ

According to Eq. (17), the Eq. (21) is converted to the wear life prediction model as: Nmax2 ¼ 3:9228  106 hmax þ 0:08873

ð22Þ

Taking hmax = 0.41872 mm into the Eq. (17), we obtain Nmax2 = 1642555. Turn into the number of steel balls. 0 Nmax2 ¼

Nmax2 30

ð23Þ

Take the integer value, N′max2 = 54752, this means the unfolding wheel detect 54752 steel balls will cause failure. Comparing the wear life of the microstructure surface unfolding wheel and smooth surface unfolding wheel, the improvement rate of the wear life is calculated as: gm ¼

0 0 Nmax2  Nmax1  100% 0 Nmax1

ð24Þ

Substituting data for calculation, gm ¼ 10:67%, that means the wear life of microstructure surface unfolding wheel is about 10.68% higher than that of the smooth surface unfolding wheel.

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6 Conclusion (1) By observing the wear profile and analysis wear mechanism of the unfolding wheel drive surface, the main wear type of the unfolding wheel drive surface is adhesive wear. Based on the classical Archard adhesion wear model and finite element theory, the discretized Archard adhesion wear model is established. (2) Through the numerical simulation of wear on the smooth surface unfolding wheel and the microstructure surface unfolding wheel, the cumulative wear amount of the single node is obtained, and the relationship equation between the number of wear and the wear depth is established by data fitting. (3) According to the unfolding wheel structure and the unfolding principle, the critical failure conditions of the unfolding wheel are established, and based on the above theory, the wear life prediction model of the unfolding wheel is established. Finally, the effectiveness of the unfolding wheel wear life prediction model is verified by an example. It is found that the wear life of the microstructure surface unfolding wheel is about 10% higher than that of the smooth surface unfolding wheel.

References 1. Zhao, Y.L., Zhao, Z.Q., Bao, Y.D.: Principle and method of full surface development of steel balls. Chin. J. Mech. Eng. 52(17), 205–212 (2016) 2. Sun, M.M.: Analysis of Friction and Wear Characteristics of Steel Ball Unfolding Wheel Based on Finite Element Method, pp. 1+29–40. Harbin University of Science and Technology (2017) 3. Feldman, Y., Kligerman, Y., Etsion, I.: A hydrostatic laser surface textured gas seal. Tribol. Lett. 22(1), 21–28 (2006) 4. Otero, N., Romero, P., Gonzalez, A.: Surface texturing with laser micro-cladding to improve tribological properties. J. Laser Micro Nenoengineering 7(2), 152–154 (2012) 5. Sun, S.N., Xie, L.Y., Zhang, Y.Z.: Finite element analysis of friction and wear performance of non-smooth surface brake disc. J. Northeastern Univ. (Nat. Sci. Edn.) 35(11), 1597–1601 (2014) 6. Bortoleto, E.M., Rovani, A.C., Seriacopi, V., et al.: Experimental and numerical analysis of dry contact in the pin on disc test. Wear 301(1–2), 19–26 (2013) 7. Archard, J.F., Hirst, W.: An examination of a mild wear process. Proc. Roy. Soc.: Math. Phys. Eng. 238(1215), 515–528 (1957) 8. Zhao, Y.L., Geng, W., Bao, Y.D.: Analysis of friction and wear properties of microstructure on the unfolding wheel used for steel ball inspection. J. Tribol. 37(3), 348–356 (2017) 9. Kong, Y.L.: Study on Micro-structure Dry Friction Characteristics of Steel Ball Detecting Surface, pp. 22–57. Harbin University of Science and Technology (2016) 10. Xuan, J.P.: Research on Key Parts Structure of Steel Ball Full Surface Unfolding Device, pp. 23–34. Harbin University of Science and Technology (2014)

Design of Passive Gravity Balance Mechanism for Wearable Exoskeleton Suit Chenxi Qu1, Peng Yin2(&), Xiaohua Zhao3, and Liang Yang3 1

College of Automotive Engineering, Jilin University, Changchun 130025, China [email protected] 2 School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China [email protected] 3 Intelligent Technology R&D Center, Guangzhou Hyetone Mechanical and Electrical Equipment Co., Ltd., Guangzhou 510640, Guangdong, China {zhaoxiaohua,yangliang}@hyetone.com

Abstract. The wearable exoskeleton suit is a man-machine system which can combine the human limbs with machinery and environment. The key point of wearable exoskeleton suit is the design of passive gravity balance mechanism to achieve passive gravity balance in the system. Based on the principle of passive gravity balance technology, this paper deduces the theoretical equation of passive gravity balance. Then, the equations were applied to the passive gravity balance for single parallelogram mechanism and double parallelogram mechanism. Simultaneously, the analysis was also conducted using MATLAB optimization tool. The results show that the parallelogram passive gravity balance mechanism can achieve any position to hover within a certain range of spring tension. It can make the operating force at low level when doing the up and down movement. Consequently, with the help of this system, the vibration damage in some work conditions to human musculoskeletal can be significantly reduced, it can be introduced to many work conditions, such as pneumatic impact drilling. Keywords: Exoskeleton  Mechanical structure design  Optimization design  Passive gravity balance

1 Introduction In recent years, exoskeleton technology has become a new research hotspot in robotics, automatic control technology, artificial intelligence and other disciplines, and has been widely used in scientific research, industrial production, medical rehabilitation [1]. The wearable exoskeleton suit is an industrial exoskeleton mechanism that transmits the load of the tool held on the wearer’s hand to the ground under the premise of ensuring This project is supported by the 2017 Guangzhou Industrial Technology Major Research Projects (No 201802010067). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 531–545, 2020. https://doi.org/10.1007/978-981-32-9941-2_44

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the flexibility of the wearer, saving the wearer’s physical strength and preventing musculoskeletal diseases. The basic principle is the principle of leverage, that is, the hand tool is connected to the hip joint of the wearable exoskeleton suit through the parallelogram passive gravity balance mechanism, with the hip joint as the fulcrum, and the two mechanical legs of the wearable exoskeleton suit serve as the gravity transmission rod, passing through the lower limb The way the rear end of the exoskeleton increases the weight, so that the front end hand tool balances the moment between the hip joint and the rear end weight on the hip joint, so that the wearer can almost bear zero load. The design of passive gravity balance mechanism is an important part of exoskeleton design. The so-called passive gravity balance aimed at the system designed to be able to maintain the balance state within the range of activities without external force interference [2]. The basic principle is as follows: the center of mass of the whole system is always at a constant position at first, then, the total mechanical energy of the system is always be a constant [3, 4]. The design of the passive gravity balance mechanism can take the following two measures: one is to ensure the relative position of the center of mass of the system under the motion condition is constant, and the other is that the total value of the mechanical energy at any position of the system does not change, and the gravity balance design of the system can be completed. In the realization of the gravity balance of the system, there are generally the following practices: First, the center of mass of the system is kept at a fixed position; second, the spring is used reasonably, keeping the sum of the elastic potential energy and the gravitational potential energy of the system unchanged; the third is performing centroid positioning When using a mechanical structure of the parallelogram type. In the design process of the gravity balance system, this paper mainly adopts the second method, using the spring with the appropriate elastic coefficient, so that the mechanical energy of the whole system is always constant. The passive balancing mechanism is used to connect the wearable exoskeleton suit with the hand tool while achieving the following functions: (1) Ensuring that the hand tool can move flexibly in the horizontal space; (2) Offsetting the heavy torque of the hand tool and enable the hand tool to stay at the comfortable working surface height of the human body; (3) Can be applied to handheld tools of different weights; (4) Applying a small force to the human hand, the hand tool can be moved up and down in a vertical direction within a certain height range, and can be hovered at any height position; (5) Reducing hand-held tools with continuous impact, such as pneumatic impact drills, to damage the human muscles and bones. In order to achieve the above functions, this paper uses a spring with a proper elastic coefficient combined with a parallelogram structure to achieve the passive gravity balance of the design mechanism. One end is connected to the hip joint of the exoskeleton suit, and one end is connected with a hand tool, which is mainly used to balance the hand tool. The weight, while having a shock absorbing effect, both reduces the operator’s muscle fatigue and reduces the vibration damage to the operator’s joint muscles.

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2 Passive Gravity Equilibrium Theory System The static and dynamic stability of the equipment largely depends on whether the structure of the system can reach a balance of gravity [5]. At present, there are many studies on the passive gravity balance in the field of industrial application, and the theory is relatively mature. Its basic means focus on the mutual offset of torques at mechanical joints [6], which greatly improves the stability of equipment. The use of a parallelogram to achieve gravity balance is based on the special properties of the parallelogram [7], the prototype of which has been around since the last century, SunilK and Agrawal reported the property of this type of parallel unit mechanism in the relevant published papers. The application of this parallel unit in low speed and low precision of the simple situations, such as lamp fixtures [8]. After entering the 90s generation, the characteristics of this type of mechanism has caused a certain degree of attention, the design can guarantee the structure mechanical node torque offset between each other, making equipment to enhance the stability, and promoting the industrial applicability of this design [9]. The model and principle of passive balance technology are shown in Fig. 1.

Fig. 1. Schematic diagram of passive equilibrium

In order to ensure the structure designed to achieve static equilibrium (Friction was neglected here), We can know from the Eq. (1) that the system has zero kinetic energy at condition of rest when this system only consider the gravity factor but except the external force and the torque disturbance: s¼

  d @T @T @V þ ¼0  dt @ q_ @q @q

ð1Þ

Due to the kinetic energy is unrelated with generalized coordinates in this system, then Eq. (1) can be simplified as: @V ¼0 @q

ð2Þ

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Hence, if the mechanical energy of the system is to be kept constant, V should be kept constant. As shown in Fig. 1, two values need to be calculated to determine the final spring stiffness coefficient and ensure the passive balance of gravity of the system: the elastic potential energy of the spring, and the gravitational potential energy of the bar. According to the model of bar (Fig. 1), one end of the bar is connected with a rotating hinge, and the other end is connected with a stretching spring. The horizontal plane where the rotating hinge in had selected be the zero potential energy surface [10]. Assuming that the system is static, the mechanical energy of the system is the sum of gravitational potential energy and elastic potential energy: E ¼ EPG þ EPF

ð3Þ

EPG ¼ Mglc sin h

ð4Þ

1 EPF ¼ kðx  x0 Þ2 2

ð5Þ

And:

Among them: EPG ——System gravity potential; EPF ——Systemic potential energy; M——Mass of the rod; E——System mechanical energy; LC ——The distance from the center of mass of the rod to the hinge; x0 ——Initial length of the tension spring; k——Elastic coefficient of tension spring; x——The length of the spring when the angle between the rod and the horizontal plane is h. Substituting Eqs. (4) and (5) into Eq. (3), hence: E ¼ Mglc sin h þ

1 k ð x  x0 Þ 2 2

ð6Þ

Based on geometrical relationship: x2 ¼ d 2 þ l2  2dl sin h

ð7Þ

And: d——Distance between the mounting point on the left side of the spring and the rotating hinge; l——Length of the rod.

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Then the mechanical energy of the system can be rewritten as: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2dl sin h 2 2 2 2 2 E ¼ Mglc sin h þ k d þ l  2dl sin h þ x0  2x0 d þ l 1  2 2 2 d þl Hence, Eq. (9) is then established:   2dl sin h    d 2 þ l2   1

ð8Þ

ð9Þ

The Taylor series was used to get simplification in Eq. (8), the approximation is obtained as:   pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2dl sin h E ¼ Mglc sin h þ k d 2 þ l2  2dl sin h þ x20  2x0 d 2 þ l2 1  2 2 ð10Þ 2 d þl In order to make the system statically balanced, then: @E ¼0 @h

ð11Þ

At this time, the mechanical energy of the system is a constant, that is, does not change with the change of the rotation angle of the member, and when the Eq. (12) satisfies the Eq. (11): 2kdlx0 Mglc  kdl þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0 d 2 þ l2

ð12Þ

Then, the spring coefficient of the spring is: k¼

Mglc  2x0 ffi dl 1  pffiffiffiffiffiffiffiffiffi 2 2 d þl

ð13Þ

In this paper, the above steps have been verified the feasibility of the parallelogram passive gravity balance mechanism which used in terms of passive balance, and it always provides a theoretical calculation Equation. Using the theoretical calculation equations, structural parameters and spring elastic coefficients can be determined by calculation results to achieve the passive balance of the parallelogram mechanism [11].

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3 Characteristic Analysis of Passive Gravity Balance Mechanism of Parallelogram Mechanism Figure 2 shows a spring parallelogram mechanism. The reference plane is X0 during analysis, and the initial length of the spring is X0. The upper and lower long rod are the same rods, and the total mechanical energy of the mechanism can be represented as Eq. (14): E ¼ m1 glc sin h þ m1 gðd þ lc sin hÞ þ m2 gðdc þ l sin hÞ þ

1 k ð x  x0 Þ 2 2

1 ¼ ð2m1 lc þ m2 lÞg sin h þ m1 gd þ m2 gdc þ kðx  x0 Þ2 2

ð14Þ

Among them: m1 ——The mass of long rod; m2 ——The mass of the short rod; x0 ——The initial length of the spring; dc ——The distance from the center of the short rod to the right lower end of the hinge; lc ——The distance from the center of the long rod to the left end of the hinge; l——The length of the long rod; d——The length of the short rod; h——The angle of rotation of the parallelogram; k——The spring constant of the tension spring; x——The length of the spring when the parallelogram rotation angle is h;

Fig. 2. Schematic diagram of a single-section spring parallelogram mechanism.

From the geometrically related: x2 ¼ l2 þ r 2  2lr sin h

ð15Þ

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In the equation, r——The distance from the left side of the spring mounting point to the left end of the hinge Then the mechanical energy of the system can be rewritten as: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 k l þ r2  2lr sin h þ x20  2x0 l2 þ r 2  2lr sin h 2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2lr sin h ¼ ð2m1 lc þ m2 lÞg sin h þ m1 gd þ m2 gdc þ k l2 þ r 2  2lr sin h þ x20  2x0 l2 þ r2 1  2 2 l þ r2

E ¼ ð2m1 lc þ m2 lÞg sin h þ m1 gd þ m2 gdc þ

ð16Þ Hence, Eq. (17) is established:   2lr sin h    d 2 þ l2   1

ð17Þ

Using the Taylor series reduction (16), the approximation has been obtained: E ¼ ð2m1 lc þ m2 lÞg sin h þ m1 gd þ m2 gdc   pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2lr sin h þ k l2 þ r 2  2lr sin h þ x20  2x0 l2 þ r 2 1  2 2 l þ r2

ð18Þ

In order to make the system statically balanced, then: @E ¼0 @h

ð19Þ

At this time, the mechanical energy of the system is a constant, that is, it does not change with the change of the rotation angle of the member, when the Eq. (20) satisfies the Eq. (19): 2klrx0 ð2m1 lc þ m2 lÞg  klr þ pffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0 l2 þ r 2

ð20Þ

The elastic potential energy of the spring: ð2m1 lc þ m2 lÞg k¼  2x0 lr 1  pffiffiffiffiffiffiffiffiffi 2 2 l þr

ð21Þ

It can be seen from Eq. (21) that k is a constant independent of h, the mechanical energy in this case is also unchanged, and the mechanism can perform the balance of any angle at 180°. If the structure is modified into two parallel four sides in series, and a weight of m3 is placed at the end of one of them, and the rotational degree of rotation in the vertical direction is increased, the structure can still achieve the balance at any angle, as shown in the Fig. 3.

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Fig. 3. Schematic diagram of two-section parallelogram passive gravity balance system.

Taking the X0 axis as the reference plane and performing static analysis on the mechanism of Fig. 3, the mechanical energy of the system is:   pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2lr sin h1 k1 l2 þ r2  2lr sin h1 þ x20  2x0 l2 þ r 2 1  2 2 l þ r2   pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2lr sin h2 þ ð2m1 lc þ m2 lÞg sin h2 þ m1 gd þ m2 gdc þ k2 l2 þ r 2  2lr sin h2 þ x20  2x0 l2 þ r2 1  2 2 2 l þr

E ¼ð2m1 lc þ m2 lÞg sin h1 þ m1 gd þ m2 gdc þ

þ ð2m1 þ m2 Þgl sin h1 þ ðl sin h1 þ l sin h2 þ d  H Þm3 g

ð22Þ Among them, m1 ——The mass of the long rod; m2 ——The mass of the short rod; m3 ——The mass of the weight suspended at the end of the parallelogram; k1 ——The elastic coefficient of the tension spring of the first parallel parallelogram mechanism; k2 ——The elastic coefficient of the tension spring of the second parallel parallelogram mechanism; h1 ——The angle of rotation of the first parallelogram mechanism; h2 ——The angle of rotation of the second parallelogram mechanism; dc ——The distance from the center of the short rod to the right lower end of the hinge; x0 ——The initial length of the spring; lc ——The distance from the center of the long rod to the left end of the hinge; H——The distance from the center of mass of the weight to the suspension point; x——The length of the spring when the parallelogram rotation angle is h; l——Length of the long rod; r——The distance from the left side of the spring mounting point to the left end of the hinge; d——The length of the short rod. Since the mechanism can maintain equilibrium at any position, it is known from the conservation of energy that the mechanical energy of the mechanism is constant, that is:

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@E ¼0 @h

ð23Þ

When the Eq. (22) satisfies the Eq. (23), it means:   @E 2k1 lrx0 p ffiffiffiffiffiffiffiffiffiffiffiffi ffi ¼ ð2m1 þ 2m2 þ m3 Þgl þ 2m1 lc g  k1 lr þ cos h1 ¼ 0 @h1 l2 þ r 2 " # @E 2k2 lrx0 ¼ ð2m1 lc þ m2 l þ m3 lÞg  k2 lr þ pffiffiffiffiffiffiffiffiffiffiffiffiffi cos h2 ¼ 0 @h2 l2 þ r 2

ð24Þ

ð25Þ

Constantly established, then: 2k1 lrx0 ð2m1 þ 2m2 þ m3 Þgl þ 2m1 lc g  k1 lr þ pffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0 l2 þ r 2

ð26Þ

2k2 lrx0 ð2m1 lc þ m2 l þ m3 lÞg  k2 lr þ pffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0 l2 þ r 2

ð27Þ

Then the spring coefficient of the spring is: k1 ¼

ð2m1 þ 2m2 þ m3 Þgl þ 2m1 lc g  2x0 lr 1  pffiffiffiffiffiffiffiffiffi 2 2 l þr

ð28Þ

ð2m1 lc þ m2 l þ m3 lÞg  2x0 lr 1  pffiffiffiffiffiffiffiffiffi 2 2 l þr

ð29Þ

k2 ¼

In the manufacturing process of the spring, the spring’s elastic coefficient has a property of uncertainty. Therefore, when designing the parallelogram passive balancing mechanism, the left side mounting position of the spring can be made adjustable, and its specific structure is shown in Fig. 4.

Fig. 4. Spring mounting position adjustment mechanism and spring installation position physical photo.

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4 Optimization Design of Parallelogram Passive Gravity Balance Mechanism When the suspension tool of the parallelogram passive gravity balance mechanism moves up and down in the vertical direction under the action of external force, the movement of the system is relatively slow, the change of the kinetic energy of the system is neglected, the elastic potential energy and the gravity potential energy of the system are transformed into each other. When the rate of change and the gravitational potential energy are infinitely close to the rate of change of the angle, the work done by the external force will reach a minimum, that is, the operating force of the human hand reaches a minimum value [12]. 4.1

Optimization Design Model

Taking the single-parallel quadrilateral passive gravity balance mechanism as the optimization object, the mass of the end suspension tool of the mechanism is equivalent to the short rod of the mechanism. According to Eq. (16), the gravitational potential energy and elastic potential energy of the system at a certain position are: EPG ¼ ð2m1 lc þ m2 lÞg sin h þ m1 gd þ m2 gdc

ð30Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  EPF ¼ k l2 þ r 2  2lr sin h þ x20  2x0 l2 þ r2  2lr sin h 2

ð31Þ

Then the change rate of the system’s gravitational potential energy and elastic potential energy with angle h is: dEPG ¼ ð2m1 lc þ m2 lÞg cos h dh

ð32Þ

dEPF kx0 lr cos h ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  klr cos h dh l2 þ r 2  2lr sin h

ð33Þ

According to the design theory of the parallelogram passive gravity balance mechanism, combined with the reasonable range of the human working space, the parallelogram mechanism is designed, as shown in Fig. 5. The determined parameter values are as follows: the length l of the long rod is 200 mm, and the length d of the short rod is 70 mm, the distance lc of the long rod centroid to the left end rotating hinge is 100 mm, the distance dc of the short rod centroid to the right lower end rotating hinge is 35 mm, and the distance r of the left mounting point of the spring from the lower left end rotating hinge is 0–70 mm.

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Fig. 5. (a) Three-dimensional model of the parallelogram mechanism; (b) Physical photo of the parallelogram mechanism.

The 6061 aluminum alloy in the T4 heat treatment status was selected as the body material for the parallelogram mechanism. According to the material density and the volume of the component design, the long rod mass m1 is calculated as 0.1 kg, the short rod mass is about 0.1 kg, and the defined tool mass is 8 kg. Equivalent to the short rod of the parallelogram mechanism, m2 is 8.1 kg. Substituting the parameter values into Eqs. 32 and 33 that: dEPG ¼ 16 cos h dh

ð34Þ

dEPF kx0 r cos h 1 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  kr cos h 2 dh 1 þ 25r  10r sin h 5

ð35Þ

Among them, h——The angle of rotation of the parallelogram mechanism, variable; x0 ——The original length of the spring, design variable; k——Spring modulus of spring, design variable; r——The distance between the left side of the spring mounting point and the left end of the rotating hinge, design variable. According to the characteristics of the spring and the size of the parallelogram mechanism and the range of the movable space, the following constraints have been designed: G1 ¼ k  103

ð36Þ

G2 ¼ k  104

ð37Þ

G3 ¼ r [ 0

ð38Þ

G4 ¼ r\0:07

ð39Þ

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G5 ¼ x0 [ 0:05

ð40Þ

G6 ¼ x0 \0:2

ð41Þ

G7 ¼ h  45

ð42Þ

G8 ¼ h   45

ð43Þ

The difference between the rate of change of the system gravitational potential energy with the angle h and the rate of change of the elastic potential energy with the angle h is the objective function: Mingð xÞ ¼ max½absðDMi Þ

ðð44ÞÞ

Among them, DMi ——The value of the difference between the rate of change of the system’s gravitational potential energy with the angle h and the rate of change of the elastic potential energy with the angle h at different positions, i = 1, 2, 3 …n; gðxÞMMi ði ¼ 1; 2; 3. . .nÞ is the target function. The result of the optimized design is to minimize g (x), which means that the work done by the external force will reach a minimum, that is, the operating force of the human hand reaches a minimum value [13]. 4.2

Optimization Design Calculation and Result Analysis

Run the optimization main program in MATLAB just like Fig. 6. The optimization results are as follows:

Fig. 6. MATLAB optimization main program diagram.

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Spring modulus: k = 5508.241047; The distance between the left mounting point of the spring and the left end turning hinge: r = 0.066899; Original length of the spring: x0 = 0.197499; Rotation angle of the parallelogram mechanism: h = 42.690315; Objective function optimization value: minfgðhÞg = 0.000001065387323. It can be seen from the optimization results that when the appropriate tension spring is selected, the objective function optimization value is close to 0, indicating that the parallelogram passive gravity balance mechanism can well realize the functions of hovering at any position and moving up and down.

5 Passive Gravity Balance Mechanism Design In the design of the specific scheme, the spring with the appropriate elastic coefficient is combined with the parallelogram structure, one end is connected to the hip joint of the wearable exoskeleton suit [14], and one end is connected with the hand tool, which is mainly used for balancing the weight of the hand tool and has the shock absorption effect [15]. It not only reduces the operator’s muscle fatigue, but also reduces the vibration damage to the operator’s joint muscles. The assembling drawing is shown in Fig. 7. The physical photo of the parallelogram passive gravity balancing mechanism is presented in is presented in Fig. 8. It would be a beneficial tool for workers in many work conditions.

Fig. 7. Parallelogram passive gravity balancing mechanism.

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Fig. 8. Physical photo of the parallelogram passive gravity balancing mechanism.

6 Conclusions In this paper, the theoretical equations of passive gravity balance system is derived. Then, the mechanical energy of the whole system is always constant to achieve passive gravity balance by using the spring with the appropriate elastic coefficient. The passive balance mechanism is used to connect the wearable exoskeleton suit with the hand tool. Consequently some functions have been realized as following: (1) The handheld tool can move flexibly in a horizontal space; (2) The heavy torque in the hand tool has been counteracted, so that the hand tool can stay at the comfortable height of the human body from the working surface; (3) The handheld tools can be applied to of different weights; (4) Applying a small force from the human hand, the hand tool can be moved up and down in a vertical direction within a certain height range, and can be hovered at any height position; (5) The vibration damage in some work conditions to human musculoskeletal can be significantly reduced, it can be introduced to many work conditions, such as pneumatic impact drilling.

References 1. Rosen, J., Brand, M., Fuchs, M.B., et al.: A myosignal-based powered exoskeleton system. IEEE Trans. Syst. Man Cybern.-Part A Syst. Humans 31(3), 210–222 (2001) 2. Gang, H., Ditzinger, T., Ning, C.Z., et al.: Stochastic resonance without external periodic force. Phys. Rev. Lett. 71(6), 807 (1993) 3. Nathan, R.H.: A constant force generation mechanism. J. Mech. Transmissions Autom. Des. 107(4), 508–512 (1985)

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4. Sunil, K.A., Abbas, F.: Gravity-balancing of spatial robotic manipulators. Mech. Mach. Theor. 39, 1331–1344 (2004) 5. Mahrt, L.: Momentum balance of gravity flows. J. Atmos. Sci. 39(12), 2701–2711 (1982) 6. Wang, G.S.: Analysing the onset of multiple site damage at mechanical joints. Int. J. Fract. 105(3), 209–241 (2000) 7. Banala, S.K., Agrawal, S.K., Fattah, A., et al.: Gravity-balancing leg orthosis and its performance evaluation. IEEE Trans. Robot. 22(6), 1228–1239 (2006) 8. Latassa, F.M., Ray, J.G.: Compact fluorescent lamp assembly: U.S. Patent 4,347,460, 31 August 1982 9. Sunil, K.A., Abbas, F.: Theory and design of an orthotic device for full or partial gravitybalancing of a human leg during motion. IEEE Trans. Neural Syst. Rehabil. Eng. 12(2), 157–165 (2004) 10. Bernardi, F., Olivucci, M., Robb, M.A.: Potential energy surface crossings in organic photochemistry. Chem. Soc. Rev. 25(5), 321–328 (1996) 11. Morita, T., Kuribara, F., Shiozawa, Y., et al.: A novel mechanism design for gravity compensation in three dimensional space. In: Proceedings 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2003), vol. 1, pp. 163–168. IEEE (2003) 12. Kruskal, J.B.: Nonmetric multidimensional scaling: a numerical method. Psychometrika 29 (2), 115–129 (1964) 13. Esch, F., Baird, A., Ling, N., et al.: Primary structure of bovine pituitary basic fibroblast growth factor (FGF) and comparison with the amino-terminal sequence of bovine brain acidic FGF. Proc. National Acad. Sci. U.S.A. 82(19), 6507 (1985) 14. Low, K.H.: Robot-assisted gait rehabilitation: from exoskeletons to gait systems. In: 2011 Defense Science Research Conference and Expo (DSR), pp. 1–10. IEEE (2011) 15. Chiu, H.T., Shiang, T.Y.: Effects of insoles and additional shock absorption foam on the cushioning properties of sport shoes. J. Appl. Biomech. 23(2), 119–127 (2007)

Design and Analysis of Underwater Drag Reduction Property of Biomimetic Surface with Micro-nano Composite Structure Xuezhuang Ren1, Lijun Yang1, Chen Li1(&), Guanghua Cheng2,3, and Nan Liu1

2

1 School of Mechanical and Electrical Engineering, Shaanxi University of Science and Technology, Xi’an 710021, China [email protected], {yanglijun,lichen}@sust.edu.cn, [email protected], [email protected] Xi’an Institute of Optics and Precision Mechanics of the Chinese Academy of Sciences, Xi’an 710021, China [email protected] 3 School of Electronics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China

Abstract. Underwater drag reduction has an important impact on the speed and energy consumption of underwater vehicles. This is directly related to whether it can improve the operating efficiency of the underwater vehicle and whether it plays a role in energy-conservation and emission-reduction. A new type of bionic surface with micro-nano composite structure, which is designed to achieve drag reduction of the underwater vehicle is presented. And it is applied to a fish dart. The design source of the structure comes from dolphins’ ridge skin and mosquitoes’ mouthparts. The design of the structure is based on the method of bionics. A fluid mechanics method is taken to simulate the drag reduction effect of the micro-nano composite structure. According to the results of simulation optimization, the drag reduction mechanism of the composite structure is analyzed. From the analysis, the optimal structural parameters can be obtained. The simulation results show that the underwater drag reduction rate can reach 89.49% in the optimal structural parameters. Keywords: Bionic

 Micro-nano composite structure  Drag reduction

1 Introduction The rapid development of the marine industry relies on advanced marine engineering equipment and materials. The running speed and energy consumption of ships, vessels, torpedoes, and other marine vehicles are important indicators to evaluate their This project is supported by (1) Special Research Project of Shaanxi Provincial Department of Education (18JK0101) (2) Open Foundation of Chinese key laboratory of transient optics and photonic technology (SKLST201708) (3) National Natural Science Foundation of China (61705124) (4) Doctoral Scientific Research Foundation of Shaanxi University of Science and Technology (2016BJ-78). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 546–559, 2020. https://doi.org/10.1007/978-981-32-9941-2_45

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performance, and frictional resistance has an important impact on the speed and energy consumption of the vehicle. Through research on underwater vehicles, it can be found that the ratio of the frictional resistance of the surface of the underwater vehicle to the total resistance can reach 70% [1]. If the frictional resistance is reduced by 50%, the speed can be increased by 26%. Therefore, the design and mechanism of structure about underwater drag reduction have been given attention for a long time. The structural design of the flow drag reduction and the mechanism of flow drag reduction have been studied in the past sixty years. Early in the 1960s, Kramer [2] pioneered the study of dolphins skin and made bionic dolphin skin which achieved a 60% drag reduction effect when the bionic dolphin skin was put on the surface of a model. Huang [3] of the Institute of Marine Chemical Industry imitated the size of the dermal ridge of the dolphin skin and carried on numerical simulations to prove that the dermal ridge of the dolphins act as a traveling wave when they were cruising. Germany’s Scholle [4, 5] theoretically analyzed the drag reduction of different shapes and sizes with traveling waves, and he discussed the theoretical analysis of applying ridge structures which are perpendicular to the direction of flow (transverse grooves) to lowspeed creep flow for drag reduction. Ridgway [6] tested the sensitivity of dolphins’ skin, suggesting that the dolphins’ skin is sensitive enough to fell the surface vibrations and changes of pressure, which can cause small fluctuations in muscle contraction and reduce surface pressure. Grüneberger [7] investigated the drag reduction performance of longitudinal grooves and transverse grooves with small spacing. The resistance of longitudinal grooves increased by about 20% relative to that of transverse grooves. At present, the Northwest Institute of Technology, Tsinghua University, and other university are carrying on the research work. The study shows that the corrugated surface of the accompanying wave will achieve drag reduction under a certain Reynolds number. By systematic analysis, Yang [8] obtained that the wavy surface of the traveling wave has a better drag reduction effect at a certain speed. Zhang [9] compared the drag reduction effects of transverse grooves with longitudinal grooves detailedly and obtained that the two grooves have different drag reduction effects in different parts. However, most of the previous research work focused on the periodic arrangement of single grooved drag reduction elements. Cheng [10] studied the drag reduction of single-scale groove, designed the second-order grooved surface. And the calculation results show that the drag reduction effect is good. But this is also limited to the periodic arrangement of the periodic drag reduction elements. There are few reports on the application of bionic micro-nano composite structures to underwater drag reduction. As an underwater high-speed navigation instrument, the underwater high-speed fish dart has the characteristics of simple structure which is convenient to be researched. So a bionic drag reduction micro-nano structure is prepared on the surface of the underwater high-speed fish dart.

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2 Structural Design In the process of long-term evolution and natural selection, natural organisms have formed various functional features which provide rich structural resources for human creation and design. As a swimming expert among fish, dolphins swim freely in the water at speeds of 40–48 km per hour. Most of the body of the toothed cetacean, such as the dolphin, is coated by corrugated regular gullies which are called skin ridge [11], as shown in Fig. 1. It shows a sketch map of the microscopic structure of the skin ridge. After observing the structure of the skin ridge, Babenko [12] considered that the skin ridge on the epidermis of the living dolphins is relatively small, and skin ridge is more similar to the p and U shape than the sinusoidal shape.

Fig. 1. Skin ridge of dolphin and sketch map of the skin ridge

The mouthparts of mosquitoes are stinging and sucking, and Fig. 2 shows a sketch map of the structure of the mosquitoes’ mouthparts [13]. From the figure, we can see that the mouthparts consist of six needles, which are relatively long and can penetrate into the host’s capillaries smoothly when feeding. And Fig. 2 also shows an SEM photograph of a mosquito’s mandible, and it can be seen that the side of the mandible has a distinct sawtooth structure.

Fig. 2. Sketch map of the mouthparts of mosquitoes and SEM of a mosquito’s mandible [13]

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Mosquitoes can be undetected when biting people because the mouthparts produce rolling friction during the process of penetrating into the organism to reduce the resistance [14]. In view of the dolphin skin ridge, mosquito mouth device can play a role in drag reduction, the designed composite structure of them is applied to the surface of the fish dart. Figure 3(a) gives out the actual fish dart, used to shoot fish in fishery. Figure 3(b) gives out the fish gun, used to launch the fish dart. In the study, the front end of the fish dart has a groove. In order to avoid the influence of the grooves on the underwater resistance in the study, the model shown in Fig. 3(c) is adopted.

(a)

(b)

(c)

Fig. 3. (a) The actual fish dart (b) fish gun (c) the model of fish dart

A kind of grooved composite structure is designed by referring to the micro-nano structure of dolphins skin ridge and mosquito mouth device, and its structural unit is Ushaped groove and sawtooth structure, as shown in Fig. 4(a) (b). The designed composite structure starts with a different arrangement of the grooves and a combination of different micro-nano structures. In order to utilize the best of the U-shaped structure’s characteristics, the following aspects are arranged: the periodic order is arranged longitudinally and transversely (P1 = P2 = P3 = … = Pn); the progressive order is arranged transversely (P1 < P2 < P3 < … < Pn); the quasi-periodic order [15, 16] is arranged longitudinally (Q1 * Qn are arranged according to the Fibonacci sequence, with default values, Q1 = 0.3 mm, and Q2 = 0.4854 mm). The sawtooth structure is formed by arranging the longitudinal U-shaped structures in a quasi-periodic order based on the transverse U-shaped structures arranged in a progressive order, as shown in Fig. 4(b). The U-shaped structure and the combined structure of the different arrangements described above are planned and laid out to obtain the composite structure shown in Fig. 4(c). And mark 1 in Fig. 4(c) shows a Ushaped structure arranged longitudinally (U-L) in a periodic order. Mark 2 in Fig. 4(c) is shown as a U-shaped structure arranged transversely (U-T) in a periodic order. Mark 3 in Fig. 4(c) is U-T in a progressive order, and mark 4 in Fig. 4(c) shows a sawtooth structure.

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spanwise P1

P2

direction P3

P4

P5

(a)

flow direction

P1 P2

P3 P4

P5

Q1

Q2

Q3

(b)

4

2

1

3

(c) Fig. 4. (a) U-shaped groove (b) sawtooth structure (c) composite structure

3 Simulation and Optimization 3.1

Conditions of Fluid Mechanics Calculation

The standard k-e model was selected in the Viscous mode using the hydrodynamics simulation software. The standard model is a semi-empirical Equation based on the turbulent flow energy and dissipation rate. The turbulent flow energy equation is an exact equation, and the turbulent dissipation rate equation is an empirical equation. The specific equations are as follows: The turbulent flow energy equation:   @ @ @ l @k ðqkÞ þ ðqkui Þ ¼ ðl þ i Þ @t @xi @xj rk @xj þ Gk þ Gh  qe  YM þ Sk

ð1Þ

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The turbulent dissipation rate equation:   @ @ @ l @e ðqeÞ þ ðqeui Þ ¼ ðl þ i Þ @t @xi @xj re @xj e e2 þ Gle ðGk þ G3e Gh Þ  G2e q þ Se k k

ð2Þ

In the above equations, k is the turbulent flow energy, e is the turbulent dissipation function, t is the time, q is the fluid density (the fluid in this paper is water, and the density of water is 103 kg/m3); xi and ui are the coordinate components and the timeaveraged velocity component respectively in the i-coordinate direction; li is the turbulent motion viscosity coefficient, Gk and Gh are the turbulent flow energy generated by the laminar velocity gradient and buoyancy respectively; YM is the diffusion fluctuation, Sk and Se are user-defined parameters; rk and re represent the k equation and the e equation respectively, the Prandtl constants are rk = 1.0 and re= 1.3; G1e, G2e, and G3e are constants, respectively G1e= 1.44, G2e = 1.92, G3e = 1.0. Figure 5 shows the three-dimensional simulation model by the grooved structure of the composite arrangement. The other different arrangement of the grooved structures is arranged in this computational domain. In the computational domain, flow direction x length is 160 mm, the spanwise y width is 80 mm, and the vertical z height is 80 mm.

flow direction

z x y

1:1.5

Fig. 5. Sketch map of the computational domain

For convenient for comparing, differently arranged grooved structures are placed in the same computational domain for simulation. At the same time, in order to simplify the calculation process and improve the calculation accuracy, the top, bottom, left and right boundary of the computational domain are all in the condition of slip boundary which can be considered as boundary conditions that are not constrained by other physical surfaces. The grooved structural face is set to a wall function boundary condition, that means no-slip boundary condition. For the analysis of the turbulent flow state, in addition to setting the speed of 10 mm/s at the inlet, the turbulence intensity

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I = 0.04, the turbulent energy k = 0.271856, and the turbulent dissipation rate e = 83.18247 were also specified. For the outlet, the pressure P = 0 and the nonviscous stress are chosen to eliminate the viscous stress limitation of the Dirichlet boundary condition. In order to study the fluid drag reduction characteristics of the boundary turbulent state, the fluid dynamics mode is selected, and the finite volume method is used to discretely generate the mesh. However, for the corner angle of the primitive, it is difficult to adopt a high-quality structured mesh. In order to accommodate the complex structure, an automatic generation of the mesh is employed and the denser process is performed in the grooved region. After repeated attempts, the size of the mesh is determined as follows: The outer domain of the grooved structure is sparse, and the length from the two sides to the center grid is gradually reduced by 0.87. The mesh is densely divided inside the groove (curvature resolution is 0.6, and the resolution of the narrow domain is 0.7). 3.2

Calculation Results and Analysis

3.2.1 Optimization of Composite Structure Parameters Referring to the structural dimensions of the actual dolphin skin ridge, a U-shaped structure is a better choice. In order to determine the optimal drag reduction parameters of the U-shaped structure, the width or depth is changed while ensuring the same depth or width. Ridgway [17] showed that the skin ridge peak spacing of the whales is 0.41– 2.35 mm and the peak-to-valley depth is 7–114 lm. Accordingly, the width variation range of the U-shaped structure is set to 0.25–2 mm, and the depth variation range is set to 0.01–2 mm. For the convenience of calculation, the width of the U-shaped structure in this paper is a chord of a circle, and the depth is the height of the arc corresponding to the chord. Through simulation, it is found that not all sizes of grooves can reduce drag. As shown in Fig. 6, at a width of 1.40 mm and a depth of 1.80 mm, the fish dart having the grooved surface of the size acts to increase the resistance. Under the size parameter of 0.38 mm in width and 0.10 mm in depth, the U-shaped structure has a better effect on drag reduction. The sawtooth structure is composed of a progressive U-T and a quasi-periodic U-L, and which is applied to the front end of the fish dart model, as shown in Fig. 7. Since the front end of the fish dart is tapered, in order to avoid the situation that the U-shaped grooves are deeper and deeper at the front of the model when the depth and width of the grooves are kept constant, a progressive arrangement is adopted. So at the front end of the tapered portion of the fish dart, the depth and width of the U-shaped groove are smaller, and the magnitudes of the depth and width is increased until the U-shaped groove size parameter is set as the U-groove size parameters described below and continue to align the transverse U-shaped grooves which are set as the U-groove size parameters described above (a depth is 0.1 mm and a width is 0.38 mm) in the tapered portion. Since the bursting of the water flow generated by the movement of the taper in the water is different from the flat’s, the dimensionless measurement is defined according to the idea and method of studying the plane groove by Bhushan [18].

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Fig. 6. Drag reduction rate of different scales (a) same depth (b) same width

Q1 Q2 Q3 Q4 Q5 P1

P2

progressive U-T

P3

P4 P5

Fig. 7. The sawtooth structure

quasi-periodic U-L

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Dimensionless Equation: sþ ¼

sVs v

Vs ¼ ðs0 =qÞ0:5 s0 ¼ 0:0592

qU 2 1=5 R 2 e

ð3Þ ð4Þ ð5Þ

s+ is the dimensionless grooved width, s is the true grooved width dimension, m is the kinematic viscosity, Vs is the wall shear rate, q is the fluid density, s0 is the wall shear stress, U is the inflow velocity, Re is the Reynolds number. m is set to 1.308  10−6 m2/s, q is 103 kg/m3, U is set to 10 m/s, Re is 39808. Referring to the experimental results of Walsh [19], it shows by calculation that the minimum width of the U-T arranged in tapered position in a progressive order is 0.1 mm, and the depth is 0.025 mm; the maximum width is 0.2 mm, and the depth is 0.05 mm. 3.2.2 Flow Field on the Surface of the Structure During the analysis of flow field, simulate the movement of water, the fish dart stays in a stationary state. In order to intuitively reflect the influence of different grooved arrangements to the movement of fish dart, Fig. 8 shows the distribution of velocity contour at a cross-section (z = 40) on a smooth surface, a U-L aligned on the tail, a U-T arrangement combined with a U-L arrangement (U-T&U-L), and composite structure (the structure combines U-L, U-T, and sawtooth structure). As we can see from Fig. 8, the arrangement of the groove structure has a significant influence on the water flow velocity. Whether in the grooved domain or at the outlet, there are fluids of lower flow velocity in the vicinity of the grooves arranged in different structures. By comparing Fig. 8(a) and (b–d), it is known that the large flow velocity field is concentrated on the surface of the smooth fish dart, so that the flow velocity through the surface is relatively high while the surface velocity of fish darts with grooves is lower, which can bring less resistance to the movement of fish darts. Comparing Fig. 8(b–d), it can be concluded that the U-T can enlarge the low-speed fluid domain on the surface of the fish dart; the U-L of the tail can extend the low-speed fluid domain at the outlet; the sawtooth structure of the tip of the fish dart can make the speed of the water flow of the fish darts decrease during the forward movement, and the resistance, of the water flow to it, is reduced. Because of these structures, the effect of drag reduction is achieved. Through the above analysis, it can be concluded that the composite structure has the best drag reduction effect. 3.2.3 Numerical Analysis of Drag Reduction Characteristics In order to study the drag reduction properties of differently arranged grooved structures, the frictional resistance of the structural surfaces was analyzed, and the drag reduction effect of the groove was studied to obtain the surface friction coefficient. The Equation for calculating the surface friction coefficient Cf is as follows:

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(a)

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(b)

(c)

(d)

Fig. 8. Velocity distribution of fluid in different grooves (a) smooth surface (b) U-T (c) U-T & U-L (d) composite structure

sw 2 2 qref vref

Cf ¼ 1

ð6Þ

sw is the wall shear stress, qref and vref is the defined reference density and velocity. The numerical calculation results of the surface friction coefficient are shown in Fig. 9 (a). It can be seen from Fig. 9(a) and Eq. (6) that the magnitudes of the shear stress of the differently arranged grooved structures are smaller than the smooth faces’, and the magnitudes of the grooved shear stress arranged by the composite structure are the smallest. In order to have a detailed comparison of the drag reduction effect of different structures, calculate the surface drag reduction rate. The Equation is as follows: g¼

Cf ðsmoothÞ  Cf ðgrooveÞ  100% Cf ðsmoothÞ

ð7Þ

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0.00373

surface friction coefficient

0.0035 0.0030 0.0025 0.0020 0.0015 0.0010 4.96276E-4

0.0005

3.1208E-4

2.41893E-4

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composite

0.0000 smooth

U-T

(a)

drag reduction rate

1.0

0.5

0.0 smooth

U-T

U-L & U-T

composite

(b) Fig. 9. (a) Surface friction coefficient of different grooves (b) Drag reduction rate of different grooves

η is the drag reduction rate and Cf is the friction coefficient. The results are given in Fig. 9(b). Compared with the single structural groove, the composite arrangement of the grooved structure has a better drag reduction effect, and the drag reduction rate can reach 89.49%.

4 Drag Reduction Mechanism To study the drag reduction mechanism of the grooved composite structure, we can start from the two aspects of grooved action and arrangement. Choi [20] believes that the longitudinal groove limits the spanwise motion of the flow vortex, causing the wall to burst to weaken, resulting in a reduction in wall frictional resistance. Bhushan [12] believes that the drag reduction of the rib structure can hinder the conversion of eddy currents and enhance the area of high-speed flow away from the surface.

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(a)

(b) Fig. 10. Wall shear stress (a) the composite structure (b) the smooth plane

The disturbance generated in the fluid is successive, that means, the disturbance is successively superimposed after the interaction of the fluid with grooves. Therefore, after the fluid passes through various ordered grooves, the shear stress is redistributed on the surface of the grooves due to coherent superposition. So when the actual fluid passes through the different ordered arrangement of the grooved structure, the direction and fluidity of the fluid change due to the shear stress. An important idea of this paper is to analyze the drag reduction mechanism of the composite structure by studying the wall shear stress. Figure 10(a) and (b) respectively show the wall shear stress distribution of the composite structure and the smooth surface. It can be seen from the figure that due to the existence of the composite structure, the wall shear stress exhibits a relatively large change. In the middle of the fish dart model, the wall shear stress of the composite structure is smaller than the smooth wall surface, and sometimes even larger than the smooth wall surface, that means, a viscous thrust is generated. The shear stress in the transverse U-shaped structure can reduce the turbulent burst and also make the free flow not directly in contact with the model wall, which is similar to “hydraulic bearings”, thereby reducing drag. By comparing the Fig. 10(a) and (b), the shear stress of the smooth plane at the front end of the fish dart is in the range of 5.466  102 − 1.083  103 Pa, which is about 1.5 times of the composite structure. Especially in the tip, middle and the tail of the fish dart, after the wall shear stress is

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modulated by the sawtooth structure and the U-L, the wall shear stress is no longer parallel to the fluid, and its direction is inclined to the flow direction at a certain angle, so the shear stress of the component acting on the model is greatly reduced, and the low-velocity fluid remains in the grooves. The modulation effect of the composite structure on the wall shear stress is 43% relative to the smooth plane, thereby the composite structure can achieve a better result of the drag reduction.

5 Conclusion (1) A bionic micro-nano composite structure was designed to achieve underwater drag reduction with the structure of the dolphin skin ridge and the mosquito mouth device being the reference. The fluid mechanic’s simulation method was used to simulate and optimize the size parameters of the composite structure to obtain the optimal structural parameters. (2) Applying the composite structure to the fish dart, when it moves in the water, the grooved structure can expand the area of the low-speed watershed, so that the high-speed watershed is far away from the surface, reducing the resistance of the water flow. The wall shear stress on the composite structure of the fish dart is greatly reduced by the action of the groove, and the direction of some wall shear stress is no longer parallel to the surface, so that the surface friction coefficient is reduced, thereby achieving the purpose of drag reduction. (3) It is found that, by means of simulation, the micro-nano composite structure which is suitable for the surface of the fish dart achieve the effect of a drag reduction rate is 89.49% when moving in water. It is proved that the micro-nano composite structure can greatly improve the operating efficiency of the underwater vehicle and reduce the underwater navigation resistance.

References 1. Li, H.: Numerical simulation and mechanism analysis of drag reduction technology for underwater vehicles. Harbin Institute of Technology (2006) 2. Kramer, M.R., Cooper, H.L., Drews-Botsch, C.D., et al.: Metropolitan isolation segregation and Black-White disparities in very preterm birth: a test of mediating pathways and variance explained. Soc. Sci. Med. 71(12), 2108–2116 (2010) 3. Huang, W., Wang, B., et al.: Simulation numerical calculation of geometry of bionic baffle reducing material with accompanying wave. J. Ship Mech. 9(1), 14–17 (2005) 4. Scholle, M., Rund, A., Aksel, N.: Drag reduction and improvement of material transport in creeping films. Arch. Appl. Mech. 75, 93–112 (2006) 5. Scholle, M.: Hydrodynamical modeling of lubricant friction between rough surfaces. Tribol. Int. 40, 1004–1011 (2007) 6. Ridgway, S., Samuelson, D., Van, A.K., et al.: On doing two things at once: dolphin brain and nose coordinate sonar clicks, buzzes, and emotional squeals with social sounds during fish capture. J. Exp. Biol. 218(Pt 24), 3987 (2015) 7. Grüneberger, R., Hage, W.: Drag characteristics of longitudinal and transverse riblets at low dimensionless spacings. Exp. Fluids 50(2), 363–373 (2011)

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8. Yang, Y.: Design and mechanism analysis of underwater drag reduction components of river raft appearance. Jiangsu University of Science and Technology (2017) 9. Zhang, F.: Study on drag reduction performance of non-smooth surface of bionic robot fish. Shandong University (2017) 10. Cheng, P., Jiang, C., Wu, C.: Numerical simulation of drag reduction characteristics of bionic secondary micro-grooves. Chin. J. Sci. Tech. Pap. 9(8), 940–943 (2014) 11. Yu, J., Liu, Z., Wu, W.: Progress in anti-noise and noise reduction of dolphin skin. In: The 30th Anniversary of the Establishment of the Underwater Noise Group of the Chinese Shipbuilding Engineering Society Academic Seminar (2015) 12. Babenko, V.V.: Boundary layer flow over elastic surfaces. Boundary Layer Flow over Elastic Surfaces (2012) 13. Gu, S.: Research on bionic syringe based on insect sucking mouth device. Jilin University (2008) 14. Qi, X.: Research on biomimetic low-resistance and antibacterial medical injection needle based on insect mouthpart. Jilin University (2014) 15. Wang, X., Qi, X., Qu, D.: Study on fluid drag reduction characteristics of one-dimensional periodic and quasi-periodic groove structures. Acta Phys. Sin. 62(5), 00075–82 (2013) 16. Zhang, M., Yan, X., Zhang, Y., et al.: Drag reduction effect and simulation analysis of onedimensional short-groove composite quasi-crystal structure. Acta Phys. Sin. 61(19), 000287–293 (2012) 17. Shoemaker, P.A., Ridgway, S.H.: Cutaneous Ridges in Odontocetes. Mar. Mammal Sci. 7 (1), 66–74 (1991) 18. Bhushan, B.: Biomimetics (2012) 19. Wood, C.M., Walsh, P.J., Kajimura, M., et al.: The influence of feeding and fasting on plasma metabolites in the dogfish shark (Squalus acanthias). Comp. Biochem. Physiol. Part A Mol. Integr. Physiol. 155(4), 435–444 (2010) 20. Kim, W., Choi, H.: Effect of the spanwise computational domain size on the flow over a twodimensional bluff body with spanwise periodic perturbations at low Reynolds number. Comput. Fluids 183, 102–106 (2019)

A Method of Parametric Stability Region Determination for Non-linear Gear Transmission System Dongping Sheng1(&), Xiaozhen Li1, and Rupeng Zhu2 1

Changzhou Institute of Technology, Changzhou 213032, China [email protected] 2 College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Abstract. A general method of parametric stability region calculation for a non-linear transvers-torsional coupled gear train’s vibration model with multiple-clearances is studied. There are six steps in the method, and the first step is strength and fatigue life threshold determination, and the second step was deciding numerical integration time according to the motion state of the system when the parameters discussed changed in their test range, the third step is calculating the maximum displacement of the system when the parameters discussed changed in their range by using nested loop algorithm, the forth step is calculating the value which equals the maximum displacement subtracted by minimum displacement by the same method with third step, the fifth step is the stability judgment by comparing the value which is calculated in step four and five with threshold which is set in second step, and the last step is make the parametric stability region map of the system. As an example, the stability region calculation of a coupling transverse-torsional gear train vibration model with multiple-clearances is studied under the parameter of the backlash, mesh damp ratio, input rotation speed and the bearing clearance of the driving wheel and driven wheel, and the stable region of input rotation speed, backlash, meshing damp ratio and the bearing clearances are calculated respectively. Keywords: Transverse-torsional coupling  Non-linear vibration Multiple-clearances  Parametric stable region



Gear transmission system has the characteristics of high power and speed, harsh work conditions, small shape and low weight as well as high design objective. Gear system has been more and more extensive use in the field of aviation, watercraft, automobile and heavy machine, and many scholars has been attracted into the research area of gear dynamics and stability demotic and overseas [1, 2]. Not only resonance would happen when excitation frequency close to natural frequency, but also close to multi-fold frequency in nonlinear system, which could cause instability. So finding out the stable and unstable region could guide the design and generate practical significance. System parametric stable region includes the motion stability, vibration strength stability and fatigue life stability, motion stability means the motion condition does not This project is supported by Changzhou Institute of Technology. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 560–569, 2020. https://doi.org/10.1007/978-981-32-9941-2_46

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change under small disturbance; strength stability means system vibration amplitude does not mutation under small disturbance and not cause gear crack under instantaneous peak stress; Fatigue life stability means gear would be disabled because of periodic or random stress Dr, the life of the system could be predicted by S-N curve. When under the periodic one motion, the amplitude of the system will change periodically under the periodic change of the meshing stiffness. Normally, the amplitude of the system will not surpass the stress limit except the severe overload condition. When system under the multi-periodic or chaos motion, Unilateral or bilateral impact would happen corresponding. The amplitude of vibration would not surpass stress limit, but the stress change range could cause failure with the time. In other words, those parametric region which bring failures called fatigue life instability. Lin [7] studied the parametric instability region caused by time-varying meshing stiffness, but ignored the influence generated by backlash. Li [8] studied the stability region of planetary gear transmission system, and the parameters including input speed, backlash and damping ratio are considered. From the available literature on gear system stability, the main research work focuses on the stability of the periodic motion state of a single pair of gears [4, 6], but it is rare to calculate the stability domain of multiple clearance and bending-torsion coupled nonlinear vibration system based on the concept of the stability of static vibration strength and fatigue strength. In this paper, the stability domain based on vibration strength and fatigue life of multiple clearances of nonlinear vibration system has been researched, and the parameters including input speed, backlash and mesh damping has been considered. The stable domain has been analyzed under the above parameters in different combinations.

1 Modeling The multiple clearances and bending-torsional nonlinear gear transmission system is consist of a pair of gear, shaft and bearing, the gear is assumed to be spur gear and without considering friction. This mathematical model is shown in Fig. 1. In Fig. 1, the angle displacement of active and passive gear are denoted by hd and hp , base radius are symbolized by rd and rp , ed and ep are the eccentric errors, ud and up are phase errors. The active gear’s supporting stiffness, backlash and damping are described by kd , bd and cd , the passive gear’s stiffness, backlash and damping are denoted by kp , bp and cp . The comprehensive meshing error, time-varying meshing stiffness, backlash and meshing damping are denoted by eðtÞ, kðtÞ, b and cm , ed and ep are active and passive gear’s eccentric error, ud and up are the active and passive gear’s initial phase. According to the characteristics of meshing stiffness of the spur gear, it could be assumed to be square wave. Periodical curve could be expressed by Fourier series, the first item is adopt and the time-varying meshing stiffness could be expressed as follows kðtÞ ¼ km þ ka sinðxt þ uÞ

ð1Þ

Where, km is the average value of meshing stiffness, ka is alternating stiffness, u is initial phase, and x is meshing frequency.

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Fig. 1. Multiple-clearance transverse-torsional coupled model

The system has four degrees, and it’s coordinate could be expressed by ðhd ; Xd ; hp ; Xp ÞT , where hd and Xd are the active gear’s rotating and longitudinal freedom, hp and Xp are the passive gear’s rotating and longitudinal freedom. 1.1

Dynamic Meshing Force

For single pair external meshed gear, the relative displacement Xr on the meshing line and comprehensive error could be expressed as 8 < Xr ¼ xd  xp  eðtÞ eðtÞ ¼ e cos xt þ ed cosðxd t þ ud Þ ð2Þ : þ ep cosðxp t þ up Þ Where, eðtÞ is the project on the meshing line of the comprehensive error, xd and xp are the displacement on the meshing line of active and passive. The nonlinear function of backlash and supporting clearances could be expressed as 8 > < Xr  b Xr [ b f ðXr ; bÞ ¼ 0 jXr j  b > : Xr þ b Xr \  b 8 > < Xd  bd Xd [ bd fd ðXd ; bd Þ ¼ 0 jXd j  bd ð3Þ > : Xd þ bd Xd \  bd 8 X p [ bp Xp  bp > > <   Xp   bp fp ðXp ; bp Þ ¼ 0 > > : X p þ bp Xp \  bp

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The dynamic force is consist of elastic restoring force and damping force, and could be expressed as F ¼ kðtÞf ðXr ; bÞ þ cX_ r

ð4Þ

Damping coefficient is expressed as cm ¼ 2f

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi km =ð1=md þ 1=mp Þ

ð5Þ

Where, f is the damping ratio, md is the mass of active gear, mp is the mass of passive gear. 1.2

Controlling Equation

Under the effect of torque Td and load Tp , the differential equation for the system shown in Fig. 1 could be expressed as 8 €d þ cd X_ d þ kd fd ðXd ; bd Þ md X > > > > ¼  cm X_  km f ðX; bÞ > > > > € m X þ cp X_ d þ kp fp ðXp ; bp Þ > > < p p ¼ cm X_ þ km f ðXr ; bÞ € > Id hd þ rd cm ðrd h_ d  rp h_ p þ X_ d  X_ p  eðtÞÞ > > > > þ ðkm  kc cosðxtÞÞf ðXr ; bÞ ¼ Td > > > > Ip €hp þ rp cm ðrp h_ p  rd h_ d  X_ d þ X_ p þ eðtÞÞ > : ðkm  kc cosðxtÞÞf ðXr ; bÞ ¼ Tp

ð6Þ

In order to eliminate the rigid displacement and simplify the equation, under the condition of without affecting the solution of equation, the relative coordinates is introduced as follows X ¼ xd  xp þ Xd  Xp  eðtÞ

ð7Þ

Where X is the superposition of the relative displacement on the meshing line, which has the same dynamic characteristics with xd and xp . The dimensionless time is introduced, which could be expressed as s ¼ xn t, where pffiffiffiffiffiffiffiffiffiffiffiffiffi xn ¼ km =me , km is the average value of meshing stiffness, me ¼ md mp =ðmd þ mp Þ, the nominal displacement scale bc is introduced as well. Based on the above parameters, the dimensionless displacement, velocity and acceleration could be expressed as € x2 , b ¼ bb , X ¼ x=x , X ¼ x =x , X ¼ x =x  c , X_ ¼ Xb _ c xn , X € ¼ Xb X ¼ Xb c n c n d d n p p n respectively. Put all the above parameters into Eq. (6), and simplify it into matric form, the dimensionless equation could be expressed as

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1 2 30 1 € _ n11 n12 n13 X X 7B _ C 6 7B € C 6 4 0 1 0 5@ X d A þ 4 n21 n22 0 5@ X d A € _ p 0 0 1 n31 0 n33 X X p 2 30 1 0 1  bÞ 1 k11 k12 k13 f ðX; F 6 7B   C B C þ 4 k21 k22 0 5@ fd ðXd ; bd Þ A ¼ @ 0 A p ; bp Þ k31 0 k33 f p ðX 0 2

1

0

0

30

ð8Þ

  Where n11 ¼ cm =me xn þ cm =md xn þ cm mp xn , n12 ¼ cd =md xn , n13 ¼ cp mp xn ,    n21 ¼ cm =md xn , n22 ¼ cd =md xn , n31 ¼ cm mp xn , n33 ¼ cp mp xn , k12 ¼ kd md x2n ,      k13 ¼ kp mp x2n , k11 ¼ ðkm  ka cosðXtÞÞ ð1 me x2n þ 1 md x2n þ 1 mp x2n Þ, k21 ¼     ðkm  ka cosðXtÞÞ md x2n , k22 ¼ kd md x2n , k31 ¼ ðkm  ka cosðXtÞÞ mp x2n , k33 ¼ kp    1 ¼ F bc me x2n þ ex2 cosðXtÞ bc x2n þ ed x2d cosðXd tÞ bc x2n þ ep x2p cosðXp tÞ mp x2 , F . n bc x2n .

2 Calculation Method of Parametric Region Refer to connotation of the static strength and fatigue life stability region, the calculation method of stable region of multiple clearances and bending-torsional coupled gear system could obey the following steps: 1. In order to analyze the stable and unstable region quantitatively, two index have been defined. According to the bending strength and fatigue life, a vibration static unstable displacement threshold value X and fatigue life unstable threshold value DX have established. 2. Choose appropriate Poincare section R ¼ fðs; X Þ 2 R  Rn js ¼ mod ð2p=xÞ; xi ¼ maxðabsðxi0 ! xiT Þg; where xi means the maximum displacement under a certain periodic excitation force of the ith state variable, x is the meshing frequency. 3. Choose appropriate Poincare section R ¼ fðs; XÞ 2 R  Rn js ¼ mod ð2p=xÞ; Dxi ¼ absðmaxðxi0 ! xiT Þ  minðxi0 ! xiT ÞÞg; Dxi ¼ absðmaxðxi0 ! xiT Þ  minðxi0 ! xiT ÞÞ means the absolute value of the difference for the maximum and minimum value under a certain periodic excitation force of the ith state variable. 4. By the method of numerical integration and in a certain time region, system’s maximum and minimum stable displacements are obtained, and absolute value of the subtraction is gained as well [8]. 5. Use the method of loop nesting, calculate system’s maximum and minimum displacement under different parameter combination, and compare the subtraction with the unstable threshold value. Evaluate whether the system motion is in unstable condition, and put “1” into the matrix if the motion is unstable. 6. System’s stable and unstable region could be obtained by outputting the data in the matrix graphically.

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3 Stable Region Calculation Taking the multiple clearances and bending-torsional coupled gear transmission system as study object, and select a group of parameters, including m = 3 mm, a = 20°, zd = 40, zp = 80, ed = 10 lm, ep = 10 lm, bc = 10 lm, bd = 10 lm, bp = 10 lm, kd ¼ 0:2 GN=m, kp ¼ 0:35 GN=m, input power P = 200 kw. Choose input speed n, backlash b, damping ratio n, active and passive gear’s supporting clearances bd and bp as research parameters. Set the five times of backlash as the strength threshold, and ten times of backlash as the fatigue life threshold. 3.1

Single Parameter Stable Region

There are five main parameters in multiple clearances and bending-torsional coupled gear transmission system, including input speed, backlash, meshing damping, active and passive gear’s supporting clearances. In order to reduce the computing scale, only taking input speed as single parameter to study the stable region. When backlash b ¼ 4  105 m, damping ratio n = 0.05, input speed is in between 1000–10000 r/min, the curve of strength threshold X  versus input speed is obtained, as shown in Fig. 2. As shown in Fig. 2, the speed n is mostly located in between 5300– 5400 r/min and 6200–7600 r/min when maximum displacement surpass the 5b. In this region, the maximum displacement exceed the 5b, and could be regarded as the unstable region, the other speed range could be considered as stable region.

Fig. 2. System motion static strength threshold-rotation speed

Under the same backlash and damping ration, when input speed is in between 1000–10000 r/min, the curve of fatigue life threshold DX  versus input speed is obtained as well, as shown in Fig. 3, where the speed n is mostly located in between 4800–5200 r/min and 5600–9000 r/min when maximum displacement surpass the 10b, which means the speed in this range could cause system unstable. In this region, the maximum displacement exceed the 5b, and could be regarded as the unstable region, the other speed range could be considered as stable region.

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Fig. 3. System motion fatigue strength threshold-rotation speed

Think Figs. 2 and 3 together, the single parameter stable region based on the static strength and fatigue life could be obtained. When fatigue life threshold becomes bigger, the stable region will be compressed. Both considering static strength and fatigue life threshold, the unstable region is located in between 4800–5400 r/min and 5600– 9000 r/min. Additionally, the first critical speed of the system could be obtained from Figs. 2 and 3, which almost located in between the range of 6000–8000 r/min, by theoretical calculation, the critical speed of this system is 6837 r/min. 3.2

Double Parameters Stable Region

Because the system has many kinds of double parameter combinations, now take input speed and backlash for example to study the stable region. Assume the damping ratio equals 0.05, active gears supporting clearance is 2  10−5 m, and study the stable region when speed located in between 1000-10000r/min and backlash in between 1  10−5–10  10−5 m. In Figs. 4, 5 and 6, “” means stable region. Figure 4 is the stable region calculated by strength threshold value, Fig. 5 is the stable region calculated by fatigue value threshold value, and Fig. 6 is the double parameter stable region calculated by static strength threshold and fatigue life threshold value. By comparing the Figs. 4, 5 and 6, it could be conclude that the double parameter stable region is the common region of the Figs. 4 and 5, which is mostly located in the range of 5000– 9000 r/min.

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Fig. 4. Parametric stable region of rotation speed-backlash (Static strength threshold equals 5b)

Fig. 5. Parametric stable region of rotation speed-backlash (Fatigue strength threshold equals 10b)

Fig. 6. Parametric stable region of rotation speed-backlash (Static and fatigue strength threshold equal 5b and 10b)

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Triple Parameters Stable Region

Figure 7 is the triple stable region of speed versus backlash versus damping ration diagram by the method above, where the range of damping ratio is in between 0–0.4, backlash is in between 1  10−5 and 8  10−5m, the speed range is from 1000 to 8000 r/min, and “” means the stable region. As shown in Fig., it could be seen that the unstable region mostly located in the range of big backlash, low speed and low damping. Figure 8 is the triple parameter stable region of backlash versus active gear’s supporting clearances versus passive gear’s supporting clearance by the same method. From Figs. 7 and 8, the stable region and appropriate parameters group could be obtained and guide the detail design. By the same method, the four or five parameter stable region could be calculated as well.

Fig. 7. Stable region of rotation speed-backlash-damp ratio

Fig. 8. Stable region of backlash-drive bearing clearance-driven bearing clearance

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4 Conclusion 1. A kind of stable region calculation method have been proposed for the multiple clearances and bending-torsional coupled gear transmission system. By choosing appropriate static strength and fatigue life threshold, calculate the related parameter range, and the stable region could be achieved correspondingly. 2. A four degree nonlinear gear transmission system has been established, and the parameters including backlash, supporting clearance, input speed and damping ratio has been considered to calculate the stable region. By the calculate method, the single parameter, double parameter and triple parameter stable region was obtained which could guide the design of gear transmission system.

References 1. Zhu, F., Li, W., Maropoulos, P.G.: Tolerance analysis of a planetary gear reducer under cad circumstance. Chin. J. Mech. Eng. 18(3), 342–345 (2005) 2. Sun, D., Qin, D., Wang, H.: Control strategy of a parallel hybrid car with a metal beltplanetary gear continuously variable transmission system. Chin. J. Mech. Eng. 15(3), 199– 203 (2002) 3. Sun, Z., Ji, H., Shen, Y.: Nonliear dynamics of 2 K-H planetary gear train. J. Tsing-hua Univ. Sci. Technol. 43(5), 636–639 (2003) 4. Gao, Z., Shen, Y., Li, S.: Research on the periodic solution structure and its stability off nonlinear system with clearance. Chin. J. Mech. Eng. 40(5), 17–22 (2004) 5. Chen, A., Luo, S., Wang, W.: Numerical investigations on dynamic transmission error and stability of a geared rotor-bearing system. J. Mech. Eng. 40(4), 21–25 (2004) 6. Yu, Y., Yu, L., Liu, H.: Stability and bifurcation of nonlinear bearing-rotor system. J. Mech. Eng. 40(10), 62–67 (2004) 7. Lin, J., Parker, R.G.: Planetary gear parametric instability caused by mesh stiffness variation. J. Sound Vib. 1, 129–145 (2002) 8. Li, T., Zhu, R., Bao, H.: Method of stability region determination for planetary gear train’s parameters based on nonlinear vibration model. J. Aerosp. Power 27(6), 1416–1423 (2012) 9. Zhang, W.: The application of fatigue damage theory for gear fatigue calculation under nonstable and varying load. 15(supp.), 52–57 (1987) 10. Wang, S., Shen, Y., Dong, H.: Chaos and bifurcation analysis of a spur gear pair with combine friction and clearance. Chin. J. Mech. Eng. 38(9), 8–11 (2002) 11. Li, T., Zhu, R., Bao, H.: Nonlinear torsional vibration modeling and bifurcation characteristic study of a planetary gear train. Chin. J. Mech. Eng. 47(21), 76–83 (2011) 12. Sun, Z., Shen, Y., Wang, S., Li, H.: Bifurcation and chaos of star gear system. Chin. J. Mech. Eng. 37(12), 11–15 (2001) 13. Ahmadian, M., DeGuilio, A.P.: Recent advances in the use of piezoceramics for vibration suppression. Shock Vibr. Dig. 33(1), 15–22 (2001) 14. Gu, H.C., Song, G.B.: Active vibration suppression of a flexible beam with piezoceramic patches using robust model reference control. Smart Mater. Struct. 16(4), 1453–1459 (2007) 15. Lamarque, C.H., Bastien, J.: Numerical study of a forced pendulum with friction. Nonlinear Dyn. 23(4), 335–352 (2000) 16. di Bernardo, M., Kowalczyk, P., Nordmark, A.: Bifurcations of dynamical systems with sliding: derivation of normal form mapping. Phys. D 170(3–4), 175–205 (2002) 17. Louroza, M.A., Roitman, N., Magluta, C.: Vibration reduction using passive absorption system with Coulomb damping. Mech. Syst. Sig. Process. 19(3), 537–549 (2005)

Performance and Parameter Sensitivity Analysis of Finger Seal with Radial Clearance Hua Su(&) School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China [email protected]

Abstract. Finger seal is an advanced compliant seal which can be utilized to separate high pressure (HP) and low pressure (LP) zones in high speed rotating shaft environment. The work concerns leakage simulation of a multi-layer finger seal with radial clearance and the effects of structural and operating parameters on finger seal performance. Leakage, viscosity friction and load capacity of finger seal under different conditions are calculated by computational fluid dynamics method. Using single factor method six input parameters influence rules to sealing behavior are investigated. Leakage and friction increase with increasing radial clearance or finger number. When lengthening the flow path the leakage decrease sharply but friction and load increase slightly. Leakage, friction and load all increase approximate linearly with pressure increase. Decreases of leakage are observed when raising gas temperature or rotor rotating speed. Six input parameters sensitivity analysis to finger seal performance are conducted combined with orthogonal design and fuzzy satisfactory function evaluation. It is concluded that radial clearance is the most sensitive factor of all. Pressure and radial clearance and rotating speed are the top three factors impact on friction. Flow length and pressure have significant roles on load capacity. Finger number has the least effect on all performance. The work presented makes sense to study the finger seal performance accurately and economically. It also provides useful insights to design the finger seal with better performance. Keywords: Finger seal Load-carry capacity

 Radial clearance  Leakage  Friction 

1 Introduction Finger seal is a new compliant seal presented after brush seal which is regarded as a revolutionary new technology in air-to-air sealing for secondary flow control and gas path sealing in gas turbine engines [1, 2]. A finger seal is composed of multiple staggered laminates with each having a large number of flexible fingers around the rotor surface. The interface between the free end of the finger named as finger foot pad and the rotor surface is the main sealing path. However, the flow path is not evenly around the circumferential direction due to the gaps between finger element sticks. The leakage This project is supported by National Natural Science Foundation of China (Grant No. 51575445). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 570–591, 2020. https://doi.org/10.1007/978-981-32-9941-2_47

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clearance is influenced by the finger seal installation status and operating conditions [3– 5]. Sometimes in order to reduce heat and wear of the seal, an initial clearance is set between the finger foot pad and rotor surface. In addition, the hysteresis of the finger seal [6] and heat deformation may change the clearance between finger pad and rotor. This radial clearance is variable for different working conditions which affect the leakage of the finger seal significantly. It is helpful to understand the leakage and other flow behavior such as sealing force and viscosity friction of finger seal in different radial clearance and working conditions. And this work is fundamental to design and analyze the finger seal with high performance. The radial clearance between the finger foot pad and rotor surface can be derived by theoretical analysis or experimental method. However, how to calculate the leakage with a given radial clearance exactly has not been studied in detail. In previous work the radial clearance of finger seal is often assumed as simple annular gap and the gaps between the finger sticks are neglected [7, 8]. Some researchers use the annular incompressible flow to compute the leakage of the finger seal. Many researchers use relative clearance to compare the performance of gas seal based on the annular gap assumption [5, 9]. In the annular leakage formula only the diameter of the gap is considered then others structural parameters affecting the clearance, such as the number of the fingers and the length of the axial flow path, are not included yet. And the rotating speed is not considered in the procedure of leakage estimation. Furthermore, the gas flow tribology behavior such as viscosity friction and gas film load capacity are also important for study the performance and dynamic stability of the seal-rotor system, which are seldom studied in the field of contacting finger seal applications. All these work must be established on understanding the finger seal flow state more accurately. In addition, the finger seal performance is affected by many structural and operating parameters. The problem how these parameters effect the seal leakage has always received extensive attention by many researchers [2–5, 10]. However, most are qualitative analysis, or study the leakage under structural and operating conditions separately. The difference and importance of every input parameter is not specific. Also, how the parameters effect on the film viscosity friction and load capacity of contacting finger seal has not been concerned yet. Therefore, the quantitative or the sensitivity analysis of the structural and operating parameters on sealing properties is inadequate by now. Whereas, this information is an indispensable part for seal design. The 3D numerical model of the finger seal radial clearance flow field is established in the presented work. The numerical analysis in this study is carried out using the computational fluid dynamics (CFD) module of COMSOL software. The leakage, viscosity friction and load capacity are calculated under different structural and operating conditions. The gaps between finger sticks are included in the model. Thus, a more accurate set of results could be expected from the current analysis. Furthermore, in order to ascertain the parameters importance to the performance of finger seal, the effects of structural and working conditions on finger seal performance are investigated by single factor analysis firstly. Then based on orthogonal design the simulation scheme is presented and fuzzy satisfactory function is established to estimate the satisfactory degree of the performance of finger seal. Through the range analysis of the satisfactory function, the sensitivity of the structural and operating

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parameters to seal leakage, friction and load are determined respectively. And the sequence of influence degree to seal performance from big to small is obtained consequently.

2 Geometry of Finger Seal The structure of finger seal studied in this work is shown in Fig. 1. The gap between finger foot pad (see Fig. 1(b)) and rotor surface is very thin that is magnified in Fig. 1 (d). The repetitive pattern of the seal in circumferential direction allows the application of periodic symmetric boundary conditions on a sector of the seal. Therefore, the flow field of the seal corresponding one finger section constitutes the computational domain, which is shown in Fig. 2 (the middle part). The main parameters of the finger seal which affect the flow path geometry include the following parameters: finger slice numbers, ns, means the number of finger slices; finger number, s, means the number of fingers around the circumference of a “finger slice”; gap between finger sticks, d; thickness of a finger slice, tf; finger foot height, x, and radial clearance between finger pad and rotor, h, shown in Fig. 1.

(a) One finger slice of seal face

(b) Details of finger foot

(c) Configuration of finger seal

(d) Details of radial clearance

Fig. 1. Structure of finger seal

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3 Simulation Method The radial clearance between the finger foot pad and rotor is very thin from a few microns to a dozens of microns and the flow in axial direction is very short (about 1 to 3 mm). In this thin and short flow field the flow distribution will vary greatly. In order to describe the gas flow reasonably and actually, parts of inlet and outlet cavity are integrated in the simulation model according to the structure of the seal system. The finger seal flow field model with radial clearance is established based on commercial software COMSOL (5.1). Figure 2 shows the mesh model of the computational domain. The raised parts in the middle of the model represent the gaps between finger sticks. 3.1

Governing Equations

For compressible and iso-viscous fluid, the governing Navier-Stokes momentum and continuity equations in the absence of any body force such as gravity can be written in the following vector form in the steady state flow conditions [11]: ~  ðq~ r VÞ ¼ 0

ð1Þ

~~ ~ þ gr ~2 ~ qð~ V  rÞ V ¼ rp V

ð2Þ

Where, q is gas density, p is pressure, η is dynamic viscosity of gas. In cylindrical coordinates the gradient, convective and vector Laplacian and ordinary Laplace operators take the following form, respectively: @ ~  ð @ þ 1Þ^r þ 1 @ ^ h þ ^z r @r r r @h @z

ð3Þ

~  Vr @ þ Vh 1 @ þ VZ @ ~ V r @r r @h @z

ð4Þ

1 2 @Vh 1 2 @Vr ^ ~2 ~ r V  ðr2 Vr  2 Vr  2 Þ^r þ ðr2 Vh  2 Vh þ 2 Þh þ r2 Vz^z r r @h r r @h

ð5Þ

r2 

1@ @ 1 @2 @2 ðr Þ þ 2 2 þ 2 r @r @r r @h @z

ð6Þ

In addition, the density of the gas (air) is replaced from the ideal gas law: q¼

p RT

Where, R is specific gas constant, T is temperature.

ð7Þ

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For the numerical analysis in the current study, the circumferential Reynolds number and axial Reynolds number can be determined by Eqs. (8) and (9) respectively [12]. If the axial Reynolds numbers of the finger seal are less than 2100 the flow may be regarded as laminar flow. Reh ¼

qrxh g

ð8Þ

m_ gpr

ð9Þ

Rez ¼

For gas flow the Knudsen numbers Kn is commonly used to decide if the gas rarefaction effects need to be considered. According to Eq. (10), if Kn < 0.01, continuum flow with no slip boundary conditions can be employed. k g Kn ¼ ¼ h ph

rffiffiffiffiffiffiffiffiffi pRT 2

ð10Þ

Where, r is average rotor radius, x is angular velocity, h is clearance, m_ is mass flow, k is molecular mean free path, η is the dynamic viscosity of the gas. Besides, the surface of finger seal and rotor are assumed as smooth and the asperities are not considered in this paper. 3.2

Boundary Conditions

The boundary conditions of flow simulation are shown in Fig. 2. The pressure boundary condition over the inlet is set to given pressure drop and the outlet is considered to be constant and given by 1 atmosphere. The surface contacting with the rotor is set to be the moving wall and the rotating speed is given on it. Two cutting surfaces are set periodic boundary conditions. And the others are set to fixed walls. The fluid is regarded as ideal gas with a given temperature. The computational domain shown in Fig. 2 is covered by a mesh of quadrilateral and tetrahedral elements. Because the film thickness grid has a great influence on the results, in order to verify the grid independence, the grid in the film thickness direction takes 5–10 layers, and the other grid sizes are changed accordingly to ensure the grid quality. It is found that the leakage and friction increases 1.66% and 2.17% respectively, and the load decrease 0.29% when the number of mesh elements increase from 17,646 to 63,360. Considering the computation time and accuracy, the next results are achieved by using the element number of 36,624 with 6 layers of grids in the film thickness direction.

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(a) Mesh of flow field and boundary conditions

(b) Radial clearance meshed layers Fig. 2. Finger seal flow field with radial clearance

3.3

Performance Parameters

The gas film load capacity is calculated as ZZ Fload ¼

pdA

ð11Þ

qvdAout

ð12Þ

Where, Aout is the area of outlet surface. The viscosity friction is calculated as ZZ sf dA Ffriction ¼

ð13Þ

A

Where, A is the area of load surface. The mass flow leakage is calculated as ZZ m_ ¼ AOUT

A

Where, sf is sheer stress.

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4 Simulation Results and Discussions The finger seal flow behavior with variations of finger seal geometry and working conditions are analyzed by single factor method, that is, the finger seal performances are determined by sequentially varying each of the input factors and by fixing all other factors to constant values. The seal geometry of this and operating parameters are provided in Table 1.

Table 1. Geometrical and operational data for finger seal Parameter Finger number, s Gap between finger, d Finger slice number, ns Thickness of a finger slice, tf Flow path length, l = ns  tf Finger foot height, x Radial clearance, h Radius of rotor, rr Pressure drop, Dp Rotating speed, n Operating temperature, t

4.1

Value 30–45 0.4 8 0.15–0.3 1.2–2.4 0.53 5–25 33 0.1–0.5 0–15000 293–873

Unit – mm – mm mm mm lm mm MPa rpm K

Compare with Compressible and Incompressible Flow

Figure 3 shows the finger seal leakage with different radial clearance in compressible and incompressible conditions. From the graph it can be seen that the leakage increase with the radial clearance for compressible or incompressible condition. However, the leakages for compressible flow are obviously greater than that of the incompressible

Fig. 3. Leakage for different radial clearance in compressible/incompressible conditions

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577

condition at the same clearance, even if the Mach number in the presented conditions are less than 0.3 which is often considered as incompressible flow. So the compressibility effect should be considered when calculate the leakage of finger seal. Figure 4 shows the viscosity friction and load capacity of finger seal with different radial clearance in compressible and incompressible conditions. These results are obtained under the following conditions: finger number is 33, flow length is 1.6 mm (8 slices, tf is 0.2 mm), pressure drop is 0.1 MPa, rotation speed is 5000 rpm, and gas temperature is 293 K. It is found that the load decreases and the friction increases with the radial clearance increasing. When radial clearance increases, the flow velocity increases obviously and varies sharply. These can be found from the Fig. 5(a) and (b) of velocity contour under the radial clearance of 5 lm and 25 lm respectively. The velocity variation gradient along the film thickness increases, which results in friction increase. Compared with the compressible and incompressible model, the load capacity is bigger and the friction is lesser in compressible condition.

Fig. 4. Friction and load with different radial clearance in compressible/incompressible conditions

In order to get more accurate flow results of finger seal, the following analysis results are all obtained in consideration the gas compressibility effect. In order to express clearly, the flow performance parameters such as leakage, load and friction are expressed as relative values with relative variations of conditions. The relative parameters are defined as: relative finger number, S = s/s0; relative flow length, L = l/ l0; relative pressure, P = Dp/p0; relative speed, N = n/n0; relative temperature, T = t/t0. Here, the basic parameters are set to: s0 = 33, l0 = 1.6 mm, p0 = 0.1 MPa, n0 = 5000 rpm, t0 = 293 K. The relative leakage, relative friction and relative load are _ m_ 0 , FF = Ffriction/Ffriction0, FL = Fload/Fload0. Here, m_ 0 , Ffriction0, and defined as: M ¼ m= Fload0 are obtained when the geometrical and operating parameters are set to the basic values.

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H. Su V(m/s)

(a) Gas flow velocity field when h=5μm in compressible conditions

V(m/s)

(b) Gas flow velocity field when h=25μm in compressible conditions Fig. 5. Gas flow velocity field in different radial clearance

4.2

Change Finger Numbers

Figure 6 show the finger seal relative leakage, friction and load vary with relative finger numbers. It is found that the leakage increase with the finger number increasing while the gap between the adjacent finger stick is constant (=10 lm). When adding the finger numbers, the width of finger stick decreases which is similar to widen the leakage path. This result could not be observed by using the approximation circular ring formula to calculate the leakage of finger seal. It is also seen that the finger number has small effect on flow friction and load capacity. The friction increase slightly with the finger number increasing, while contrary to the load capacity. Actually, when the finger number increases, the flow path becomes more complicated adding the flow resistance a bit. According to the calculation the friction just increases about 0.9% for finger number changing from 30 to 45.

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Fig. 6. Relative leakage, friction and load with different finger number

4.3

Change Flow Length

The variations of finger seal leakage, friction and load with different flow length are shown in Fig. 7. If the number of finger slice is constant (here it is 8) and every slice has the same thickness, when changing the thickness of a finger slice we can get different flow length of the seal. Figure 7 shows the performance results when a slice thickness is set from 0.15 mm to 0.30 mm respectively. It can be seen that the leakage decrease obviously with the flow length increasing, while the friction and load increase slightly.

Fig. 7. Relative leakage, friction and load with different flow length

4.4

Change Pressure Differential

Figure 8 shows the finger seal leakage, friction and load varying with the pressure differential between HP and LP. It is found that the leakage, friction and load all increase obviously with increasing pressure and almost maintain linear relationships respectively. This means pressure flow works remarkably in finger seal flow.

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Fig. 8. Relative leakage, friction and load with different pressure

4.5

Change Rotating Speed

The finger seal leakage, friction and load capacity variation with the rotor rotating speed can be found in Fig. 9. It shows that the leakage declines slightly with the speed increasing. It is because that the flow direction changes due to the rotation and results in more flow keeping in the clearance which reduces the leakage. This can be demonstrated from the gas flow velocity distributions shown in Figs. 10 and 11 with zero rotating speed and 15000 rpm respectively.

Fig. 9. Relative leakage, friction and load with different rotating speed V(m/s)

Fig. 10. Gas flow velocity field when n = 0 rpm

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V(m/s)

Fig. 11. Velocity field when n = 15000 rpm

It is also seen that the flow viscosity friction increase slightly with the rotating speed and the load capacity is almost keep constant in the varying range. Figures 12 and 13 show the gas pressure distributions with the rotating speed of zero and 15000 rpm respectively. It is found that the pressure distribution is almost same under different velocity. As a whole, the rotor’s rotating speed has small effects on radial clearance gas flow of finger seal. The results also prove that pressure flow hold a dominant position for finger seal.

Fig. 12. Pressure distribution of finger bottom surface when n = 0

Fig. 13. Pressure distribution of finger bottom surface when n = 15000 rpm

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H. Su

Change Temperature

From Fig. 14 it is found that the gas operating temperature may influence the leakage and viscosity friction obviously. When the gas operating temperature rises, the leakage decreases and load increases mainly due to an increase in the gas viscosity. And we can find that the flow friction increase with the temperature increasing.

Fig. 14. Relative leakage, friction and load with different gas temperature

4.7

Validate Simulation Results

In order to validate the simulation method and results presented in this paper, we test the finger seal leakage using the seal test rig shown in Reference [13]. The test hardware, apparatus, and experimental procedures were described in Reference [13]. With the limitations of test device, only leakage rate were tested at room temperature (293 K). The testing finger seal geometry are as follows: finger number, s, is 33; the thickness of a finger slice, tf, is 0.2 mm; the designed initial built radial clearance between finger pad and rotor, h, is 30 lm. The other parameters are shown in Table 1. Figure 15 shows a comparison of leakage varying with pressure differential in static condition gained with experiments and simulations. It is found that the leakages increase with the increasing pressure differential referring to the test or simulation results. Similar results could be found in Reference [3].

Fig. 15. Static leakage comparison between simulation and experiment results

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Here, only the static results are compared because the radial gap leakage of the finger seal is affected by hysteresis, frictional heat, and circumferential flow caused by rotor rotation under dynamic conditions. And it is currently impossible to measure the radial gap under dynamic conditions, so the accurate result of the leakage cannot be calculated. The presented results demonstrate that the CFD simulation results are consistent with those of experiments, although there are some errors between them. It is shown that the leakage experiment results are slightly larger than that of the simulation results. Because the simulation is the amount of radial gap leakage, in fact, in addition to the radial gap leakage, the surface roughness effect and unevenness between the finger slices will also cause certain leakage from circumferential gap. This is also pointed out in the literature [9]. In addition, there are some measurement errors in the test.

5 Parametersensitivity Analysis 5.1

Parameter Sensitivity Analysis Method

In above analysis, the impacts of the structural and operating parameters on the finger seal performance are analyzed through the single factor method. In order to identify parameters of finger seal that contribute to most to the variability of leakage, viscosity friction or film load, the parameters sensitivity analysis (SA) are conducted in this study. The SA is based on the relationship between the input factors and the outputs considerations. For finger seal it is difficult to establish the mathematical functions to describe the relationship of so much input structural and working parameters and output performances, including leakage, friction and load capacity. Thus we use the CFD model discussed above to establish the implicit functions of finger seal performance. Another issue that deserves concern is the large computational demand in SA. In order to get the reasonable and accurate results large samples must be used in the procedure. However, the use of more strategic, efficient, and effective sampling approaches, can significantly reduce calculation amount. Therefore, this research integrates orthogonal design into the SA to provide a ‘sufficient’ number of inputoutput samples. Further study needs to perform the quantitative measure of output caused by each input factor, that is, a measure of sensitivity. Since the input factors for finger seal include structural and working parameters and there are multi output factors need attention such as seal leakage, friction and load, the satisfactory functions of the seal performance are presented based on fuzzy evaluation [14, 15]. This method could unify the parameters with different dimension and physical interpretation by a unified

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satisfactory function. According to range analysis of the satisfactory function, we can understand the effects of individual input factors on outputs. 5.2

Orthogonal Design and Simulation Results

The simulation program of finger seal for SA is created by orthogonal method. The 25 simulation tests totally shown in Table 2 are arranged with 6 factors and 5 levels [16]. Table 3 refers to the corresponding factors and levels of finger seal. Literatures indicate that proper assignment of input ranges is more influential on SA results [17]. Different variation range of the levels for each factor generate different SA results. In order to avoid the assessment deviation due to the different variation range selected, the same relative increment is set to every level for each factor. In this case, the relative change rate of the level for each factor is set as 15 percent, shown in Table 4. And all the levels should meet the operating and manufacturing demands of finger seal. By using the CFD method mentioned above, the 25 simulation results of the combination with different factors and level inputs are obtained, which are shown in Table 4.

Table 2. Simulation experiments layout_Factors No. Factors h s l 1 1 1 1 2 1 2 2 3 1 3 3 4 1 4 4 5 1 5 5 6 2 1 2 7 2 2 3 8 2 3 4 9 2 4 5 10 2 5 1 11 3 1 3 12 3 2 4 13 3 3 5

Dp 1 2 3 4 5 3 4 5 1 2 5 1 2

n 1 2 3 4 5 4 5 1 2 3 2 3 4

t 1 2 3 4 5 5 1 2 3 4 4 5 1

No. Factors h s l 14 3 4 1 15 3 5 2 16 4 1 4 17 4 2 5 18 4 3 1 19 4 4 2 20 4 5 3 21 5 1 5 22 5 2 1 23 5 3 2 24 5 4 3 25 5 5 4

Dp 3 4 2 3 4 5 1 4 5 1 2 3

n 5 1 5 1 2 3 4 3 4 5 1 2

t 2 3 3 4 5 1 2 2 3 4 5 1

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Table 3. Levels and factors of finger seal Level Factors h(lm) s 1 14 29 2 16.1 33 3 18.5 38 4 21.3 44 5 24.5 51

l(mm) 1.6 1.84 2.08 2.4 2.8

Dp(MP) 0.1 0.115 0.132 0.152 0.175

n(rpm) 5000 5750 6612.5 7604 8745

t(K) 293 337 387.5 445.6 512.5

Table 4. Simulation experiments layout_Results Results No. m(g/s) 1 0.2481 2 0.2137 3 0.1866 4 0.1595 5 0.1397 6 0.1923 7 0.4988 8 0.4352 9 0.1517 10 0.2264 11 0.4556 12 0.1599 13 0.4067 14 0.5804 15 0.5114 16 0.4289 17 0.3703 18 0.5370 19 1.1699 20 0.5065 21 0.9121 22 1.2009 23 0.5176 24 0.4555 25 1.0334

5.3

_ f ðmÞ 0.8064 0.8524 0.8853 0.9149 0.9340 0.8787 0.4189 0.5157 0.9226 0.8360 0.4839 0.9145 0.5608 0.3080 0.4008 0.5255 0.6191 0.3648 0.0083 0.4078 0.0545 0.0065 0.3919 0.4841 0.0239

Ffriction(N) 0.0969 0.1153 0.1357 0.1591 0.1886 0.1536 0.1637 0.1957 0.1227 0.1279 0.2203 0.1391 0.1509 0.1510 0.1793 0.1714 0.2032 0.2036 0.1894 0.1411 0.2321 0.2157 0.1596 0.1876 0.1840

f(Ff) 0.7760 0.6984 0.6086 0.5053 0.3831 0.5289 0.4854 0.3556 0.6660 0.6431 0.2700 0.5934 0.5408 0.5406 0.4200 0.4526 0.3281 0.3268 0.3797 0.5844 0.2338 0.2850 0.5029 0.3870 0.4010

Fload(N) 51.5852 62.9112 75.6010 93.3152 117.1623 66.9610 79.5531 99.0014 90.7940 54.7536 86.0140 77.6820 95.0988 56.8674 70.7982 81.2058 100.9833 61.0584 74.0344 66.2388 105.7949 63.3105 58.5352 70.5320 84.0990

f(Fl) 0.2411 0.3365 0.4471 0.5945 0.7590 0.3718 0.4811 0.6380 0.5745 0.2671 0.5356 0.4650 0.6084 0.2848 0.4053 0.4952 0.6526 0.3206 0.4335 0.3655 0.6866 0.3400 0.2990 0.4029 0.5196

f(z) 0.6277 0.6514 0.6708 0.6959 0.7162 0.6217 0.4575 0.5043 0.7412 0.6074 0.4352 0.6833 0.5691 0.3708 0.4079 0.4946 0.5419 0.3401 0.2473 0.4481 0.2979 0.1901 0.3973 0.4306 0.2857

Sensitivity Measurement Based on Fuzzy Evaluation

It is found that the output factors, such as leakage, friction and load of finger seal, have different values and dimensions in simulations. It is difficult to evaluate the sensitivity

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and importance of each input parameter to the output performance of finger seal. Hence, a satisfactory function based on fuzzy evaluation is presented. For leakage and friction, which are expected as small as possible, the satisfactory function of leakage and friction are defined as follows respectively: _ ¼ ekm m_ ; f ðmÞ

km [ 0

ð14Þ

f ðFf Þ ¼ ekf Ff ;

kf [ 0

ð15Þ

2

2

Load capacity, the bigger the better, whose satisfactory function is set as f ðFl Þ ¼ 1  ekl Fl ; 2

kl [ 0

ð16Þ

Where, km, kf, kl is the coefficient of leakage, friction and load, respectively, which relates the variation and acceptance level of each performance indicator. In this study the extreme values of the simulation results are used to determine the coefficients ki, (i = m, f, l). For example, the max satisfactory function of leakage is set to 0.9 for the minimum leakage among the all results, and the min satisfactory function is set to 0.1 for the maximum leakage. Then we can get the range of km when the max and min satisfactory function is substituted into Eq. (14) respectively. The average is taken as the coefficient km. Under the analysis conditions in this paper, km is calculated as 3.4967. By the same way, we can get the coefficient kf as 26.9841. For load coefficient kl, the max satisfactory function of load is set to 0.9 for the maximum load, and the min satisfactory function is set to 0.1 for the minimum load, then the load coefficient kl, 1.0366  10−4, is obtained similarly. _ f(Ff), When the coefficients, km, kf, kl are determined, the satisfactory function f ðmÞ, f(Fl), for every simulation set, could be calculated by Eqs. (14), (15) and (16) respectively. The satisfactory function results for every simulation sample are shown in Table 3. Then the range analysis of unified satisfactory function are used as quantitative indicators of each input variable’s importance, that is measure of sensitivity. For _ f(Ff) or f(Fl), the range of all samples for each input different output function, f ðmÞ, parameter is calculated. The relative importance of each of these input factors could be judged according to the order of the range value from the perspective of different seal performance. If one wants to know the influence of parameters on the integrated performance of finger seal, a multi-index synthesis satisfactory function, f(z), could be defined by weighted arithmetic average of every single satisfactory function of seal performance, shown in Eq. (17). Definitely, the weight coefficients should be determined in advance according to the importance of every indicator. f ðzÞ ¼

n X i¼1

wi f ðxi Þ

ð17Þ

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5.4

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Sensitivity Analysis Results

Through the orthogonal table, the range analysis results for leakage, friction and load are shown in Tables 5, 6 and 7, respectively. Where, Ki is the average of satisfactory function for level i, i = 1–5. The range value is helpful to intuitively indicate how the input parameters impact the sealing performance. From Table 5, it is found that the order of the influence of parameters on leakage from big to small is: radial clearance (h), temperature(t), pressure drop(Dp), flow length(l), rotating speed(n), and finger number(s). Among these parameters, radial clearance gain the highest range value among the others. It means that the radial clearance has a high influence on the leakage of finger seal as we expected. Next, temperature, pressure drop and flow length also have important effects on leakage changes. Both rotating speed and finger number have least impacts on leakage relatively. As a result, radial clearance should be determined accurately which would influence the result of leakage sensitively. As we know, the radial clearance is varying in operating conditions, which will changed due to rotor run out, thermal deformation, hysteresis and blow down effect. So determination the accurate radial clearance of finger seal is challenging and important work whether in theory calculation or practice test. In addition, the flow length should be paid more attention in leakage analysis, however, in previous researches it was not considered in contacting finger seal leakage analysis.

Table 5. Range analysis of satisfactory function for leakage K1 K2 K3 K4 K5 Range Order

h 0.8786 0.7144 0.5336 0.3851 0.1922 0.6864 1

s 0.5498 0.5623 0.5437 0.5276 0.5205 0.0418 6

l 0.4643 0.5064 0.5360 0.5789 0.6182 0.1539 4

Dp 0.6886 0.6518 0.5430 0.4308 0.3897 0.2990 3

n 0.5652 0.5295 0.5397 0.5537 0.5157 0.0495 5

t 0.3637 0.4277 0.5481 0.6491 0.7152 0.3515 2

Table 6. Range analysis of satisfactory function for friction h 0.5943 K1 0.5358 K2 0.4730 K3 0.4143 K4 0.3619 K5 Range 0.2323 Order 2

s 0.4523 0.4781 0.4670 0.4957 0.4863 0.0434 6

l 0.5143 0.5060 0.4671 0.4616 0.4304 0.0839 4

Dp 0.6245 0.5444 0.4815 0.3943 0.3347 0.2898 1

n 2.2668 2.3623 2.4587 2.4444 2.3646 0.1919 3

t 0.5166 0.4826 0.4865 0.4499 0.4439 0.0727 5

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h 0.4756 0.4665 0.4598 0.4535 0.4496 0.0260 3

s 0.4660 0.4551 0.4626 0.4581 0.4633 0.0110 6

l 0.2907 0.3692 0.4464 0.5425 0.6562 0.3655 1

Dp 0.3890 0.4220 0.4552 0.4976 0.5412 0.1522 2

n 0.4680 0.4574 0.4599 0.4560 0.4638 0.0119 5

t 0.4567 0.4623 0.4524 0.4698 0.4639 0.0173 4

In Table 6, we may rank the parameters according to the range value of friction satisfactory function from big to small as: pressure drop,radial clearance, rotating speed, flow length, temperature, and finger number. The first three factors have similar effects on viscosity friction. It indicates that these parameters play important roles in thermal power loss consideration. Relatively, the impacts of flow length, temperature, and finger number on friction are small. From Table 7, it is seen that the influence of parameters on load from big to small is: flow length, pressure drop, radial clearance, temperature, speed, and finger number. The first two parameters, especially flow length, play more significant roles than others. Therefore, adding the size of axial flow length is the most efficient to improve the film load capacity. Such structure can be found in non-contacting finger seal with an extended pad along axial in LP. It is concluded that for different performance the relative importance of the input parameters are different. Among the 6 input factors studied here, radial clearance keeps in the top three, which is very important to finger seal performance. However, the influence of finger number is the least one relatively, which is always in the last place. While, it is worthy to note that finger number would have influence on finger stiffness which result in variation of hysteresis clearance. It may be considered in study the real radial clearance change of finger seal. Moreover, not only the structural parameters, but also the operating conditions would influence the performance of finger seal distinctively, sometimes the operating parameters are more sensitive to the performance of finger seal than structural factors. If we hope to know the importance of parameters to the whole performance of finger seal, the synthesis satisfactory function may be calculated by Eq. (17). Similarly, the range analysis is used to judge the order of importance of parameters to the integrate performance of finger seal. For example, the weigh coefficient for leakage, friction and load is set to 0.4, 0.3 and 0.3, respectively. The satisfactory function, f(z), is listed in Table 4 and the range analysis results are shown in Table 8. The sequence of influence of parameters on the integrate performance from large to small is: radial clearance, pressure drop, flow length, temperature, rotating speed, and finger number. The results indicate that the radial clearance is a significant parameter in finger seal, then pressure drop, flow length, temperature, are also closely related to the whole performance of finger seal. While rotating speed and finger number have little impacts on the ranking of integrate performance.

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Table 8. Range analysis of satisfactory function for integrate performance K1 K2 K3 K4 K5 Range Order

h 0.6724 0.5864 0.4933 0.4144 0.3203 0.3521 1

s 0.4954 0.5048 0.4963 0.4972 0.4931 0.0118 6

l 0.4272 0.4651 0.4885 0.5328 0.5733 0.1460 3

Dp 0.5795 0.5506 0.4982 0.4399 0.4186 0.1609 2

n 0.5025 0.4908 0.5014 0.5050 0.4873 0.0177 5

t 0.4375 0.4545 0.5009 0.5355 0.5584 0.1209 4

6 Conclusions With the same sealing diameter and manufacturing conditions, radial clearance, flow length and finger number can influence the geometry of leakage path of finger seal, which result in the variation of sealing performance combined with different operating conditions such as pressure drop, rotating speed and temperature. CFD simulation is an effective method to investigate the finger seal flow behavior with complicated and detailed geometry. The leakage, viscosity friction and film load of finger seal are calculated by different combination of input parameters. The flow behavior is quite different whether the gas compressibility is considered even as the Mach number is less than 0.3. Then it is suggested that compressibility should be taken into account in course of numerical simulation of finger seal. Single factor method has advantage to get the influence rule of any parameter on the performance of finger seal qualitatively. The leakage and friction increase but the load decrease with increasing radial clearance. When the sealing diameter and radial clearance are constant, changing the finger number may influence the leakage and friction and load capacity, which cannot be shown by former simplified annular flow model. When adding the finger numbers the leakage and friction increase and the load decreases slightly. When the thickness of finger slice increases, the flow path is lengthened which results in the leakage decline and the friction and load capacity increase. Operating conditions such as pressure drop, rotating speed and temperature influence the finger seal flow behavior in different ways. The leakage, friction and load are found to be proportional to the pressure drop approximately. When temperature increase the leakage decreases, the friction and load increase, in contrast to what would be expected of liquids. The rotating speed affects the flow direction in gas film which leads to the variation of leakage and friction at different speed. Parameters SA is necessary to judge the proportional impacts of multi input parameters on output indicators. A procedure to perform the SA combined with CFD, orthogonal design and fuzzy evaluation has been proposed. Using orthogonal design is helpful to select reasonable and uniform samples to deduce the computation amount. A kind of fuzzy evaluation function is presented to measure the sensitivity of parameters to different outputs. It is found that the same parameter has different sensitivity to leakage, friction or load performance, respectively. Leakage is most significantly

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influenced by the radial clearance. While, temperature, pressure and flow length are also important and sensitive parameters to leakage secondly. Rotor speed and finger number have relatively small impact on leakage. In addition, the parameters SA to the friction and load capacity are analyzed in this research. It is found that pressure drop, radial clearance and rotating speed have more significant impact on friction and the flow length influence the load capacity mostly. The parameter SA of the comprehensive performance of finger seal is conducted using integrated satisfactory function according to the expected weight coefficient defined to every output indicator. In the case presented, radial clearance is the most worthy concerned input parameter and significant to overall finger seal performance. Among the six inputs parameters discussed here, the finger number has the least impact on finger seal performance. SA results allows analyzing quantitatively the contribution of each input parameter to the output performance variance, providing important insights to design finger seal effectively.

References 1. Arora, G.: Fingerseal: a novel approach to air to air sealing. NASA/CP-2006-214329/VOL1, pp. 21–37 (2006) 2. Gibson, N.E., Takeuchi, D., Hynes, T.: Second generation air-to-air mechanical seal design and performance. In: 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, San Diego, California, USA, 31 July–03 August (2011) 3. Proctor, M.P.: High-Speed, High-Temperature Finger Seal Test Results. AIAA–2002–3793 (2002) 4. Proctor, M.P.: Leakage and Power Loss Test Results for Competing Turbine Engine Seals. NASA/TM-2004-213094 (2004) 5. Delgado, I.R.: Continued Investigation of Leakage and Power Loss Test Results for Competing Turbine Engine Seals. AIAA 2006-4754 (2006) 6. Arora, G.K.: Pressure Balanced, Low Hysteresis, Finger Seal Test Results. AIAA-99-2686 (1999) 7. Wang, L.N., Chen, G.D., Su, H., et al.: Effect of temperature on the dynamic performance of C/C composite finger sea. Proc. IMechE Part G: J. Aerosp. Eng. 230(12), 2249–2264 (2016) 8. Wang, L.N., Chen, G.D., Su, H., et al.: Transient performance analysis of finger seal considering compressed fluid in the leakage gap effect. J. Aerosp. Power 30(8), 2004–2010 (2015) 9. Jahn, I.H.: Design approach for maximising contacting filament seal performance retention. Proc. IMechE Part C: J. Mech. Eng. Sci. 229(5), 926–942 (2015) 10. Chen, G.D., Xu, H., Yu, L., et al.: analysis to the hysteresis of finger seal. Chin. J. Mech. Eng. 39(5), 121–124 (2003) 11. Su, H., Rahmani, R., Rahnejat, H.: Performance evaluation of bidirectional dry gas seals with special groove geometry. Tribol. Trans. 60(1), 58–69 (2017) 12. Denecke, J., Farber, J., Dullenkopf, K., et al.: Dimensional analysis and scaling of rotating seals. In: ASME Turbo Expo2005, Reno-Tahoe, Nevada, USA, 6–9 June 2005, GT200568676 (2005) 13. Zhang, Y.C., Chen, G.D., Zhou, L.J., et al.: New method for performance optimization of finger seals. J. Mech. Eng. 46(10), 156–163 (2010)

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14. Su, H., Lang, D.X., Qi, F.: Structural parameters sensitivity analysis of hydrodynamic finger seal with herringbone-grooved rotor based on fuzzy valuation. Lubr. Eng. 37(5), 7–12 (2012) 15. Su, H.H., Yao, Z.J.: Fuzzy analysis method for multi-orthogonal test. J. Nanjing Univ. Aeronaut. Astronaut. 36(2), 29–33 (2004) 16. Chen, K.: Design and Analysis of Experiments. Tsinghua University Press, Beijing (2005). (in Chinese) 17. Muleta, M.K., Nicklow, J.W.: Sensitivity and uncertainty analysis coupled with automatic calibration for a distributed watershed model. J. Hydrol. 306, 127–145 (2005)

Calculation and Experimental Study on Comprehensive Stiffness of Angular Contact Ball Bearings Peng Sun, Weifang Chen(&), Chuan Su, and Yusu Shen College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China [email protected], [email protected], [email protected], [email protected]

Abstract. The stiffness of the rolling bearing has a great influence on the dynamic characteristics of motorized spindle. In order to obtain the stiffness of angular contact ball bearing under oil-jet lubrication, the theoretical calculation model and experiment method are proposed in this paper. Based on hertz contact theory and elastohydrodynamic lubrication theory, the quasi-static analysis model of angular contact ball bearing is established. The factors including ball centrifugal force, gyro moment, preload and oil film thickness are taken into consideration and theoretically analyzed. The test platform on comprehensive stiffness is designed and the stiffness is experimentally verified under different factors. The results show that the comprehensive stiffness increases with the increase of axial, radial load and preload but decreases with the increase of rotational speed. Therefore, the adjustment of the working condition of angular ball bearing can make it work in a better mechanical state and thus improve the bearing life. Keywords: Angular contact ball bearings Oil film stiffness  Contact stiffness

 Comprehensive stiffness 

1 Introduction Angular contact ball bearings are important driving and supporting parts in numerical control machines. In the process of supporting loads, the boundary conditions of bearings are constantly changing, so the description of the stiffness matrix is more complicated. Besides, as an elastomer, the mechanical properties of bearings play a key role in the dynamic characteristics of a motorized spindle system and can significantly influence the dynamic performance of the motorized spindle system. Many scholars had done some research on this. Chen [1] regarded angular contact ball bearing as the research object and derived five-DOF expression of stiffness without considering factors such as oil film or centrifugal force. Yu [2] established a calculation model of angular contact ball bearings according to the principle of elastohydrodynamic This project is supported by National Natural Science Foundation of China (Grant No. 51775277). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 592–601, 2020. https://doi.org/10.1007/978-981-32-9941-2_48

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lubrication and the result showed that the stiffness of bearing tends to decrease when considering the lubricating oil. Tang [3] built a quasi-dynamics analysis model with centrifugal force, gyroscopic moment and lubricating oil film, which demonstrated that the contact stiffness and oil film stiffness are not much different when the rotational speed of bearings reaches a certain level. Xiong [4] developed a calculation model of bearing considering lubricating oil, the deformation of ring, the effects of temperature and the centrifugal force. Other factors were also studied under different preload and speed condition. Shi [5] set up the test platform on axial stiffness of bearing, concluding that the hertz analytical solution is rather consistent with the measured value when the load value is small. However, as the load increases, the error will increase. Li [6] obtained the dynamic stiffness of the angular contact ball bearing by making use of the synchronous rotational radial load with unbalanced mass. However, the rotational speed and the radial load have an inter-related relationship. Besides, the test platform has certain limitations and can’t comprehensively analyzes the influencing factors. Fang [7] established the deformation expression of angular contact ball bearing with the coordinate transformation method and designed the relevant test platform. However, what the test platform measured is the absolute displacement of the bearing and can’t fully meet the exact requirement. Ali [8] and Lambert [9] obtained the radial stiffness of bearing by measuring the mass, acceleration and relative displacement of the inner and outer ring, which indirectly expresses the contact force between the shaft and the inner ring by the product of acceleration and mass of shaft and provides a new idea for solving the stiffness of bearing through the reasonable matching of sensor position and data processing method. At present, the existing mechanical model of bearings can realize the approximate calculation of stiffness, but the comprehensive factors have not been fully analyzed. It has not yet reached the precise level in the test part of stiffness. Due to the poor repeatability of the test results, it can not play a good guiding significance. There are not many related references about the test part of the rolling bearing comprehensive stiffness. Thus, a perfect test plan has not yet been formed. Based on above investigation and survey, angular contact ball bearing will be carefully studied with an improved quasi-static model. Furthermore, a complete experimental scheme is proposed to verify the theoretical analysis.

2 Theoretical Calculation Model According to the hertz elastic contact theory [10] and elastohydrodynamic lubrication theory, analysis of the stress condition of angular contact ball bearings has been conducted. As shown in Fig. 1, the position change of inner and outer ring curvature center, before and after the angular contact ball bearing is loaded, has been showed in the schematic diagram. Since the outer ring and the housing are fixed, point E and E′ coincide.

P. Sun et al. Radial

594

X aj The end position of inner ring curvature center j-h

0.5 (f i -

(f o

-0. 5)D w

+u

ojh

Y rj

oj

αij

αoj α 0

O'

O

)

ui Dw+

I'

ij

I

urcosΨ

ua+θRicosΨ The first position of inner ring curvature center The end position of ball center

The first position of the ball center The first(end) position of outer ring curvature center

E (E')

Axial

Fig. 1. The position change of inner and outer ring curvature center before and after loaded

2.1

Geometric Equation

According to Fig. 1, for the ball in any position j, the following formula holds: 8 < Xaj ¼ LIE sin a0 þ ua þ hRi cos wj Y ¼ LIE cos a0 þ ur cos wj : rj Ri ¼ 0:5Dm þ ðfi  0:5ÞDw cos a0

ð1Þ

where a0 is the initial contact angle; LIE is the distance between inner and outer ring curvature center when the bearing is not loaded; ua, ur and h are respectively axial and radial deformation and rotation angle after the bearing is loaded; Ri is the radius of the circle where the inner ring curvature center is located; Dm is the diameter of the bearing pitch; Dw is the diameter of the ball; fi(o) is the curvature of inner (outer) groove. Considering the axial and radial load, the centrifugal force of balls, the gyro moment and the lubricating oil film, the contact angle of the inner ring (outer ring is the same) can be expressed as: 8 < sin aij ¼ Xaj ½ðfi 0:5ÞDw þ uoj hoj  sin aoj ðfi 0:5ÞDw þ uij hij : cos aij ¼ Yrj ½ðfi 0:5ÞDw þ uoj hoj  cos aoj

ð2Þ

ðfe 0:5ÞDw þ uij hij

where uij and uoj are the hertz deformation between the jth ball and the contact point of inner and outer ring; hij and hoj are the oil film thickness between the jth ball and the contact point of inner and outer ring. 2.2

Force Balance Equation Between the Ball and the Inner and Outer Ring

When the angular contact ball bearing rotates in high speed, in addition to the contact force generated by external load, the combined effect of centrifugal force and gyro

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moment are also applied on the ball. The force on the ball and the inner ring is shown in Fig. 2

Qoj F cj

λijM ij/D b

λojM oj/D b αoj

αij

Qij M gj ΣQij

F a0

j=1

ΣλijM ij/D b j=1

Fig. 2. The force on the ball and the inner ring

The force balance relationship is determined by the following formulas: (

Mgj Mgj Db cos aij þ koj Db cos aoj M M Qoj cos aoj þ kij Dgjb sin aij  koj Dgjb sin aoj

Qij sin aij  Qoj sin aoj  kij

¼0

Qij cos aij 

þ Fcj ¼ 0

ð3Þ

where Qij and Qoj are the forces between the ball and the inner and outer ring, they could be expressed as: (

Qij ¼ Kij u1:5 ij Qoj ¼ Koj u1:5 oj

ð4Þ

When the system is statically balanced, the radial load and bearing load on the inner ring of the bearing can be expressed respectively as: 8 Z P Mgj > > > Fa þ Fa0  ðQij sin aij þ kij Db cos aij Þ ¼ 0 > > j¼1 > > < Z P M Fr  ðQij cos aij  kij Dgjb sin aij Þ cos wj ¼ 0 > j¼1 > > > Z > P > M M > : M  ½ðQij sin aij þ kij Dgjb cos aij ÞRi  ri kij Dgjb  cos wj ¼ 0

ð5Þ

j¼1

where Z is the number of balls; Fa0 is the initial preload; ri is the radius inner ring curvature. Equations (1), (2), (3), (4) can be combined as the first group of equations, and (5) as the second group of equations, then they can be solved jointly by Newton-Raphson

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iterative method. Under the condition, the axial and radial deformation and the angle of the bearing could be solved and then the comprehensive stiffness of the bearing with these parameters can be obtained.

3 Test and Analysis 3.1

Test Platform

In order to verify the correctness of the theoretical model, a test platform of bearings on comprehensive stiffness is designed in this paper. As shown in Fig. 3, the test platform consists of five parts: power output system, spindle transmission system, axial and radial loading system, lubrication system and data acquisition system.

Fig. 3. The test platform of bearing on comprehensive stiffness

The axial loading and testing part includes a loader, a piezoelectric force sensor and a displacement sensor. The axial force is applied on the outer ring of the bearing through a cylinder by the axial loader and can be measured by the force sensor located between the loader and the cylinder. The displacement sensor is mounted in the center hole of the cylinder for measuring the axial displacement of the end face of the shaft. The value measured by the axial displacement sensor represents the relative displacement of the inner and outer ring since the inner ring and the shaft, the outer ring and the cylinder have the same displacement in the axial direction. The radial loading and testing part includes a loader, a piezoelectric force sensor, a displacement sensor and the housing. Similar to the principle of axial testing, the inner ring and the shaft, the outer ring and the housing have the same displacement in the radial direction and the radial value measured by the sensor which is embedded in the housing represents the relative displacement of the inner and outer ring in the radial direction. The supporting assembly fixed on the baseboard is used to support for the transmission shaft. Several oil and gas holes and rotating shaft seals are provided on the outer surface of the housing for bearing lubrication.

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597

Principle

The test principle of comprehensive stiffness is shown in Fig. 4. The slowly increasing load in the axial and radial direction will be applied on the bearing, and then the physical output signal of each sensor is converted into an identifiable analog signal through the transmitter. After filtering and other calculation, the actual forcedisplacement data can be obtained. Finally the axial and radial stiffness of bearings are obtained by deriving the force-displacement curve which is obtained by data fitting. Radial loader

Force sensor

Data acquisition system Displacement sensor

Cylinder transmitter

analog signal

filter and other calculation

data fitting

comprehensive stiffness

transducer

Axial loader

Motor water tank

Force sensor

Coupling Supporting assmebly

housing

Displacement sensor

Fig. 4. The test principle of comprehensive stiffness

3.3

Result and Analysis

The type of the angular contact ball bearing selected in this paper is S7212AC. The basic parameters are shown in Table 1. Table 1. The basic parameters of S7212AC Parameter Outer diameter Inner diameter Width Ball number Elasticity modulus Density Ball diameter Initial contact angle Curvature of outer groove Curvature of inner groove Poisson’s ratio material

Symbol D d B Z E P Dw a fe fi l /

Value 110 mm 60 mm 22 mm 16 2.07  1011 Pa 7800 kg/m3 12.5 mm 25° 0.53 0.52 0.3 9Cr18

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The Utel dynamic signal acquisition device is used for data acquisition. The acquired displacement and force data are polynomial fitted to obtain a fitting curve. The slope of the curve represents the stiffness in a certain working condition. Figure 5 shows the stiffness comparison of the test processing result and the theoretical result.

(a) The stiffness comparison in radial direction

(b) The stiffness comparison in axial direction

Fig. 5. The stiffness comparison of the test processing result and the theoretical result

When the radial load changes from 0 to 5000 N, the test of comprehensive stiffness on the angular contact ball bearing under operating conditions is carried out. When the bearing is running, the displacement data is periodically fluctuated. The mean value of the displacement data corresponding to the related load is fitted to obtain the forcedisplacement relationship of the angular contact ball bearing and then the bearing stiffness is obtained.

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As shown in Fig. 6, comparative tests have been done under different working conditions. It can be seen that the stiffness generally decreases with the increase of the rotational speed. And the larger the radial load at the same speed is, the larger the radial comprehensive stiffness becomes.

(a) Radial stiffness under different working conditions

(b) Axial stiffness under different working conditions

Fig. 6. The comparative test under different working condition

The comparative test of the comprehensive stiffness of angular contact ball bearings subjected to different preload has been carried out. As the preload increases, the contact load between the ball and the inner and outer ring increases when other factors remain unchanged, which will lead to the increase of the contact stiffness and account for why the axial and radial comprehensive stiffness increase in Fig. 7.

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(a) Radial stiffness under different preload

(b) Axial stiffness under different preload

Fig. 7. The stiffness under different preload

4 Conclusions In this paper, the calculation model of the comprehensive stiffness of angular contact ball bearings was established. The effects of external load, centrifugal force, rotational speed, lubricating oil film, preload and gyro moment were fully considered. The test platform of comprehensive stiffness was built and the influence under different working conditions was analyzed. The main conclusions are as follows: (1) Under the premise that other factors remain unchanged, the axial and radial comprehensive stiffness of angular contact ball bearings increase with the increase of axial and radial loads. The maximum error between the theoretical radial comprehensive stiffness and the measured radial stiffness is 6.5%, while the maximum error between the theoretical axial stiffness and the measured axial stiffness is 13% and the error decreases with the increase of the load; (2) The comprehensive stiffness of the angular contact ball bearing will decrease when the elastohydrodynamic lubrication effect is considered; (3) With the increase of the rotational speed, the axial comprehensive stiffness of the angular contact ball bearing will decrease, for the oil film thickness of the lubricating oil is reduced, which leads to the increase of the oil film stiffness. Different from the axial comprehensive stiffness, the radial comprehensive stiffness is almost unchanged;

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(4) The increase of the preload will make the axial and radial comprehensive stiffness of the angular contact ball bearing increase.

References 1. Chen, S.J., Zhang, C.Y.: Analytical derivation and computer solution of bearing stiffness matrix. Bearing 2, 1–4 (2006) 2. Yu, Y.J., Chen, G.D.: Study on stiffness characteristics of high speed angular contact ball bearings considering elastohydrodynamic lubrication. J. Northwestern Polytechnical Univ. 1, 125–131 (2016) 3. Tang, Y.B.: Research on Mechanical Characteristics of Aeroengine High Speed Rolling Bearings. Nanjing University of Aeronautics and Astronautics (2005) 4. Xiong, W.L., Zhao, Z.S.: Research on dynamic stiffness of ball bearing considering the influence of ferrule deformation and lubrication. Chin. Mech. Eng. 26(11), 1421–1428 (2015) 5. Shi, S.C., Wu, J.W.: Axial stiffness analysis and experiment of thin-wall angular contact ball bearings. J. Harbin Eng. Univ. 44(7), 32–37 (2012) 6. Li, C.J.: Experimental study on dynamic stiffness of angular contact ball bearings. J. Xi’an Jiaotong Univ. 47(7), 68–72 (2013) 7. Fang, B., Zhang, L.: Theoretical calculation and experiment of angular contact ball bearing stiffness. J. Jilin Univ. (Eng. Edn.) 42(04), 840–844 (2012) 8. Ali, N.J., García, J.M.: Experimental studies on the dynamic characteristics of rolling element bearings. ARCHIVE Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 224(7), 659–666 (2010). 1994–1996 (vol. 208–210) 9. Lambert, R.J., Pollard, A., Stone, B.J.: Some characteristics of rolling-element bearings under oscillating conditions. Part 1: theory and rig design. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 220(1), 171–179 (2006) 10. Harris, T.A., Mindel, M.H.: Rolling element bearing dynamics. Wear 23(3), 311–337 (1973) 11. Huang, Z.Q.: Design and Calculation of Ball Beaing. Mechanical Industry Press (2003)

Design of a New Hydraulic Manipulator with Kinematic and Dynamic Analysis Yao Sun1, Yi Wan1(&), Xichang Liang1, Xin Huang1, and Ziruo Liu2 1

Key Laboratory of High-Efficiency and Clean Mechanical Manufacture, College of Mechanical Engineering, Shandong University, Jinan 250061, China [email protected], [email protected] 2 National Demonstration Center for Experimental Mechanical Engineering Education, Shandong University, Jinan 250061, China

Abstract. Since the traditional hydraulic manipulator is heavy and serious in stress concentration, a new 6-DOF hydraulic manipulator was presented with high deadweight ratio and its 3D solid model was constructed. The kinematics of the manipulator was analyzed according to the structural characteristic and the kinematic constraint. A forward kinematics model of the manipulator was conducted, and the complete analytical solution of the inverse kinematics was obtained. In addition, a dynamic analysis method based on Lagrangian equation is used to optimize the structure of hydraulic manipulator. The application of Lagrangian equation to dynamic modelling and force analysis leads to an elegant and geometrically meaningful formulation. The method is implemented for the hydraulic manipulator and simulation results are provided. All the results show that the designed manipulator have a better Kinematic characteristic and work performance. Keywords: Hydraulic

 Manipulator  Kinematic analysis  Dynamic analysis

1 Introduction Manipulator is the most widely used mechanical device in the field of robot at present. It is used to replace manual operation in automobile manufacturing, electronic and electric industries, which greatly reduces labor cost, and effectively improves product quality [1]. Most traditional mechanical arm are designed for a single application, used to complete a specific task, and with the method of motor and reducer, the carrying capacity is relatively small. Therefore, a new type of drive mode of manipulator which has a large carrying capacity and high reliability is developed. This research has designed a hydraulic mechanical arm with light weight, small inertia, large output and stiffness. In addition, the pressure of the hydraulic system is adjustable, which can improve the output characteristics, such as increase or decrease output power and deadweight ratio. In particular, it needs to be point out that carrying capacity of

This project is supported by the Fundamental Research Funds of Shandong University (2017JC041) and the Key Research Project of Shandong Province (2017CXGC0917). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 602–614, 2020. https://doi.org/10.1007/978-981-32-9941-2_49

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manipulator, an important indicator, is one of important standards to judge the robot arm performance. The BigDog from Boston Dynamics company which use hydraulic system as driving power is mainly used for rugged handling work. The robot, used for military or engineering, has a outstanding sport ability. The hydraulic actuator of BigDog that together with four institutions and based on the two characteristics of hydraulic transmission is chosen as the joint driving element. Hydraulic load capacity of the hydraulic system depends on pressure and the size of actuator, and its speed hinge on flow of the hydraulic system [2–6]. In order to achieve automation of the hydraulic manipulators, the automation of excavators [7, 8], dumpers, cranes and telescopic handler [9, 10] have been developed. Dynamics and kinematics research are the hotspot of robot research [11–17]. The kinematic algorithm can meet the real-time requirements of general robot control system [18]. However, dynamic and kinematic analysis is an important research direction in the automation of hydraulic machines, especially for manipulator. Through the analysis of dynamic and kinematic, we can obtain the output characteristics including motion performance and working performance, which are important standards of hydraulic robot. In this paper, we propose a new 7-DOF redundant manipulator that has better flexibility and higher deadweight ratio. The double-manipulator rescue robot, which have two hydraulic mechanical arms, only weight 4 tons, but have a load capacity of 2 tons and 10 mm motion accuracy. In order to improve the velocity and force properties of the hydraulic manipulator, we need to analyze kinematic and dynamic of the mechanical arm. Then we carried out ADAMS analysis of the manipulator to verify the correctness of the dynamic analysis. The results of speed and force curves show that the hydraulic manipulator of the double-rescue robot has a good speed and force properties, which is suitable for rescue mission.

2 Kinematics 2.1

Base System Model

In order to meet the requirement of the mobile flexibility of the manipulator, the mechanical structure adopts the design idea of redundant degrees of freedom. Since human arm has good flexibility, mechanical arm is designed according to ergonomic principles. Human arm is a typical 7-DOF redundant mechanism that can achieve four basic forms of motion: flexion, extension, rotation and translation. Studying the structure of human arm is conducive to better design of related anthropomorphic robot arm. However, it should be noted that the bone structure of human body cannot be directly applied to the design of mechanical arm, which needs reasonable and practical improvement. Hydraulic cylinder is taken instead of arm muscle in hydraulic manipulator. Considering the feasibility of installing the hydraulic drive components, a new 7DOF

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Fig. 1. The double-manipulator rescue robot

Fig. 2. Geometric structure of the manipulator

Fig. 3. Geometric structure of swing freedom

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hydraulic manipulator, combined with the human arm configuration, is proposed as Fig. 2, which can achieve basic movement of human arm. The design of the wrist joint adopts the double-cylinder collaborative mode, so that the wrist has the structure of abduction, with 2-DOF includes swing and rotation. The wrist of the hydraulic manipulator shows in Fig. 3. The control system of hydraulic manipulator is based on electro-hydraulic proportional control technology design, which can control the flow of hydraulic system through electrical signals and flow direction. The hydraulic system of the mechanical arm includes hydraulic pump, electromagnetic proportional valve, hydraulic cylinder, motor and other components. hydraulic cylinders and motors are driving parts, including six hydraulic cylinders and two motors. The six hydraulic cylinders include 5DOF and three types of action, that is rotation, pitch and swing. And the two hydraulic motors correspond to the rotational motion of the wrist joint and base joint, respectively. 2.2

D-H Coordinate System

The kinematic equations of manipulator have varieties of methods that like early space vector polygon method and Quaternion Algorithm. The current common methods include: homogeneous coordinate, Denavit-Hartenberg Matrix and screw theory. The forward kinematics equation is solved by Denavit-Hartenberg Matrix method. The double-manipulator rescue robot is shown in Fig. 1. Each manipulator of the robot has 7-DOF, and the two mechanical arms have 14 degrees of freedom in total. In order to obtain larger unit torque, the double-manipulator robot is driven by hydraulic. the hydraulic driven system, which includes motors and serve values, is inside the doublemanipulator rescue robot. In this paper, the mathematical model is extracted from the entity model of the manipulator, according to the method of D-H Matrix. The coordinate system of the connecting rod is shown in Fig. 4. The coordinate system {0} is the base coordinate, the coordinate system {7} is the end effector coordinate of the mechanical arm, and the coordinate system {1} to {5} is the link coordinate system.

Fig. 4. D-H coordinate system of the manipulator

Firstly, the rod and connection mode of the mechanical arm are defined. Torsion angle a, rod length l, joint angle h and joint distance d were used to describe each link. Torsion angle a and bar length l are used to describe the characteristics of the ith link

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itself, and joint angle h and joint distance d are used to represent the relationship between the ith and i + 1 bar. 2.3

Kinematic Equation

The articular angles of the manipulator is given in Table 1, which includes the angle between the x-axis of the adjacent coordinate system. In this section, the end effector position of the manipulator in coordinate system relative to the base coordinate system is solved. Table 1 defines the parameters of solving the forward kinematics of the manipulator that the angle values of each joint are defined or given.

Table 1. Notation di hi li ai qi M R P

Distance between the x axes in the adjacent coordinate system Angle between the x axis in the adjacent coordinate system Distance between the z axis in the adjacent coordinate system Angle between the z axis in the adjacent coordinate system Variable of the ith joint Position of the manipulator in the D-H coordinate system Position matrix of the end-effector coordinate system relative to the base coordinate system Position vector of the end-effector coordinate system relative to the base coordinate system

The math model of kinematic equation is given as follow: X M¼ f ð qi Þ

ð1Þ

The homogeneous transformation matrix from system {0} to system {1} is given as Eq. (2): M01 ¼ Rotðz; h1 Þ  Transð0; 0; l1 Þ  Rotðx; a1 Þ

ð2Þ

Where, M01 is the homogeneous transformation matrix. Rot(x, a1) represent {0} coordinate system rotates about the x0 axis by a1 degree. Trans(0, 0, l1) represent {0} frame shift along the z0 axis by l1. Similarly, M12 ¼ Rotðz; h2 Þ  Transðl2 ; 0; 0Þ

ð3Þ

M23 ¼ Rotðz; h3 Þ  Transðl3 ; 0; 0Þ

ð4Þ

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M34 ¼ Rotðz; h4 Þ  Transðl4 ; 0; 0Þ

ð5Þ

M45 ¼ Rotðz; h5 Þ  Transðl5 ; 0; 0Þ  Rotðz; h6 Þ  Rotðx; 90Þ

ð6Þ

M56 ¼ Rotðz; h7 Þ  Transðl6 ; 0; 0Þ

ð7Þ

The coordinate of the terminal position of the hydraulic manipulator can be obtained by continuous multiplication of six homogeneous coordinate transformation matrices, so the homogeneous transformation matrix: 

M06 ¼ M01 M12 M23 M34 M45 M56

X ¼ 0

P 1

 ð8Þ

where P ¼ ½ px py pz T . Input the D-H parameters into Eq. (8), we can obtain kinematic equation of the hydraulic manipulator. Then, the transformation equation of the end effector coordinate system relative to the base coordinate system is obtained by further solving: nx ¼  cos h1 cos x6 cos h7 þ sin h1 sin h7

ð10Þ

ny ¼  sin h1 cos x6 cos h7 þ cos h1 sin h7

ð11Þ

nz ¼  sin x6 cos h7

ð12Þ

ox ¼ cos h1 cos x6 sin h7 þ sin h1 cos h7

ð13Þ

oy ¼ sin h1 cos x6 sin h7  cos h1 cos h7

ð14Þ

oz ¼ sin x6 sin h7

ð15Þ

ax ¼ cos h1 sin x6

ð16Þ

ay ¼  sin h1 sin x6

ð17Þ

az ¼ cos x6

ð18Þ

px ¼ cos h1 ðl6 cos x6  l5 cos x4 þ l4 cos x3 þ l3 cos h2 þ l2 Þ

ð19Þ

py ¼ sin h1 ðl6 cos x6  l5 cos x4 þ l4 cos x3 þ l3 cos h2 þ l2 Þ

ð20Þ

pz ¼ l6 sin x6  l5 sin x4 þ l4 sin x3 þ l3 sin h2 þ l1

ð21Þ

Where xi ¼

i P

hi .

j¼2

The matrix R and P can be solved according to the above transformation equation. Given a vector of joint angles hðh1 ;    ; h7 Þ, we can obtain the end effector position vector of the manipulator

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 T P ¼ px ; py ; pz

ð22Þ

and attitude matrix 2

nx X ¼ 4 ny nz

2.4

ox oy oz

3 ax ay 5 az

ð23Þ

Joint Variable Analysis

Different from the manipulator driven by motor, the hydraulic manipulator is driven by hydraulic cylinder, whose joint parameters cannot be given directly, but can be calculated by the stroke of the hydraulic cylinder and the length of the arm structure. Therefore, for hydraulic manipulator, joint parameters need to be analyzed and calculated. In order to calculate joint parameters, we take joint 2 as an example. Joint 2 model diagram and structure diagram are shown in Fig. 5.

Fig. 5. Structure of the 2th joint

According to the geometric relationship, the following equation can be obtained: /2 ¼ arccos

jOM j2 þ jON j2 jMN j2 jAM j þ arcsin 2jOM jjON j jOM j h2 ¼ /2 þ b2 

p 2

ð24Þ ð25Þ

Where jMN j 2 ½h; h þ a. joint range can be obtained: "

jOM j2 þ jON j2 h2 jAM j jOM j2 þ jON j2 ðh þ aÞ2 jAM j ; arc þ arcsin þ arcsin q2 2 arccos 2jOM jjON j 2jOM jjON j jOM j jOM j

#

ð25Þ

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Where, OA, OB, ON, OM, b are known constants, MN is a variable parameter, the value range of u2 is the joint range q2 of the hydraulic manipulator. The relationship between the joint variable h2 and the hydraulic cylinder stroke a is also obtained. Similarly, the range of other joints variables qi and hi of the manipulator can be calculated.

3 Inverse Kinematic The purpose of inverse kinematic is to obtain the trajectory of each joint after determining expected trajectory of the end effector. In order to solve joint parameters, we should determine position vector of end effector firstly. In other words, the inverse motion analysis of the manipulator is to calculate the joint parameters hðh1 ;    ; h7 Þ from the known end effector position vector P. according to Eq. (26)   p px ; py ; pz  f fh1 ; h2 ; h3 ; h4 ; h5 ; h6 ; h7 g ¼ 0

ð26Þ

The obtained hðh1 ;    ; h7 Þ is the solution of the inverse motion calculation of the manipulator. However, in actual working environment on site, it is difficult to set Eq. (26) to be exactly zero. The inverse solution obtained from Eq. (26) may have multiple solutions, and what we need is the optimal solution. We define G(h) as follows: GðhÞ ¼ min

7 X

j hi j

ð27Þ

i¼1

In order to obtain the optimal solution, we use penalty function method: 

Fðx; MÞ ¼ min f ðhÞ þ M  GðhÞ VðhÞ ¼ max f_ ðhÞ

ð28Þ

Where v(h) is the rotational velocity of the revolute joint. M is the penalty function playing the role of “punishment”. The penalty function can first take the value of 1 to calculate the optimal solution x_ of F(x, M). If x_ does not meet the constraint conditions, the value of the penalty function M will be magnified by 10 times and repeated in turn until the solution satisfying the constraint conditions is obtained.

4 Dynamic Analysis 4.1

Lagrangian Dynamics

Dynamic model is derived by Jacobian matrix. Lagrange equation is shown as Eq. (29).

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d dt

@L

! 



@ hi

@L ¼ si @hi

ð29Þ

Where L¼KP

ð30Þ

K and P present the kinetic energy and potential energy of the system, respectively. hðh1 ;    ; h7 Þ presents generalized coordinate system. According Eq. (29), we can obtain simplified formula as follows:

M ðhÞ€h þ H h; h_ þ GðhÞ ¼ s

ð31Þ

Where in Eq. (30), M is a symmetric positive definite matrix 2

M11 6 .. MðqÞ ¼ 4 . M71

3    M17 .. 7 . 5

ð32Þ

   M77

_ presents generalized force vector of Coriolis force and centrifugal force. where, Hðh; hÞ GðhÞ ¼ ½P1    P6 T presents gravity vector matrix. Derived from the Jacobian matrix, we can obtain Eq. (32). R_ 7 ¼ J7 h_  R_ 7 ¼ P_ 7

x7

T

¼



x_ 7

y_ 7

ð33Þ z_ 7

a_ 7

b_ 7

c_ 7



ð34Þ

Equation (33) presents the terminal velocity and angular velocity of the manipulator. Differentiate Eq. (32), we can obtain Eq. (33): dR7 ¼ J7 dh

ð35Þ

dh is virtual joint displacement, dR7 is virtual displacement and virtual angular displacement of the manipulator at the terminal. According to the virtual displacement principle, the sum of the virtual work done by each joint is equal to the virtual work done by the end of manipulator. sT dh ¼ F7T dR7

ð36Þ

Where F7 ¼ ½ F7X F7Y F7Z s7X s7Y s7Z T . F7 is the force and torque of the terminal of manipulator. Input Eq. (34) into Eq. (35):

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sT dh ¼ F7T J7 dh

611

ð37Þ

According Eqs. (29) to (37), we can obtain the equation as follows: M ðqÞ€q þ H ðq; q_ Þ þ GðqÞ ¼ J7T F7

4.2

ð38Þ

ADAMS Simulation

ADAMS software is selected for dynamic simulation in this paper. Firstly, the virtual prototype model of manipulator is established. Then, add revolute pair and driven force on the model. In order to make the simulation more consistent with the actual situation, we add friction at the rotation (Figs. 6 and 10).

Fig. 6. The manipulator model in ADAMS

Figure 7 shows the displacement curves of the end effector of the doublemanipulator rescue robot, which includes three directions. Figures 8 and 9 shows velocity and acceleration curve of the end effector, respectively. In the first 4 s of applying force, the speed of the manipulator increases steadily. It reaches maximum speed at the 4th second. The displacement of the manipulator steadily increases after 4 s, then it turns into decrease. As it shows in Figs. 7, 8 and 9, we can come to the conclusion that the driving force of each hydraulic cylinder is stable. And the torque increases or decreases steadily that is basically the same as the displacement curve during the movement of the manipulator. The above indicates that the hydraulic manipulator has a good force and velocity performance.

Fig. 7. Displacement curve

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Fig. 8. Velocity curve

Fig. 9. Acceleration curve

Fig. 10. Force curve of the end-effector

5 Conclusions After the above theoretical analysis and counter seismic calculation, the following conclusions are obtained: (1) The designed manipulator has 7-DOF, which can simulate the movement of human arm and keep the dynamic stability that proves the rationality of manipulator structure. (2) The D-H method was used to establish the kinematics model of the 7-DOF hydraulic manipulator, and the position matrix of the end-effector was obtained.

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Aiming at the motion planning problem of redundant hydraulic manipulator, the inverse kinematics solution is solved. On the basis of the commonly used methods at present, considering the joint angle limit of the manipulator, the avoidance of singular form and the accuracy of the solution, the inverse kinematics solution based on penalty function method is proposed. (3) Based on the Lagrangian dynamics analysis, the mathematical model of joint torque is derived, and the robot control system can be optimized according to the dynamics parameters, which provides a basis for the closed-loop servo control of hydraulic manipulator in the future. (4) Using the ADAMS software for the dynamic simulation analysis of hydraulic manipulator obtained the joint torque as well as the end-effector of velocity and force curve, from the point of the final result, manipulator parameters meet the use requirement, although there are some error, but will not affect the realization of the kinematics and dynamics characteristics of manipulator.

References 1. Choi, J.: Robust position control of electro-hydrostatic actuator systems with radial basis function neural networks. J. Adv. Mech. Des. Syst. Manuf. 7(2), 257–267 (2013) 2. Nelson, G., Saunders, A., Neville, N., et al.: Petman: a humanoid robot for testing chemical protective clothing. J. Robot. Soc. Jpn. 30(4), 372–377 (2012) 3. Dedonato, M., Dimitrov, V., Du, R.X., et al.: Human-in-the-loop control of a humanoid robot for disaster response: a report from the DARPA robotics challenge trials. J. Field Robot. 32(2), 275–292 (2015) 4. Fallon, M., Kuindersma, S., Karumanchi, S., et al.: An architecture for online affordancebased perception and whole-body planning. J. Field Robot. 32(2), 229–254 (2015) 5. Ding, L.: Key technology analysis of big dog quadruped robot. J. Mech. Eng. 51(7), 1–23 (2015) 6. Wu, W.G.: Research progress of humanoid robots for mobile operation and artificial intelligence. J. Harbin Inst. Technol. 47(7), 1–19 (2015) 7. Kim, Y.B., Ha, J., Kang, H., et al.: Dynamically optimal trajectories for earthmoving excavators. Autom. Constr. 35, 568–578 (2013) 8. Kim, D., Kim, J., Lee, K., et al.: Excavator tele-operation system using a human arm. Autom. Constr. 18(2), 173–182 (2009) 9. Park, J.Y., Chang, P.H.: Vibration control of a telescopic handler using time delay control and commandless input shaping technique. Control Eng. Pract. 12(6), 769–780 (2004) 10. Činkelj, J., Kamnik, R., Čepon, P., et al.: Closed-loop control of hydraulic telescopic handler. Autom. Constr. 19(7), 954–963 (2010) 11. Zhao, Y.N., Gao, F., Hu, Y.: Novel method for six-legged robots turning valves based on force sensing. Mech. Mach. Theor. 133, 64–83 (2019) 12. Wu, G.L., Bai, S.P.: Design and kinematic analysis of a 3-RRR spherical parallel manipulator reconfigured with four–bar linkages. Robot. Comput.-Integr. Manuf. 56, 55–65 (2019) 13. Andrej, C., Olav, E.: Dynamic modelling and force analysis of a knuckle boom crane using screw theory. Mech. Mach. Theor. 133, 179–194 (2019)

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14. Zhang, D.S., Xu, Y.D., Yao, J.T., Zhao, Y.S.: Design of a novel 5-DOF hybrid serial-parallel manipulator and theoretical analysis of its parallel part. Robotics and Computer-Integrated Manufacturing 53, 228–239 (2018) 15. Liu, Q., Ge, W.M., Wang, X.F., Zhang, H.Y.: Dynamics modeling and simulation of constrained flexible load with manipulator operation. 42(3) (2018) 16. Han, Y., Wu, J.H., Liu, C., Xiong, Z.H.: Static model analysis and identification for serial articulated manipulators. Robot. Comput.-Integr. Manuf. 57, 155–165 (2019) 17. Liang, X.C., Wan, Y., Zhang, C.R., Kou, Y.Y.: Design of position feedback system with data fusion technology for large hydraulic manipulator. In: Advances in Mechanical Design, pp. 349–361 (2017) 18. Wan, Y., Kou, Y.Y., Liang, X.C.: Closed-loop inverse kinematic analysis of redundant manipulators with joint limits. Mech. Mach. Sci. 55, 1241–1255 (2018)

Research on Electro-Hydraulic Servo System Based on BP-RBF Neural Network Tao Chen, Wenqun Zhang, and Jianggui Han(&) College of Power Engineering, Naval University of Engineering, Wuhan 430000, Hubei, China [email protected], [email protected], [email protected]

Abstract. Aiming at the accuracy of the severe interference control system commonly used in marine electro-hydraulic servo system, a nonlinear model of the control system is established. In order to control the excess force, a composite PID controller with BP neuron algorithm is proposed. The integration and setting of parameters were carried out by neurons. The tracking ability of RBF neurons was used to construct a PID composite tracker, and simulation experiments were carried out to show that the relevant parameters were self-corrected. The controller has high control stability and fast speed. The other characteristics significantly suppress the excess force in the electro-hydraulic servo system, thus effectively optimizing the stability of the entire electro-hydraulic servo control system against external load force interference. Keywords: Electro-hydraulic servo system PID controller  BP neural network

 Redundant force control 

1 Introduction The rudder electromechanical servo system has the characteristics of high precision, high speed and high power. It is widely used in the marine and aerospace sectors. One of the applications is the electro-hydraulic servo cooperative control system. Suppressing excess power is a difficult problem between them. There are many ways to solve this problem, such as the single pendulum load suppression method with single pendulum load drive frequency and load frequency [1–3], the dual valve parallel compensation scheme to meet the double ten index of the loading system [4, 5], or the double differential structure decoupling. Compensation control significantly reduces excess force [6]. There is also the problem of solving the problem that the nonlinear excess force is too large by the composite controller, which succeeds in reducing the original ±22N to about ±4N [7]. In this paper on the basis of establishing the nonlinear control problem of composite controller PID control, the idea of negative feedback correction is adopted. The PID composite control module is constructed by BP-RBF neural network unit to complete the optimization function of the electro-hydraulic servo system [8]. The simulation data shows that the nonlinear model monitored by the PID module shows good monitoring accuracy and successfully produces less than 10% of the given input, thus completing the effective suppression of the excess force in the electro-hydraulic © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 615–622, 2020. https://doi.org/10.1007/978-981-32-9941-2_50

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servo system. The suppression of the excess force of the servo system provides new help and method.

2 Mathematical Modeling of Electro-Hydraulic Servo System The rudder electromechanical servo system is mainly composed of oil source, filter (sparse filter, fine filter), overflow valve, electro-hydraulic servo valve and oil cylinder. According to the needs of experimental simulation, therefore, the system structure is properly idealized, and only the mathematical model of the key parts is considered. Figure 1 is a schematic diagram of the principle of the rudder electromechanical servo system.

Fig. 1. Schematic diagram of electro-hydraulic system

In The flow equation for the nonlinearization of the electro-hydraulic servo valve is shown in the following formula. 8 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pS  pL > > ; Xv  0 xx > C < v v q QL ¼ Kq ðpL ÞXv ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > pL  pS > > ; Xv \0 C xx : v v q

ð1Þ

In the formula, the load flow is QL , the flow gain is kq , the load pressure drop is pL , the spool displacement is xv , the flow coefficient is Cv , the area gradient is x, the oil supply pressure is PS , and the liquid density is q. The total flow of the hydraulic cylinder is composed of the flow required by the propulsion cylinder piston, the total compression flow, and the total leakage flow. The continuity equation of the total flow of the hydraulic cylinder:

Research on Electro-Hydraulic Servo System Based on BP-RBF Neural Network

QL ¼ Ap

dxt Vt dpL þ þ Ct pL dt 4be dt

617

ð2Þ

In the formula, the effective area of the piston is AP , the displacement of the piston is xt , the total volume of the two oil chambers is Vt , the comprehensive elastic modulus of the system is be , and the total leakage coefficient of the hydraulic cylinder is Ct . The force balance equation is: Ap pL ¼ m

d 2 xP dxP þ FL þ kxP þ Bp dt2 dt

FL ¼ kP ðxP  x0 Þ

ð3Þ ð4Þ

Among them, the total mass of the piston and the load is m, the viscous damping coefficient of the piston and the load is BP , the spring stiffness of the load is k, and any external load force acting on the piston is FL . The second-order part is mainly composed of the leakage flow, the quality of the valve core, and the compressibility of the liquid. The natural frequency of the hydraulic pressure is large, so there is no influence on the dynamic performance of the valve. On the other hand, the open-loop gain coefficient of the pressure feedback loop is the maximum. It is also much smaller than the minimum value of the open-loop gain coefficient of the force feedback loop, so it can be ignored, so its transfer function is: GðsÞ ¼

Ksv 2 SðxS2 sv

þ

2nsv xsv

S þ 1Þ

ð5Þ

In this formula, the speed amplification factor is Ksv , the natural frequency of the second-order factor of the closed-loop system is xsv , the damping ratio is nsv .

3 Basic Principles of BP and RBF Neural Network The error back propagation algorithm relies on the idea of least squares in mathematics. Through the gradient search scheme, the difference between the true value of the control system and the ideal value is averaged, and the mean square is minimized. The input value of the BP neural network system passes through the input segment, the recessive segment and the output segment at the same time, and the neuron mesh of each segment only controls the characteristics of the next segment. When the expected output of the output segment does not conform to the actual output error, then the reverse propagation is performed, and the correlation weight and the closed value of each layer of neurons are changed, so that the error function is reduced to the negative gradient side, thereby achieving the true output value and The mean square between the ideal output values is the smallest. The radial basis function, the neural network contains a single recessive layer of three-layer pre-feedback network, is a partially approaching neural network. The characteristic of the RBF network is that only a few connection weight segments in a small area of the input area determine the output of

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the network, and finally the local network has the advantages of fast learning speed and high precision.

4 Design of PID Controller Based on BP-RBF Identification In order to obtain a high-speed, high-precision output load force for the load control system, a series of optimization measures are needed to overcome the excess force. In order to make the PID controller complete excellent and precise control functions, this paper uses BP neural network to integrate and set related parameters for the PID controller to achieve three parameters (xd , xi xp ) and dynamic self-stability. The role of the RBF neural network is to identify the state of the monitored person, thereby inputting its state to the control system to optimize the accuracy of the control system. Finally, after RBF neural network identification is used to assist the optimization of the entire PID controller system, the control stability and accuracy of the system are significantly enhanced [6]. The abbreviated algorithm of the PID controller control system based on BP neural network identification based on RBF neural network is divided into the following steps: ① Set the basic structure of the BP neural network, that is, set the number of input segment points N and the number of recessive segment nodes R, and set the initial segment of each segment weighting coefficient y1ij ð0Þ, Select the learning efficiency k and set the inertia coefficient b to get x ¼ 1. ② Set the input segment node in the RBF network a, the number of recessive segments C, and set the vector of the recessive segment dj ð0Þ, the vector initial value of the base band cj ð0Þ, the weighting coefficient yj ð0Þ, the learning efficiency k1 and the inertia coefficient b1 to get x ¼ 1. ③ Extract the parameter to get rinðxÞ and youtðxÞ, the calculated instantaneous error is eðxÞ ¼ rinðxÞ  youtðxÞ. ④ According to the formula, the output of each segment of the BP neural network is obtained. The result of the BP neural network output segment is the relevant basic parameters (xd , xi , xp ) of the PID controller. Calculate the result value of its PID controller is uðxÞ, at the same time, uðxÞ is output to the RBF recognition neural network and the electro-hydraulic control system, and the output value youtðx þ 1Þ of the control system is calculated. ⑤ According to the formula, the value of each segment of the neurons in the RBF recognition neural network is ymoutðx þ 1Þ. ⑥ The gradient reduction method after optimization is used to adjust the weighting coefficient and learning efficiency of the neural network. ⑦

Fig. 2. PID block Diagram

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Network learning is adopted for the control system, and the weighting coefficients y1ij ðxÞ and y2ij ðxÞ are optimized in real time, thereby completing the self-optimization function of the PID controller related data. Last reset, loop to ① (Fig. 2).

5 Simulation Analysis The composition of the RBF neural network is 3-6-1, and the BP is 3-4-3. At the same time, the given values are sum, and then the ideal curve of the comparison is compared with the theoretical curve. Figure 3 is a given three output curves. Comparing the nonlinear output curve with the linear output curve, it can be seen that when the system is at low frequency, the system is found to have a good tracking and monitoring function; at the same time, the comparison curve of Fig. 3 can be found that the nonlinear curve has a large difference from the linear curve. The change of the nonlinear curve is more stable, and the optimization of the theoretical output curve is good. In order to compare the optimization results of the electro-hydraulic control system with the non-linear control algorithm assisted by the composite controller PID, as shown in Fig. 4, the image of the PID module compared with the general electrohydraulic servo system is obtained.

Fig. 3. Nonlinear, theoretical, and linear output

According to the comparison output in the figure, with the help of the composite module PID, the optimized excess force is 1.5N, while the general linear electrohydraulic servo system has a peak force of 12N, which is found to be negative for the

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Fig. 4. Excess force simulation curve

excess force of the PID module. The feedback is higher than 87.5%, which has a more significant optimization effect.

6 Experimental Verification The experimental setup includes a loading test rig, a force object, an electrohydraulic servo system, a pump source, and corresponding mechanical and electrical connections [9]. The test oil source pressure is 17 MPa, and the test environment is room temperature. The motion track of the stressed object is SðtÞ ¼ 4 sin pt, and load instruction is 0N. When the electro-hydraulic system inputs a sinusoidal signal with a amplitude of 0.08 m and a frequency of 0.5 Hz, the results of the excess force experiment using the ordinary PID control method and the BP-RBF-based composite control method are shown in Figs. 5 and 6. It can be seen from the experimental results that the excess force is obviously reduced after the introduction of the composite controller, and we also found that when the system turns, the excess force will be jagged [10].

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Fig. 5. The experimental curve without BP-RBF

Fig. 6. The experimental curve with BP-RBF

7 Conclusions In this paper, the ship rudder electro-hydraulic servo system is taken as the research subject, and a high-precision nonlinear model is constructed. According to the experimental results, it can be seen that the system works in the nonlinear low

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frequency band and the characteristics in the linear low frequency band are basically the same, but high. The tracking effect during band operation is more accurate. When the sinusoidal signal is input through the BP-RBP composite PID controller, the actual error of the system with the general controller is small, and the control advantage with high precision is provided, indicating the effectiveness of the control system, and further on the ship rudder electro-hydraulic system. The simulation and characterization of the simulation have the meaning of throwing bricks.

References 1. Zhen, L.: Research on the method of suppressing the excess force of single pendulum load electro-hydraulic servo dynamic loading system. Lanzhou University of Technology (2013) 2. Yang, H., Hui, W., Yi, Z., Yang, P.: Excessive force analysis of electro-hydraulic servo loading system. Hydraulics Pneumatics 36(09), 55–58 (2016) 3. Wu, J.: Nonlinear dynamic system identification method based on BP neural network. In: Proceedings of the 12th Annual Conference of Control and Application of Chinese Aeronautical Society, China Aviation Society Automatic Control Professional Branch, p. 6. Session: China Aviation Society (2006) 4. Xue, J.: Design of PLC-based electro hydraulic servo position closed loop system. In: Proceedings of 2016 2nd International Conference on Materials Engineering and Information Technology Applications (MEITA 2016), International Society for Information and Engineering: International Society for Computer Science and Electronic Technology (Computer Science and Electronic Technology International Society), p. 5 (2016) 5. Ma, C.: Simulation studies of CMAC-PID combined control for electro-hydraulic position servo system. In: Proceedings of 2017 2nd International Conference on Computer, Mechatronics and Electronic Engineering (CMEE 2017), Advanced Science and Industry Research Center: Science and Engineering Research Center, p. 5 (2017) 6. Liu, X.: Research on Residual Force Compensation and Digital Control Strategy of Electrohydraulic Servo System. Beijing Jiaotong University (2008) 7. Cheng, X., Jin, X., Zhang, M., Zheng, B.: Study on the excess force of passive electrohydraulic loading system. Mach. Des. Manuf (09), 71–75 (2018) 8. Zhao, S., Sun, S., Li, G.: A structural compensation method for the excess force of electrohydraulic load simulator. J. Henan Univ. Sci. Technol.: Nat. Sci. Edn. 36(04), 23–26+31+5 (2015) 9. Jin, Y., Yun, N.: Research on the mechanism of excessive force generation and its elimination method in passive loading system. Helicopter Technol. (01), 18–22 (2003) 10. Yang, F., Liu, C., Hao, Y., Ma, X.: Residual force suppression based on composite control. Mach. Tool Hydraulics 43(19), 82–85+90 (2015)

Collision Simulation of GQ70 Light Oil Tank Car at the Level Crossing Maopeng Tian, Ronghua Li, Xiujuan Zhang(&), and Miao Jin School of Mechanical Engineering, Dalian Jiaotong University, Dalian 116028, China [email protected], [email protected], [email protected], [email protected]

Abstract. The simulation and analysis of the collision process between GQ70 light oil tank car and truck at the level crossing are carried out by using the theory of explicit dynamics. The results are obtained which are the equivalent stress values of the tank, the vertical uplift and transverse displacement of each wheel set. Meanwhile, it is studied that is the influence of two collision parameters (mass and speed) on tank strength. It is concluded that the speed and mass of the collision vary with the intensity of the collision in the primary curve and the quadratic curve, respectively. The effect of the former on the collision performance is higher than that of the latter. The research in this paper provides a certain reference for the optimization design of tank car. Keywords: Railway tank car  Collision mass Collision performance  Explicit dynamics

 Collision speed 

1 Introduction Railway tank car is one of the main types of railway freight traffic, which is widely used and plays an important role in railway freight traffic. When the railway tank car passes through the level crossing and collides with the passing vehicle, it is easy to cause the derailment of the tank car, the damage of the tank body and so on. Therefore, it is very important to study the side crash-worthiness of railway tank car. Many scholars have simulated and analyzed the collision process of rail vehicles. Among them, Yang et al. [1], used the method of multi-rigid-body dynamics to simulate the rail vehicle collision. Lu [2] has studied the collision among different groups of trains under nonlinear conditions by using the method of multi-body dynamics, and derived the calculation formula of the collision energy allocation of the train. Dalapati et al. [3], proposed an agent-based solution to study the real-time collision process in train operation. Lu et al. [4], established a vertical vehicle collision model considering the track model by using the method of multi-body dynamics. Lei et al. [5], used the method of explicit dynamics to simulate and analyze train collision behavior. Deng [6] used the method of explicit dynamics to study the collision performance of a G70 modified light oil tank car at different speeds in front-line operation. Wang et al. [7], used the method of one-dimensional energy allocation and the method of threedimensional vehicle collision simulation to study the influence of empty travel of train © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 623–633, 2020. https://doi.org/10.1007/978-981-32-9941-2_51

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energy absorption system on train crash performance. Wang et al. [8], used the method of finite element and multi-body dynamics to simulate the collision resistance of the track train, and optimized energy absorbing and climbing device for the train. Zhou et al. [9], used the method of finite element and multi-rigid body dynamics to simulate the collision scene of rail vehicle and studied the derailment risk of the train. The above researches mainly focus on the straight-line frontal collision of rail vehicles, but there is little research on the side collision of vehicles at the level crossing. Compared with the normal collision, the railway tank car is more prone to derailment and other safety accidents under side collision. In this paper, the theory of explicit dynamics is used to simulate the collision accident of GQ70 light oil tank car at the level crossing under the condition of empty vehicle. The maximum equivalent stresses of the tank during the collision are obtained. The influence of truck mass and collision speed on the maximum equivalent stress of the tank is also analyzed. The research result of this paper provides a certain reference for the optimization design of the tank car.

2 Basic Theory of Explicit Dynamics Compared with implicit algorithm, the best advantage of the explicit algorithm is that the calculation has good stability. For the Lagrangian formulations currently available in the explicit dynamics system and the mesh moves and distorts with the material variation. The conservation of mass is automatically satisfied. The density at any time can be determined from the current volume of the zone and its initial mass, and can be described as: q¼

p0 V0 m ¼ V V

ð1Þ

Where q is the element density at any time; q0 is element initial density; V0 is element initial volume; m is element mass; and V is element volume at any time. Represented by the following formula, the partial differential equations express the relation between the acceleration and the stress tensor rij . @rxx @rxy @rxz þ þ @x @y @z @ryx @ryy @ryz € y ¼ by þ þ q þ @x @y @z @rzx @rzy @rzz € z ¼ bz þ þ þ q @x @y @z € ¼ bx þ q

ð2Þ

Where q is element density at any time; €x; €y; €z are acceleration of elements in x, y and z directions, respectively; rij is stress tensor.

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3 Finite Element Analysis 3.1

Finite Element Model

The location of light oil tank car is uncertain when its collision is happened at level crossing. But the location is mainly divided into two kinds: one is the direct collision between the truck and the middle part of the tank, the other is the collision between the truck and the tractor frame of the tank car. In this paper, two kinds of collision models of GQ70 light oil tank car and truck at the level crossing are established by using CREO software as shown in Fig. 1. And the finite element simulation is carried out with ANSYS/Explicit Dynamics module. Where the tank car runs in a straight line at 20 km/h speed in the X direction. The truck moves in a straight line along the Z direction at the same speed and crashes into the middle part of the tank car and the tractor frame of the tank car, respectively. The total weight of GQ70 light oil tank car is 23.6t. Its material is Q345A, its density is 7850 kg/m3, its elastic modulus is 206GPa, its Poisson’s ratio is 0.28, and its yield limit is 345 MPa. When the constraints are established, the ground and rail are fixed and the gravity acceleration is added to the whole system.

a) Collision in the middle part of tank car

b) Collision in the tractor frame Fig. 1. Collision of tank car at the level crossing

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Finite Element Analysis Results

Equivalent stress σ/MPa

3.2.1 Results of Collision in the Middle Part of Tank Car When the middle part of GQ70 light oil tank car is impacted by the side of 8t truck, its maximum stress variation is shown in Fig. 2. The collision time is 0.2 s and the maximum stress occurs at the 0.006 s. The equivalent stress cloud diagram of the tank is shown in Fig. 3. The value of the maximum equivalent stress is 344.54 MPa, which has reached the yield limit of the tank material. Subsequently, because of collision and separation between the tank car and the truck, the equivalent stress value decreases gradually, and its average value is approximately 100 MPa. 400 300 200 100 0 0

0.05

0.1 Time t/s

0.15

0.2

Fig. 2. Equivalent stress curve of tank

Fig. 3. Equivalent stress contour of tank at maximum stress time

During the collision process, a large vertical lift and lateral displacement occurred in the tank car. The four wheel sets are calibrated along the motion direction of the tank car as Wheel sets A, B, C, and D, where Wheel sets A and B are the wheel sets on the collided side as shown in Fig. 4. Figure 5 shows the curves of maximum vertical uplift over time for each wheel set. It can be seen that the vertical uplifts of Wheel sets A and B increase linearly within the time of 0.2 s, and the maximum vertical uplift reaches 357.4 mm. Meanwhile, the vertical lifts of Wheel sets C and D are smaller than those of Wheel sets A and B. The tank car has a obvious roll-over trend. Figure 6 illustrates

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the time-dependent curves of the transverse displacement of four wheel sets. The four wheel sets all have the large lateral displacements within the time of 0.2 s, and the maximum lateral displacement is up to 178.28 mm.

Vertical uplift d/mm

Fig. 4. Diagram of wheel sets

400 350 300 250 200 150 100 50 0 -50

A

0

0.05

B

0.1

C

D

0.15

0.2

Time t/s

Transverse displacement d/mm

Fig. 5. Vertical uplift of four wheel sets

200 180 160 140 120 100 80 60 40 20 0 -20

A

0

0.05

B

0.1

C

0.15

D

0.2

Time t/mm

Fig. 6. Transverse displacement of four wheel sets

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Equivalent stress σ/MPa

3.2.2 Collision Results of Tractor Frame of Tank Car When the tractor frame of GQ70 light oil tank car is collided by the side of 8t heavy truck, the maximum equivalent stress changes are shown in Fig. 7. It can be seen that the collision time is 0.2 s and the equivalent stress curve reaches the maximum equivalent stress at 0.004 s. Figure 8 shows the equivalent stress cloud of the tank at this time, and the maximum equivalent stress is 193.84 MPa. Subsequently, there is a collision and separation between the tanker and the truck. However, due to the coupling between the tank and the tractor frame, the maximum equivalent stress value of the tank is always in a large vibration. In this paper, it is only considered the maximum equivalent stress of the tank at the moment of collision, so the maximum equivalent stress for the first collision is taken as the research object.

300 250 200 150 100 50 0 0

0.05

0.1

0.15

0.2

Time t/s

Fig. 7. Equivalent stress curve of tank

Fig. 8. Stress contour of tank at maximum stress time

During the collision process, the tank car also has a large vertical lift and lateral displacement. Figure 9 shows the time-dependent curves of the maximum vertical uplift for each wheel set. It can be seen that the maximum vertical uplift occurs in the Wheel set B with the value of 265.32 mm. Figure 10 shows the time-dependent curves of the transverse displacement of each wheel set. Wheel sets B and D have the same trend of transverse displacement and the values of those are always greater than those of wheel sets A and C. And the maximum value of transverse displacement is

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161.01 mm. The simulation results show that serious derailment will still occur when 8t truck crashes into the tractor frame.

Vertical uplift d/mm

300

A

B

C

D

250 200 150 100 50 0 -50

0

0.05

0.1

0.15

0.2

Time t/s

Transverse displacement d/mm

Fig. 9. Vertical uplift of wheel sets

200 180 160 140 120 100 80 60 40 20 0 -20 0

A

0.05

B

0.1

C

0.15

D

0.2

Time t/s

Fig. 10. Transverse displacement of wheel sets

4 Effect of Design Parameters on the Collision Performance When the truck crashes into the tank car, the mass and collision speed of the truck have a great effect on the equivalent stress of the tank. Taking the truck with the collision speed of 20 km/h as an example, the truck mass is set to be 2t, 3t, 4t, 5t, 6t, 7t and 8t, respectively. The influence of truck mass on the equivalent stress of tank is obtained by means of collision simulation analysis of tank car. In addition, truck with the weight of 8t is also take as an example, the collision speeds are set at to be 10 km/h, 20 km/h, 30 km/h, 40 km/h, 50 km/h, 60 km/h and 70 km/h, respectively. The influence of collision speed on the equivalent stress of tank is obtained by means of collision simulation analysis of tank car.

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Collision in the Middle Part

4.1.1 Truck Mass When the truck crashes into the middle part of the tank car at the speed of 20 km/h, the maximum equivalent stress of the tank caused by the truck of different mass is shown in Table 1. It can be seen that the maximum equivalent stress of the tank is 344.54 MPa when the truck mass is 8t. It is close to the yield limit of the tank material, which indicates that the plastic deformation of the tank has begun to occur during the lowspeed collision of the medium-sized truck. Therefore, the truck mass is an important factor for the collision performance of the tank car. In addition, the maximum equivalent stress of the tank increases with the increase of truck mass, and the variation curve is approximate to the quadratic function. In this paper, the curve fitting module of MATLAB software is used to fit the data with quadratic polynomial. The fitting equation can be written are as: r ¼ 1:763m2 þ 42:43m þ 118:1

ð3Þ

Where r is maximum equivalent stress of tank (MPa) and m is truck mass(t), m 2 ð2; 8Þ.

Table 1. The maximum equivalent stresses of tank caused by different truck masses Truck mass m/(t) Maximum equivalent stress of tank r/(MPa) 2 202.78 3 216.33 4 261.79 5 290.97 6 311.82 7 325.79 8 344.54

4.1.2 Collision Speed When the truck with the weight of 8t crashes into the middle part of the tank car, the maximum equivalent stress of the tank caused by the truck at different speeds is shown in Table 2. It can be seen that the maximum equivalent stress of the tank will exceed the yield limit of the tank material when the truck speed exceeds 20 km/h. It indicates that the plastic deformation of the tank has begun to occur during the low-speed collision of the medium-sized truck. Therefore, the impact speed is an important factor that affects the collision performance of the tank car. In addition, the maximum equivalent stress of the tank increases with the increase of collision speed, and the variation curve is approximate to the linear function. The fitting results can be expressed as:

Collision Simulation of GQ70 Light Oil Tank Car at the Level Crossing

r ¼ 13:94v þ 61:57

631

ð4Þ

Where r is maximum equivalent stress of tank (MPa) and v is the collision speed of truck (km/h), v 2 ð10; 70Þ. Table 2. The maximum equivalent stresses of tank caused by different collision speeds Truck speed v/(km/h) Maximum equivalent stress of tank r/(MPa) 10 208.23 20 344.54 30 470.4 40 610.13 50 753.53 60 899.9 70 1043.3

4.2

Collision of Tractor Frame

4.2.1 Truck Mass When the truck crashes into tractor frame of tank car at the speed of 20 km/h, the maximum equivalent stress values of tanks caused by trucks of different mass are shown in Table 3. It can be seen that the maximum equivalent stress of the tank is 193.84 MPa, when the truck mass is 8t. At this time, the yield limit of the tank is not reached, indicating that the tractor frame has a certain protective effect on the tank. In addition, the maximum equivalent stress of the tank increases with the increase of truck mass, and the change curve is approximate to the quadratic function. The quadratic polynomial is expressed as: r ¼ 2:638m2 þ 43:23m þ 15:35

ð5Þ

Where r is maximum equivalent stress of tank (MPa) and m is truck mass(t), m 2 ð2; 8Þ. Table 3. The maximum equivalent stresses of tank caused by different truck masses Truck mass m/(t) Maximum equivalent stress of tank r/(MPa) 2 89.268 3 122.99 4 149.19 5 164.35 6 177.38 7 187.92 8 193.84

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4.2.2 Collision Speed When the truck with the weight of 8t crashes into the tractor frame of the tank car, the maximum equivalent stress value of the tank caused by the truck at different speeds is shown in Table 4. It can be seen that the maximum equivalent stress of the tank body is 409.36 MPa when the truck speed is 40 km/h. At this time, the material yield limit has been exceeded, indicating that plastic deformation has taken place in the tank during the medium-speed collision of the medium-sized truck. Therefore, the collision speed is an important factor affecting the collision performance of the tank car. In addition, the maximum equivalent stress of the tank increases with the increase of collision speed, and the variation curve is approximate to the primary function. The primary polynomial is written as: r ¼ 10:31v  4:593

ð6Þ

Where r is maximum equivalent stress of tank(MPa) and v is the collision speed of truck (km/h), v 2 ð10; 70Þ.

Table 4. The maximum equivalent stresses of tank caused by different collision speeds Truck speed v/(km/h) Maximum equivalent stress of tank r/(MPa) 10 102.38 20 193.48 30 307.2 40 409.36 50 511.6 60 613.89 70 715.99

5 Conclusions In this paper, the simulation and analysis of the collision process between GQ70 light oil tank car and truck with different masses and collision speeds at the level crossing are carried out by using the theory of explicit dynamics. The conclusions have been reached as follows: (1) When the truck with the weight of 8t crashes into the middle part of the tank car at the speed of 20 km/h, the maximum equivalent stress value is 344.54 MPa, which has reached the yield limit of the tank material. And the plastic deformation of the tank will begin. The maximum vertical lift of each wheel set is 357.4 mm and the maximum transverse displacement is 178.28 mm. Derailment has occurred in tank car. (2) When the truck with the weight of 8t crashes into the tractor frame of the tank car at the speed of 20 km/h, the maximum equivalent stress value is 193.84 MPa, the maximum vertical uplift is 265.32 mm, and the maximum transverse

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displacement is 161.01 mm. under both operating conditions. Derailment has also occurred in tank car. (3) The effect of collision mass on the maximum equivalent stress of the tank is accorded with the law of quadratic polynomial. The effect of collision speed on the maximum equivalent stress of tank is accorded with the law of primary polynomial. It shows that the impact of collision speed on the tank car is higher than the collision mass. Therefore, speed limit of tank and truck is very important.

References 1. Yang, L.J., Zhang, C., Zhou, H.C., et al.: Impact factors on city tram derailment during collision. Tongji Daxue Xuebao/J. Tongji Univ. 46(2), 247–252, 259 (2018). (in Chinese) 2. Lu, G.: Energy absorption requirement for crashworthy vehicles. Proc. Inst. Mech. Eng. Part F: J. Rail Rapid Trans. 216(1), 31–39 (2002). (in Chinese) 3. Dalapati, P., Padhy, A., Mishra, B., et al.: Real-time collision handling in railway transport network: an agent-based modeling and simulation approach. Transp. Lett. 223, 1–11 (2017) 4. Lu, Y.J., Xiao, S.N., Zhu, T., et al.: Construction of dynamic coupling model of longitudinal-vertical train crash. J. China Railway Soc. 36(12), 6–13 (2014). (in Chinese) 5. Lei, C., Xiao, S.N., Luo, S.H. Research on the energy-absorbing theory of high speed train energy-absorbing component based on the explicit finite element. Railway Locomotive Car (2012). (in Chinese) 6. Deng, H.: Crashworthiness Research of G70 Retrofit Light Oil Rail Tanker. Central South University (2014). (in Chinese) 7. Wang, L., Li, B.H., Li, C.L., Zhang, Y.L.: Influence of collision energy absorption in noacted stroke of train crash energy absorption system. J. Dalian Jiaotong Univ. 02, 16–19 (2019). (in Chinese) 8. Wang, W.B., Kang, K., Zhao, H.L: Joint simulation of crashworthy train set based on finite element and multi-body dynamic. J. Tongji Univ. (Nat. Sci.) 39(10), 1552–1556 (2011). (in Chinese) 9. Zhou, H.C., Zhan, J., Zhang, C., et al.: Simulation of the city tram collision at the level crossing. J. Mech. Eng. 54(8), 35–40 (2018). (in Chinese) 10. Zheng, Y., Wang, K., Xi, C.P., et al.: Investigation of bearing fault diagnosis based on explicit dynamics analysis in ANSYS/LS-DYNA. Int. J. Plant Eng. Manag. 20(3), 156–169 (2015). (in Chinese) 11. Xiong, L.F., Hu F.J.: ANSYS LS-DYNA nonlinear dynamic analysis method and engineering application. China Railway Publishing House (2015). (in Chinese)

Reason Study of Collision Between Valves and Piston of Diesel Engine Valve Train Dameng Wang, Xiujuan Zhang(&), Deyu Yue, and Weipeng Fan College of Mechanical Engineering, Dalian Jiaotong University, Dalian 116028, China [email protected], [email protected], [email protected], [email protected]

Abstract. Thermal-mechanical coupled finite element simulation of valve train for 265 diesel engine is carried out by using CREO and ANSYS softwares. The temperature field, thermal stress, thermal strain and thermal deformation re obtained for the system. Meanwhile, the cause of the collision between the valves and the piston is also got. The results of this paper will provide a certain theoretical basis for the further optimization design of valve system of the diesel engine. Keywords: Valve train  Thermal-mechanical coupled Finite element simulation  Collision reason



1 Introduction Diesel engine is an important power supply device in rail transition, and the reasonable clearance between components of diesel engine is an important index to ensure the normal operation of diesel engine. At present, many scholars have conducted in-depth research on the clearance between the piston and the valves. Chen [1] used the mathematical function to calculate the clearance between the valve and piston of the 4160A diesel engine. Liu et al. [2]. Constructed a new algorithm for the extreme motion clearance between the valve and the piston, and edited the analysis program of valve piston clearance using Excel software. By establishing a mathematical model, Shi et al. [3]. Calculated the thermal expansion and dimension chain tolerance of piston and valve, so as to derive the minimum clearance between piston and valve. Li [4] used the method of changing the cam phase to analyze the minimum clearance between the piston and the valve. Wang et al. [5]. used UG software to couple and assemble the single cylinder and obtained the minimum clearance between the piston and valve. Wang et al. [6–8] used Pro/E software to establish a multi-body kinematics simulation model of valve and piston motion system, and measured the real-time motion clearance between the valve and the piston. Zhang [9] simulated the kinematics of the whole valve train and got the reasonable clearance between the piston and the valve. In the above literature, the clearance between valve and piston is analyzed without considering the thermal effect of diesel engine. However, there is no relevant report on the clearance change caused by the deformation of piston and valve due to the thermal effect. In this paper, the 265 diesel engine is taken as an example to perform the related © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 634–646, 2020. https://doi.org/10.1007/978-981-32-9941-2_52

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analysis. The whole valve train is systematically modeled by CREO and ANSYS software. The interaction between the thermal expansion of the fittings is fully considered. The thermal-mechanical coupled analysis of the valve train is carried out to obtain the temperature field, strain, stress and thermal deformation of the whole valve train. Thus, the reason of collision between the piston and the valve is derived. The research performed in this paper provides a certain theoretical basis for the further study of diesel engine valve train.

2 Basis of Theoretical Analysis The theory of heat transfer defines that the temperature of a substance varies with time s and space. The expression is as follows: t ¼ f ðx; y; z; sÞ

ð1Þ

where x, y and z represent the space Cartesian coordinates, respectively; and s represents time. As the basic theory of thermal theory, Fourier law can be expressed as: q ¼ kgradt ¼ k

@t @n

ð2Þ

where q represents the heat flux density with the unit of W/m2; k represents the thermal conductivity of the material with the unit of W/m °C; @t=@n represents the derivative of the temperature in the n direction; the minus sign represents that the direction of Q is consistent with the direction of T reduction. The radiation capacity of an object is related to temperature, and the radiation and absorption capacity of different objects are different under the same temperature condition. An ideal object is Imagined as a black body that absorbs all of the heat radiation energy applied to its surface. The thermal radiation heat emitted by the black body in unit time is revealed by Stefan-Boltzmann law, and can be expressed as: W ¼ ArT 4

ð3Þ

where A is the radiation surface area; r is the Stefan-Boltzmann constant and its value is 5.67  10−8W/(m2 K4); T is the thermal-mechanical coupled temperature of the black body. The thermal radiation heat of the actual object is modified by the empirical formula of Stefan-Boltzmann law and can be written as: W ¼ eArT 4

ð4Þ

where e is the emissivity of the object, e  1. In the light of classical thermal-mechanical coupling analysis, the governing equation of three-dimensional temperature field is derived by using finite element

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method. The basic finite element solution equations of this kind of problems can be obtained as: C U_ þ KU ¼ P

ð5Þ

This is a set of linear ordinary differential equations with time as independent variables. C is the heat capacity matrix, K is the heat conduction matrix, C and K are symmetric positive definite matrices; P is the temperature load array; U is the node temperature array; U_ is the derivative matrix of node temperature to time. The elements of the matrix C, K, P are integrated by the corresponding matrix elements of the unit. That is: Kij ¼

X Z

@Ni @Nj @Ni @Nj @Ni @Nj þ ky þ kz ÞdX ðkx @x @x @y @y @z @z Xe Z X þ hNi Nj dC e e

ð6Þ

Ce3

Cij ¼ Pi ¼

X Z e

Xe

X Z

qQNi dX þ

e

Xe

X Z e

ð7Þ

pcNi Nj dC

Ce2

qNi dC þ

X Z e

Ce3

hUa Ni dC

ð8Þ

The above formula has discretized the partial differential equation problem in time domain and space domain into the initial value problem of N node temperature Ui(t) ordinary differential equation in space domain. The core of solving temperature field problem by finite element software is to solve ordinary differential Eq. (5) by corresponding numerical method.

3 Thermal-Mechanical Coupled Finite Element Analysis of Valve Train 3.1

Model Establishment

In this paper, the thermal-mechanical coupled finite element analysis of the valve train of 265 diesel engine is carried out by using CREO3.0 and ANSYS Workbench software. The finite element analysis model is shown in Fig. 1. The material properties of the key parts in the model are shown in Table 1. In the finite element analysis, in order to improve the analysis accuracy, the model mesh is divided by the curvature control function, which generates 7315253 units and 10521715 nodes. The temperature points of the piston, valve and cylinder liner are shown in Figs. 2, 3 and 4. The specific values of the temperatures are shown in Tables 2, 3 and 4. The thermal-mechanical coupled analysis of the valve train carried out in this paper includes two kinds of transfer modes which are heat transfer and heat radiation. The external temperature of the system is 40 °C. The valve train is cooled using the water cooling. The water temperature is 72 °C after cooling. The system is set to be the exhaust stroke.

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Fig. 1. Valve train of 265 diesel engine Table 1. Material properties of each part Components

Exhaust valve

Intake valve

Piston skirt Piston top

Cam

Material

Nickel alloy

4Cr9Si2

42CrMoA

HT250

Density q/(g/cm3) Elastic modulus E/(GPa) Poisson’s ratio Thermal conductivity CAL/(W/(m.K)) Thermal expansion coefficient CTE/ ((lm/m)/°C)

8.22

7.70

Aluminum alloyLD11 2.70

7.83

7.8

214

206

72

207

130

0.3 12

0.3 16.

0.33 170

0.28 42

0.27 50

(21–93 °C) 12.0 (20–500 °C) 22.0 (21–315 °C) (21–538 °C) (21–760 °C)

11.0 12.9 13.5 14.1

(20–300 °C) 12.1 (300–400 °C) (400–500 °C) (500–600 °C)

12.9 14.0 14.9 16.0

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(a) Exhaust valve

(b) Intake valve

Fig. 2. Temperature measurement points distribution of Intake and exhaust valves

Fig. 3. Temperature measurement points distribution of Piston

Fig. 4. Temperature measurement points distribution of Cylinder sleeve Table 2. Measuring points temperature values of Intake and exhaust valve Measuring point 1 2 3 4 5 6 Exhaust valve Q(°C) 399 408 399 363 \ \ Intake valve Q(°C) 537 543 541 \ 543 536

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Table 3. Measuring points temperature values of Piston Measuring point Piston Q(°C) Measuring point Piston Q(°C) Measuring point Piston Q(°C)

1 131 10 319 19 180

2 158 11 316 20 164

3 154 12 320 21 308

4 164 13 313 22 260

5 160 14 312 23 257

6 183 15 311 24 259

7 257 16 419 25 253

8 9 283 366 17 18 330 282 26 284

Table 4. Measuring points temperature values of Cylinder sleeve Measuring point 1 2 3 4 5 6 7 8 9 10 11 Cylinder liner Q(°C) 206 216 255 221 172 179 206 185 123 134 158

3.2

Results of Thermal-Mechanical Coupled Analysis

3.2.1 Distribution of Temperature Field After the simulation analysis, the temperature field of the valve train is shown in Fig. 5 (a). It can be seen that the highest temperature occurs at the top of the exhaust valve and the temperature is 540 °C, as shown in Fig. 5(b). This is because the high-temperature exhaust gas of the exhaust stroke of the diesel engine is exhausted through the exhaust valve, which has the effect of secondary heating to exhaust valve. The intake valve temperature is low and has the value of 438 °C as shown in Fig. 5(c). This is because the cold air flow outside the intake valve has a certain cooling effect on the intake valve. At the same time, the temperature drops significantly after the radiant heat transfer of the valve through the cooling surface, which indicates that it is necessary to consider the cooling effect for the thermal analysis of valve train. The distribution gradient of temperature at the top of the piston is small and its maximum temperature is 419 °C as shown in Fig. 5(d). This is because the four-stroke cycle in the cylinder is relatively stable, and the surface of the piston is only affected by the temperature of the oil and gas explosion. 3.2.2 Distribution of Equivalent Stress The equivalent stress distribution of the valve train is shown in Fig. 6(a), and the maximum value and generation position are given in Table 5. The maximum equivalent stress occurs at the top of the piston near the exhaust valve side. Because the exhaust gas is stayed on the exhaust valve side for a period of time, it makes the temperature on this side relatively high as shown in Fig. 6(b). In this case, the maximum equivalent stress of the valve is at the tail end of the exhaust valve connected to the transverse arm of the valve as shown in Fig. 6(c). Because the valve cross arm pushes the exhaust valve to open, which results in the large stress on the interface between their contact surface.

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(a) Valve train

(c) Intake valve

(b) Exhaust valve

(d) Piston and connecting rod

Fig. 5. Distribution of Temperature Field

3.2.3 Distribution of Equivalent Elastic Strain The equivalent strain of the valve train is shown in Fig. 7(a), and the maximum value and position of each component are shown in Table 6. It can be seen that the distribution law of the equivalent strain is the same as that of the equivalent stress. The maximum equivalent strain is located on the exhaust valve side as shown in Fig. 7(b). The equivalent strain of the valve is concentrated near the contact position between the valve and the valve cross arm. But the position of the maximum equivalent strain is slightly different from the that of the maximum equivalent stress, which occurs on the cross arm of the exhaust valve as shown in Fig. 7(c).

Reason Study of Collision Between Valves and Piston of Diesel Engine Valve Train

(a) Valve train

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(b) Piston and connecting rod

(c) Exhaust valve and valve arm Fig. 6. Equivalent stress distribution

Table 5. The values and position of the Maximum Equivalent Stress Components Maximum stress/ (MPa) Position

Valve train 241.77

Piston 241.77

Valve 230.77

Top side exhaust valve side

Top side exhaust valve side

Connection between exhaust valve and valve arm

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(a) Valve train

(b) Piston and connecting rod

(c) Exhaust valve and valve arm Fig. 7. Equivalent strain distribution

Table 6. Values and position of the maximum equivalent strain Components

Valve train

Piston

Maximum strain/(mm) Position

0.0013

0.0012

Lower part of the valve

Top side exhaust valve side

Valve cross arm 0.0013 Lower part of the valve

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4 Cause Analysis of Collision Between Valve and Piston 4.1

Distribution of Thermal Deformation

The overall thermal deformation distribution of the valve train is measured in the direction of the combustion chamber and shown in Fig. 8(a). The values of thermal deformation and the minimum clearance reduction are shown in Table 7. The cam-

(a) Valve Train

(b) Piston and connecting rod

(c) Exhaust valve and valve arm Fig. 8. Heat distribution distribution Table 7. The amount of heat deformation and the minimum gap reduction of the valve train Components

Valve train Piston

Maximum thermal 0.96044 deformation/(mm)

Valve Front end Tail end 0.96044 0.52688 0

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connecting rod-piston structure of the system generate the thermal deformation. As shown in Fig. 8(b), the maximum thermal deformation of the piston top is 0.96044 mm. At this time, the maximum thermal deformation generates on the exhaust valve as shown in Fig. 8(c). Its thermal deformation is 0.52688 mm. The minimum clearance between the piston and valve is reduced by 1.48732 mm. 4.2

Collision Cause

During the analysis, it is found that if the cam is varied from 48.39° to 129.16°, the thermal deformation of part of the piston reaches a negative value, that is, its direction is downward along the axial direction of the piston. So it can be determined that the piston collides with the valve under this condition as shown in Fig. 9. As shown in Fig. 10, the contact stress between the exhaust valve and the piston surface is abruptly increased to 1203.2 MPa, which may induces the failure of the piston and the valve.

Fig. 9. Equivalent stress distribution in piston valve collision

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Fig. 10. Partial enlargement of piston valve thermal deformation

5 Conclusions This paper focuses on the study of collision between valve and piston of 265 diesel valve train. From the analysis results, the following conclusions can be derived as: (1) under the stable temperature field of valve train, the maximum displacement of the piston is 0.96044 mm, the maximum equivalent stress is 241.77 MPa, and the maximum equivalent strain is 0.0012 mm; (2) the maximum displacement of the valve is 0.52688 mm, and the maximum equivalent stress is 230.77 MPa; (3) if the cam is varied from 48.39° to 129.16°, the piston collides with valve and their contact stress will be 1203.2 MPa.

References 1. Chen, W.B.: Calculation method of distance between valve and piston. Diesel Engine (03), 35–37 (2006). (in Chinese) 2. Liu, F., Tian, R.Y., Tao, L.F., Liu, J.H.: Application research of new algorithm for limiting gap analysis of valve piston. Mech. Eng. (10), 96–97+102 (2018). (in Chinese) 3. Shi, Y.C., Wang, J.F., Wang, Z.G., et al.: The calculation of minimal moving clearance between 4G15 V gasoline engine valve and piston. Automob. Appl. Technol. (2016) 4. Li, Z.T., Zong, Y.P.: Failure analysis of diesel engine piston top valv. Diesel Engine (06), 59–60+62 (2008). (in Chinese) 5. Wang, D.Y., Zhang, P., Bie, L.F., et al.: Analysis of minimum clearance between piston and valve. Intern. Combust. Eng. (2016) 6. Wang, J.P.: Diesel engine motion system simulation and valve piston minimum motion gap measurement. Mod. Manuf. Eng. (9), 113–116 (2014). (in Chinese) 7. Yang, J., Hu, C.Z.: Dynamic simulation analysis of engine valve and piston clearance. Technol. Dev. Enterp. 37(08), 48–50 (2018). (in Chinese)

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8. Jiang, E.J., Fu, W.Y., Li, S.Q., et al.: Motion simulation analysis of the V6 engine with pro/engineer. Mech. Res. Appl. (2015) 9. Zhang, H.: Simulation analysis of gas distribution system of 140 diesel engine. Shan Dong Univ. (2012). (in Chinese) 10. Yang, S.M.: Heat transfer. Higher education press (2006). (in Chinese)

Macroscopic Topology Optimization of Fusion Cages Used in TLIF Surgery Hongwei Wang1,2, Yi Wan1,2(&), Xinyu Liu3, Bing Ren1,2, Zhanqiang Liu1,2, Xiao Zhang1,2, and Mingzhi Yu1,2 1

Key Laboratory of High Efficiency and Clean Manufacturing, School of Mechanical Engineering, Shandong University, Jinan 250061, China [email protected], {wanyi,melius}@sdu.edu.cn, [email protected], [email protected], [email protected] 2 National Demonstration Center for Experimental Mechanical Engineering Education, Shandong University, Jinan 250061, China 3 Department of Orthopedics, Qilu Hospital, Shandong University, Jinan 250061, China [email protected]

Abstract. Titanium (Ti) cage is commonly used in transforaminal lumbar interbody fusion (TLIF) surgery. However, complications such as subsidence usually occur due to high mechanical stiffness of Ti. Meanwhile, the limited packing volume for bone grafts influences the fusion performance of fusion cage. Topology optimization was employed for the structure and stiffness adjustment of the fusion cage. A finite element model of L3–L4 lumbar spine was reconstructed based on CT images. Two commonly used cages (crescent and flat shaped) were optimized adopting the solid isotropic material with penalization model method. Optimized cages were built based on the result of topology optimization. The origin and optimized cages were implanted in the TLIF model and compared under four load conditions (flexion, extension, bending and torsion). The range of motion, stress on endplates and cages, the strain energy of cancellous were investigated for biomechanical evaluation of cages. The volume of optimized cages was reduced by 36% and 34% for the crescent and flat shaped cages, respectively. Macroscopic topology optimization of cages showed negligible influence to the ROM, von-Mises stress on the endplate and strain energy of cancellous. The stress on the optimized cages increased significantly. Macroscopic topology optimization increased the volume for bone grafts packing, which might improve the fusion performance. However, no significantly reduced risk of subsidence was observed with macroscopic topology optimization of cages. The effects of posterior pedicle screw system might not be considered in biomechanical evaluation of fusion cage, but should be considered in personalized customization of fusion cage. Keywords: Topology optimization TLIF  Lumbar spine

 Fusion cage  Finite element analysis 

This project is supported by National Natural Science Foundation of China (Grant No. 51575320), Natural Science Foundation of Shandong Province (Grant No. ZR2018ZB0106). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 647–660, 2020. https://doi.org/10.1007/978-981-32-9941-2_53

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1 Introduction Transforaminal lumbar interbody fusion (TLIF) procedure is currently one of the main surgical treatments after physiotherapy fails to treat disc degeneration and degenerative spondylolisthesis. Within the last decades, there has been a series of researches about approach, numbers of fusion segments and effect to adjacent intervertebral levels [1]. Intervertebral fusion cages are implanted for restoration of the intervertebral height. Bagby [2] firstly implanted a cage of stainless steel in the 1980s. Since then, metal and its alloys were commonly used in fusion cages. Due to superior corrosion resistance, lower density and satisfactory biocompatibility, titanium (Ti) and its alloys were the preferred materials among them. Satisfactory fusion rate and high osseointegration were demonstrated in clinical studies [3–5]. However, complications such as stress shielding and subsidence were produced due to high mechanical stiffness of Ti, which led to bone resorption and fusion failure [6]. Polyetheretherketone (PEEK) cages were introduced in fusion procedure given its closer elastic property to bone. However, as a polymer, poor osteointegration of PEEK was reported in previous studies [7, 8]. The influence of Ti versus PEEK as the material of fusion cages has been evaluated. However, discrepant results in fusion rates and fusion effect were demonstrated [1, 9– 11]. Further experiments and clinical researches are required for evaluation of Ti versus PEEK. Up to now, Ti is still the preferred materials of fusion cage. The approach of reducing the risk of subsidence and improving the fusion performance has been a research hotspot for years. Topology optimization is an optimization method to rearrange the materials in the specified design domain under prescribed constraints. Optimal materials distribution was achieved to fulfill maximized stiffness objective after optimization [12]. Recent prosperous development of additive manufacturing (AM) technologies enables the production of obtained complex structure from topology optimization. AM implants have been extensively studied in the research of orthopedic treatment up to now [13, 14]. Sutradhar et al. [15] used a novel topology optimization method to design a patient-specific craniofacial implants. Chang et al. [16] optimized the morphology of dental implants using a topology optimization method. The newly designed dental implant increased the volume for bone graft. However, stress level of implant was higher than that of the traditional implant. Al-Tamimi et al. [17] employed topology optimization to reduce the stress shielding effect for orthopedic applications. In addition, several studies have employed topology optimization method to design macrostructure of fusion cage [18, 19]. Slight deviations were demonstrated in these studies. However, fusion surgery with posterior pedicle screw fixation was not discussed in the published results, which is necessary to mimic clinical lumbar fusion surgery. Meanwhile, finite element models were oversimplified and the analysis was not comprehensive. The main theme of the study was application of macroscopic topology optimization in two different-shape commonly used fusion cages (crescent and flat cages) and evaluation of the biomechanical influence of optimized cages to the lumbar spine.

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A finite element model (FEM) of L3–L4 lumbar spine was developed. Optimized cages were built according to the result of topology optimization of two commonly used cages. The range of motion (ROM), stress on endplates and cages, the strain energy of cancellous were compared for the biomechanical evaluation in the study.

2 Materials and Methods 2.1

FEM of the Lumbar Spine

The FEM of the L3–L4 lumbar spine was reconstructed based on the CT images of a man (height: 180 cm, weight: 78 kg) with no spinal disease. The reconstructed model preserved its original vertebrae morphology. Ligaments were set based on their anatomic location. The materials of model were assumed to be homogeneous. The properties data adopted from the previous literature [20, 21] was summarized in Table 1 Ligaments and annulus fibrosus were modeled by two-node truss elements with no compression. Hexahedral element was used to mesh cortical bone, endplate, and disc. The FEM consisted of 429245 elements and 114753 nodes (Fig. 1).

Fig. 1. The finite element model of the L3-L4 lumbar spine

2.2

Macroscopic Topology Optimization

As the reduction of the interface results in the increment of the pressure under the same compression force, the inferior and superior surface of cages were not included in the design domain. In the study, optimization method of solid isotropic material with penalization model (SIMP) was adopted. The topology optimization was performed in the OptiStruct software (Altair Engineering, Troy, MI) to obtain the optimized result. The optimization problem was as stated below: Objective function: minimize (Uc ) Limitation: 0 \ gi \ 1ði ¼ 1; 2; 3; . . .; nÞ V  V0  V  X V¼ gi Vi

ð1Þ ð2Þ

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E i ¼ E ð gi Þ

ð3Þ

fri g ¼ ½Ei fei g

ð4Þ

Uc : the energy of structural compliance, gi : the density variable, V: the computed volume, V0 : the original volume, V  the amount of material to be removed, Vi : the volume of element (i), Ei : the elasticity tensor for each element, E: the elasticity tensor, ri : the stress tensor of element (i), ei : the strain tensor of element (i). The element density gi was varied between 0 and 1. The value of density close to 0 indicated material could be removed. Meanwhile, the value close to 1 indicated material should be retained. There was a functional relationship between the element density and the elastic modulus of the material. The inferior surface of cage was constrained by all degrees of freedom. The moment was imposed on the superior surface. The displacement response of superior surface under moment was constrained. Minimization of the energy of structure compliance was the so-called objective function of topology optimization. The distribution of materials in the design domain was optimized so as to tune the topology structure of cages, reduce the stiffness of cages and increase the packing volume of bone graft. 2.3

FEM of Transforaminal Lumbar Interbody Fusion

Unilateral facetectomy, partial annulotomy and discectomy were applied to simulate transforaminal lumbar interbody fusion (TLIF). In addition, part of capsular ligament was removed. The original cages and optimized cages were placed according to the operative procedure. In order to evaluate the influence of cage optimization to the PLIF, the models with bilateral pedicle screw fixation and without it were all simulated in the present study. The PEEK fixation rod was adopted in TLIF surgery. 2.4

Boundary and Loading Condition

The inferior surface of L4 vertebrae was constrained by all degrees of freedom. The 150 N compression force and 10 Nm moment (flexion, extension, bending and torsion) were imposed on the superior surface of L3 vertebrae. Small teeth which supposed to prevent movement of the cage were ignored and high friction coefficient of 0.8 was defined between the vertebrae and the cage [22]. The interface between facet joints was set as no friction. Tie constraints were set to the interface between screw and vertebrae and the interface between screw and rod.

Macroscopic Topology Optimization of Fusion Cages Used in TLIF Surgery Table 1. Material properties of finite element model Component name Cortical bone Cancellous bone Bone endplate Annulus ground substance Nucleus pulposus ALL

Young’s modulus (MPa) 12000 100

Poisson’s ratio

Cross-section area (mm2)

0.3 0.2

– –

25 4.2

0.25 0.45

– –

1

0.4999



7.8(12.0%) PLL 10(11.0%) LF 15(6.2%) – 26 ISL 10(14.0%) SSL 8(20.0%) TL 10(18.0%) CL 7.5(25.0%) AF layer 1 550 0.3 0.7 AF layer 2 495 0.3 0.63 AF layer 3 440 0.3 0.55 AF layer 4 420 0.3 0.49 AF layer 5 385 0.3 0.41 AF layer 6 360 0.3 0.3 Titanium 110000 0.3 – PEEK 3600 0.3 – Note: ALL: anterior longitudinal ligament; PLL: posterior longitudinal ligament; LF: ligamentum flavum; ISL: interspinous ligament; SSL: supraspinal ligament; TL: transverse ligaments; CL: capsular ligament; AF: annulus fibrosus.

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3 Results 3.1

Validation of the Intact FEM

The ROM of L3–L4 segment under 10Nm moment accompanied with 150N compression force was compared with previous studies [23–25]. The ROM under flexion, extension, lateral bending and torsion load conditions was demonstrated in Fig. 2. The result was in agreement with previous literature, which verified the validity of the model.

Fig. 2. Comparison with the previous FEM study and the vitro experimental study in the ROM

3.2

Optimization Result and Optimized Cage

Macroscopic topology optimization was performed on the original cages (Fig. 3(a) and (d)). The result of optimization was shown in Fig. 3(b) and (e). The reserved parts

Fig. 3. The optimization process of fusion cages. (a) the origin crescent cage; (b) the optimized result of crescent cage; (c) the optimized crescent cage; (d) the origin flat cage; (e) the optimized result of flat cage; (f) the optimized flat cage.

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indicated the regions where stress concentrated on. The disappeared regions of cage were representative of regions which could be removed. The two optimized cages were produced according to the optimized results and shown in Fig. 3(c) and (f). The structure continuity and machinability were assured in the reconstruction process of optimized cages architectures. The volume of the optimized cages was decreased by 36% and 34% for the crescent and flat cages, respectively. 3.3

The ROM of Models

As showed in Fig. 4, there was negligible difference of ROM between origin cages and optimized cages both with bilateral pedicle screw fixation and without it. Macroscopic topology optimization showed slightly effects on the ROM. However, the influence of the crescent and flat cage to TLIF surgery was different. The bilateral pedicle screw fixation restricted the mobility of vertebrae which resulted in the decreased ROM with fixation.

Fig. 4. The comparison of the ROM among the nine finite element models

3.4

The von Mises Stress on the Endplate

As showed in Fig. 5, macroscopic optimization of two cages had the negligible influence to the maximum von Mises stress of the upper endplate both with pedicle screw fixation and without it. For the crescent cage, the stress on the upper endplate was lower than the flat one under four load conditions, regardless of the original or optimized cages. The stress on the upper endplate was significantly decreased with pedicle screw fixation. A similar tendency was found on the lower endplate with the exception of the flat cage under torsion load condition (Fig. 6).

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Fig. 5. The comparison of the maximum von-Mises stress on the upper endplate

Fig. 6. The comparison of the maximum von-Mises stress on the lower endplate

The flexion load condition was appropriate representatives of the von Mises stress distribution under physiological load, therefore, it was used to perform the sensitivity study of stress distribution. The von Mises stress distribution on the upper and lower endplates under flexion load condition was demonstrated in Figs. 7 and 8. Different implantation position and morphology of cages accounted for the different stress distribution on the endplates. However, there was no significant difference in stress distribution between original cages and optimized cages. The stress on the interface between endplate and cage was higher than the same position of the intact model. Meanwhile, the stress on the endplate of no-contact position was lower than the same position of the intact model.

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Fig. 7. The stress distribution on the upper endplate under flexion load condition. (a) the intact model; (b) the origin crescent cage without fixation; (c) the optimized crescent cage; (d) the origin crescent cage with fixation; (e) the optimized crescent cage with fixation; (f) the origin flat cage; (g) the optimized flat cage; (h) the origin flat cage with fixation; (i) the optimized flat cage with fixation

Fig. 8. The stress distribution on the lower endplate under flexion load condition. (a) the intact model; (b) the origin crescent cage; (c) the optimized crescent cage; (d) the origin crescent cage with fixation; (e) the optimized crescent cage with fixation; (f) the origin flat cage; (g) the optimized flat cage; (h) the origin flat cage with fixation; (i) the optimized flat cage with fixation

3.5

The Stress of Cage

The macroscopic topology optimization tuned stress distribution on cages (Fig. 9). The maximum von Mises stress of two optimized cages increased significantly under same flexion load condition. The maximum stress of crescent cage was significantly lower than that of the flat cage both with posterior pedicle screw fixation and without it. The stress of optimized crescent cage increased more significantly than the flat cage with

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Fig. 9. The stress distribution on the cages under flexion load condition. (a) the origin crescent cage; (b) the optimized crescent cage; (c) the origin crescent cage with fixation; (d) the optimized crescent cage with fixation; (e) the origin flat cage; (f) the optimized flat cage; (g) the origin flat cage with fixation; (h) the optimized flat cage with fixation.

fixation. However, different result occurred without fixation. The maximum stress of the optimized flat cage increased more significantly. The region of maximum stress of two origin cages was on the upper and lower surface of cages. After optimization, the region of maximum stress was near the hole on the side of cages. Meanwhile, more uniform contact stress distribution on the two optimized cages was demonstrated in Fig. 9. 3.6

Stress Shielding Signal

Different criterions [26, 27] were adopted to evaluate the stress shielding in bones. Variation of strain energy (SE), which has been used in a finite element analysis of hip replacement, was used to evaluate the stress shielding in this analysis [28]. This calculation was defined as Stress shielding signal (SSS): SSS ¼

SEImpanted  SEIntact SEIntact

ð5Þ

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Fig. 10. The comparison of the SSS of L3 and L4 cancellous among the eight finite element models

The SSS of L3 and L4 cancellous was calculated and demonstrated in Fig. 10. There was a negligible effect of topology optimization to SE of cancellous both models with pedicle screw fixation and without it. Meanwhile, there was a significant effect of fixation to SE of cancellous. Compared with the intact model, the SE of cancellous was increased under all load conditions without fixation for the four cages. With the fixation, the SE was decreased under flexion and extension load conditions. However, the SE increased under bending and torsion load conditions.

4 Discussion A verified finite element model of L3–L4 lumbar spine was adopted in present study. Quantitative analysis of biomechanical influence of four different cages (two origin cages and two optimized cages) was performed. ROM of the segment, von Mises stress on endplates and cages, SE of cancellous were compared, which were important factors for the effect evaluation of the cages in TLIF surgery. The FEM of TLIF surgery was adopted for simulating the surgery treatment, which was beneficial for clinical reference. The preserved original vertebrae morphology improved the accuracy of FEM. The analysis of the biomechanical influence of the macroscopic topology optimization of cages was more comprehensive. According to the result of macroscopic topology optimization, the crescent and flat cages were reconstructed. The volume of the crescent and flat cages was decreased by 36% and 34%, respectively. The increased interspace permitted more bone graft to be filled in cages, which might enhance bony fusion performance. It contributed to reducing the risk of cage slipping out. No significant influence of macroscopic topology optimization to ROM was demonstrated both with posterior pedicle screw fixation and without it. Considered

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high Young’s modulus of Ti, the decreased volume of full-solid cages affected the stiffness weakly. In addition, the compression force and moments which was subjected to the L3 vertebrae to simulate the physiological load were not great enough to produce significant deformation of the cages. Hence, the macroscopic topology optimization could not mitigate the adverse effects of Ti cage on adjacent segments. However, the posterior pedicle screw fixation affected the ROM more significantly. The adjustment of fixation rods stiffness might play a more significant role in the mitigation of adverse effects to adjacent segments. There was no significant influence of macroscopic topology optimization to the von Mises stress distribution of the upper and lower endplates. A similar result was obtained by Zhong [18]. No reduction of stress accounted for the same risk of subsidence for optimized cages to original cages. The stress on the endplates caused by crescent cages was lower than caused by the flat cages. The difference attributed to the different implant position and cage morphology. As shown of von Mises stress distribution on the endplate, the stress on the contact part with the cage increased significantly. The stress on endplate where the nucleus pulposus was replaced by bone graft decreased significantly. The reduction of stress on the endplate might result in degeneration of endplate according to the Wolff’s rule. Therefore, the macroscopic topology optimization might not reduce the risk of cage subsidence. Significant difference occurred on the stress distribution on the cages. The maximum stress on the cages increased significantly after optimization. The maximum stress of two optimized cages was not distributed on the upper and lower surface of cages, which was different from origin cages. The stress remained far below the yield strength of the titanium alloy (848.4 MPa). In addition, the fixation decreased the stress on the cages except the origin flat cage. Due to the lower stress on the cages and endplates, the optimized crescent cage may be a more favorable choice for the TLIF surgery. Stress shielding affected the long-term success of implantation [29]. SSS was adopted to evaluate the risk of stress shielding in the present study. As showed in Fig. 10, macroscopic topology optimization had a negligible effect on the strain energy of cancellous of the operated segment both with posterior pedicle screw fixation and without it. The minor variation of the cage stiffness led to the minor variation of strain energy of cancellous. Thus, the significant reduction of cage stiffness or the adaptation of low elastic modulus materials may reduce the risk of stress shielding significantly. The porous architecture might be an appropriate option which has been proven a significant reduction of stiffness. In a recent study of topology optimization in knee replacement, the similar conclusion was drawn [27]. In addition, the posterior pedicle screw system seemed to be a significant factor to stress shielding too. The limitations of the present analysis were as follows: The stage after the complete fusion of the cage was not analyzed. The fusion of endplate and bone graft affected the stress distribution on the endplate. The influence of disc degeneration, such as reduced disc height and dehydration, were not considered in the present study because of a diverse symptom of disc degeneration. The mechanism which is called the distractioncompression principle [2] was not modeled in the present study.

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5 Conclusions With macroscopic topology optimization, the volume of the crescent and flat cages was decreased by 36% and 34%, respectively, which means more bone graft can be filled in cage to enhance fusion. However, the biomechanical influence of macroscopic topology optimization to PLIF surgery was negligible. The posterior pedicle screw system has no significant influence to the biomechanical evaluation of cage. However, the influence of posterior pedicle screw system should be considered in personalized customization of fusion cage. In the future study, microstructure topology optimization of porous cage and macroscopic topology optimization of fixation rods will be our emphases for research.

References 1. Seaman, S., Kerezoudis, P., Bydon, M., et al.: Titanium vs. polyetheretherketone (PEEK) interbody fusion: Meta-analysis and review of the literature. J. Clin. Neurosci. Official J. Neurosurg. Soc. Australas. 44, 23–29 (2017) 2. Bagby, G.W.: Arthrodesis by the distraction-compression method using a stainless steel implant. Orthopedics 11(6), 931–934 (1988) 3. Cabraja, M., Abbushi, A., Koeppen, D., et al.: Comparison between anterior and posterior decompression with instrumentation for cervical spondylotic myelopathy: sagittal alignment and clinical outcome. Neurosurg. Focus 28(3), E15 (2010) 4. Schmieder, K., Wolzik-Grossmann, M., Pechlivanis, I., et al.: Subsidence of the wing titanium cage after anterior cervical interbody fusion: 2-year follow-up study. J. Neurosurg.: Spine 4(6), 447–453 (2006) 5. Hwang, S.L., Hwang, Y.F., Lieu, A.S., et al.: Outcome analyses of interbody titanium cage fusion used in the anterior discectomy for cervical degenerative disc disease. J. Spinal Disord. Tech. 18(4), 326–331 (2005) 6. Lin, C.Y., Hsiao, C.C., Chen, P.Q., et al.: Interbody fusion cage design using integrated global layout and local microstructure topology optimization. Spine 29(16), 1747–1754 (2004) 7. Kurtz, S.M., Devine, J.N.: PEEK biomaterials in trauma, orthopedic, and spinal implants. Biomaterials 28(32), 4845–4869 (2007) 8. Olivaresnavarrete, R., Gittens, R.A., Schneider, J.M., et al.: Osteoblasts exhibit a more differentiated phenotype and increased bone morphogenetic protein production on titanium alloy substrates than on poly-ether-ether-ketone. Spine J. Official J. North Am. Spine Soc. 12 (3), 265–272 (2012) 9. Chen, Y., Wang, X., Lu, X., et al.: Comparison of titanium and polyetheretherketone (PEEK) cages in the surgical treatment of multilevel cervical spondylotic myelopathy: a prospective, randomized, control study with over 7-year follow-up. Eur. Spine J. 22(7), 1539–1546 (2013) 10. Nemoto, O., Asazuma, T., Yato, Y., et al.: Comparison of fusion rates following transforaminal lumbar interbody fusion using polyetheretherketone cages or titanium cages with transpedicular instrumentation. Eur. Spine J. 23(10), 2150–2155 (2014) 11. Cabraja, M., Oezdemir, S., Koeppen, D., et al.: Anterior cervical discectomy and fusion: comparison of titanium and polyetheretherketone cages. BMC Musculoskeletal Disord. 13 (1), 172 (2012)

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12. Xiao, D., Yang, Y., Su, X., et al.: An integrated approach of topology optimized design and selective laser melting process for titanium implants materials. Bio-Med. Mater. Eng. 23(5), 433–445 (2013) 13. Zhang, Z., Li, H., Fogel, G.R., et al.: Finite element model predicts the biomechanical performance of transforaminal lumbar interbody fusion with various porous additive manufactured cages. Comput. Biol. Med. 95, 167–174 (2018) 14. Tsai, P.I., Hsu, C.C., Chen, S.Y., et al.: Biomechanical investigation into the structural design of porous additive manufactured cages using numerical and experimental approaches. Comput. Biol. Med. 76, 14–23 (2016) 15. Sutradhar, A., Park, J., Carrau, D., et al.: Designing patient-specific 3D printed craniofacial implants using a novel topology optimization method. Med. Biol. Eng. Comput. 54(7), 1123–1135 (2016) 16. Chang, C.L., Chen, C.S., Huang, C.H., et al.: Finite element analysis of the dental implant using a topology optimization method. Med. Eng. Phy. 34(7), 999–1008 (2012) 17. Al-Tamimi, A.A., Peach, C., Fernandes, P.R., et al.: Topology optimization to reduce the stress shielding effect for orthopedic applications. Proc. CIRP 65, 202–206 (2017) 18. Zhong, Z.C., Wei, S.H., Wang, J.P., et al.: Finite element analysis of the lumbar spine with a new cage using a topology optimization method. Med. Eng. Phys. 28(1), 90–98 (2006) 19. Chuah, H.G., Rahim, I.A., Yusof, M.I.: Topology optimisation of spinal interbody cage for reducing stress shielding effect. Comput. Methods Biomech. Biomed. Eng. 13(3), 319–326 (2009) 20. Wong, C., Gehrchen, P.M., Darvann, T., et al.: Nonlinear finite-element analysis and biomechanical evaluation of the lumbar spine. IEEE Trans. Med. Imaging 22(6), 742–746 (2003) 21. Guo, L.X., Wang, Z.W., Zhang, Y.M., et al.: Material property sensitivity analysis on resonant frequency characteristics of the human spine. J. Appl. Biomech. 25(1), 64–72 (2009) 22. Polikeit, A., Ferguson, S.J., Nolte, L.P., et al.: Factors influencing stresses in the lumbar spine after the insertion of intervertebral cages: finite element analysis. Eur. Spine J. 12(4), 413–420 (2003) 23. Chen, C.S., Cheng, C.K., Liu, C.L., et al.: Stress analysis of the disc adjacent to interbody fusion in lumbar spine. Med. Eng. Phys. 23(7), 483–491 (2001) 24. Schmoelz, W., Huber, J.F., Nydegger, T., et al.: Dynamic stabilization of the lumbar spine and its effects on adjacent segments. J. Spinal Disord. Tech. 16(4), 418–423 (2003) 25. Zhao, X., Du, L., Xie, Y., et al.: Effect of lumbar lordosis on the adjacent segment in transforaminal lumbar interbody fusion: a finite element analysis. World Neurosurg. 114, e114–e120 (2018) 26. Boyle, C., Kim, I.Y.: Comparison of different hip prosthesis shapes considering micro-level bone remodeling and stress-shielding criteria using three-dimensional design space topology optimization. J. Biomech. 44(9), 1722–1728 (2011) 27. Zhang, Q.H., Cossey, A., Tong, J.: Stress shielding in periprosthetic bone following a total knee replacement: effects of implant material, design and alignment. Med. Eng. Phys. 38 (12), 1481–1488 (2016) 28. Weinans, H., Sumner, D.R., Igloria, R., et al.: Sensitivity of periprosthetic stress-shielding to load and the bone density-modulus relationship in subject-specific finite element models. J. Biomech. 33(7), 809–817 (2000) 29. Schmidutz, F., Agarwal, Y., Müller, P.E., et al.: Stress-shielding induced bone remodeling in cementless shoulder resurfacing arthroplasty: a finite element analysis and in vivo results. J. Biomech. 47(14), 3509–3516 (2014)

Fuzzy Optimization Design of Disc Brakes Based on Genetic Algorithm Jianbin Wang1(&) and Jishu Yin2(&) 1

School of Mechanical Engineering, University of South China, Hengyang, Hunan Province, China [email protected] 2 School of Civil Engineering, University of South China, Hengyang, Hunan Province, China [email protected]

Abstract. The braking torque and the temperature rise of the brake are the two key indexes in the design of a disc brake for motor vehicles and have great effects on the safety of brakes. In the present study, by using the maximum braking torque and the minimum temperature rise as the objective functions and by considering the fuzziness of all the constrained boundaries, we established the mathematical model for fuzzy optimization design of disc brakes. The parameters, including the inside and outside radius of the friction plate, the diameter (D) and thickness (a) of the brake disc, the piston diameter, and the oil pressure (p) in the cylinder, were determined by Genetic Algorithm (GA) in the Matlab optimum tool box. This study provides an optimized solution for the design of disc brakes. Keywords: Disc brakes

 Optimization design  Fuzzy analysis

1 Introduction The disc brake can satisfy the needs for the development of modern vehicles with stable braking performance, good water stability, big output torque in a small size, good heat dissipation, and easiness in maintenance, etc. The maximum braking torque is an essential assurance for the safety of automotive disc brakes. Equally important, experience shows that the temperature rise plays a decisive role in the life span of disc brakes [1, 2]. However, neither the traditional design method nor the general optimization for disc brakes can take the various fuzzy factors that impact the design into consideration and their “optimal solutions” is hardly realistic. Therefore, in order to obtain a better design effect, the theory of fuzzy optimization design was adopted in this study. Fuzzy optimization design with multiple targets, such as maximum braking torque and minimum braking temperature rise, was carried out with full consideration of all kinds of fuzzy factors that would affect the design of a disc brake for motor vehicles. The attempt to design a solid disc for the front wheel of a car requires the maximum braking torque of the vehicle braking. In order to improve the safety coefficient of the car, the parameters at full load were used in this design given that the braking effect at © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 661–668, 2020. https://doi.org/10.1007/978-981-32-9941-2_54

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full load is worse than that at empty load. The main design parameters of a certain type of car are shown in Table 1 [1, 3].

Table 1. Design raw data Quality at full load Running speed

Wheel radius

Allowed disc diameter

ma = 1510 kg Synchronous adhesion coefficient between tire and ground w = 0.6

r = 300 mm Allowable pressure of brake disc

[D] = 300 mm hg = 85 cm Number of Rim diameter brake

V = 160 km/h Friction coefficient between friction plate and brake disc l = 0.4

[r] = 30 MPa n = 4

Height of the center of mass of a fully loaded car

D0 = 381 mm

Coefficient of traction distribution b = 0.73 Dissipation rate of specific energy

[e] = 6 kg/mm2

2 Braking Torque Determination of a Disc Brake As shown below, Figs. 1 and 2 are the structural diagrams of disc brakes and friction plates, respectively. a and D, the thickness and diameter of the brake disc. Dp, the piston diameter. p, oil pressure in the cylinder. R2 and R1, the outer and inner radius of the friction disc. Assume that the friction plate is in good contact with the brake disc and that they are uniform everywhere, the braking torque of the friction plate acting on the brake disc can be calculated using calculus [1]: Tf ¼ 2

Z h2 Z h2

R2

R1

 1  lrR2 dRdh¼ lr R32  R31 h 3

ð1–1Þ

Where Tf is the pressure on the unit area between the friction plate and the brake disc, l is the friction coefficient of the friction plate, and l = 0.4; h is the center of the circle. The sum of braking torque on the both sides is: 2 Tf ¼ lrðR32  R31 Þh 3

ð1–2Þ

Braking torque is obtained by a hydraulically actuated piston and thus, A = pS according to balanced forces, which is: 2

pD2p p r¼ 1 2 p ¼ 2 2hðR22  R21 Þ 2ðR2  R1 Þh p Dp 4

ð1–3Þ

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Where Dp is the piston diameter (m); P is the pressure in the hydraulic cylinder (MPa); R1 is the inner radius (m) of the friction disc; R2 is the outer radius (m) of the friction disc. Then, Tf ¼ 2l

pD2p 4

p

2ðR32  R31 Þ 3ðR22  R21 Þ

ð1–4Þ

2ðR3 R3 Þ

Make Re ¼ 3ðR22 R12 Þ, which is usually called the effective braking radius. 2

1

Fig. 1. Structure diagram of disc brake

Fig. 2. Schematic diagram of friction plate structure

3 Determination of Temperature Rise of the Brake Per Braking The heat generated during braking will increase the temperature of the brake disc. The energy of motion consumed by the vehicle is all converted to frictional heat energy. The heat distributed in the front wheel is proportional to the braking power distribution coefficient of the automobile brake. Then the temperature rise of the brake disc for one brake is [3]: DT ¼ Gv2 b=254cM1  ½DT

Where G—The total weight of a car; G = ma g C—Specific heat of cast iron [4], c ¼ 482 J=ðkg  KÞ, c—The density of cast iron and steel, c ¼ 7:8  103 kg=m3 , M1 ¼c Accordingly, DT ¼ 0:01423 D2 a

pD2 a ; 4

ð1–5Þ

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4 Mathematical Model Establishment for the Fuzzy Optimization Design of Disc Brakes 4.1

Determination of the Target Function

The biggest braking torque can effectively shorten the braking time in the process of braking, which determines the safety of driving. Moreover, the temperature rise plays a decisive role in the life span of disc brakes. Therefore, the maximum brake torque and minimum brake temperature rise are taken as the objective functions for the optimization design. Then: Because sub-objectives are the two kinds of objective functions with different properties: one is the bigger the better; the other is the smaller the better. Therefore, the method of multiply-divide can be used to unify the objective function [5], that is minf ðxÞ ¼ f 2 ðxÞ. f1 ðxÞ

f 1 ðx) ¼ Tf ¼ l

pD2p p ðR32  R31 Þ

3 ðR22  R21 Þ 0:01423 f2 ðxÞ ¼ DT ¼ D2 a

ð1–6Þ

Then the objective function can be determined as: minf ðxÞ ¼

4.2

f 2 ðxÞ 0:034ðR22  R21 Þ ¼ f1 ðxÞ paD2p D2 ðR32  R31 Þ

ð1–7Þ

Determination of Design Variables

In the design of disc brakes, some design parameters can be calculated according to known data, such as the former tire size is 185/60. R15 can be calculated as:: Effective rolling radius of wheels r ¼ 12  ð185  0:6 þ 25:4  15Þ ¼ 300 mm Rim diameter D0 ¼ 25:4  15 ¼ 381 mm When the car is fully loaded, the distance between the center of mass and the front axle is L1 = 1180 mm, the distance between the center of mass and the rear axle is L2 = 1280 mm, height of center of mass is hg = 85 cm and car wheelbase is L = L1 + L2. Vehicle traction coefficient at full load: b¼

L2 þ uhg 1:280 þ 0:6  0:85 ¼ 0:73 ¼ 2:460 L

ð1–8Þ

The value of parameters including the outer radius (R2) and inner radius (R1) of the friction disc, piston diameter (Dp), the thickness (a) and diameter (D) of the brake disc and the oil pressure in cylinder (p), directly determines whether the performance and structure of the brake is reasonable or not. Therefore, these parameters are regarded as the design variables, that is: X = [R1 ; R2 ; Dp ; p, D, a]T ¼ ½x1 ; x2 ; x3 ; x4 ; x5 ; x6 T .

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4.3

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Determination of Constraint Conditions

(1) The boundary geometric constraint conditions of all variables are [7]: ~0 ~ 0; g7 ðxÞ ¼ 0:01  a  g1 ðxÞ ¼ 1:0  104  R1  ~ ~ g2 ðxÞ ¼ R1  0:14  0; g8 ðxÞ ¼ a  0:02  0 ~0 ~ 0; g9 ðxÞ ¼ 0:243  D  g3 ðxÞ ¼ 1:0  104  R2  ~ ~0 g4 ðxÞ ¼ R2  0:14  0; g10 ðxÞ ¼ D  0:281 

ð1–9Þ

~0 g11 ðxÞ ¼ 8  106  p  6 ~ g12 ðxÞ ¼ p  12  10  0

~ 0; g5 ðxÞ ¼ 1  104  Dp  ~ g6 ðxÞ ¼ Dp  0:14  0;

(2) The brake disc diameter D is generally 64%–74% of the rim diameter. 64%D0  D  74%D0 g13 ðxÞ ¼ 0:243  D  0; g14 ðx) = D  0:281  0

ð1–10Þ

(3) The mounting position of the friction disc should be within the diameter of the brake disc, and the friction disc and wheel hub should not be interfered. D2 is the space allowance. Take D2 = 0.2 (mm) [1]. g15 ðx) ¼ R2 þ D1  D 2  0;

g16 ðx) ¼ R1  R2  0 ;

ð1–11Þ

(4) The ratio between the outer and inner diameter of the friction plate should be within a specified value. Beyond the specified value, the friction plate will be easy to break, while less than the specified value will reduce the braking efficiency and accelerate the wear [6]. g17 ðxÞ ¼ 1:27  g18 ðxÞ ¼

R2 0 R1

R2  1:63  0 R1

ð1–12Þ

(5) The force of the brake cylinder on the brake block (F) has the following relation with the diameter (Dp) and the hydraulic pressure(p) of the brake cylinder [1]: sffiffiffiffiffiffi F Dp ¼ 2 pp

ð1–13Þ

Where p takes into account the pressure of the cylinder or pipeline under the action of the power regulator [2], p ¼ 8  12 MPa, so:

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g19 ðxÞ ¼ 8  106  p  0

ð1–14Þ

g20 ðxÞ ¼ p  12  106  0

(6) The strength of friction plates shall not exceed the maximum allowable value of friction materials [3]. ½rmax  ¼ 30 MPa, r  ½rmax  r¼

pD2p p 2ðR22  R21 Þh

g20 ðxÞ¼

 ½rmax ¼30  106

pD2p p 2ðR22  R21 Þh

ð1–15Þ  30  10  0 6

(7) In order to prevent the wheel from skidding, the braking torque shall not be greater than the adhesion moment between the wheel and the ground [6], The related parameters can be substituted into kTf  12uma gbr for simplification: g21 ðxÞ ¼

0:481D2p ðR32  R31 Þ ðR22  R21 Þ

 972:229  0

ð1  16Þ

Where, the reliability coefficient (k) is set at 1.15, coefficient of road adhesion w is set at 0.6, braking force distribution coefficient b is set at 0.73. (8) Specific energy dissipation rate constraint: if the specific energy dissipation rate is too high, it will not only accelerate the wear of brake friction plates, but may also cause cracks in brake disks [1]. Thus the constraint is: Specific energy dissipation rate of a single front wheel brake in a biaxial car is: e1 ¼ b 

dma ðv22  v21 Þ ; 2  2tA



v2  v1 j

ð1–17Þ

Where d is Mass coefficient of automobile rotation, d = 1; V2 is the initial braking speed; V1 is the final braking speed (m/s); t is the braking time(s); A is the friction area of the front brake gasket (liner); j is the braking deceleration, j ¼ 0:6g; b¼0:73 is braking power distribution coefficient. The value of center circle angle of the friction disc is generally p3  p2 and h ¼ 0:8762 [8] by referring to the known information. A ¼ pðR22  R21 Þ 

h ðR2  R21 Þh ¼ 2 2p 2

ð1–18Þ

Combined with ( 1–15 and (1-16), the calculation is as follows: e1 ¼ 165046:37  ½e ðR2 R2 Þ 2

1

 6  106  0 g22 ðxÞ ¼ 165046:37 ðR2 R2 Þ 2

1

ð1  19Þ

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The value of performance constraint of automobile disc brakes is affected by fuzzy factors such as the design level, material selection, processing and manufacturing level, maintenance and use environment, etc. Therefore, it is a good way to deal with each constraint condition by the fuzzy method. The performance constraint condition of fuzzy strength is transformed into general performance constraint condition by the horizontal truncation method. x  ½xu   k ð½xu  xL Þ

ð1–20Þ

Take b ¼ 0:75; b ¼ 1:05. ½r  30  106 k ð1:05  300:75  30Þ  106 ½r  ð309k Þ  106

ð1–21Þ

The maximum allowable temperature for one braking ½DT  288:15; ðKÞ. To prevent the wheel from skidding, the braking moment should not be greater than the friction moment between the wheel and the ground kTf  12uma gbr. When the data is 2 0:481Dp ðR32 R31 Þ  972:229. included, the following equation can be obtained: ðR2 R2 Þ 2

1

Take the same fuzzy treatment as above: ½DT  288:15k ð1:05  288:150:75  288:15Þ 0:481D2p ðR32  R31 Þ ðR22  R21 Þ

 972:229k ð1:05  972:2290:75  972:229Þ

ð1–22Þ ð1–23Þ

The fuzzy method is also applied in geometric fuzzy constraint conditions. k ¼ 0:515 can be obtained by using the fuzzy comprehensive evaluation method and then substituted into the above equations. The function models after fuzzy treatment are as follows: ~ 0; f1 ðxÞ ¼ 1:006  104  R1  ~ 0; f3 ðxÞ ¼ 1:006  104  R2  ~ 0; f5 ðxÞ ¼ 1:006  104  Dp  ~ 0; f7 ðxÞ ¼ 8:048  106  p  ~ 0; f9 ðxÞ ¼ 0:245  D  ~ 0; f11 ðxÞ ¼ 0:01006  a  ~ 0; f13 ðxÞ ¼ 0:002 þ R2  D2  ~ 0; f15 ðxÞ ¼ 1:27 RR21 

~0 f2 ðxÞ ¼ R1 0:139  ~0 f4 ðxÞ ¼ R2 0:139  ~0 f6 ðxÞ ¼ Dp 0:139  ~0 f8 ðxÞ ¼ p11:928  106  ~0 f10 ðxÞ ¼ D0:279  ~0 f12 ðxÞ ¼ a0:01988  ~0 f14 ðxÞ ¼ R1 R2  ~0 f16 ðxÞ ¼ RR21 1:63 

ð1–24Þ

1:8D D ~0 ~ 0; f18 ðxÞ ¼ 0:481D2p pðR22 R1 Þ  680:56  f17 ðxÞ ¼ ðR2 Rp 2 Þ  25:365  106  R2 R1 2 1 ~0 ~ 0; f20 ðxÞ ¼ 0:01423201:71D2 a  f19 ðxÞ ¼ 165046:37  5:073  106  R2 R2 2

2

2

3

3

1

The above equations were solved by GA in the Matlab optimum tool box, and the comparison of optimization results are shown in Table 2.

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Variate Current value Multi-objective optimization Multi-objective fuzzy optimization

Tf (Nm) DT (K) R1 (m) R2 (m) Dp (m) P (MPa) D (m) a (m) 1090 15 0.1 0.13 0.05 6 0.28 0.012 1271 9.01 0.063 0.102 0.055 8 0.281 0.02 1882

9.14

0.108

0.137

0.055

8.048

0.279 0.02

5 Conclusion The results of the multi-objective fuzzy optimization design are as follows: the range of temperature rise is reduced by 37.3%, and the range of torque is increased by 72.66%, which are mainly achieved by increasing the pressure and reducing the thickness of brake discs. In the process of optimization, the maximum thickness of the brake disc obtained by the multi-objective optimization design is 0.281 m and become 0.279 m after the fuzzy analysis treatment. The pressure obtained by the multi-objective optimization design is 8 MPa and become 8.048 MPa after the fuzzy analysis treatment. The moment obtained by the multi-objective optimization design is 1271 Nm and become 1882 Nm after the fuzzy analysis treatment. Collectively, these data reflects the superiority of the fuzzy optimization theory.

References 1. Liu, W.: Vehicle Design. Tsinghua University Press, Beijing (2001) 2. Jiang, P., Huang, W.: Optimal design of disc brake based on MATLAB. Mech. Eng. Autom. 34(6), 158–161 (2007) 3. Chen, X.: Mechanical Optimization Design, pp. 153–158. Zhejiang University Press, Hangzhou (2010) 4. Zhou, J.: Structural optimization design of disc brakes based on variation coefficient (2009) 5. Wang, L., Sun, G., Yu, P.: Calculation and research on efficiency factor of drum brake. J. Nanjing Univ. Technol. 23(3), 220–223 (1999) 6. Ge, Y., Xue, Y., Yao, C.: Optimization design of disc brakes based on genetic algorithm. Manuf. Autom. 35(10), 122–125 (2013) 7. Feng, G., Yang, S.: Vehicle Modern Design Methods. Science Press, Beijing (2006) 8. Liu, Y., Li, W.: The Fuzzy Method of Mechanical Design, pp. 77–90. Machinery Industry Press (2009)

Modeling Design and Evaluation of Rotary Tiller Based on Multidisciplinary Optimization Wang Jianwei1,2(&), Jianmin Zhang1, and Qin Yang1 1

2

School of Mechanical Engineering, Guizhou University, Guiyang 550025, China [email protected] Haier Industrial Design Center, Haier Group, Qingdao 266101, Shandong, China

Abstract. In order to solve the problem of increasing diversification of user demand for rotary tiller and mismatch between product shape and function, a product shape optimization design method based on image cognition, parametric modeling, ergonomics, eye movement analysis and other multi-disciplinary was proposed. The designer quantified and reduced the dimension of the user’s perceptual image vocabulary of the rotary tiller, and designed the sketch according to the user’s perceptual cognition of the typical samples. Under the comprehensive analysis of parametric modeling, ergonomics, eye tracking and color theory, the optimal modeling design of rotary tiller was obtained by using the cross-coupling of diverse disciplines. Aiming at the modeling design of complex products of rotary tiller, it is necessary to actively carry out modeling optimization by integrating multi-disciplinary knowledge. Through the transfer, superposition and combination of diverse disciplinary design knowledge, the modeling design model based on multi-disciplinary optimization can stimulate the creation of innovative thinking of designers and improve the design quality of rotary tiller products. Keywords: Multi-disciplinary optimization  Rotary tiller  Product modeling  JACK  Eye movement analysis  Industrial design

1 Introduction Agricultural machinery design is a complicated system of engineering, involving multidisciplinary system research. At the same time, through the comparison with the previous conventional design, designer find out the shortcomings and effective improvement, so as to better foster the development of agricultural machinery industry product innovation. Multidisciplinary design optimization is usually divided into three

This work is supported by Project supported by the Guizhou Natural Science Fund Project (Guizhou Technology Cooperation Support Program [2017] 1047), the Guizhou Science and Technology Major Project (LH [2014] 7629, LH [2016] 7432, LH [2017] 7232), the Academic New Seedling Cultivation and Innovation Exploration Specialization of Guizhou University(Guizhou Platform Talents [2017] 5788). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 669–685, 2020. https://doi.org/10.1007/978-981-32-9941-2_55

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aspects: in scheme design, model design and drawing. This requires designers must have a substantial knowledge base, in the design process, can reasonably use design, engineering and economics related theories, and to a certain extent, can accurately measure and flexibly use the relevant knowledge and technology. In order to satisfy the fatigue strength and reduce the noise of wheels, Nielsen, et al. proposed a multidisciplinary optimization design method by combining experimental design with automatic design, which further improved the design performance of wheels [1]. Choi et al. carried out the system design of aero-rocket physical installation constraints by using the multidisciplinary feasible design optimization method [2]. Ying Liu and others proposed an optimization design method for the engine compartment lid, through the comprehensive use of structural stiffness, acoustic and vibration roughness characteristics and pedestrian protection performance of the multidisciplinary automatic calculation process [3]. In order to overcome the difficulty of optimization caused by the high nonlinearity of passenger car roll-over analysis, Su Ruiyi et al. carried out multidisciplinary optimization on the frame structure of a fully loaded bus body, thus improving the comprehensive performance of passenger cars [4]. Qi et al. established the mathematical model of submarine shape by using Jackson linear control equation and studied the multidisciplinary optimization of submarine shape design in order to meet the objectives of minimizing flow noise, minimizing tape drag and maximizing volume of submarine [5]. At present, multidisciplinary optimization is mainly used in the research and development of the core components of complex systems and shape performance, such as aircraft, automobiles and other components and submarine shape, compared with the increasingly diverse needs of consumers, the research on multidisciplinary optimization of product modeling design is relatively less. At present, the research and development of rotary tiller are limited to meet the requirements of function and performance, lack of modeling in aesthetic, man-machine and other aspects of the integration of function and product identification. It has certain significance and reference for the design and development of other complex products to optimize the scheme of rotary tiller modeling and construct the modeling optimization design model of related complex products.

2 Knowledge of Multi-disciplinary Optimization The main idea of multidisciplinary design optimization is to integrate the knowledge of diverse disciplines and apply the applicable design optimization strategy to the whole process of complex system design. Designers can reasonably use the interdisciplinary relationship between different disciplines, through a collaborative design, to obtain the optimal solution of the entire complex system. The coordination mechanism takes into account the interdisciplinary relationship, and coordinates and controls these subsystems through a specific framework, thus obtaining the optimal solution of the whole complex system [6]. In the scheme design of multidisciplinary optimization rotary tiller, adopting concurrent design can improve the quality of a rotary tiller, reduce the development cost of a rotary tiller, shorten the design cycle, and develop more competitive rotary tiller products in the market.

Modeling Design and Evaluation of Rotary Tiller

lDesign ¼

n X

671

! lDesign

þ lMDO

ð1Þ

i¼1

l

Design

(

n P

represents the total benefits of a complex product system design; lDesign ) represents the sum of the design benefits of using different disciplines in

i¼1

a complex product system; lMDO denotes the additional benefits resulting from the use of multidisciplinary design optimization methods, taking into account the interactions between the various disciplines in a comprehensive manner. The formula shows that MDO can further tap the design potential and optimize the system objectives. In this paper, the multi-disciplinary analysis of the rotary tiller, through the perceptual image, parametric modeling, ergonomic analysis, morphological semantics and color theory module analysis, respectively, through the coupling between disciplines, get the realization of the optimization model of the relevant rotary tiller. The multidisciplinary design optimization flow chart is shown in Fig. 1.

Fig. 1. Multi-disciplinary optimization of the rotary tiller modeling design process

In the process of multidisciplinary optimization design of rotary tiller products, designers through the mining of customer demand, get the hidden demand of customers for rotary tiller products, and according to image cognition sketch design. In order to refine the sketch the designer carries on the joint multidisciplinary optimization through

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the product parameter modeling the human factor analysis the morphological eye movement analysis and the color and so on to obtain the design plan which meets the user demand.

3 Design and Evaluation of Rotary Tillers Cheme Based on Multi-disciplinary Optimization 3.1

The Perceptual Imagery and Design of Rotary Tiller

Kansei design gets a new design concept in the process of product development. It is new product development technology based on the rational analysis of consumers’ perceptual factors and multiple needs. This technology can open up perceptual thinking and express it formally. In the whole development process, designers design and develop by extracting perceptual requirements. Perceptual information is the synthesis of perceptual and illogical feelings, impressions, emotions, feelings and other subjective thoughts and images produced by the human mind through cognitive processing. “Perceptual information” refers to that emotional colors produce by the user of the product modeling itself evolve into the emotional design language of the user to the product in the cognitive mechanism of product design [7]. With the development of society and the change of people’s lifestyle, consumers do not only consider the function and practicality of products, but also consider the stimulation of products to the senses. Perceptual information is not determined by a single product attribute, but by the comprehensive analysis of product attributes. As a consequence, perceptual information is not easily discover by manufacturers or even by consumer themselves. Compared with product function and manufacturing, designers have more uncertainties in extracting perceptual information in product design and development [8]. The innovative design of hand-held rotary tiller was taken as an example to test the method. Through a variety of ways, including Taobao, physical stores, official websites, we collected a large number of sample pictures, and carried out multiple analysis and screening, through the analysis of the characteristics of the hand-held rotary tiller, and according to its modeling characteristics selected four typical samples, see Fig. 2.

Fig. 2. Typical sample

The 100 cognitive adjectives were related to that shape style image of a hand-held rotary tiller were extracted from the objective natural language of the user. In the end, the 4 kinds of hand-held rotary tillers were selected as samples. The subjects included

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10 senior designers (4 agricultural machinery designers, 6 graduate students of industrial design), 5 hand-held rotary tillers without relevant operating experience, and 15 hand-held rotary tillers with a precise understanding of the personnel. The subjects of the survey were mainly hand-held rotary tiller with driving experience and ordinary users. Then, through the effective questionnaire statistical analysis, the designer preliminarily clustered and extracted 12 adjectives, as the reference vocabulary of the hand-held rotary tiller. Designer looked for the antonyms to form an adjective group, but some adjectives were not entirely orthogonal because of the semantic overlap between them. Under the comprehensive consideration, designer selected the first four representative samples, and used Likert 7-point scale to divide the existing adjectives into semantic scales [7]. Principal component analysis (PCA) was utilized to analyze the perceptual image adjectives of hand-held rotary tillage machine, so as to select the adjectives that can better represent hand-held rotary tillage machine. 6 groups of perceptual phrases include, Dynamic-Static, Coordinated-Dysfunctional, FashionableStylish, Safe-Dangerous, Comfortable-Hard, Useful-Fancy.

Fig. 3. One of the questionnaires

Questionnaire survey was conducted on selected experimental samples by semantic difference method. Users of 4 samples were investigated with 7-level scale and 6 pairs of adjectives. Perceptual settings are −3, −2, −1, 0, 1, 2, 3. Among them, 3 indicates that the image of this sample is more consistent with the right adjective, and -3 indicates that the image of this sample is more consistent with the left adjective [9]. Thirty subjects were investigated by questionnaires, see Fig. 3. Among them, 6 senior industrial designers, 4 engineers engaged in agricultural machinery design, 5 college students with some design knowledge, 5 people with driving experience in rotary tiller, and 10 ordinary users. Table 1. Factors and their levels Adjective pair Dynamic-static Coordinated-dysfunctional Fashionable-stylish Safe-dangerous Comfortable-hard Useful-fancy

Sample 1 Sample 2 Sample 3 Sample 4 −2.0 −1.5 1.2 −1.9 1.0 −2.1 −1.4 0.5 −2.1 −1.6 2.1 −2.2 2.6 1.2 −1.7 0.3 −0.6 −1.8 0.9 −1.8 1.5 1.8 −2.1 −2.5

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The designer combined the perceptual image results of the above samples, extracted the corresponding perceptual characteristics of each sample, and designed the handheld rotary tiller. Designer used cured surface design method for hand-held rotary tiller head, through the use of large areas of blue, with small pieces of geometric white block, so that the overall shape of hand-held rotary tiller has changed, to convey to the user a bright, refreshing feeling. Through precise mathematical relations, the designer used streamlined body language to form a concise and harmonious overall shape of the hand-held rotary tiller connecting rod and the machine head, and collocated a reasonable color proportion to visually reduce the overall volume sense of the hand-held rotary tiller. The designer divided the main view and the top view of the hand-held rotary tiller reasonably in order to stimulate the user’s sense of stability and harmony and the experience of good operation. Along with the brand influence thorough, the design was must melt into the enterprise culture, increases consumer’s trust and the approval to the product. In the design process, the designer should consider the overall color and shape of the rotary tiller in a systematic way, see Fig. 4.

Fig. 4. Design sketch

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Ergonomic Optimization of Rotary Tiller

In order to make the conceptual sketch more refined, it is generally necessary to analyze and compare the sketches, and improve the analysis of the sketch structure and related dimensions. After synthetically analyzing the product sketch design, in order to express and display the design results better, the designer needs to simulate the scheme on the computer by means of computer aided design, and fully display the whole form of the product through the three views and perspective view of the established model, namely the so-called digital model design [10]. This process belongs to computer aided design, with the continuous development of computer technology, digital modeling

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technology continues to evolve, through the model building, with rendering plug-in can quickly reflect the product effect. The model built into the human factor analysis software can be rapid human factor analysis, timely modification and adjustment of the model [11]. As shown in Fig. 5, that design of the digital model of the rotary tillage machine is shown.

Fig. 5. RHINO software rotary tiller modeling

JACK software is a set of three-dimensional simulation, high-end simulation software, which integrates the main functions of digital human modeling and human factor analysis, has abundant digital human models (especially Chinese human models). It is more convenient for the ergonomics analysis and the ergonomics simulation analysis of the rotary tiller on the mainland. The ergonomics simulation system is composed of two basic conditions: (1) The first condition is the virtual driver model, which has JACK software to build the digital model, and also refers to the model of the agricultural machinery driver; (2) The model of virtual simulation environment, which has other types of three-dimensional software, can be created by CATIA, PRO-E, UG or RHINO, 3DS MAX, and imported into JACK to create virtual simulation environment. Based on the virtual simulation system, the comfort, accessibility and visibility of the rotary tiller were analyzed by using JACK ergonomics analysis tools [12]. Figure 6 is the simulation scenario of JACK software. It can be seen that the design of the rotary tiller through the baffle and the distance between the rotary tiller and the model is more reasonable. Lower back analysis can be used to analyze the impact of the human spine in a specific working environment on the lower back, and simulate whether the driver complies with the NIOSH standard during the driving process. As shown in Fig. 7, that force exerted on the driver is far less than 3,400 N, and the drive is relatively safe. Fast Upper Limb Analysis (FULA) is a manual task designed by a designer to detect the risk of a given digital model. The endurance of the upper limb is simulated and the danger of the driver is judged according to the simulation data. As shown in

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Fig. 6. JACK simulation scenario

Fig. 7. Lower back analysis

Fig. 8, the driver scored 2 on the upper limb when operating the rotary tiller, illustrating that the upper limb is tolerable in the case where the driver drives the rotary tiller for a long period of time. Working posture analysis is to detect the driver’s posture while driving the rotary tiller, analysis of the driver’ s back, arms and legs load requirements, in order to analyze the driver’s operating posture is not appropriate. As shown in Fig. 9, a level of 1 indicates that the posture is normal and there is no need to correct it.

Fig. 8. Rapid upper limb assessment

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Fig. 9. Ovako working posture analysis

3.3

The Perceptual Imagery and Design of Rotary Tiller

The optimization of product form can be carried out under the condition of satisfying the function of a rotary tiller, so as to meet the demand, functions, spirits and values of users at different levels of rotary tiller. In fact, product bionic design is not simply copying design, but fully considers the situation of product function, the relevant semantic relationship given to product form. Through the establishment of product semantic relations, designers can beautify the product form on the basis of the product in the function and emotional aspects of deep-seated connotation, thus increasing the usability of products, emotional and cultural. The angle coupling of bionic design should first consider the reasonableness of semantic signifier and signified of product modeling, which should be part of the most basic criteria for judging morphological bionics. For semantic analysis of the design scheme, see Fig. 10. Rotary tiller was designed by using the shape of cattle, fully considering the combination of biomimetic form and product design. Cattle are the embodiment of hard work and strong, and the form of cattle is steady. The basic form of rotary tillage is determined by the shape of cattle, and the traditional custom of “cattle cultivated land” is used as the cultural keynote, which serves as the core, and “cattle” and “rotary tiller” are interlinked in the signifier. The ox here stands for hard work, strength and wealth. In Christianity, the ox stands for obedience. Biomimetic shape of cattle is used as the basic form of rotary tiller, and its connotation is thick and semantic.

Fig. 10. Modeling semantic analysis

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In the form design of a rotary tiller, there are differences between users and designers in cognitive mode. Although the design is user-centered, the understanding and description of the perceptual image of the rotary tiller are still not equal to the real image of the user [13]. As an effective means of acquiring user tacit knowledge and design object knowledge, eye movement mode concretizes the tacit knowledge which is hard to express, and forms the knowledge system required by design [14]. Through data analysis and hot-spot map, the average fixation time, fixation time, perceptual interest area and other conversion methods, the visual attraction of rotary tiller form to users was obtained, and the explicit and tacit knowledge of users was mined. Design procedure of eye movement experiment of rotary tiller: (1) Identify samples and perceptual images: In order to eliminate the influence of color on modeling, the sample images were gray-level processed, as shown in Fig. 11. In order to ensure the accuracy of the experimental data, the order of the samples was dislocated during each perceptual image cognitive observation, a total of 6 samples were sorted, as shown in Fig. 12. Image vocabulary was derived from the previous dimension reduction, including dynamic, coordinated, fashionable, safe, comfortable, useful.

Fig. 11. Modeling test sample

(2) Participants: 30 subjects, including 15 graduate students of industrial design, 10 graduate students in mechanical engineering and 5 operators, were selected. The subjects were trained briefly before the experiment, which ensured that the subjects could pay attention to the experimental samples accurately under the drive of the perceptual image. (3) Experiment process: According to eye movement manual (EyeSoEc60), the experimental environment was adjusted through experimental prediction to ensure the smooth progress of eye movement experiment [15]. After learning the perceptual vocabulary, the subjects watched the sample pictures (the order of each project was different). And complete the next sample test one by one until all samples were completed. 30 subjects were tested by repeating the previous procedure. (4) Experimental discussion: The eye movement hot-spot map was that cumulative observation of 30 observers under each perceptual vocabulary, as shown in Fig. 13. It displays the user’s visual residence time by color change. Red indicates the area where the user’s gaze is longest and green is shortest. The test results show that Scheme 5 ranks second in terms of attention under dynamic and safe vocabulary, and first in terms of attention under coordinated and practical

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Fig. 12. Dislocation sorting of modeling samples

perceptual vocabulary. Scheme 5 attracts more attention from users in the scheme test when combined with six perceptual word analyses. 3.4

Optimization of Color Theory of Rotary Tiller

In the era of brand competition, enterprises create a distinctive brand image, gain consumer value recognition, and expand brand awareness. Product color is an important factor of brand image recognition. It has unique visual expression and cultural semantics. However, in the field of agricultural machinery, product color design is

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Fig. 13. Hot spot map of sample scheme

often ignored, and color matching is single, leading to the market agricultural machinery color is single and identical, enterprise identification is also poor. Color design is the focus of product modeling development. In order to obtain a more comprehensive and reasonable color scheme, it is necessary to conduct a comprehensive analysis of the factors affecting the color design of agricultural machinery. Through the investigation of the design of agricultural machinery products of wellknown brands at home and abroad, the main factors affecting the color design of

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agricultural machinery are: color culture, product structure and function, ergonomics, aesthetic rules. At present, color matching of domestic agricultural machinery products is based on red and blue, with white and gray as auxiliary colors. This color matching in the industry has formed a specific agricultural machinery color characteristics, but also recognized by users. In general, designers should consider the historical and cultural attributes of the product location in addition to the function, user needs and other aspects when matching the product color. Agricultural machinery color matching to consider the overall product function, shape, use, as well as the environment. Reasonable color matching can make the structure and function of agricultural machinery more harmonious. By referring to the principle of plane formation, reasonable color area can also be taken into account as plane formation. The designer utilizes the division, proportion and position between the color blocks to create a sense of movement and weight of the modeling, thus making up for the imbalance of the modeling scale caused by the special structure of the agricultural machinery [16]. When drivers drive large-scale agricultural machinery, reasonable color design can play a warning role, so as to avoid the driver’s misoperation of agricultural machinery, reduce the driver’s sense of fatigue and tension, can also make the driver feel comfortable, improve the efficiency of the operator ‘s work. Enterprises can grasp the main keynote of agricultural machinery products, so as to maintain the unity and beauty of agricultural machinery products as a whole. Agricultural machinery design should not only focus on technical and functional requirements, but also to meet the spiritual need of drivers. Color is an important consideration of plastic art. The rational use of color can make the “shape” of agricultural machinery more prominent, more compelling. Appropriate color matching can coordinate or make up for some shortcomings in product modeling. With the increasing personalization of consumption, due to the characteristics of most products, quality, material differences are very small, appearance differences become one of the important goals of people’s consumption. With the maturity of technology, many enterprises change the color of products to improve the design, hoping to attract more customers through more beautiful, personality, reasonable color modelling. In the color design of agricultural machinery, attention should be paid to the color of the product, especially the prompting function of the product function, to match the color with the function as much as possible, and to better assist the display of the product function effect. Therefore, in the color design, the influence of color on the operator’s psychology must be considered. Figure 14 shows the color series of the rotary tiller. Rotary tiller is generally used in the outdoor, in color design, to fully consider the outdoor environment. As the outdoor environment cannot be changed, the environment should be the main color in color matching of agricultural machinery, and agricultural machinery color should be treated as auxiliary color. Because our country land is vast, the color of the land is different, the northeast area is black soil, the central plains area is yellow soil, the southern area of the Yangtze River is red soil, brown soil. In the performance of color painting, the use of warm and cold color difference to strengthen the contrast of color, distance, showing a special sense of visual contrast and balance, so that the screen enrichment has a sense of depth. Rotary tiller can achieve visual

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Fig. 14. Color series of hand-held rotary tiller

balance and distance to ensure driving safety by cold and warm contrast color matching. Considering the warm hues of yellow soil, laterite and purple soil in southwest China, combined with the theory of color contrast and complementation, the main color of the hand-held rotary tiller is chosen as the cool hues blue. Color selection ivory white, pearl white for local decoration, so that the overall shape of agricultural machinery three-dimensional light, to achieve “natural, agricultural machinery, people” harmony of the three, other regions can refer to the color theory of targeted sales, see Fig. 15.

Fig. 15. Color scheme

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4 Optimization Design of Rotary Tiller Combined with the tendency of consumers and the research of structural innovation method, the hand-held rotary tiller’s appearance and technical functional design should meet consumers’ physiology and psychology need. In this work, some elements of bull front face shape were extracted for the design of the front face of the hand-held rotary tiller, and the front face and hand-held rod assembled a cattle head image. The traditional cattle head image was iterated into a modern cattle head. As shown in Fig. 16. It expressed the traditional cultivation culture. Finally, we used computer-aided industrial design software to model the hand-held rotary tiller with this image, and got an innovated conceptual design scheme, as shown in Fig. 17.

Fig. 16. Iterative design of front face pattern of rotary tiller

Fig. 17. Conceptual design scheme of hand-held rotary tiller

5 Conclusions Based on the analysis of design psychology ergonomics morphological semantics and color of a rotary tiller, a multi-disciplinary optimization model design and evaluation scheme of rotary tiller is proposed. On the basis of fully understanding the perceptual image of the user, the designer draws conceptual sketch. In order to optimize the conceptual sketch, the designer searches for the optimal design scheme of the rotary tiller to meet the needs of the users by means of parametric modeling, human factor analysis, eye movement evaluation and color matching under the comprehensive analysis of multiple disciplines., which is conducive to reduce the time of product

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development and the design changes in the later stage of development, and reduce the design costs. In the future, personalized requirements of agricultural machinery design will be constantly changing. It is necessary to establish multi-disciplinary optimization methods of design, engineering, psychology, market and other related modeling design for agricultural machinery and other related complex products. In the future, the innovative design of agricultural machinery products driven by multi-objective integration of technology, process and cost will need to be further explored to improve the applicability and completeness of the method.

Appendix Appendix and supplement both mean material added at the end of a book. An appendix gives useful additional information, but even without it the rest of the book is complete: In the appendix are forty detailed charts. A supplement, bound in the book or published separately, is given for comparison, as an enhancement, to provide corrections, to present later information, and the like: A yearly supplement is issue.

References 1. Nielsen, J.C.O., Fredo, C.R.: Multi-disciplinary optimization of railway wheels. J. Sound Vib. 293(3–5), 510–521 (2005) 2. Choi, Y.C., Noh, K.-H., Lee, J.-W., et. al.: Optimal air-launching rocket design using system trades and s multi-disciplinary optimization approach. Aerosepace Sci. Technol. 13(7), 406– 414 (2009) 3. Ying, L., Xu, Y., Xin, Q.: Multidiscipline design optimization method for engine hood. J. Automot. Saf. Energy (04), 456–462 (2018). (in Chinese) 4. Gui, L., Wu, Z., Tian, C., et al.: Multidisciplinary design and collaborative optimization for bus body. J. Mech. Eng. 18, 128–133 (2010). (in Chinese) 5. Qi, X., Tang, X., Qi, H.: Multi-disciplinary design optimization of submarine shape based on mathematical ship hull. Ship Sci. Technol. 11, 35–39 (2018). (in Chinese) 6. Li, Y.: Theory and Method of Product Innovation Design. Science Press, Beijing (2011) 7. Wang, Z.Y., et al.: Research on Kansei engineering and its application in massage chair design. Key Eng. Mater. 480–481, 1014–1017 (2011) 8. Joana, V., Osório, J., Sandra, M., Pedro, D.: Kansei engineering as a tool for the design of in-vehicle rubber keypads. Appl. Ergon. 61(1), 1–11 (2016) 9. Shieh, M.-D., Yeh, Y.-E.: Developing a design support system for the exterior form of running shoes using partial least squares and neural networks. Comput. Ind. Eng. 65, 704– 718 (2013) 10. Smith, J., Mansfield, N., Gyi, D., et al.: Driving performance and driver discomfort in an elevated and standard driving position during a driving simulation. Appl. Ergon. 49, 25–33 (2015) 11. Summerskill, S., Marshall, R., Cook, S., et al.: The use of volumetric projections in digital human modelling software for the identification of large goods vehicle blind spots. Appl. Ergon. 53, 267–280 (2016)

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12. Wang, J., Zhang, J.: Analysis and simulation of agricultural machinery cab based on jack. J. Agric. Mech. Res. (6), 246–251 (2018). (in Chinese) 13. Wang, Y., Liu, Q., Xiong, D., et al.: Research on assessment of eye movement sensitivity index through aircraft cockpit man-machine interface based on eye movement tracking technology. In: Proceedings of the 15th International Conference on Man-MachineEnvironment System Engineering (2015) 14. Vallières, B.R., Chamberland, C., Vachon, F., et al.: Insights from eye movement into dynamic decision-making research and usability testing. In: International Conference on Human-Computer Interaction, pp. 169–174 (2013) 15. Borgianni, Y., Maccioni, L., Basso, D.: Exploratory study on the perception of additively manufactured end-use products with specific questionnaires and eye-tracking. Int. J. Interact. Des. Manuf. (IJIDeM) 04, 1–17 (2019) 16. Zhang, J.-M., Wang, J.-W., Yang, Q., et al.: The modeling design of hand-held tillers based on TRIZ. Packag. Eng. (04), 133–139 (2019). (in Chinese)

Experimental Investigation of Thermal Elasto-Hydrodynamic Lubrication Based on Temperature Control Shuaihong Yu, Yazhen Wang(&), Jiacheng Shen, and Huihui Yue School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China [email protected]

Abstract. The heat generated from the working tribo-pairs will make the temperature of the lubricant rise which deficiently affects the performance of the lubricant and make the lubricant film thinner or broken which is the main cause leading to the failure of mechanism parts and equipment. In order to study the performance of lubricants under different temperatures, an improved test rig for lubrication film thickness is developed based on classical ball-on-disc contact and the heating system and oil storage device are innovatively added to control the temperature. This paper proposes a new method for judging the interference order of contact center based on image process, which is convenient and accurate. A series of temperature tests are conducted on oil and grease. Results show that when load and speed are constant, temperature has a great effect on the central film thickness of both oil and grease. When temperature is below 60 °C, the grease may not be completely melted, so the central film thickness is greatly affected by the speed and load, but when over 70 °C, the grease has melted and become soften, and the change in the central film thickness tends to be relatively stable. Keywords: Film thickness  Temperature control  Thermal elastohydrodynamic lubrication  Image process

1 Introduction Lubrication is the main way to reduce friction and wear. The function of lubricants is to provide a layer of lubricating film between the friction pairs to reduce the direct contact between the friction surfaces. Since the theory of hydrodynamic lubrication was put forward by Reynolds in 1886, the lubrication theory has been studied deeply in both experiment and theory [1]. In 1963, Gohar and Cameron [2] first observed the classic horseshoe shape of EHL film by the contact of steel ball and glass disc through optical interferometry, which initiated the research in the field of Optical Elastohydrodynamics. At present, optical interferometry is one of the most accurate and widely used methods. According to the basic principle of relative optical interference intensity, the film thickness at any location is determined by the relative position of the intensity between the maximum and minimum intensities of each interference order [3]. In practice, the © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 686–696, 2020. https://doi.org/10.1007/978-981-32-9941-2_56

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intensity change of light follows a cosine curve as the film thickness increases [4]. Sometimes the mechanical vibration of the disc caused by motor vibration and mechanical assembly errors brings shake to the image, so it is difficult to obtain the intensity value data of contact center and plot the intensity value change curve to determine the interference order. A new approach to get the central intensity value is proposed based on image process which can get the intensity data automatically. However, most of experiments have been devoted to EHL at different speeds and loads in recent decades, and very few work was done to put the temperature into consideration. Hili et al. [5] conducted the experiments under high speeds (up to 20 m/s) at different temperatures and high slide-roll ratios, the results of which indicate that inlet thermal effects are the main factor for the reduction of film thickness at high speeds and high slide-roll ratios. Liang et al. [6] pointed out that for cases involving moderate or high slide-roll ratio, both the inlet thermal effect and the contact thermal effect tend to reduce the film thickness, but inlet heating has greater effect on the central film thickness while the shear heating in the contact zone mainly affects the minimum film thickness near the outlet zone. This paper presents an improved test rig for lubrication film thickness based on the relative optical interference intensity (ROII) approach. And the heating system and oil storage device are innovatively added to control the lubricant temperature. Results at different temperatures are discussed.

2 Experimental Apparatus and Conditions This improved optical EHL test rig is developed based on ball-on-disc contact. The flat glass has a diameter of 160 mm coated with a layer of semi reflective Chromium film. The optical system of the test apparatus consists of an industrial camera with a monochromatic spectrum. The camera is controlled by the PLC for capturing the interference images. At present, the glass disc is driven by servo-motor and the steel ball supported by a four-bearing assembly is driven by the friction force between itself and the rotating disc in tractive rolling condition. In order to support the balls of various diameters, the fourbearing supporting system shown in Fig. 1 is designed as an adjustable structure for the convenience of experiment.

Fig. 1. Four bearing supporting system

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Lubricant Heating System

To control the temperature of lubricant, oil storage cup and heating system are added based on four-bearing supporting system. The heating system is equipped with a thermostat with RS485 bus, a solid-state relay (SSR), two electric heating rods, a resistance temperature detector (RTD) and a host computer. The power of the heating rod is 5V2.5 W with maximum dry burning temperature up to 120 °C. The temperature range of the experiment can be heated from 20 °C at room temperature to a maximum up to 80 °C. The schematic diagram of the heating control system is shown in Fig. 2.

Fig. 2. Schematic diagram of heating system

The GUI design which supports real-time interference image acquisition, storage, and temperature acquisition is presented in Fig. 3.

Fig. 3. Overview of the GUI

3 Image Process of Interference Image Traditionally it is hard to judge the interference order by eyes and may cause misjudgment which lead to the wrong calculated film thickness. And because of the shake of the images, it is also not a proper way to use a fixed point to obtain the intensity value. In order to determine the interference order, it is necessary to get the intensity value change curve of the contact center. Contours extraction for the Newton rings of interference image makes it possible to locate the circle, find the center of the fringes

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and obtain the central intensity value. A Block diagram of the image process is shown in Fig. 4. Contours extraction in this paper is based on image edge detection algorithm and the classical Canny operator are used. Figure 5 shows the result of edge detection after log operator.

Fig. 4. Block diagram of the image process.

Fig. 5. Interference image after Canny operator

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Circle Detection

After obtaining the binary image by the boundary extraction, Hough transform is used to extract the circle from the fringes which is the first bright fringe from the contact center. For the points of the corresponding circle taken out, the least square method is used to fit them. Then the coordinates of the circle center are obtained to get the light intensity. The results are shown in Fig. 6.

Fig. 6. Fitting circle with least squares after Canny operator

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The three pictures shown in Fig. 7 are light intensity curves of the contact center extracted by the new approach presented in this paper. From these three pictures, we can clearly judge the change of the interference order of the images. The light intensity in picture (a) first drops, then rises, and finally decreases, so the interference order is 2; the light intensity in (b) and (c) graph rises first and decreases, so the interference order is 1. It can be concluded that the method is very effective.

(a

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4 Test Condition In the present work, the experimental conditions of oil are all carried out at 45 r/min, the corresponding linear velocity is 0.306 m/s, and the corresponding maximum Hertz contact pressure is 419 Mpa under 9 N load. The viscosity data of oil measured by the viscometer at different temperatures is shown in Table 1. In the experiment of grease, not only the temperature is changed, but also the load and speed are changed. Two loading conditions were carried out which were 9 N and 13 N with the corresponding maximum Hertz contact stresses of 418Mpa and 473Mpa respectively. The test speed starts at 10 r/min and changes every 5 r/min until the maximum speed is 30 r/min. The experimental speed conditions include the corresponding line velocities are shown in Table 2.

5 Discussion and Result 5.1

Effect of Temperature

Figure 8 shows the interference images of the oil at different temperatures. It can be found from Fig. 11 that at 35 °C and 45 °C, the horseshoe shape is obvious in the interference images; at 55 °C the horseshoe shape is almost invisible; at 65 °C the horseshoe shape has disappeared; at 75 °C the horseshoe shape appears again, and its color changed from dark to bright, showing a meniscus shape. And as the temperature rises, the intensity value of contact enter will decrease. The light intensity data is shown in Fig. 9.

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Fig. 8. Interference images at 45 r/min (load is 9 N).

Fig. 9. Light intensity data

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In Fig. 9, the maximum light intensity of contact center is 102 at 35 °C, which decreases generally until 65 °C. The light intensity at 75 °C shares the same value with 65 °C. According to the new method of judging the interference order in this paper, it can be obtained that at 35 °C, 45 °C, 55 °C and 65 °C interference order is 1, while at 75 °C the interference order is 0. Therefore, the decrease of light intensity between 35 °C and 65 °C means that the central film thickness of oil decreases. Although the light intensity value at 65 °C and 75 °C is the same, the interference order of film thickness decreases from 1 to 0, so the calculated central film thickness decreases. The specific film thickness is shown in Fig. 10. From the Fig. 10, it can be found that the temperature has a great influence on the film thickness from 35 °C with 96 nm to 75 °C with 35 nm, decreased by 63.5%, which makes the Elasto-hydrodynamic Lubrication into the thin film lubrication.

Fig. 10. Central film thickness at different temperature

Fig. 11. (a) Central film thickness under load 9 N (b) Central film thickness under load 13 N

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a)

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Fig. 12. (a) Interference image at 15 r/min (b) Interference image at 25 r/min

The grease in this paper are all carried out under starvation condition. Figure 12 shows the interference images captured at different temperatures with speed of 15 r/min and 25 r/min. It can be seen from Fig. 12 that at the same speed, as the temperature rises, the Newton rings in the interference image will also change significantly like oil. It is known that when 15 r/min, the interference order of contact center is 1 from 40 °C to 80 °C, and the light intensity decreases with the rise of temperature, which means the decrease of central film thickness; when 25 r/min, the horseshoe shape appears at 40 °C and 50 °C, the interference order of which is judged as 2, but at 60 °C, 70 °C, 80 °C the film thickness level is judged as 1, and as the temperature rises, the central film thickness decreases, and the horseshoe shape becomes increasingly unnoticeable. The calculated central film thickness values are shown in Fig. 11.

Table 1. The viscosity of oil 45 55 65 75 Temperature ðt0 Þ, °C 35 Viscosity ðg0 Þ; mPas 82.50 54.15 37.05 26.4 19.5

Table 2. The speed Speed of disc 10 r/min 15 r/min 20 r/min 25 r/min 30 r/min Line speed (m/s) 0.068 0.102 0.136 0.17 0.204

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Effect of Speed

Figure 13 shows the interference images of grease captured at the temperature of 40 °C and 70 °C. It can be seen from Fig. 15 that the interference image changes dramatically with the increase of the speed, which means that the thickness of the film increases too. The calculated central film thickness values are shown in Fig. 14.

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It can be seen that the temperature also has a great effect on the central film thickness of grease. When the temperature is between 40 °C and 60 °C, the change of the central film thickness at 25 r/min and 30 r/min is more obvious. At 50 °C, when the speed is reduced from 30 r/min to 20 r/min, the film thickness at the center point is reduced by 43%, and 40.7% when the velocity decreases from 30 r/min to 20 r/min at 60 °C. However, when the temperature is higher than 60 °C, the change of film thickness at the central point slows down, and the average decrease of film thickness between 70 °C and 80 °C is 12%. a)

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Fig. 13. (a) Interference image at 40 °C (b) Interference image at 70 °C

Fig. 14. Central film thickness of different speeds (a) 9 N (b) 13 N

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The Effect of Load

Figure 15 shows the effect of load on central film thickness at the same temperature and speed. It can be seen that the lower the temperature, the greater the effect of load on film thickness. For example, the difference of central film thickness between the two load conditions is 36 nm at 40 °C, 20 nm at 50 °C, 9 nm at 60 °C, 7 nm at 70 °C and 4 nm at 80 °C.

Fig. 15. Central film thickness under two load conditions

6 Conclusion 1. The method of extracting the intensity value of contact center proposed in this paper is proved to be effective and can help to judge the change of the interference order. 2. The supporting system is composed of four bearings to make sure that the ball is in pure-roll mode. And to support the balls of various diameters, the four-bearing supporting system innovatively is designed as an adjustable structure. 3. Under starvation condition, the central film thickness of 13 N is obviously lower than that of 9 N, especially in the case of low temperature (40 °C, 50 °C, 60 °C), the influence of load on the central film thickness is greater.

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4. At 40 °C, 50 °C and 60 °C, the thickener in grease may not be completely melted, so the central film thickness is greatly affected by the speed and load, but at 70 °C and 80 °C, the grease has melted and become soften. The change in the central film thickness tends to be relatively stable.

References 1. Guo, F., Wong, P.L.: A multi-beam intensity-based approach for lubricant film measurements in non-conformal contacts. Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol. 216(5), 281–291 (2002) 2. Gohar, R., Cameron, A.: Optical measurement of oil film thickness under elastohydrodynamic lubrication. Nature 200(4905), 458–459 (1963) 3. Luo, J.: Thin film lubrication part i: study on the transition between EHL and thin film lubrication using a relative optical interference intensity technique. Wear 194(1–2), 107–115 (1996) 4. Chen, Y., Huang, P.: An improved interference method for measuring lubricant film thickness using monochromatic light. Tribol. Lett. 65(4), 120 (2017) 5. Hili, J., Olver, A.V., Edwards, S., et al.: Experimental investigation of elastohydrodynamic (EHD) film thickness behavior at high speeds. Tribol. Trans. 53(5), 658–666 (2010) 6. Liang, H., Guo, D., Reddyhoff, T., et al.: Influence of thermal effects on elastohydrodynamic (EHD) lubrication behavior at high speeds. Sci. China Technol. Sci. 58(3), 551–558 (2015)

Study on Nonlinear Characteristics of Spatial Spreading Mechanism with Multiple Clearance Joints Wenzhou Lin(&), Xupeng Wang, Xiaomin Ji, and Chunqiang Zhang Department of Industrial Design, Xi’an University of Technology, Xi’an 710048, China [email protected], {wangxupeng,jixm}@xaut.edu.cn, [email protected]

Abstract. Based on an improved contact force model with variable stiffness coefficient and Coulomb friction model, the nonlinear characteristics of spatial mechanism with multiple clearance joints are studied. The effects of clearance size, clearance number and gravity on the nonlinear characteristics of mechanical systems are numerically simulated. It is found that the variation of clearance size, the asymmetry of clearance number and the existence of gravity have significant influence on the nonlinear characteristics of the system. The research results have certain theoretical significance for the design of spatial spreading mechanism with multiple clearance joints. Keywords: Nonlinear characteristics  Spatial spreading mechanism Multiple clearance joints  Numerical simulation



Because of the errors in assembly and manufacturing process, the requirement of relative motion of components and wear during operation, the clearance at the joints of mechanical system is inevitable. The contact-impact phenomenon caused by the clearance will affect the key technical indicators such as the accuracy and stability of the system, and even cause the failure of the motion pair to be invalid [1–3]. Therefore, the study of the dynamic performance of the joints with clearance is an important research topic in the field of precision instrument manufacturing and aerospace equipment. It is a key point to establish a contact force model that accurately describes the contact-impact effect under different working conditions. Based on a contact force model with variable stiffness coefficient and the improved Coulomb friction model, the nonlinear characteristics of the mechanism with clearance joints are studied in this paper. The effects of clearance size, clearance number and gravity on the nonlinear characteristics of spatial spreading mechanism with multiple clearance joints, a wingspan mechanism for space equipment, are numerically simulated and analyzed.

This paper is supported by The Youth Project of Humanities and Social Sciences Financed by Ministry of Education (Project No. 19YJC760057). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 697–707, 2020. https://doi.org/10.1007/978-981-32-9941-2_57

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1 Summary Since the 1970s, domestic and foreign researchers have developed a series of contact force models, and continue to make improvement and perfection according to practical engineering problems. The Hertz contact theory lays the foundation for research in this field, but the limitations are also obvious: pure elastic contact force model; poor adaptability to different contact surface shapes and clearance sizes. In view of the shortcomings of poor adaptability, Ciavarella et al. [4], Liu et al. [5] put forward different improved models to meet the needs of different working conditions. Based on the Kelvin-Voigt model, Lankarani and Nikravesh proposed a continuous contact force model named L-N model [6]. The model considers the energy dissipated during the contact-impact process and decomposes the deformation into elastic deformation and plastic deformation. The expression is as follows: "

  # 2 3 1  c d_ r Fn ¼ Kd þ Dd_ ¼ Kd 1 þ 4 d_  n

n

ð1Þ

where K is stiffness parameter; D is damping coefficient; d is the local relative penetration; cr is the restitution coefficient; d_ is the relative impact velocity; d_ ðÞ is the initial impact velocity; n is the force index, for metal contact, n value is 1.5. The L-N model has extensively been used to study the dynamics of mechanisms with clearance joints [7]. Based on the L-N contact force model, Flores et al. studied the effects of parameters such as clearance size and friction coefficient on system dynamics performance [8, 9]. Based on a large number of numerical simulation studies, Liu found that the L-N contact force model is only suitable for the working conditions of large clearances, small loads, and high restitution coefficients (close to 1). Zhengfeng BAI et al. proposed an improved nonlinear normal contact force model based on the improvement of L-N model [10]; and based on the improved model, the dynamic performance of the spacecraft’s mechanism with clearance joints was studied [11]. However, the above models except the model presented by bai assumes that the stiffness coefficient of the contact process is a constant only related to the material properties and dimension of contact bodies. Actually, the experiments and numerical calculations in the existing experiments show that the stiffness coefficient is also related to other factors [10, 12]. Bicai xu and xupeng wang proposed another nonlinear normal contact force model based on the L-N model, Coulomb’s friction law and variable stiffness coefficient [13, 14]. Based on this model, this paper intends to study the nonlinear characteristics of the spatial spreading mechanism with multiple clearance joints.

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2 An Improved Contact Force Model Based on Variable Stiffness Coefficient 2.1

Contact Force Model

On the basis of L-N model and improved elastic foundation model [15], Wang and Liu introduced an improved nonlinear contact force model, the expression is as follows Fn ¼ Ki dn þ Dd_ " #   3 1  c2r e2ð1cr Þ d_ n ¼ Ki d 1 þ ðÞ 4 d_

ð2Þ

where Ki is the nonlinear coefficient of contact stiffness, is expressed as  1=2 pE  Ldn 1 Ki ¼ 2ðDR þ dÞ 2

ð3Þ

where L is the axial length of the colliding body, DR is the difference in radius, and E  is the equivalent elastic modulus of material of colliding bodies, which can be defined as 1 1  v21 1  v22 ¼ þ E E1 E2

ð4Þ

in which E1; 2 and v1; 2 are Young’s modulus and Poisson’s ratio of material respectively. 2.2

Friction Force Model

WANG and LIU, based on Coulomb’s friction model, presented a modified friction model. This model can deal with the problem of the transformation of friction state during numerical integration, which is caused by different tangential velocity [13, 16]. The expression is as follows FT ¼ lðvT ÞFn signðvT Þ

ð5Þ

where lðvT Þ is the dynamic friction coefficient, which is defined as follows 8 ld signðvT Þ j vT j  vd > 8  2 9 > > > j v jv T s < = > > <  ld þ hðls  ld Þ vd v is signðvT Þ vs  jvT j  vd :  3  2 jvT jvs ; lðvT Þ ¼ > vd vs >    > 2  3 > > > v þ v T d : 2ld 3 2vd 2 vT2vþdvd 0:5 jvT j  vs

ð6Þ

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where vs and vd are critical velocities of static friction and dynamic friction, ls and ld are coefficients of static friction and dynamic friction, respectively.

3 Study on Nonlinear Characteristics of Spatial Spreading Mechanism with Multiple Clearance Joints 3.1

Spatial Spreading Mechanism

A spatial spreading mechanism, which has multiple clearance joints (OL, OR), two connecting rob links (l3, l4) and two wings (l1, l2), is described in Fig. 1. In the numerical simulation of this paper, all the components are considered as rigid bodies and joints except OL, OR are ideal joints.

Fig. 1. Diagram of mechanism

The value of mass, inertia properties and coefficients in dynamic simulation are given in Tables 1 and 2. According to [17], the value of critical velocity of static friction is 0.1 mm/s and dynamic friction is 10 mm/s, as well as coefficient of static friction is 0.3 and dynamic friction is 0.25, respectively. Table 1. Value of parameters in simulation (1) [13] Body Length (m) Mass (kg) Jx (kgm2) Jy (kgm2) Jz (kgm2)

l1 0.13 12.52 1.8 1.74 0.54

l2 0.13 12.52 1.8 1.74 0.54

l3 0.226 0.03 7.075  10−7 1.432  10−4 1.436  10−4

l4 0.226 0.03 7.075  10−7 1.432  10−4 1.436  10−4

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Table 2. Value of parameters in simulation (2) Coefficient cr E1, E2 (GPa) v1, v2 Radius of bearing (mm) Width of bearing (mm)

Value 0.8 207 0.3 8 12

As depicted in Fig. 1, the mechanism is driven following the Y-direction by a piston rod with radius of 8 mm, and the driving force is supplied by the high pressure air, which is illustrated in Fig. 2.

Fig. 2. High air pressure curve

3.2

Numerical Simulation

The modeling and numerical simulation are finished in the ADAMS software, and the integrator scheme of Runge-Kutta is used. Meanwhile, maximum integration step size is 10−4 and integration tolerance is 10−5, respectively. The simulation results are shown as follows. 3.2.1 The Influence of Clearance Size Assume that the clearance values of the left and right joint in this mechanism are the same. Figures 3 and 4 show the numerical simulation results under different clearance values of 0.01 mm, 0.05 mm and 0.1 mm. The simulation results show that (1) due to the influence of clearance joints, the angular acceleration of the left and right wings, and the contact force at the clearance joints are all appearance obvious oscillation phenomenon. (2) With the increase of clearance value from 0.01 mm, 0.05 mm to 0.1 mm, the amplitude of the oscillation is gradually increased, and the time required to reach the stability of motion is correspondingly gradually extended, where the time changes from 0.0285 s, 0.0305 s to 0.032 s. (3) But the motion of the left and right wings is always consistent.

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3.2.2 The Influence of Clearance Number Assume that the left joint of the mechanism is an ideal joint, and the right joint is a clearance joint, and the clearance value is 0.01 mm. Figures 5 and 6 show numerical simulation results. The simulation results show that (1) under the influence of the clearance, the angular acceleration of the right wing and the contact force at the joint show obvious oscillation phenomenon. (2) Meanwhile, the angular acceleration of the left wing and the contact force at the joint also show obvious oscillation phenomenon. (3) Compared with the case where the left and right joints are all clearance joints, the time required to achieve the stability of motion is greatly prolonged, where the time increases considerably from 0.0285 s to 0.072 s. (4) The motion of the left and right wings is less consistent.

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3.2.3 The Influence of Gravity Figure 7 shows the numerical simulation results considering the influence of gravity. The simulation results show that (1) under the influence of gravity, the contact force at the left and right joint has obvious oscillation amplitude increase. (2) And the time required to reach the stability of motion increases to 0.038 s, where the one ignoring the influence of gravity is 0.034 s. (3) Gravity has less influence on the consistency of left and right motion.

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(b) Fig. 7. The influence of gravity on the contact force

4 Conclusion In this paper, based on an improved contact force model with variable stiffness coefficient, the influence of clearance size, clearance number and gravity on the nonlinear dynamic characteristics of a spatial spreading mechanism are studied by numerical simulation. The following conclusions have been obtained (1) As the clearance size becomes larger, the oscillation phenomenon of the mechanism motion is gradually strengthened, and the time for achieving the stability of motion is correspondingly increased. (2) Because of the imbalance of the left and right joint, the oscillation phenomenon of the motion of wings will be affected and the consistency of motion becomes worse, and the time required to reach the stability of motion is significantly prolonged. (3) The gravity of the mechanism has obvious influence on its nonlinear dynamic characteristics. Therefore, in order to obtain better dynamic characteristics, the research results have the following guiding significance for the design and manufacture of the spatial spreading mechanism with multiple clearance joints (1) On the premise of meeting the

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requirements of manufacturing process and relative motion of components, the clearance should be as small as possible. (2) The symmetry of the number and size of the clearance should be ensured. (3) The influence of gravity cannot be ignored.

References 1. Liu, C.S., Chen, B.: Some basic problems in the study of dynamic contact of flexible multibody systems. J. Vib. Shock, 18(3), 5–12 (1999) 2. Garcia Oeden, J.C.: Analysis of clearance in multibody system. Multibody Syst. Dyn. 13, 401–420 (2005) 3. Yao, W.L., Wang, Y.P., Bian, L., et al.: Survey for dynamics on impact and contact of multirigid-body systems. Mech. Eng. 29(6), 9–12 (2007) 4. Ciavarella, M., Decuzzi, P.: The state of stress induced by the plane frictionless cylindrical contact 1: the case of elastic similarity. Int. J. Solid Struct. 38, 4507–4523 (2001) 5. Liu, C.S., Zhang, K., Yang, L.: The compliance contact model of cylindrical joints and clearance. Acta Mech. Sinica 21(5), 451–458 (2005) 6. Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112, 369–376 (1990) 7. Tian, Q., Flores, P., Lankarani, H.M.: A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints. Mech. Mach. Theory 122, 1–57 (2018) 8. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamic behavior of planar rigid multibody systems including revolute joints with clearance. Proc. IMechE Part K: J. Multibody Dyn. 221(2), 161–174 (2007) 9. Flores, P.: A parametric study on the dynamic response of planar multibody systems with multiple clearance joints. Nonlinear Dyn. 61, 633–653 (2010) 10. Bai, Z.F., Zhao, Y.A.: hybrid contact force model of revolute joint with clearance for planar mechanical systems. Int. J. Non-Linear Mech. 48, 15–36 (2013) 11. Bai, Z.F., Liu, Y.Q., Sun, Y.: Investigation on dynamic responses of dual-axis positioning mechanism for satellite antenna considering joint clearance. Mech. Sci. Technol. 29(2), 453– 460 (2015) 12. Wang, X.P., Lin, W.Z., Ji, X.M., Gao, Z., Bai, X.B., Guo, Y.X.: Dynamic analysis of a planar multibody system with multiple revolute clearance joints. J. Mech. Eng. Sci. (2019). https://doi.org/10.1177/0954406218819022 13. Xu, B.C., Wang, X.P., Ji, X.M., Tong, R.T.: Dynamic and motion consistency analysis for a planar parallel mechanism with revolute dry clearance joints. J. Mech. Sci. Technol. 31(7), 3199–3209 (2017) 14. Wang, X.P., Liu, G., Ma, S.J.: Dynamic analysis of planar mechanical systems with clearance joints using a new nonlinear contact force model. J. Mech. Sci. Technol. 30(4), 1537–1545 (2016) 15. Liu, C.S., Zhang, K., Yang, L.: The FEM analysis and approximate model for cylindrical joints with clearances. Mech. Mach. Theory 42, 183–197 (2007) 16. Wang, X.P., Liu, G., Ma, S.J., Tong, R.T.: Effects of restitution coefficient and material characteristics on dynamic response of planar multi-body systems with revolute clearance joint. J. Mech. Sci. Technol. 31(2), 587–597 (2017) 17. MDI: Building Models in ADAMS/View, Software Handbook (2012)

A Novel Design of Tapered Sub-array Structure for SSPS-OMEGA Tong Wu1,2(&), Yingzhong Tian1, Meng Li2, and Long Li1 1

School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China [email protected], {troytian,lil}@shu.edu.cn 2 Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China [email protected]

Abstract. In this paper, a novel design of hexagonal tapered sub-array structure for SSPS-OMEGA is proposed. Based on this structure, geometric characteristics of sub-array are analyzed. One side of the sub-array structure be taken as research object to study the division method of its sub-unit based on graph theory and two types of sub-unit configuration are obtained. According to the geometric characteristics and the sub-unit configuration of this sub-array structure, the computer-aided design models composed with 24 Bricard linkages are built by Solidworks. Then the expression of the folding ratio for the structure is obtained by geometric characteristics and 3D model. Keywords: Hexagonal sub-array Configuration design  3D model

 Tapered and deployable structure 

1 Introduction The Space Solar Power Station (SSPS) is a huge energy system that collects and converts solar energy into electricity in space and then transmits it to the Earth by wireless transmission [1]. Since Dr. Peter Glaser proposed conceptual design of space solar power station in 1968 [2], it has drawn worldwide attention. Many countries such as United States, Japan, Europe and China have proposed various concepts of space solar power station [3]. In 2014, a team from Xidian University, led by Prof. Duan Baoyan, proposed a scheme named Orb-shape Membrane Energy Gathering Array for Space Solar Power Station (SSPS-OMEGA) [4]. The SSPS-OMEGA concept can be described as a modular, spherical system concept in which sunlight is collected by a primary reflector and produces power in a series of PV cell arrays [4]. In this scheme, a spherical structure with a diameter of several kilometers is divided into different kinds of hexagonal sub-array structures by a method of polygon segmentation. For the same spherical surface, building a polygonal mesh will use less material than a triangle or quadrilateral, resulting in a smaller overall quality and a higher power-to-quality ratio [5]. Therefore, according to the characteristics of SSPS-OMEGA, the sub-array configuration is divided into different kinds of hexagons [6]. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 708–718, 2020. https://doi.org/10.1007/978-981-32-9941-2_58

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Currently, research on the sub-array structure of large-scale space solar power stations has focused on the study of single-layer sub-array structures composed of links and hinges. However, for large-scale spatial structures, the stability and stiffness of such single-layer sub-array structures are inferior to the three-dimensional truss structure. Santiago-Prowald et al. proposed a conical ring structure constructed with V-fold bars that has higher stiffness and lower quality than cylindrical truss structures [7, 8]. In general, a large deployable spatial structure consists of many deployable mechanisms. Chen et al. are the pioneers who first attempt to utilize the overconstrained mechanisms such as the Bennett linkage, the Myard linkage and the Bricard linkage as building blocks for construction of large deployable mechanism [9, 10]. As the basic sub-unit for a deployable structure, the plane-symmetric Bricard linkage is one of the most widely used unit found in many deployable structures [11–13]. This paper proposes a new hexagonal tapered sub-array structure for SSPSOMEGA. First, the article extracts geometry edges of the frustum and converts them into a tapered configuration as the sub-array structure configuration. Next, we obtain the conditions that represent its geometric properties based on geometric characteristics. Then the configuration of several unfolded sub-units in the tapered sub-array structure obtained by the method of point symmetric splitting based on the graph theory. Finally, a simple 3D model for the hexagonal tapered sub-array structure composed of 24 Bricard linkages is presented. Conclusions are drawn in the last section of the paper.

2 Mechanical Design of Sub-arrays As shown in Fig. 1, the regular hexagonal sub-array structure of the thin-film reflector modules obtained by polygon partitioning method in SSPS-OMEGA is studied [4].

Fig. 1. Construction of spherical reflector for SSPS-OMEGA

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Based on the columnar truss structure, a tapered sub-array structure constructed with deployable mechanism for SSPS-OMEGA is proposed. The tapered sub-array structure is a deployable truss mechanism similar to the shape of frustum in an unfolded state. In the unfolded state, the deployable mechanism locks into a structure with stiffness. As shown in Fig. 2, the football structure shown in the picture consists of twelve regular pentagons and twenty regular hexagons.

Fig. 2. Extracting the frustum geometry edge

The axial section of the truss structure is a regular polygon whose side length changes linearly, if the straight line in the transformed structural configuration is considered to be a bar member, the tapered conversion structure in Fig. 2 can be considered as a peripheral truss structure in nature. For a tapered subarray structure, due to the existence of the structural taper and the high structural stiffness [5, 6], the spheroidal structure composed of the tapered subarray can be regarded as a two-layer spheroid structure with higher structural stiffness. This provides a new and feasible design idea for the sub-array design of SSPSOMEGA and it can be considered as an assembled sub-array structure of SSPSOMEGA. The thin-film reflector modules of SSPS-OMEGA can be equipped with an unidirectional permeable film. In order to facilitate the construction of the overall spherical power plant structure and achieve higher concentration efficiency, the larger polygon in the upper and lower layers of the structure be considered as the support of the thin-film. Since the tapered sub-array structure is in the form of a closed peripheral truss structure, a plurality of film connection nodes can be provided on each side of the formed hexagonal sub-array. As shown in Fig. 3, compared with six-nodes film connection method of the single-layer sub-array, multi-nodes connection method of the peripheral truss structure can better tighten the film, so it has superior surface accuracy of the film.

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a)Tapered sub-array

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Fig. 3. Two types of regular hexagonal sub-array axial diagrams

Assuming the diameter of the bar is d, the axial projection area of the two sub-array structures can be obtained: (

  L St  6d n þ b ; d  n\m Ss  6md

ð1Þ

Where St and Ss represent the axial projection area of regular hexagonal sub-array structure and single-layer sub-array structure respectively, m and n represent the length of the upper and lower sides of the side unit of the sub-array respectively, b L represent the axial projection length of the diagonal bar in the side unit. From the geometric parameters of the regular hexagonal sub-array structure, an equality relationship: m ¼ n þ b L can be obtained. So that the shading rates of the two structures are considered as equal (St  Ss ). However, the tapered sub-array structure has superior stiffness characteristics. Since the design of the sub-array structure involves various factors such as concentrating efficiency, power-to-quality ratio and stiffness, the advantages and disadvantages of other aspects will be further studied in the future.

3 Geometric Analysis As shown in Figs. 4 and 5, the sub-array unit has an isosceles trapezoidal shape in an unfolded state, where the longer bottom edge (AB) is defined as the upper string of the sub-array unit, and the shorter bottom edge (DC) is the lower string of the sub-array unit, and the two trapezoidal sides represent the oblique side of the sub-array unit. Given the length parameters of the four sides, the isosceles trapezoidal unit and the geometry of the element can be determined. Then the overall geometry of the tapered sub-array structure is determined.

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Fig. 4. Geometric parameters of the regular hexagonal sub-array structure

m

A

B

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C α O

Fig. 5. Geometric parameters of the isosceles trapezoidal unit

When the isosceles trapezoidal and foldable unit is in the unfolded state, we define the length of the oblique side is L, and the height is h; the intersection angle of the trapezoidal foldable unit at the intersection of the two waist extension lines is a, a range of a from Fig. 5 can be obtained: a\60o . The circumradius where the upper string located represented by R, the circumradius where the lower string located represented by r, and the center angle corresponding to the string represented by h(h ¼ p3), the axial height of regular hexagonal sub-array structure is H, then expressions of these parameters can be obtained as follow: R ¼

m n p ¼ m; r ¼ ¼ n; [ h [ 0 2 sin p6 2 sin p6 3 a ¼ 2 arcsin

mn ;m[n[0 2L

ð2Þ ð3Þ

A Novel Design of Tapered Sub-array Structure for SSPS-OMEGA

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð m  nÞ 2 ;m[n[0 h ¼ L2  4 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H ¼ L2  ðm  nÞ2 ; m [ n [ 0

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ð4Þ ð5Þ

The expanded aperture area (S) is: pffiffiffi 3 3 2 S¼ m ;m[0 2

ð6Þ

For an isosceles trapezoidal and foldable unit, the necessary and sufficient conditions for the network to form a tapered and deployable sub-array structure can be shown as: 

o 90o [ arccos mn 2L [ 60 mþn L [ 2 [ 0; m [ n [ 0

ð7Þ

In general, the taper is defined as the ratio of the diameter of the cone bottom surface to the axial height of the cone. If it is a circular table, the taper is defined as the ratio of the difference between the diameters of the two bottom circles and the axial height of the circular table. In this paper, the taper of the tapered sub-array structure is defined as the ratio of the difference between the diameters of the circumscribed circles of the upper and lower regular polygons and the axial height of the sub-array structure in unfolded state, denoted by the symbol b. It can be shown that:   tan 2 arcsin mn 2L b ¼ arcsin tan Np pffiffiffi  3 m  n ¼ arcsin tan 2 arcsin 2L 3 

ð8Þ

Since the tapered sub-array structure belongs to the two-layer structure from the radial direction of the whole ball structure, the networking of the sub-array is not only affected by the spherical mesh division method but also affected by taper of the subarray.

4 Configuration Design of Sub-units One side of the hexagonal tapered sub-array structure can be taken as research object to study the division method of its sub-unit based on graph theory due to the symmetry of the tapered sub-array structure. In order to facilitate the configuration analysis, here are some assumptions for configuration analysis in the conceptual stage: this paper

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considers the connecting bars forming the foldable mechanism as rigid straight line segments with length measurement and regards the hinges of the constituent mechanisms as nodes. At the same time, the geometric shape of the connecting bars, the type of joint and the type of freedom are ignored. Then a single closed loop structure can be represented by a simple graph by lines and points. The basic shape design of the foldable unit is carried out by using the method of point symmetry splitting. Two basic division methods: single-point splitting and two-point splitting can be obtained. As shown in Fig. 6, we use the line segment AB at the midline of the isosceles trapezoid as the baseline. The black point and line stands for the connecting hinges and the link respectively. The single-point splitting means that one point is fixed and the other point is split in the opposite direction. And the two-point splitting means that point A and point B are split in the opposite direction at the same time.

(a)Single point splitting at point B

(b)Single point splitting at point A

(c)Two-point splitting situation 1

(d)Two-point splitting situation 2 Fig. 6. Sub-unit division based on graph theory

According to the above analysis and design, two types of foldable sub-unit configuration: triangular sub-unit configuration and quadrilateral sub-unit configuration can be obtained.

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In recent years, many scholars have used space over-constrained linkages with good stiffness and high folding ratio as possible building blocks for deployable structure such as the Bennett linkage, the Myard linkage and the Bricard linkage. The Bricard linkage is obviously a better choice, because each side of the hexagonal tapered sub-array structure requires only simple in-plane folding. As shown in Fig. 7, the plane-symmetric Bricard linkage is a closed-loop over-constrained spatial mechanism composed of six hinge-jointed bars, which has one plane of symmetry during its deployment.

Fig. 7. Polygons can be determined by Bricard linkages

It can be shown that the plane-symmetric Bricard linkage can form a variety of shapes such as triangle, quadrangle, pentagon and hexagon, which has 3-DOF. Its 3DOF can be reduced to 1-DOF by designing drive motors and adding constraint mechanisms. In this article, as a deployable sub-unit of the sub-array, Bricard linkage is an implementation example.

5 3D Modeling of the Tapered Sub-array Structure Based on the above analysis and design, a simple model of this hexagonal tapered subarray structure is derived utilizing its geometrical characteristics. The locked state after expansion and collapsing state of the tapered structure are built by Solidworks as shown in Fig. 8. The parameters of the 3D model are shown in Table 1 below.

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Fig. 8. 3D model of the hexagonal tapered sub-array structure

Table 1. Basic parameter Parameter h/mm H/mm s/mm t/mm d/mm L/mm h/o

Value 594.00 477.40 592.09 238.70 12.00 621.80 60.00

As shown in Fig. 8, the hexagonal tapered sub-array structure includes 24 Bricard linkages. Its unfolded state and folded state are both cone-shaped and the non-foldable triangular unit on each side can be regarded as one side of the Bricard linkages. Each deployable sub-unit is arranged with two elastic hinges that have stored elastic potential energy for self-propulsion of the overall structure. At the same time, flexible ropes and wheeled mechanisms for ensuring simultaneous deployment of both side units are arranged in the hexagonal tapered sub-array structure. In order to reduce the vibration shock after the structure unfolded, a motor is arranged for the release of flexible ropes. In this paper, the folding ratio (k) is defined as follow: k¼

V1 V2

ð9Þ

Where V1 is the volume of the truncated cone formed by the hexagonal tapered subarray structure in the fully collapsed state, V2 is the volume of the truncated cone formed by the hexagonal tapered sub-array structure in the fully unfolded state. Assuming the diameter of the bar is d, we can get expressions of V1 and V2 :

A Novel Design of Tapered Sub-array Structure for SSPS-OMEGA

 4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V1 ¼ p L2  4t2 3N 2 d 2 þ t2 þ 3Ndt ; t [ 0; d [ 0 3  2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V2 ¼ p L2  4t2 N 2 s2 þ 2t2 þ 3Nst ; 3 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð m  nÞ 2 L2  [ s [ 0; t [ 0 4

717

ð10Þ

ð11Þ

Where t is the side length of the triangular unit, L is the side length of a hypotenuse of the triangular unit, s is the side length of the sub-unit, N is the number of sub-units. Based on the previous analysis, an equality relationship: m = Ns + t, n = Ns can be obtained. According to Eqs. (9), (10) and (11), the folding ratio can be obtained: k¼

V1 3N 2 d 2 þ t2 þ 3Ndt ¼2 2 2 N s þ 2t2 þ 3Nst V2

ð12Þ

For this example, the folding ratio is 0.03.

6 Conclusions (1) This paper presents a hexagonal tapered sub-array structure for SSPS-OMEGA based on columnar truss structure. A plurality of film connection nodes can be provided on each side of the hexagonal tapered sub-array structure, so the multinode connection of the peripheral truss structure can better tighten the film and achieve superior film accuracy. That will help improve the light collection efficiency of the space solar power station. (2) Based on graph theory, two types of foldable sub-unit configuration:triangular sub-unit and quadrilateral sub-unit, are presented. Bricard linkage is used as the foldable sub-unit in this paper due to the simple folding property in-plane. (3) The numerical model for the hexagonal tapered sub-array structure are built as a typical design implementation example. Folding ratio of the hexagonal tapered sub-array structure is obtained according to the above analysis and design. To a certain extent, the design of the hexagonal tapered sub-array structure can provide technical support for research on sub-array of space solar power station. Acknowledgements. The work was supported by the National Nature Science Foundation of China (grant no. U1637207).

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References 1. Li, X., Zhou, J., Duan, B., et al.: Performance of planar arrays for microwave power transmission with position errors. IEEE Antennas Wirel. Propag. Lett. 14, 1794–1797 (2015) 2. Glaser, P.E.: Power from the sun: its future. Science 162(3856), 857–861 (1968) 3. Xinbin, H., Li, W., Xinhua, Z.: Concept design on multi-rotary joints SPS. J. Astronaut. 36 (11), 1332–1338 (2015) 4. Yang, Y., Zhang, Y., Duan, B., et al.: A novel design project for space solar power station (SSPS-OMEGA). Acta Astronaut. 121, 51–58 (2016) 5. Dongxu, W.: Structural analysis and design for spherical concentrator grid of OMEGASSPS. Xidian University (2017) 6. Cun, J.: Research on meshing, optimization and mechanica properties of free-form grid structures. Zhejiang University (2015) 7. Scialino, L., Ihle, A., Migliorelli, M., et al.: Large deployable reflectors for telecom and earth observation applications. Ceas Space J. 5(3–4), 125–146 (2013) 8. Medzmariashvili, N., Medzmariashvili, E., Tsignadze, N., et al.: Possible options for jointly deploying a ring provided with V-fold bars and a flexible pre-stressed center. Ceas Space J. 5 (3–4), 203–210 (2013) 9. Chen, Y.: Design of structural mechanisms. Oxford University, Oxford (2003) 10. Chen, Y., You, Z.: An extended Myard linkage and its derived 6R linkage. J. Mech. Des. 130(5), 052301 (2008) 11. Qi, X., Huang, H., Miao, Z., et al.: Design and mobility analysis of large deployable mechanisms based on plane-symmetric Bricard linkage. J. Mech. Des. 139(2), 022302 (2017) 12. Baker, J.E.: An analysis of the Bricard linkages. Mech. Mach. Theory 15(4), 267–286 (1980) 13. Chen, Y., You, Z., Tarnai, T.: Threefold-symmetric Bricard linkages for deployable structures. Int. J. Solids Struct. 42(8), 2287–2301 (2005)

Research on Multiresponse Robustness Optimization for Unmanned Aerial Vehicle Electrostatic Spray System Yangdong Wu1,2(&), Jiajie Lu1, and Yiquan Wang1 1 Key Laboratory of Modern Manufacturing Technology (Ministry of Education), Guizhou University, Guiyang 550025, China [email protected] 2 School of Mechanical Engineering, Guizhou University, Guiyang 550025, China

Abstract. Response surface methodology (RSM) based robustness optimization design is a fine technique to improve product quality, it is very suitable for solving multivariable robustness optimization problems. The rationale of response surface methodology is presented in this paper firstly, the central composite face centered design, which is one of three central composite design types, is used in RSM’s design of experiments (DOE), then the desirability function is applied to solve multiple design objectives so that the multiple responses can be changed into one function. After that, simulated annealing is used to solve overall desirability function. Finally, unmanned aerial vehicle electrostatic spray system is optimized using our method. Keywords: Response surface methodology UAV  Electrostatic spray

 Central composite design 

1 Introduction Robustness refers to insensitivity to small deviation from various factors, for example, if product performance is insensitive to variations in manufacturing dimensions and mechanical properties of materials, the Low quality materials can substitute for high quality materials, so product manufacturability can be improved and the product cost can be reduced, if the product is insensitive to changes of the environment, the reliability of the product would be ensured and the operation cost would be reduced. Robust design is an engineering design method, it can obtain high-quality and low-cost product through considering the performance, quality and cost of the product. Robust design was proposed by G. Taguchi firstly, it based on orthogonal experimental design and signal to noise ratio. Figure 1 shows the robust design principle, its essential elements include input y0 (signal factor), control factor z, noise factor x and output y (response).

This project is supported by National Natural Science Foundation of China (Grant No. 51505094), Guizhou Provincial Science and Technology Support Program of China (Grant No. [2016] 2037). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 719–728, 2020. https://doi.org/10.1007/978-981-32-9941-2_59

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Since robust design was proposed, many scholars from various countries have carried out a series of research work on this issue, and some different robust design methods are put forward, such as response surface methodology, double response surface method, tolerance polyhedron method, generalized linear model method, sensitivity method, random model method and so on. Farazkish [1] described various reliability and robustness modeling techniques and design and control issues, bionanorobots are composed of nano-scale components, even if bio-nanorobotics are different than macro robots, there are many similarities in modeling techniques, they utilize the bio-nanorobots characteristics to design fault-tolerant system, this system is more powerful in terms of implementing robust digital functions. Jun [2] proposed a robust optimal design method through a hybrid response surface method, this method can find an optimal point satisfying a target Z-value, or a probability of failure, they increase the open-circuit airgap flux and decrease its variation using the hybrid response surface method. Hong [3] analyzed the non-robust problem of rotor systems dynamics characteristic, they presented a novel robust design method of contact status, their method can decrease the sensitivity of mechanical properties and show preferable engineering value. Sun [4] proposed a novel multi-objective discrete robust optimization algorithm, which was used in design of engineering structures involving uncertainties, grey relational analysis and principal component analysis were used as a multicriteria decision making model, so multiple conflicting objectives were converted into one unified cost function. Wei [5] proposed to employ the basic principles of robust design in the module partition schemes, by considering the dynamically changing customer preferences as a noise factor, they make the schemes less sensitive to the preferences, and an pareto archive particle swarm optimization algorithm is applied to solve the multi-objective optimization problem. Zhou [6] proposed a Kriging metamodel based multi-objective robust optimization approach, it would obtain the robust Pareto set under the interval uncertainty. Donoso and Bellido [7] presented an robust design method for multimodal piezo transducers. Park [8] investigated the effect of normal model departure on the optimal operating condition estimates and constructed a methodology to deal with the effect of normal model departure. das Neves Carneiro [9] presented a new approach to the reliability based robust design Optimization for angle-ply composite laminate structures. Park [10] estimated a dual

Fig. 1. Robust design principle

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quadratic response surface model, it is for the expected value and logarithmtransformed variance of the target response, when the data are contaminated, alternative estimators are quite efficient. Ashouri [11] investigated the sensitivity of the design to selected boundary conditions, compared for several uncertainties in the deterministic and stochastic optimizations, when a robust design is attained, the size of devices may vary by up to 100%.

2 Response Surface Methodology and Multiple Response Optimization Response surface methodology(RSM) is a set of statistical processing techniques based on design of experiments, it could process modeling and analysis of multivariable problems. RSM was proposed by G.E.P. BOX and K.G. Wilson, since Taguchi robust design method came out, many researchers devote themselves to improve it by statistical analysis, a considerable number of algorithm apply response surface method to replace Taguchi’s signal-to-noise ratio analysis method. Recently, RSM has become a powerful tool for robust design. The second-order response surface model is the most widely used model [12], the fitted second-order model may be written as ^

^

y ¼ b0 þ

n X i¼1

^

bi xi þ

n X i¼1

^

bii x2i þ

X

^

bij xi xj

ð1Þ

i\j

xi(i = 1,2, …, n) are n independent experimental factors, each regression coefficient could be calculated by least square method. RSM based robust design is generally divided into the following stages: (1) Determining controllable and noise factors, then determine the level of controllable factors and noise factors (2) Selecting the appropriate method for design of experiments (3) Obtaining data related to each parameter and response through experiments, fitting the response surface model according to the experimental data and test the fitted model. (4) Constructing robust design model by the response surface model. (5) Solving the best combination of design parameters In the actual product design process, multiple design output problems are often encountered, a product must satisfy multiple design goals at the same time. The response surface methodology has evolved from single response optimization to multiresponse optimization. Scholars have put forward many solutions to the multi-response problem. Harrington first proposed a solution to transform multiple responses into a single function by mathematical transformation, that is, the desirability function method, derringer improved this method. This method is adopted in this paper.

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In robust design, product quality characteristics can be divided into three types, nominal the best, smaller the better and larger the better, their desirability function are given as

di ð^yi Þ ¼

8  si ^yi li > > <  ti li  ^yi hi ti hi

pi

li  ^yi \ti

ti  ^yi  hi 0 other nominal the best > > :

8 < 0

^yi [ hi di ð^yi Þ ¼ li  ^yi  hi : 1 ^yi ^yi \li smaller the better ^yi hi li hi

qi

di ð^yi Þ ¼

8 < 0

^yi \li li  ^yi  hi : 1 ^yi [ hi larger the better ^yi li hi li

qi

ð2Þ ^

where di is a desirability function of yi , li is minimum value, hi is maximum value, ti is target value, si, pi and qi are arbitrarily positive constants. The overall desirability function D can be defined as D¼ð

n Y

diwi Þ1=

P

wi

ð3Þ

i¼1 ^ P where wi is weight of yi ; wi ¼ 1. Then maximize the D to determine the best combination of design variables, thus, the multi-response problem is transformed into a single response problem. The overall satisfaction function is a nonlinear function, it is difficult to solve with the traditional optimization algorithm, here the simulated annealing algorithm is used to solve the problem.

3 Design of Experiments in RSM Experimental design is the fundament of response surface methodology based robust design, in response surface methodology, the most widely used experimental design methods are central composite design, Box-Behnken design and orthogonal design, etc. The central composite design is applied in this paper. Among the various kinds of experimental design used for fitting a response surface model, central composite design(CCD) is the most widely used method for fitting a second order response surface, it was introduced by Box and Wilson. CCD involves the use of a two level factorial or fraction combined with 2k axial or star points, where k is a number of factors. Thus, the CCD is composed of F factorial points, 2k star points and nc center runs, as shown in Fig. 2. Five repetitions of experiments are usually required at the central point in conventional 2 factors central composite design, repetitive experiments are not shown here.

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Fig. 2. A 2 factors central composite design

There are three types of central composite designs, central composite circumscribed design (CCC), central composite face centered design (CCF) and central composite inscribed design (CCI). In central composite circumscribed design, axial point is higher or lower than the high (+1) or low level (−1) of the factor, each factor has five levels, ±a, 0, ±1. In central composite inscribed design, the value of ±a is set on the maximum and minimum bounds of the factor design domain, CCI has all the characteristics of CCC, each factor has five levels too, ±0.7, 0, ±1. When five levels are difficult to meet or constrained by conditions, placing the axial point at the center of each surface of the design space, it is central composite face centered design, CCF requires only three levels per factor, 0, ±1. We apply CCF in our design of experiments. Three types of 2 factors central composite designs are shown in Fig. 3.

Fig. 3. Three types of central composite designs

4 Unmanned Aerial Vehicle Electrostatic Spray System Optimization Aerial spraying can get rid of the restriction of terrain, it can also be carried out in complex environments. Compared with ground machinery, aerial spraying equipment does not directly contact with plants, which greatly reduces the damage caused by

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mechanical operation to plants. Electrostatic spray is a new spray technology, it can refine fog droplets, improving spray uniformity. It also allows pesticide droplets to reach the back of the plant leaves which could not be sprayed by conventional spray. The spray effect can be further improved by combining UAV spray with electrostatic spray. There are many factors that affect the spray performance of UAV electrostatic spray system, including spray pressure, distance between nozzle and target crop, gas flow speed, electrostatic voltage and nozzle diameter, etc. According to previous study results, nozzle diameter, spray pressure and electrostatic voltage are the major factors which affect spray effect, so these factors would be optimized by RSM robust design. In order to reduce the complexity of the experiment, the electrostatic spray nozzle (Fig. 4) parameter would be optimized in two steps. First, analysis of spray performance under different spray pressures and different nozzle diameter, then, on this basis, the performance of electrostatic spray device is further analyzed under different electrostatic voltage .

Fig. 4. Electrostatic spray nozzle

In first step, the optimizing factor are nozzle diameter (x1) and spray pressure (x2), the performance indicators to be examined are deposition density (y1) and uniformity (y2). Experimental factor and their level are shown in Table 1. Table 1. Factor and their levels Level rank Factor x1/mm −1 0.8 0 1.0 1 1.2

x2/MPa 0.4 0.7 1.0

Experimental design adopt 2 factor CCF central composite design, in center point, repeated five experiments are adopted quasi-level method, a total of 13 experiments are conducted. Experimental arrangement and result are shown in Table 2.

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Table 2. Experimental arrangement and results No. 1 2 3 4 5 6 7 8 9 10 11 12 13

x1 1.0 1.0 1.2 1.0 1.0 1.0 0.8 0.8 1.2 1.0 1.0 1.2 0.8

x2 0.7 0.7 0.7 1.0 0.4 0.7 0.7 0.4 1.0 0.7 0.7 0.4 1.0

y1 55.11 55.11 63.08 81.11 51.32 55.11 57.74 51.29 98.17 55.11 55.11 63.93 94.58

y2 1.66 1.66 1.9 0.61 1.44 1.66 1.46 1.68 1.23 1.66 1.66 1.93 1.03

Estimated regression coefficients for y1 and significance test, and the analysis of variance for y1 are shown in Fig. 5.

Fig. 5. Regression coefficients and analysis of variance for y1

Thus, the fitted second-order model for y1 using data in coded units is listed as y1 ¼ 54:354 þ 3:595x1 þ 17:887x2 þ 7:944x1  x1 þ 13:749x2  x2  2:263x1  x2 The surface and contour of y1 are shown in Fig. 6.

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Fig. 6. The surface and contour of y1

In a similar manner, the fitted second-order model for y2 using data in coded units is listed as y2 ¼ 1:602 þ 0:148x1  0:363x2 þ 0:224x1  x1  0:431x2  x2 Deposition density is larger the better, in many experiments, its maximum is 127 and it minimum is 25.39, so we take its maximum value is 130 and minimum is 25 on the desirability function. Uniformity is nominal the best, it is the dispersion degree of droplet population size. The closer the droplet uniformity is to 1, the more uniform the droplet size is. If the droplet uniformity is greater than or equal to 0.6 or less than or equal to 1.5, it is considered to be an ideal uniformity. So we take its nominal value is 1. The weight value of every response is established by designer, are 0.5 and 0.5, thus, according to formulas (2) and (3), the overall desirability function is D ¼ ðddep Þ0:5 ðdnui Þ0:5 Using simulated annealing, rounding the nozzle diameter value according to process conditions, the optimizing result of step 1 is listed in Table 3.

Table 3. Design result in step 1 Varible x1 = 1.0 mm, x2 = 0.5 Mpa Response y1 = 95.6, y2 = 1.01 Desirability dpep = 0.670, duni = 0.652, D = 0.661

After that, experiments are carried out at different electrostatic voltage, nozzle diameter value fixed to 1, experiment factors are electrostatic voltage (z1) and spray pressure (z2), the performance indicators is charge to mass ratio (ycm). Apply the method described above, the fitted second-order model for ycm using data in coded units is listed as

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Ycm = 1.677 + 0.205z1 + 0.222z2−0.092z1 * z1−0.053z1 * z2 Because there is only one response in step 2, the optimizer could be used directly. The optimal value in the experiment is 1.94, Let’s set the minimum value of ycm to 1.0 and the maximum limit to 2.5, the optimal value obtained from the running optimizer is 1.96. The optimization settings is shown in Fig. 7.

Fig. 7. The optimization setting

5 Conclusions (1) In this paper, the response surface method is introduced into the optimization design of spray parameters for electrostatic sprayer. The response surface model with spray pressure and nozzle diameter as design variables and deposition density and uniformity as optimization targets was constructed, And a response surface model with electrostatic voltage and spray pressure as design variables and charge to mass ratio as the optimization target was constructed too. The model has been proved to be reasonable and reliable. The performance test of new electrostatic spray system under different nozzle diameter, spray pressure and electrostatic voltage was carried out. The test results show that the nozzle meets the theoretical requirements of optimum biological particle size, it meets the requirements of hydraulic spraying for controlling most crop diseases and insect pests. (2) The multi-factor variance analysis shows that the nozzle diameter, spray pressure and electrostatic voltage have significant effects on the performance. The influence of two factors on deposition density and uniformity is in turn the spray pressure, nozzle diameter. The effect of electrostatic voltage and spray pressure on

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charge mass ratio is basically the same. In order to achieve the best results, the optimal combination of factors level is as follows: nozzle diameter is 1.0 mm and spray pressure is 0.5 Mpa, electrostatic voltage is 10 kV, under this condition, the uniformity is close to 1. (3) The two order regression model of nozzle diameter, spray pressure and electrostatic voltage are established, y1 = 54.354 + 3.595x1 + 17.887x2 + 7.944x1 * x1 + 13.749x2 * x2 − 2.263x1 * x2, y2 = 1.602 + 0.148x1 − 0.363x2 + 0.224 x1 * x1 − 0.431x2 * x2, ycm = 1.677 + 0.205z1 + 0.222z2 − 0.092z1 * z1 − 0.053z1 * z2. The judgment coefficients of model fitting degree are bigger, so the regression effect is better. Acknowledgment. This work is supported by the National Natural Science Foundation of China (Grant No. 71161006), Guizhou Provincial Science and Technology Support Program of China (Grant No. [2016] 2037).

References 1. Farazkish, R.: Robust and reliable design of bio-nanorobotic systems. Microsyst. Technol. 25(4), 1519–1524 (2019) 2. Jun, C.-S., Kwon, B.-I., Kwon, O.: Tolerance sensitivity analysis and robust optimal design method of a surface-mounted permanent magnet motor by using a hybrid response surface method considering manufacturing tolerances. Energies 11(5), 1159 (2018) 3. Hong, J., Xu, X., Liang, T.: Interface failure analysis and robust design method in rotor structural system. J. Aerosp. Power 33(3), 649–656 (2018) 4. Sun, G., Zhang, H., Fang, J.: A new multi-objective discrete robust optimization algorithm for engineering design. Appl. Math. Model. 53, 602–621 (2018) 5. Wei, W., Liang, H., Wuest, T., Liu, A.: A new module partition method based on the criterion and noise functions of robust design. Int. J. Adv. Manuf. Technol. 94(9-12), 3275– 3285 (2018) 6. Zhou, Q., Shao, X., Jiang, P., Xie, T.: A multi-objective robust optimization approach for engineering design under interval uncertainty. Eng. Comput. (Swansea, Wales) 35(2), 580– 603 (2018) 7. Donoso, A., Bellido, J.C.: Robust design of multimodal piezoelectric transducers. Comput. Methods Appl. Mech. Eng. 338, 27–40 (2018) 8. Park, C., Ouyang, L., Byun, J.-H., Leeds, M.: Robust design under normal model departure. Comput. Ind. Eng. 113, 206–220 (2017) 9. das Neves Carneiro, G., António, C.C.: Reliability-based robust design optimization with the reliability index approach applied to composite laminate structures. Compos. Struct. 209, 844–855 (2019) 10. Park, C., Leeds, M.: A highly efficient robust design under data contamination. Comput. Ind. Eng. 93, 131–142 (2016) 11. Ashouri, A., Petrini, F.: Sensitivity analysis for robust design of building energy systems. Energy 76, 264–275 (2014) 12. Chen, L.: Robust Design. Machinery Industry Press, Beijing (2005)

Research on Trajectory Optimization of Six-Axis Manipulator Based on Watchcase Polishing Xiang Wang, Ying Xi(&), Chao Gu, and Mengru Li School of Mechanical Engineering, Tongji University, Shanghai 201804, China [email protected], {yingxi,limengru}@tongji.edu.cn, [email protected]

Abstract. In the watchcase polishing industry, due to the complexity of the watchcase surface to be polished and the variety of the watchcase surface, as well as the low manual efficiency and poor quality, this paper proposes an optimization strategy for the trajectory generation of industrial manipulators for polishing. By analyzing the effective optimization parameters of the manipulator, the spline curve interpolation satisfies the validity and rationality of the point-to-point trajectory in the polishing process. Finally, the path optimization is completed on the basis of these. A simulation experiment was carried out on a certain manipulator, and a trajectory curve for actual polishing process was obtained. Keywords: Six-axis manipulator  Genetic algorithm  Trajectory generation  Point-to-point trajectory

1 Introduction Intelligence is the pursuit in all fields of industry. It is common to use industrial robots to polish workpieces. However, there are still many problems in the research of watchcase polishing. The polishing system fixes the polishing motor and polishes the polished parts by the manipulator. This polishing process is seldom used to process complex and precise surface parts with small volume. Compared with the polishing behavior of fixed parts with polishing tools, the path generation and path planning of the manipulator are more difficult. Compared with the contour diameter of watchcase, the diameter of industrial polishing wheel is too large, which also increases the difficulty of manipulator’s transition. Moreover, the surface of workpiece is very complex, especially when polishing some curved surfaces, the path of general trajectory planning can not meet the requirements.

Foundation projects: Deep-sea breaking equipment development of self-propelled working platform with mechanical cutting equipment (2017YFC0307004), Ganzhou City, Jiangxi Province, a major scientific and technological project: the development of flexible polishing industrial robots for complex surfaces. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 729–739, 2020. https://doi.org/10.1007/978-981-32-9941-2_60

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Yu [1] proposed a method of calculating the feedback through the magnitude of polishing force, so that the position of the manipulator can be compensated according to the calculated value. Wei [2] simulated and analysed it in the simulation software Robot studio. Zhao [3] and Choset [4] explain this from different angles. The former calculates obstacle avoidance conditions based on spatial geometry, while the latter provides ideas for obstacle avoidance environment by improving the artificial potential field method. He [5] uses RRT to optimize the artificial potential field method to solve the local dead point problem. Wang [6] simplifies the obstacle model without causing accidents by using the cylindrical envelope configuration. Cheng [7] combination of A* method and artificial potential field method has some enlightening significance in dealing with local minima, but it does not relate to the actual working environment. Huang [8] describes the processing of speed and location in path planning. In this paper, manipulator (The model of this is LT-1850-D-6) is modelled as an object, and the kinematics of the manipulator is solved by the modified DH method. Then, using space geometry, the constraint conditions of the manipulator in the working space are obtained. PTP path planning and actual polishing process are used to obtain point arrays covering the surface of the case, and motion equations are generated by cubic spline function trajectory. Finally, time-oriented optimization [9, 10] is carried out to obtain a trajectory curve that meets all constraints.

2 Analysis of Manipulator Kinematics In Cartesian space coordinate system, the transformation equation between adjacent arms is as follows: Modified DH model is used to solve kinematics in MATLAB Robotics. The parameters of model is as followed in Table 1. 2

chi 6 shi i1 6 i T ¼4 0 0

shi cai chi cai sai 0

shi sai chi sai cai 0

3 ai chi ai shi 7 7 di 5 1

Table 1. Manipulator motion parameter Joint 0 1 2 3 4 5 6

ai1 /rad 0 0 1.57 0 −1.57 −1.57 1.57

ai1 /mm 0 0 209.12 603.12 102.75 722.5 0

di /mm 0 351.42 61.49 0 287.45 0 154.24

hi 0 h1 h2 h3 h4 h5 h6

ð1Þ

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In Eq. (1), sin hi ; cos hi ; sin ai ; cos ai are expressed to shi ; chi ; sai ; cai . And hi ; ai ; ai ; di mean the parameters of robotics. Considering that the body of the fifth joint of the manipulator is embedded in the fourth axis, the fifth joint has its own angle feasible region, while the actual feasible region and the theoretical feasible region of the manipulator are usually smaller, as shown in Table 2. Table 2. Mechanical arm joint range of motion rad Joint 1 2 3 4 5 6

Actual lower limit Actual upper limit −2.234 2.234 −1.092 1.344 −1.361 0.990 −2.234 2.234 −0.843 3.657 −2.109 4.195

3 PTP Path Optimization Strategy The position control of the manipulator is usually realized by point-to-point trajectory planning (PTP). Time-oriented point-to-point trajectory optimization uses interpolation function to connect each point to form a trajectory. Requirements for trajectories: (1) The trajectory must pass through a specific position and posture sequence; (2) The trajectory must meet the constraints of polishing requirements (speed, acceleration, acceleration, etc.). (3) There should be a suitable distance between the trajectory and the obstacle. (4) To shorten the time as much as possible under the conditions of 1, 2 and 3. For posture point series fQ1 ; Q2 ;    Qn g, A joint coordinate sequence fh1 ; h2 ;   hn g can be obtained by calculating Eq. (1). And it’s a vector of 6 in length. The s segments difference function s T ðtÞ is constructed between each two points, and the trajectory function according to the points can be obtained by the difference. The space of the i arm of the manipulator is SL ðiÞ, The space of the j obstacle of the manipulator is SL ð jÞ. Time-oriented optimization can be expressed as:

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min tn subject to :   8 s T ðtis Þ ¼ hi i ¼ 1; 2;   ; ns ; > > > > js T 0 ðti Þj  vmax ; > > > > js T 00 ðti Þj  amax ; > > > > < js T 000 ðti Þj  jmax ; SL ðiÞ \ SL ðjÞ ¼ £; SO ðiÞ \ SO ðjÞ ¼ £; > > > SL ðiÞ \ SO ðjÞ ¼ £; > > s > > T ðtis Þ 62 SO ðjÞ; s T ðtis Þ 62 SL ðjÞ; > > > > 0  t1i  t2i      tn ; > : t 2 ½0; tn 

ð2Þ

Among them, ft1 ; t2 ;    tn g is the partition of time variable t in ½0; tn  and tis is the movement time of from posture Qi1 to Qi . The vectors vmax ; amax ; jmax are composed of the extreme values of joint velocity, acceleration and jerk. Considering the linear independence of the constructed spline function between any two adjacent points, a group of them is chosen as the object of discussion for analysis.

s

Ti ðtÞ ¼

s

8 > > > > > > > > > > < > > > > > > > > > > :

t ¼ 0; t 2 ð0; t1 ; t 2 ð0; t1 ; .. .

P0 s T1 ðtÞ s T2 ðtÞ .. . s

.. .

t 2 ðti1 ; ti ; .. .

Ti ðtÞ

ð3Þ

Tn ðtÞ t 2 ðtn1 ; tn  Ti ðtÞ ¼ Pi1 þ vi1 ðt  ti1 Þ þ 1 1 ai1 ðt  ti1 Þ2 þ ji1 ðt  ti1 Þ3 2  6  t 2 ti1; ti s

In Eq. (3), s Ti ðtÞ is the equation of the i-th spline function, with domain ðti1 ; ti , and si ; vi ; ai ; ji considered the position, velocity, acceleration and acceleration of the spline curve. Then the curve is marked by s Ti ðt; g; h; a0 ; v0 ; s0 Þ. From the following aspects, time-oriented PTP path optimization is carried out by the agreed time tðhÞ, tðhÞ ¼

n=s 6 X X i

hi;k

ð4Þ

k

hi;k is the i -th spline movement time of the s-th path. The time discrete distribution deviation eti for arbitrary s interpolation between adjacent points,

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eti ¼ ð

s X k1 ¼1

hi;k1  avgðkk11 ;1þ s;6 h; 6ÞÞ2

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ð5Þ

By introducing Eq. (5) into Eq. (4), we can get the global time dispersion DB1 . And it should be noted that kk11 ;1þ s;6 h refers to a subarray from ðk1 ; 1Þ to ðk1 þ s; 6Þ. DB1 ¼

n=s 6 X X

s X

ð

i¼1 k¼1 k1 ¼sðk1Þ þ 1

hi;k1  avgðkk11 ;1þ s;6 h; 6ÞÞ2

ð6Þ

Considering the angular error after s interpolation, the angular motion deviation ean of the manipulator segment is recorded over a period of time. ean ¼

Ti ðts Þ 

s X

!2 hi;k

ð7Þ

k¼1

By introducing Eq. (7) into Eq. (4), accumulated angular deviation DB2 in time can be obtained. DB2 ¼

6 X n X i¼1

ðTi ðts;k Þ  hi;k Þ2

ð8Þ

k

Taking into account the constraints on speed, acceleration and acceleration, the acceleration deviation eve of the arm joints during this period is recorded. eve ¼ penðjai j  amax;i Þ

ð9Þ

ðsgnðxÞ þ 1Þx2 . Where penðxÞ ¼ 2 In Eq. (9), the function penðxÞ is a penalty function with inequality constraints. By combining Eqs. (9) and (4), the cumulative offset of acceleration DB3 in polishing process can be obtained.

DB3 ¼

6 X n X i

  penðai;k   amax;i Þ

ð10Þ

k

For the same reason, DB4 is the cumulative offset of jerk. DB4 ¼

6 X n X i

  penðji;k   jmax;i Þ

ð11Þ

k

The cumulative velocity migration DB5 is deduced by Eqs. (9) and (11) together ( 0 ai;k ai;k1 [ 0 with the limit velocity vpeak;i;k ¼ in that period. a2i;k vi;k  2jmax ai;k ai;k1 \0

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DB5 ¼

6 X n X i

6 X n X     penðvpeak;i;k   vmax;i Þ þ penðvi;k   vmax;i Þ i

k

ð12Þ

k

Considering the motion constraints of the end effector, the motion boundary function EdgeðÞ is set up. EdgeðÞ ¼n6 sgnðv20  v2max Þ  v20 þ n7 sgnða20  a2max Þ  a20 þ n8 sgnðj20  j2max Þ  j20

ð13Þ

The problem of obstacle avoidance during the operation of the manipulator [11] can be concluded as ObstacleðÞ. By synthesizing Eqs. (4–13), the adaptive function EðhÞ and ni are obtained as optimization coefficients. E ð hÞ ¼ n0 t ð hÞ þ

5 X

ni DBi þ EdgeðÞ þ ObstacleðÞ

ð14Þ

i¼1

4 Simulation and Experiment In Robot Studio environment, the trajectory points of the manipulator are obtained, the polishing system model is established and the initial position of the polishing watch shell is obtained. According to the point position and polishing requirements, adaptive genetic algorithm is used to optimize the trajectory to ensure the constraints of motion parameters and the guarantee of polishing effect. 4.1

Optimization of Adaptive Genetic Algorithm

In genetic algorithm, the crossover effect is better when using binary coding in [12]. The crossover parent is randomly paired according to fitness probability. For the variation link, boundary variation is used to enhance the ability of early maturity resistance. At the same time, 20% of the population is migrated once every 20 generations to enhance the ability to resist early maturity. The end effector speed is constrained between ½80; 80 mm=s, the acceleration is constrained between ½10; 10 mm=s2 , and the acceleration is constrained between ½3; 3 mm=s3 . The crossing probability K1 ; K2 were 0.5 and 0.7 respectively, the population size was 5000, the mutation probability K3 ; K4 were 0.1 and 0.3 respectively, and the discrete precision was 0.01. Figures 1 and 2 are optimization curves. The optimization results are slightly different from those of the general descent algorithm. The ordinate axis of the relationship between the number of iterations and the penalty function in the genetic algorithm can be seen. After 39000 iterations, the descent speed is dramatic, and then the descent process is relatively slow, which is one of the characteristics of descent algorithm.

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Fig. 1. Penalty function value drop curve using the genetic algorithm

Fig. 2. The average value of the whole population objective function

4.2

Experiment and Analysis

Figure 3 is one of the operations of the polishing system. It is an action that the shell of the part to be processed is feeding to the polishing wheel. Figures 4 and 5 are the controller of the manipulator and the control system of the whole polishing system, respectively. After 1:1 modelling in SOLIDWORKS, the model is imported into Robot Studio for point acquisition. The point group is substituted into Eq. (1) to solve the joint angle and then optimize it. Figure 4 is the trajectory of the optimized six-axis in a period. Figure 5 is the trajectory of the manipulator when t = 1. Figure 6 describes the displacement of the optimized six-axis when the manipulator passes through four

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Fig. 3. One of the postures of the watchcase polishing

Fig. 4. The trajectories of six-axes in a period

Fig. 5. t ¼ 64  78 s, the axes trajectories of the manipulator

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positions. The global character of the algorithm can be seen from the trajectory. For q3 in Fig. 8, the second displacement of joint 3 (the absolute value of displacement) has the behavior of “waiting” for other axes to be in place before the third node. Compared with the general method of waiting in the static state, this method uses the “conscious” reverse motion and then accelerates to node 3, so that the trajectory of the next posture point has a larger starting speed to reduce the running time in the next trajectory.

Fig. 6. The average value of the whole population objective function

In Fig. 3, we can see the obstacles are feeding mechanism, polishing motor and polishing wheel body. Figure 7 shows the trajectories of the polishing system before and after five optimizations. From Fig. 8, we can see that the optimized motion parameters have met the requirements. At the same time, it reduces the impact strength and improves the polishing quality of watch case. At the same time, it significantly reduces the time required to run a cycle, and the time consumed by a single cycle is 76.9%–83.7% of the original.

Fig. 7. Contrast before and after polishing trajectory optimization

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Fig. 8. Comparison of motion parameters before and after polishing trajectory optimization

5 Conclusions To solve the problem of trajectory generation of manipulator for watchcase polishing, this paper designed a PTP-based trajectory generation method. The design method realizes the requirement of polishing contact for complex surface of watchcase. The adaptive genetic algorithm theory is used to optimize the initial trajectory and a more suitable trajectory is obtained. The results of simulation and practice have shown that the curve is more stable, reliable and high-speed. The generated trajectory curve reduces the impact strength during polishing, and improves the surface quality of the machined surface of the case. At the same time, the time consumption of a single cycle is reduced by at least 16.3% on the original basis.

References 1. Yu, H., Xu, H., Yuan J.-L.: Research on on-line compensation strategy of polishing wheel wear based on contact force control. J. Instrum. 5, 991–997 (2010) 2. Wei, Q.: Research on key technology of flexible automatic polishing production line for stainless steel kitchenware, Guangdong University of Technology (2016) 3. Zhao, Z.: Industrial robot interference judgment and path planning research. Shenyang University of Technology (2018) 4. Choset, H., Lynch, K.M., Hutchinson, S.: Principles of Robot Motion. MIT Press (2005). ISBN 0-262-03327-5 5. He, Z., He, Y., Zeng, B.: Robotic obstacle avoidance planning based on RRT combined with artificial potential field method. Ind. Eng. 56–63 (2017) 6. Wang, Z.: Research on obstacle avoidance path planning of six-degree-of-freedom mechanical arm, Southwest Jiaotong University (2018) 7. Cheng, G.: Research on obstacle avoidance path planning based on six-degree-of-freedom manipulator, Northeastern University (2012) 8. Huang, J.: Research on spatial trajectory generation method of six-degree-of-freedom series robot, Anhui University of Engineering (2017)

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9. Li, R.: Time-optimized robot point-to-point trajectory planning problem, Dalian University of Technology (2016) 10. Chen, B.: Optimization Theory and Algorithms, 2nd edn. Tsinghua University Press, Beijing (2005) 11. Sun, S.: Research on obstacle avoidance method of manipulator based on artificial potential field-genetic algorithms. Comput. Measur. Control 12, 3078–3081 (2011)

Reverse Modeling of the Helix Roller in the Omni-Directional Wheel Based on NURBS Xie Xia(&) Military Vehicle Engineering Department, Army Military Transportation University, Tianjin 300161, China [email protected]

Abstract. The helix roller of the omni-directional wheel was measured by the three-coordinate measuring machine and then the obtained data was preprocessed. The principle of the least squares approximating NURBS (Non-Uniform Rational B-Spline) curve fitting algorithm was analyzed and with this algorithm the contour line of the roller was reconstructed in MATLAB software, thus the outside silhouette surface was generated on the basis of the fitting curve and finally the three-dimensional solid model of helix roller was built in Pro/Engineer. The results laid a good foundation for further finite-element analysis and manufacturing. Keywords: Omni-directional wheel  Three coordinate measuring  NURBS curve fitting  Least squares approximation  Reconstruction

1 Introduction Omni-directional wheel is a structure that can move in either direction in a plane with a differential gear train. This mechanism is used widely in the automated guided vehicle, mobile robots and other institutions [1–4] to save working space, improve work efficiency and simplify the operation, especially the operations in the crowded and narrow space. Omni-directional wheel usually consists of some pairs of the spiral rollers which shape has great influence on the accuracy and stability of the movement of the mobile platform. But the contour curve is abnormal and complex and reverse modeling can contribute to its design and manufacture and lay the foundation for its secondary design and product innovation. There are many ways to realize free-surface reverse modeling, such as non-uniform rational B-spline (NURBS), radial basis function (RBF) neural network, drawing software, and so on. Qiu [5] applied reverse technique to a type of four-cylinder crankshaft’s self-replication and model reconstruction, and set up NURBS surfaces with more better precise and quality. Lei [6] took a free surface handicraft as an This project is supported by Tianjin Science and Technology Key Project (Grant No. 12ZCZDGX02200). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 740–748, 2020. https://doi.org/10.1007/978-981-32-9941-2_61

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example to carry out the NURBS reconstruction of free surface products. Zhao [7] suggested an improved surface reconstruction algorithm based on radical basis function (RBF), and the results showed that the presented method could obviously improve the efficiency of surface reconstruction. The NURBS method could accurately represent the quadratic regular curve (surface), and moreover, the weight factor made shapes be controlled and implemented easily. Therefore, the NURBS (Non-Uniform Rational BSpline) method was selected to reconstruct the helix roller for its accuracy test and finite element analysis in this paper.

2 Three-Coordinate Measuring of the Spiral Roller Data acquisition was the foundation of spiral roller reconstruction and the three coordinate measurement technology was adopted to realize it in this paper. Before the measurement, some early preparation was done, including deburring, cleaning, wiping on the roller, calibrating the probe by the standard ball, and setting up the measurement area’s parameters of the software. At first, the roller was vertically placed on the measuring platform with the axis perpendicular to the work table. And the actual measurements were done in accordance with the planned path, namely along the circumferential direction of a circle (that is to say, Z coordinate is fixed). The measurement process was shown in Fig. 1.

Fig. 1. Three coordinate measuring of the spiral roller surface

The cross section was a round in the direction of the equal height because of the rotary body of the spiral roller. Through the measurement of 6 points on each section, the section of the spiral roller profile was approximated using the principle of least square method (namely residual sum of squares was the least). The parameters (such as radius, etc.) of round section could be obtained by the computation, and thus the equation of circle section was obtained, too. After a circle’s measurement, reduce the measuring head height to a step, and measure the points on the next cross section contour. And so on, a total of 318 points’ coordinates were measured.

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Then, keep the coordinates of the axis direction (Y coordinates) unchanged, the other two coordinates values were measured in turn to get the coordinates of 90 points. And then the measurement data was pretreated by filtering, smoothing and radius compensation [8] and saved for later processing.

3 Curve Reconstruction of the Spiral Roller Contour Curve reconstruction is the premise and necessary condition for model reconstruction. According to the requirement of curves and experimental data of spiral roller precision, the non-uniform rational b-spline (NURBS) algorithm was selected for curve reconstruction. 3.1

NURBS Curves Relevant Principles

NURBS curve is a piecewise rational polynomial function of vector values, its k times curve expression [9] is: n P

cðuÞ ¼

wi pi Ni;k ðuÞ

i¼0 n P

wi Ni;k ðuÞ

¼

m X

pi Ri;k ðuÞ

ð1Þ

i¼0

i¼0

where c(u) is the coordinate vector the parameter u correspond to, w(i) is a weight factor, p(i) is the coordinate vector of the control vertex, Ri,k(u) is rational odd function, Ni,k(u) represents the i-th k times normalized B-spline basis function, which is defined by the recursive formula [10] expressed as follows: 8 > > >
> > :

um ui ui þ k ui

1; if ui  um  ui þ 1

0; other um Ni;k1 ðum Þ þ uui þi þk kþþ1 1u Ni¼1;k1 ðum Þ iþ1 Regulation

0 0

ð2Þ

¼0

where u(i) is the element of node vector, while the node vector U = [u0, u1, …, un+k] is a non-subtraction column. 3.2

Spiral Roller Least Squares Approximation of NURBS Curves

The least squares approximation of NURBS is that to parameterize the data points in the case of knowing contour data points, determine weighting factor, find the knot vectors and control points, and then obtain the whole curve.

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3.2.1 Parameterization of Data Points [11] The accumulated chord length method is used to parameterize the spiral roller data, and the formula is as follows: 

u¼0 u ¼ ui1 þ jpi  pi1 j

ð3Þ

This parameterization accurately reflects the distribution of data points, and the resulting curve has good smoothness. 3.2.2 Determination of Weighting Factor The spiral roller outer contour curvature changes gradually, and each node of the contour line may be considered to have the same influence to the curve, so the weight is taken as 1. 3.2.3 Determination of Vector Using the algebraic method to construct the node vector which is obtained by the formula (4) [12]: 8 u0 ¼ u1 ¼ . . . ¼ uk ¼ 0 > > > < j þP k1 uj ; j ¼ 1; . . .; h  k uk þ j ¼ 1k > i¼j > > : umk ¼ umk þ 1 ¼ . . . ¼ um ¼ 1

ð4Þ

U ¼ ðu0 ¼ u1 ¼ . . . ¼ uk ¼ 0; uk þ j ; umk ¼ umk þ 1 ¼ um ¼ 1Þ where m = h + k + 1. 3.2.4 Inverse Solution of Control Vertex Inverse solution of control points dj (j = 0, 1, n − 1) is achieved by the method of least square. The error can be expressed as: E¼

m X

e2i

ð5Þ

i¼0

Among them, m is the number of data points, n P

e i ¼ oi 

wi pi Ni;k ðuÞ

i¼0 n P

wi Ni;k ðuÞ

i¼0

where oi is the data point and the rest is as the former.

ð6Þ

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In the formula (1), introduce a variable ri, make ri ¼ oi  o0 N0;k ðui Þ  om Nn;k ðui Þ; i ¼ 1; 2; . . . m  1

ð7Þ

And substitute it into Eq. (5), and then Eq. (8) can be obtained. E¼

m1 X

½oi  cðui Þ2 ¼

i¼1

m1 X

½ri 

i¼1

n1 X

dj Nj;k ðuÞ2

ð8Þ

j¼1

To minimize the objective function, the derivatives of the n control vertices should be equal to 0. Its lth derivative is m1 n1 X @E X ¼ ½2ri Nl;k ðui Þ þ 2Nl;k ðui Þ dj Nj;k ðui Þ @d1 i¼1 j¼1

ð9Þ

Namely, n1 X m1 m1 X X ð Nl;k ðui ÞNj;k ðui ÞÞdj ¼ ri Nl;k ðui Þ j¼1

i¼1

ð10Þ

i¼1

Take l = 1, 2, …, n − 1, an Eq. (11) can be gotten with n − 1 unknowns dj ðN T NÞD ¼ R 2

N1;k ðu1 Þ 6 : 6 : Where, N ¼ 6 6 4 : N1;k ðum1 Þ

ð11Þ

3 Nn1;k ðu1 Þ 7 : 7 7 : 7 5 : : : Nn1;k ðum1 Þ

: : : :

:

: :

N T is the transposed matrix of N, 2 6 6 6 R¼6 6 6 4

N1;k ðu1 Þr1

: :

: :

:

:

: :

:

: Nn1;k ðu1 Þr1

: :

N1;k ðum1 Þrm1

: : : Nn1;k ðum1 Þrm1

3 d1 6 : 7 7 6 7 D¼6 6 : 7 4 : 5 dn1

3 7 7 7 7 7 7 5

ð12Þ

2

ð13Þ

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According to the equations, control point vectors can be calculated and fitting curve can be obtained. 3.3

Implementation of NURBS Least Squares Approximation by MATLAB

According to the data obtained from the measurement and after preprocessing of spiral roller, the NURBS curve was fitted implicating least squares approximation through the MATLAB software programming. Figure 2 showed the algorithm process and Fig. 3 was the roller outer contour curve fitted out by the algorithm. Parameterization of data points

Determination of weight factors

Determination of vector

Reverse control points

Curve fitting

Fig. 2. Program flow diagram of the NURBS curve fitting

4 Surface Reconstruction of the Spiral Roller As the spiral roller was rotary body, the contour curves obtained from curve reconstruction was rotated around the spiral roller axis and thus the outer contour surface could be gotten. Figure 4 gave the spiral roller surface after programming.

Fig. 3. NURBS reconstruction curve of the roller contour

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Fig. 4. Outer surface of the helix roller after programming

5 Construction of the Three Dimensional Model of the Spiral Roller Through pre-modeling, outer contour surface model of the spiral roller was established in MATLAB, and then the coordinates of each point on the surface could be gotten. After that, the three-dimensional outer contour surface mesh model was constructed shown in Fig. 5 with the reconstructed data put into Pro/Engineer software. Based on reestablishing the outer and inner contour of the spiral roller surface model, the three dimensional model was gotten. And Fig. 6 showed the full assembled solid model of the helix roller.

Fig. 5. Outer contour surface mesh model of the roller

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Fig. 6. Full assembled solid model of the spiral roller

6 Conclusions According to the measurement planning, coordinate measuring and data preprocessing of the spiral roller were conducted. NURBS curve fitting algorithm was selected for curve reconstruction, and achieved through the MATLAB programming language. On this basis, surface reconstruction for the outer contour of the spiral roller was done and a three-dimensional solid model was constructed in the PRO/E. This model will lay a good foundation for the subsequent mechanical analysis, manufacturing precision analysis and processing.

References 1. Shen, A.M., Zhao, Z.L.: Coupled control algorithm for rotation and revolution of omnidirectional automated guided vehicle based on mecanum. J. Mech. Trans. 42(9), 106– 110,148 (2018). (in Chinese) 2. Li, X.R., Wang, Y.L., Ou, Y., et al.: Dead reckoning positioning method of 3 wheels omnidirectional mobile robot. Ordnance Ind. Autom. 36(5), 62–65 (2017). (in Chinese) 3. Tang, W., Liu, Y., Hu, H.X., et al.: Kinematics analysis and self-adaptive controller design of omni-directional movement platform. Mech. Sci. Technol. Aerosp. Eng. 36(6), 883–889 (2017). (in Chinese) 4. Gao, P.F., Peng, J.T., Yu, W.W.: Design and motion analysis of a mecanum three-round omni-directional mobile platform. J. Northwest. Polytech. Univ. 35(5), 857–862 (2017). (in Chinese) 5. Qiu, H.F.: Self-replication design of crankshaft based on reverse technique. Mod. Manuf. Eng. (7), 47–50, 108 (2017). (in Chinese) 6. Lei, M., Lv, J., Liu, Z.H., et al.: Design and manufacturing of surface product based on reverse engineering and CNC technology. J. Manuf. Autom. 36(10), 52–55 (2014). (in Chinese) 7. Zhao, J., Kang, B., Kang, J., et al.: An improved surface reconstruction algorithm based on RBF. J. Northwest Univ. (Nat. Sci. Ed.) 42(5), 744–748 (2012). (in Chinese)

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8. Ji, T., Guo, D.M., Jia, Z.Y.: Study of data processing of measurement and reconstruction of random inner surface. Dalian Ligong Daxue Xuebao 45(4), 570–574 (2005). (in Chinese) 9. Ma, X.L.: Research on the rotor profile of double-screw compressors based on NURBS. Jiang Nan University (2008). (in Chinese) 10. Lan, H.: Research and application of whole fairing and approximation algorithm of NURBS curve. Xi’an University of Technology (2008). (in Chinese) 11. Deng, Z.H.: Research on the method to generate tool path directly from reverse engineering measure data. Jiang Su University (2006). (in Chinese) 12. Li, X.W.: Key technology of reverse engineering. He Fei University of Technology (2007). (in Chinese)

Research on Automatic Matching Model of Power Battery Chuanfu Xin, Fengxia Zhao(&), Yujin Wu, and Jianshe Gao School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China [email protected]

Abstract. In order to realize the intelligent matching of power battery, an automatic battery sorting and matching system were designed. The intelligent matching algorithm based on the optimized fuzzy clustering algorithm and support vector machine was studied, and an automatic matching prediction model of power battery was proposed. Firstly, the model introduces the Xie-Beni validity index to find the best number of classifications, then uses the genetic adaptive algorithm and the optimized fuzzy clustering algorithm to classify the power battery data. Finally, the classification results were taken as input samples to establish a prediction model of SVM. In order to ensure the accuracy of the model and improve the generalization degree of the model, the cross-validation method is used to optimize the parameters of the training model. The experimental results show that the average prediction accuracy of the proposed model is more than 95%, which meets the actual needs of enterprises. Keywords: Battery matching  Support vector machines Fuzzy clustering algorithm  Adaptive genetic algorithm



1 Introduction As the power source of electric vehicles, the power battery pack is generally applied by forming a battery module in a series or parallel mode with hundreds or thousands of single cells. The performance of single batteries often determines the performance of the whole electric vehicle. The performance level of the module is not simply determined by a single cell, nor is it equal to the average performance of all the cells, but is determined by the multiple cells with the worst performance of each single performance parameter [1]. Due to the “barrel” effect, the capacity of a series-parallel battery system depends on the capacity, internal resistance, voltage (soc) and self-discharge rate of a single parallel group. Inconsistency of batteries seriously affects the service life and performance of batteries [2]. Therefore, it is of great significance to adopt a matching process to improve the consistency of the single cells in the module.

This project is supported by Intelligent Battery Package Manufacturing Based on Material Feature Recognition and Operating Trajectory Optimization (Grant No. 2018YFB0104101). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 749–759, 2020. https://doi.org/10.1007/978-981-32-9941-2_62

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At present, domestic and foreign scholars have conducted a lot of research on the consistent matching of battery electrical performance parameters for the matching process of power batteries. Raspa et al. [3] sorted batteries according to SOV changes of batteries by self-organizing graphs. Kim et al. [4] proposed a method based on capacity and internal resistance to improve the voltage and SOC consistency of lithiumion power battery packs in view of the situation that voltage equalization techniques may cause voltage consistent and inconsistent state of the SOC. Ji et al. [5] proposed a multi-parameter matching process method. The matching parameters mainly include the capacity and voltage difference. The voltage difference is obtained by subtracting the voltage values before and after the battery pack is connected to the resistive load. Zhang et al. [6] proposed a matching process based on voltage V, internal resistance R, capacitance C (capacity), charge curves and discharge curves, etc. According to the consistency of voltage V, internal resistance R, capacitance C, discharge curve and charging curve, he selected N M parallel groups, and then matched them according to the consistency of capacity of each parallel group. Based on the above research, most of the matching processes are completed in a full manual or semi-automatic manner, which has the disadvantages of low efficiency, low optimization of the matching group, large manual error, etc., and can not meet the normal production needs of the enterprise. Therefore, there is an urgent need to study the battery automatically sorting and matching system based on dynamic pipeline. Aiming at the existing problems, this paper builds a battery automatic sorting and matching system based on dynamic pipeline, and studies the battery intelligent matching algorithm which combines the optimized fuzzy C-means algorithm with the support vector machine, and proposes a new battery matching prediction model. The experimental verification and results comparison show that the prediction accuracy of the model is more than 95%.

2 Design of Battery Automatic Sorting and Matching System According to the detection requirements of the battery, the sorting and matching system is designed as shown in Fig. 1. The system consists of three conveyor belts: conveyor belt 1, conveyor belt 2 and conveyor belt 3. Among them, conveyor belt 1 is the detection area, whose main function is to complete the detection of parameters such as battery voltage and internal resistance. The platform structure used for the detection is shown in Fig. 2. If a parameter of the battery does not meet the specified single parameter limit, the system will determine that the battery is unqualified (NG), and the battery will be transported to the NG area by the conveyor belt 1, and the qualified battery will be pushed to the different gear area of the conveyor belt 2 by the push rod. The qualified batteries are transported to different gear areas on the conveyor belt 2 which is the matching area according to the classification standard of electrical performance parameters after calculation by the matching algorithm. When the battery in a gear is on the conveyor belt 2 reaches the specified module scale at the exit position, the robot grabs the battery pack in the same gear position and transports it to the conveyor belt 3. The conveyor belt 3 is a module area, which transports the battery pack to the next station to be assembled into a module unit.

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Fig. 1. Matching system

Fig. 2. Electrical parameter detection platform

3 Battery Sorting Algorithm In fact, the sorting of batteries is based on their electrical performance parameters. In this paper, an adaptive genetic algorithm is used to optimize the fuzzy C-means clustering algorithm to realize battery sorting. 3.1

Adaptive Genetic Algorithm

Adaptive genetic algorithm [7] is a way to simulate the evolution of natural organisms to find the optimal solution of the problem parameters. It mainly uses selection operation, crossover operation and mutation operation to make the individual of the population exchange feature information continuously, and uses fitness evaluation function to evaluate the individual of the population, so as to select the best individual. Adaptive genetic algorithm is an improvement of the basic genetic algorithm and uses the dynamic changing operators according to the population fitness to perform the

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crossover and mutation operations, which improves the convergence accuracy and speed of the algorithm and makes its performance more excellent. The calculation formulas of Pc and Pm of crossover and mutation operators are as follows:  8  < k1 1  arcsinðfave =fmax Þ p=2   Pc ¼ : k1 arcsinðfave =fmax Þ p=2 ( Pm ¼

fave =fmax Þ k2 ð1  arcsinðp=2 Þ fave =fmax Þ k2 ðarcsinðp=2 Þ

arcsinðfave =fmax Þ  p=6 arcsinðfave =fmax Þ  p=6 arcsinðfave =fmax Þ  p=6 arcsinðfave =fmax Þ  p=6

ð1Þ

ð2Þ

Where, fave represents the average fitness of the population, fmax represents the maximum fitness of the population, k1 and k2 is proportionality coefficient. 3.2

Fuzzy C-Means Algorithm

Fuzzy C-means algorithm [8] is an unsupervised clustering algorithm, which has a simple clustering idea, fast calculation speed and can effectively process large-scale data, so it is a commonly used sorting algorithm. However, the algorithm ignores the influence of the distribution density of data samples on classification, and its objective function only reflects the consistency of samples within the same class, but does not reflect the difference between different classes. Therefore, this paper uses Gauss density function to weigh it, and introduces Xie-Beni efficiency index to construct a new objective function. The new objective function is as follows: c P n P

!

uij dij2 =n i¼1 j¼1 J ðU; V; cÞ=n J ðU; V; cÞ ¼ ¼ SepðV; cÞ min jjvj  vk jj2 0

ð3Þ

j6¼k

Where, n is the total number of samples, SepðV; cÞ is the minimum value of Euclidean distance in each cluster center. 3.3

Fuzzy C-Means Clustering Algorithm Based on Adaptive Genetic Algorithm

Firstly, the clustering center is initialized by adaptive genetic algorithm, then a fuzzy Cmeans algorithm weighted by Gauss density function is used to classify batteries, and the classification results are used as input to train an automatic battery matching prediction model based on support vector machine. The flow chart of sorting algorithm is shown in Fig. 3.

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Fig. 3. Sorting algorithm flow chart

4 Battery Matching Prediction Model Based on Support Vector Machine Support vector machine is a machine learning algorithm based on statistical theory [9]. Due to its good generalization performance, which is often used in machine learning such as classification, regression, density function estimation and so on. Assuming a sample T0 ¼ fðxi ; yi Þ : xi 2 Rn ; yi 2 f1; 1g; i ¼ 1; 2; 3. . .ng, xi is the multidimensional input value of the sample, yi is the output value. The classification hyperplane function is defined as: f ð xÞ ¼ x T x þ b

ð4Þ

Where, x is a hyperplane normal vector. The geometric spacing of any sample point to the hyperplane is:   c ¼ yi xT xi þ b =jjxjj

ð5Þ

The larger the value of the geometric interval c, he greater the geometric distance from the point to the hyperplane, which means that the classification effect is better. In order to find the optimal solution, a Lagrange function is introduced: Xn     1 L(x; b; aÞ ¼ jjxjj2  a y x T xi þ b  1 i¼1 i i 2 Where, a is a Lagrange multiplier.

ð6Þ

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By SMO algorithm, the optimal values x and b of x and b can be solved. Finally, we can get the classification decision functions: f ðxÞ ¼ signðx x þ b Þ

ð7Þ

It can be known from Eq. (8) that it is mainly used to solve the linear separable sample data, but in practice, most of the problems are non-linear separable. Therefore, a non-linear transformation is needed to map the sample data to the high-dimensional eigenvector space and obtain the optimal classification decision function in the highdimensional eigenvector space. In mapping data from low-dimensional space to highdimensional space, by using non-linear transformation, the data processing is very complex, which may lead to “dimension disaster”. By introducing kernel function, support vector machine makes the data can be calculated in the low dimensional space, avoiding the complex calculation in the high dimensional space, and reducing the computational complexity. 4.1

Kernel Function Selections

Support Vector Machine uses different kernel function, which will generate different support vector machine algorithms. The commonly used kernels are as follows: (1) Gaussian radial basis kernel function:    kðx; xi Þ ¼ exp jjx  xi jj2 = 2g2

ð8Þ

(2) Polynomial kernel function: kðx; xi Þ ¼ ððx  xi Þ þ 1Þd

ð9Þ

kðx; xi Þ ¼ tanhðcðx  xi Þ þ dÞ

ð10Þ

(3) Sigmoid kernel function:

Gauss Radial Basis Kernel Function not only has the characteristics of strong locality, few kernel parameters and small error, but also has good performance for small sample data or large sample data. Therefore, Gauss radial basis kernel function is selected in this paper. 4.2

Kernel Parameter Optimization

The accuracy of the model is closely related to the kernel parameters g and c. The value of the parameter g has a great influence on the distribution complexity of the sample in the feature space: when the g value is too large, the training samples are correctly classified, but when it is too large, it will lead to over-fitting, which will reduce the

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generalization ability of the model; when the value of g is small, the generalization ability of SVM will be enhanced, but the sample classification error will be increased. A large value of c will reduce the generalization ability of SVM, while a small value will increase the fitting error. Therefore, in order to obtain the best classification model, kernel parameters g and c should be selected at the same time. Methods of optimizing parameters are: grid search method, cross validation method, genetic algorithms and particle swarm optimization algorithm, and the cross validation method is used to optimize the nuclear parameters g and c in this paper. Cross-validation is a method for evaluating generalization ability of machine learning algorithms, which divides data sets into k subsets, each of which makes a test set, and the rest as a training set. K-fold CV cross-validation is repeated k times, each of which selects a subset as a test set, and takes the average cross-validation recognition rate of k time as a result. Since all samples are taken as training sets and test sets, each sample is verified once, so the overfitting problem can be effectively avoided. The diagram of cross validation optimization parameter is shown in Fig. 4.

Fig. 4. Cross-validation optimization parameter graph

The horizontal axis and the vertical axis in Fig. 4 respectively indicate that c and g take the value of the base 2 logarithm, and the contour line indicates the corresponding prediction accuracy. In this paper, the classification accuracy is selected as the verification criterion. Since the smaller c is, the higher the generalization of the model will be. Therefore, in the case of the same accuracy, a group of parameters with smaller c is selected. 4.3

Matching Prediction Model Establishment

The matching prediction model first uses the optimized fuzzy C-means algorithm to sort the data collected by the automatic battery matching system. Then, the selected battery is given a label, and according to the battery label, a certain amount of the batteries are randomly selected from the sorted battery as sample data. Finally, a battery

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automatic matching prediction model based on a support vector machine is established by using different types of battery sample data. The flow chart is shown in Fig. 5.

Fig. 5. Flow chart of matching prediction model

5 Experimental Verification 5.1

FCM Sorting Experiment

In this paper, a certain type of battery is used as the research object. From a batch of batteries, 1000 batteries are randomly selected and the data of electrical parameter are measured as a sample for experiment. Firstly, the optimized fuzzy c-means algorithm is used to classify the batteries. When FCM classifies batteries, it is necessary to specify the number of classifications C, which is unknown in practice. Therefore, the fuzzy clustering division is also different for different classification numbers. The Xie-Beni validity indicator introduced in this paper can help determine the optimal partition and find the best number of classifications. It can be seen from formula (3) that when the molecule is smaller, the intra-class spacing will be smaller and the classification effect is will be better; when the denominator is larger, the distance between the class and the class will be larger and the classification effect will be better. Therefore, the value of the objective function J 0 ðU V cÞ is a very small index, and the number of classifications corresponding to the minimum value within a certain range is the best classification number. In this paper, the number of classifications is 2, 3, 4, 5, 6, 7, 8, 9 and 10. When the number of classifications is greater than 10, the number of classifications is too large, which has little significance for battery sorting and matching. Therefore, this paper does not consider it. The objective functions value’s changing curve is shown in Fig. 6.

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Fig. 6. Objective function value

As can be seen from the figure above, when the number of classifications is 4, the objective function value is the smallest. Therefore, the batteries are sorted into four categories A, B, C and D by using the optimized fuzzy C-means algorithm. The sorting results are shown in Table 1.

Table 1. Sorting result Classification Cluster center Number of samples Sorting result A (11.8267, 44.3851) 207 3, 9, 16, 20, 23, 30, 33, 36, 50 51, 56, 58, 60, 73, 103, 107, 109 139, 141, 144, 145, 146, 152 etc. B (11.7854, 45.1676) 231 2, 7, 10, 11, 17, 19, 31, 32, 35 39, 43, 48, 49, 52, 55, 59, 68, 74 78, 81, 82, 85, 86, 87, 90, 96 etc. C (11.6495, 44.7944) 337 6, 8, 12, 13, 14, 15, 18, 21, 24 25, 26, 28, 29, 37, 44, 47, 53, 54 57, 61, 63, 64, 65, 66, 70, 71 etc. D (11.9856, 44.7892) 225 1, 4, 5, 22, 27, 34, 38, 40, 41 42, 45, 46, 62, 69, 72, 80, 88, 93 95, 102, 106, 108, 111, 113 etc.

5.2

SVM Matching Experiment

According to the sorting results of the optimized fuzzy c-means algorithm, 50 groups of batteries were randomly selected from each category as sample data, and the sample data were divided into training set and test set in different proportions. The experimental results are shown in Table 2.

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As can be seen from Table 2, the more training sets are, the higher the test accuracy is. When the number of training sets is 10, the number of errors in the prediction model is 13 (the sum of class A, class B, class C and class D). When the number of training sets is 30, the number of misclassifications is one, the accuracy rate is the highest, and the accuracy rate is 98.75%, which verifies the feasibility of the model established in this paper.

6 Conclusions In order to solve the problem that most enterprises can’t realize automation by using a matching method to ensure consistency in power battery packs, an automatic battery sorting and matching system is built, and an optimized fuzzy C-means algorithm combined with support vector machine is proposed, and a prediction model of power battery automatic matching based on support vector machine is established in this paper. The data samples collected by the electrical measurement system are sorted by the optimized fuzzy C-means algorithm, which is used as the input of the training model to establish a matching prediction model. The experimental verification results show that the model established in this paper can obtain higher matching accuracy, not only ensures the automation and intelligence of the power battery sorting and matching, but the production needs of enterprises.

References 1. Wang, L., Xie, L., Zhang, G., He, X.: Research progress in consistency screening of lithium ion batteries. Energy Storage Sci. Technol. 7(02), 194–202 (2018) 2. Wang, Z., Sun, F., Lin, C.: Analysis of the influence of inconsistency on the service life of power battery packs. J. Beijing Inst. Technol. 26(7), 577–580 (2006)

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3. Raspa, P., Frinconi, L., Mancini, A.: Selection of lithium cells for EV battery pack using selforganizing maps. Automot. Saf. Energy 2(2), 157–164 (2011) 4. Kim, J., Shin, J., Chun, C.: Stable configuration of a Li-Ion series battery pack based on a screening process for improved voltage SOC balancing. IEEE Trans. Power Electron. 27(1), 411–424 (2012) 5. Ji, M., Yuan, C., Li, E.: A Lithium Ion battery matching method. CN 101924247A, 22 December 2010 6. Zhang, S.: Battery optimization matching technology based on charge and discharge characteristics, CN 101814632A, 25 August 2010 7. Yan, C., Li, M., Zhou, X.: Application of improved genetic algorithm in function optimization. Appl. Res. Comput. 2019(10), 1–6 (2019) 8. Bezedk, J.C., Christian, J.: Fuzzy mathematics in pattern classification. Cornell University, Ithaca (1973) 9. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)

Random Vibration Analysis of Optical Adjustable Frame Based on ANSYS Workbench Nan Xu1, Yuan Wang1,2(&), and Kelin Xu2 1

2

School of Mechanical and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, China [email protected] School of Mechanical Engineering, Shandong Vocational and Technical University of Engineering, Jinan 250200, China

Abstract. In this paper, aiming at the random vibration of optical adjusting frame, the modal analysis and random vibration analysis of optical adjusting frame are carried out by using ANSYS Workbench finite element software, and the frequency, corresponding vibration mode and strain cloud diagram of the adjusting frame are obtained. The strength of the adjusting frame structure is checked, and the results show that the optical adjusting frame meets the overall design requirements. Keywords: Modal analysis Optical adjustment frame

 Random vibration analysis 

The interference of vibration environment to optical system is universal [1]. The vibration of the environment leads to the vibration of the working parts and the jitter of the beam of the optical system, which leads to the decrease or even failure of the working efficiency of the optical device. The instability of beam pointing caused by environmental vibration widely exists in all kinds of optical systems and has a great impact on the efficiency of optical systems and hinders the practical process of some precision optical systems. In order to ensure that the optical system can work normally under the interference of field vibration and noise, it is necessary to consider the overall stability and anti-vibration performance of the optical system. Therefore, vibration will become one of the main interference factors of optical system stability in practical application field, and the evaluation of its anti-vibration performance will also become a research focus of optical system field application. Therefore, to improve the antivibration performance of optical system in harsh environment and improve the working stability of optical system has become an urgent problem to be solved in practical application. The influence of mechanical vibration on the imaging quality, measurement accuracy and target tracking accuracy of the optical system is unavoidable. Mechanical mechanisms that are excited by the outside can cause stability errors in beam pointing. When the excitation frequency is near the natural frequency of the object, both the amplitude amplification factor and the vibration amplitude of the object will be © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 760–768, 2020. https://doi.org/10.1007/978-981-32-9941-2_63

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particularly large if the damping is small. At this time, the mechanical structure carrying the optical element will resonate. And resonance is the main factor in the pointing stability error of the beam in the optical path [2, 3].

1 Scheme Design of Optical Adjustment Frame The optical adjustment frame is designed to realize the four-dimensional transformation to meet the transmission requirements of the laser beam, and the vibration analysis of the optical adjustment frame. The optical adjustment frame can realize four-dimensional transformation, displacement adjustment (x, y) and tilt adjustment ðhx ; hz Þ. The main components of the optical adjustment frame include a mirror base support, a front mirror base plate, a rear mirror base plate, sleeves, a mirror base and adjusting bolts. The main components are connected by bolts, tension springs and spring pins. The overall design of the optical adjustment frame is shown in Fig. 1.

Fig. 1. Overall design of the optical adjustment frame design

The subsystem of the optical adjustment frame includes a support system and an adjustment system. The support system includes a support member, a front mirror seat plate, a rear mirror seat plate, and a sleeve. The support member is fixed on the workbench to carry the entire adjustment frame and ensures overall stability; the front mirror seat plate is the main body of the mirror base connection and adjustment; the rear mirror seat plate is connected with the support member on one hand to maintain stability, and on the other hand, the Angle can be adjusted by connecting the connecting member; the sleeve ensures the distance between the front and rear mirror plates. The adjustment system includes a mirror mount, an adjustment bolt and a spring pin. The lens holder is the mounting position of the optical component, and the adjustment of the optical component can be achieved by adjusting the lens holder. The rotation adjusting bolts 1 and 2 can realize the two-dimensional translation of the mirror seat in the x and y directions, and the rotation adjusting bolt 3 realizes the front mirror seat plate and the component rotates around the x-axis as a whole. The rotation adjusting bolt 4 realizes the front mirror seat plate and the component rotates around

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the y-axis as a whole. The spring pin is in the symmetrical position of the adjusting bolts 1, 2 and the position compensation can be realized by balancing the force on the mirror seat. The same threaded hole is machined on the bottom surface of the front and rear mirror plate. When the optical adjustment frame only needs two-dimensional translation in the x and y directions, the front lens base plate can be directly connected with the support member to achieve the corresponding function. The dynamics modeling of the optical adjustment frame is mainly to establish a support system, an adjustment system, and a dynamic model of the connected component including the thread pair.

2 Modal Analysis The influence of mechanical vibration on the imaging quality, measurement accuracy and target tracking accuracy of the optical system is unavoidable. The stability error of the beam pointing is the response of the mechanical structure after being excited by the outside. The kinetic analysis can evaluate whether the strength and stiffness of the structure of the optical adjustment frame in the dynamic environment meet the requirements, verify the correctness of the design scheme; simulate the dynamic environment of the mount through the finite element model, and solve various responses in the corresponding dynamic environment. The modal analysis method can clearly understand the characteristics of the main modes of the optical adjuster in a certain vulnerable frequency range, and predict actual vibration response that the frame structure will be generated by internal or external vibration sources in this frequency band [4]. Extract the 6th order natural frequency and mode shape of the optical adjustment frame. The first 6 natural frequencies and vibration modes of the optical adjustment frame are shown in Table 1.

Table 1. Description of the 6th natural frequency and mode shape of the optical adjustment frame Order 1 2 3 4 5 6

Frequency/Hz 442.43 1024.2 1060.4 1154.6 1818.9 2484.4

Mode description Torsion around the X axis Torsion around the Z axis Torsion around the Y axis Swing back and forth along the Z axis Swing up and down along the Y-axis Swing left and right along the X axis

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The front 6th mode of the optical adjustment frame is shown in Fig. 2.

a

1st order mode

b 2nd order mode

c

3rd order mode

d 4th order mode

e

5th order mode

f 6th order mode

Fig. 2. The 1st to 6th mode of the optical adjustment frame

It can be seen from the 1st to 6th order modal frequency of the optical adjustment frame that the lowest frequency is 447.88 Hz, which is higher than the building frequency of the module assembly laboratory, 100 Hz, and does not resonate with the pedestal. In addition, the vibration mode of optical adjustment frame reflects the whole vibration of all parts except the supporting members. The support of the optical adjustment frame is main support member, and its first and second modes are analyzed to obtain the following results, as shown in Figs. 3 and 4. In the first-order mode, the connection between the support member and the rear

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mirror base plate has a tendency to twist around the X-axis direction, and the maximum deformation occurs at the front end of the joint portion. In the second-order mode, the support member and the rear mirror seat plate are connected. There is a tendency to twist around the Z-axis, and the maximum deformation occurs at the front ends of the left and right sides of the joint.

Fig. 3. 1st mode of the optical adjustment frame

Fig. 4. 2nd mode shape diagram of the optical adjustment frame

Since the optical collimated light source itself does not involve a power component, the vibration mainly comes from external excitation. It is only necessary to avoid the external excitation frequency being close to its natural frequency during use of the optical collimated light source. In addition, the optical module should be collimated and adjusted when the external vibration is small.

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3 Random Vibration The amplitude, frequency and phase of the structural vibration are the three elements of vibration. The amplitude is a sign of vibration intensity, which can be expressed by different methods such as peak value, effective value, and average value. Vibration displacement is an important basis for studying strength and deformation. Acceleration of vibration is proportional to force or load, and is an important basis for studying dynamic strength and fatigue. Vibration speed determines the level of noise, and the human sensitivity to mechanical vibration is determined by the vibration velocity in a large frequency range. The vibration velocity is related to energy and power and determines the momentum of the force. The ultimate goal of structural dynamics analysis is to determine the variation of the internal force, displacement and reaction force of the structure with time under dynamic load, so as to find the maximum value as the basis for design analysis. The random vibration analysis is used to determine the response analysis of the random load to the structure. It mainly determines the probability and statistics of the structure response to the random dynamic load. It is the power spectral density-frequency relationship curve, which reflects the intensity and frequency information of the time history load [5]. The solid element has only the translational freedom along the three axes of X, Y and Z. The three-direction optical adjustment frame model can be used to participate in the quality evaluation from the analysis information in the modal analysis. The specific values are shown in Table 2. It can be seen from the table that the mass concentration in the X-axis direction is the largest, which has the greatest influence on the modal analysis, so the random vibration mainly analyzes the X-axis direction.

Table 2. Participation in quality assessment of optical adjustment frame models based on X, Y and Z directions Order 1 2 3 4 5 6 Sum

Frequency/Hz 442.43 1024.2 1060.4 1154.6 1818.9 2484.4

X-axis direction 0.000410 0.367817 0.011759 0.010499 0.070715 0.004809 0.466009

Y-axis direction 0.013803 0.003884 0.002363 0.001045 0.122744 0.132485 0.276324

Z-axis direction 0.400061 0.000045 0.001139 0.006019 0.000602 0.028726 0.436592

The random vibration analysis of the optical adjustment frame model is carried out, and the calculated 1r displacement response cloud diagram of the optical adjustment frame is shown in Figs. 5 and 6. 1 r displacement and stress can be used for fatigue life prediction.

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Fig. 5. Optical adjustment frame stress cloud

Fig. 6. Partial view of the stress cloud of the optical adjustment frame

It can be seen from Figs. 5 and 6. The maximum vibration of the optical adjustment frame appears on the support member of the mount and the rear mount plate connector and the support member. The lens holder is the main component in the optical adjustment frame. Therefore, a certain point on the lens holder is selected as the research object. The selected point is shown in Fig. 7. According to the PSD spectrum data of Table 3, the displacement response analysis is performed, and the displacement response cloud image is shown in Fig. 8.

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Fig. 7. Optical adjustment frame selection point

Table 3. Partial PSD spectral data Spectrum points Frequency/Hz 1 442 2 442 3 442.12 4 442.24 5 442.31 … … 58 1032.2 59 1037.2 60 1045.4 61 1058.6 62 1060

PSD spectral response/mm 1.01E−07 1.01E−07 1.01E−07 1.00E−07 9.99E−08 … 1.99E−04 1.32E−04 7.45E−05 5.93E−05 6.19E−05

Frequency /Hz

4.88E-04 2.44E-04 1.22E-04

6.10E-05 3.05E-05 1.53E-05

7.63E-06 3.81E-06 1.91E-06 9.54E-07

4.77E-07 2.38E-07 1.19E-07

PSD spectral response /mm

5.96E-08

442

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534

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626

656

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717

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779

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838

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899

929

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1,021

1,052

Fig. 8. PSD spectrum of a point shift of the optical adjustment frame

The PSD records the relationship between the mean square value of the excitation and response and the frequency, extracts the displacement PSD spectrum curve and the displacement response power density spectrum value at the instantaneously increasing

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peak. The displacement change rate increases sharply when the frequency exceeds 1000 Hz. The excessive frequency should be avoided when the optical adjustment frame is actually working.

4 Conclusion According to the flow of dynamic analysis, the modal analysis of the optical adjustment frame is carried out to obtain the first 6 natural frequencies and vibration modes. Secondly, the natural frequency is obtained by analyzing the mirror support to avoid resonance of the optical adjustment frame caused by external excitation, which affects the optical imaging quality. According to the modal analysis results, the X-axis direction is selected for random vibration analysis to determine the response of the random load to the geometric model by comparing the concentrated mass. In addition, the displacement response analysis is performed on a point on the key component lens holder to obtain the displacement response curve, which has guiding significance for the frequency control in the work.

References 1. Wang, Q., Tan, L., Ma, J., et al.: A novel approach for simulating the optical misalignment caused by satellite platform vibration in the ground test of satellite optical communication systems. Opt. Express 20(2), 1033–1045 (2012) 2. Zhenhua, N.: Vibration Mechanics, pp. 6–124. University of Science and Technology of China Press, Hefei (2007) 3. Fan, G., Jia, J., Chen, G., Zhao, J.: Influence of mechanical vibration on the pointing accuracy of optical system. China Mech. Eng. (02), 12–14+19 (2005) 4. Liu, J.: Detailed Explanation of ANSYS 14.5 Workbench Mechanical Simulation Example. China Machine Press (2015) 5. Li, J., Ding, H., Pang, S.: Analysis of random vibration response of BKX-I parallel machine tool. Mach. Tool Hydraulics (10), 61–62 (2005)

Analysis of Influence of Eccentricity Error on Transmission Performance of Micro-segment Gears Rui Xu1,2,3(&), Lielong Wang1,2, Peidao Pan1,2, and Kang Huang3 1

School of Mechanical and Electrical Engineering, Chizhou University, Chizhou 247000, China [email protected] 2 Advanced Materials Preparation and Forming Technology Engineering Research Center, Chizhou University, Chizhou 247000, China 3 School of Mechanical Engineering, Hefei University of Technology, Hefei 230009, China

Abstract. In order to further improve the applicability of micro-segment gears and give full play to their advantages in transmission performance, the influence of eccentricity error on the transmission performance of micro-segment gears is studied. Based on the forming principle of the micro-segment gear tooth profile, the mathematical model of the tooth profile is established. According to the characteristics of discrete profile of micro-segment gears, the meshing process of micro-segment gears is analyzed using discrete TCA (tooth surface contact analysis). The calculation method of transmission error of micro-segment gears considering eccentricity error is studied. Based on the calculation program, the influence of different eccentricity errors on transmission errors of involute and micro-segment gears is compared and analyzed. The results show that the eccentricity error will cause the transmission error of the micro-segment gears to fluctuate continuously in each meshing cycle, and the amplitude of fundamental frequency is much smaller than that of involute gears. However, as the eccentricity error increases, the influence of the high frequency part of the transmission error becomes more and more obvious. In addition, the influence of the high frequency part of the transmission error of micro-segment gears can be effectively reduced by changing the eccentricity angle. In order to design highperformance micro-segment gears, the transmission performance impact caused by eccentricity errors can be reduced by improving the machining and installation accuracy of the micro-segment gear holes and shafts. Keywords: Micro-segment gear Transmission error

 Involute gear  Eccentricity error  TCA 

This project is supported by National Natural Science Foundation of China (Grant No. 51775156), Chizhou University-level Natural Science Research Project (No. CZ2018ZRZ03) and Mechanical Design and Manufacturing and Automation Professional Certification (No. 2017XZYRZ02). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 769–784, 2020. https://doi.org/10.1007/978-981-32-9941-2_64

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1 Introduction As one of the important basic components of mechanical transmission, the performance of gears directly affects the performance of mechanical systems or mechanical equipment. With the development of science and technology, higher requirements are placed on the performance of gears. In order to improve the performance of the gear system, it is possible to carry out research from the aspects of constructing a new tooth profile, modifying the tooth surface, adopting a new transmission structure and so on. The micro-segment gear is one of new types of gears proposed according to the new tooth profile theory. The tooth profile curve is a curve similar to the stepped arc profile formed by a number of micro-line segments, which breaks the limitation that the traditional tooth profile curve must be second-order smooth and continuous [1]. The micro-segment has the characteristics of strong bearing capacity, good wear resistance, high transmission efficiency and easy miniaturization [2–5]. It can be seen that the use of micro-segment gears can effectively improve the comprehensive performance of gear transmission system. Relevant scholars have made in-depth research on the performance of microsegment gears. Literature [1] elaborated the construction principle of micro-segment tooth profile in detail. The literature [2–5] carried out the theoretical and experimental research on the bending strength, transmission efficiency and bearing capacity of micro-segment gears. The literature [6] calculated the meshing stiffness of the microsegment gears according to the potential energy calculation principle. Literature [7] studied the normal contact stiffness of micro-segment gears based on fractal theory. Literature [8] studied the grinding method of micro-segment gears and analyzed its performance. Literature [9] established the dynamics model of micro-segment gear and analyzed its dynamic characteristics. It can be seen from the above literature that most of the literatures are based on the ideal tooth profile of the micro-segment gears, and the research literature on the meshing performance of the micro-segment gears considering the actual error is still rare. Eccentricity error is an important factor affecting gear transmission error, and it is also one of the main sources of gear vibration and noise [10]. Due to the particularity of the tooth profile of the micro-segment gear, the influence of the eccentricity error on the transmission error of micro-segment gears will be different from that of the involute gear. Therefore, it is necessary to study the influence of eccentricity error on the transmission error of micro-segment gears, which can not only provide guidance for the design and processing of micro-segment gears, but also lay a foundation for the follow-up study of dynamics of micro-segment gears considering actual deviations. In this paper, the mathematical model of micro-segment gear profile is established, and the discrete TCA method is used to construct the transmission error calculation models of micro-segment gear and involute gear, and the calculation program is compiled. Finally, the influence of eccentricity error on the transmission error of microsegment gear and involute gear is analyzed and compared.

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2 Construction of Mathematical Model of Tooth Profile of Micro-segment Gear Micro-segment gear is a kind of gear with special tooth profile, which is made up of many fine micro-segments and the transmission is realized by convex-concave meshing, as shown in Fig. 1. Figure 2 shows the construction principle of micro-segment rack profile. Figure 3 shows the process of constructing micro-segment gear profile by using micro-segment rack.

micro-segment gear profile involute gear profile

Fig. 1. Comparison of tooth profile between micro-segment gear and involute gear

Fig. 2. Construction principle of micro-segment rack tooth profile

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Fig. 3. Construction process of teeth profile of micro-segment gear

In the coordinate system Og xg yg shown in Fig. 3, the mathematical model of the tooth profile of micro-segment gears is constructed as follows: 

xg ¼ qmk cos ak cos r  ðqmk sin ak  rg Þ sin r yg ¼ qmk cos ak sin r þ ðqmk sin ak  rg Þ cos r

ð1Þ

Where, r is the angle of gear rotation, qmk and ak is the radius of curvature and pressure angle of the k th zero point, respectively. Set the micro-segment rack to move a distance b, then: b ¼ xk þ

yk tan ak

ð2Þ

The angle r of gear rotation can be described as: r ¼ b=rg

ð3Þ

The pressure angle can be expressed as: ak ¼ ak1 þ ðd þ dk Þ

ð4Þ

In the formula, d is the initial pressure angle increment and dk is the kth pressure angle increment, which can be expressed as follows: dk ¼ cos1 ½2 cosðak1 þ dÞ  cos ak1   ðak1 þ dÞ

ð5Þ

The expression of curvature radius qmk is: qmk ¼ qm0 þ rb0 ðd  d1 Þ þ . . . þ rbk1 ðd  dk Þ

ð6Þ

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Where, rb0 is the initial base circle radius and rbk is the kth base circle radius, which can be described as: rbk ¼ rb0 ½1  sinð0:6ak Þ

ð7Þ

3 Mathematical Modeling of Gear Tooth Profile Considering Eccentricity Error In order to study the influence of eccentricity error, a coordinate system is established as shown in Fig. 4, in which the coordinate system Og xg yg is a gear fixed coordinate system with the geometric center of the gear as the origin and the coordinate system Oxy is a fixed coordinate system with the rotating axis as the center.

Fig. 4. Coordinate system conversion considering eccentricity error

According to the geometric relationship, the transformation matrix of gear profile from coordinate system Og xg yg to coordinate system Oxy can be described as follows: 2

3 2 1 0 cos½/  /0   sin½/  /0  0 Rg ¼ 4 sin½/  /0  cos½/  /0  0 5  4 0 1 0 0 0 0 1

3 fe cos de fe sin de 5 1

ð8Þ

Where, /0 and / are the initial corners respectively; fe is the eccentricity; de is the eccentric angle, which is the angle between the line connecting the origin of the two coordinate system and the horizontal axis.

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Then, the mathematical model of gear profile considering eccentricity error is as follows: ! r ¼ Rg  ! rg

ð9Þ

4 Discrete Tooth Contact Analysis Method Tooth contact analysis (TCA) is a classic method to assess the meshing quality of a gear pair allowing the designer to predict the performance of the transmission [11]. The main purpose of TCA is to obtain the position and size of contact ellipse, the contact trace and transmission error [12], which is mostly related to the dynamic performance of the gear system. For involute gears, the traditional TCA method is generally used, that is, contact analysis is carried out by solving meshing points according to the meshing conditions of gear pairs. For micro-segment gears, the traditional TCA method cannot be used to solve meshing points because its tooth profile is a discrete profile composed of a large number of micro-segments. In order to effectively analyze the influence of deviation on the transmission performance of micro-segment gears, a discrete TCA method for discrete tooth profile is adopted to solve the meshing point and obtain the transmission error from the perspective of discrete geometry. 4.1

Discrete TCA Method

The discrete TCA method is to discretize the profile of gear teeth and determine the contact points according to the geometrical relationship of motion, so as to obtain the transmission error [13]. As shown in Fig. 5, gear 1 is the driving wheel and gear 2 is the driven wheel. The tooth profiles of two gears are discretized separately, that is, the tooth profiles are composed of several finite points, and the points are connected with each other by a short straight line. The gear 1 rotates around the coordinate origin O, and the gear 2 rotates around the point ðxm ; ym Þ. The purpose of the discretization TCA is to use the discrete points on the gear 2 as the contact points, and calculate the rotation angle of the driven wheel 2 through the geometric relationship, thereby obtaining the transmission error.

Fig. 5. Discrete TCA schematic diagram

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In order to achieve the above purpose, it is necessary to determine the intersection point ðxs ; ys Þ between the circle with point ðxm ; ym Þ as the center and the distance from point mðxi ; yi Þ to point ðxm ; ym Þ as the radius and discrete tooth profile of gear 1. The corresponding solution equation is: 8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > < ymi ¼ ym þ ri  ðx  xm Þ2 ð10Þ y n ¼ m n  x þ tn > : max x 2 ½xmin ; x  n n max Where, xmin are the two endpoints of the nth line on the tooth profile of gear 1, n ; xn respectively. Then, as shown in Fig. 6, the rotation angle of gear 2 can be expressed as:

/0i ¼ arcsinð

ys  ym yi  ym Þ  arcsinð Þ ri ri

ð11Þ

Fig. 6. Schematic diagram of transmission error calculation

According to the above analysis, each discrete point on the tooth profile of gear 2 can correspond to a rotation angle and the smallest of them is the actual rotation angle of gear 2: /2 ¼ minð/0i Þ

ð12Þ

By substituting the above formula into the formula (11) for calculating transmission error, the transmission error which varies with the rotation angle of the driving gear can be obtained. The transmission error can be described as: z1 e ¼ rb1 ½ð/2  /02 Þ  ð/1  /01 Þ  z2

ð13Þ

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In the formula, /01 , /02 are the initial rotation angles of gear 1 and 2, /1 , /2 are the actual rotation angles of gear 1 and 2, A and B are the number of teeth of gear 1 and 2, and a is the radius of base circle of gear 2. Based on the above-mentioned transmission error solving principle, a discrete TCA method solving program is developed and its flow chart is shown in Fig. 7.

Fig. 7. Flow chart of discrete TCA method and traditional TCA method

Based on the TCA program, the influence of eccentricity error on transmission error of micro-segment gears in meshing process can be analyzed. In order to verify the correctness of the above method and the program, the transmission error curve when fe ¼ 0:01; de ¼ 0 is simulated based on discrete TCA. The results are compared with those obtained by traditional TCA method,as shown in Fig. 8. From the graph, the simulation results of the two methods are consistent, which verifies the correctness of the discretization program.

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Fig. 8. Comparison of simulation results between discrete TCA method and traditional TCA method

4.2

The Influence of Eccentricity Error on Transmission Error of MicroSegment Gears

Taking the involute gear and micro-segment gear with the same basic parameters as examples, this paper compares and analyses the influence of eccentricity error on transmission error of involute gear and micro-segment gear. The specific parameters are shown in Tables 1 and 2, respectively. (1) The influence of eccentricity fe on transmission error For the convenience of research, de is taken as 0 in the subsequent analysis. Table 1. Involute gear parameters Parameter Module/mm Tooth number/ Pressure angle/° Outside diameter/mm Root circle diameter/mm Center distance/mm

Value 1 26 20 26 23.5 26

Table 2. Micro-segment gear parameters Parameter Module/mm Tooth number/ Initial pressure angle/° Initial pressure angle increment/° Initial basic circle radius/mm Outside diameter/mm Root circle diameter/mm Center distance/mm

Value 1 26 20 0.00065 400000 26 23.5 26

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Figures 9, 10 and 11 show the variation of transmission errors of involute gears and micro-segment gears when eccentricity is 0.005, 0.010 and 0.015, respectively. As can be seen from the figure below, as the eccentricity increases, the amplitude of the transmission error of the involute gear and the micro-segment gear increases, and the overall change trend is the same, similar to the trigonometric curve.

Fig. 9. Transmission error curve when eccentricity is 0.005

Fig. 10. Transmission error curve when eccentricity is 0.010

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Fig. 11. Transmission error curve when eccentricity is 0.015

In order to compare the amplitude-frequency characteristics of the transmission errors of the involute gears and the micro-segment gears, given the speed of the driving wheel is 500 r/min, the amplitude-frequency curves of the transmission errors of the involute gears and the micro-segment gears at the eccentricity errors of 0.005, 0.010 and 0.015 are shown in Figs. 12, 13 and 14, respectively. From the figures below, we can see that the transmission errors of involute gears have only one cycle, and its frequencies are about 8 Hz; while the transmission errors of micro-segment gears have many cycles and their frequencies are distributed at 8 Hz, 210 Hz, 415 Hz, among which the maximum amplitude exists around 8 Hz, but smaller than that of involute gears. It can be seen that the eccentricity error will produce low frequency and high frequency fluctuations in the operation of the micro-segment gear, but the amplitude of the low-frequency fluctuation is smaller than that of the involute gear. The influence of high frequency fluctuation on the gear system will become more and more obvious as the eccentricity error increases.

frequence

Fig. 12. Amplitude-frequency curve when eccentricity is 0.005

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frequence

Fig. 13. Amplitude-frequency curve when eccentricity is 0.010

frequence

Fig. 14. Amplitude-frequency curve when eccentricity is 0.015

In summary, it can be seen that when there is eccentricity error, the involute gear and the micro-segment gear have certain fluctuations during operation, but the involute gears are relatively flat, mainly showing low-frequency fluctuations. The microsegment gear has a certain degree of fluctuation in each meshing period, and there are low-frequency and high-frequency fluctuations, but the amplitude of the fundamental frequency is smaller than the amplitude of the involute gear. When the eccentricity error is small, the influence of high frequency fluctuation is not obvious, but as the eccentricity error increases, the influence of high frequency fluctuation becomes more and more obvious. (2) The influence of eccentricity angle de on transmission error Let the eccentricity fe be 0.01, and the eccentric angle de of the driving wheel and the driven wheel are as shown in Table 3.

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Table 3. The value of the eccentric angle de of the driving wheel and the driven wheel Value de1 /° de2 /° 1 0 180 2 90 180 3 180 180

Figures 15, 16 and 17 show the variation of transmission error of involute gear and micro-segment gear when the eccentricity angle of driven wheel is 180° and the eccentricity angle of driving wheel is 0°, 90° and 180° respectively. Figures 18, 19 and 20 show the amplitude-frequency curves of the transmission errors of the involute gears and the micro-segment gears when the eccentricity angle of the eccentricity angle of driving wheel is 0°, 90° and 180° respectively. From the figures below, for microsegment gears, when the eccentricity angle increases from 0 to 180, the low-frequency vibration amplitude of micro-segment gears decreases gradually, while the highfrequency vibration amplitude increases gradually. For involute gears, when the eccentricity angle increases from 0 to 90, the amplitude of low-frequency vibration decreases obviously. When the eccentricity angle increases from 90 to 180, the amplitude of low-frequency vibration does not change much. It can be seen that the micro-segment gear is more sensitive to the change of eccentric angle. From the above analysis, it can be seen that the vibration amplitude can be reduced by adjusting the eccentricity angle of involute gear or micro-segment gear. Therefore, in order to reduce the vibration and noise of gears, it is an effective measure to adjust the eccentricity angle of meshing gears.

Fig. 15. Transmission error curve when eccentricity angle is 0°

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Fig. 16. Transmission error curve when eccentricity angle is 90°

Fig. 17. Transmission error curve when eccentricity angle is 0°

frequence

Fig. 18. Amplitude-frequency curve when eccentricity angle is 0°

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Fig. 19. Amplitude-frequency curve when eccentricity angle is 90°

frequence

Fig. 20. Amplitude-frequency curve when eccentricity angle is 180°

5 Conclusion (1) This paper introduces the discretization TCA analysis method based on the mathematical model of the micro-segment tooth profile and uses this method to analyze the influence of different eccentricity errors on the transmission error of involute gear and the micro-segment gear. This provides a research method for further studying the static and dynamic transmission performance of microsegment gears under different machining and assembly precisions. (2) By comparing the influence of eccentricity error on transmission error of involute gear and micro-segment gear, it is found that: When there is eccentricity error, the involute gear and the micro-segment gear have certain fluctuations during operation, but the involute gear fluctuation is relatively flat, mainly showing low-

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frequency fluctuation. The micro-segment gear has a certain degree of fluctuation in each meshing period, which has both low-frequency fluctuation and highfrequency fluctuation, and its fundamental frequency amplitude is smaller than that of the involute gear. However, as the eccentricity error increases, the high frequency portion of the transmission error will have a significant effect. (3) In order to give full play to the good transmission performance of micro-segment gears, on the one hand, the influence caused by eccentricity error can be reduced by improving the machining and assembly accuracy of micro-segment gear holes and shafts. On the other hand, the vibration amplitude can be reduced by adjusting the eccentricity angle.

References 1. Zhao, H., Liang, J.H., Liu, H.Y., Chen, A.S.: Constructing principle and features of tooth profiles with micro-segments. J. Mech. Eng. 33(5), 7–11 (1997) 2. Huang, K., Zhao, H.: Comparison and analysis of the bending strength of micro-segment gear and involute gear. Trans. Chin. Soc. Agric. Mach. 32(1), 115–117 (2001) 3. Huang, K., Zhao, H., Jang, X.B.: Comparative experimental study on transmission efficiency of micro-segment gear and involute gear. J. Mech. Eng. 26(4), 3–5 (2006) 4. Huang, K., Zhao, H., Tian, J., et al.: Experimental research on temperature rise comparison between micro-segment gear and involute gear. China Mech. Eng. 17(18), 1880–1883 (2006) 5. Liu, P., Zhao, H., Huang, K., et al.: Experimental research on temperature rise comparison between micro-segment gear and involute gear. J. Hefei Univ. Technol. 17(18), 1880–1883 (2006) 6. Liu, P., Zhao, H., Huang, K., et al.: Research on meshing stiffness calculation model for micro-segment gear based on potential energy method. Chin. J. Appl. Mech. 32(6), 1069– 1074 (2015) 7. Liu, P., Zhao, H., Huang, K., et al.: Research on normal contact stiffness of micro-segments gear based on improved fractal model. Chin. J. Appl. Mech. 54(7), 114–121 (2018) 8. Wu, Q.L., Zhao, H., Qiu, M.M., et al.: Grinding method and performance analysis of microsegment gears. J. Mech. Eng. 53(7), 114–121 (2017) 9. Huang, K., Wang, T.: Grinding method and performance analysis of micro-segment gears. J. Vib. Shock 37(2), 248–253 (2018) 10. Guangjian, W., Lin, C., Li, Y., et al.: Research on the dynamic transmission error of a spur gear pair with eccentricities by finite element method. Mech. Mach. Theory 109, 1–13 (2017) 11. Sanchez-Marin, F., Iserte, J.L., Roda-Casanova, V.: Numerical tooth contact analysis of gear transmissions through the discretization and adaptive refinement of the contact surfaces. Mech. Mach. Theory 101, 75–94 (2016) 12. Litvin, F.L., Fuentes, A.: Gear Geometry and Applied Theory, pp. 375–403. Cambridge University Press, Cambridge (2004) 13. Schleich, B., Wartzack, S.: A discrete geometry approach for tolerance analysis of mechanism. Mech. Mach. Theory 77(7), 148–163 (2014)

Research on the Design of Wearable Equipment for Intelligent Emotion Detection for Empty Nester Yan-min Xue(&), Chang Ge, Shi-yi Xu, Xu-yang Zhang, and Bo-xin Xiao Department of Industrial Design, Xi’an University of Technology, Xi’an 710054, China {xueym,gechang}@xaut.edu.cn, [email protected], [email protected], [email protected]

Abstract. Objective: The lack of spiritual comfort for the empty nesters is a great harm to the elderly. There are few products on the market that combine the emotional detection and wearable devices for the elderly with empty nests. Product demand, emotional needs, to guide the design of empty nest elderly emotional detection products. Methods: Through the investigation and the emotional needs of the empty nest elderly, establish the functional requirements of the product; analyze the user’s functional demand indicators for the empty nest elderly emotional detection products, and obtain the user demand importance to guide the product design. Results: Complete the needs of the empty nest elderly for the emotional detection of wearable products, build the functional requirements of the product, reflect the demand for the product function of the empty nest elderly, and ensure that the product can better meet the specific needs of the empty nest elderly. Conclusion: It proves that the product design for the emotional detection products of the empty nest is broad market, in line with the future social trend, with practical feasibility, theoretical pertinence and development necessity. Keywords: Interaction design  Empty nest elderly Emotional detection  Demand acquisition



Wearable devices



1 Introduction With the deepening aging of the population, the Empty-nest elderly has become a social problem that cannot be neglect. Lack of affective comfort is a greater harm to many “empty-nesters” [1]. Most of the existing researches by scholars and designers focus on the functional development and application field of the wearable devices for the elderly [2]. There are, however, only very few studies on the emotional detection of This paper is supported by Chinese Ministry of education of Humanities and Social Science (project No. 17YJAZH100) and Humanities and Social Science Program of Shaanxi Province (Project No. 2018K13). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 785–794, 2020. https://doi.org/10.1007/978-981-32-9941-2_65

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the elderly, especially the empty nesters. This situation makes the function of medical emotional demand products for empty nesters is single, and it is unable to accurately understand the individual needs of users. This paper through the research on the function, shape, emotion and market demand of wearable equipment, collecting the basic information and the “pain and refresh”-points of using smart Bracelet wearable devices of empty-nesters. From this, we can get the functional and usage needs of the user group and establish a product function list suitable for the empty-nester group, then guide the design of emotional detection products for empty nesters.

2 The Significance of Empty Nest Elderly’s Emotion Detection According to statistics, there are more than 200 emotional-related diseases, and more than 70% of all the patients are emotionally related. Prolonged exposure to certain emotions (whether positive or negative) can have adverse effects on health, according to psychiatrists. The empty-nesters are more likely to be emotionally fluctuant and over-excited. Negative emotions may be the promoter of tumorigenesis in the elderly and become an important reason for the sudden deterioration of the disease. Eliminating negative emotions and establishing positive and optimistic emotions are one of the most important ways for the elderly to get rid of illness and prolong their life [3]. As the age increases, the emotional experience of the elderly will be stronger than that of the young. And because of the decline of homeostasis adjustment ability in the body, the aged will take longer to recover mood. At the same time, the ability of the elderly to accept new things is limited, the willingness to use technology products is generally low, and the willingness to use technology products is generally low. Emptynesters, whose children are living away from their parents and have small social circles, are more prone to suffer from physical or psychological diseases. Therefore, emotional detection of empty-nesters is of great significance in regulating emotions of the elderly.

3 The Research on Emotional Interaction for Empty-Nesters 3.1

The Research on Interaction Design for the Elderly

The existing electronic products for the elderly are not perfect enough. The overall design of electronic products ignores the physiological and psychological characteristics of the elderly, so that there are many obstacles in man-machine communication between the elderly and electronic products. Introducing the concept of barrier-free interaction design into the research of interaction design of electronic products for the elderly can not only make the concept of interaction design integrated into the electronic products for the elderly better, but also make the experience of electronic products more pleasant for the elderly. Existing principles of interaction design: (1) Symbolic Interaction Patterns Matching User Cognition. (2) Operational Guidance to Promote User Participation.

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(3) Personalized Operational Feedback to Satisfy Users’ Needs. (4) Intelligent Enhancement of User Sense and Reduction of Misoperation [4]. Existing interaction design principles for the elderly: (1) Simple and clear interface. (2) Use the language familiar to the user: the icons, texts, etc. in the interface should use the familiar or usual expressions of the elderly. (3) Reduce the user’s memory burden. (4) Quick return after an error: When an elderly person makes an error during the manipulation process, he should quickly return to the previous operation and find the correct operation steps [5]. However, empty-nesters and older people are very different. They (empty nesters) need more emotional care and coping mechanisms in the event of an emergency. The interaction design principles added for the empty-nesters are as follows. (1) Customizable interface section for emotional comfort for empty nesters. (2) Emergency call interface: In response to the emergency of the empty nest elderly, (emergency call) should be placed in a convenient and eye-catching place, so that the elderly can call for help. But to increase the protection against false touches. 3.2

Research on the Development Status of Emotional Interaction Design

According to the content of interaction design, the emotional interaction design in electronic products can be roughly divided into three levels, namely, emotional interaction at the formal level, emotional interaction at the content level, and emotional interaction at the behavioral level [6]. Among them, the form of emotional interaction is the visual expression and presentation result of interaction design, including Emotional icon design and Fascinating visual style; the emotional interaction of content is the main part to show the function of the product, including the organization of specific functions and information. Impressive functional design and textual information to maintain emotion are important in this part; the emotional interaction of behavior is the core of design, which runs through the whole process of interaction design. At present, in mobile applications, emotional interaction at the behavioral level is mainly manifested in emotional interactions between physical behavior and facial expressions [7].

4 Investigation of Emotional Detection Needs of Empty Nesters 4.1

Interview Survey

(1) Subjects: 21 elderly people (from Xi’an University of Technology and others). (2) Task description: Interview the research subjects, and fill in the daily interpersonal relationship questionnaire, depression questionnaire, smart device usage questionnaire, Personality Features Scale. Figure 1 shows some elderly interview scenes. (3) Introduction to the interview: there are 21 interviewed seniors, and each interview time is controlled at around 30 min. There are 10 males and 11 females, aged between 60 and 75 years old (Table 1).

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Fig. 1. Elderly interview scenes Table 1. Interview form Interview points

Introduction of the interview points

The basic information for the elderly The emotional comfort situation for the empty nest elderly The situation of the smart device usage

The elderly’s gender, age, education, marital status, living status, etc. The elderly’s common contacts, contact methods, content, mood changes, daily life arrangements, etc. The elderly’s type of mobile phone used, the duration of use, the frequency of use, common functions, whether you can use your own smartphone, etc. The emotional fluctuation frequency, causes, consequences, mitigation measures, specific circumstances of recent mood swings, etc.

The emotional fluctuate situation for the empty nest elderly

4.2

Time of the spent 5 10

5

10

Interview Results and Analysis

The information collected on the elderly was grouped, the daily situation of the elderly group and the mood fluctuations are analyzed, and the necessity of developing the emotional detection products of the empty-nesters is finally obtained. The information obtained from the interviews is summarized below. Whether it is an empty nest elderly: 1person’s other half died and living with his grandson. 1 person’s other half died and living alone. 2 people living alone. 1 person living with their parents. 16 people living with their other half. Contact with children: 5 children and old people living in the same city. 11 people will contact their children frequently (weekly). 5 people contact few with their children (three months and above). Common contacts for the elderly: 14 people’s common contacts are friends, colleagues, students, etc. 4 people’s common contacts are brothers and sisters. 3 people’s common contacts are children.

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Regularity of daily activities of the elderly: 15 people will go out regularly to do exercises, go to parks, etc. 4 people take care of their parents or spouses at home every day and rarely go out. 2 people often go out to work or meet with leaders. Use of Intelligent Equipment: 1 person uses a mobile phone for the elderly. 20 people use smart phones. Another 5 people will use other smart devices (such as tablets, smart robots, etc.). 13 people regularly use smart devices every day (more than three hours). 4 people occasionally use smart devices every day (1–3 h). 3 people use smart devices less frequently every day (0–1 h). 2 people can’t use smart devices independently. 9 people can use other functions besides basic functions (such as Taobao, Weibo, etc.). Common contacts: 8 people’s common contacts are colleagues. 5 people’s common contacts are classmates. 5 people’s common contacts are friends. 5 people’s common contacts are brothers. 3 people’s common contacts are comrades-in-arms. 2 people’s common contacts are their children. Chat content: 4 people talk about body. 3 people talk about health. 3 people talk about family. 3 people talk about national events. 2 people talk about their children. Daily arrangement: 12 people go out every day. 10 people do housework. 10 people watch TV. 8 people often go to parks. 7 people are often at home. Purpose of using smart devices: 13 people for chatting. 7 people for watching the news. 3 people for playing games. 2 people for taking pictures. 2 people for going shopping. 2 people for watching factual news. Common software: 20 people use Wechat. 3 people use Taobao. 3 people use QQ. 2 people play games. The Consequences of Emotional Fluctuation: 21 people were affected by emotions. Positive emotions will feel comfortable and delighted while negative emotions will cause bad conditions such as loss of appetite, poor sleep, physical illness and so on. Emotional prevention or mitigate-on measures: 7 people choose to see a doctor. 9 people choose to chat with friends. 6 people choose to go out and relax. 4 people choose to adjust by themselves. Summary: Emotional detection devices for empty-nesters are extremely necessary. The 21 elderly people who are randomly surveyed are empty-nesters. Among these elderly people, smart phone penetration rate and usage rate are extremely high, they often go out alone and have a high risk. Most of the elderly have mood swings and negative emotions. Negative emotions cause illness. The empty-nesters are substantially less willing to communicate. 4.3

Questionnaire Survey

(1) Subjects: 211 elderly people (from Xi’an). (2) Task Description: Create a survey questionnaire, collect use “pain and refresh”points on smart bracelet-type wearable devices and basic information about empty-nesters, then obtain functional requirements and usage requirements of user groups. Figure 2 shows the questionnaire survey of some elderly people.

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Fig. 2. Questionnaire survey of elderly people

Analyze the questionnaire, summarize the situation of the elderly using smart equipment (taking the smart bracelet as an example) using pain points and refresh points, function and modeling requirements. The situation of empty nest elderly using smart equipment (taking the smart bracelet as an example) is summarized below. Number of smart bracelets owned: 73% of the elderly do not have Bracelets. 27% of the elderly have Bracelets. Buying way: 13% by themselves. 7% from their friends. 80% by their children. Functions concerned about smart Bracelets: 40% real-time monitoring of physical indicators. 60% GPS function. 50% care about emergency contact hospital rescue function. Whether it is sick: 20% suffer from hyperglycemia. 60% have high blood pressure. 30% have hypotension. 30% other diseases. Currently known functions: 60% can detect the state of motion. 60% can detect heartbeat. 30% can detect sleep quality. 40% can detect pulse. Functions of smart Bracelet Products: 35% used for sports records. 20% used to monitor heart rate and sleep. 17% used for safety positioning. 28% used for health care. Focus: 15% are concerned about brand. 20% are concerned about how to use it. 25% are concerned about price. 40% are concerned about function. Purchase reason: 60% worry about their parents’ health. 30% make contact easier. 10% prevent themselves from forgetting things. 10% other reasons. Most of the elderly do not understand the smart bracelet, do not know how to use or even understand what the bracelet is. The elderly in the survey, including those who own bracelets and those who do not, most do not think that smart bracelets will bring them great changes and benefits. Most people think that the bracelet is inconvenient or not so important, and the phone can replace its function. From the data results, there are more men than women using bracelets. Older people with bracelets usually have higher incomes, higher education, better quality of life, and have the habit of exercising. According to the summary of interviews and survey data, this article summarizes the use pain points and refresh points of the elderly using smart devices (taking smart bracelets as an example) as follows (Table 2):

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Table 2. Pain points and refresh points Pain points Slow response, inconvenient to use Not comfortable to wear Some functions are unnecessary Incorrect monitoring of steps, blood pressure and other data Most of the functions can be replaced by mobile phone Electronic products are easily damaged and consume electricity exorbitant price Modeling is more masculine, not suitable for women Complex operation, not suitable for the elderly Consider it impractical after purchase The font can’t be read clearly

Refresh points The elderly can’t hear the phone when they go out. Smart bracelets can be used to remind them Location function Reducing Event Forgetting Body data can be detected It’s lighter and easier to wear than a mobile phone In case of emergency, timely contact and safety are guaranteed It’s more convenient to watch time Facilitate contact with people

Overall, it can be seen that the elderly (including empty-nesters in the data) think that smart bracelets are helpful for their lives, but many functions are not applicable or even useless for this group of users. Therefore, when designing products, it is necessary to use pain points in combination with refresh points. Under the premise of emotional detection, try to choose the functions that are useful, available and convenient for the empty-nesters group. From Fig. 3, some features that can be replaced with a mobile phone or other product can be appropriately weakened or cancelled.

5 Design Strategy of Empty-Nesters Emotional Detection Products Through the research on the functional requirements of the wearable device for the emotional detection of empty nesters, the collection and analysis of the survey data are analyzed and summarized. 5.1

Interaction Design Principles

5.1.1 Technical Considerations Low power consumption design and improved battery life. Wearable medical products require long-term wear by users. The actual power consumption of most wearable products on the market is higher than that of wireless human LAN standards. Therefore, the low power consumption design and improved battery life of the equipment are an urgent problem to be solved.

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Fig. 3. Functional requirements of intelligent devices used by the empty nest elderly

Improve device sensitivity. Wearable medical devices use wireless sensors to aggregate human body health data. One of the outstanding problems is the lack of operational sensitivity, especially in some special cases, such as high temperature or low temperature. Sweat will affect the sensor’s acquisition sensitivity, resulting in slower response, even re-verify the sensing. This is the technical point for future wearable medical devices that need further improvement. Good user experience. A good user experience is critical in the design of smart medical products. The user’s needs are easy to operate without professional knowledge, friendly interface, simple setup and perfect functions. Adjustments in function positioning. Most of the popular wearable medical devices on the market provide basic health management and motion monitoring, which cannot meet the needs of users. This (meet user needs) requires a huge adjustment in the

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functional positioning of the later products, and truly plays the role of intelligent medical care. 5.1.2 Security Issues and Recommendations Due to the special properties of electronic devices, human skin needs to be exposed to wearable medical devices for a long time, exposed to the radiation of electronic products, which inevitably raises questions about the physical security of the device. Privacy data security. For data security, it can be secured by a more secure security protocol and by using user identity biometrics, privacy data based on chip-layer encryption, and anonymous communication technologies. 5.2

Form Design Principles

5.2.1 Functional Simplicity Versatility is a feature of smart products, but smart devices for the elderly must be designed according to the needs of this particular group of people. Therefore, when designing the functions of the elderly electronic products, it is necessary to collect the living habits and usage requirements of the user group, summarize the necessary product functions, and simplify the operation as much as possible. 5.2.2 Ease-of-Use When designing wearable smart products for the elderly, it is important to consider the interaction between the product and the daily behavior of them. The sensory function of the elderly group has been somewhat degraded, and it is not sensitive to external information feedback. Therefore, the information interface of the product needs to be laid out simply and clearly. The image of the interface should be intuitive, the interface animation should be simple and easy to understand; and the operation of the entire interface should be reduced, avoid getting confused and not understanding. 5.2.3 Fault-Tolerance In the process of using smart products, there are often misoperations that cause alarms. The probability of mistakes in the elderly is far beyond that of young people, and it is easy to combat the enthusiasm of the elderly. Therefore, smart products for the elderly need to have certain fault tolerance. This will improve the operational efficiency of the elderly, increase the enthusiasm of the elderly to use the product, and create a benign interactive environment between the elderly and smart products.

6 Conclusions This paper integrates the interaction design in the concept of the design of the wearable equipment for the elderly, and collects the research on the needs of the empty nest elderly emotional detection products, and summarizes the design principles and design requirements of the product. The final form of the product suitable for the empty nest is the smart watch + smart phone + APP mode, real-time dynamic and emotional detection.

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References 1. Liu, Z.M.: Research on the status Quo and countermeasures of loneliness among empty nesters in China. Theory Rese. 17, 46–47 (2014) 2. Liu, H.H., Wu, W., Xu, W.: Based on Elderly User Experience of Medical Wear Equipment. Xi’an Engineering University (2018) 3. Li, R., Lin, Z., Lin, H.L., Wang, W.P., Meng, D.: Text emotion analysis: a survey. J. Comput. Res. Dev. (2018) 4. Zeng, L.X., Jiang, X., Dai, C.Q.: Design principle of gesture interaction in the wearable device. Packag. Eng. 36, 135–137 (2015) 5. Yuan, L.: Based on perception research on mobile phone interface design and operation of elderly. Art Des. (2018) 6. Liu, H.: Analysis of the interactive product design of the elderly from the perspective of user experience. Technol. Wind (2016) 7. Sun, X.X., Jin, W.K.: The affective interaction design in mobile applications. Packag. Eng. (2014)

Narrative Design of Old Brand Image: A Case Study of Demaogong Yanmin Xue1(&), You Wu1, Yihui Zhou1, and Yang Liu2 1

Xi’an University of Technology, Xi’an 710000, China [email protected] 2 Xi’an Jiaotong University, Xi’an 710000, China

Abstract. The research aims to explore the innovative application of narratology in the package design of old brands. This paper first studies the application of narratology in package design through literature and field research, analyzes and summarizes the commonalities contained in narrative package design, which includes narrative theme, legibility, cultural connotation and narrative expression. A case study of Shaanxi Province old brand Demaogong is carried out to analyze the characteristics of development in its package design. At last, its product package is redesigned innovatively by the method of combination of the characteristics and narrative design. In order to adapt to the tide of development, Chinese old brands must upgrade. This paper applies the narrative theory into package design, which gives the package more functional value and enables the product information and the culture contained in the old brand more easily to be understood and accepted by consumers, thereby providing a new method for the development of the package design in old brand. Keywords: Old brand

 Package design  Narrative design  Demaogong

According to the statistics of the Ministry of Commerce, there are only 1128 registered China time-honored brand enterprises [1]. Most of which are difficult to operate, and only 10% of them are “flourishing”. One of the important reasons which restrict the development of old brands is that the packaging is obsolete and has not been changed for many years. With the development of new media technology, the improvement of audiences’ aesthetics and the change of information acquisition mode, China time-honored brand are forced to make innovations and changes [2]. This paper proposes to combine narratology with old brand package design, and pass on the unique cultural charm and product characteristics of old brand to consumers through “story-telling package design”.

1 Summary of Narrative Package Design Narratology was first applied in a theoretical study of literary works, which is about the theory of narrative text. The three elements of narratology are mainly divided into narrator, narrator and narrator. The medium that events need in the process of communication is the carrier of narration. Narrator is the implementer of narrative action, the receiver of narrative action, and narration is the event itself. Roland Barthes once said in his Introduction to the Structural Analysis of Narrative Works that narrative © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 795–803, 2020. https://doi.org/10.1007/978-981-32-9941-2_66

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carriers can be oral or written syllabic language, a fixed picture of activity, gestures, and an organic mix of all these materials [3]. Thus, the carrier of narrative is not single. The narrator conveys the event to the recipient through the narrative carrier, and the recipient receives the information through the senses. Applying this concept to the package design of old brands, the corresponding relations are: the narrator - the old brand of China, the Narrative - the theme conveyed by the old brand, the narrator - the consumer of the old brand, the narrative carrier - the package design of the old brand products. Figure 1 shows the relationship between narratology and brand communication.

Fig. 1. Narrative design overview of old brand packaging

2 Characteristic Analysis of Packaging Narrative Design At present, narratology has some successful application cases in package design, especially in Jiangsu, Zhejiang and Taiwan. This paper analyses and refines the existing cases, and summarizes the commonness of packaging narrative design, which includes the following aspects. 2.1

Narrative Theme

The core of narrative design is “events”, which are the carrier of meaning and the theme of narration [4]. For the old package design, “thing” is the central idea that the brand hopes to convey to consumers through packaging. It is divided into two parts: the external theme and the internal theme. “External theme” refers to the theme conveyed by the combination of elements such as shape, color and graphics. “Internal theme” has more profound connotations, such as cultural, social, emotional and so on. “Internal theme” conveys deep-seated ideas to consumers through “external theme”. External theme is the external expression of “internal theme”. Figure 2 is the “Laoshe Teahouse” gift box series package. The case of “external theme” uses Beijing rhyme drum, skillful flower beds, double reeds, cross talk and other scenes. The “internal theme” is the old Beijing cultural landscape, which through the selection of familiar scenes in life to increase brand intimacy, while inheriting the old Beijing culture. It is more successful in narrative and brand culture expression. 2.2

Narrative Readability

Readability refers to the ease with which information is understood [5]. And narrative readability means that the degree of convenience that the message conveyed in narrative package design is understand by consumers. On the one hand, the story plot, the

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Fig. 2. Lao She Tea House’s “Yun Xiang” series packaging

environment created and the emotions nurtured need to be universal, which can arouse the familiarity and resonance of consumers, and substitute consumers into the narrative context of package design; on the other hand, more clear expression methods should be used in drawing creation. Visual communication theory holds that for a complex image, people need to spend a certain amount of effort to recognize it. For a simpler image, people can quickly know and recognize it. Figure 3 is the sweet food gift box of the old-fashioned CaizhiZhai in Suzhou. The package chooses the well-known game “hide-and-seek” as the design point, which combines the outer package with the inner package closely to arouse the emotional resonance of consumers and achieve the goal of substituting consumers into the narrative situation of package design.

Fig. 3. Caizhizhai’s dessert package

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Cultural Connotations

The core value of the old brand is culture, which is the foundation of its survival, continuity, innovation and development [6]. The cultural connotation needs to be displayed and expressed. It mainly includes the cultural gene and regional culture of the old brand in package design. On the one hand, the design and expression of cultural genes can continue the development of the old-fashioned culture, on the other hand, bread package design can also become the media for the external dissemination of the old-fashioned culture. Figure 4 is the packaging of Mung Bean Ice Cake in Wufangzhai. It simplifies the complex process into the key process and shows the traditional craft culture of Wufangzhai through the graphic expression of comic strips, which is the inheritance and development of its excellent cultural gene. At the same time, the development of old brands is always closely linked with a certain regional culture. Regional culture can also help the old brands to be called “business card products” that can represent the place. In the narrative package design of the old brand, the combination of the local culture and the old brand will not only help the old brand to enhance its own brand characteristics, but also help to enhance the local image. As the “Shanghai Style Culture” implied by Shanghai’s old brands [7], like Wu Culture Embodied in Jiangsu’s Old Brands [8] and the “Huizhou Merchant Culture” in Anhui’s Old Brands [9]. They all have strong regional cultural characters.

Fig. 4. Wufangzhai “mung bean ice cake” packaging

2.4

Narrative Performance

Image is one of the important carriers in the process of narrative communication. In terms of narrative mode and angle, image narrative is not only intuitive but also threedimensional [10]. In the narrative design of package, image narrative method is widely used. The main performance is the use of comic strips, illustrations for package design, which itself has narrative. The narrative of illustration design has the function of expressing implicit time. It is mainly static and solidified picture that shows the dynamic process of occurrence and development, moreover, predicts the results [11]. Applying it to package design can transmit more comprehensive information to consumers. Writing is one of the important carriers in the process of narrative communication. Writing narrative method of package refers to package design by typesetting. Writing is used as the carrier of packaging narrative. The information transmitted is in the form of

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writing. The packaging is designed by changing the font, size, color and other elements of the text. Its advantage is that the way of transmission is more direct, the accuracy of information is high, and the audience can reach a consensus. The disadvantage is that the way of transmitting the information is slightly monotonous. This method has been used in narrative package design, but not frequent. In the narrative design of packaging, “image + text” narrative method is widely used. There are two aspects: one is that the image plays the main role in transmitting information, the other is that the text plays the main role in transmitting information, and the image plays the auxiliary role. The combination of image and text design method can make the picture richer, more hierarchical, and more effective transmission of packaging information.

3 Narrative Design of Shaanxi Old Brand Demaogong Package Through the above design analysis, the package of Shaanxi old brand Demaogong is redesigned in the paper, which aims to promote the development of the old brand and release the product vitality of the old brand. 3.1

Development of Demogong Package Design

The early Demaogong crystal cake has a strong Northwest National style. Its packaging material chooses popular kraft as the prominent color of the brand image. It conveys joy to consumers through red color. On this basis, the packaging style formed has continued. Before 2007, Demaogong only had one product of crystal cake. In the Spring Festival of 2007, De Maogong first attempted to introduce the packaging of crystal cakes for New Year’s festival. In 2008, De Maogong began to introduce more than a dozen kinds of crisp paper, vegetarian food, peach crisp and so on. The traditional package style and festival style have been used up to now, which can be seen in Fig. 5.

Fig. 5. The development line of Demaogong package design

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3.2

Design Position

As one of the “four ancient capitals” in China, Demaogong brand is located in Xi’an, which has abundant natural and human tourism resources. Demaogong is known as “the first of Qin-style pastries” and is the “visiting card” product of the ancient city of Xi’an. Therefore, this topic positioned the product as “Shaanxi tourism commodity” and “tourism companion gift series”. Meanwhile, the terracotta warriors and horses are the most famous scenic spots in Xi’an. Accordingly, the package design is positioned as a series of travel companion gifts with terracotta warriors and horses. 3.3

Narrative Design Performance

Narrative Theme: Demaogong originated in Shaanxi Province, which belonged to the “Qin” area in the ancient times. The Qin Dynasty created a unified situation and was well known to the world. Therefore, according to the Qin culture in Shaanxi, the narrative framework of this topic is as follows: after the Qin Shihuang unified the six countries, Qin soldiers ate Qin cakes and visited the six countries leisurely scene; the narrative theme of “external theme” is set as the classic historical story of “Qin soldiers eat Qin cakes” and “Qin Shihuang swept the six in one (box) and unified the world”; the “internal theme” is defined as the dissemination of Qin culture, through which the dissemination of Qin culture can be achieved. The narrative design of external theme transmits the internal theme to consumers. Narrative Readability: Readability is mainly reflected in the use of the well-known story history of the unification of the Qin Dynasty and the six countries, and the attraction of consumers will be enhanced through the combination of narrative techniques and interesting design, Therefore, the “unity” in the story of the unification of the Qin Dynasty is chosen as a readable way of development, and the “split” as a contrast method to reflect the ultimate result of “unity”. Because regional and territorial unification are more persuasive and intuitive than culture or custom, the maps before unification are designed on different types of snack packages to form product packages. The narrative stories are completed through the combination of packages to achieve the unification of packaging form and function. Cultural connotation: Qin culture was formed on the ancient land of Qin in Guanzhong region, which is the most representative of Shaanxi regional culture. The old brand of Demaogong also contains the historical culture. This topic completes the inheritance of Chinese traditional culture by the old brand and regional culture. Design method: In cognitive psychology, people understand visual images faster than words [12]. Therefore, this paper uses the method of combining image and text to design product packaging; the main way of information transmission in narrative is the combination of maps to form a complete image of Qin territory, and the text spoken by the “Qin Xiaobing” as the representative image of the brand plays a supporting role in narration.

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Design Exhibition

The Terracotta Warriors and Horses of Qin Shihuang is one of the greatest discoveries in the World Archaeological history. The terracotta warriors are as tall as real people, and their weapons are all physical objects rather than artifacts. Among them, crooked bun and armor constitute the distinct image of Qin soldiers. Therefore, study abstracts the morphological characteristics of Qin soldiers and the brand representative figure is designed as a cartoon Qin soldier characters with crooked bun and Qin cakes to improve the recognition of the design for different ages (Fig. 6).

Fig. 6. The image design of Qinxiaobing with Qin cake

In the image representation with more details, omitting the unnecessary components and flattening the image can reduce the cognitive burden and improve the image recognition. This topic uses illustrations to design maps of six countries (Fig. 7). According to the territorial division of different countries in history, color distinction is used. Animals, plants and landforms embodying regional characteristics are designed in different layout. In the selection of color, the classical style of DeMaoGong package design is retained. The design also enhances the performance of traditional culture. Figure 8 is the application of narrative design in the old brand Demaogong. This scheme has been applied to the latest product packaging of Demogong.

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Fig. 7. Design of Qin state territory map

Fig. 8. “Unify the six country” serialized package design

4 Conclusion As a commercial wonder inherited for hundreds of years, China time-honored brand is an important part of Chinese commercial culture and a window for the external display of Chinese traditional culture. Using narrative design method to design the package of famous products can make the package information more easily be understood and accepted by consumers. At the same time, narrative design methods can better display and disseminate the cultural connotations in the old brands, and create new attractions for consumers. This method also provides a new channel for consumers to recognize

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and understand the old brands and thus helps the revival of the China time-honored brand.

References 1. Ministry of Commerce of the People’s Republic of China. http://zhlzh.mofcom.gov.cn 2. Yang, M., Yao, Y.: Time-honored brand dynamic design and promotion. Packaging Engineering (2018). (in Chinese) 3. Bredin, H.: Narratology: the form and functioning of narrative: Gerald Prince. Br. J. Aesthet. 24, 84 (1984) 4. Zhang, Z., Lu, J.: Product Narrative design based on regional cultural themes. Packaging Engineering (2016). (in Chinese) 5. White, A.W.: Thinking in type: the practical philosophy of typography. Allworth Communications, Inc. (2005) 6. Wang, F., Liao, X.: The cultural inheritance and innovation of Chinese old brands. Business Culture (2014). (in Chinese) 7. Chen, L.: On the collective emotional resonance of Shanghai culture in the package design of Shanghai old brand. Shanghai Packaging (2017). (in Chinese) 8. Xu, Y.: Wu culture application in the packaging of products of china time honored brand in Suzhou area. Design (2016). (in Chinese) 9. Liu, Y., Huang, Y.: Empirical study on the influence of old brand of Huishang. J. Chongqing Inst. Sci. Technol. (Soc. Sci. Ed.) (2015). (in Chinese) 10. Chen, Z.: The narrative symbol of image in visual design. Packaging Engineering (2012). (in Chinese) 11. Zhang, T.: A study on the patterns of time and space expression in illustrator narrative. Central Academy of Fine Arts, Beijing (2008). (in Chinese) 12. Johnson, J.: Designing with the Mind in Mind: Simple Guide to Understanding User Interface Design Guidelines, 2nd edn (2014)

Study on the Theory and Practice of Mechanical Design Yunna Xue(&), Xuehui Shen, and Baolin Wang School of Mechanical and Automotive Engineering, Qilu University of Technology, Jinan 250353, China [email protected], [email protected], [email protected]

Abstract. Mechanical design is an important course combined with theory and practice. Usually, the course design is arranged after the theory course to train the ability of the machine design. The practice content of course design can be reasonably separated according to the theory knowledge of the relevant chapter. In the reform process, the course specific chapter and the content of the design example are combined and studied. By means of detailing and early studying the design practicing content, student can know the purpose and significance of studying after the part of course studying. In the paper, the measures are also put forward in response to the problems during the reform implementation. Keywords: Mechanical design

 Course design  Divide  Combination

1 Introduction Mechanical design is a very important professional course of machinery major students of Engineering. The course contents are the basic theory knowledge of machine designing and elements designing. And on the basis, the ability to design simple machines independently is trained and provided to students. So the course must be assisted by a special course practice link, namely, course project of mechanical designing. The traditional course project is arranged after the mechanical design course. It may be arranged before the final examination, or after. This will lead to some problems. Students learn many courses in one semester. And the contents of each section of the mechanical design course are scattered. Each section is basically independent of the design knowledge of a class of parts. After the completion of the course, students are usually passive in memorizing and studying to deal with the examination, and don’t know the purpose of learning. When the curriculum design process starts, the design process of a certain machine or machinery is completed in a relatively concentrated time. At the same time, students must draw the assembly diagram and part diagram of the machine. Students have no enough time to think, to digest, and to gain deeper knowledge and experience [1–4]. This paper proposes to combine the design practice of simple mechanical devices with the content of the mechanical design course. The design processes are inserted in to the theoretical course explanation process. And the corresponding solutions are put © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 804–810, 2020. https://doi.org/10.1007/978-981-32-9941-2_67

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forward to deal with the specific problems. On the premise of no increasing the workload of students, the paper selects more perfect measures and programs.

2 Specific Requirements for Mechanical Design Course and Project Design As we all know, the theoretical knowledge system of the mechanical design course consists of five parts, namely, the general theory of mechanical design, connecting parts, transmission parts, shafting parts and other parts [5]. Although the title of the course is mechanical design, most of the specific chapters are the design of mechanical parts. This arrangement reduces the difficulty of the examination of the mechanical design course, strengthens the theoretical nature of the course, and reduces the requirements for the design practice. In addition, the mechanical design course is a relatively scattered course learning process, not only the learning time is scattered, but also the knowledge points are scattered. Therefore, centralized curriculum design practice is essential as a useful supplement to the mechanical design curriculum. The course design of mechanical design is a main practical link for students to transform the knowledge learned in mechanical design and other advanced courses into actual design ability. It is a process for students of corresponding majors in engineering colleges to receive more comprehensive basic ability training of engineers in school. The project design plays an important role in realizing the overall training goal of students. It aims to cultivate the ability to analyze and solve mechanical design problems by comprehensively applying the theory and practical knowledge of mechanical design and other pre-requisite courses, to cultivate students’ innovative design consciousness, engineering design ability, modern design technology application ability, and to improve students’ comprehensive design ability. At the same time, it enables students to learn the general methods and procedures of mechanical design, master the general laws of mechanical design, and carry out basic skills training of mechanical design, such as calculation, drawing, consulting data and manuals, applying standards and specifications, etc. The main content of the course design is to make the students receive the preliminary training of drawing up the motion scheme design of the mechanical system under the condition of given input and output power. And then the mechanism is designed and analyzed. And the components are check in the transmission system check. Through curriculum design, students’ ability to design mechanical movement schemes, analyze and calculate with computers, and write design instructions are improved. In general, the subject of the course design is the design of the secondary cylindrical gear reducer (or other mechanical transmission devices, simple machinery), such as the design of the stamping press stamping mechanism, feeding mechanism and transmission system, the design of the platform printer, the design of the rivet automatic cold header, etc. The student’s topic can also be self-designed. And after the topic selection, the instructor will examine and approve it. Its workload is equivalent to

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the design of the two-stage cylindrical gear reducer or the design of the single-stage worm reducer. Students are advocated and encouraged to make innovative topics. The design time for mechanical design courses is relatively concentrated, usually two or three weeks. During this period of time, students usually use one week to complete the design and calculation of the whole machine, including the design and calculation of transmission parts and shafting parts, to complete the structural design of the machine, and write the designing instructions. Then it takes another one to two weeks to draw the assembly drawing of the whole machine and the part drawing of key parts. Through the course design of mechanical design, students should meet the following basic requirements. (1) According to the functional requirements of the machine, formulate and analyze the design scheme, and reasonably select the motor, transmission mechanism and parts. (2) According to the working condition analysis and calculation of the load acting on the parts, reasonably select the materials, correctly calculate the working capacity of the parts, and determine the main parameters and dimensions of the transmission parts. (3) Fully consider the processing technology, installation and adjustment, use and maintenance, economy and safety and other issues to carry out structural design on machines and parts. (4) The projection of the designed drawing view is correct, in line with the drawing standard, the dimensional tolerance is marked correctly, and the technical requirements are reasonable. (5) Ability of drawing with computer.

3 Intersection and Fusion of Theory and Practice 3.1

Design Example and Specific Machine

The diffusion of knowledge points in the mechanical design course requires a specific machine or mechanical device to fuse them. The purpose is to make students feel that mechanical designing is not only part designing and simple formula and calculation, but also the structural design. The knowledge should be experienced by the students themselves in the learning process, rather than after learning all the theoretical knowledge. Therefore, teachers should not only strengthen the classroom learning, but also let students practice in class and in homework after class. The traditional design object is a two-stage gear reducer or a single-stage worm and worm gear reducer. The design object is quite closely related to the learning chapters of the course. As a kind of mechanical transmission device, reducer plays a vital role in the whole process of mechanical transmission of motion and power. First of all, it is closely combined with the transmission text. Secondly, the shafts, bearings, couplings, etc. supporting the gears in the reducer are closely integrated with the parts of the shaft system. Finally, there are connecting parts and shell parts. If the design object is

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changed to a gearbox, the theoretical knowledge will not change, but the number of gears is too large for students to do in a short period of time. If the design object is changed to the ball screw, the structural complexity is enough, but it cannot cover all important chapters of mechanical design. Therefore, it is most appropriate to choose the reducer as the link between the chapters of the mechanical design course. 3.2

Specific Implementation Process of Combination

The introduction of reducer as a specific device into the mechanical design course needs to be carried out step by step, mainly in the following links in the course explanation process. (1) Mechanical Design and Parts Design in General Theory of Mechanical Design After teaching the basic concepts of mechanical design, the requirements of mechanical design is that of mechanical parts. And the design criteria of mechanical parts are putting forward. Then the reducer in the belt conveyer is taken as an example to illustrate that mechanical design is the design of mechanical parts, and the requirements of machinery are that of mechanical parts. Students studies the mechanical principles in last semester and are not unfamiliar with the working principles of machinery or machines. Therefore, students can accept the explanation of belt conveyer’s working principles, structural composition and transmission scheme diagram. If the belt conveyer is not advanced enough to arouse students interest, a machine that includes speed reducers can be cited, such as elevator, printing press, packaging machine, etc. The structure of the belt conveyer is relatively simple. The motor is used as the power source, the drum is used as the working part, and the transmission part in the middle only completes the transmission of rotating motion and the change of motion parameters. After understanding the transmission scheme diagram, students can focus on speed reducer, which consists of shell parts, transmission parts, shafting structure parts and connection parts, respectively corresponding to the four major parts in the course. (2) Strength of mechanical parts The strength of mechanical parts is a difficult chapter in the mechanical design course, which mainly guides students to understand and master the allowable stress under different stress types. Here, an example can be given to illustrate that the bending stress and contact stress of the gear are pulsating or symmetrical cyclic variable stress, and the bending stress of the rotating shaft is symmetrical cyclic variable stress. In the belt transmission link of the belt conveyer, the stress of the belt is asymmetric cyclic variable stress. Students can understand that the common stress type of mechanical parts is variable stress, and its failure form is fatigue failure. In this way, students can be more interested in learning the allowable stress under variable stress. (3) Transmission part After learning the four transmission parts of belt transmission, chain transmission, gear transmission and Worm drive, it is necessary to summarize the mechanical transmission. Some schematic diagrams of power and transmission schemes of

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belt conveyer can be listed and compared and analyzed, and one of them can be selected as the emphasis. In the process of explanation, the calculation methods of power, efficiency, torque, rotational speed and other parameters of different shafts are simultaneously learned. And students learns to select the motor of belt conveyer, to allocate transmission ratio, and to complete the overall design of belt conveyer transmission scheme. The overall design and calculation of the transmission scheme is completed, and the power, torque and rotation speed of each shaft are determined. Next the various wheel parts installed on the shaft The following can be designed, such as gears, pulleys, etc. And the structural shape and size of wheel parts can be work out under this working condition. (4) Shafting parts In the third part, for example, the transmission parts of belt conveyer have been designed. After studying the chapter on shaft and bearing, the shaft and bearing of belt conveyer can be designed. The normal force in the gear meshing process and the compression force in the belt drive are finally carried by the shaft and the bearing. Therefore, it is necessary to design shafts with specific structural shapes and choose bearings of different types and sizes, especially rolling bearings. The design process of shell parts is inserted into the design process of shaft and bearing, such as the upper box cover, the lower box body of reducer and the box body accessories. (5) Connecting parts Threaded parts, keys and other connecting parts, as the final component of the reducer, are simpler than the previous parts, but they are also essential parts in the reducer. Finally, the key chapters of the course is studied, and the whole reducer device is designed, too. The design calculation and structural design are completed simultaneously. Sufficient time was set aside in the course design to draw assembly drawings and part drawings.

4 Problems and Solutions 4.1

Emergence of Problems

The theoretical content of mechanical design course and the practical design of belt conveyer reducer can be perfectly integrated and intersected together. However, in the actual implementation process, the following problems will occur. (1) Increasing in student workload As a specialized course, the mechanical design course has many hours and requires students to complete certain homework after class. On this basis, if we add more practical homework for curriculum design, the amount of homework will be increased a lot, and the burden on students is increased. But if students do not assign homework, they will not be impressed without practice.

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(2) Increasing in class hours Although the reducer in belt conveyer is a design example, it is a relatively large machine after all. If this application example is inserted into the teaching process, it will add at least 4 h. (3) No enough attention to practical content Although the teacher added the practical content of the machine, the students did not pay enough attention to it. And the textbook also lacked corresponding chapters. Therefore, in the class and the revision, the learning effect cannot meet the expected expectations of teachers. 4.2

Solution Measures

In view of the above problems, combined with the actual situation of the students, after several semesters of experiments, the corresponding solutions are found. (1) Increased workload Although the design of belt conveyer reducer appeared about 5 times in the course, not every time related homework was assigned. The number of design and calculation operations that need to be arranged is 3, namely, the overall design and calculation of the transmission system, the design and calculation of gears and the design and calculation of shafting components. These three parts are the key contents of the course examination. Even if no big practical homework is assigned, homework should be assigned after class. Therefore, in order not to increase the workload of the students, the three design calculations can be respectively taken as supplementary parts of the traditional homework under class, and the repeated exercises in the design calculation homework can be deleted. (2) Increased class hours With 5 design examples, class hours will be increased. So other irrelevant knowledge in the course will need to be appropriately reduced, and classroom teaching will be changed to self-study, such as welding, gluing and riveting chapters, and spring chapters. (3) No enough attention to practical content The problem that students do not pay attention to the practice content can be solved by incorporating the mechanical design into the examination link. Mechanical design is the integration of parts design and machine design. Usually the examination only focused on the design of parts and did not pay enough attention to the mechanical design. Integrating the design of the overall transmission scheme and the structure into the examination process can increase students’ attention to the machine design.

5 Results In conclusion, in the process of the mechanical design course, the theoretical knowledge and practical links of the course can be perfectly crossed and integrated. Different design contents of the same design example are introduced in different links of the

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course. And the scattered parts design knowledge is combined into a machine design process. The difficulties of increasing students workload and class hours are overcome. And the corresponding solutions are put forward. In this way, mechanical design courses have been proceeded for several semesters. The results shows that, through the combination of theoretical course and project design, the studying enthusiasm and initiative of the students can be increased. Students deeply understands that mechanical design is the design of the whole machine. Mechanical design is not only the design calculation, but also the question of structural design. It points out the direction for subsequent young teachers to offer mechanical design courses.

References 1. Hao, X.H., Qiu, X.S., Wang, Q., Bai, W.P.: Exploration on teaching reform of mechanical design course design. Res. Teach. 34(3), 51–54 (2011). (in Chinese) 2. Yu, G.H., Wei, W., Yan, L.Q.: Exploration on teaching reform of mechanical design course design. Light. Ind. Sci. Technol. 1, 165–166 (2015). (in Chinese) 3. Wei, J.Y., Li, X.Y., Wang, H.X., Zhen, J.: Exploration on teaching reform of mechanical principle course based on cultivation of innovative ability. Univ. Educ. 4, 160–161 (2015). (in Chinese) 4. Song, L.: Teaching reform in course design of mechanical design. Intern. Combust. Engine Parts 7, 52–55 (2018). (in Chinese) 5. Zhang, M.Y.: Exploration on practice teaching and ability cultivation of mechanical design course design. Times Agric. Mach. (9), 84, 86 (2018). (in Chinese)

Simulation Analysis of Pipe Bending Under Multiple Conditions Guodong Yi(&), Zhenan Jin, and Shaoju Zhang School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China {ygd,jzn,shaojuz}@zju.edu.cn

Abstract. The paper analyzed the pipe bending of the under multiple conditions by simulation method. The force parameters of the upper and lower clamps during the bending process and the thickness of the pipe wall after bending were investigated. A half of the pipe was taken to establish a finite element model for the analysis under seven conditions. The dynamic process and temperature distribution of pipe bending were demonstrated. The horizontal force, vertical force and torque act on the upper and lower clamps are analyzed. Results show that the clockwise torque is beneficial to prevent thinning of the lateral pipe wall. Keywords: Pipe bending Multiple conditions

 Simulation analysis  Finite element model 

1 Introduction The process of medium frequency induction heating and bending is widely used for pipe bending with large pipe diameter and small bending radius. Compared with the conventional process, its advantages are moldless, low energy consumption, high productivity, and excellent mechanical properties of the pipe after bending. During the bending process, the lateral pipe wall becomes thinner due to tensile stress, and the medial pipe wall becomes thicker due to compressive stress. In the highpressure pipeline, the thickness reduction of the lateral pipe wall should be controlled within a certain range (typically less than 12.5%) to ensure strength. Reverse torque can be applied to reduce the thinning of the lateral pipe wall. Some researches on the pipe bending have been carried out. Cho et al. carried out the parametric studies involving a change of geometry of the pipe bends and loading type by means of the linear matching method, and derived two semi-empirical equations from correlations of the reverse plasticity limit and the limit pressure with the bend characteristic [1]. Iwamoto et al. showed the effect of fill sand on the bending behavior of a single walled pipe, and evaluate the elasto-plastic behavior of the pipe by using digital image processing method [2]. Yuan et al. presented a solution procedure for establishing the onset of the first bifurcation buckling of a lined pipe under bending, This project is supported by National Key R&D Program of China (Grant No. 2018YFB1701601) and National Natural Science Foundation of China (Grant No. 51875515). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 811–822, 2020. https://doi.org/10.1007/978-981-32-9941-2_68

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and studied the post-buckling behavior of the lined pipe under bending by introducing to the liner initial imperfections in the form of the wrinkling buckling mode [2–5]. Shlyannikov et al. investigated the influence of internal pressure, operation time and shape imperfections of pipe bend on stress-strain redistributions and creep-fatigue crack growth rate using FE-analysis and experiments at elevated temperature [6, 7]. Shim et al. proposed a double-stage forming for pipes to regulate the shrinking load, analyzed material behavior to figure out the reason for the cross-section shrinkage, and minimized the cross-section distortion by regulating the pre-bending radius at the first stage [8]. Li et al. presented the effect of bend angle on plastic limit loads of pipe bends under different load conditions using three-dimensional non-linear finite element analyses, and made the solutions of limit load under single load condition [9]. Kim et al. proposed a reference stress based J-integral estimation scheme of circumferential through-wall cracked pipe bend with un-uniform thickness under in-plane opening bending loading condition [10]. Kang et al. described the development of the insituation pipe bending tool and its validations, and verified the in-situation bending procedure by structural analysis and mock-up test [11]. Thome et al. presented a calculation model for offline and real-time optimization of the large-diameter steel pipe production process chain, and discussed influencing factors (e.g. variations in yield stress and wall thickness) on the basis of extensive simulations [12]. Yu et al. derived the analytical solution for limit load of orthotropic pressure pipe with constant-depth internal circumferential crack under combined pressure, axial force and bending considering three directional stress of pressure pipe, based on the Hill yield criterion [13]. Mandal carried out systematic investigation to understand the effect of plate-to-pipe forming (U-bending) strain on the microstructure and mechanical properties of X80 linepipe steel and to establish a structure-property correlation [14]. Buckshumiyan et al. investigated the combined effect of ovality and thinning/thickening on collapse load of pipe bends under in-plane opening bending moment using finite element limit analysis considering large geometric change effect [15]. Sumesh et al. carried out a comparative evaluation of limit moments based on small displacement and collapse moments based on large displacement for structurally distorted throughwall circumferentially cracked pipe bends, under in-plane closing bending [16–18]. Lukassen et al. presented a repeated unit cell finite element model for analyzing flexible pipes subjected to combined constant tension and curvature, which is suitable for resolving the local tensile armor stress distribution and the global pipe response [19]. Li et al. used a 3D finite element method to determine plastic limit load solutions for pipe bends under combined bending and torsion moment, suggested plastic limit load solutions considering a wide range of non-dimensional parameters for pipe bends [20]. Gavriilidis et al. focused on the mechanical behaviour of mechanically lined pipes subjected to monotonic bending, considering for the presence of low and moderate levels of internal pressure, aimed at preventing or delaying wrinkle formation [21]. Balakrishnan et al. presented a detailed investigation of the combined effects of variable wall thinning and ovality on B2 stress indices for pipe bends under closing moment using three dimensional finite element nonlinear analyses [22].

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In this paper, the finite element analysis for induction heating and bending of the pipe is carried out to investigate the force parameters of the upper and lower clamps during the bending process and the thickness of the pipe wall after bending.

2 Finite Element Model of Pipe Bending The principle of induction heating and bending of the pipe is shown in Fig. 1. The upper clamp moves vertically, pressing the pipe downward with force Fy; the lower clamp rotates counterclockwise, applying a clockwise torque Mr to the pipe.

Fig. 1. Principle of the pipe bending

The material of the pipe is 42CrMo with excellent mechanical properties, and the change of yield stress with temperature is shown in Fig. 2 [23]. The yield stress of the material decreases slowly from 20 °C to 400 °C, rapidly from 400 °C to 750 °C, and slowly from 750 °C to 1150 °C. The yield stress of the material at 950 °C is only about 12% at 20 °C. During induction heating and bending, the temperature of the pipe varies continuously from 25 °C to 950 °C with time and space. The mechanical properties of the material vary greatly over this temperature range and the plastic deformation is also large. Therefore, MSC.Marc, MSC.Patran, and MSC.Mentat were used as solver, preprocessor and post-processor, respectively.

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Fig. 2. The change of yield stress of 42CrMo with temperature

According to the symmetry of the pipe bending, a half of the pipe is taken to establish a finite element model to reduce the analysis time, as shown in Fig. 3. The upper and lower clamps are treated as rigid bodies, which are abstracted as their contact surface with the pipe (the green semi-cylindrical surface in Fig. 3). with two nodes each being used to control displacement and load. The pipe is treated as a flexible body, and 5 to 8 units are arranged along the wall thickness direction. The middle portion of the pipe will be bent, so the mesh in it is dense, while the mesh in upper and lower portions is sparse. In the process of bending, the deformation of the pipe is very large, so the deformation of the unit is also large. Therefore, a regular hexahedral unit with 20 nodes Hex20 was used to obtain higher precision and ensure smooth convergence of the solution.

Fig. 3. Finite element model for pipe bending

During the bending process, the temperature of the pipe at the induction heating coil is 950 °C, and gradually decreases toward both ends. The temperature of different parts of the pipe changes significantly with time. Therefore, the field control method in Patran was used in this analysis to control the temperature of each node at any time.

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Table 1. Seven conditions Condition number C1 C2 C3 C4 C5 C6 C7

Control method for the upper clamp

Control method for the lower clamp

Active. Move 298.45 mm downward uniformly Passive. Move upward and downward freely Active. Move 298.45 mm downward uniformly Active. Move 298.45 mm downward uniformly Active. Move 298.45 mm downward uniformly Active. Move 298.45 mm downward uniformly Active. Move 298.45 mm downward uniformly

Active. Rotate 90° counterclockwise uniformly Active. Rotate 90° counterclockwise uniformly Passive. Rotate freely (torque is 0) Passive. Apply a reverse torque of 3 KN m Passive. Apply a reverse torque of 6 KN m Passive. Apply a reverse torque of 9 KN m Passive. Apply a reverse torque of 12 KN m

3 Simulation of the Bending Process In order to fully investigate the influence of the load and movement of the upper and lower clamps on the characteristics of the bent pipe, seven conditions listed in Table 1 were analyzed, and the direction definition is shown in Fig. 1. The dynamic process and temperature distribution of pipe bending are shown in Fig. 4 (corresponding to working condition 1). It can be seen that the lateral pipe wall becomes thinner and the medial pipe wall becomes thicker. The result of bending is in line with expectations, close to a quarter arc.

Fig. 4. Temperature distribution and deformation of the tube during bending

External loads need to be applied to the upper and lower clamps to keep them balanced. The load direction is defined as follows according to Fig. 1: rightward is positive in horizontal direction; upward is positive in vertical direction; counterclockwise is positive in rotational direction. It should be noted that all the loads given

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in this paper are based on a half of the model, and in fact there is another half of the symmetry, so all the loads need to be multiplied by 2 times listed here. The horizontal force Fx1 and vertical force Fy1 act on the upper clamp, respectively, and the horizontal force Fx2, vertical force Fy2 and torque Mr act on the lower clamp, respectively. The specific values of them are shown in Figs. 5, 6, 7, 8 and 9, and all the abscissas are time in seconds (s).

Fig. 5. Fx1 acting on the upper clamp (KN)

Fig. 6. Fy1 acting on the upper clamp (KN)

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Fig. 7. Fx2 acting on the lower clamp (KN)

Fig. 8. Fy2 acting on the lower clamp (KN)

In Fig. 5, the force Fx1 acting on the upper clamp is mainly distributed between 50 KN and 80 KN, and the direction is rightward. Under condition 1, both the upper and lower clamps are active, and Fx1 is the smallest. Under condition 2, only the lower clamp is active, and Fx1 is gradually increased. Under conditions 3-7, Fx1 increases as the reverse torque increases. Comparing Figs. 5 and 7, it can be seen that Fx2 and Fx1 are almost equal with opposite directions, which indicates that the bending is approximately a quasi-static process.

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Fig. 9. Mr acting on the lower clamp (KN m)

In Fig. 6, the force Fy1 acting on the upper clamp is mainly distributed between 90 KN to 180 KN, and the direction is downward. Under condition 1, the upper and lower clamps are active, and the value of Fy1 is the smallest, about 90 KN. Under condition 2, only the lower clamp is active, and the upper clamp can move freely in vertical direction, so the value of Fy1 is 0. Under conditions 3–7, the reverse torque increases from 0 to 12 KN m, and Fy1 increases from about 115 KN to about 180 KN. Comparing Figs. 6 and 8, it can be seen that Fy2 and Fy1 are almost equal with opposite directions, which also indicates that the bending is approximately a quasi-static process. The torque Mr acting on the lower clamp is shown in Fig. 9. Under condition 1, both the upper and lower clamps are active, and an external counterclockwise torque of about 5 KN m is required to act on the lower clamp. Under condition 2, only the lower clamp is active, and an external counterclockwise torque of about 20 KN m is required to act on the lower clamp. Under conditions 3–7, the clockwise torque by active control acts on the lower clamp.

4 Results and Discussion The thinning rate of the pipe is defined as the ratio of the reduction in the thickness of the lateral pipe wall after bending to the thickness of the pipe wall before bending. The thickening rate of the pipe is defined as the ratio of the increase in the thickness of the medial pipe wall after bending to the thickness of the pipe wall before bending. The thinning rate is an important performance indicator for pipe bending.

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(1) Condition 2

(2) Condition 7 Fig. 10. Comparison of the thickness of the pipe wall after bending

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Figure 10 demonstrates the thickness of the lateral pipe wall after bending under conditions 2 and 7. The counterclockwise torques acting on the clamps under conditions 2 and 7 are 20 KN m and 12 KN m, respectively, and the thickness under condition 7 is 2.2 mm thicker than condition 2. However, it should be noted that if the upper clamp is pressed down by the length of a quarter arc (298.45 mm) when applying the clockwise torque on it, the lower end of the pipe is not rotated by 90°, that is, there is an angle between the lower end surface and the vertical surface, which will increase as the reverse torque increases. Figures 11, 12, 13 and 14 show the variation of the thickness of the lateral pipe wall and medial pipe wall after bending under the seven conditions. The abscissas are the working condition numbers. Figure 11 shows that the greater the clockwise torque is, the greater the thickness of the lateral pipe wall is, which indicates that the clockwise torque is beneficial to prevent thinning of the lateral pipe wall. Figure 12 shows that the thinning rate of the pipe is about 15% overall, and the thinning rates under conditions 2 and 7 are 21.5% and 14.9%, respectively. In Fig. 13, the thickness of the medial pipe

Fig. 11. Thickness of the lateral pipe wall after bending (mm)

Fig. 12. Thinning rate (%)

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Fig. 13. Thickness of the medial pipe wall after bending (mm)

Fig. 14. Thickening rate (%)

wall is significantly small only under condition2. The thicknesses under other conditions are very close and decrease slightly as the clockwise torques increase. The overall thickening rate is around 35%.

References 1. Cho, N.-K., Chen, H.: Shakedown, ratchet, and limit analyses of 90° back-to-back pipe bends under cyclic in-plane opening bending and steady internal pressure. Eur. J. Mech.A/Solids 67, 231–242 (2018) 2. Iwamoto, T., Kanie, S.: Evaluation of bending behavior of flexible pipe using digital image processing. In: 3rd International Conference on Sustainable Civil Engineering Structures and Construction Materials - Sustainable Structures for Future Generations, vol. 171, pp. 1272– 1278 (2017) 3. Yuan, L., Kyriakides, S.: Plastic bifurcation buckling of lined pipe under bending. Eur. J. Mech. A-Solids 47, 288–297 (2014)

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4. Yuan, L., Kyriakides, S.: Liner wrinkling and collapse of bi-material pipe under bending. Int. J. Solids Struct. 51(3–4), 599–611 (2014) 5. Yuan, L., Kyriakides, S.: Liner wrinkling and collapse of girth-welded bi-material pipe under bending. Appl. Ocean Res. 50, 209–216 (2015) 6. Shlyannikov, V.N., Tumanov, A.V., Boychenko, N.V., et al.: Effect of pipe bend shape imperfections on creep-fatigue crack growth. Press. Vessel. Technol.: Prep. Future 130, 868– 878 (2015) 7. Shlyannikov, V.N., Tumanov, A.V., Boychenko, N.V., et al.: Loading history effect on creep-fatigue crack growth in pipe bend. Int. J. Press. Vessel Pip. 139, 86–95 (2016) 8. Shim, D.S., Kim, K.P., Lee, K.Y.: Double-stage forming using critical pre-bending radius in roll bending of pipe with rectangular cross-section. J. Mater. Process. Technol. 236, 189–203 (2016) 9. Li, S.J., Zhou, C.Y., Li, J., et al.: Effect of bend angle on plastic limit loads of pipe bends under different load conditions. Int. J. Mech. Sci. 131, 572–585 (2017) 10. Kim, C.G., Bae, K.D., Kim, Y.J.: Quantification of thickness effects for circumferential through-wall cracked pipe bend with un-uniform thickness under in-plane opening bending. Press. Vessel Technol.: Prep. Futur. 130, 1779–1787 (2015) 11. Kang, K.-O., Noh, C.H., Hur, J., et al.: Investigation on the in-situation pipe bending tool for the sector sub-assembly of ITER thermal shield. Fusion Eng. Des. (2019). https://doi.org/10. 1016/j.fusengdes.2019.02.122 12. Thome, M., Zeller, S.: On course to smart large-diameter pipe production. Procedia Manuf. 29, 544–551 (2019) 13. Yu, Q., Zhou, C.Y., Wang, Z.W., et al.: Analytical solution for limit load of orthotropic pressure pipe with internal circumferential crack. Int. J. Mech. Sci. 149, 201–211 (2018) 14. Mandal, A., Syed, B., Bhandari, K.K., et al.: Cold-bending of linepipe steel plate to pipe, detrimental or beneficial? Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 746, 58–72 (2019) 15. Buckshumiyan, A., Veerappan, A.R., Shanmugam, S.: Plastic collapse loads in shapeimperfect pipe bends under in-plane opening bending moment. Int. J. Press. Vessel Pip. 111, 21–26 (2013) 16. Sasidharan, S., Arunachalam, V., Subramaniam, S.: Ramifications of structural deformations on collapse loads of critically cracked pipe bends under in-plane bending and internal pressure. Nucl. Eng. Technol. 49(1), 254–266 (2017) 17. Sumesh, S., Veerappan, A.R., Shanmugam, S.: Assessment of plastic loads of critical throughwall circumferentially cracked pipe bends with structural distortions under in-plane bending. Thin-Walled Struct. 104, 144–151 (2016) 18. Sumesh, S., Veerappan, A.R., Shanmugam, S.: Evaluation of postulated cross sections with ovality and thinning for 90 pipe bends with circumferential throughwall cracks subjected to in-plane closing bending. Eng. Fail. Anal. 75, 82–91 (2017) 19. Lukassen, T.V., Gunnarsson, E., Krenk, S., et al.: Tension-bending analysis of flexible pipe by a repeated unit cell finite element model. Mar. Struct. 64, 401–420 (2019) 20. Li, J., Zhou, C.Y., Cui, P., et al.: Plastic limit loads for pipe bends under combined bending and torsion moment. Int. J. Mech. Sci. 92, 133–145 (2015) 21. Gavriilidis, I., Karamanos, S.A.: Bending and buckling of internally-pressurized steel lined pipes. Ocean Eng. 171, 540–553 (2019) 22. Balakrishnan, S., Veerappan, A.R., Shanmugam, S.: Effect of cross section on B2 stress index for Nuclear Pipe Bends subjected to closing bending. Mater. Today: Proc. 5(5), 11941–11949 (2018) 23. Li, Y.Y., Zhao, S.D., Fan, S.Q., et al.: Study on the material characteristic and process parameters of the open-die warm extrusion process of spline shaft with 42CrMo steel. J. Alloy. Compd. 571, 12–20 (2013)

Simulation Analysis of Sealing Performance of Double-Offset Butterfly Valve Guodong Yi(&), Shaoju Zhang, and Zhenan Jin School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China {ygd,shaojuz,jzn}@zju.edu.cn

Abstract. The paper analyzed the sealing performance of double-offset butterfly valve by simulation method. The axial sealing performance was analyzed under conditions of friction coefficient and eccentricity as the independent variables. The lateral sealing performance was analyzed under conditions of gas pressure and ring compaction as independent variables. Conclusions show that the key factors affecting the reliability of axial sealing and lateral sealing are the eccentricity, gas pressure and ring compaction, respectively. As the eccentricity decreases, the axial sealing will be more reliable, and as the gas pressure or the ring compaction increase, the reliability of the lateral sealing will also increase. Keywords: Double-offset butterfly valve  Sealing performance Simulation analysis  Axial sealing  Lateral sealing



1 Introduction Butterfly valve is an important component in fluid transmission and control system, and its sealing performance directly affects the efficiency and stability of the system. Some research work on the performance of butterfly valves has been carried out. Rao et al. developed a butterfly check valve model to enhance the capability of the thermal–hydraulic system, and carried out both steady-state calculations and transient calculations compared with the experimental data for verification purpose [1]. Valeh-eSheyda et al. made an numerical attempt to improve the internal geometry of butterfly valve to avoid the high shear stress based on its peculiar internal geometry [2]. Naseradinmousavi et al. described high fidelity modeling and analysis of the opening and closing processes of butterfly valves driven by solenoid actuators using multiphysics models [3, 4]. Kwuimy et al. studied the nonlinear dynamics of a butterfly valve actuated by the induced electromotive force of a permanent magnet, with a focus on the on–off dynamics of the valve and its nonlinear response under ambient perturbation [5]. Liu et al. built a coupling computational fluid dynamics model combined multiphase, cavitation and discrete phase model of butterfly valve to simulate the cavitation erosion and particle erosion [6]. Ogawa et al. focused on the prediction of This project is supported by National Key R&D Program of China (Grant No. 2018YFB1701601) and National Natural Science Foundation of China (Grant No. 51875515). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 823–831, 2020. https://doi.org/10.1007/978-981-32-9941-2_69

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torque characteristics of butterfly valves and proposed a prediction equation derived from theoretical investigation and experimental results [7]. Yang et al. proposed a condition monitoring scheme using statistical feature evaluation and support vector machine to detect the cavitation conditions of butterfly valve which used as a flow control valve at the pumping stations [8]. Corbera et al. proposed a novel multiobjective approach for the design optimization of a butterfly valve using advanced genetic algorithms based on Pareto dominance, and carried out structural and computational fluid dynamics analysis to increase the performance [9]. Song et al. made the initial model of a butterfly valve, and carried out the fluid and structural analysis, and handled the optimization in the form of mathematical functions, which considers single or multiple objective and discipline [10]. Toufique Hasan et al. investigated effects of spontaneous condensation of moist air on the shock wave dynamics around butterfly valves in transonic flows by experimental and numerical simulations [11]. Hummer et al. studied the throttle characteristic of a butterfly valve using both theoretical and experimental methods, and applied the Monte Carlo technique to a simplified model for the geometry of the butterfly throttle valve [12]. This paper focuses on a double-offset butterfly valve with a metal hard seal, and its structure is shown in Figs. 1 and 2. The sealing performance of double-offset butterfly valves depends on the axial sealing and the lateral sealing. The axial sealing refers to the line contact sealing between the butterfly plate and the sealing ring, and the lateral sealing refers to the surface contact sealing between the pressing ring and the sealing ring.

Fig. 1. Axial sealing and lateral sealing of a double-offset butterfly valve

Fig. 2. Eccentricities ex and ez of double-offset butterfly valve

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The double-offset butterfly valve has two eccentricities, as shown in Fig. 2. The eccentricity ex refers to the distance between the center plane of the sealing ring and the rotary axis of the butterfly plate when the butterfly valve is fully opened, and the eccentricity ez refers to the distance between the axis of the valve body and the rotary axis of the butterfly plate. The double-offset butterfly valve has two eccentricities, as shown in Fig. 2. The eccentricity ex refers to the distance between the center plane of the sealing ring and the rotary axis of the butterfly plate when the butterfly valve is fully opened, and the eccentricity ez refers to the distance between the axis of the valve body and the rotary axis of the butterfly plate. When the butterfly valve is fully opened, the sealing ring floats in the groove formed by the valve body and the pressing ring with an uncertain position, so the eccentricity ex cannot be quantified. Considering that the sealing ring is in tight contact with the pressing ring when the butterfly valve is closed, it is stipulated that the sealing ring is just in contact with the pressing ring without any pressure, and the distance between the center plane of the sealing ring and the rotary axis of the butterfly plate is the eccentricity ex. Since the position of the pressing ring relative to the valve body can be fine-tuned by the spacer, the eccentricity ex can be adjusted during installation. However, the eccentricity ez is determined after manufacturing and cannot be adjusted.

2 Simulation Analysis of Axial Sealing Performance As the major sealing of the butterfly valve, the axial sealing is mainly affected by the friction coefficient l and the eccentricity ex. Two experiments are performed by finite element analysis, under conditions with l and ex as independent variables, as shown in Tables 1 and 2. The simulation of finite element analysis in this paper was completed in MSC software. In detail, the solver is MSC.Marc, the preprocessor is MSC.Patran, and the postprocessor are MSC.Patran and MSC.Mentat. Table 1. Conditions with the friction coefficient l as an independent variable (ex = 36.2 mm, ez = 6.2 mm) Condition number l 1 0.06 2 0.08 3 0.10 4 0.15 5 0.20 6 0.25 7 0.30

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Table 2. Conditions with the eccentricity ex as an independent variable (l = 0.06, ez = 6.2 mm) Condition number ex (mm) 8 36.4 9 36.6 10 36.8 11 37.0 12 37.2 13 37.4

The reliability of the sealing increases with the contact stress rc and contact width b. After the butterfly valve is closed, the larger the seal ring is swollen by the butterfly plate, the greater the equivalent stress r ring, and the more reliable the contact is. After take all these factors into account, it can be considered that the equivalent stress r of the sealing ring is the dominant parameter affecting the axial sealing performance, and the contact stress rc and the contact width b are reference parameters. In fact, the product of rc and b is linear with r. In the above-mentioned analysis, it is assumed that the sealing ring is not plastically deformed. The stress of the sealing ring under condition 12 after the butterfly plate is completely closed and the driving torque is released is shown in Fig. 3. The stress decreases from left to right, and the maximum appears on the right side of the sealing ring and near the butterfly plate.

Fig. 3. Stress distribution of the sealing ring under the condition 12 (MPa) (5% model)

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The contact position of the sealing ring and the butterfly plate determines the axial sealing performance, and the maximum stress of the sealing ring must be limited because the plastic deformation is not allowed. The results under other conditions are shown in Fig. 4. It can be seen that under conditions from 1 to 7, the stress at the contact point is about 370 MPa, indicating that the friction coefficient has no effect on the stress of the sealing ring. Under conditions from 8 to 13, the stress at the contact point of the sealing ring decreases linearly, indicating that the eccentricity ex has a significant influence on the stress of the sealing ring. The maximum stress is 30 to 50 MPa larger than the stress at the contact point.

Fig. 4. Stress of the sealing ring under each working condition (MPa)

After the butterfly plate is completely closed and the driving torque is released, the contact stress of the butterfly plate and the sealing ring under the condition 12 is shown as Fig. 5. The maximum contact stress is 132 MPa, and the contact width is 0.95 mm (The region where the contact stress is greater than 1 MPa is considered.). It can be seen that the linear contact stress of the butterfly plate and the sealing ring rapidly decreases from the contact center to both sides, and the width of the region where the contact stress is greater than 50 MPa is about 0.5 mm. Figure 6 demonstrates the distribution of the contact stress of the butterfly plate and the sealing ring under each condition. It can be seen that the contact stress is mainly distributed between 110 and 130 MPa. The stress of the sealing ring decreases significantly with the increase of the eccentricity ex, but the contact stress is almost constant, indicating that the contact width changes.

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Fig. 5. Distribution of the contact stress under the condition 12 (MPa) (1% model)

Fig. 6. Contact stress of the butterfly plate and the sealing ring under each condition (MPa)

3 Simulation Analysis of Lateral Sealing Performance The lateral sealing uses the contact stress rc1 and the force F between the sealing ring and the pressing ring, and both are related. The basis of this consideration is that the greater the contact stress is, the greater the force is, and the more reliable the sealing is. It is speculated that the gas pressure p and the ring compaction d have a large influence on the lateral sealing. The ring compaction is defined as follows: the initial position is that the two large ends of the sealing ring are in close contact with the valve body and the pressing ring, respectively, without pressure (the ring compaction is 0), and the reduction of the distance between the valve body and the pressing ring relative to the initial position during operation is the ring compaction. In this paper, the analysis conditions are established with p and ring compaction d as independent variables, as shown in Tables 3 and 4. The friction coefficient under all conditions is 0.06, and the eccentricities ex and ez are 37.2 mm and 6.2 mm, respectively.

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Table 3. Conditions with the gas pressure p as an independent variable (d = 0.1 mm) Condition number l 1 0.00 2 0.45 3 0.90 4 1.35

Table 4. Conditions with the ring compaction d as an independent variable (p = 0.45 Mpa) Condition number l 5 0.06 6 0.08 7 0.10

Figure 7 demonstrates the contact stress distribution in lateral sealing under the condition 2. Since stress is large at the intermediate node and small at the end node in a grid element, the average value of them is taken as the contact stress in lateral sealing in the analysis.

Fig. 7. Contact stress in lateral sealing under the condition 2 (MPa) (2% model)

The contact stress and force in lateral sealing under other conditions are shown in Figs. 8 and 9. Figure 8 shows that if the gas pressure gets greater, the contact stress will be larger, and finally the sealing effect will be better. Figure 9 shows that if the ring compaction gets greater, the force will be larger, and finally the sealing effect will be better.

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Fig. 8. Contact stress of lateral sealing under various conditions (MPa)

Fig. 9. Force between the sealing ring and the pressing ring under various conditions (N)

4 Conclusions Gas pressure is determined by actual conditions and cannot be controlled. The larger the ring compaction is, the better the lateral sealing effect is, but the maximum stress of the sealing ring is significantly increased. If the yield stress of the material is 230 MPa, then d  0.06 mm. However, stainless steel materials will be significantly strengthened in practical applications. In addition, 230 MPa is also considered for thicker stainless steel plates (about 8 mm), while the sealing ring is thinner and the yield limit should be significantly greater than 230 MPa. Conclusions are as follows: The key factor affecting the reliability of the axial sealing is the eccentricity ex. As the eccentricity decreases, the axial sealing will be more reliable. The key factors affecting the lateral sealing are the gas pressure and the ring compaction. As the gas pressure or the ring compaction gets greater, the reliability of the lateral sealing increases.

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References 1. Rao, Y.X., Yu, L., Fu, S.W., et al.: Development of a butterfly check valve model under natural circulation conditions. Ann. Nucl. Energy 76, 166–171 (2015) 2. Valeh-e-sheyda, P., Rashidi, H., Azimi, N.: Structural improvement of a control valve to prevent corrosion in acid gas treating plant pipeline: an experimental and computational analysis. Int. J. Press. Vessel Pip. 165, 114–125 (2018) 3. Naseradinmousavi, P., Nataraj, C.: Nonlinear mathematical modeling of butterfly valves driven by solenoid actuators. Appl. Math. Model. 35(5), 2324–2335 (2011) 4. Naseradinmousavi, P., Nataraj, C.: Transient chaos and crisis phenomena in butterfly valves driven by solenoid actuators. Commun. Nonlinear Sci. Numer. Simul. 17(11), 4336–4345 (2012) 5. Kwuimy, C.A.K., Ramakrishnan, S., Nataraj, C.: On the nonlinear on–off dynamics of a butterfly valve actuated by an induced electromotive force. J. Sound Vib. 332(24), 6488– 6504 (2013) 6. Liu, B., Zhao, J.G., Qian, J.H.: Numerical analysis of cavitation erosion and particle erosion in butterfly valve. Eng. Failure Anal. 80, 312–324 (2017) 7. Ogawa, K., Kimura, T.: Hydrodynamic characteristics of a butterfly valve—prediction of torque characteristics. ISA Trans. 34(4), 327–333 (1995) 8. Yang, B.S., Hwang, W.W., Ko, M.H., et al.: Cavitation detection of butterfly valve using support vector machines. J. Sound Vib. 287(1–2), 25–43 (2005) 9. Corbera, S., Olazagoitia, J.L., Lozano, J.A.: Multi-objective global optimization of a butterfly valve using genetic algorithms. ISA Trans. 63, 401–412 (2016) 10. Song, X.G., Wang, L., Baek, S.H., et al.: Multidisciplinary optimization of a butterfly valve. ISA Trans. 48(3), 370–377 (2009) 11. Toufique Hasan, A.B.M., Matsuo, S., Setoguchi, T.: Characteristics of transonic moist air flows around butterfly valves with spontaneous condensation. Propuls. Power Res. 4(2), 72– 83 (2015) 12. Hummer, G., Halter, G., Grossl, M.: Calculated and measured flow conductance for butterfly valves. Vacuum 41(7–9), 2126–2128 (1990)

Motion Performance Analysis of the Sawyer Ankle Rehabilitation Robot Yongfeng Wang1,2,3, Xiangzhan Kong4, Jing Yang5, and Guoru Zhao2,3(&) 1

2

School of Mechanical and Electronic Engineering, Hubei Polytechnic University, Huangshi 435003, China CAS Key Laboratory of Human-Machine Intelligence-Synergy Systems, Shenzhen Institutes of Advanced Technology (SIAT), Chinese Academy of Sciences (CAS), Shenzhen 518055, China [email protected] 3 Research Center for Neural Engineering, SIAT, CAS, Shenzhen 518055, China 4 Intelligent Robotics Institute, Beijing Institute of Technology, Beijing 100081, China 5 Handan University, Handan 056001, China

Abstract. The ankle joint is the major weight bearing joint of human bodies, it have complex physiologic structure that can be easily traumatized. The rehabilitation robot is medical equipment, and it is used to assist even replace the rehabilitation physician, which would help the ankle injury patients to complete the training of the joint flexibility and muscle strength. Existing ankle rehabilitation robots have some problems that the axes of joints of robot are not aligned with the axes of ankle, the center or rotation axes of platform for rehabilitation robot are not aligned. A Sawyer ankle rehabilitation robot is proposed, each joint have some force sensors with high performance, it can replace the hands to take the dull, repeatability and susceptibility of rehabilitation physician. The kinematics model of robot was established base on D-H method, the forward and inverse solutions of robot were solved and some special configurations of robot were obtained. Combine kinematic characteristics of ankle with SimMechanics modules in Matlab, change regulation of angles for the joints of robot was studied, which under the different forces and torques. The results showed that the angles of joints increase with the values of forces and torques, and the angles of joints cause by forces are smaller than the torques. However, the joint 6 take reverse rotation when the torques rotation about the X-axis acts on the moving platform. This study will provide theoretical basis for the control system of novel ankle rehabilitation robots. Keywords: Ankle rehabilitation SimMechanics

 Sawyer robot  Kinematics characteristics 

This work has been financed partially by the National Natural Science Foundation of China (61761166007), National Key R&D Program of China (2018YFC2001404), Natural Science Foundation of Guangdong Province (2018A030313065), the Shenzhen Science and Technology Development Fund (JCYJ20170818163505850, JCYJ20170818163445670). Handan Science and Technology Research and Development Project (1721202044). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 832–846, 2020. https://doi.org/10.1007/978-981-32-9941-2_70

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1 Introduction Ankle is the major active joint of human bodies, it bears the total weight of bodies during walking, and the running, jumping, squatting, rising and other movements are closely related to the motion characteristics of ankle [1]. There are two major influencing factors of ankle injury: (1) Sudden ankle injury. The movement amplitude of ankle exceed the limit of boundary of anatomy when the body suffer inner or external force, it will cause ankle injury [2]. (2) Stoke and diseases. The wounds of the nervous system also cause ankle disease [3], such as foot drop caused by the stroke, spinal cord injury, brain damage, and so on. The foot drop disease is the most common long-term after effect of the stroke. It restricts walking ability, hinders further recovery of ankle motor function, and causes great inconvenience to patients’ daily life. Damage to the nervous system such as stroke, spinal cord injury, brain and cranial injury leads to malfunction of the ankle proprioceptor, further disrupting the information of the central afferent position, motor, tactile and vibration senses, and finally the ankle does not work properly [4]. Robot-assisted therapy is one of the important methods for functional recovery of ankle injury patients. At present, ankle rehabilitation robots are divided into platform ankle rehabilitation robot and wearable ankle rehabilitation robot. For the platform rehabilitation robot usually adopt the 3-Dof rotational parallel mechanisms, as shown in Fig. 1(a), Girone et al. [5] proposed the Rutgers ankle rehabilitation robot, it was a remote controllable ankle joint rehabilitation robot with virtual reality force feedback based on the Stewart platform. Dai et al. [6] proposed the 3-SPS/SP ankle rehabilitation robot, which had three degrees of freedom. Liu and Zhao et al. [7, 8] proposed the 3RSS/S ankle rehabilitation robot. Jamwal et al. [9] proposed a soft parallel ankle rehabilitation robot. Yin et al. [10] proposed the 3-PUS/S ankle rehabilitation robot. Yu et al. [11] proposed a cable-driven parallel mechanism ankle rehabilitation. Ai et al. [12] proposed a pneumatic muscles driven ankle rehabilitation robot with two rotational. Liu et al. [13] proposed a soft ankle rehabilitation robot with three rotational, Liu et al. [14] proposed a constrained 3-PSP ankle rehabilitation robot. The wearable ankle rehabilitation robots uses for reference the structure of orthosis and prosthesis, as shown in Fig. 1(b). Besides, considering the biomimetic machine principle. It can not only take ankle rehabilitation training during walking, but also improve motion performance of lower limbs. Jamwal et al. [15] proposed a house wearable ankle rehabilitation robot with three rotational. Shibata et al. [16] proposed a semi active wearable ankle rehabilitation robot with self-determination power supply technology. Yeung et al. [17] proposed an Exoskeleton Ankle Robot for RobotAssisted Gait Training of Stroke Patients. Roy et al. [18] proposed a wearable ankle rehabilitation robot with three rotational, it can help stroke patients take resistance training. Bharadwaj et al. [19] proposed a 3-Dof gait training device, it is driven by spring over muscle actuators, and can help stroke patients take dorsiflexion/plantar flexion and inversion/eversion training. Ferris et al. [20] proposed an ankle-foot orthosis powered by artificial pneumatic muscles. Noël et al. [21] proposed an electro hydraulic actuated ankle foot orthosis. Ren et al. [22] proposed a wearable ankle robot for in-bed acute stroke rehabilitation.

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The platform rehabilitation robots have some defects such as inflexibility, large size, bulky, controls complicated, it easily leads to reinjury of ankle. The wearable ankle rehabilitation robots with lower mobility, and the axes of joints of robot are not aligned with the axes of ankle, and it is detrimental to the complete rehabilitation training. Moreover, the wearable ankle rehabilitation robots have less driving ability.

Fig. 1. Moving axes of ankle and rehabilitation robot

The Sawyer robot is a revolutionary appliance from Rethink Robotics Company. It consists of flexible arms with limited power and force. It is equipped with a variety of elastic actuators and high-resolution sensors. It can move freely in the space of 1260 mm and has good visual interaction. It is widely used in industrial production, agriculture, medical and other fields. In this paper, according to the anatomical structure and injury mechanism of the ankle joint, a flexible ankle rehabilitation robot is reconstructed by means of the motion characteristics of the sawyer robot. This paper proposed an ankle rehabilitation robot based on the Sawyer robot, and as shown in Fig. 2. It can take the foot rotates around a point in space, and it can meet different demands of ankle patients.

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Fig. 2. The Sawyer ankle rehabilitation robot

2 Methods Vectors 2.1

Ankle Structure

The ankle is one of the most sophisticated human joints, as shown in Fig. 3. The ankle consists of the lower shine, the lower fibula and the talus. The nose of the lower shine is named as the ‘malleolus medialis’, the external nose of fibula is named as the ‘external malleolus’, and the quadrate pit is named as the ‘ankle mortise’. The talus is embedded in the mortise to develop the ankle. The moving pattern, movement range of ankle, and the moment required are summarized in Table 1.

Fig. 3. The Sawyer ankle rehabilitation robot Table 1. Physiological parameters of ankle Movement mode Inversion Eversion Dorsiflexion Plantarflexion Adduction Abduction

Movement range (°) Moment required (N m) 48 14.5o–22o 10o–17o 34 20o–30o 50 37o–45o 50 40 22o–35o 15o–25o 40

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Kinematics Analysis of Rehabilitation Robot

Lock the rotating motor that is close to the moving platform, and the structure of the robot becomes a 6R series mechanism. Set the fixed coordinate system to a fixed platform, each joint coordinate system is represented by Ti, and the coordinate system of the moving platform is P. As shown in Fig. 4.

Fig. 4. Sketches of the robot structure

Let the transformation matrix of the fixed coordinate system to the joint 1 coordinate system be 1T, and so on, 2T, 3T, 4T, 5T, 6T, 7T, establish the homogeneous transformation matrix of the coordinate system of moving platform relative to the coordinate system of fixed platform: 2

nx 6 ny p T ¼ 1 T 2 T3 T 4 T5 T6 T7 T ¼ 6 4 nz 0

ox oy oz 0

ax ay az 0

3 px py 7 7 pz 5 1

ð1Þ

Wherein, iT is a homogeneous transformation matrix of the coordinate system i with respect to the coordinate system i − 1, and the formula (2) can be referred to. 2

chi 6 shi i T¼6 4 0 0

shi cai chi cai sai 0

shi sai chi sai cai 0

3 ai chi ai shi 7 7 di 5 1

ð2Þ

Wherein shi—sinhi, chi—coshi, the D-H parameter table is constructed from the structural parameters of the sawyer robot, as shown in Table 2. hi is the angle between the i-th rod and the i-1th rod; di is the distance between the i-th rod and the i-th rod; ai is the angle of rotation of the i-th arm member; ai is the length of the i-th rod. Combining formula (1), formula (2) and Table 2, the position and posture of the moving platform can be determined from the angle values of the joints. For example, when the moving

Motion Performance Analysis of the Sawyer Ankle Rehabilitation Robot Table 2. D-H parameter of robot structure ai ai 1 0° 0 2 90° a1 3 −90° a2 4 90° a3 5 −90° a4 6 90° a5 7 −90° 0 60

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di d1 d2 d3 d4 d5 d6 d7

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40 20 0

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1

2 Time(s) 3

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Fig. 5. Drive angle of robot joints

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platform drives the ankle joint to realize the Inversion/Eversion movement, the angle of rotation of each joint is as shown in Fig. 5(a); when the moving platform drives the ankle joint to achieve the Adduction/Abduction movement, The angle of the joint rotation is shown in Fig. 5(b); when the moving platform drives the ankle joint to realize the Dorsiflexion/Plantarflexion movement, the angle of rotation of each joint is as shown in Fig. 5(c). The inverse kinematics solution process of the robot is: the position of the end platform are known, the angle values of the joints are solved. In this paper, the inverse inverse transform method is used to solve the inverse solution of the robot. The structural parameters ai-1, ai-1, di of the mechanism, the position of the moving platform P, and the attitudes /, u, c are known, multiply the left and right sides of the known pose matrix by the inverse matrix of the homogeneous transformation of each joint. The elements with constant terms in the matrix are selected, and the simultaneous equation is used to obtain the angle hi of each joint, as in Eq. (3). Since the square root and inverse tangent functions are used in solving the angle, the joint angle may correspond to multiple solutions. 2

ox oy oz 0

nx 6 ny p T¼6 4 nz 0

ax ay az 0

3 px py 7 7 ¼ 1 T 2 T3 T 4 T5 T6 T7 T pz 5 1

ð3Þ

Multiply the left and right sides of the above matrix by the inverse matrix of T1 and T7: 1 1p 7 1

T

T T

¼ 2 T3 T4 T5 T6 T

ð4Þ

From the left and right elements of the upper matrix, the elements are equal, and the simultaneous equations can be used to obtain h1. Similarly, other joint angles hi can be obtained. Some of the results are shown in Table 3. In addition, some special shapes are obtained as shown in Fig. 6.

Table 3. The result of the inverse solution Parameter /(°) u(°) c(°) P(m) h1(°) h2(°) h3(°) h4(°) h5(°) h6(°)

1 5 5 5 0, 0.25, 0.35 −1.7394 −3.4 2.9531 0.7814 −4.8507 5.1356

2 10 5 15 0.1, 0.2, 0.3 −2.1329 −19.5886 5.5709 −4.5882 −2.5324 6.5881

3 5 10 15 0.4, 0.3, 0.5 0.6933 −28.5369 13.2458 −17.7770 −3.2455 10.6215

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Fig. 6. Some special configurations of robot

2.3

Stability Analysis of Rehabilitation Robot

The stability of a rehabilitation robot is one of the important parameters of its performance. Its influencing factors include not only the structure of the robot itself, but also the speed, acceleration, inertia and external forces of the robot during the movement. The platform type ankle rehabilitation robot has compact structure, strong carrying capacity and excellent stability, but its control system is complex and slow. The wearable ankle rehabilitation robot has a simple structure and is attached to the limb, but its load carrying capacity is weak and the stability is uncontrollable. In addition, Sawyer robots combine the advantages of industrial robots such as stability, flexibility, simple control and automatic adjustment capabilities, enabling them to perform rehabilitation training for specific ankle joint patients. According to the actual situation of the human ankle rehabilitation exercise, combined with Table 4, the stability of the robot was studied by the sudden loading of the three directions. The results are shown in Figs. 7, 8, 9 and 10. Among them, (a) the angle generated by each joint and the corresponding moment after a sudden loading of 5, 25, 50 N in the vertical direction, (b) the angle of each joint produced after the sudden loading of 5, 25, 50 N/m moment in the X axis, Y axis and Z axis.

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Values 230 130 270 130 300 80 80 140 45 130 40

Parameters d7(mm) Mass of Rod 1(kg) Mass of Rod 2(kg) Mass of Rod 3(kg) Mass of Rod 4(kg) Mass of Rod 5(kg) Mass of Rod 6(kg) Mass of moving platform(kg) Length of moving platform(mm) Width of moving platform(mm) Mass of fixed platform(kg)

Values 80 4.5 1.3 2.2 1.8 1.7 1 0.8 30 15 15

During the ankle rehabilitation training preparation phase, when placing the foot on the platform, due to the effect of gravity, it is assumed that the platform suddenly receives a vertical downward force, which will cause the rotation angle of each joint to change, as shown in Fig. 7. The angle of each joint of the robot changes in proportion to the magnitude of the force. Among them, compared with other joints, joint 2 and joint 5 change significantly, joint 1 is slightly weaker, and joints 3, 4, and 6 tend to be roughly the same. At this time, the control system of flexible drive motor needs to be adjusted so that it can quickly produce corresponding angle to ensure the stability of the robot. When the Inversion/Eversion preparation phase is performed, it is assumed that a rotational moment about the X axis is suddenly provided to the moving platform, the rotation angles of the joint of the robot are as shown in Fig. 8. In the case of a small driving torque, the angle of each joint of the robot is proportional to the magnitude of the torque. However, when the applied rotational torque reaches a certain value, the rotation angle of some joints exceeds 180°, causing it to rapidly rotate. As is shown in Fig. 7(b), when t = 0.78 s, the joint 6 rotates by 180°, and the rotation phenomenon occurs, and the time when the rotation occurs is related to the magnitude of the applied torque. The larger the torque, the earlier the joint 1 turns. When the Dorsiflexion/Plantarflexion preparation phase is performed, it is assumed that the rotational moment of the joint of the robot is suddenly provided to the moving platform, the rotation angles of each joint of the robot are shown in Fig. 9. The angle of each joint of the robot is proportional to the magnitude of the force. The angle of rotation of the joint 2 and the joint 3 is almost equal, but in the opposite direction. In addition, during the application of the torque, the joints do not rotate. The variation of joints 2, 4, 5 is significantly smaller than the other three. When the Adduction/Abduction preparation phase is performed, it is assumed that when a rotational moment about the Z axis is suddenly provided to the moving platform, the rotational angle of the joints of the robot is shown in Fig. 10. In the case where the driving rotational torque is small, the rotation angle of the joint 3 and the joint 6 is almost the same, but as the moment increases, the degree of change of the

Motion Performance Analysis of the Sawyer Ankle Rehabilitation Robot 1

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Joint1 Joint2 Joint3 Joint4 Joint5 Joint6

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Fig. 7. Angle of each joint when the platform is subjected to sudden loading

joint 6 is significantly larger than that of the joint 3, and the rotation angles of joint 6 and the rotation of the joint 2 are roughly the same but in the opposite direction. In addition, the rotation angle of the joint 1, the joint 4 is small with respect to other joints, and at a certain moment, their rotation angles are the same, and this time occurs earlier as the loading torque increases.

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200

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(c) 50 N/m torque Fig. 8. Angle of each joint when the platform is subjected to sudden loading in the X direction

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Time(s) (c) 50 N/m torque Fig. 9. Angle of each joint when the platform is subjected to sudden loading around the Y direction.

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Fig. 10. Angle of each joint when the platform is subjected to sudden loading in the Z direction

3 Conclusion In response to some problems of the ankle rehabilitation robot, combined with the motion characteristics of the sawyer robot, a flexible ankle rehabilitation robot was reconstructed. The kinematics model of the robot is established by D-H method, and

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the forward and inverse kinematics are analyzed, several special configurations were obtained. In addition, based on the initial stage of the foot touch platform, Inversion/Eversion, Dorsiflexion/Plantarflexion, Adduction/Abduction, the change of the joint angle is obtained. (1) The effect of the same force on the platform on each joint is less than the influence of the moment on the joint. (2) The influence on each joint of the torque of the initial state of the ankle joint rehabilitation training. If the platform is subjected to the rotation moment of the X-axis, the joint 6 has the largest rotation angle, which can reach 180°. Under the action of the micro moment, the influence on each joint is the rotation torque around the X axis, Y axis, Z axis, and the linear relationship of the joint changes caused by the Y axis rotation torque is the best. During the application of the moment, there are some joints whose angles are equal in magnitude, but in opposite directions, such as joints 4 and 5 under the action of tiny X-axis rotational moments, joints 2 and 3 when rotating around the Y-axis, around Z Joints 2 and 6 when the shaft is rotated. Through the change characteristics of the joint angle, the control system of the flexible drive motor is rationally designed, which lays a certain theoretical foundation for the practical application of the robot. Acknowledgment. The authors would like to thank all reviewers for their valuable comments. This study has been financed partially by the National Natural Science Foundation of China (61761166007), National Key R&D Program of China (2018YFC2001404), Natural Science Foundation of Guangdong Province (2018A030313065), the Shenzhen Science and Technology Development Fund (JCYJ20170818163505850, JCYJ20170818163445670). Handan Science and Technology Research and Development Project (1721202044).

References 1. Han, Y.L., Yu, J.M., Song, A.G., et al.: Parallel robot mechanism for ankle rehabilitation. J. Southeast Univ. (Nat. Sci. Edn.) 45(1), 45–50 (2015) 2. Zheng, J.P., Dong, X.P., Shen, L.F., et al.: The curative of aircast ice cold pressurized capsule in treatment of actute ankle sprain. Clin. Med. Eng. 17(3), 35–36 (2010) 3. Langhorne, P., Bernhardt, J., Kwakkel, G.: Stroke rehabilitation. Lancet 377(9778), 1693– 1702 (2011) 4. Li, Z.W., Xu, X.Y.: Stability and proprioceptors of ankle. Int. J. Orthop. 30(1), 21–22 (2009) 5. Girone, M., Burdea, G., Bouzit, M.: A Stewart platform-based system for ankle telerehabilitation. Auton. Robots 10, 203–212 (2001) 6. Dai, J., Zhao, T.S.: Sprained ankle physiotherapy based mechanism synthesis and stiffness analysis of a robotic rehabilitation device. Auton. Robots 16(1), 207–218 (2004) 7. Zhao, T.S., Yu, J.H., Dai, J.S.: An ankle rehabilitation device based on 3-RSS/S parallel mechanism. J. Yanshan Univ. 29(6), 471–475 (2005) 8. Liu, G.Q., Gao, J.L., Yue, H., et al.: Design and kinematic simulation of parallel robots for ankle rehabilitation. In: Proceedings of the 2006 IEEE International Conference on Mechatronicsand Automation, Luoyang China, 25–28 June 2006, pp. 253–258 (2006) 9. Jamwal, P.K., Xie, S.: Kinematic design optimization of a parallel ankle rehabilitation robot using modified genetic algorithm. Robot. Auton. Syst. 57(1), 1018–1027 (2009) 10. Yin, S.: Design and human machine motion mapping analysis of an ankle rehabilitation robot. China Mech. Eng. 23(21), 2552–2555 (2012)

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11. Yu, R.T., Fang, Y.F., Guo, S.: Design and kinematic performance analysis of a cable driven parallel mechanism for ankle rehabilitation. Robot 37(1), 53–63 (2015) 12. Ai, Q.S., Zhu, C.X., Zuo, J., et al.: Disturbance-estimated adaptive backstepping sliding mode control of a pneumatic muscles-driven ankle rehabilitation robot. Sensors 18(66), 1–21 (2018) 13. Liu, Q., Liu, A.M., Meng, W., et al.: Hierarchical compliance control of a soft ankle rehabilitation robot actuated by pneumatic muscles. Front. Neurorobotics 11, 1–19 (2017) 14. Liao, Z.W., Yao, L.G., Lu, Z.X., et al.: Screw theory based mathematical modeling and kinematic analysis of a novel ankle rehabilitation robot with a constrained 3-PSP mechanism topology. Int. J. Intell. Robot. Appl. 2(3), 351–360 (2018) 15. Jamwal, P.K., Hussain, S., Nasiri, N.M., et al.: Tele-rehabilitation using in-house wearable ankle rehabilitation robot. Assist. Technol. 30(1), 1–10 (2018) 16. Shibata, K., Yoshio, I., Hironobu, S.: Intelligent ankle-foot orthosis by energy regeneration for controllable damping during gait in real time. In: IFIP Conference on Human-Computer Interaction. Springer, Cham, 30 August 2015, pp. 563–568 (2015) 17. Yeung, L.F., Ockenfeld, C., Pang, M.K., et al.: Design of an exoskeleton ankle robot for robot-assisted gait training of stroke patients. In: 2017 International Conference on Rehabilitation Robotics (ICORR), London, UK, 17–20 July 2017, pp. 211–215 (2017) 18. Roy, A., Krebs, H.I., Patterson, S.L., et al.: Measurement of human ankle stiffness using the anklebot. In: International Conference on Rehabilitation Robotics, Noordwijk, Netherlands, 13–15 June 2007, pp. 356–363 (2007) 19. Bharadwaj, K., Sugar, T.G., Koeneman, J.B., et al.: Design of a robotic gait trainer using spring over muscle actuators for ankle stroke rehabilitation. J. Biomech. Eng. 127(1), 1009– 1013 (2005) 20. Ferris, D.P., Czerniecki, J.M., Hannaford, B.: An ankle-foot orthosis powered by artificial pneumatic muscles. J. Appl. Biomech. 21(1), 189–197 (2005) 21. Noël, M., Cantin, B., Lambert, S., et al.: An electrohydraulic actuated ankle foot orthosis to generate force fields and to test proprioceptive. IEEE Trans. Neural Syst. Rehabil. Eng. 16 (4), 390–399 (2008) 22. Ren, Y.P., Xu, T., Wang, L., et al.: Develop a wearable ankle robot for in-bed acute stroke rehabilitation. In: 33rd Annual International Conference of the IEEE EMBS, Boston, USA, 30 August–3 September 2011, pp. 7483–7486 (2011)

Automated Sustainable Low-Carbon Design of Offshore Platform for Product Life Cycle Qianyi Yu and Bin He(&) Shanghai Key Laboratory of Intelligent Manufacturing and Robotics, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, People’s Republic of China [email protected]

Abstract. Faced with the severe situation of carbon emissions, low carbon has become a new trend of social and economic sustainable development. Product low-carbon design originates from green design, which can reduce the carbon footprint of products from the source and achieve sustainable development. This paper is devoted to optimizing the product low-carbon design method based on graph theory. Alternative solutions for the five life cycle stages of the product constitute a design space. Graph theory is applied to the product low-carbon design to effectively find the optimal decision-making scheme with minimum carbon footprint in the entire design space. However, this method is only applicable to the case where the carbon footprint of solutions at each life cycle stage is static. In the face of a dynamically changing carbon footprint, the design result of this method may be erroneous. In this paper, the idea of “break up the whole into parts” could be used to search for the best design scheme of minimizing carbon footprint respectively from each raw material solution as the starting point. The carbon footprint of solutions at several life stages is constrained to the product raw materials and it results in an inaccurate calculation of carbon footprint. This problem in the original method is solved. The product low-carbon design software and the case of low-carbon design of offshore platform leg are the applications of this method. Keywords: Low-carbon design  Life cycle  Carbon footprint  Bellman-Ford algorithm  Sustainable design  Offshore platform

1 Introduction The massive emissions of greenhouse gas (GHG) have had a huge negative impact on the global climate [1]. How to reduce GHGs and slow global warming has become a worldwide concern. The UK first proposed the concept of carbon footprint [2, 3], but the definition of carbon footprint has not yet been unified [4, 5]. At present, most of the relevant studies usually adopt the definition by Wiedmann et al. [6] that carbon footprint should include both direct and indirect emissions, and the unit of carbon footprint This project is supported by National Natural Science Foundation of China (Grant No. 51675319), Shanghai Science and Technology Commission Project (Grant No. 17DZ1204603). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 847–863, 2020. https://doi.org/10.1007/978-981-32-9941-2_71

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is defined as the mass of carbon dioxide which accounts for the largest proportion of GHG. Other gas need to be converted to carbon dioxide equivalent [7] for calculation according to their global warming potential (GWP). With the promulgation of a series of standards such as PAS 2050 and ISO 14064, the research on quantification of product carbon footprint has been further deepened and promoted. The EU has proposed and gradually improved the carbon tax mechanism, and the US congress has decided to impose a carbon tax on high-carbon products from 2020, including China [8]. In the future low-carbon economy, the product carbon footprint will be marked on the product in the form of carbon label [9], as an important basis for enterprises to pay the carbon tax in the future, and guide consumers to purchase in the market. Therefore, reducing the carbon footprint of products and carrying out low-carbon design of products is an important part of improving product competitiveness. Currently, quantitative research of product carbon footprint is mainly focused on life cycle assessment (LCA) [10]. Mayyas et al. [11] analyzed combined environmental effect of electrification on the operational phase of vehicles and the generation of the GHG in the different life-cycle phases of vehicles. Used a holistic LCA approach to address pre and post manufacturing phases.Sung et al. [12] have developed a lowcarbon design embedded system for products based on GHG emissions. In view of the uncertainty of product information, He et al. [13, 14] studied the product carbon footprint estimation model based on the unascertained mathematics theory to estimate product carbon footprint for product life cycle. And the product conceptual design for product environmental footprint integrated with unascertained measure model based evaluation approach is introduced in detail. Tao [15] evaluated the carbon emission of ceramic products in the whole life cycle in the research of low carbon manufacturing system of ceramic enterprises. Based on product life cycle and product category specifications, Kuo et al. [16] collected and calculated greenhouse gas emissions data, cost and capacity of supplier production for components in the product life cycle to determine operational parameters and constraint equations. A low-carbon optimal assessment model was established to improve the efficiency of product carbon footprint calculations and help companies design low-carbon products. Mainly according to the multi-level requirement information description of the products, He et al. [17] proposed an approach to achieve the transforming fuzzy sustainable functional requirements into design parameters, so as to carry out sustainable product life cycle design. A lot of scholars have conducted detailed research on the carbon footprint of the manufacturing stage. Narita [18] developed an evaluation system for calculating equivalent CO2 emissions and machining costs by using an activity-based model to evaluate the cutting speed of an end mill operation and determine the optimal cutting conditions. Andriankaja et al. [19] proposed a sustainable machining approach for CAD/CAM/CNC systems based on a dynamic environmental assessment and established cognitive links between the machining data included in Standard for the Exchange of Product model data—compliant Numerical Control and environmental indicators. Seow et al. [20] put forward a new ‘Design for Energy Minimization’ approach, which is intended to provide increased transparency with respect to the energy consumed during manufacture in order to help inform design decisions. An energy simulation model based on this approach is then presented to aid designers

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during the design phase. Zhang et al. [21] analyzed the carbon footprint of the welding process and established the carbon emission characteristic function of the welding process. Yin et al. [22] analyzed the carbon emission sources of mechanical manufacturing process, and established the carbon emission characteristic function of mechanical manufacturing, which can be used to identify and quantify the various carbon emissions of the process. It is also considered that the carbon emission in mechanical manufacturing process can be effectively reduced by process selection and process planning combined with the carbon emission function. On the basis of analyzing the carbon emissions from the sand casting process, Zheng et al. [23] proposed the carbon efficiency model and evaluation method for the sand casting production process, so that the enterprises can carry out activities of energy saving and emission reduction in a targeted manner. Li et al. [24] have studied the carbon emissions of mechanical processing system. The direct and indirect carbon emissions in the process of machining are divided into 4 parts which are respectively caused by energy consumption of equipment operation, workpiece materials consumption, cutting fluid consumption and cutting tools consumption. And a quantitative method of carbon footprint was proposed. Zhang [25] analyzed the energy consumption in the manufacturing process of mechanical parts, and carried out research from various aspects. Through scheduling of manufacturing process routes, the optimal energy-saving production scheduling scheme was obtained, which reduced the carbon emission of mechanical products at MS. In this paper, the graph algorithm applied to the decision-making at each product life cycle stage [26] is improved, and a theoretical model that is more accurate and more suitable for product life cycle low carbon design is established. The unimproved graph-based product low-carbon design model does not take into account the problem that the carbon footprint value between the same decision-making schemes is not unique. The carbon footprint generated at the manufacturing, transport and recycle and disposal stages must have a certain constraint relationship with the choice of raw materials. Therefore, the carbon footprint of the recycle and disposal scheme is dynamic, and it is obviously defective to simply apply the graph algorithm to the product low carbon design model with no carbon footprint value constraint. The improved model adopts the idea of “break up the whole into parts”. The digraph of decision-making schemes in the product life cycle is split into some sub- digraphs starting from specific schemes at the acquisition of raw materials stage. In the case of determining the raw materials of the products, it is possible to more accurately find the optimal comprehensive design scheme for the carbon footprint index by calculating. The rest of this paper is organized as follows: Sect. 2 introduces the product carbon footprint accounting method based on LCA. In the Sect. 3, the application method of graph algorithm in the low-carbon product design is elaborated in detail, and proposes an improved method. Section 4 introduces the software of product low-carbon design based on this improved graph algorithm, and test the reliability of the accounting model and software by taking the pile leg in marine equipment as an example. Section 5 summarizes this paper.

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2 Product Carbon Footprint Accounting Method Based on Life Cycle Assessment Life Cycle Assessment, first proposed by a research institute in the US, tracked the entire process of Coca-Cola’s products from acquiring manufacturing materials to disposal after using. LCA refers to the analysis of environmental impacts of a product at all life cycle stages, including energy use, resource consumption, pollutant emissions, etc. This method is a top-down process for carbon footprint accounting of products. Its analysis results are very specific, in other words, the analysis results are only applicable to a certain product. Therefore, this method is more suitable for carbon footprint accounting of micro-systems. When LCA is used to account the carbon footprint of a product, the manufacturing flowchart of product need to be established firstly, and the raw materials, activities and processes involved in the whole life cycle of the product are listed. Secondly, there is need to determine the system boundary and point out the calculation range of product carbon footprint, including materials, energy and other activities that are required to be included in all life cycle stages of the carbon footprint assessment. Then the data are collected and they are mainly divided into all material activities and emission factors (CO2 equivalents discharged by per unit of material or energy) covered by the whole life cycle of the product. After the calculation of carbon footprint is completed, the results are tested to check the accuracy of the carbon footprint calculation results and minimize the uncertainty to improve the credibility of carbon footprint evaluation. The calculation of carbon footprint requires the establishment of a mass balance equation “input = accumulation + output”. This equation is used to ensure the balance of material input, accumulation and output, and to calculate the direct and indirect carbon emissions at different stages of the product life cycle. The equation is as follows: Ex ¼

X

Qi  Ci

ð1Þ

i¼1

Where Ex —Carbon footprint of a product at a certain stage, x—Five stages of the whole life cycle: the Acquisition of Raw Materials Stage (AS), the Manufacturing Stage (MS), the Transport Stage (TS), the Usage Stage (US), the Recycle and the Disposal Stage (RS) according to the PAS 2050 standard, Qi —Quantity or intensity data of substances or activities of i in stage x (mass/volume/kilometer/kilowatt-hour, etc.) of a product, Ci —Carbon emission factor of unit substance (CO2/unit). Finally, add up all carbon footprint of the product at each life cycle stage, the carbon footprint in the whole life cycle of the product is obtained as follows: E ¼ EAS þ EMS þ ETS þ EUS þ ERS

ð2Þ

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Where E—Total carbon footprint at all life stages of the product, EAS —Carbon footprint at AS, EMS —Carbon footprint at MS, ETS —Carbon footprint at TS, EUS —Carbon footprint at US, ERS —Carbon footprint at RS. The calculation of carbon footprint throughout the product life cycle is studied previously and a carbon footprint accounting model of mechanical products based on LCA is established [27–29]. He et al. [30]. proposed 14 kinds of calculation model of product environmental footprint. The carbon footprint of different types of products puts the emphasis on different aspects at five life cycle stages. For screwdriver, vernier caliper, bicycle and other products which do not need energy consumption in using process, its carbon footprint generated in the whole life cycle mainly come from the manufacturing stage. The carbon footprint of the products like automobile, printer, electric kettle which must consume energy in the using process, generated in using process will be much larger than that in other life cycle stages. However, due to the uncertain activities at US and the influence of various human factors, it is very difficult to establish the carbon footprint accounting model in this stage. But the production process and manufacturing steps for each type of product at MS are clear, and manufacturing industry is also the main source of carbon emissions. Therefore, it is more practical to refine the product life cycle model and establish a set of formulas suitable for accounting product carbon footprint at MS.

3 Improvement of Low-Carbon Product Design Method Based on Graph Algorithm 3.1

The Shortest Path Problem in Graph Theory

Graph theory originated from the famous classical mathematics problem in the eighteenth century, the Königsberg problem, that is, the Eulerian path. Graph theory is based on graphs. Graph in graph theory is an important data structure, which consists of a number of given points and lines that connecting two points. The graph is usually used to describe a specific relationship between things. A graph is an ordered binary set of ðV; EÞ, denoted by G ¼ ðV; EÞ, where the vertex set V ¼ fv1 ; v2 ; v3 ;    ; vn g is a finite non-empty set, and the elements in the set are vertices (nodes), representing things. The edge set E ¼ fe1 ; e2 ; e3 ;    ; em g is a finite set, and the elements in the set are edges, representing the corresponding relationship between the two things. Edge e can have directions, so graphs are divided into directed graphs and undirected graphs. The directed edge e corresponds to the ordered node pair ðu; vÞ, at this time, u is called the starting point of e, and v is the end point of e. The undirected edge e corresponds to the unordered node ðu; vÞ, in which case u and v are called the two endpoints of e. A typical problem in undirected and directed graphs is the shortest path problem. Exploring the shortest path problem requires introducing the concept of a weight

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function w for the edge, and the weight function w : E ! R maps each edge to a specific real number weight. Then calculating the weight wðpÞ of a path p ¼ fv1 ; v2 ; v3 ;    ; vk g in the graph is to calculate the sum of the weight on each edge of the path: wðpÞ ¼

k X

wðvi ; vi þ 1 Þ

ð3Þ

i¼1

Where wðpÞ—Weight of the path, k—Count of nodes in the path, vi —Starting point of an edge, vi þ 1 —End point of an edge. The shortest path problem needs to be solved is how to find the path with the least weight in more than one connected path (from node u to node v) in a graph. Define dðu; vÞ as the weight of the shortest path which is from u to v as follows: ( dðu; vÞ ¼

n o p min wðpÞ : u ! v 1 1 2

ð4Þ

Case 1 is existing one or more paths from u to v, and case 2 is the situations of others. Thus it can be seen that the shortest path is not unique. Any path pi with the weight wðpi Þ ¼ dðu; vÞ from u to v is the shortest path of the graph. 3.2

Create a Carbon Footprint Digraph for Product Life Cycle

The product life cycle can be divided into five phases: AS, MS, TS, US, and RS. The optimal carbon footprint at one life cycle stage does not mean that a product produces the minimum carbon footprint in its whole life cycle. Therefore, a comprehensive consideration of the carbon footprint at each life stage is required in product lowcarbon design. There are a variety of options available at each stage, and arbitrarily selecting the solution in each stage can form a huge number of complete product designs. Different designs have different carbon footprint values. How to find a lowcarbon design in many product designs could be transformed into the problem of finding the shortest path in a digraph. Five vertex sets of V1 , V2 , V3 , V4 , V5 are created to correspond to the five life cycle stages of a product, and the elements in each set are alternative design options for each stage. V1 ¼ fv11 ; v12 ; v13 ;    ; v1a g, a is the number of design options at AS. V2 ¼ fv21 ; v22 ; v23 ;    ; v2b g, b is the number of design options at MS. V3 ¼ fv31 ; v32 ; v33 ;    ; v3c g, c is the number of design options  at TS. V4 ¼ fv41; v42 ; v43 ;    ; v4d g, d is the number of design options at US. V5 ¼ v51 ; v52 ; v53 ;    ; v5f , f is the number of design options at RS. The weights between adjacent nodes are assigned the carbon footprint value of the upstream scheme node. So the carbon footprint of the fifth layer nodes is missing. In

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order to complete the carbon footprint of the product life cycle, the sixth vertex set is added as the end layer so that the carbon footprint produced at RS can be mapped to the edges which are from the fifth layer node to the sixth layer node. The digraph of the product life cycle is shown in Fig. 1.

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Fig. 1. Carbon footprint digraph of product life cycle

3.3

Selection of Graph Algorithms for Low-Carbon Product Design

The shortest path problem in graph theory could be divided into the shortest path problem of single source and all pairs of nodes. To solve the shortest path problem in graph theory, the commonly used algorithms are Dijkstra’s algorithm [31] and Floyd algorithm [32]. The Floyd algorithm can directly calculate the shortest path between any two points. However, as shown in Fig. 1, all the paths are in the order of life cycle, and the direction points from the upstream to the adjacent downstream. The starting points and end points can be roughly determined. The first layer nodes are the starting points, and the sixth layer nodes are the end points. Therefore, from the perspective of efficiency and time complexity, single-source path algorithm is more suitable for lowcarbon product design in the whole life cycle. Dijkstra’s algorithm is based on greedy algorithm, and it currently recognized as the best algorithm for solving the problem of single source shortest path with no negative weight (no negative value of the edge). However, Dijkstra’s algorithm is incapable of action when confronts to the graphs with negative weights. The carbon

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footprint generated at RS may be negative, that is, the carbon footprint subtracted from the recycled material is greater than that generated by the energy and materials consumed in recycling the product, so the Dijkstra’s algorithm is not applicable. The Bellman-Ford graph algorithm [33] based on dynamic programming is another commonly used algorithm for solving the single-source shortest path problem. It was invented by American mathematician Richard Bellman, the proponent of dynamic programming, and Lester Ford. This algorithm is good at time efficiency and the time complexity is oðVE Þ. The Bellman-Ford algorithm is able to applied in digraph with negative weight, which is different from Dijkstra’s algorithm. The basic idea of the Bellman-Ford algorithm is successive approximation and the algorithm flow is: initialization, iteration, and judgment of negative weight loops. The following is a detailed introduction to the Bellman-Ford algorithm. (1) Initialization: set the distance from the starting point v1 to all other nodes to infinity (indicating unreachable), that is, create an array Distance½vi  to record the path length (weight) from the source point v1 to the node vi (i ¼ 2; 3;    ; n), and initialize that Distance½vi  ¼ INF, Distance½v1  ¼ 0. (2) Iteration: traverse all the edges in the graph, and perform a slack operation on the two vertices of the edge until no node can be relaxed again. Bellman-Ford algorithm asymptotically reduces the shortest distance estimation from the source point v1 to the node vi by relaxation operation until the estimated value is the same as the shortest path weight value dðv1 ; vi Þ. For each edge eðu; vÞ, if Distance½u þ wðu; vÞ\Distance½v, Distance½v ¼ Distance½u þ wðu; vÞ, wðu; vÞ is the weight of edge eðu; vÞ. If Distance½v is not updated, it means the shortest path has been searched or some nodes are unreachable, jumping out of the loop. Therefore, each successful relaxation represents finding a shorter path. (3) Judgment of negative weight loops: for the graph with negative weight loops, it is meaningless to find the shortest path, and the path weights are infinitesimal if there are countless negative loops, because the path weight is infinitesimal if the negative loops are repeated countless times. The algorithm can return a Boolean to indicate if there is a reachable path through a negative weight loop. 3.4

Improvement of Product Low-Carbon Design Model Based on Graph Theory

The low-carbon product design model established in Fig. 1 has certain defects in the calculation of carbon footprint. As shown in Fig. 2, when the source points are different raw material solutions (V11 and V13 ) and the paths pass through the same solution node V53 at RS, since the carbon emission coefficients of different material recycling operations are different, the carbon footprint at RS is not unique on the edge from V53 to V61 . The algorithm is difficult to judge and search the correct shortest path. Therefore, it 0 is necessary to derive a virtual node V61 , so that the weight between the last two nodes is wðV53 ; V61 Þ in the path started from V11 and the weight between the last two nodes is  0  w V53 ; V61 in the path started from V13 . This method is used to distinguish the weight on the same edge but not in the paths of the same starting point.

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Fig. 2. Carbon footprint digraph of product with derivative nodes

The energy consumption of different materials is different under the same processing technology. The manufactured product has a uniform volume, but the weight is not unique due to the difference in material density. The weight of the product affects the carbon footprint at TS. For the same reason, corresponding virtual nodes are derived when the paths starting from different raw material solutions pass through the same manufacturing or transport solution node. In the complete graph, multiple weights are prohibited between two nodes. Therefore, in order to obtain the more accurate carbon footprint of the product life cycle, the graph should be divided into sub-graphs with a single starting point, as shown in the Fig. 3. When the material solution is determined, the weight on each edge in subgraphs is unique. The Bellman-Ford algorithm could quickly and accurately find the shortest path in this condition. Only the path with the least weight, that is, the product design with the minimum carbon footprint, can be found using the Bellman-Ford algorithm. However, an excellent product design is not only measured by the carbon footprint index, and it often needs to be combined with economic index, technical index, resource index, and so on. Thus, it is obvious that product design with good comprehensive evaluation cannot be obtained only relying on the traditional Bellman Ford algorithm. The algorithm needs to be improved. If all the reachable paths are saved in the calculation process of Bellman-Ford algorithm, and then all saved paths are sorted, several paths with smaller weights can be output as alternatives, and the problem that the minimum carbon footprint design is not the one with best integrated evaluation is solved. Figure 4 shows the modified Bellman-Ford algorithm pseudocode.

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Fig. 3. Subgraphs of single material starting point FIND_SHORTEST_THREE_PATHES(Vertices,Edges,Weights) 1 get Vertices,Edges,Weights data from user input 2 Graph Create_Graph(Vertices,Edges,Weights); 3 Startpoints Find_All_Startpoints(Graph); 4 foreach Startpoint in Startpoints 5 All_Pathes Bellman_Ford_Algorithm(Graph,Weights,Startpoint); 6 SavedPathes Save_All_Useful_Pathes(All_Pathes); 7 Sort_All_Saved_Pathes(SavedPathes); 8 ThreeMininumPathes Find_Three_Minimum_Pathes(); 9 return ThreeMininumPathes

Fig. 4. Pseudocode of modified Bellman-Ford Algorithm

Pseudocode Description: The input of the algorithm is node, edge and weight, which correspond to the alternatives at each state, selecting solutions and carbon footprint of corresponding activities. Firstly, get the information of node, edge and weight from the user input and create the digraph. Find all material solutions as the starting points and split the parent graph into subgraphs. For-loop traverses all starting points and all paths in subgraphs are obtained by using Bellman-Ford algorithm and all reachable paths are saved. Finally, sort all saved paths and find the shortest three paths. Three designs with smaller carbon footprint could be found in each subgraph. After looping through all subgraphs, comprehensive designs with good carbon footprint index could be obtained corresponding to all selected material solutions. Sorting all obtained integrated designs from subgraphs based on carbon footprint is equivalent to recombining the subgraphs, and the final output results are still the designs with better carbon footprint index in the parent graph, so that the designers can choose the best one according to the actual situation.

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4 Application 4.1

Product Life Cycle Low-Carbon Design Software

Based on the modified graph algorithm in Sect. 3, the product life cycle low-carbon design software is developed. The interface is shown in Fig. 5. The purpose of this software is to assist designers to make decisions on the solutions of each life cycle stage more conveniently in the process of product design so that integrated product designs with better carbon footprint index can be obtained. Users can selectively add solutions for each stage in the product life cycle from a comprehensive basic information database. The equipped database includes all kinds of carbon emission factors required for carbon footprint calculation, basic data of various machining processes and transportation methods, etc. The strong support in data ensures the correctness and objectivity of the calculation results. Finally, the designs are arranged in ascending order of carbon footprint, so that users can choose what they want according to the actual situation. The balance between carbon footprint index and other considerations could be optimized.

Fig. 5. Sustainable low-carbon design system for product life cycle

The main users of the software are product designers. First of all, according to the functional requirements of the product, the designer adds corresponding solutions in order of the life cycle. After adding solutions, all the solutions at each stage are checked. If there are mistakes, delete or modify them. If there is no problem, proceed to the next step. Add carbon footprint between two solutions respectively in adjacent life cycle stages, in other words, establish a connection between upstream and downstream options. So it could be integrated into a comprehensive design that can be connected

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from AS to RS. After the edges and carbon footprint being added, all the information of paths will be checked. If there are mistakes, delete or modify them. If there is no problem, proceed to the next step. Calculate the carbon footprint of the complete designs starting from each raw material solution. Not only the first three complete designs with less carbon footprint can be viewed, but also the designs which belong to different raw material solutions are able to be compared by comparing carbon footprint values. Users make choices based on the result of comparing. The software operational flowchart is as follows in Fig. 6.

Start

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Fig. 6. Software operational flowchart

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Case Study

The reliability of the low-carbon design model and software based on graph theory is verified by taking the pile leg of an offshore platform with a height of 85 m and a volume of about 5,500 cubic meters as an example. Cylindrical pile leg is an important component of a jack-up platform, mainly composed of cylindrical wall and racks. Establish all solutions for its life cycle stages as shown in Table 1. Table 1. Solutions at each life cycle stage Node v11 v12 v13 v21

v22

v31 v32 v33 v34 v41 v42 v51 v52

Solution The material of cylindrical wall is 45 # steel and the material of ranks is 45 # steel. The material of cylindrical wall is cast steel and the material of ranks is 45 # steel. The material of cylindrical wall is cast iron and the material of ranks is cast steel. cylindrical wall manufacturing process: Casting ! Sand cleaning ! Rough turning ! Carburizing ! Quenching ! Grinding. Racks manufacturing process: Blanking ! Blank processing ! Normalizing ! Roughing ! Tooth surface processing ! Heat treatment ! Fine grinding. cylindrical wall manufacturing process: Modelling and core making ! Casting ! Cleaning ! Rough turning ! Tempering ! Finishing Grinding. Rack manufacturing process: Casting ! Cleaning ! Rough milling ! Finishing ! Gear surface processing ! Heat treatment. Highway gasoline vehicle transportation. Highway diesel vehicle transportation. Waterway power-driven vessel transportation. Railway electric train transportation. Working 4 h a day. Working 6 h a day Recycle all the materials of cylindrical wall and racks. Only recycle the material of cylindrical wall.

Using the software mentioned above to carry out the low-carbon design of pile leg, and the connection between upstream and downstream solutions is established as shown in Fig. 7. The software calculates the corresponding carbon footprint values as shown in Table 2. u is the starting point of the connection and v is the ending point. CF is the carbon footprint and the unit is kgCO2 e. Note: ➀ Superscript 1 indicates that the solution node is traveled by the path starting from v11 . Superscript 2 indicates that the solution node is traveled by the path starting from v12 . Superscript 3 indicates that the solution node is traveled by the path starting from v13 . ➁ The carbon footprint of v1i ! v2j is determined only by the raw material solutions and it is independent of the choice of the manufacturing solutions in the second layer.

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Fig. 7. Low-carbon design model of pile leg based on Graph Algorithm Table 2. Carbon footprint values of digraphs calculated by software u v11 v11 v12 v12 v13 v13

v v21 v22 v21 v22 v21 v22

CF 194,204 194,204 289,242 289,242 148,605 148,605

v121 v131 6,739 v121 v133 6,739 v122 v122 v221

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u

v

v221 v222 v222 v321 v321 v322 v322 v131 v132 v133 v134

v233 v232 v234 v331 v333 v332 v334 v141 v142 v142 v141

CF 20,594 20,602 20,602 12,419 12,419 12,428

u

v

1,342

v231 v232 v233 v234 v331 v332 v333 v334

v241 v242 v242 v241 v341 v342 v342 v341

1,092 921 633

v41 v51 661,847 v41 v52 661,847 v42 v51 992,770

12,428

CF 1,167 1,003 830 544 1,074 913

u v CF v42 v52 992,770 v151 v161 –145,477 v152 v161 –130,927 v251 v261 −221,918 v252 v261 –199,725 v351 v361 –96,478

775

v352 v361 –86,827

512

➂ The carbon footprint of v2i ! v3j is related to the processing materials and processes and it is independent of the choice of the transport solutions in the third layer. ➃ The carbon footprint of v3i ! v4j is related to the weight of product and the mode of transport, regardless of the usage solutions in the fourth layer. ➄ The carbon footprint of v4i ! v5j is related to product life and usage mode and it is irrelevant to the recycle and disposal solutions in the fifth layer. ➅ The carbon footprint of v5i ! v61 is determined by materials of product and the recycle and disposal solutions.

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The carbon footprint values of the top three shortest paths in the sub-digraphs respectively starting from three raw material solutions are calculated by the software as shown in Table 3.

Table 3. Carbon footprint values of the top three shortest paths in the sub-digraphs v11 1 732,504 2 733,206 3 1,049,158

v12 772,520 773,139 1,081,528

v13 736,565 737,118 1,058,092

The software automatically recommends the shortest three paths of the whole digraph as the best alternative for the low-carbon design of the pile leg. The carbon footprint values of the designs are 732,504, 733,206, 736,565, and the unit is kgCO2 e. The corresponding detailed designs are as follows. (1) The integrated design of 732,504 kgCO2 e carbon footprint: v11 ! v22 ! v34 ! v41 ! v52 ! v61 . (2) The integrated design of 733,206 kgCO2 e carbon footprint: v11 ! v21 ! v31 ! v41 ! v52 ! v61 . (3) The integrated design of 736,565 kgCO2 e carbon footprint: v13 ! v22 ! v34 ! v41 ! v52 ! v61 . The integrated design is composed of the corresponding nodes above which represent the solutions in all life stages. Add all carbon footprint between two nodes of each design according to Table 2 to verify the accuracy of the results. Obviously, the calculated results are right. It is more convenient to obtain the designs with better carbon footprint index by using this software.

5 Conclusion Low-carbon design is not only an important part of improving the market competitiveness of product, but also is great significant in environmental protection and sustainable development. The improved graph-based product low-carbon design model in this paper can calculate the product life cycle carbon footprint more accurately, and it can assist designers to make more scientific decisions and obtain the best comprehensive product design more efficiently. Taking the pile leg of offshore platform as an example, it is shown that this method is worthy of application in low-carbon design of products.

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Comfort of Minors’ Sitting Posture in Learning Based on Motion Capture Chunqiang Zhang1(&), Xiaomin Ji1, Yanmin Xue1, and Chunmei Zhang2 1

Xi’an University of Technology, Xi’an 710054, China [email protected], [email protected], [email protected] 2 Air Force Engineering University, Xi’an 710051, China [email protected]

Abstract. The poor sitting posture caused by unreasonable design of desks and chairs has caused great damage to minors’ health. In case of constantly increasing time for home study, a comfortable sitting posture is of great significance. This study used motion capture technology to analyze the parameter settings of learning desks for minors and the rules of human joints angle change of in sitting posture. It was found that different design parameters of learning desks affect the comfort of human sitting posture. Compared with the sitting posture in reading, the height and angle of desktop have a greater impact on the comfort of sitting posture in writing. Desktops are required to be designed in varying angles for the sitting posture in writing and reading. Thus, the two functions are separated in desktop design. Keywords: Sitting posture in learning  Comfort  Joint angle  Motion capture

1 Introduction There are a large number of minors in China, accounting for about a quarter of the national population. Most of the children in cities have their own rooms of furniture, leading to the demand for children’s furniture purchase in families. Desk and chair are important parts of children’s furniture. However, there are some problems that can not be ignored when minors are intimately exposed to such furniture in learning. And a poor sitting posture has caused some diseases, including myopia, hunchback and so on. According to the survey data of children’s furniture market, children have an extremely high incidence of myopia in China, the reason for which lies in the unreasonable scale design in the children’s desks and chairs, thus resulting in an urgent need for designers to study and analyze the problems under the new environment and standards. Moreover, parents should attach importance to such problems. Especially when the time for home study is constantly prolonged, a comfortable sitting posture is of great significance. This project is supported by MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Project NO.14YJCZH199). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 864–876, 2020. https://doi.org/10.1007/978-981-32-9941-2_72

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2 Review of Literature The research on the comfort of sitting posture is mainly involved in office desks and chairs [1, 2], seats for vehicles [3] and seats for operators in equipment [4]. At present, the definition of comfort or the comfort of sitting posture itself has not been widely recognized, while some researchers explain the comfort of sitting posture as two extremes in a continuum and believes that comfort and discomfort are two opposite ends, and have continuous grades, ranging from extreme discomfort to moderate state and then to extreme comfort. Since people tend to classify the grades of the process from extreme positive to extreme negative naturally and subjectively, the grading scale is used to evaluate the seats according to such principle [5]. Some researchers hold that the comfort of sitting posture refers to two sets of varied factors [6–8], and then conceptualize comfort into two discrete states, namely, existence of comfort and lack of comfort. So the comfort is defined as non-existence of discomfort, and vice versa [9], which means that comfort does not necessarily exert a positive impact [10]. In view of this, the ultimate goal of the seat designer is to eliminate the discomfort, so that users will not be affected by the seat because of the discomfort when using it [11]. Besides, some researchers believe that comfort and discomfort are two separate concepts, each of which has a continuous hierarchy. Studies show that comfort and discomfort are obviously affected by various variables [12]. According to the grading scale of the factors related to comfort and discomfort, the seat with high score of comfort is merely associated with the low score of discomfort, while the seat with a low score of discomfort does not mean that it is highly comfortable. Moreover, the score of comfort will drop sharply with the increase in the score of discomfort, which indicates that discomfort factors play a leading role in the perception of comfort and discomfort while comfort factors occupy a secondary position [7, 13]. However, researchers generally believe that comfort or discomfort of sitting posture is a subjective feeling, which is affected by various physiological and psychological factors, while comfort and discomfort of sitting posture is a response to the environment [14]. Therefore, the study on comfort of sitting posture is mainly carried out by means of subjective evaluation, as comfort or discomfort of sitting posture is based on subjective perception. Subjective evaluation is the most direct way to test the comfort of sitting posture, especially for the change in pain, subjective evaluation is the only approach [15]. However, there are some difficulties in quantitative interpretation by means of subjective evaluation. First of all, seat users must be aware of the differences between comfort and discomfort. Compared with discomfort in varying degrees, it is more difficult to perceive the comfort in varying degrees. Second, it is quite difficult for everyone to describe the feeling of comfort and discomfort. Finally, it may be less likely for the source of comfort or discomfort to be associated with some features of chair design. In the comparison of varying degrees of seat comfort, it is difficult to remember the feelings of comfort and discomfort [16]. The advantage of objective measurement is that it has little dependence on the subjects and less likely to have errors or deviations. It is more appropriate in the earlier stage of product design. However, it is always indirect to determine the comfort and discomfort of sitting posture by means of objective measurement. After the factors concerning the comfort or discomfort of sitting posture are

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defined, the corresponding measurement method is determined. At present, a number of objective methods can be used to quantify the subjective comfort and discomfort of chairs [14], including anthropometric evaluation [17, 18], pressure distribution [19, 20] on the seat and back, spinal load and posture [21–23], electromyogram (EMG) [24], heart rate variability [25–27] and body movement frequency. An uncomfortable seat affects the muscular and skeletal systems of the waist and back. Because the pelvis moves forward with a small amount of activity in sitting posture, human spine may be protruded. The relationships between lumbar curvature, pelvic inclination and their corresponding discomfort was studied and analyzed, indicating that the discomfort of seats can be determined by the changes in posture [28]. Different tasks and sitting postures, such as writing, computer office, notebook operation and so on, will affect the comfort of human neck, wrist and other parts [29, 30]. As for the different motions in sitting posture, the angle and moment of trunk, thigh and knee can be obtained by means of motion capture and relevant software analysis. The comfort of seats can be evaluated by a comparative analysis of data differences [31]. Sitting postures in learning are mainly divided into postures in writing and those in reading. In writing, the trunk of the human body is supported by the seat and the trunk can be in a forward, vertical or backward posture. There is a certain angle between the head and the trunk to keep the eyes effectively positioned on the desktop. The upper limbs can be suspended or supported by the desktop, with fingers grasping the pen holder tightly and the waist moving. When the arm is suspended, it is necessary to adjust the position of the upper limb joints in the three-dimensional space to ensure that the pen tip moves along the fixed line of the desktop. When the arm is supported by the desktop, the forearm gets close to the desktop and the upper arm drives the forearm and hand to move on the desktop to ensure that the pen tip is accurately positioned. In reading, the postures and movements of the trunk and head are similar to those of the one writing, but the upper limbs do not need to be positioned in a continuous and accurate way for a long time. The movement and requirement of human body vary from each other in writing and reading, so desks and chairs should be designed in different ways. But in general, the two are intersected in the process of learning. In other words, desks and chairs should not only meet the needs of those who are writing, but also meet the needs of those who are reading. This study analysis the variation of sitting posture and joint angles. The relationship between these parameters and comfort and discomfort of sitting posture in learning will be constructed.

3 Experiment Settings 3.1

Subjects

Six students (4 boys and 2 girls) aged between 15 and 17 were selected. They were 1,750 mm tall, plus or minus 5 mm, and they were in good condition, without any spine diseases. All subjects volunteered to complete the experimental tests.

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Neuron Motion Capture System

Neuron motion capture system is not restricted by the experimental environment and portable. The system was used in this study in order to obtain related data in a real environment. Neuron motion capture system, a motion capture system based on the MEMS inertial sensor with small child nodes and modules, integrates accelerometer, gyroscope and magnetometer for inertial measurement of sensor nodes. Neuron sensor nodes output data at a rate of 60/120 fps and the data of all sensors will be imported into Hub master node. Then the Hub master node transmits the data to computer by cable ways of USB or wireless ways of WIFI. While users can also record the data on the memory card through the built-in Micro SD card slot. By connecting the Axis Neuron or Axis Neuron Pro platforms on the computer, users can manage and calibrate the hardware of the Neuron motion capture system, record and output high-quality motion capture data. (1) Human dimensions of Neuron motion capture system 12 human dimensions are defined in the Neuron motion capture system for the main joints and parts of the human body, including the height of head from upper lip to head top, the length of neck from upper lip to C7 (7th vertebra), the length of body from C7 to head of femur, shoulder width, upper arm length, forearm length, palm length, hips width, thigh length, leg length, ankle height and foot length. Through actual measurement, as shown in Table 1, the dimension parameters of subjects were input into the Neuron motion capture system. Table 1. Dimensions of subjects mm No.

Head Neck Body Shoulder width

Upper arms

Forearm Palm

Hip Upper width legs

Lower legs

Heel Foot height length

1 2 3 4 5 6 Mean

165 98 170 96 162 102 168 100 172 96 166 94 167.2 97.7

255 265 260 262 268 265 262.5

250 248 252 250 245 245 248.3

240 235 245 240 236 240 239.3

410 405 415 416 414 420 413.3

78 80 75 79 75 82 78.2

574 583 588 576 573 575 578.2

340 345 342 340 345 338 341.7

185 180 190 187 182 186 185.0

415 418 412 410 418 420 415.5

260 265 258 263 262 256 260.7

(2) Skeleton and rotation angle of Neuron motion capture system Neuron motion capture system defines 21 major skeleton structures. Three displacements and three rotation variables of the hips are the actual spatial coordinates. Now the hips coordinate system is defined, as the origin of coordinate is given according to the human dimension parameters of the Neuron system. The intersection line between the horizontal plane and the coronal plane of the human body passing through the origin is X-axis, and the left side of the human body is positive. The intersection line of the coronal plane and the median plane of human body passing through the origin is Y axis, and the direction of human head is positive. The intersection line between the horizontal plane and the median plane

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of the human body passing through the origin is Z axis, and the front of the human body is positive. The displacement and rotation of other skeletal structures are relative motions concerning the parent skeleton. The skeletal data obtained by the coordinate system and the Neuron motion capture system are transformed into visual human skeleton, as shown in Fig. 1.

Fig. 1. Skeleton structures and coordinates

3.3

Tasks and Desk and Chair Setup in Sitting Posture

The height of the seat can be adjusted, its width is larger than the hips width actually measured. The desktop is adjustable in height and angle. The subjects were required to complete the writing and reading tasks for a certain time respectively. 3.4

Testing Process

After completing a day’s schooling task normally, the subjects were asked to write for 30 min and read for 30 min after dinner at seven o’clock at night. Data was recorded by Axis Neuron platform, as shown in Fig. 2. After the task, the subjects filled in the comfort questionnaire according to their own feelings, including the comfort level of the whole body, waist, neck, upper limbs and other local parts. Each part is divided into seven levels, “1” represents very uncomfortable, “4” represents normal and “7” represents very comfortable. After each experiment, the subjects rested for 30 min and then repeated the task more than once. According to the experimental settings of different desktop parameters, one test item should be completed every day and the next test item should be carried out every two or three days. Each test captured about 100,000 frames of displacement and angle changes of various parts and joints of the human body.

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Fig. 2. Motion capture

3.5

Data Analysis

By comparing the joint angle of human body under different tasks and desk and chair parameters acquired by 100,000 frames of motions captured, the motion threshold of joint angle was determined. The frequency of the change of spine angle and the comfortable angle of the head to make the body comfortable in different sitting postures was analyzed. Then the comfortable angles of the spine, arms and head of human body in sitting posture were analyzed.

4 Experiment Design and Analysis The seat height, desktop height and desktop angle are set up. The relationship between these parameters and learning environment comfort will be constructed by analysing the variation of sitting posture and joint angle. 4.1

Settings of Desk and Chair Parameters

(1) Desktop heights The subjects are 1,750 mm tall, and the height of the seat was adjusted to 440 mm according to the popliteal height in human dimensions, and its width was 500 mm, larger than the hips width actually measured in sitting posture, and its depth was 450 mm. By referring to the elbow height of a person with a height of 1,750 mm, the height of the desk was set. On the basis of the seat height, the average heights of the desktop were H1 (662 mm) which plus 60 mm when it is lower than the elbow height in sitting posture, H2 (722 mm) when it is equal to the elbow height, H3 (782 mm) when it is higher than the elbow height and H4 (842 mm) when it is higher than the elbow height respectively, as shown in Table 2.

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No. H1 H2 H3 H4 Desktop height Elbow height-60 Elbow height Elbow height + 60 Elbow height + 120 Test Height 662 722 782 842

(2) Desktop angles The subjects in this part were 1,750 mm tall, and the height of the seat was the same as that in the above-mentioned tests. The height of the side of the desktop close to human body was set as 760 mm according to the functional sizes of chairs and desks for educational institutions in china, and the angles of the desktop were set as A1 (level), A2 (10°), A3 (30°) and A4 (45°) respectively. 4.2

Data Processing and Analysis

The data of bones including 9 rotation angles of hips, spine, spine 1, spine 2, spine 3, neck, head, right arm and right fore arm were processed and analyzed. The bending angle of human trunk in sitting posture can be obtained based on the dimensions and rotation angles of hips, spine, spine 1, spine 2, spine 3, and neck. Figure 3 shows the real-time changes of the forward tilt angle (X-axis rotation, 15000 Frames) of the human trunk under different heights of sitting postures in writing. It can be seen that human body needs to adjust itself to a comfortable state through periodic changes of body angle under any height in sitting posture. The height of H3 has a strong rule of adjustment interval of 3000 frames. This means that the body needs to adjust every minute.

60

H1 H3

50

H2 H4

X-axis rotation

40 30 20 10 0 1 683 1365 2047 2729 3411 4093 4775 5457 6139 6821 7503 8185 8867 9549 10231 10913 11595 12277 12959 13641 14323

-10

Time

Frames

Fig. 3. X-axis rotation of trunk

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Table 3 shows the mean joint angles when minors are writing and reading with four desktop heights. Table 3. Joint rotation at different desktop heights Desktop heights Writing H1 H2 H3 H4 X-Axis rotation (°) Trunk 33.0 29.8 18.7 18.3 Head 55.7 39.9 41.1 32.4 RightArm −29.4 −27.0 −22.6 −25.7 RightForeArm 8.1 3.2 −5.3 −12.4 Y-Axis rotation (°) Trunk −4.1 −2.1 −0.5 −2.5 Head 1.1 −4.1 −3.1 1.5 RightArm 49.7 51.1 40.2 51.0 RightForeArm 90.2 84.4 97.0 90.9 Y-Axis rotation (°) Trunk −5.7 −4.0 −5.0 −4.5 Head 0.2 −6.8 −5.1 −2.4 RightArm 35.9 34.2 27.1 13.1 RightForeArm −7.7 −8.1 7.8 4.1

Reading H1 H2

H3

H4

40.6 31.4 23.4 18.6 49.0 36.6 30.7 26.9 −21.6 −25.0 −25.9 −27.2 19.9 11.1 3.3 −8.7 −4.0 −2.7 2.2 4.3 −16.5 −13.0 −13.2 −13.9 49.2 46.6 34.3 42.9 96.1 93.7 103.9 104.3 −10.1 −14.1 38.2 4.3

−8.2 −8.5 35.3 12.4

−8.8 −9.3 33.7 20.9

−2.2 −2.0 19.5 23.8

Table 4 shows the mean joint angles of minors with different desktop angles in writing and reading. Table 4. Joint rotation at different desktop angles Desktop heights Writing H1 H2 X-Axis rotation (°) Trunk 18.7 22.3 Head 41.1 28.8 RightArm −22.6 −26.1 RightForeArm −5.3 14.9 Y-Axis rotation (°) Trunk −3.3 −10.1 Head −3.1 −12.6 RightArm 40.2 57.4 RightForeArm 97.0 96.9 Y-Axis rotation (°) Trunk −5.0 −6.3 Head −5.1 −12.2 RightArm 27.1 29.3 RightForeArm 7.8 10.8

H3

Reading H4 H1 H2

19.2 25.3 −30.7 40.8

– – – –

22.9 22.5 17.3 8.0 30.7 22.0 21.2 18.7 −25.9 −28.8 −20.2 −23.5 3.3 31.2 32.1 36.1

−16.3 −19.0 45.3 88.7

– – – –

−13.0 −23.4 −16.4 −23.2 −13.2 −22.2 −17.5 −18.7 34.3 47.6 37.0 41.3 103.9 97.8 103.1 99.1

−8.2 −7.4 52.9 −1.1

– – – –

−8.8 −11.8 −7.8 −7.3 −9.3 −12.2 −11.5 −13.2 38.2 47.3 54.4 58.9 20.9 −4.6 3.6 −4.0

H3

H4

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In writing, it can be seen that the trunk of human body which compose of hips, spine, spine 1, spine 2, spine 3, and neck along the X axis bends greater when the desktop is too low, and that when the desktop is as tall as H3, the joint angle changes slightly. The mean values of trunk angle are H1 (32.96°), H2 (29.83°), H3 (18.74°) and H4 (18.27°). In reading, the trunk bends are same as the writing. The mean values are H1(40.57°), H2 (31.43°), H3 (23.39°) and H4 (18.55°). Figure 4 shows the X-axis rotation angles of the trunk with four different desktop when minors writing and reading. In both writing and reading, the Z-axis rotation angles of trunk are negative that reflects the human body tilts to the left.

50.00 Trunk X-axis rotation

40.00 30.00 20.00 10.00 0.00 H1

H2 Writting

H3

H4

Reading

Fig. 4. X-axis rotation of trunk (desktop heights)

Head X-axis rotation

The X-axis rotation angle of the head varies with four different desktop heights, resulting in different visual angles, with the values of H1 (55.66°), H2 (39.89°), H3 (41.13°) and H4 (32.42°) in writing, and H1 (48.97°), H2 (36.61°), H3 (30.66°) and H4 (26.90°) in reading. It can be seen that the head angle of reading is less than writing at the same height of desktop, as shown in Fig. 5.

60.00 50.00 40.00 30.00 20.00 10.00 0.00 H1

H2 Writting

H3

H4

Reading

Fig. 5. X-axis rotation of head (desktop heights)

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The Z-axis rotation angles of right arm are restricted by desktop heights, with the values of H1 (35.91°), H2 (34.16°), H3 (27.09°) and H4 (13.15°) in writing, H1 (33.69°), H2 (35.26°), H3 (38.22°) and H4 (19.54°) in reading. Figure 6 shows the higher desktop (H4), the lower arm angle. The X-axis rotation angles of right arm range from 20 to 30°, and Y-axis rotation angles range from 40 to 50°.

40.00 RightArm Z-axis rotation

30.00 20.00 10.00 0.00 H1

H2

Writting

H3

H4

Reading

Fig. 6. Z-axis rotation of right arm (desktop heights)

The Y-axis rotation reflects the included angle of right fore arm and right arm to keep comfort, the angles range from 85 to 105°. The forward tilt angle (X-axis rotation) of the human trunk were about 20° when minors sit in front of the desktop with different angles. When the angles of desktop are more than 10° (A3, A4), the arm is not supported by the desktop. So the data of writing posture in A4 state was not captured. The X-axis rotation angle of the head varies greatly under different angles of desktop. The mean values of head angle are A1 (41.13°), A2 (28.78°) and A3 (25. 28°) in writing, and A1 (30.66°), A2 (21.57°), A3 (21.20°) and A4 (18.66°) in reading, as shown in Fig. 7.

50.00

Head X-axis rotation

40.00 30.00 20.00 10.00 0.00 A1

A2 Writting

A3

A4

Reading

Fig. 7. X-axis rotation of head (desktop angles)

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5 Discussion The different height of desktop has a great influence on the local comfort of human trunk and arm in writing. When the desktop is too low (662 mm), the human trunk has a larger bending angle. The frequency of sitting posture adjustment is higher with lower desktop for a long time sitting. While at the height of desktop (782 mm), the sitting posture adjustment is more regular. In order to fit the body comfortable, spine should be kept in a natural bending state. At the low height of desktop (662 mm) which elbow can not been support by desktop will affect the accuracy of hand positioning and lead to fatigue for a long time writing. When the desktop is too high (842 mm), the human spine maintains a certain bending angle as the height of 782 mm which be considered comfortable. But the arm is raised too high, static muscle force is produced, and longterm writing leads to arm fatigue. Desktop height has a certain influence on the visual angle of the head in reading. The lower desktop is, the larger head angle will be lead to, and vice versa. Comfortable visual distance is obtained by adjusting the angle of the spine bending. Most of the subjects feel that the higher the desktop height, the more comfortable and visual clarity it is. But there are other factors that effect on comfort of visual distance, such as the size of the font and the light in reading, and so on. The influence of different angles of the desktop on the comfort of writing state is mainly manifested in the force exerted on the arm of the human body. When the angle is greater than 10°, the desktop can not support the elbow better and it is difficult to write. While the angle is greater than 30°, the subjects think that it is almost impossible to write. If the drawing operation is carried out, the angle is more appropriate at 30°of desktop. But the objects on the desktop need other devices to be fixed to prevent falling off. This study mainly focuses on writing and reading, so there is no data capture for the angle of 45°. The influence on the comfort of reading is mainly manifested in the visual direction formed by the head angle. When the head tends to natural angle, the line of sight and the textbook form a comfortable angle. When the larger angle of the desktop is, the smaller angle of the head will be lead to and the more comfortable it is.

6 Conclusions (1) Compared with reading, the desktop height has a greater impact on the comfort in writing. In case of too low desktop, the elbow is unable to be supported by the desktop. Too high desktop, the upper arm will get fatigued after a long time of writing, which may be caused by the static muscle strength. (2) Excessive tilt angles of the desktop, usually more than 10°, are not conducive to writing, the main reason for which is that the desktop with such a tilt angle is unable to support the right arm. But in reading, it achieves better results when the angle is 45°. (3) The desktop is required in varying angles for the sitting postures in reading and writing, and the two functions should be separated in desktop design.

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References 1. Bendix, T., Winkel, J., Jessen, F.: Comparison of office chairs with fixed forwards or backwards inclining, or tiltable seats. Eur. J. Appl. Physiol. Occup. Physiol. 54(4), 378–385 (1985) 2. Van Dieen, J.H., De Looze, M.P., Hermans, V.: Effects of dynamic office chairs on trunk kinematics, trunk extensor EMG and spinal shrinkage. Ergonomics 44(7), 739–750 (2001) 3. Jianghong, Z., Long, T.: An evaluation of comfort of a bus seat. Appl. Ergon. 25(6), 386– 392 (1994) 4. Mehta, C.R., Tewari, V.K.: Seating discomfort for tractor operators – a critical review. Int. J. Ind. Ergon. 25(6), 661–674 (2000) 5. Shackel, B., Chidsey, K.D., Shipley, P.: The assessment of chair comfort. Ergonomics 12, 269–306 (1969) 6. Lueder, R.K.: Seat comfort: a review of the construct in the office environment. Hum. Factors J. Hum. Factors Ergon. Soc. 25(6), 701–711 (1984) 7. Helander, M.G., Zhang, L.: Field studies of comfort and discomfort in sitting. Ergonomics 40(9), 895–915 (1997) 8. Girard, M., Maciejewski, A.A.: Computational modeling for the computer animation of legged figures. Comput. Graph. 19(3), 263–270 (1985) 9. Floyd, W.F., Roberts, D.F.: Anatomical and physiological principles in chair and table design. Ergonomics 2(1), 1–16 (1958) 10. Branton, P.: Behaviour, body mechanics and discomfort. Ergonomics 12, 316–327 (1969) 11. Bishu, R.R., Hallbeck, M.S., Riley, M.W., et al.: Seating comfort and its relationship to spinal profile: a pilot study. Int. J. Ind. Ergon. 8(1), 89–101 (1991) 12. Zhang, L., Helander, M.G., Drury, C.G.: Identifying factors of comfort and discomfort in sitting. J. Hum. Factors Ergon. Soc. 38(3), 377–389 (1996) 13. Helander, M.G.: Forget about ergonomics in chair design? Focus on aesthetics and comfort! Ergonomics 46(13–14), 1306–1319 (2003) 14. De Looze, M.P., Kuijt-Evers, L.F.M., Van Dieen, J.: Sitting comfort and discomfort and the relationships with objective measures. Ergonomics 46(10), 985–997 (2003) 15. Richards, L.G.: On the psychology of passenger comfort. In: Oborne, D.J., Levis, J.A. (eds.) Human Factors in Transport Research. vol. 2, pp. 15–23. London: Academic Press (1980) 16. Zemp, R., Taylor, W.R., Lorenzetti, S.: Are pressure measurements effective in the assessment of office chair comfort/discomfort? A review. Appl. Ergon. 48, 273–282 (2015) 17. Mohamad, D., Deros, B.M., Daruis, D.D.I., et al.: Comfortable driver’s car seat dimensions based on Malaysian anthropometrics data. Iran. J. Public Health 45(1), 106–113 (2016) 18. Chung, J.W.Y., Wong, T.K.S.: Anthropometric evaluation for primary school furniture design. Ergonomics 50(3), 323–334 (2007) 19. Thakurta, B., Koester, K., Bush, N., Bachle, S.: Evaluating Short and Long Term Seating Comfort, pp. 33e37. SAE Technical Paper 950144 (1995) 20. Guo, L.X., Dong, R.C., Zhang, M.: Effect of lumbar support on seating comfort predicted by a whole human body-seat model. Int. J. Ind. Ergon. 53, 319–327 (2016) 21. Helander, M.G., Zhang, L., Michel, D.: Ergonomics of ergonomic furniture a study of adjustability features. Ergonomics 38, 2007–2029 (1995) 22. Zemp, R., Taylor, W.R., Lorenzetti, S.: In vivo spinal posture during upright and reclined sitting in an office chair. Biomed. Res. Int. 2013(2), 916045 (2013) 23. Baumgartner, D., Zemp, R., List, R., et al.: The spinal curvature of three different sitting positions analysed in an open MRI scanner. Sci. World J. 2012(2), 184016 (2015)

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24. Salewytsch, A.J., Callaghan, J.P.: Can quantified lumbar spine postures and trunk muscle activation levels predict discomfort during prolonged sitting? In: Proceedings of the 31st Annual Conference of the ACE (on CD-rom) (1999) 25. Appelhans, B.M., Luecken, L.J.: Heart rate variability and pain: associations of two interrelated homeostatic processes. Biol. Psychol. 77(2), 0–182 (2008) 26. Le, P., Marras, W.S.: Evaluating the low back biomechanics of three different office workstations: Seated, standing, and perching. Appl. Ergon. 56, 170–178 (2016) 27. Weston, E., Le, P., Marras, W.S.: A biomechanical and physiological study of office seat and tablet device interaction. Appl. Ergon. 62, 83–93 (2017) 28. Vergara, M., Page, M.: Relationship between comfort and back posture and mobility in sitting-posture. Appl. Ergon. 33(1), 1–8 (2002) 29. Asundi, K., Odell, D., Luce, A., et al.: Changes in posture through the use of simple inclines with notebook computers placed on a standard desk. Appl. Ergon. 43(2), 400–407 (2012) 30. Asundi, K., Odell, D., Luce, A., et al.: Notebook computer use on a desk, lap and lap support: effects on posture, performance and comfort[J]. Ergonomics 53(1), 74–82 (2010) 31. Qing, T., Jinsheng, K., Wen-Lei, S., et al.: Analysis of the sitting posture comfort based on motion capture system and JACK software. In: 2017 23rd International Conference on Automation and Computing (ICAC), pp. 1–7. IEEE (2017)

Lightweight Design of Dump Truck Frame Based on Finite Element Method Gongxue Zhang, Sen Yang(&), Shanshan Guo, and Qichen Niu Shaanxi University of Science and Technology, Xi’an 71002, Shaanxi, China [email protected]

Abstract. With the gradual enhancement of people’s awareness of environmental protection, the demand for energy saving and emission reduction of dump trucks is getting higher and higher. In this paper, the finite element analysis software is used to simulate and analyze the two working conditions of a certain type of dump truck frame with greater damage. The simulation results show that the strength and stiffness meet the normal working requirements. Based on this, the lightweight design of the frame is carried out. A new material, high strength steel A610L, is selected to optimize the thickness of the original frame according to the thin shell theory. Then the frame is re-modeled and simulated again under different working conditions. The strength and stiffness of the optimized frame meet the design requirements. After optimization, the weight of the dump truck frame is reduced by 9.47%, the toxic gas in the exhaust is reduced by 4.5%, and the fuel consumption is reduced by 8%. Keywords: Dump truck frame Equivalent iteration

 Lightweight  Simulation analysis 

1 Introduction With the gradual improvement of the regulations on road safety protection by the relevant state departments and the enhancement of people’s awareness of environmental protection, the more stringent the emission control of automobile exhaust is, the lightweight design of automobile has become one of the hot research directions in China. Vehicle’s own weight consumes more fuel than 50% of total fuel consumption in the course of driving. According to incomplete statistics, each vehicle’s own weight reduces one-tenth of the original total weight. Vehicle’s fuel consumption will decrease by 6%–8%, and the emission of toxic gas CO will reduce by 4.5% [1]. The lightweight design of automobiles can effectively reduce exhaust emissions, reduce manufacturing costs and improve vehicle carrying capacity [2]. Dump truck is a kind of vehicle that can automatically unload cargo and reset the carriage through the hydraulic or mechanical control system. According to statistics, the total weight of the dump truck body will be reduced by 0.01 tons, and the emission of carbon monoxide will be reduced by 0.045 cubic meters. However, the quality of Natural Science Research Projects of Shaanxi Science and Technology Department (2014 JM7264). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 877–887, 2020. https://doi.org/10.1007/978-981-32-9941-2_73

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dump truck frame accounts for about 16% of the total quality, so the lightweight design of the dump truck frame is an important part of dump truck optimization design. Many experts and scholars in China have devoted themselves to the lightweight design of dump trucks and put forward many lightweight improvement schemes, such as structural optimization, material substitution, fatigue analysis, and frame. In 2005, Xu and Gao elaborated on the lightweight design of automobiles through CAD/CAE and put forward a research method combining NVH optimization with collision theory optimization [3]. In 2009, Wang of Wuhan University carried out lightweight design and Research on the dump truck body, used hyper mesh to optimize the structure of the car and body, improved the stress concentration and unreasonable parts of the structure design through stress analysis, and reduced the overall quality of the car body by 14% [4]. In the same year, Zhang of Hunan University used a multi-objective genetic algorithm to optimize the body-in-white. Through the design of occupant protection in a frontal collision, the effective arrangement of shock absorber plate thickness and material was realized, and the effect of reducing the body quality was achieved [5]. In 2016, Wang of Chang’an University, based on volume minimization theory, selected Optistruct software to optimize and used Ncode to verify the service life. The final frame quality was reduced by 120 kg [6]. In 2017, Chen, Li and Su of Nanchang Institute of Active Power adopted the method of combining topology optimization with size optimization to lightweight the design of a certain type of lawnmower, and the quality of the optimized frame was reduced by 34.3%[7].In this paper, the dump truck frame is taken as the research object, the finite element method is used to establish the model, and the lightweight design of the dump truck frame is carried out.

2 Three-Dimensional Model Building of Vehicle Frame For the outside width of the dump truck frame, there is no international standard, only the reference width 780 mm, 800 mm, 860 mm. However, domestic automobile enterprises usually determine the width of the frame according to the configuration of parts. Figure 1 is a three-dimensional solid model of frame CATIA.

Fig. 1. Three dimensional solid drawings of the frame

In order to prevent errors in the process of building a finite element model, some structures are simplified without affecting the results. The simplified frame is shown in Fig. 2. The frame is mainly composed of the left longitudinal beam, right longitudinal

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beam, multiple crossbeams, and overturning shaft. The length of the beam studied in this paper is 5900 mm and the width is 772 mm. The frame size data are shown in Table 1.

Table 1. Frame dimension data Left longitudinal beam thickness (mm) 40

Right longitudinal beam thickness (mm) 40

Web thicknes (mm)

Beam thickness (mm)

Transverse front concave thickness (mm)

Lateral back concave thickness (mm)

16

25

20

20

Fig. 2. Frame simplified diagram

3 Establishment of Finite Element Model of Dump Truck Frame The frame is the main assembly base of the dump truck, which accounts for a large proportion of the whole, so its lightweight design space is relatively large [8]. Because there are many components in the frame structure, the grid division of the frame adopts a combination of various methods. In the process of meshing, the unit size is 20 mm, and the frame of the dump truck meshes as shown in Fig. 3.

Fig. 3. Fame grid partition diagram

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4 Working Condition Analysis of Dump Truck Frame (1) Bending condition Bending condition refers to the condition that the dump truck runs at a uniform speed on a straight road under full load and all four wheels of the dump truck land. According to the actual working condition of the dump truck, ANSYS analysis is carried out on the bending condition to check the strength and stiffness. In order to ensure the loading accuracy, the dynamic load coefficient is multiplied by the original load. According to the relevant data, the dynamic load coefficient of dump truck frame under full load and the bending condition is 1.5 [9]. The results of the stress distribution of the dump truck frame under a bending condition are shown in Fig. 4. The maximum stress of the truck frame is 157.63 MPa, which is located on the longitudinal beam. The maximum stress value is less than the yield strength of the material and meets the strength requirements. The stress of the main structure of the frame is shown in Table 2. Table 2. Maximum stress value of components under bending conditions Parts Crossbeam Crossbeam Crossbeam Crossbeam

Maximum stress value (MPa) Parts 1 157.63 2 157.63 3 43.425 4 41.18

Maximum stress value (MPa)

Crossbeam 5 53.273 Crossbeam 6 12.16 Other components 157.63 Longitudinal beam 157.63

Fig. 4. Cloud diagram of stress distribution under bending condition

The displacement distribution of the dump truck frame under a bending condition is shown in Fig. 5. The maximum displacement deformation is 2.355 mm, and the maximum deformation occurs at the longitudinal beam and the third cross beam.

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Fig. 5. Torsional displacement distribution cloud diagram

(2) Torsion condition Torsional condition refers to the condition that one wheel leaves the ground and the other wheels are in a horizontal state when the vehicle is running at full load. By applying 15 mm displacement to the front wheel, the front left and right wheels are required to exert displacement in the opposite direction. Dump trucks under torsional conditions are generally traveling on low-speed, muddy roads. The inertia force of dump trucks is small and the dynamic load coefficient is small. Therefore, the dynamic load coefficient is chosen to be 1.3. The maximum stress of dump truck under full-load torsion condition is 235.42 MPa, which appears at the joint of longitudinal beam and front and rear suspensions. The stress distribution is shown in Fig. 6. The maximum stress value is less than 345 MPa of yield strength of the selected material Q345, so the original dump truck frame meets the strength requirements. Because there is no restraint at the connection position between the front wheel and the frame when the torsion condition is analyzed, the stress value at the connection of the left and right front wheels and the two longitudinal beams of the frame is larger.

Fig. 6. Cloud diagram of torsional stress distribution

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The maximum deformation of the dump truck frame is 10.292 mm under full load and torsion condition. The displacement distribution of the dump truck frame under torsion condition is shown in Fig. 7.

Fig. 7. Torsional displacement distribution cloud diagram

5 Alternative Lightweight Scheme of High Strength Steel for Car Frame The main ways of vehicle lightweight are structural optimization, material optimization, processing technology optimization and so on. Among them, structural optimization and material optimization are widely used. In view of this research object, a new material high strength steel is selected to replace the original material Q345 to achieve a lightweight design. Although the most widely used new materials in recent years are high strength steel, Al-Mg alloy, and composite materials, the frame is the main load-bearing device of the main and auxiliary dump truck. The parameters of alloy and plastic composite materials generally do not meet the requirements of the frame materials. Therefore, the high strength steel A610L is selected to replace the original Q345 to achieve the lightweight design of the frame. 5.1

Equivalent Iteration of High Strength Steel

Dump truck frame is mainly composed of I-beam, channel and square steel, which are assembled by welding or riveting. The high strength steel is selected to replace the original steel plate. According to the thin shell theory, the main stress and shear stress in the X and Y directions of thin-walled parts are known.     Nx  6Mx     jrx jmax ¼   þ  2  t t     Ny  6My     ry  ¼   þ   t   t2  max           sxy  ¼ S þ 6Mxy   t   t2  max

ð1Þ

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In the formula: r; s—Normal stress and bending stress; N—Unit Tension and Compression Internal Force; Mx ; My —Unit bending moment; Mxy —Reverse; t—Microelement thickness; S—internal force. According to formula (1), the maximum values of each stress can be obtained. As the main installation parts of the dump truck, in order not to affect the assembly of other parts, the frame is only changed in thickness and size, and its structure is not changed. Because the stress, bending moment and torsion of the frame before and after material replacement are the same, the formulas are used to iterate the thickness of the original frame. The concrete iteration formulas are as follows: ½r l0 ¼ ½ r 0 l

ð2Þ

In the formula: ½r; ½r0 —Allowable Stress of Existing Steel Plate and High Strength Steel Plate (MPa); l; l0 —Thickness of original steel plate and high strength steel plate(mm). The safety factor of high strength steel plate is unchanged before and after replacing the original steel plate, so the allowable stress in the replacement formula (2) can be calculated by the yield stress of the steel plate.: ðrs Þ l0 ¼ l ðrs Þ0

ð3Þ

In the formula: ðrs Þ—Yield Strength of Original Steel Plate (MPa); ðrs Þ0 —Yield Strength of High Strength Steel (MPa). If subjected to bending stress, (3) is substituted for (1): sffiffiffiffiffiffiffiffiffiffi ðrs Þ l ¼ l ðrs Þ0 0

ð4Þ

In actual working conditions, the frame is subjected to both bending stress and film stress. When high strength steel replaces conventional steel plate, the thickness of high strength steel plate is between bending stress and film stress.:

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ðrs Þ  l0  ðrs Þ0

sffiffiffiffiffiffiffiffiffiffi ðrs Þ l ðrs Þ0

ð5Þ

High strength steel A610L and yield limit of 550 MPa were optimized. The original frame is made of Q345 and its yield limit is 345 MPa. Then, the yield limit of the optimized steel and its original steel is substituted into the formula (5): rffiffiffiffiffiffiffiffi 345 l ¼ l 550 0

ð6Þ

In the iteration process of replacing the original steel plate with high strength steel, the maximum plate thickness is selected due to safety considerations. An integer is taken in steel plate production process. The thickness of each plate of the original frame is substituted into the formula (6), and the thickness data of high strength steel plate are obtained after calculating roundness. Thickness comparison between old and new boards is shown in Table 3.

Table 3. New and old plate thickness comparison table Component name Left longitudinal plate Right longitudinal plate Crossbeam 1 Crossbeam 2 Crossbeam 3 front concave plate Crossbeam 3 after concave plate Crossbeam 4 front concave plate Crossbeam 4 after concave plate Crossbeam 5 front concave plate Crossbeam 5 after concave plate Upper web of the beam

5.2

The thickness of original frame steel plate (mm) 40 40 25 25 20 20 20 20 20 20 16

Plate thickness of high strength steel frame (mm) 32 32 20 20 16 16 16 16 16 16 13

Analysis of Optimized Working Conditions

According to the parameters in Table 3, the frame is re-modeled and the bending and torsion conditions of the frame are analyzed. The stress and deformation of the optimized frame under full-load torsion and bending conditions are obtained by simulation analysis as shown in Figs. 8 and 9.

Lightweight Design of Dump Truck Frame Based on Finite Element Method

a) Torsional deformation nephogram

b) Torsional stress nephogram Fig. 8. Analysis result diagram of frame torsion condition

a) Bending deformation nephogram

b) Bending stress nephogram Fig. 9. Analysis result diagram of frame bending condition

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From Fig. 8(a) it is known that the maximum deformation of the frame is 10.375 mm under full load torsion condition, and the maximum deformation occurs at the longitudinal beam and the first cross beam. From Fig. 8(b), it is known that the maximum stress in full-load torsion occurs at the longitudinal beam, and the maximum stress is 333.13 MPa. The maximum stress in the torsion frame is less than 550 MPa of material yield strength, which meets the strength requirements of dump truck frame. According to the deformation cloud of bending condition Fig. 9(a), the maximum deformation of full load bending condition is 3.4674 mm, and the maximum strain occurs at the joint of the longitudinal beam and rotating shaft. From the full load bending stress cloud Fig. 9(b), it can be seen that the maximum stress of the optimized dump truck frame occurs at the longitudinal beam position of the truck frame under the bending condition, and the maximum stress value of the truck frame is 291.23 MPa, and the maximum stress value of the truck frame is less than the yield strength of material A610L, so the optimized dump truck frame meets the strength requirements. In summary, the optimized dump truck frame meets the normal working requirements of the dump truck. 5.3

Frame Optimization Before and After Comparison

Compared with the parameters of the frame before and after optimization, the weight of the frame after optimization is reduced by 9.5%, the manufacturing cost of the frame is reduced by 9.467%, the maximum stress value is increased by 39.72%, and the maximum deformation is increased by 6.45%. The parameters of the dump truck frame before and after optimization are compared, as shown in Table 4. Table 4. Comparison before and after a lightweight Comparison parameter Maximum stress (MPa) Maximum deformation (mm) Maximum deformation (kg) cost (RMB)

Before optimization 238.42 10.292 607.69 2479.98

After optimization 333.13 10.375 550.17 2245.24

Amount of change Increase 39.72% Increase 6.45% Reduce 9.47% Reduce 9.467%

6 Conclusion In this paper, the light weight of the frame is achieved by using a material optimization method. Firstly, based on the thin shell theory, the relationship between the thickness of the frame and the stress is reduced, and the thickness of the original frame is reduced iteratively. In order to ensure the safety of the frame, the optimized dump truck frame is simulated. The results show that the strength and stiffness of the frame meet the working requirements of the dump truck. After optimization, the weight of the dump truck frame is reduced by 9.47%, the toxic gas in the exhaust is reduced by 4.5%, and the fuel consumption is reduced by 8%. Therefore, the lightweight design of the dump truck body achieves the purpose of energy saving and emission reduction and meets the requirements of green manufacturing.

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References 1. Huai, T., Shah, S.D., Miller, J.W.: Analysis of heavy-duty diesel truck activity an emissions data. Atmos. Environ. 40, 2333–2344 (2006) 2. Wang, H., Yuan, D., Zhang, L.: Analysis of the bearing capacity of the chassis frame of 2500 shale gas fracturing truck. J. Gansu Sci. 27(04), 69–73 (2015) 3. Xu, Y.: Application of CAE optimization technology in automobile body lightweight design. In: Conference of China Mechanics Society, Beijing (2005) 4. Wang, X.: Study on Lightweight of Large Tonnage Dump Truck. Wuhan University of Technology, Wuhan (2009) 5. Zhang, Y., Li, G., Wang, J.: Application of multi-objective genetic algorithm in vehicle lightweight optimization design. China Mech. Eng. 20(04), 15–20 (2009) 6. Wang, G., Ren, J., Fu, N., et al.: Subframe lightweight based on numerical simulation and dynamic and static test. J. Chang’an Univ. (Nat. Sci. Ed.) 35(05), 137–144 (2015) 7. Chen, Y., Li, S., Su, Y.: The lightweight design of the mower frame combined with topology optimization and size optimization. J. Chongqing Univ. Technol. (Nat. Sci.) (01), 28–35 (2017) 8. Liu, W.: Automobile Design. Tsinghua University Press, Beijing (2001) 9. Zhong, P.-s, Zhao, D., Sun, X.: Modeling and modal analysis of automobile frame based on ANSYS [J]. Mech. Des. Manuf. 06, 52–54 (2008)

Topological Optimization of the Front Beam in Metal Extruders Xugang Zhang1, Peilin Yang1(&), Xiaole Cheng2, and Yi Hou1 1

2

School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China [email protected], [email protected], [email protected] State Key Laboratory of Metal Extrusion and Forging Equipment Technology, Xi’an 710032, China [email protected]

Abstract. According to the outlet shape of the front beam in metal extruders, a topology optimization model of the front beam structure based on the variable density method is established. The effects of the penalty factor on the optimization results are analyzed. By changing the volume fraction, the front beam topology structure with suitable strength and the maximum stiffness is obtained. Based on the topology optimization results and combined with the manufacturing process, the structure of the front beam is redesigned to ensure the manufacturability of the optimized front beam. Keywords: Front beam Extruder

 Topological optimization  Finite element method 

1 Introduction Metal extruder is a kind of important equipment for extruding process. Designers usually use analogy and empirical methods to design the front beam structure of extruders. Those methods are often tedious and inefficient, which will lead to a front beam with excessive safety factor and material waste. Therefore, it is of great significance to optimize the front beam of extruders. In recent years, researchers have adopted finite element method to optimize the design of the components of the frame [1–3]. Pu et al. [4], used finite element to optimize the frame by changing some parameters of the structure. Jiang et al. [5], carried out dimension optimization design for the front beam of the extruder. In their approach, several parameters of the front beam and weight are taken as optimization variables and objective function respectively. Li [6] optimized the dimension of the front beam of a large extruder by using finite element method and genetic algorithm. Zhou et al. [7], took the position of the pull rod of the frame and the thickness of the This project is supported by the fund of the State Key Laboratory of Metal Extrusion and Forging Equipment Technology (Grant No. B1608101.w1801). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 888–897, 2020. https://doi.org/10.1007/978-981-32-9941-2_74

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beam as optimization variables, used the particle swarm optimization algorithm and finite element method to optimize the stress of the pull rod, and reduced the weight of the frame. In the current research, the structural optimization of the front beam of the extruder mainly focuses on dimension optimization, which is conducted when the structure of an extruder has been determined. In this paper, according to the outlet shape of the front beam required by an extruder to extrude wide flat profiles, a optimization model of the front beam in metal extruder that is based on the variable density method is established. The effects of penalty factor and volume fraction on topology optimization results are analyzed. According to the results of topology optimization and combined with the manufacture technology of the front beam, the structure of the front beam is redesigned.

2 General Requirements of the Front Beam Structure In order to extrude wide flat profiles and match with the flat container, the outlet of the front beam is required to have an elliptical shape, as shown in Fig. 1.

Fig. 1. Main dimensions of the front beam

The front beam in metal extruder is usually a box-like beam structure welded with strengthening ribs, so the six sides of the front beam are required to be retained. In addition, the front beam should have: (1) Blind holes with a diameter of 330 mm in the center of the front beam (for fitting pressure pads); (2) Four through-holes with a diameter of 145 mm arranged symmetrically in the front beam (for fitting pull rods). According to the above requirements, the optimized areas and the non-optimized areas of the front beam are shown in Fig. 2. The detailed description is as follows:

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(1) The inner and outer side plates with thickness of 50 mm in the front beam are retained. (2) The inner surface of the fitting holes of the pull rods and the inner surface of the outlet of the front beam are retained. (3) The outer surface of the surrounding lateral plates and the loading surface of the front beam are retained. (4) The minimum dimension constraint of the model entity is set as 40 mm to facilitate manufacturing.

Fig. 2. Schematic diagram of the optimized areas and the non-optimized areas

3 Topological Optimization Model of the Front Beam 3.1

Load and Boundary Conditions

The load acting on the front beam includes: 00

(1) The residual preload F on the contact surface of the front beam and the pressing 00 sleeve, F ¼ 36:46 Mpa. (2) Working load F acting on the loading surface of the front beam, F = 73.91 Mpa. The displacement boundary conditions of the front beam include: (1) The displacement constraint of Y-direction is applied to the bottom surface of the front beam; (2) The displacement constraint of X-direction is applied to the foot on both sides of the front beam; (3) The displacement constraint of Z-direction is applied to the contact surface of the front beam and nuts. Figure 3 is a schematic diagram of load and boundary conditions for topological optimization of the front beam, where A1 is the contact surface of the front beam and pressing sleeve, A2 is the surface of applying working load, A3 is the contact surface of the front beam and nuts.

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Fig. 3. Schematic diagram of load and boundary conditions

3.2

Optimization Objective and Constraints

In this paper, the front beam is optimized by taking the minimum compliance (maximum structural stiffness) as an objective, and the volume fraction of the front beam and the maximum principal stress as constraints. The mathematical model of topology optimization based on the variable density method is as follows. P minC¼ ni¼1 cðqi Þ s:t: Vi =V0  D r1  ½r > : 0  qmin  qi  1ði ¼ 1; 2; 3; . . .; nÞ 8 >
30%), and achieve clearer order spectra than those of the single-stage generalized phase demodulation based tacho-less OT. In addition, our method is time saving as only the simple calculations (such as coarse time-frequency transform, Fourier transform and Hilbert transform) are employed. The rest of the paper is organized as follows: the theoretical basis of generalized demodulation is demonstrated in Sect. 2. The flowchart of multi-stage generalized phase demodulation based tacho-less order tracking method is illustrated in Sect. 3. Simulation verification and experiment verification are investigated in Sects. 4 and 5, respectively. Finally, conclusions are given in Sect. 6.

2 Theoretical Basis of Generalized Demodulation [2] For a signal xðtÞ, its Fourier transform can be defined as follows: Xð f Þ ¼

þZ1

xðtÞ expðj2pftÞdt

ð1Þ

1

Supposing the signal x(t) is a sinusoidal component whose frequency is f0, the Fourier transform of x(t) will peak at f0, The sinusoidal component can be extracted by

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a band pass filter whose center frequency is f0 and it may be transformed to time domain by an inverse Fourier transform. Considering the signal x(t) containing two time-varying frequencies of f0 + s(t) and 2f0 + 2s(t), its Fourier transform may not peak at f0 and 2f0. When the IFs of two components are overlapped in the frequency domain, any one of them cannot be extracted by means of a band pass filter. The following generalized demodulation operator is taken into account: Z OPðtÞ ¼ expðj2p

^sðtÞdtÞ

ð2Þ

The Fourier transform (Xd (f)) of the demodulated signal (x(t)OP(t)) is shown as follows: Z Xd ðf Þ ¼

þ1 1

Z ^sðtÞdtÞ  expðj2pftÞdt

xðtÞ  expðj2p

ð3Þ

The first and second component of x(t) will peak at f0 and distribute in the frequency range of 2f0 to 2f0 + s(t) in the Xd (f), respectively, when the ^sðtÞ in Eq. (2) is equal to sðtÞ of the IFs. Thus, the first component in Xd (f) may be extracted by means of a conventional band pass filter and transformed in the time domain by an inverse Fourier transform, which is defined as follows: Z xðtÞ ¼

þ1

1

Z Xd ðf Þ  expðj2p

^sðtÞdtÞ  expðj2pftÞdf

ð4Þ

3 Multi-stage Generalized Demodulation Based Tacho-Less Order Tracking The proposed multi-stage generalized demodulation based tacho-less OT is a multiiteration approach in whose first stage the 1st shaft rotational harmonic for demodulation; subsequently, signals are resampled in accordance with the phase (demodulated from the extracted harmonic) in the first stage. Afterwards, resampled signals are used for the next iteration, whose higher orders are utilized for demodulation. The iteration is terminated until the order spectra are satisfactorily clear. It is schematically shown in Fig. 1 and three main steps of the approach are demonstrated in detail as follows: Step 1: To preliminarily estimate the instantaneous rotational frequency (IRF) based on the time-frequency distribution. The first few shaft rotational harmonics and gear meshing content in the frequency spectra of the vibration signal are usually visible as the shaft vibration signal and the gear meshing vibration signal are dominant in the vibration response of gear [10]. However, they may not be extracted by means a typical band pass filter when the rotational speed changes relatively greatly (>30%) as they are overlapped with adjacent harmonics in the frequency domain. Thus, the time-frequency distribution based IF estimation method is applied to preliminary estimate the IF of a desired rotational

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Fig. 1. Flowchart of multi-stage generalized demodulation based tacho-less order tracking

related harmonic (the 1st shaft rotational harmonic is recommended). Since the signal is not resampled directly according to the estimated IRF, the coarse time-frequency transform such as spectrogram can be used in this step to reduce the computation time. The ridge extraction algorithm in article [22] can be used to extract the IF from the time-frequency distribution of the signal.

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Step 2: To extract the mono-component of the shaft rotational harmonics base on generalized demodulation. Supposing the extracted IF of the 1st shaft rotational harmonic in Step 1 is close to the actual IRF (fs (t)) and is expressed as ^fs ðtÞ. The generalized demodulation operator is constructed in accordance with ^fs ðtÞ, which is defined as follows: Z OPðtÞ ¼ expðj2p

T

ð^fs ðtÞ  ^fs ð0ÞÞdtÞ^fs ðtÞ

ð5Þ

0

where T and ^fs ð0Þ represent the time duration of signals and the ^fs ðtÞ at t = 0, respectively. The demodulated signal is defined as follows: xd ðtÞ ¼ ðxðtÞ þ HTðxðtÞÞÞ  OPðtÞ

ð6Þ

where HT(x(t)) is the Hilbert transform of x(t), which is used to avoid the meaningless negative frequency in the time-frequency plane [22, 23]. The IF trajectory of the 1st shaft rotational harmonic of xd(t) is parallel to the time axis approximately and separable from other harmonics in the frequency domain. Thus, the spectra of the 1st shaft rotational harmonic of xd(t) can be extracted by means of a band pass filter, and expressed as (Xs(f)). The shaft rotational harmonic (expressed as xs(t)) of x(t) can be calculated by: Z xs ðtÞ ¼ Reð

þ1

1

Z Xs ðf Þ expðj2p

T

ð^fs ðtÞ  ^fs ð0ÞÞdtÞdf

ð7Þ

0

Step 3: To resample vibration signals and obtain the order spectra. The instantaneous phase (uðtÞ) of the shaft rotational harmonic can be calculated by: uðtÞ = unwarpðarctanð

HTðxs ðtÞÞ ÞÞ xs ðtÞ

ð8Þ

Vibration signals are resampled with an equal angular increment in accordance with uðtÞ. The order spectra can be obtained by performing Fourier transform to resampled vibration signals.

4 Simulation Verification Vibration signal of a gear are usually consists of shaft rotational harmonic (fs), gear meshing content (fm = Kfs, where K is the number of teeth), and their harmonics (nfs and mfm) as the shaft rotational vibration and the gear meshing vibration are dominant in the vibration response of the gear [10]. Any local fault on gear leads to amplitude and frequency modulation to the vibration signal [1]. A simulation vibration signal model of a gear with local fault can be defined as Eq. (9) [12, 24].

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xfault ðtÞ ¼ þ

XN n¼1

XM

An cosð2pnfs ðtÞt þ un Þ

B ð1 þ am ðtÞÞ cosð2pmKfs ðtÞt þ hm þ bm ðtÞÞ m¼1 m

ð9Þ

where: M, N, An, Bm, un and hm represent the number of shaft harmonics, the number of gear meshing harmonics, the amplitude of the nth shaft rotational harmonic, the amplitude of the mth gear meshing harmonic, the initial phase of the nth shaft rotational harmonics and the initial phase of the mth gear meshing harmonics, respectively. The amplitude and phase modulation functions (am(t) and bm(t)) are described as: am ðtÞ ¼ bm ðtÞ ¼

XL l¼1

XL l¼1

aml cosð2plfs ðtÞt þ aml Þ

ð10Þ

bml cosð2plfs ðtÞt þ bml Þ

ð11Þ

where: L, aml , bml , aml and bml represent the number of modulation harmonics, the amplitude of the lth amplitude modulation harmonics, the lth amplitude of frequency modulation harmonics, the initial phase of the lth amplitude modulation harmonics and the initial phase of the lth frequency modulation harmonics, respectively. A nonlinear rotational speed function fs ðtÞ ¼ 11 þ 10t  1:5t2 (shown in Fig. 2(a)) is utilized to simulate a rotational speed varied from 11 Hz (660 rpm) to 27.7 Hz (1662 rpm) in a period of 5 s. For the simplicity of the simulation, the first two orders of the shaft rotational harmonics and gear meshing harmonics, the first orders of amplitude and the phase modulation functions are only taken into account. The sampling frequency is 4096 Hz and parameters of the simulation signals are listed in Table 1.

Fig. 2. Simulation signal of the gear with local fault: (a) nonlinear instantaneous rotational frequency, (b) waveform in time domain, (c) frequency spectra (0–1000 Hz), (d) spectrogram (0– 1000 Hz).

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Table 1. Parameters of the simulation signal A1

u1

A2

u2

B1

h1

B2

h2

a11 a11

a21 a21

b11 b11

b21 b21

1.2 0.1 p 0.6 0.4 p 3.0 1.6 p 2.0 1.2 p 0.8 0.33 p 0.6 0.2 p 0.1 0.17 p 0.1 –0.5 p

Gauss noise are added to the simulation signal (SNR = −6.4 dB) to simulate those additional noises during the measurement period. The waveform and the frequency spectra of the noisy simulation signal are shown in Fig. 2(b) and (c), respectively. Any fault signature can be identified from the waveform and the frequency spectra as gear vibration signal are submerged by severe noise. The spectrogram of the signal is shown in Fig. 2(d). The general trajectories of IF of the 1st and 2nd gear meshing harmonics can be seen in the spectrogram, whereas the sidebands cannot be clearly identified due to the low resolution of spectrogram and the interference of noise. The spectrogram in the frequency range of 0–60 Hz is shown in in Fig. 3(a). It can be seen that the 1st and the 2nd shaft rotational harmonics are overlapped in the frequency domain so that these two harmonics cannot be separated by means of a conventional band pass filter. The IF of the 1st shaft rotational harmonic is estimated based on the ridge extraction algorithm and plotted in Fig. 3(b). A generalized demodulation operator is constructed in accordance with the estimated IF and the spectrogram of the demodulated vibration signals is shown in Fig. 3(c). The trajectory of IF of the 1st shaft rotational harmonic is approximately parallel to the time axis and the 2nd shaft rotational harmonics may be separated out. Those frequency spectra within the frequency range of 9–14 Hz are extracted and vibration signals are resampled with an equal angular increment of 0.0174 rad (360 samples per revolution)

Fig. 3. Results of the first-stage: (a) spectrogram (0–60 Hz), (b) IF extracted from the spectrogram, (c) spectrogram of the generalized modulated signal (0–60 Hz), (d) Order spectrum obtained by the first stage generalized phase demodulation.

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according to the demodulated phase. The order spectra is shown in Fig. 3(d). It can be seen that the amplitudes of the 1st and the 2nd shaft rotational harmonic are close to the theoretical values in Table 1. However, the higher order spectra (gear meshing harmonics and their sidebands) remains smearing as the higher orders contain progressively growing residual speed variations [12]. The resampled vibration signals in the first-stage are used for the iteration, whose revolution-order spectrogram is shown in Fig. 4(a). It indicates that the gear meshing component (the 15th order) and sidebands (the 14th and 16th orders) are separated during the period of 20–117 revolutions while they are overlapped during the period of 4-10 revolutions. The IF of the gear meshing component (Fig. 4(b)) is estimated from the order-revolution spectrogram. The gear meshing content and its sidebands of demodulated signals are separated and is shown in Fig. 4(c). The resampled signals in the first-stage are resampled again according to the phase demodulated based on the gear meshing content. As shown in Fig. 4(d), the 1st and the 2nd gear meshing harmonics and sidebands introduced by local fault are clear in the order spectra of the second-stage. It can be seen from Figs. 3(d) and 4(d) that the order spectra achieved by the two-stage generalized modulation based order tracking is clearer than those of the single-stage generalized phase demodulation based tacho-less OT. The computation time of the simulation case (20480 data points) is about 0.38 s when the algorithm is run on a laptop with a 2.30 GHz Intel® Core™ i5-6300HQ CPU and an 8.00 GB RAM, using MATLAB 2010b platform.

Fig. 4. Results of the second-stage: (a) revolution-order spectrogram of the resampled signal in first-stage (13–17 orders), (b) IF extracted from the revolution-order spectrogram, (c) revolutionorder spectrogram (13–17 orders) of demodulated signal, (d) Order spectrum of the resampled signal.

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5 Experiment Verification An experiment case was carried out on the gear test rig of our laboratory to validate the effectiveness of the proposed multi-stage generalized phase demodulation method. As shown in Fig. 5(a), the test rig mainly consists of a motor, a testing gearbox, a torque sensor, a reduction gearbox and a magnetic brake. A tachometer outputting one pulse per revolution are located between the motor and the testing gearbox to measure the rotational speed of the shaft of the motor. An accelerometer is mounted on the shell of the testing gearbox to collect the vibration signal. The testing gearbox is a single-stage gearbox with two spur gears, the pinon with 31 teeth and the gear with 42 teeth. A manmade crack with 1 mm depth on the full-width was manufactured on the pinon tooth to simulate the local gear fault (Fig. 5(b)). The sampling frequency of this case is 24 kHz.

Fig. 5. Experiment environment: (a) test rig made up of an AC motor, a testing gearbox, a torque sensor integrated with a speed sensor, a reduction gearbox and a magnetic brake (from right to left), (b) pinon with a man-induced root crack.

The measured IRF of the pinon shaft, the waveform and the spectra of measured vibration signals are shown in Fig. 6(a), (b) and (c), respectively. The IRF of the pinon shaft varies from 12.5 Hz (750 rpm) to 25.1 Hz (1506 rpm) in a period of 8 s. The frequency spectra are blurred due to the time-varying rotational speed. The frequency spectra in the range of 0–60 Hz is shown in Fig. 6(d). It is hard to extract the 1st shaft rotational harmonic by means of a bandpass filter as no clear boundary between the 1st and 2nd shaft rotational harmonics can be identified. The spectrogram between 10 Hz and 30 Hz of the measured vibration signal is shown in Fig. 7(a). It can be seen that the 1st pinon shaft rotational harmonic is dominant in the frequency range (10–30 Hz). However, the 1st pinon shaft rotational harmonic is overlapped with other harmonics (high order pinon shaft rotational harmonics and 1st gear shaft rotational harmonic) in the frequency domain. The estimated IF of the 1st pinon shaft rotational harmonic shown in Fig. 7(b). It can be seen that the estimated IF is similar to the measured IRF (Fig. 6(a)), whereas, is not precise due to the low resolution of the spectrogram. Thus, it is not recommended to directly resample measured vibration signals in accordance to the estimated IF as it shall cause large

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Fig. 6. Measured signal on the test rig: (a) measured instantaneous rotational frequency, (b) waveform of the measured vibration signal, (c) frequency spectra (0–2000 Hz) of the measured vibration signal, (d) frequency spectra (0–60 Hz) of the measured vibration signal.

residual speed fluctuation to the resampled signal and smear the order spectra. A generalized modulation operator is constructed in accordance with the estimated IF. The spectrogram of demodulated vibration signals is shown in Fig. 7(c) where the trajectory of IF of the 1st pinon shaft rotational harmonics is parallel to time axis and they may be separated out of other harmonics in the frequency domain. The frequency spectra ranging in 11–15 Hz is extracted by means of a bandpass filter. The measured vibration signal is resampled in accordance with the demodulated phase, and the order spectrum is shown in Fig. 7(d). It can be seen that the gear meshing content (31th order) and its sidebands (29th, 30th, 32th and 33th orders) can be identified in the order spectrum. However, the order spectrum is not clear enough since the residual speed fluctuation in the resampled signal leads to additional frequency modulation to the resampled signal. The revolution-order spectrogram of the resampled signal is shown in Fig. 7(e) which indicates that the order spectra within the 30.5th and 31.5th order may be extracted for demodulation due to the separation of gear meshing components and sidebands. The resampled signals in the first-stage is resampled again in accordance with the phase demodulated based on gear meshing content and the order spectra are shown in Fig. 7 (f) where the gear meshing contents and sidebands are very clear. The computation time of the experiment case (192000 data points) is about 0.98 s when the algorithm is run on a laptop with a 2.30 GHz Intel® Core™ i5-6300HQ CPU and an 8.00 GB RAM, using MATLAB 2010b platform.

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Fig. 7. Result of the first-stage and the second-stage: (a) spectrogram between 10 Hz and 30 Hz, (b) IF of the 1st pinon shaft rotational harmonic extracted from the spectrogram, (c) spectrogram between 0 Hz and 30 Hz of the demodulated signal, (d) Order spectra of the resampled signal in first-stage, (e) the revolution-order spectrogram of the resampled signal in first-stage, (f) the order spectra of the resampled signal in second-stage.

6 Conclusions Generalized demodulation based tacho-less order tracking is applicable to gear fault diagnosis under large rotational speed condition (larger than ±30%). However, the order spectra achieved by the current single-stage generalized demodulation based tacho-less order tracking remains smearing due to the relative large residual speed variations in the resampled signal. Address to this issue, a multi-stage generalized demodulation based tacho-less order tracking is proposed in this paper, where the spectral smearing can be alleviated based on the progressive iteration. The effectiveness of the proposed method was validated by simulation and experiment signals. Comparative studies showed that the multi-stage generalized demodulation based tacho-less order tracking achieved a clearer order spectra than those of the single-stage generalized phase demodulation based tacho-less OT.

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In addition, the proposed method is time saving due to its only being based on simple calculations such as coarse time-frequency transform, Fourier transform and Hilbert transform, therefore, is promising in applications (such as field diagnosis) which have strict computation time requirements.

References 1. Zhao, M., Lin, J., Wang, X., Lei, Y., Cao, J.: A tacho-less order tracking technique for large speed variations. Mech. Syst. Signal Process. 40, 76–90 (2013) 2. Wang, Y., Xu, G.H., Luo, A.L., Liang, L., Jiang, K.S.: An online tacholess order tracking technique based on generalized demodulation for rolling bearing fault detection. J. Sound Vib. 367, 233–249 (2016) 3. Xiao, H., Zhou, X., Shao, Y.: Application of an improved dynamic time synchronous averaging method for fault diagnosis in conditions of speed fluctuation and no tachometer. Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci. 230, 2517–2531 (2016) 4. Urbanek, J., Barszcz, T., Antoni, J.: A two-step procedure for estimation of instantaneous rotational speed with large fluctuations. Mech. Syst. Signal Process. 38, 96–102 (2013) 5. Jiang, X.X., Li, S.M., Wang, Q.: A study on defect identification of planetary gearbox under large speed oscillation. Math. Prob. Eng. (2016) 6. Bonnardot, F., El Badaoui, M., Randall, R.B., Daniere, J., Guillet, F.: Use of the acceleration signal of a gearbox in order to perform angular resampling (with limited speed fluctuation). Mech. Syst. Signal Process. 19, 766–785 (2005) 7. Hu, Y., Tu, X.T., Li, F.C., Li, H.G., Meng, G.: An adaptive and tacholess order analysis method based on enhanced empirical wavelet transform for fault detection of bearings with varying speeds. J. Sound Vib. 409, 241–255 (2017) 8. Cao, H.R., He, D., Xi, S.T., Chen, X.F.: Vibration signal correction of unbalanced rotor due to angular speed fluctuation. Mech. Syst. Signal Process. 107, 202–220 (2018) 9. Wang, T., Liang, M., Li, J., Cheng, W., Li, C.: Bearing fault diagnosis under unknown variable speed via gear noise cancellation and rotational order sideband identification. Mech. Syst. Signal Process. 62–63, 30–53 (2015) 10. Hong, L., Qu, Y., Dhupia, J.S., Sheng, S., Tan, Y., Zhou, Z.: A novel vibration-based fault diagnostic algorithm for gearboxes under speed fluctuations without rotational speed measurement. Mech. Syst. Signal Process. 94, 14–32 (2017) 11. Borghesani, P., Pennacchi, P., Randall, R.B., Ricci, R.: Order tracking for discrete-random separation in variable speed conditions. Mech. Syst. Signal Process. 30, 1–22 (2012) 12. Coats, M.D., Randall, R.B.: Single and multi-stage phase demodulation based ordertracking. Mech. Syst. Signal Process. 44, 86–117 (2014) 13. Rodopoulos, K., Yiakopoulos, C., Antoniadis, I.: A parametric approach for the estimation of the instantaneous speed of rotating machinery. Mech. Syst. Sign. Process. 44, 31–46 (2014) 14. Daubechies, I., Lu, J., Wu, H.-T.: Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Appl. Comput. Harmonic Anal. 30, 243–261 (2011) 15. Xi, S.T., Cao, H.R., Chen, X.F., Zhang, X.W., Jin, X.L.: A frequency-shift synchrosqueezing method for instantaneous speed estimation of rotating machinery. J. Manuf. Sci. Eng.Trans. ASME 137, 031012 (2015) 16. Mei, J., Xiao, Y., Chen, X., Qiao, L.: Fault diagnosis of a gearbox based on the analysis of a fractional energy gathering band. Measurement 46, 3662–3670 (2013)

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17. Lu, Y., Tang, J., Luo, H.: Wind turbine gearbox fault detection using multiple sensors with features level data fusion. J. Eng. Gas. Turbines Power-Trans. ASME 134, 8 (2012) 18. Alkhadafe, H., Al-Habaibeh, A., Lotfi, A.: Condition monitoring of helical gears using automated selection of features and sensors. Measurement 93, 164–177 (2016) 19. Bechhoefer, E., Zhang, X.: Improved fault detection by appropriate control of signal bandwidth of the TSA. In: Proceedings Annual Conference of the Prognostics and Health Management Society, Coronado, California, 18–24 October 2015 (2015) 20. Feng, Z., Chen, X., Liang, M.: Joint envelope and frequency order spectrum analysis based on iterative generalized demodulation for planetary gearbox fault diagnosis under nonstationary conditions. Mech. Syst. Sign. Process. 76–77, 242–264 (2016) 21. Coats, M.D., Sawalhi, N., Randall, R.B.: Extraction of tacho information from a vibration signal for improved synchronous averaging. In: Proceedings of Acoustics 2009, Adelaide, Australia, 23–25 November 2009 (2009) 22. Thakur, G., Brevdo, E., Fuckar, N.S., Wu, H.-T.: The synchrosqueezing algorithm for timevarying spectral analysis: robustness properties and new paleoclimate applications. Sign. Process. 93, 1079–1094 (2013) 23. Zheng, K., Luo, J., Zhang, Y., et al.: Incipient fault detection of rolling bearing using maximum autocorrelation impulse harmonic to noise deconvolution and parameter optimized fast EEMD. ISA Trans. 89, 256–271 (2018) 24. He, G., Ding, K., Li, W., Jiao, X.: A novel order tracking method for wind turbine planetary gearbox vibration analysis based on discrete spectrum correction technique. Renew. Energy 87, 364–375 (2016)

Gear Fault Diagnosis Under the Run-Up Condition Using Fractional Fourier Transform and Hilbert Transform Qi Zhou, Chaoqun Wu(&), and Qingrong Fan School of Mechanical and Electronic Engineering, Wuhan University of Technology, No. 122 Luoshi Road, Wuhan 430070, China {zhouqi_945,chaoqunwu}@whut.edu.cn, [email protected]

Abstract. The sidebands spaced around the gear meshing content and its harmonics are the commonly used fault indicator in the gear fault diagnosis under the constant rotational speed condition. However, when the gear works under the run-up condition, the variable rotational speed causes smearing to the frequency spectrum, which makes it difficult to recognize the sidebands caused by the local gear fault. This paper proposed a method which combines Fractional Fourier Transform (FrFT) and the Hilbert Transform (HT) to identify the sidebands of signal measured under the run-up process. The HT is utilized to construct the analytic representation of the measured signal, which has a better energy concentration than the measured signal in the fractional domain. Thus, the ability of extracting weak sidebands of FrFT is enhanced. Simulation case study and experimental case study are carried to verify the effectiveness of the proposed method. Tooth cracks of different depth are manufactured artificially to simulate the local fault of different severity. The results show that the weak sidebands which is invisible in the time-frequency representation can be identified by the proposed method. The amplitude of gear meshing content and its sidebands ascends with the growth of the crack depth. Keywords: Gear fault diagnosis  Sidebands identification  Run-up condition  Hilbert transform  Fractional Fourier transform

1 Introduction Condition monitoring and fault diagnosis of gears are critical to optimize the maintenance schedule and reduce the financial cost of gearbox damage in practical industrial environments [1]. In the last three decades, the condition monitoring and fault diagnosis of gears via vibration analysis have been broadly studied. A lot of research papers [2–5] were published on this topic. Most of current studies thus far have focused on diagnosing gear faults under the constant rotational speed condition. The gear fault diagnosis under variable rotational speed condition, especially under the run-up and This project is supported by National Natural Science Foundation of China (Grant No. 51775394), Hubei Province Major Science and Technology Innovation Plan (2018AAA024). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 918–943, 2020. https://doi.org/10.1007/978-981-32-9941-2_77

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run-down condition has been studied rarely. However, a substantial literature [6–9] has indicated that the weak signatures of the early gear fault are more easily exposed during the run-up and run-down process. Accordingly, the gear fault diagnosis under run-up and run-down conditions is an interesting research topic and has attracted more and more researchers. As is well known, the vibration signals measured under the run-up and run-down condition have time-varying instantaneous frequency. The traditional FFT spectrum cannot reveal the time-varying frequency structure of the nonstationary signal. However, time-frequency analysis (TFA) [10–14] is a powerful tool which can give insight into the time-frequency structures of the nonstationary signal measured under the runup and run-down condition. Various TFA methods have been proposed and validated by the real world measurement data. The linear TFA methods, such as Short Time Fourier Transform (STFT) and Wavelet Transform (WT), cannot achieve the best time and frequency resolution since they are subject to the Heisenberg uncertainly principle. The bilinear TFA methods, such as Wigner–Ville Transform (WVT) and Pseudo Wigner–Ville Transform suffer from the interference of cross-term. Address to these issues, a lot of improved TFA methods which retain the excellent time-frequency resolution and reduce the interference of cross-term were proposed. Feng et al. proposed the iterative generalized synchrosqueezing transform [10], iterative generalized time–frequency reassignment [11] and iterative generalized demodulation [12] to analyze the gear vibration signal measured under the variable rotational speed condition, and it is shown that the time varying fault signatures were identified successfully. Wang et al. [13] proposed the matching synchrosqueezing transform and recognized the sidebands spaced around the gear meshing content successfully from the TimeFrequency distribution (TFD). Ruobin Sun et al. proposed the structured sparsity timefrequency analysis [14] to extract the steady modulation components and impulsive components of the defective gear vibration signals and obtain the time-frequency distribution with high resolution by piling different components in the same diagram. These improved TFA methods made a considerable contribution to the gear fault diagnosis under the run-up and run-down condition. The presence of the local fault in gear will cause amplitude modulation and phase modulation to the vibration signal, which in turn generates sidebands spaced around the gear meshing content and its harmonics [15]. The sidebands are the commonly used indicator in the gear fault diagnosis. When the gear is operated under the constant rotational speed condition, the sidebands caused by local gear fault can be identified in the spectrum. However, when the gear is operated under the run-up or run-down condition, the spectrum of the vibration signal is smearing, it is hard to recognize the sidebands caused by gear fault. The FrFT is the generalization of the conventional Fourier transform. It can provide a higher time–frequency resolution than STFT and avoid the effect of cross-terms caused by the WVD [16]. Since its orthonormal chirped kernel, it is suitable to analyze the linear frequency modulation (LFM) signals produced during the linear run-up and run-down process. The FrFT has been introduced to gear fault diagnosis by Luo [8] and Mei [6]. Luo et al. [8] employed the FrFT to detect sidebands from the vibration signal measured under the run-up and run-down condition. The results shown that the sidebands can be extracted in the fractional domain. In the implementation of extracting sidebands by FrFT, the most important thing is to

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estimate the optimal FrFT orders and the concentrated points of gear meshing content and sidebands. It was presented in Luo’s articles and Mei’s articles that the optimal FrFT order and the concentrated point is determined by the initial frequency and the frequency modulation slope of the signal. However, it should be noted that the dimensional normalization should be performed before the numerical calculation of FrFT. The initial frequency and the frequency modulation slope change a lot before and after the dimensional normalization. This property has not been studied in Luo’s articles and Mei’s articles, which lefts barriers for the application of FrFT in gear fault diagnosis. Address to this issue, the variation of the initial frequency and the frequency modulation slope before and after dimensional normalization is studied in detail in this paper. Furthermore, the measured vibration signal is real-valued signal, which has a poor energy concentration in the fractional domain even at the optimal FrFT order. This characteristic troubles the extraction of the weak sidebands caused by the early fault of gear. The HT is broadly applied in signal processing to construct the analytic representation of real-valued signal. Motivated by the phenomenon that the analytic representation of the real-valued signal has good energy concentration in the fractional domain, we employed the HT to transform the real-valued signal to its analytic representation. Therefore, the ability of extracting the weak sidebands of FrFT is enhanced by the addition of HT. These are the two major contributions of this paper. Cracks of different depth (1 mm and 2 mm) are manufactured artificially to simulate the local gear fault with different severity. The FrFT is applied to extract gear meshing content and sidebands from the vibration signal measured under the linear run-up condition. The result shows that the amplitude of gear meshing content and sidebands ascend gradually with the growth of crack depth. The rest of this paper is organized as follows: In Sect. 2, the theoretical foundation of FrFT is presented, in addition, the calculation of optimal FrFT order and the concentrated point is presented in detail. The reason that real-valued signal cannot energy concentrated well in the fractional domain is investigated, and the solution is proposed. In Sect. 3, the scheme of the proposed method is described by the flowchart. In Sect. 4, a simulation verification is demonstrated, the performance improvement by HT is revealed by a comparison. In Sect. 5, the gearbox test rig is described and the measured signal is applied to verify the effectiveness of the proposed method. Finally, conclusions are given in Sect. 6.

2 Theoretical Foundation 2.1

The Principles of Fractional Fourier Transform

The Fourier Transform (FT) is one of the most commonly used mathematical tools in signal processing. Almeida [17] described the effort of FT on the time domain signal: In time-frequency representations, one normally uses a plane with two orthogonal axes corresponding to time and frequency, respectively (see Fig. 1). If we consider the time domain signal x(t) is represented along the t axis, the FT of x(t) (designated by Fx(t)) is represented along the x axis. The FT operator (designated by F) can be considered as change in the representation of the signal corresponding to a counterclockwise axis

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rotation of p/2 rad. The FrFT is a generalization of the classical Fourier transform. It can be considered as variation in the representation of the signal corresponding to a counterclockwise axis rotation of any angle (not merely limited in integer multiple of p/2 rad).

Fig. 1. The time-frequency plane, the set of coordinates (u-v) is rotated by an angle a relative to the original coordinates (t-x)

The p-order FrFT of x(t) can be defined as Eq. (1) [18]. Z Xp ðuÞ ¼

þ1

1

Kp ðu; tÞxðtÞdt

ð1Þ

where p ¼ 2a=p. The kernel of p-order FrFT is shown in Eq. (2). 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi < 1  j cot a exp½jpðu2 cot a  2ut csc a þ t2 cot aÞ; a 6¼ np Kp ðu; tÞ ¼ dðu  tÞ; a ¼ 2np : dðu þ tÞ; a ¼ ð2n  1Þp

ð2Þ

where a ¼ pp=2, n is integer. When p = 1, the a ¼ p=2, the definition Eq. (1) becomes Eq. (3) Z X1 ðuÞ ¼

þ1

expðj2putÞxðtÞdt 1

ð3Þ

It can be seen that the kernel of FrFT coincides with the kernel of the FT when p = 1. Thus, the FrFT can be considered as a generalization of the classical FT. The time-frequency representation of a signal with two LFM components is shown in Fig. 2. By rotating the axes t with an angle of a ¼ p=2 þ arctanðlÞ, that is transforming the signal by p (p ¼ 2a=p) order of FrFT, one LFM component in the signal concentrates at the point u0 (which also called concentrated point in fractional domain).

922

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Fig. 2. The FrFT of a signal with two LFM components.

This characteristic is very useful in the detection of LFM signal. It should be noted that the c0 and the l is the initial frequency and the frequency modulation slope of the signal after the dimensional normalization. 2.2

Calculation of the Optimal FrFT Order and the Concentrated Point

The numerical method of FrFT derived by Ozaktas [18] in 1996 is one of the most commonly used numerical method of FrFT. Before the numerical computation of FrFT, the dimensional normalization should be performed. Assuming that the time-domain representation of the signal is approximately confined to the interval [−Δt/2, Δt/2] and its frequency-domain representation is confined to the interval [−Δf/2, Δf/2]. Since the signal has different dimensions in the time domain and frequency domain, the scale is not uniform, it brings inconvenience to the numerical computation of FrFT. Ozaktas pffiffiffiffiffiffiffiffiffiffiffiffiffi introduced the scaling parameter S ¼ Dt=Df with the dimension of time and introduced scaled coordinates x ¼ Dt=S and v ¼ Df  S to solve the problem. With the new coordinates, the time domain and the frequency domain representations will be confined in the interval [Dt=2S, Dt=2S] and [Df  S=2, Df  S=2], respectively. The pffiffiffiffiffiffiffiffiffiffiffiffiffiffi dimension of the interval is Dx ¼ Dt  Df . The lengths of both intervals are now equal pffiffiffiffiffiffiffiffiffiffiffiffiffiffi to the dimensionless quantity Dx ¼ Dt  Df . The detailed description can be found in Ozaktas’s article [18]. On the consideration of the paper length, we only give an example to describe the variation of the initial frequency and the frequency modulation slope before and after the dimensional normalization. The original signal y(t) (shown in Fig. 3(a)) is represented by Eq. (4). The f0 and k are the initial frequency and the frequency modulation slope of the original signal, respectively.  yðtÞ ¼ cosð2pðf0 t þ kt2 2ÞÞ; t ¼ ½0; T

ð4Þ

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Fig. 3. The signal waveform: (a) before the dimensional normalization, (b) after the dimensional normalization.

The expression of signal after the dimensional normalization (shown in Fig. 3(b)) is shown in Eq. (5). T 1 T yn ðxÞ ¼ cosð2pðf0 ðSx þ Þt þ ðSx þ Þ2 ÞÞ; x ¼ ½Dx=2; Dx=2 2 2 2

ð5Þ

The initial frequency and the frequency modulation slope of the signal after the dimensional normalization are f0S + kTS/2 and kS2, respectively. In practice, the bandwidth of the signal in time domain and frequency domain can be set to observation time T and sampling frequency fs, namely, the Δt and Δf in the scaling parameter are set to T and fs, respectively. The accurate estimation of the optimal FrFT order and the concentrated point is critical to detect the LFM component. The optimal rotation angle a, the optimal FrFT order p and the frequency modulation slope l of LFM component in Fig. 2 have a relation shown in Eqs. (6) and (7). a ¼ p=2 þ arctanðlÞ

ð6Þ

2 arctanðlÞ p

ð7Þ

p ¼ 1þ

As shown in Fig. 2, concentrated point u0 can be calculated by Eq. (8). u0 ¼

Dx p fs þ c0 cosða  ÞSfs 2S 2

ð8Þ

A case study is employed to show the error caused by neglecting the dimensional normalization. As shown in Table 1, there are four LFM signals, represented as x1(t), x2(t)), x3(t) and x4(t). The sampling frequency is 128 Hz, the time duration is 1 s. The initial frequency f0 and the frequency modulation slope k of the aforementioned four LFM signal are listed in the 2nd column and 3rd column in Table 1. The initial frequency c0 and the frequency modulation slope l after the dimensional normalization are listed in the 5th column and 6th column in Table 1. The optimal FrFT orders p listed in the 7th column are calculated by substituting the frequency modulation slope l into

924

Q. Zhou et al. Table 1. The optimal order and the incorrect order of four LFM signal. Signals f0 k S x1(t) 0 8 0.0884 x2(t) 10 8 0.0884 x3(t) 0 16 0.0884 x4(t) 10 16 0.0884

c0 0.3536 1.2374 0.7071 1.5910

l 0.0625 0.0625 0.1250 0.1250

p 1.0397 1.0397 1.0792 1.0792

u0 68 78 72 82

pin 1.9208 1.9208 1.9603 1.9603

uin / / / /

Eqs. (6) and (7). The incorrect FrFT order pin which are calculated by substituting the frequency modulation slope k into the Eqs. (6) and (7) directly are shown in the 9th column. The p order and pin order FrFT of the four LFM signal are shown in Fig. 4. It can be seen that a part energy of the LFM signals is concentrated in their optimal order fractional domain (as shown in Fig. 4(a)–(d)), peaks are located in the concentrated points u0. However, the energy of the four LFM signals is dispersed in their incorrect order fractional domain (as shown in Fig. 4(e)–(h)). We can also find in Fig. 4(a–d) that a part energy of the LFM signal is not concentrated in the fractional domain even in the optimal FrFT order (marked by the red ellipses). This phenomenon will be discussed in detail in Sect. 2.3.

Fig. 4. The p order FrFT and the pin order FrFT of the four LFM signals: (a) the p = 1.0397 order FrFT of x1(t), (b) the p = 1.0397 order FrFT of x2(t), (c) the p = 1.0792 order FrFT of x3(t), (d) the p = 1.0792 order FrFT of x4(t), (e) the pin = 1.9208 order FrFT of x1(t), (f) the pin = 1.9208 order FrFT of x2(t), (g) the pin = 1.9603 order FrFT of x3(t), (h) the pin = 1.9603 order FrFT of x4 (t).

Gear Fault Diagnosis Under the Run-Up Condition Using FrFT and HT

2.3

925

The Performance Improvement by HT

The real-valued LFM signal has a poor energy concentration in the fractional domain even in the optimal FrFT order. This characteristic troubles the extraction of the weak sidebands caused by the early fault of gears. However, the analytic representation of realvalued LFM signal can be energy concentrated well in the fractional domain. Assuming that the real-valued LFM signal after dimensional normalization is shown in Eq. (9). yn ¼ cosð2pðc0 t þ

1 2 lt ÞÞ 2

ð9Þ

The instantaneous frequency f of signal presented by Eq. (9) is shown in Eq. (10) f ¼ c0 þ lt

ð10Þ

The rotation angle a and the FRFT order p can be calculated by Eqs. (6) and (7). Thus, the kernel of FrFT illustrated in Eq. (2) is become Eq. (11). Kp ðu; tÞ ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi 1 þ jl expðjpðlu2  2 1 þ l2 ut  ut2 ÞÞ

ð11Þ

The real-valued LFM signal yn(t) (shown in Eq. (9)) can be transformed to the exponential representation shown in Eq. (12) according to Euler’s formula. 1 1 1 yn ðtÞ ¼ ðexpðj2pðc0 t þ lt2 ÞÞ þ expðj2pðc0 t þ lt2 ÞÞÞ 2 2 2

ð12Þ

The p order FrFT of signal yn(t) now is shown in Eq. (13). pffiffiffiffiffiffiffiffiffiffiffiffi Z þ1 pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ jl expðjplu2 Þð Xp ðu; tÞ ¼ expðj2pðc0  1 þ l2 uÞtÞdt 2 1 Z þ1 pffiffiffiffiffiffiffiffiffiffiffiffiffi þ expðj2pðlt2 þ ðc0  1 þ l2 uÞtÞÞdtÞ

ð13Þ

1

The first term of the right of Eq. (13).is similar to the conventional FFT of a pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ lt2 . harmonic and energy concentrate at u ¼ c0 The second term of the right of Eq. (13) is the integration of expðt2 Þ which cannot be calculated by elementary function. On the consideration of the paper length, the numerical solution process is omitted here, the reader can refer to the monograph of Numerical Analysis [19]. The analytic representation ya(t) constructed by HT of real-valued LFM signal yn(t) is shown in Eq. (14). ya ðtÞ ¼ yn ðtÞ þ HTðyn ðtÞÞ

ð14Þ

926

Q. Zhou et al.

The p-order FrFT of signal of the complex LFM signal ya(t) is shown in Eq. (15). Xpa ðu; tÞ

Z pffiffiffiffiffiffiffiffiffiffiffiffi 2 ¼ 1 þ jl expðjplu Þð

þ1 1

expðj2pðc0 

pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ l2 uÞtÞdt

ð15Þ

The second term of the right of Eq. (13) is the integration of expðt2 Þ, it does not exist in Eq. (15). Thus, the energy leakage caused by the second term of the right of Eq. (13) disappears. The analytic representation of LFM signal constructed by HT has a better energy concentration than the real-valued . LFM signal itself. Moreover, the pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ l2 in Eq. (15) is two times amplitude of the peak at concentrated point u ¼ c0 .pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ l2 in Eq. (13). of the amplitude of the peak at concentrated point u ¼ c0 A simulation study is given to illustrate the performance improvement by HT. Assuming a real-valued LFM signal s1 ðtÞ which is presented in Eq. (16). The sampling frequency fs = 1000 Hz, observation time T = 1 s. The initial frequency and the frequency modulation slope before and after dimensional normalization are shown in Table 2. The theoretical analytic representation of s1(t) is shown in Eq. (17). The analytic representation constructed by HT is shown in Eq. (18). s1 ðtÞ ¼ cosð2p100t2 Þ

ð16Þ

s2 ðtÞ ¼ expðj2p100t2 Þ

ð17Þ

s3 ðtÞ ¼ s1 ðtÞ þ HTðs1 ðtÞÞ

ð18Þ

The optimal order FrFT of signals s1(t), s2(t), s3(t) are shown in Fig. 5. It can be seen in Fig. 5(a), the real-valued LFM signal s1(t) has a poor energy concentration in the concentrated point. The energy leakage occurs in the optimal fractional domain. The signal s2(t) (the theoretical analytic representation signal of s1(t)) concentrates well in the fractional domain as shown in Fig. 5(b). The signal s3(t) (the analytic representation constructed by HT) is also concentrates in the concentrated point as shown in Fig. 5(c). The amplitude of the peak in the Fig. 5(c) is 25.36, which is close to the amplitude of 25.76 in Fig. 5(b). Compared to the amplitude of 12.54 in Fig. 5(a), the amplitude in Fig. 5(c) is about two times of the amplitude of the peak in the Fig. 5(a), it is consistent with the conclusion of the theoretical analysis aforementioned.

Table 2. The parameters of the s1(t) S c0 l p u0 f0 k 0 200 0.0316 3.1623 0.2 1.1257 598

Gear Fault Diagnosis Under the Run-Up Condition Using FrFT and HT

927

Fig. 5. The p-order FrFT of three signals: (a) the FrFT of s1(t) (b) the FrFT of s2(t) (c) the FrFT of s3(t).

3 Scheme of the Proposed Method The proposed method uses FrFT and HT to extract the gear meshing content and sidebands under the linear run-up condition. The flowchart of proposed method is shown in Fig. 6. It is a new perception which can be structured in the following steps: Step 1: Capturing the vibration signal and the rotational speed signal. First of all, the vibration signal of the gear is collected. Since the optimal FrFT order is determined by the initial frequency and the frequency modulation slope, the rotational speed of gear should be provided. The rotational speed of the gear can be calculated form the tachometer signal. A tachometer with one impulse output per revolution is enough for this method. Step 2: Selecting the signal segment for FrFT. As the FrFT is suitable to detect the LFM components, therefore, the vibration signal segment in which the rotational speed is in good linearity should be selected. Since the rotational speed is calculated from the tachometer signal, it is quite easy to select the signal segment for FrFT. Step 3: Constructing the analytic representation of the real-valued vibration signal by HT. The analytic representation of the real-valued vibration signal is constructed by HT. Step 4: Calculating the FrFT order and the concentrated points of the gear meshing content and sidebands. As the rotational speed, the number of teeth are known, the initial frequency and the frequency modulation slope of the gear meshing content and sidebands can be

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Fig. 6. Flowchart of the proposed method.

calculated. The optimal order and the concentrated points in fractional domain of the gear meshing content and sidebands can be calculated by the Eqs. (6) and (7). Step 5: Transforming the analytic representation of the real-valued vibration signal to fractional domain using FrFT. Transforming the signals to fractional domain by performing the respectively order FrFT of gear meshing content and sidebands.

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929

Step 6: Recognizing the healthy condition of the gearbox by the extracted sidebands and the gear meshing content. The amplitude at the concentrated points of sidebands can be treated as fault indicators. The larger the amplitude, the severer the gear fault.

4 Numerical Simulation 4.1

Vibration Model of the Mear with a Local Fault During the Run-Up Process

This section starts with the vibration model of healthy gears under the constant rotational speed condition, and then, extend the model to the scenario that a defective gear under the run-up condition. Based on observations, McFadden [19] proposed a mathematics model to describe the vibration behavior of gear under constant rotational speed condition. Generally, the measured vibration signal of healthy gearbox mainly consists of the gear meshing content and its harmonics. Which can be given in Eq. (19) (refer to article [20]). xperfect ðtÞ ¼

XN n¼1

Xn cosð2pnKfr t þ un Þ

ð19Þ

where the N, Xn, un, K, fr are the number of gear meshing harmonics, the amplitude of the nth harmonic, the phase angle of the nth harmonic, the number of teeth, the rotational frequency of gear, respectively. When a local fault occurs, the local fault leads to amplitude and phase modulation of the signal [21]. These modulations create sidebands spaced around the gear meshing content (fm = Kfr) and its harmonics at a distance equal to the gear rotational frequency fr in the measured vibration spectrum. The amplitude modulation function an(t) and the phase modulation function bn(t) are periodic with the gear rotational frequency fr, can be written in Eqs. (20) and (21). an ðtÞ ¼ bn ðtÞ ¼

XM m¼1

XM m¼1

Anm cosð2pmfr t þ anm Þ

ð20Þ

Bnm cosð2pmfr t þ bnm Þ

ð21Þ

where M is the number of sidebands around gear meshing harmonics; and Anm and anm are the amplitude and phase of the nth sideband of an(t) around the nth gear meshing harmonic, respectively. Bnm and bnm are those of bn(t) around the nth gear meshing harmonic. Considering the influences of amplitude modulation and frequency modulation, the vibration signal model of gear with a local fault can be represented by Eq. (22). xfault ðtÞ ¼

XN n¼1

Xn ð1 þ an ðtÞÞ cosð2pnKfr t þ un bn ðtÞÞ

ð22Þ

930

Q. Zhou et al.

When the gear run-up with the rotational speed ascending linearly, the vibration signal can be regarded as a multi-component LFM signal. 4.2

Gear Meshing Content and Sidebands Extraction Using the Proposed Method

Assuming that the rotational speed of gear ascends linearly from 600 rpm to 1200 rpm in 2 s. The initial rotational frequency is 10 Hz, and the slope of the rotational frequency kr = 5 Hz/s. The teeth number K = 30. The sampling frequency fs = 10 kHz. Take the 1st gear meshing content and the 1st harmonics of amplitude modulation function and the phase modulation function into consideration. According to Eq. (22), the vibration signal of gear with a local fault can be written as Eq. (23). xðtÞ ¼ X1 ð1 þ A11 cosð2pð10t þ 2:5t2 Þ þ a11 ÞÞ cosð60pð10t þ 2:5t2 Þ þ u1 þ B11 cosð2pð10t þ 2:5t2 Þ þ b11 ÞÞ

ð23Þ

Assuming that the amplitude of meshing frequency harmonic X1, the amplitude of the modulation function A11, the amplitude of the phase modulation function B11, the phrase of meshing frequency harmonic u1, the phrase of amplitude modulation function a11, the phrase of phase modulation function b11 are 1, 1.2, 0.5, 0.2, 1.5, 0.3, respectively. The STFT spectrum of the simulation signal is illustrated in Fig. 7. It can be seen that the gear meshing frequency (fm) varies from 300 Hz to 600 Hz. However, the sidebands (fm – fr, fm + fr) are not clear in the STFT spectrum due to the low timefrequency resolution of STFT.

Fig. 7. The STFT representation of the simulated signal.

The FrFT is applied to the simulation signal. The optimal FrFT orders and the concentrated points in fractional domain of the gear meshing content and the sidebands are listed in Table 3.

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931

Table 3. Optimal FrFT orders and concentrated points in fractional domain of the gear meshing content and sidebands. Components fm fm − fr fm − fr

f0 300 290 310

k 150 145 155

S 0.0141 0.0141 0.0141

c0 6.3640 6.1518 6.5761

l 0.0300 0.0290 0.0310

p 1.01909 1.01846 1.01973

u0 10900 10870 10930

Figure 8 is the extraction of gear meshing content and sidebands by FrFT. As shown in Fig. 8, the gear meshing content and the sidebands are concentrated in the fractional domain by their respective optimal order FrFT. The sidebands which are hardly recognized by STFT representation can be extracted by FrFT.

Fig. 8. Extraction of gear meshing content and sidebands by FrFT.: (a) gear meshing content, (b) lower sidebands, (c) upper sidebands.

The proposed method (FrFT + HT) is applied to the same simulation signal. The results are shown in Fig. 9. The gear meshing content and its sidebands are concentrated in their respective fractional domain. The amplitude of the gear meshing content and its sidebands extracted by the proposed method (FrFT + HT) is two times of that extracted by FrFT approximately. It also can be seen that the fm − fr and fm + fr in Fig. 9(a) distribute around the peak of fm in the fractional domain as the optimal FrFT order of the fm is not the optimal order of fm − fr and fm + fr. The similar phenomenon can be found in Fig. 8(b) and (c).

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Fig. 9. Extraction of gear meshing content and sidebands by the proposed method (FrFT + HT): (a) gear meshing content, (b) lower sidebands, (c) upper sidebands.

Since the noise naturally present in measured signals in the practical engineering. The sidebands extraction method is required to be robust to noise. Therefore, we add noise to the simulation signal to make the signal to noise ratio (SNR) approach to −20 dB. The STFT, FrFT and the proposed method (FrFT + HT) are applied to the sidebands extraction from the noisy simulation signal. The STFT representation of the noisy simulation signal is shown in Fig. 10. Since the noise is too strong, the sidebands are completely submerged in the noise.

Fig. 10. The STFT representation of the noisy simulation signal with SNR = –20 dB.

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933

However, the gear meshing content and the sidebands can be clearly found in the fractional domain. As shown in Fig. 11, the weak sidebands which can be hardly found in the STFT representation are extracted by the FrFT.

Fig. 11. Extraction of gear meshing content and sidebands by FrFT with SNR = –20 dB: (a) gear meshing content, (b) lower sidebands, (c) upper sidebands.

To illustrate the improvement to the FrFT by HT, the proposed method (FrFT + HT) is applied to the noisy simulation signal. The gear meshing content and sidebands in fractional domain extracted by the proposed method are shown in Fig. 12. As shown in Fig. 12, the gear meshing content and sidebands are concentrated in their respective fractional domain. It is verified in this numerical study that the proposed method has excellent ability to extract sidebands in the noisy condition with SNR as lower as −20 dB. Compared with the results shown in Fig. 11, the amplitude of gear meshing content and the sidebands extracted by the proposed method are obviously larger than that extracted by FrFT. The ability of extracting LFM components is improved by the addition of HT.

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Fig. 12. Extraction of gear meshing content and sidebands by the proposed method (FrFT + HT) in SNR = –20 dB: (a) gear meshing content, (b) lower sidebands, (c) upper sidebands.

5 Experimental Verification 5.1

The Experimental Specification

An experiment is carried out in the gearbox test rig to further verify performance of the proposed method. The gearbox test rig configuration is illustrated in Fig. 13. The whole test rig mainly consists of an AC motor with a nominal power of 22 kW, a testing gearbox, a torque sensor, a speed reducer gearbox and a magnetic brake. A frequency converter is employed to regulate the rotational speed of the motor. The testing gearbox is a single-stage reducer with a pinon at the input rotor and a gear at the output rotor. The number of teeth of pinon and gear are 31 and 42, respectively. The torque of the output rotor are recorded by the torque sensor and speed sensor. A tachometer is arranged between the AC motor and the testing gearbox. It outputs one pulse per revolution, thus the rotational speed can be calculated by the time interval between the arrivals of two pulse. The characteristics of the test spur gears are given in Table 4. The crack with different depths (1 mm and 2 mm) are manufactured artificially. Figure 14 shows the pictures of pinon in healthy condition and faults. In each experiment, the pinon of different crack level was used. The vibration signals is collected by an accelerometer positioned on the top of the testing gearbox. The sampling frequency is 24 kHz, the load is 10 Nm.

Gear Fault Diagnosis Under the Run-Up Condition Using FrFT and HT

935

Fig. 13. The test rig consist of an AC motor, a testing gearbox, a torque sensor integrated with a speed sensor, a reduction gearbox and a magnetic brake (from right to left).

Table 4. Gear pair specifications. Type Material Module of teeth Number of teeth Pressure angle Face width of teeth

(a) healthy

Standard involute profile 45 Steel/45 Steel 4 31/42 20o 16 mm

(b) 1mm crack

(c) 2mm crack

Fig. 14. The pinon with tooth crack of different levels.

5.2

Features Extraction by the Proposed Method

The rotational speed of the motor is set to accelerate from 0 rpm to 1000 rpm in 5 s. The measured rotational speed of the healthy condition, 1 mm crack condition and the 2 mm crack condition are shown in Fig. 15. We select the segment of vibration signals from 600 rpm to 1000 rpm since the linearity of the rotational speed in this segment is good. The time duration of segment of the healthy condition, 1 mm crack condition and the 2 mm crack condition are 1.973 s, 1.978 s and 2.015 s, respectively. The vibration time-history of the measured signals in the healthy condition, 1 mm crack condition and the 2 mm crack condition are shown in Fig. 16. By comparing the time serials of three condition, it is observed that impulses are visible in these three conditions. It is because that the collision between gear teeth is serious when the gear pairs working under the rapid run-up condition. The weak signatures of tooth crack cannot be distinguished in the time-history of the measured signals.

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Fig. 15. The measured rotational speed of pinon: (a) the healthy condition, (b) 1 mm crack condition, (c) the 2 mm crack condition.

Fig. 16. Vibration time-history of the measured signals: (a) the healthy condition, (b) the 1 mm crack condition, (c) the 2 mm crack condition.

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The FFT spectrum of the measured signals in the healthy condition, 1 mm crack condition and the 2 mm crack condition are shown in Fig. 17. As the rotational speed varies from 600 rpm to 1000 rpm in 2 s, the gear meshing frequency varies from 310 Hz to 516.7 Hz, the rotational frequency varies from 10 Hz to 16.7 Hz. The FFT spectrum of the measured signals are smearing. It is unable to distinguish the gear meshing content and sidebands in the FFT spectrum. Though the healthy condition of the gearbox cannot be recognized by the FFT spectrum, some useful information is still provided by the FFT spectrum. The amplitude of the spectral contents in the frequency range of 600 Hz to 1000 Hz is obviously higher than that of other frequency range. It is because that the nature frequency of the system is located in the frequency range of 600 Hz to 1000 Hz. Since the gear meshing content and sidebands cannot be extracted by FFT spectrum, the time-frequency analysis is further performed to recognize the condition of the gears.

Fig. 17. FFT spectrum (0–1000 Hz) of experimental vibration signals: (a) the healthy condition, (b) the 1 mm crack condition, (c) the 2 mm crack condition.

The STFT representations of signals are shown in Fig. 18. To highlight the gear meshing content and its sidebands, Fig. 18 only shows the low frequency range (200– 600 Hz) of the measured signals. The gear meshing content can be found in the STFT representation, but sidebands relevant to the crack fault can rarely be found in the STFT representations in Fig. 18(b) and (c). Since the low time-frequency resolution of STFT, it is hard to recognize the health condition of the pinon by STFT representation under the run-up condition.

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Fig. 18. STFT representations of experimental vibration signals: (a) the healthy condition, (b) the 1 mm crack condition, (c) the 2 mm crack condition.

The FrFT is applied to extract the gear meshing content and sidebands. As the sampling frequency and the time duration are known. The optimal FrFT orders and concentrated points (listed in Table 5) of the gear meshing content and the sidebands under the healthy condition, 1 mm crack condition and 2 mm crack condition are calculated.

Table 5. The optimal FrFT orders and concentrated points of the gear meshing content and the sidebands in the healthy condition, 1 mm crack condition and 2 mm crack condition. Condition

fm p0 Healthy 1.00548 1 mm crack 1.00548 2 mm crack 1.00548

u0 24492 24555 25014

fm − fr p0 1.00531 1.00531 1.00531

u0 24466 24528 24987

fm + fr p0 1.00566 1.00566 1.00566

u0 24519 24581 25041

The gear meshing content and sidebands in the fractional domain in the healthy condition, 1 mm crack condition and 2 mm crack condition are shown in Fig. 19. As shown in Fig. 19, the gear meshing content (fm) and the sidebands (fm − fr, fm + fr) can be clearly recognized in the fractional domain. The gear meshing contents are dominated in the fractional domain. The amplitude of the sidebands trends greater as the tooth cracks more seriously.

Gear Fault Diagnosis Under the Run-Up Condition Using FrFT and HT

939

Fig. 19. The gear meshing contents and sidebands in the fractional domain extracted by FrFT: (a) fm − fr of healthy, (b) fm of healthy, (c) fm + fr of healthy, (d) fm − fr of 1 mm crack, (e) fm of 1 mm crack, (f) fm + fr of 1 mm crack, (g) fm − fr of 2 mm crack, (h) fm of 2 mm crack, (i) fm + fr of 2 mm crack.

The actual concentrated points of the gear meshing content and the sidebands in the fractional domain are shown in Table 6. Comparing to the theoretical concentrated points listed in Table 5, it can be seen that a small error is exist. It is because that the starting moment of 600 rpm and ending moment of 1000 rpm is not absolutely accurate since the time resolution of the tachometer is low (more than 1000 samples between the two adjacent pluses). Table 6. The actual concentrated points of the gear meshing frequency and the sidebands in the fractional domain. Condition Healthy 1 mm crack 2 mm crack

fm 24494 24556 25016

fm − fr 24466 24531 24989

fm + fr 24520 24583 25043

The amplitude of the gear meshing content and sidebands under healthy condition, 1 mm crack condition and 2 mm crack condition in the fractional domain are listed in Table 7. The Amplitude of meshing contents and sidebands increase with the growth of the tooth crack, this phenomenon is consistent with the conclusion in paper [22].

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Table 7. The amplitude of the gear meshing content and sidebands under healthy condition, 1 mm crack condition and 2 mm crack condition in the fractional domain extracted by FrFT. Condition Healthy 1 mm crack 2 mm crack

fm 2.72  10– 2.82  10– 3.02  10–

4 4 4

fm − fr 0.39  10– 0.81  10– 1.57  10–

4 4 4

fm + 0.85 1.01 2.90

fr  10–  10–  10–

4 4 4

Furthermore, it is obvious that the amplitude of upper sideband fm + fr is higher than the lower sideband fm – fr. This is because that the upper sideband is near to the natural frequency band 600 Hz to 1000 Hz of the system (it can be found in Fig. 17). This phenomenon is also confirmed in the paper [23]. The amplitude of sidebands in fractional domain can be treated as the fault indicator of gear. The ability of extracting the gear meshing content and sidebands under the linear run-up condition by the proposed method is verified experimentally. In order to highlight the improvement to FrFT by HT, we use the proposed method (FrFT + HT) to process the same signals. The results are shown in Fig. 20. The amplitude of gear meshing contents and sidebands is higher than that in Fig. 18. The detailed amplitude of the gear meshing content and sidebands is shown in Table 8.

Fig. 20. The gear meshing contents and sidebands in the fractional domain extracted by the proposed method (FrFT + HT): (a) fm – fr of healthy, (b) fm of healthy, (c) fm + fr of healthy, (d) fm – fr of 1 mm crack, (e) fm of 1 mm crack, (f) fm + fr of 1 mm crack, (g) fm – fr of 2 mm crack, (h) fm of 2 mm crack, (i) fm + fr of 2 mm crack.

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Table 8. The amplitude of the gear meshing content and sidebands in healthy condition, 1 mm crack condition and 2 mm crack condition in the fractional domain extracted by the proposed method (FrFT + HT). Condition Healthy 1 mm crack 2 mm crack

fm 5.43  10– 5.65  10– 6.03  10–

4 4 4

fm − fr 0.78  10– 1.61  10– 3.13  10–

4 4 4

fm + 1.71 2.02 5.80

fr  10–  10–  10–

4 4 4

It can be obviously found that the amplitude of gear meshing content and sidebands extracted by the proposed method(FrFT + HT)is higher than that extracted by FrFT. the amplitude increments of the gear meshing content and sidebands relative to that of the healthy condition are shown in Table 9. The 2nd row and the 3rd row are the amplitude increments extracted by FrFT, the 4th row and 5th row are the amplitude increments extracted by the proposed method (FrFT + HT). The amplitude increments are obviously larger than that extracted by FrFT. In the intelligent diagnosis and pattern recognition of gear fault, the amplitude increments of the sidebands relative to that of the healthy condition is typically used to evaluate the severity of the gear fault. The classifier classify the gear fault patterns and fault severities according to the amplitude increments. The larger the amplitude increments, the more accurate the classification results. Thus, the improvement by HT is beneficial to the diagnosis of the gear fault. Table 9. The amplitude increment of the gear meshing content and sidebands relative to the healthy condition extracted by the FrFT and the proposed method (FrFT + HT). Methods FrFT

Condition 1 mm crack 2 mm crack FrFT + HT 1 mm crack 2 mm crack

fm 0.10 0.30 0.22 0.60

   

– 4

10 10– 10– 10–

4 4 4

fm − fr 0.42  1.18  0.83  2.35 

– 4

10 10– 10– 10–

4 4 4

fm + 0.16 2.05 0.31 4.05

fr    

10– 10– 10– 10–

4 4 4 4

6 Conclusions In this article, a gear meshing content and sidebands extraction method under the runup condition by FrFT and HT is proposed. The calculation of the optimal FrFT orders and the concentrated points in fractional domain of gear meshing content and sidebands are derived in detail, which makes the application of FrFT in gear fault diagnosis more easily. A case study is employed to show the error caused by neglecting the dimensional normalization. It indicate that the LFM signals cannot concentrated in the fractional domain when the FrFT orders are calculated without the consideration of the variation of initial frequency and frequency modulation slope before and after dimensional normalization. Address to the issue that the real-valued signal has a poor energy concentration in the fractional domain even in the optimal order, this paper proposed to use the HT to construct the analytical representation of the real-valued

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signal, and then extracting the gear meshing content and sidebands from the analytical representation by FrFT. The analytic representation of the real-valued signal has a better energy concentration in the fractional domain than the real-valued signal. This characteristic is meaningful to the intelligent diagnosis and fault severity assessment. The STFT, FrFT and the proposed method (FrFT + HT) are applied to the noisy simulation signal (SNR = –20 dB), the proposed method can extract the sidebands successfully. The amplitude of the gear meshing content and sidebands extracted by the proposed method is about two times of that extracted by FrFT, which is consistent with the theoretical derivation. Furthermore, an Experiment study is carried out to verify the effectiveness of the proposed method. The results show that the proposed method can extract the sidebands which can hardly be recognized in the conventional timefrequency representation.

References 1. Hong, L., Dhupia, J.S.: A time domain approach to diagnose gearbox fault based on measured vibration signals. J. Sound Vib. 333, 2164–2180 (2014) 2. Li, G., Li, F., Liu, H., Dong, D.: Fault features analysis of a compound planetary gear set with damaged planet gears. Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci. 232, 1586– 1604 (2018) 3. Wen, L., Li, X., Gao, L., Zhang, Y.: A new convolutional neural network-based data-driven fault diagnosis method. IEEE Trans. Ind. Electron. 65, 5990–5998 (2018) 4. Zhao, R., Wang, D., Yan, R., Mao, K., Shen, F., Wang, J.: Machine health monitoring using local feature-based gated recurrent unit networks. IEEE Trans. Ind. Electron. 65, 1539–1548 (2018) 5. Xu, X., Qiao, Z., Lei, Y.: Repetitive transient extraction for machinery fault diagnosis using multiscale fractional order entropy infogram. Mech. Syst. Signal Process. 103, 312–326 (2018) 6. Mei, J., Jia, J., Zeng, R., Zhou, B., Zhao, H.: A multi-order FRFT self-adaptive filter based on segmental frequency fitting and early fault diagnosis in gears. Measurement 91, 532–540 (2016) 7. Li, Z., Wu, Z., He, Y., Fulei, C.: Hidden Markov model-based fault diagnostics method in speed-up and speed-down process for rotating machinery. Mech. Syst. Signal Process. 19, 329–339 (2005) 8. Luo, J., Yu, D., Liang, M.: Application of multi-scale chirplet path pursuit and fractional Fourier transform for gear fault detection in speed up and speed-down processes. J. Sound Vib. 331, 4971–4986 (2012) 9. Li, Z., He, Y., Chu, F., Han, J., Hao, W.: Fault recognition method for speed-up and speeddown process of rotating machinery based on independent component analysis and Factorial Hidden Markov Model. J. Sound Vib. 291, 60–71 (2006) 10. Feng, Z., Chen, X., Liang, M.: Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions. Mech. Syst. Signal Process. 52–53, 360–375 (2015) 11. Chen, X., Feng, Z.: Iterative generalized time-frequency reassignment for planetary gearbox fault diagnosis under nonstationary conditions. Mech. Syst. Signal Process. 80, 429–444 (2016)

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12. Feng, Z., Chen, X., Liang, M.: Joint envelope and frequency order spectrum analysis based on iterative generalized demodulation for planetary gearbox fault diagnosis under nonstationary conditions. Mech. Syst. Signal Process. 76–77, 242–264 (2016) 13. Wang, S., Chen, X., Selesnick, I.W., Guo, Y., Tong, C., Zhang, X.: Matching synchrosqueezing transform: a useful tool for characterizing signals with fast varying instantaneous frequency and application to machine fault diagnosis. Mech. Syst. Signal Process. 100, 242–288 (2018) 14. Sun, R., Yang, Z., Chen, X., Tian, S., Xie, Y.: Gear fault diagnosis based on the structured sparsity time-frequency analysis. Mech. Syst. Signal Process. 102, 346–363 (2018) 15. Zhao, M., Lin, J., Wang, X., Lei, Y., Cao, J.: A tacho-less order tracking technique for large speed variations. Mech. Syst. Signal Process. 40, 76–90 (2013) 16. Chen, R., Wang, Y.: Efficient detection of chirp signals based on the fourth-order origin moment of fractional spectrum. Circ. Syst. Signal Process. 33, 1585–1596 (2014) 17. Almeida, L.B.: The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process. 42, 3084–3091 (1994) 18. Ozaktas, H.M., Arikan, O., Kutay, M.A., Bozdagt, G.: Digital computation of the fractional Fourier transform. IEEE Trans. Signal Process. 44, 2141–2150 (1996) 19. Press, W.H.: Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, Cambridge (2007) 20. McFadden, P.D.: Examination of a technique for the early detection of failure in gears by signal processing of the time domain average of the meshing vibration. Mech. Syst. Signal Process. 1, 173–183 (1987) 21. Samuel, P.D., Pines, D.J.: A review of vibration-based techniques for helicopter transmission diagnostics. J. Sound Vib. 282, 475–508 (2005) 22. Chen, Z., Shao, Y.: Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth. Eng. Fail. Anal. 18, 2149–2164 (2011) 23. Li, Y., Ding, K., He, G., Lin, H.: Vibration mechanisms of spur gear pair in healthy and fault states. Mech. Syst. Signal Process. 81, 183–201 (2016)

An Empirical Study of the Effect of the Completeness of Hands-on Training Design Projects on the Preservation of Tacit Knowledge Yihui Zhou(&), Wenzhou Lin, Zhi Qiao, and Xiaozhou Li Art and Design Institute of Xi’an University of Technology, Xi’an 710048, China [email protected], [email protected], [email protected], [email protected]

Abstract. Design projects providing hands-on training practice are critical for improving and upgrading student design skills and effective transfer of tacit knowledge or “know-how”. The core of design training projects is effective preservation of tacit knowledge resourses. The study in this paper is based on the hypothesis that the relationship between the completeness of design projects and the preservation of tacit knowledge forms an inverted u-shaped curve, and that increased training loads affect negatively. Subsequent empirical study is used to prove the hypothesis. Finally, the results of the paper show the boundary conditions of the relationship with an attempt to establish theoretical basis for relevant teaching planning. Keywords: Teaching planning Preservation of tacit knowledge

 Design projects development   Design education

1 Foreword With the demand for talents brought by the vigorous development of innovative enterprises, undergraduate education of industrial design discipline pays more and more attention to the cultivation of practical ability of talents. Design practical training category of curriculum is designed to meet the needs of training practical ability. The purpose of design practical training curriculum is to complete knowledge inheritance through design subject training. Knowledge can be classified into two categories of explicit knowledge and tacit knowledge, among which tacit knowledge has great influence on the ability of design practice while it is difficult to express. Nonaka described tacit knowledge as: “tacit knowledge is deeply rooted in personal actions and their own experience, as well as the values or feelings that they believe in [1]. It has been widely presumed as the fundamental factor determining the individual design This project is supported by Culture and art research project of the ministry of culture (17DH17); Youth research fund of humanities and social sciences, ministry of education (18YJC760063). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 944–951, 2020. https://doi.org/10.1007/978-981-32-9941-2_78

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practice ability. Therefore, how to inherit more important tacit knowledge through design practical training curriculum is a major practical problem faced by current design education. Designing practical training curriculum is an important way for students to acquire design experience, but there are two problems in acquiring tacit knowledge through design practical training. First, tacit knowledge is highly personal, difficult to disseminate and replicate, and there is more uncertainty in its knowledge inheritance compared with acquiring explicit knowledge [2]. Second, there are great differences in individual learning purposes, design preferences and knowledge focus. In the process of knowledge transmission and sharing [3], there are often various conflicts between teaching and learning, which leads to low efficiency in teaching. Reasonable practical training topic setting can effectively restrict the purpose of both teaching and learning, and help the effective obtaining of relative clear knowledge content. The so-called reasonable practical training topic refers to the clear determination on the content, form, design link, design direction, design method and time planning of the practical training before teaching between teaching and learning parties. Its completeness refers to the structural characteristics of the topic determination, and provide quantitative or nonquantitative constraints on relevant content through clearer design requirements. Since the topic has been basically determined before the practical training, the constraints of the subject setting, to some extent, play a directive role in the design content of the training. From the perspective of design essence, constraints are not conducive to innovation. While from the perspective of knowledge inheritance, constraints are conducive to implementation. The binding force of a topic is determined by the completeness of its settings, so what is the relationship between the completeness and the inheritance of tacit knowledge, which is the main research content of this paper.

2 Research Design 2.1 2.1.1

Research Hypothesis

The Relationship Between the Completeness of the Subject and the Inheritance of Tacit Knowledge Firstly, a complete set of topic contains relatively comprehensive design requirements, which provides an effective guarantee for the completion of knowledge inheritance in a specific category. Moreover, since it is with very specific design orientation, individuals would have clear results reference in the design practice, which is helpful for the completion of the design practical training task. Secondly, the design objectives are relatively clear, and the knowledge points covered are relatively determined, which is conducive for the teaching and learning to reach a tacit understanding in the content of knowledge inheritance. Thirdly, the predictability of the design results is relatively high, which is conducive to real-time adjustment of teaching and learning in the training process, and to improve the efficiency in inheritance of tacit knowledge. However, too completed topic setting is not conducive to the divergent thinking performance of the individual. The knowledge inheritance of teaching and learning is in a local scope, which limits the inheritance of tacit knowledge. Firstly, a completed

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set of topics has great limitations, which is often the design of a certain product or a certain kind of product. These products do not involve tacit knowledge content with no channel for inheritance. Secondly, too completed design requirements will lead to convergence of design results, which is not conducive to the innovation of design schemes, and at the same time, the weakening design possibilities will weaken the inheritance possibility of tacit knowledge. Thirdly, the absolutized specific subject also obliterates the design possibility of individual student to his/her interest points, to some extent, it eliminates the enthusiasm of learning, and is not conducive to the inheritance of tacit knowledge. In summary, it can be found that there is an inverted U-shaped relationship between the completeness of practical topic setting and the inheritance of tacit knowledge in teaching and learning. 2.1.2 Regulating Function of Training Intensity of Curriculum The design practical training curriculum belongs to a mixed learning mode, which can be set with different training intensity according to the actual situation. Training intensity refers to the difficulty, workload, time requirement and the competitiveness among individual students in the specific setting of training curriculum content [4]. When the completeness of the subject setting is relatively high and meanwhile the intensity of training is high, its combined action can promote the inheritance of tacit knowledge. Firstly, the predictability of the design results of a completed subject setting is relatively strong. Therefore, when both teaching and learning parties are trained under high intensity with unified target in solving problems, and proportionate increase of in-depth degree, which is conducive to the inheritance of tacit knowledge. Secondly, when the topic setting is relatively completed, due to the convergence of the results of the topic, there would be strong contrast between the individual practice process and the design results with high similarity in the evaluation system, thus the competition among student individuals is relatively significant, which is conducive for the student individuals to acquire tacit knowledge in a more active manner. However, when the completeness of topic setting is relatively low and the openness of practical topic is relatively strong, the training intensity will weaken its positive role in the inheritance of tacit knowledge. Firstly, due to the relative divergence of practical training topics, student individuals have different design objectivity, and their willingness to exchange information is reduced, which limits the exchange of tacit knowledge among student individuals. Secondly, the evaluation criteria of open topics are quite different, and it is easy to form different opinions on the unified evaluation, which results in behaviour of availing of loopholes and indolent of some student individuals, weakening the competitive atmosphere as a whole, and it is not conducive to the inheritance of tacit knowledge. In summary, it can be concluded that the training intensity will weaken the inverted U-shaped relationship between the completeness of practical topic setting and the inheritance of tacit knowledge in teaching and learning. 2.2

Research Method and Research Methods

2.2.1 Theoretical Analysis Based on the implicit knowledge associated with this research and some unstable factors, such as individual and group differences because of its difficulty of inheritance,

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this article was supported by continuous sampling survey. It also applied a multi-level rotation design to gather more sample information and eliminate the negative influence of rotation deviation on the estimation accuracy as much as possible [5]. It also completed the empirical analysis based on ensuring reliability and validity. 2.2.2 Survey and Data Collection of Design Practical Training Curriculum His paper mainly studies how the completeness of the design practical training courses affects the inheritance of tacit knowledge in the process of teaching and learning. Therefore, a relatively intense comprehensive training curriculum is chosen to conduct the investigation research, with the teaching staff (teachers and related practical training instructors) and students participating in curriculum as the research objects. The time is set in the first semester of the fourth year of undergraduate curriculum. The students have already gone through the design practical training curriculum in the early stage, and they have some experience and understanding of the design practical training curriculum. The design of the questionnaire is conducted based on the pre-survey of the teachers and graduates who have participated in the training practical curriculum, and it is revised according to the feedback of the pre-survey, which forming the final questionnaire. To obtain comparative data, the same training curriculum was selected for two years separately in 2017 and 2018. 2.2.3 Variable Measurement The integrated variable study was assessed based on the Likert 5-Point Scale (1 for “strong opposite”, 2 for “disagree”, 3 for “neither disagree nor opposite”, 4 for “agree” and 5 for “strongly agree”) [6]. With regard to the related content of the completeness of the topic setting, five evaluation items were designed in the content setting, design direction, design requirements, completion indicators and evaluation strategies of the topic. According to the training intensity, four evaluation items were designed. The scope of the topic (refers to the similarity of the specific topic content among student individuals and the similarity of the work link involved in the topic), two evaluation items were designed. In terms of tacit knowledge acquisition, three evaluation items were designed.

3 Empirical Analysis 3.1

Variable Analysis

Firstly, the mean value and standard deviation of variables are analysed to provide basis for subsequent modelling. This topic adopts IBM’s SPSS (Statistical Product and Service Solutions) software as a tool for data analysis. With analysis of contents in Table 1, the correlation coefficients between variables are not higher than 0.6. It can be seen that there is no multiple collinearity among independent variables, regulatory variables and control variables, so regression model can be established.

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Variables 1 Tacit knowledge acquisition 0.868 Completeness of topic setting 0.361* Training intensity –0.090 Topic scope 0.406* Note: 1. Diagonal line (in bold) is the square root of

3.2

2

3

0.810 0.078 0.815 0.415* –0.062 AVE value; 2. * P < 0.05.

4

0.850

Reliability and Validity of Measurement Model

The second step of the study is to analyse the reliability and validity of the measurement model [7], and then with hierarchical regression method to test the inverted Ushaped relationship between the topic completeness and tacit knowledge inheritance, and the weaken of training intensity on the inverted U-shaped relationship. Reliability measurement is conducted adopting Cronbach’s Coefficient Alpha (Cronbach’s a for short) and Composite Reliability (CR for short), as shown in Table 2. All variables have Cronbach’s a greater than 0.8, and CR values greater than 0.85, indicating good reliability of the component. In addition, the convergence validity is measured by factor load and average variance extraction (AVE). The factor load of the component is above 0.75, and the AVE is above 0.65, indicating shows good convergence validity of the measurement. As shown in Table 1, the diagonal values are the square root of the AVE, and all bigger than the correlation coefficients in the rows and columns, proving good discriminant validity of the listed indicators. Table 2. Reliability and validity of scale Variables

Content

Loading Cronbach’s a C.R.

Tacit knowledge acquisition

Unwritten product design skills acquired through practical training curriculum Unwritten new method application skills acquired through practical training curriculum The similarity of topic content scope setting is high The similarity of work links involved in the topic is high The topic required design content in detail The topic confirmed specific design direction The topic clearly provided specific design requirement The topic required completion index in detail The topic explained the evaluation method in detail The topic setting is relatively difficult The topic required many design contents to be completed The topic specified the time of each design node in detail Eliminate-the-Last System for the Design Achievements

0.851 0.918

0.871

0.918 0.786

0.872 0.900

0.874

0.920 0.696

0.790 0.868 0.899 0.785 0.810

0.886

0.910 0.691

0.787 0.831 0.865 0.867

0.855

0.904 0.699

Topic scope

Topic completeness

Training intensity

AVE

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Empirical Conclusion Analysis

Firstly, the analysis results of No. 1 model containing only control variables; Secondly, the analysis results of No. 2 model containing both control variables and independent variables; Thirdly, the analysis results of No. 3 model containing control variables, independent variables and regulatory variables at the same time. The analysis results are detailed in Table 3. Table 3. Results of hierarchical regression analysis Variables

Tacit knowledge inheritance No. 1 model No. 2 model

Control variable Teaching compulsory force 0.288*** Topic workload –0.165* Direct effect Completeness of topic content Completeness of design direction Completeness of design requirements Completeness of indicators for completing the project Completeness of topic evaluation method Regulating Effect Difficult of topic setting The design workload of topic content Strict check on time design node Competitive intensity among student individuals F 3.262 R2 0.90 △R Note: 1. *P < 0.05;**P < 0.01;***P < 0.001.

No. 3 model

0.036*** –0.230***

0.294*** –0.154*

0.222** 0.216** 0.203** 0.244**

0.256** 0.250** 0.205** 0.265**

–0.156*

–0.364** –0.238 0.470*** 0.125 –0.119

3.850 0.292 0.198

3.944 0.368 0.075

The hierarchical regression results of No. 2 model show that there is an inverted Ushaped relationship between the completeness of the topic and the inheritance of tacit knowledge, and the regression results of No.3 model show that the inverted U-shaped relationship will be weakened by the increase of training intensity. Further, the inverted U-shaped feature can be clearly observed through the relationship chart (Fig. 1) between the completeness of data generated topics and the inheritance of tacit knowledge. From the analysis of the relationship chart, it can be seen that in the left and right sides of the critical point of tacit knowledge inheritance in this experiment, the curve on the left shows that the inheritance effect of tacit knowledge will increase more slowly with the increase of the completeness of topic setting in high training intensity environment than in low training intensity environment, but with higher relative

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cardinality. The curve on the right shows that the inheritance effect of tacit knowledge will increase more slowly with the decrease of the completeness of topic setting in high training intensity environment than in low training intensity environment. It also shows the weakening effect of training intensity on weakening the inverted U-shaped relationship.

Fig. 1. Impact of training intensity

4 Research Conclusion This paper analyses the role of the completeness of the design practical training topic in the knowledge inheritance during teaching and learning. Through theoretical analysis, it is proposed that there is an inverted U-shaped relationship between the completeness of practical topic setting and the inheritance of tacit knowledge in teaching and learning, and meanwhile indicating the impact of training strength to this relationship. Subsequently, through investigation and evidence collection, empirical analysis confirms this point of view. The conclusion is as follows: Firstly, the inverted U-shaped relationship is verified through empirical research, which shows that the topic setting does affect the knowledge inheritance in teaching and learning. Over-rigorous and complete topics as well as too loose topics are not conducive to the teaching and learning of tacit knowledge and the acquisition of tacit knowledge for the students, while proper topic setting is of the most efficiency. Secondly, empirical research also shows the weakening effect of training intensity on weakening the inverted U-shaped relationship. When the topic is more open, the improving of the training intensity will magnify the defect of the topic, which is not conducive to the tacit knowledge exchange among individuals and reduces the efficiency of knowledge inheritance. When the topic setting is relatively completed, the higher training intensity will promote the cooperation and sharing among individual members, which can promote the inheritance of tacit knowledge. The overall study has a certain reference significance for the design category of practical training curriculum.

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The study of this paper also has some shortcomings. Firstly, this empirical study only validates the topic setting and training intensity, and does not consider the executive capability of different teachers in different curriculum. Secondly, this study does not subdivide tacit knowledge, but with a general concept. Industrial design discipline is taken as a reference for the empirical cases, which has certain limitations and does not have reference for all design categories. Thirdly, there is no specific assessment of students’ learning ability and teachers’ or teaching assistants’ teaching ability, and it is also realized that this might be a variable with great influence.

References 1. Nonaka, I., Takeuchi, H., Meng, L.: Spiral of Knowledge Creation. China Water and Power Press, Beijing (2012) 2. Polanyi, M., Tao, X.: Personal Knowledge. Shanghai People’s Publishing House, Shanghai (2017) 3. Cummings, J.L., Teng, B.S.: Transferring R&D knowledge: The key factors affecting knowledge transfer success. J. Eng. Tech. Manag. 20(1–2), 39–68 (2003) 4. Zhou, Y., Han, Y., Wang, L.: Research on learner engagement in mixed learning activities. E-Educ. Res. (11) (2018 ) 5. Chen, G.: Review of Theoretical Research on Continuous Sampling Survey. J. Math. Stat. Manag. (05) (2012) 6. Han, G., Fan, B.: The influence of semantic differences of Likert scales on scientific measurement. Sci. Technol. Prog. Policy (20) (2017) 7. Jiang, X., Shen, Z., Zhang, N., Liao, H., Xu, H.: Reliability and validity analysis of the questionnaire. Mod. Prev. Med. (03) (2010)

Research on Structural Size Optimization of 3-TPT Parallel Mechanism Based on Stiffness Characteristics Chunxia Zhu(&) and Chengzhu Hu School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang 110168, China [email protected] Abstract. Parallel mechanism is widely used in many fields because of its strong bearing capacity, high stiffness and high accuracy. However, in recent years, the concept of optimal design has been more and more applied to the design of parallel mechanisms. In this paper, the minimum eigenvalue is taken as the objective function to optimize the structural dimension of 3-TPT parallel mechanism. Firstly, the influence of structural dimension on the stiffness performance of parallel mechanism is analyzed from the point of view of the overall structural dimension of parallel mechanism, and then the influence of the size optimization of important parts on the overall stiffness performance of parallel mechanism is examined. The minimum eigenvalue method is used to optimize the parallel mechanism, which improves the stiffness performance of the boundary region, and then improves the overall stiffness performance of the 3-TPT parallel mechanism. Keywords: Stiffness performance  3-TPT parallel mechanism Minimum eigenvalue  Optimum design  Structure size



1 Introduction Optimum design is a subject that appeared in the 1960s. Combining the principle of optimization with computer technology, application and design field is an important way for product design and improvement. Through this scientific design method, researchers can find out the best design scheme from many design schemes according to actual needs, and can also re-evaluate the parameters of existing products, so as to improve the performance of products. Therefore, optimization design is widely used in various fields of science. The advantages of optimum design lie in that, firstly, it makes the design work no longer rely on experience or intuitive judgment, making the design scheme more accurate and theoretical basis; secondly, it is faster than the traditional method of scheme analysis and checking when the structural scheme is first determined; thirdly, the optimum design is not affected by various factors like experimental data analysis. Disturbance, we can use This project is supported by National Natural Science Foundation of China (Grant No. 51575365). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 952–970, 2020. https://doi.org/10.1007/978-981-32-9941-2_79

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appropriate theory to find the optimal scheme of product parameters from a certain aspect. The analysis process can be completed by computer, which has high efficiency. The idea of optimal design is widely used in the design of parallel mechanism. Yu, Wang, Chen [1] proposed a strategy of truss topology optimization design inspired by ground structure method. On this basis, a new three-degree-of-freedom translation SPM is proposed. One characteristic of the mechanism is that each branch of the mechanism consists of a passive planar 6R single-loop closed chain (6RSCC). Liu [2] and others used a fast iteration search algorithm with spherical coordinates and variable step size to analyze and solve the reachable workspace of a 3T1R parallel mechanism, and optimized the size of the mechanism by using the longhorn whisker search algorithm. Huang, Guo, Zhang [3] presents a novel reconfigurable parallel mechanism. The proposed parallel mechanism can change its structure parameters by driving a bevel gear system fixed in the base platform. Finally, a multi-objective optimization is performed by using the Genetic Algorithm, and the workspace and global performance indexes of stiffness as well as the dexterity are considered as the performance indices to improve the performance of the reconfigurable parallel mechanism. Liu [4] proposes an optimization algorithm based on multi-objective and multi-constraint, chooses appropriate constraints, takes the linear combination of workspace and leg force as the optimization function, and uses genetic algorithm to realize the optimization process of structural parameters of the parallel platform. Li, Yan, Wang, Du and Zhang [5] presents design and optimization of an 8-DoF haptic manipulator using series-parallel mechanism. Operating performance indexes such as global conditioning index, global kinematic performance fluctuant index and workspaces are evaluated to find optimal parameters in design stage. It can be seen that the idea of optimal design has been well quoted in the design of parallel mechanisms. However, these optimization methods are seldom based on the stiffness characteristics of parallel mechanisms. Therefore, this paper takes stiffness as an evaluation index to optimize the design of 3-TPT parallel mechanisms. At present, there are few studies on optimizing the stiffness performance of parallel mechanism by optimum design method. The main reasons are as follows: Firstly, the stiffness analysis of parallel mechanism is very complicated. For a long time, stiffness analysis can not consider all kinds of factors, but only assume that parallel mechanism operates in an ideal situation. At the same time, the existing stiffness analysis coverage of parallel mechanisms is not wide enough, most of them only consider the stiffness of active joints, but the analysis of the influence of friction, gravity and other factors on the stiffness of parallel mechanisms is not enough or accurate. The lack of research on the factors affecting the stiffness performance of parallel mechanisms limits the optimization of parallel mechanisms. Secondly, the research on evaluation index of parallel mechanism stiffness is still not perfect. Many years of research have proved that the stiffness of parallel mechanisms is not a simple linear relationship, but a complex stiffness matrix as a coefficient, and all elements in the stiffness matrix are not fixed values, but change with the position of the output point. This makes the evaluation of the stiffness performance of parallel mechanism very complicated. The stiffness matrix is usually irregular and can not be used as the evaluation criterion of the stiffness performance. Therefore, the evaluation index of stiffness performance is particularly important in the research of optimizing the stiffness performance. Thirdly, the application of optimization design method in stiffness optimization design of parallel

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mechanism is not mature enough. How to integrate the optimal design method with the design of parallel mechanism is still an important problem in our current research. At present, the method of optimum design has not been paid attention to in the design of parallel mechanism. Firstly, the study of basic problems of parallel mechanism is still imperfect, and the focus of research at this stage is still on the analysis of basic theory of parallel mechanism. Secondly, the products of parallel mechanism have not been widely marketed, and there is no demand for excellent products of parallel mechanism and lack of product optimization. The power of design. Although faced with various difficulties, the optimal design of parallel mechanism is imperative. Applying the optimal design method to parallel mechanism can greatly change the current situation of poor performance of parallel mechanism products, improve the product quality of parallel mechanism and its understanding of parallel mechanism in people’s minds, and further promote the development of parallel mechanism. Based on the minimum eigenvalue method and taking the minimum eigenvalue of matrix as the evaluation index of stiffness performance, this paper first optimizes the 3TPT parallel mechanism from the point of view of the whole machine structure size in order to improve the stiffness of the boundary area, then considers the size of local parts, optimizes the size of Hooke hinge, which has the greatest impact on the stiffness of the parallel mechanism, and then improves the overall stiffness of the parallel mechanism.

2 Kinematics Analysis of 3-TPT Parallel Mechanism 2.1

DOF of 2.1 3-TPT Parallel Mechanism

In parallel mechanism, the common motion pairs are moving pair, rotating pair, spherical hinge and Hooke hinge, etc. Through the cooperation between the motion pair and the rod, the moving platform can achieve the required motion state. Formula Grübler is commonly used for calculating the degree of freedom of mechanisms. Since the analysis of the degree of freedom of most parallel mechanisms by formula Grübler is correct, formula Grübler is used to calculate the degree of freedom of 3-TPT parallel mechanisms. Formula Grübler is as follows: m ¼ 6ðl  n  1Þ þ

n X

di

ð1Þ

i¼1

In formula (1), l is the total number of components in the mechanism, n is the total number of motion pair, di is the freedom of the i pair of motion, m is the required freedom of parallel mechanism. In the structure of 3-TPT parallel mechanism, the total number of components is 8 and the number of motion pair is 9, including three moving pairs and six Hooke hinges. According to formula A, the degree of freedom of 3-TPT parallel mechanism is: m ¼ 6ð 8  9  1Þ þ 3  1 þ 6  2 ¼ 3

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Inverse Solution of Parallel Mechanisms

As shown in Fig. 1, assume that the connection point between a branch chain and a stationary platform is represented by A, and the connection point between the branch chain and a moving platform is represented by B. Using the known geometric dimensions of the dynamic and static platforms, we can clearly derive the coordinates of A in the global coordinate system and B in the local coordinate system. It can be ! found that the vector AB describes the kinematics information of the parallel mechanism’s branch chain, which is the basic parameter in the inverse kinematics problem and the key to the inverse solution of the mechanism. As shown in Fig. 1, the global coordinate system O-XYZ and the local coordinate system O1  X1 Y1 Z1 are established respectively with the center of the two triangles as the origin. The Y axis and Y1 axis in the two coordinate systems point to a vertex of their respective triangles.

Fig. 1. The structure sketch of 3-TPT parallel mechanism

For 3-TPT parallel mechanism, its generalized coordinate X is the coordinate of O1 point, and has the following relations: ! ! ! ! AB ¼ AO þ OO1 þ O1 B ¼ P1 ð X Þ

ð2Þ

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! ! The vector O1 B in the global coordinate system is equal to the vector O1 B in the ! local coordinate system, so the vector AB can be determined. Let h be a twodimensional vector consisting of two turning angles of Hooke hinge and a unit vector n whose direction is the axial direction of the branch chain. ! AB ¼ l  n ¼ P2 ðh; lÞ

ð3Þ

Formulas (2) and (3) are combined and squared on both sides. ! ! ! ! ! ! l2 ¼ 2 AO  OO1 þ 2OO1  O1 B þ 2 AO  O1 B

ð4Þ

It can be seen from formula (4) that the length of three branches of 3-TPT parallel mechanism is only related to the coordinates of O1 point of output point, but not to the length of other branches. Therefore, by substituting the mechanism parameters (As shown in Fig. 2) into formula (4), the inverse position expression of 3-TPT parallel mechanism can be obtained as follows: 8 ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi > > 3 a  b > > > ða  bÞ2 þ z2 Þ2 þ ½y þ l1 ¼ ðx þ > > 6 2 > > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > pffiffiffi < 3 2 ðb  aÞ2 þ z2 l2 ¼ x þ ½y þ > > 3 > > ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > pffiffiffi > > > 3 ba 2 > > Þ þ ½y þ ða  bÞ2 þ z2 : l3 ¼ ðx þ 2 6 In order to facilitate calculation and analysis, let c ¼ a  b, the original formula can be simplified as follows: 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi > > 3 2 c 2 > > > l1 ¼ ðx þ Þ þ ðy þ cÞ þ z2 > > 2 6 > > > ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > pffiffiffi < 3 2 ð5Þ cÞ þ z2 l2 ¼ x2 þ ðy  > > 3 > > ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > pffiffiffi > > > 3 c > 2 > cÞ2 þ z2 : l3 ¼ ðx  Þ þ ðy þ 2 6

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3 Structure Size Optimization of 3-TPT Parallel Mechanism 3.1

Analysis of the Influence of Structure Size on the Stiffness of Parallel Mechanism

According to the analysis of the minimum eigenvalue method, it can be found that the stiffness distribution of the parallel mechanism is the largest in the center, and the stiffness of the point farthest from the center is the smallest in the horizontal distance. The mechanical equipment is usually based on the minimum value of performance. Therefore, the stiffness performance of the parallel mechanism can be improved by improving the stiffness performance of the point. Based on the workspace analysis of parallel mechanism, one of the farthest points in the workspace from Z axis C (0, −513.20, 610.98) is taken as the reference point. According to the simulation diagram of minimum eigenvalue method, the minimum eigenvalue kmin of K0 matrix appears at this point on the plane where C is located. The structure size of 3-TPT parallel mechanism is mainly composed of the following parts. As shown in Fig. 2. Static platform side length a, moving platform side length b, branching length li , The maximum length of branched chain is lmax and the minimum length is lmin . The size of Hooke hinge has no great influence on the structure size of the whole machine, and then it will be analyzed in the local size optimization, so the influence of Hooke hinge is not considered here.

a

li

b Fig. 2. The structure size of 3-TPT parallel mechanism

To improve the stiffness performance of parallel mechanism, it is theoretically possible to increase the size of structure and parts without restriction, but this method is also out of the essence of optimization design. Therefore, the structural optimization design of 3-TPT parallel mechanism should be limited to a certain size range.

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Restricting the area occupied by the whole parallel mechanism can optimize the size of the parallel mechanism within a certain range, avoid the infinite increase of its structure, fix the edge length a of the static platform, and keep the whole area of the parallel mechanism unchanged. In this paper, edge length difference C of dynamic and static platforms, maximum length lmax of branched chains and working length la of ball screw are selected as optimization variables. Assuming that the length of the branched chain connecting the driving joint and the static platform is proportional to the length of the branched chain connecting the moving platform, it is regarded as the same length here. Size ratio is 1:1. Since the edge length a of the static platform is a fixed value, the edge length b of the moving platform can be obtained by the difference c of the edge length. The parameters of the length of the branched chain can be obtained by lmax and la . Therefore, the overall structure size of the parallel mechanism can be determined completely by c, lmax and la . Next, the influence of size parameters on the stiffness of parallel mechanism is analyzed. (1) Analysis of the influence of dynamic and static platform dimensions on the stiffness of parallel mechanisms. Because the size of the static platform is fixed, the analysis of the dynamic platform can be obtained by the difference of the edge length between the dynamic platform and the static platform. To solve the stiffness matrix of parallel mechanism, the inverse Jacobian matrix of parallel mechanism must be solved first. The coordinate value of point C is substituted into the inverse Jacobian matrix, and the edge length difference C is regarded as a variable. It can be seen that all elements of the inverse Jacobian matrix are functions of C. It can be obtained: 2

J 1

A11 ðcÞ ¼ 4 A21 ðcÞ A31 ðcÞ

A12 ðcÞ A22 ðcÞ A32 ðcÞ

3 A13 ðcÞ A23 ðcÞ 5 A33 ðcÞ

ð6Þ

Next, the stiffness matrix of the 3-TPT parallel mechanism is required to be solved. According to the analysis of the influence of the components of the branched chain on the stiffness, taking lmax and la as variables, the elements in the stiffness matrix of the branched chain should be a function of lmax and la . The expression of the stiffness matrix is as follows: 2

3 0 0 Bðlmax ; la Þ 5 0 Bðlmax ; la Þ Kl ¼ 4 0 0 0 Bðlmax ; la Þ

ð7Þ

Through the obtained inverse Jacobian matrix and the stiffness matrix of the branch chain, the stiffness matrix of the parallel mechanism can be obtained as follows:

Research on Structural Size Optimization of 3-TPT Parallel Mechanism K ¼ J T Kl J 1 2

A211 þ A221 þ A231 6 ¼ Bðlmax ; la Þ4 A11 A12 þ A21 A22 þ A31 A32 A11 A13 þ A21 A23 þ A31 A33

A11 A12 þ A21 A22 þ A31 A32 A212 þ A222 þ A232 A13 A12 þ A23 A22 þ A33 A32

959

3 A11 A13 þ A21 A23 þ A31 A33 7 A13 A12 þ A23 A22 þ A33 A32 5 A213 þ A223 þ A233

ð8Þ By analyzing the configuration of the stiffness matrix, the following characteristics can be found: (a) The principal diagonal elements of the stiffness matrix are the sum of squares of the elements in each column of the inverse Jacobian matrix. (b) Joint stiffness B(lmax ,la ) can be regarded as the linear coefficient of stiffness matrix and Jacobian matrix. (c) The sum of the principal diagonal elements of the stiffness matrix is equal to 3. (d) It is found that although the stiffness matrix of parallel mechanism has some peculiar rules, its evaluation of stiffness performance has no good effect. As can be seen from Fig. 3, the minimum eigenvalue increases with the increase of the edge length difference between dynamic and static platforms. When the edge length difference is greater than 400, the relationship curve is basically close to a straight line. The initial value of edge length difference c is 900 mm. If the stiffness of the mechanism is to be improved, the value of C should be greater than 900 mm. In this paper, the size of the static platform remains unchanged, and the value of c should be less than 1200 mm. Therefore, the difference of side length can be obtained c 2 ð900; 1200Þ.

Fig. 3. The relationship between side length difference and minimum eigenvalue

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(2) Analysis of the influence of branch chain size on the stiffness of parallel mechanism. According to the workspace inequality of 3-TPT parallel mechanism, when the side length difference C changes, in order to meet the requirements of the working range, the maximum length of the branched chain lmax and the working stroke la of the ball screw must also change accordingly to ensure that the parallel mechanism can reach the required processing position. Therefore, it is necessary to change the structural size parameters so that the reference point can still be within its working range. Assuming that the lengths of the two connecting rods on the branched chain are equal, the structural dimensions of the branched chain can be fully expressed by the maximum length of the branched chain lmax and the working stroke la of the ball screw. For the analysis of the composition and solution of the total stiffness of the branched chain, we know that the Hooke hinge with the lowest stiffness performance is the main factor that restricts the stiffness of the branched chain, but it is not analyzed in this paper for the time being. The influence of the overall structure size of the parallel mechanism is mainly investigated. Therefore, for the stiffness analysis of branched chains, only lmax and la are used as variables, and other dimensions are unchanged. Through the analysis of the stiffness performance of the branched chain, we can know that variables lmax and la have a certain influence on the stiffness of the branched chain. The maximum length lmax affects the length of the two connecting rods on the branched chain, which leads to the change of the stiffness of the two connecting rods, while la is closely related to the axial stiffness of the ball screw. The effects of lmax and la on the minimum eigenvalue size were analyzed. (a) Considering lmax as a variable, taking the ball screw working stroke la = 300 and keeping other parameters unchanged, the variation trend of maximum length and minimum eigenvalue of branched chain can be obtained, as shown in Fig. 3. Although the trend of the change curve in Fig. 4 can be found that it has a larger inclination angle, according to the change of the minimum eigenvalue, it can be found that the change range is not large, but in fact the change trend is very gentle. It also shows that the stiffness of the connecting rod is generally large, and the stiffness change caused by the change of its length is not the main factor affecting the stiffness of the whole parallel mechanism. (b) Consider la as the variable, take the ball screw working stroke lmax = 1200, and keep the other parameters unchanged, which can get the change of the working curve of the ball screw and the change trend of the minimum eigenvalue, as shown in Fig. 4. When the maximum length lmax of the branch is fixed, the minimum length lmin of the branch can be obtained by the working stroke la of the ball screw. The working stroke of the ball screw mainly affects the axial rigidity of the screw. When the working stroke la increases, the rigidity of the screw decreases. As can be seen from Fig. 5, the minimum characteristic value also decreases. (c) Analysis of the influence of the change of the side length difference on the size of the branch.

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Fig. 4. The relationship between lmax and minimum eigenvalue

Fig. 5. The relationship between la and minimum eigenvalue

It can be seen from the above analysis that the side length difference c and the branch size lmax and la have an influence on the rigidity of the whole machine. Therefore, c, lmax and la are regarded as design variables, and a certain optimization algorithm is used to improve the structural size of the parallel mechanism. It is feasible to optimize the stiffness characteristics of the whole machine.

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While analyzing the effects of the three variables on the stiffness of the whole machine, the relationship between the three variables cannot be ignored. According to the working space inequality of the parallel mechanism: 8 pffiffiffi > 3 2 c 2 2 > > cÞ þ z2  l2max ðlmax  la Þ  ðx þ Þ þ ðy þ > > 2 pffiffiffi 6 > > < 3 2 ðlmax  la Þ2  x2 þ ðy  cÞ þ z2  l2max > 3 > > pffiffiffi > > > c > 2 2 : ðlmax  la Þ  ðx  Þ þ ðy þ 3 cÞ2 þ z2  l2max 2 6

ð9Þ

At the reference point C (0, –513.20, 610.98), when the side length difference c increases, lmax must also increase to ensure that the inequality continues. When la remains unchanged and lmax increases, the range of values of the inequality will become smaller, that is, the working space of the parallel mechanism will be significantly reduced, and the limit point of the edge will not be within its range. It can be concluded that the stiffness performance of the parallel mechanism has a very important relationship with its structural scale design. The structural scale design is one of the important means of the stiffness optimization design of the parallel mechanism. By optimizing the various dimensional parameters, the parallel mechanism can be positioned. Has a good performance indicator. 3.2

Establishment of Stiffness Optimization Model for Parallel Mechanism

According to the branch stiffness analysis of the 3-TPT parallel mechanism, it can be found that the passive joint stiffness has the greatest influence on the total stiffness of the branch, but it has no significant influence on the structural size of the parallel mechanism. It can be analyzed separately and not considered here. Consider the parameters that have a large influence on the structure size, such as the running distance of the ball screw and the length of the two links on the branch for the rigidity of the whole machine. Determination of design variables The optimization of this paper is to optimize the structural size of the 3-TPT parallel mechanism, and finally achieve the purpose of improving the rigidity of the whole machine. Through the simulation analysis of the influence of each dimension variable on the stiffness of the parallel mechanism, it is considered that the running distance of the ball screw is set to la , the maximum length of the branch elongation is set to lmax , and the length difference c between the dynamic and static platforms is taken as The design variables for the stiffness optimization of the parallel mechanism are reasonable and effective. In order to ensure that the overall occupied space of the parallel mechanism is within the control range, the static platform size a is fixed, so that the entire mechanism does not increase the footprint regardless of other parameters.

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Choice of constraints For the designed 3-TPT parallel mechanism, the constraints on structural size optimization mainly exist in the following aspects: (a) In order to ensure that the operation is singular, the length of the static platform should always be longer than the length of the moving platform. Therefore, the length difference c between the dynamic and static platforms should always be greater than zero. (b) For the coordinates of the selected reference point for stiffness optimization, after the size optimization, the working space of the parallel mechanism should still pass that point. The minimum length lmax  la of the branch can be obtained from the running distance la of the ball screw and the maximum length lmax of the branch. Through the analysis of the position inverse expression of the parallel mechanism, it can be obtained: 8 pffiffiffi > 3 2 c 2 2 > > cÞ þ z2  l2max ðlmax  la Þ  ðx þ Þ þ ðy þ > > 6 2 > > pffiffiffi < 3 2 2 2 ðl  l Þ  x þ ðy  cÞ þ z2  l2max max a > 3 > > pffiffiffi > > > c > 2 2 : ðlmax  la Þ  ðx  Þ þ ðy þ 3 cÞ2 þ z2  l2max 2 6

ð10Þ

It can be seen from the simulation of the influence of the three variables that the increase of lmax and la will greatly reduce the minimum eigenvalue, therefore, lmax and la should take the minimum value as much as possible. The analysis shows that when determining any c value, lmax ¼ maxli , la ¼ maxli  minli . Substituting the reference point coordinates into Eq. (5). pffiffiffi 8 3 2 c 2 > 2 > < ðlmax  la Þ ¼ ðx þ Þ þ ðy þ cÞ þ z2 2 6 pffiffiffi > > : x2 þ ðy  3 cÞ2 þ z2 ¼ l2 max 3

ð11Þ

According to the range of the length difference c 2 ð900; 1200Þ of the side, it can be concluded that: 8 1 2 > 2 2 > < lmax ¼ c þ 1081:67 3 pffiffiffi ð12Þ > > 2 : ðlmax  la Þ ¼ ð513:20  3 cÞ2 þ 799:972 3 Formula (1) can be used as constraints for optimization. For the dimension parameters of the optimized parallel mechanism, the reference point should satisfy this inequality. When the new workspace is required to fully satisfy the original workspace, it is also necessary to consider whether the other limit points conform to the inequality.

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Establishment of the objective function For a parallel mechanism, the stiffness matrix cannot visually show the stiffness of the working point position, and thus cannot be an indicator for evaluating the stiffness performance. This also makes the establishment of the optimization objective function of the parallel mechanism difficult. Through the analysis of the two methods of the static stiffness performance index of the parallel mechanism, it can be found that the minimum eigenvalue method is more effective for guiding the stiffness optimization of the parallel mechanism. The main reason is that it does not need to consider the influence of external force, and avoids the change due to external force. Various problems such as the change of the minimum stiffness region, only the region with the weakest static stiffness performance is considered, which makes more sense for the selection of the optimization target. In this paper, the reference point C (0, –513.20, 610.98) is selected for research. According to the simulation results of the minimum eigenvalue, the farther away from the Z axis, the smaller the minimum eigenvalue. Point C is one of the points farthest from the Z axis. Therefore, it is important to examine the minimum eigenvalue of point C. According to the trend of the minimum eigenvalue, the ultimate goal of our optimization design is to increase the minimum eigenvalue of the C-point position, that is, to maximize kmin by optimizing the structure size. Therefore, it can be concluded that the objective function is max kmin . 3.3

Solution of Stiffness Optimization Model of 3-TPT Parallel Mechanism

Through the above analysis, the stiffness optimization model of the 3-TPT parallel mechanism can be obtained as follows: 9 maxkmin ; > > = s:t: c [ 0; 1 2 2 2 lmax ¼ 3 c þ 1081:67 ; > pffiffi > ; ðlmax  la Þ2 ¼ ð513:20  33 cÞ2 þ 799:972

ð13Þ

Due to the complexity of the stiffness matrix of the parallel mechanism, when c is substituted as a variable, the eigenvalue of the matrix K T K cannot be obtained. Therefore, the mathematical model of the minimum eigenvalue kmin cannot be obtained, so the conventional optimization algorithm cannot be used to optimize the stiffness of the parallel mechanism. According to Figs. 3 and 4, the influence of lmax and la on the variation law of the minimum eigenvalue is known as a monotonically decreasing function. When the side length difference c is determined, lmax and la can be obtained. Therefore, the side length difference c can be regarded as a given value, and for a given different c value, the minimum eigenvalue can be solved, and then the influence of c on the minimum eigenvalue can be analyzed. Through Matlab, c is analyzed in steps of 1 mm, and the minimum eigenvalue kmin is analyzed point by point, and the influence of constraints is considered. The result is shown in Fig. 6:

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Fig. 6. Comprehensive analysis diagram

In comparison with Fig. 1, it is found that the structural size change on the branch only reduces the minimum eigenvalue somewhat, and the overall change trend does not change. Through the comprehensive analysis, the following conclusions are drawn: (1) When considering only the structural size, the difference in the edge length of the two platforms plays a leading role in improving the stiffness of the component, and the greater the side length difference, that is, the smaller the side length of the moving platform, the smaller the side length of the moving platform. The parallel mechanism is stiffer. (2) The main purpose of increasing the maximum length of the branch is to satisfy the original processing space condition, but the increase of the length also reduces the minimum eigenvalue. Therefore, it can only be lengthened to meet the requirements.

4 Optimization Design Effectiveness Analysis For the dynamic and static platform length difference c, it is usually affected by other factors, such as the allowable corner of the Hook hinge, the mutual interference between the components or the installation of the tool drive components, etc., and cannot be endlessly increased to the extreme. Assume that the maximum side length difference that can be achieved by the static and static platforms is 1100 mm, and lmax = 1254.3 mm and la = 445.13 mm can be obtained by calculation.

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Evaluation of Stiffness Optimization Using Minimum Eigenvalue Method

As shown in Fig. 7, the simulation results obtained by simulating the plane stiffness distribution of the parallel mechanism at Z = 800 mm by the minimum eigenvalue method are shown. Among them, the figure (a) is the pre-optimization result, the figure (b) is the result after the optimization h, and the simulation picture before and after the optimization is obtained, which can be obtained:

Fig. 7. Minimum eigenvalue method contrast figure

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Before and after the comparison optimization, the distribution of stiffness can be found: (1) The minimum value of the minimum eigenvalue before optimization is 8.397 108 , and the optimization is 1.037 109 . The minimum eigenvalue of the parallel mechanism is obviously improved when the structure is optimized. The maximum value of the minimum eigenvalue before optimization is 1.827 109 . After the 2.328 109 , it can be seen that the optimization of the mechanism stiffness has been effectively improved. (2) When optimizing the structural size of the parallel mechanism, the position of each limit point is considered, and therefore, the working space in the plane has substantially no significant change. Through the analysis, the following conclusions can be drawn. First, the limit point coordinates are used as the working performance index of the parallel mechanism, and the optimization of other characteristics of the parallel mechanism is effective. Secondly, it can be seen from the optimized comparison chart that the minimum eigenvalue of the edge region of the workspace has been significantly improved, that is, the stiffness performance of the region with the weakest stiffness of the parallel mechanism is improved, which proves that the stiffness optimization design method is Effective. 4.2

Evaluation of Stiffness Optimization by Static Stiffness Property Method

In order to analyze whether the 3-TPT parallel mechanism is optimized under the force condition, the static stiffness performance commercial method is a more effective test method. Using the dimensional data of the optimized 3-TPT parallel mechanism, the stiffness of the working point in the plane motion of Z = 800 mm is analyzed, and the external forces, Fx ð500; 0; 0Þ, Fy ð0; 500; 0Þ, Fz ð0; 0; 500Þ are respectively applied to the working point, which can be obtained as shown in Fig. 8. Through the data collection of the static stiffness performance quotient, it can be concluded that the unit is N/mm as shown in Table 1:

Table 1. P(X) value contrast before and after optimization Fx ð500; 0; 0Þ Fy ð0; 500; 0Þ Fz ð0; 0; 500Þ PðXÞmax Before PðXÞmax After PðXÞmin Before PðXÞmin After

4.370 4.674 2.602 2.897

104 104 104 104

4.284 4.582 2.695 3.120

104 104 104 104

1.534 1.641 5.813 7.991

105 105 104 104

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x 10 4.6 4

x 10

4.4

Static stiffness quotient

5

4.2

4.5

4

4

3.8

3.5

3.6

3

3.4

2.5 500 400

3.2

200

0

0

3

-200

Y(mm)

-500

X(mm)

-400

(a) 4

5

x 10

x 10 4

5

x 10

x 10

4.4

4.2 4.5 4 4 3.8 3.5 3.6 3 500

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5 Static stiffness quotient

1.6

1.8

1.5

1.6

1.4

1.4

1.3

1.2

1.2

1

1.1

0.8 500

1 400

400 200

0

0 -200

Y(mm)

-500

-400

(b)

X(mm)

200

0

0.9

0

3.2 -200

Y(mm)

-500

-400

X(mm)

(c)

Fig. 8. Optimization result of the static stiffness performance commercial method

From the optimization of the static stiffness performance quotient simulation map and the maximum and minimum static stiffness performance quotient, the following conclusions can be drawn: (1) Before and after optimization, the parallel mechanism has a constant change trend of static stiffness on the Z = 800 mm plane, and the working space is basically unchanged. (2) After optimization, the maximum and minimum static stiffness performance quotients have been significantly improved under X, Y and Z directions, that is, the static stiffness performance quotients have been significantly improved, which proves the effectiveness of the optimization method.

5 Conclusions Firstly, some applications of optimization design in parallel mechanism design are briefly introduced, and the importance of structure optimization idea to parallel mechanism structure design is expounded. The reason why the optimization design

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method has not been studied much in the field of stiffness performance optimization of parallel mechanism is analyzed. It is pointed out that the stiffness performance index is the guidance for stiffness optimization of parallel mechanism, and the optimum design potential of parallel mechanism is pointed out. It is imperative that the optimal design method will greatly change the current situation of poor performance of parallel mechanism products, improve the product quality of parallel mechanism, and further promote the development of parallel mechanism. In this paper, the optimization design type is dimension optimization. Firstly, the influence of structure size on the stiffness of the parallel mechanism is analyzed. Through simulation analysis, the influence of three main size parameters of 3-TPT parallel mechanism on the stiffness of the whole machine is pointed out. By analyzing the three important size parameters of the 3-TPT parallel mechanism that can determine the size of the whole machine, it is determined as the optimized design variables, and the constraints of the size optimization are analyzed through the geometric inequalities of the workspace. The minimum eigenvalue is used as the evaluation index of the stiffness of the parallel mechanism. Therefore, the minimum eigenvalue is taken as the objective function of this optimization. According to the special properties of the stiffness distribution, the C point with the weakest stiffness is selected as the optimization reference point, and the minimum eigenvalue at the point is maximized by the simulation method to improve the stiffness of the whole mechanism. It can be seen from the optimized comparison chart that the minimum eigenvalue of the edge region of the workspace has been significantly improved, which proves that the optimization method is effective. Through the static stiffness performance quotient method, it can be seen that the performance of the mechanism is improved when the mechanism is subjected to various directions of force, which proves the effectiveness of the optimization method again. Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant No. 51575365), the Natural Scientific Foundation of Liaoning Province (Grant No.2015020127), Project of Promoting Talents in Liaoning Province (Grant No. XLYC1807065) and Shenyang Young and Middle-aged Science and Technology Innovation Talents Support Plan (Grant No.RC180193).

References 1. Yu, W., Wang, H., Chen, G.: Design and kinematic analysis of a 3-translational-DOF spatial parallel mechanism based on polyhedra. Mech. Mach. Theory 121, 92–115 (2018) 2. Liu, Z., Luo, Y., Shi, Z., Xia, Y., Xie, D.: Size optimization design of 3T1R parallel mechanism based on workspace. J. Mech. Trans. 42(10), 77–82 (2018) 3. Huang, G., Guo, S., Zhang, D., et al.: Kinematic analysis and multi-objective optimization of a new reconfigurable parallel mechanism with high stiffness. Robotica 36(2), 17 (2018) 4. Liu, X.: Kinematics analysis and structural parameter optimization of a six-degree-offreedom parallel platform. North University of China (2018) 5. Li, Y., Yan, Z., Wang, H., Du, Z., Zhang, Y.: Design and optimization of a haptic manipulator using series-parallel mechanism. In: 2012 IEEE International Conference on Mechatronics and Automation, Chengdu, pp. 2140–2145 (2012)

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6. Dai, X., Wang, P., Gong, D.: Multi-objective optimization of redundant parallel mechanism based on immune genetic algorithm. J. Harbin Eng. Univ. 39(12), 2033–2039 (2018) 7. Guo, J., Zhao, L., Shi, J.: The Analysis on the Singularity of a 3-TPT Parallel Robot. In: International Conference on Automation, Communication, Architectonics. Trans Tech Publications (2011) 8. Lu, C.M., Xie, L.Y., Huang, Y.G., et al.: Monte-Carlo simulation for error analysis of 3-TPT parallel platform. J. Eng. Des. 14(4), 304–307 (2007) 9. Zhu, C., Wang, J., Chen, Z., et al.: Dynamic characteristic parameters identification analysis of a parallel manipulator with flexible links. J. Mech. Sci. Technol. 28(12), 4833–4840 (2014) 10. Wu, W.G., Gao, L.Y.: Parameter optimization of a stability-training platform’s 4-PSS/PS parallel mechanism based on training ability evaluation index and PSO algorithm. Chin. J. Mech. Eng. 31(1), 50 (2018) 11. Fan, R., Liu, H., Wang, D.: Workspace analysis and parameter optimization of 3-DOF parallel mechanism. Appl. Mech. Mater. 373–375, 2136–2142 (2013) 12. Chablat, D., Wenger, P.: Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the Orthoglide. IEEE Trans. Rob. Autom. 19(3), 403–410 (2007) 13. Lu, K.: Dynamics optimization design of planar 3-DoF parallel mechanism. China Mech. Eng. (2010) 14. Sharifzadeh, M., Masouleh, M.T., Kalhor, A., et al.: An experimental dynamic identification and control of an overconstrained 3-DOF parallel mechanism in presence of variable friction and feedback delay. Rob. Auton. Syst. 102, 27–43 (2018) 15. Ni, Y.: 3 UPS-RPR parallel mechanism static stiffness optimization design. Tianjin Polytechnic University (2017)

Vibration Response Analysis of Gearbox Housing of High Speed Train Under Wheel and Rail Excitation Haiyan Zhu(&), Xiao Su, Lei Tao, and Qian Xiao School of Mechanical and Vehicle Engineering, East China Jiaotong University, Nanchang 330013, China [email protected]

Abstract. In order to understand the true vibration characteristics of the gearbox housing during operation, the time domain analysis of the different positions of the gearbox housing should be carried out. This paper introduces the modeling and research methods of the vibration characteristics response of the gearbox housing of high-speed trains, and analyzes and verifies the data of each measuring point under the case of driving in a straight line. The main modal parameters of the acceleration response of each position of the gearbox housing are obtained through comparison. The result provides reference value for structural improvement of the gearbox housing of high-speed trains. Keywords: High-speed trains Vibration response

 Wheel polygon  Gearbox housing 

1 Introduction As the main vehicle of high-speed railway, the safety, stability and reliability of highspeed train structure have always been the top priority of vehicle design [1]. In the case of high-speed train operation, the dynamic operating environment of the train system and the vibration transmission between the structural components of the system are quite different compared with the general speed [2–4]. The vibration frequency range is significantly higher than that of the traditional rolling stock. The gear transmission system that plays the role of connecting and transmitting power is a key force transmission device of the train, which is prone to failure [5–7]. This paper mainly analyzes the vibration response of the wheel not round to the gearbox housing at a speed of 300 km/h.

The authors would like to thank anonymous reviewers for their helpful comments and suggestions to improve the manuscript. This research was supported by the National Natural Science Foundation of China (Grant No. 51665015), the Natural Science Foundation of Jiangxi Province (Grant No. 20181BAB206025), and the Science and technology project of Jiangxi Education Department (Grant No. GJJ170368). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 971–976, 2020. https://doi.org/10.1007/978-981-32-9941-2_80

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2 Rigid-Flexible Coupled Modeling of Vehicle Dynamics 2.1

Establishment of Vehicle Dynamics Model

Based on vehicle dynamics parameters, the vehicle dynamics model considering the gear transmission system is established in SIMPACK. The parameters of the gear transmission system are shown in Table 1. Table 1. The parameters of gear transmission Transmission gear parameters of Pinion teeth Modulus Pinion initial engagement angle Pinion tooth width Pinion displacement coefficient Meshing stiffness ratio Helix angle Young’s modulus

2.2

CRH3 high-speed EMU 35 Large gear teeth 85 6 mm Normal pressure angle 20° 0° Large gear initial meshing angle 0° 66 mm Pinion tooth width 65 mm 0.225 Gear shift coefficient 0.024 0.8 Poisson’s ratio 0.3 18° Flank clearance 0 mm 2.1e11 Damping coefficient 5000 Ns/m

Flexible Body Modeling in Vehicle Systems

The gearbox housing is a relatively complicated model, which includes structures such as ribs and oil hole housings. The gearbox housing model is imported into ANSYS, and the established finite element model is shown in Fig. 1. Then the rigid-flexible coupled dynamics model generated in ANSYS is shown in Fig. 2.

Fig. 1. Finite element model of gearbox housing body

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Fig. 2. Rigid-flexible coupling dynamic model of high-speed train

3 Vibration Response Analysis of Gearbox Housing Vibration response analysis of gearbox housing housing based on rigid-flexible coupled dynamics model. The analysis conditions are as follows: The speed is 1st, 11th and 20th steps of the wheel’s multilateral behavior when the train runs at 300 km/h in a linear orbit. The wheel harmonic depth is 0.05 mm and 0.1 mm, and the simulation time is 10 s. 3.1

Simulation Analysis of Linear Working Conditions

Table 2 shows that the maximum value of the vibration acceleration appears at the bottom vertical acceleration response of the 20-step polygon with a depth of 0.1 mm. The minimum value appears at the lateral acceleration response of the bottom of the box with a depth of 0.05 mm in the first-order polygon. It can be seen that the wheel polygon excitation has a great influence on the vertical response of the bottom of the gearbox housing and the lateral response of the top of the box. Table 2. Maximum acceleration statistics under linear conditions Sensor position Direction Velocity(km/h) First order 0.05 mm 0.1 mm 11th order 0.05 mm 0.1 mm 20th order 0.05 mm 0.1 mm

Top of the cabinet Bottom of the cabinet Vertical(g) Landscape(g) Vertical(g) Landscape(g) 300 3.7 3.81 4.58 5.34 4.39 7.31

1.46 1.45 1.91 2.63 1.82 5.73

4.67 4.83 5.16 5.74 7.59 15.3

0.81 0.86 1.58 2.67 1.31 4.79

The vibration acceleration response of the gearbox housing caused by the noncircular wheel speed of 300 km/h is shown in Fig. 3.

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1.2 Effective Value of Lateral Acceleration of Gearbox(g)

Effective Value of Vertical Acceleration of Gearbox(g)

In order to more intuitively express the vibration response of the wheel polygon excitation to the gearbox housing, this paper calculates the effective value of the vibration acceleration of the gearbox housing under linear conditions to obtain the effective value of the vibration acceleration of the wheel polygon excitation to the gearbox housing.

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Fig. 4. Comparison of effective values of gearbox housing acceleration under 300 km/h

The comparison of the effective values of the vibration acceleration of the wheel polygon excitation on the top of the gearbox housing and the bottom of the box under the linear speed of 300 km/h is shown in Fig. 4. It can be seen from Fig. 4(a) that the vertical acceleration response of the bottom of the gearbox housing is larger than the top of the box, and the wheel polygon depth is 0.1 mm, which is larger than the wave depth of 0.05 mm. It can be seen from Fig. 4(b) that the lateral acceleration response of the top of the box is larger than the bottom of the box, and the wheel polygon depth is 0.1 mm, which is larger than the wave depth of 0.05 mm. It is concluded that the vertical response of the wheel polygon excitation to the bottom of the gearbox housing and the lateral response of the top of the box are relatively obvious.

4 Conclusion The three conclusions obtained from this paper are as follows: (1) According to the rigid-flexible coupled dynamics theoretical model, the vibration response analysis of the high-speed train gearbox housing case under the wheelrail excitation can be carried out. (2) The wheel polygon excitation has a great influence on the vertical response of the bottom of the gearbox housing and the lateral response of the top of the box.

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(3) The acceleration response of the gearbox housing also increases with the increase of the wheel polygon and wave depth, and the increase is more obvious with the increase of the wave depth.

References 1. Wang, Z., Mei, G., Zhang, W., et al.: Effects of polygonal wear of wheels on the dynamic performance of the gearbox housing housing of a high-speed train. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 232(6), 1852–1863 (2018) 2. Chou, M., Xia, X., Kayser, C.: Modelling and model validation of heavy-haul trains equipped with electronically controlled pneumatic brake systems. Control Eng. Pract. 15(4), 501–509 (2007) 3. Xiang, L., Li, B., Gong, J., et al.: Maximum likelihood Identification of Multi-particle Model for High Speed EMUs. Comput. Simul. 33(1), 181–187 (2016) 4. Yang, H., Zhang, K., Wang, W.: Active fault-tolerant predictive control for multi-model switching of high-speed EMU. Control Theory Appl. 29(9), 1211–1214 (2012) 5. Miyaji, Zhou, J., Sun, W., et al.: Coupling vibration analysis of elastic body and bogies in high speed trains. J. Traffic Transp. Eng. (4), 41–47 (2011) 6. Klinger, D, Co operrider, N.K., Hedrick, J.K., White, R.H.: Guideway-Vehicle Cost Reduction. Final Report, Boston, US. DOT-TST-76–95 (1976) 7. Anis, Z., Hedrick, J.K.: Characterization of Rail Track Irregula. Final Report, Boston, US. DOT, Contract No. DOT-TST-1206 (1977)

An Intelligent Fatigue Life Prediction Method for Aluminum Welded Joints Based on Fatigue Characteristics Domain Li Zou1,2(&), Hongxin Li1, and Wei Jiang1 1 Software Institute, Dalian Jiaotong University, Dalian 116002, China [email protected], [email protected], [email protected] 2 Sichuan Provincial Key Lab of Process Equipment and Control, Zigong 643000, China

Abstract. In order to reduce the dispersion level of fatigue test samples of aluminum alloy welded joints and further improve the fatigue life prediction accuracy, the concept of fatigue characteristic domain is proposed. Based on the attribute reduction of neighborhood rough set, the division method of fatigue characteristic domain is determined. According to the attribute reduction, the key fatigue life influencing factor set of welded joint is used to divide all fatigue test samples into several sub-domain sets, and each sub-domain set corresponds to a fatigue character sub-field. Support vector machine has the characteristics of simple calculation, perfect theoretical foundation and suitable for small sample problems. Based on its characteristics, an improved support vector machine model for fatigue life prediction of aluminum alloy welded joints is established in the determined fatigue characteristics domain. The experimental results show that compared with the least squares fitting method, the support vector machine model has stronger anti-noise ability and higher prediction accuracy. Keywords: Fatigue life Intelligent prediction

 Welded joints  Fatigue characteristics domain 

1 Introduction In recent years, relevant experts from domestic and foreign country have done a lot of research on fatigue life prediction method and anti-fatigue design method of the welded joints. The literature shows that the widely used fatigue life prediction method mainly include three types: nominal stress method [1], hot spot stress method [2, 3] and master S-N curve method [4]. Among them, master S-N curve method solves the problem of inconsistent stress calculation by defining the calculation of structural stress that is insensitive to the size of the mesh finite element analysis. Based on the theory of fracture mechanics, the expression of stress intensity factor is established, which is affected by This project is supported by Liaoning Provincial Education Department Project (JDL2017025) and the Open Project Program of Sichuan Provincial Key Lab of Process Equipment and Control (GK201815). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 977–989, 2020. https://doi.org/10.1007/978-981-32-9941-2_81

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joint thickness and load mode etc. The parameters in the expression are determined by a large number of fatigue test data of welded joints. Then, a master S-N curve is obtained and can characterize the fatigue life of the welded joint [5]. Currently, master S-N curve method is one of the most striking engineering technologies for fatigue analysis of welded components. The advantage is mesh-insensitive hot spot stress calculation, higher fatigue life prediction accuracy and the broad applicability [6, 7]. Rough set theory [8] (RST), proposed by Pawlak, aims to find the inner links of the massive, imprecise, incomplete and uncertain data. RST has been proven to ban effective tool for feature selection, data minting, rule extraction and knowledge discovery from categorical data in recent years [9, 10]. However, the tradition RST just works in discrete spaces, it can’t deal directly with the numerical data in the practical application. When dealing with the numerical data, discretization is first done to transform the numerical value into the symbol value [11, 12]. This transformation inevitably brings about information loss and the computing results usually depend largely on the effect of discretization algorithm. To deal with this problem, a neighborhood rough set model is proposed based on the definitions of d neighborhood and neighborhood relations in metric spaces [13]. Therefore, the neighborhood rough set theory greatly improves the performance of attribute reduction. Support Vector Machine (SVM) is a theory proposed by Professor Vapnik et al. on the basis of statistical theory to solve linear indivisible classification problems [14]. It is based on the principle of structural risk minimization rather than the traditional empirical risk minimization principle. In the nonlinear case, the input vector is mapped into a high-dimensional feature vector space by using the kernel function, and the linear inseparable classification problem of the original input space is transformed into the linear separable classification problem in the high-dimensional space, and the optimal classification hyper plane is constructed in the high-dimensional space. The support vector machine method is a new computer learning method with strict theoretical foundation. It has wide application in computer learning, pattern recognition, computational intelligence, forecasting and other fields [15]. Its advantages involve many aspects, such as can guarantee to find the global optimal solution, has simple structure, is easy to promote and suitable for small samples [16]. The author’s team has systematically studied the analysis method of the factors affecting the fatigue life of welded joints based on classical rough set theory [17, 18]. In order to reduce the information loss caused by attribute discretization, this paper analyzes the fatigue life influencing factors of welded joints based on the neighborhood rough set, and obtains the key factors affecting the fatigue life of welded joints. According to the key factors affecting the fatigue life of welded joints, the fatigue characteristic domain is determined and the intelligent model of fatigue life prediction of welded joints is established in the determined fatigue characteristic domain. Then, the simulation experiment is carried out, and the validity of the established model is verified by the comparison with the least square method.

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2 Methodology In order to consider the influence of the key influencing factors of the fatigue life of welded joints, to further reduce the dispersion level of fatigue specimens and to improve the fatigue life prediction accuracy of welded joints, an intelligent prediction method of fatigue life of welded joints of aluminum alloy based on fatigue characteristic domain is proposed in this work. The overall scheme of fatigue life prediction method for aluminum alloy welded joints based on fatigue characteristic domain is shown in Fig. 1. As can be seen from Fig. 1, the intelligent fatigue life prediction model of welded joints mainly consists of two parts: fatigue characteristic domain determine and parameter optimization of SVM model. Among them, the fatigue characteristic domain determine mainly includes the following steps: Firstly, the fatigue test data of the aluminum alloy welded joints are collected, and the fatigue database of the welded joints is established. Fatigue samples distribution map is subsequently obtained in the coordinate system characterized by Set the search range of SVM parameters and particle swarm algorithm parameters

Fatigue specimen sample data Equivalent structural stress range - life characterization test data

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SVM model for fatigue life prediction of welded joints based on fatigue characteristic domain

Fig. 1. Intelligent fatigue life prediction of welded joints based on the fatigue characteristics domain

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equivalent structural stress range and fatigue life. Secondly, the data is pre-processed to eliminate incomplete and missing data. After that, the fatigue joint decision system of welded joints is established. Then, the forward greedy algorithm of neighborhood rough set attribute reduction is used to reduce the fatigue decision system, and the set of key affecting factors of the fatigue life of welded joints is obtained. Finally, the fatigue characteristic domain is determined based on the results of the neighborhood rough set attribute reduction. The main steps of the fatigue life prediction of welded joint SVM model parameter optimization are as follows:Firstly, set the search range of the SVM model parameters c, g, and set the initial values of the parameters such as the population size, the learning factor, the inertia weight, the maximum iteration number, and the maximum speed in the particle swarm algorithm. Secondly, randomly set the initial position and velocity of the particles in the population. Next, calculating the fitness value of the particle and initializing the individual optimal and global optimal values of the particle; After that, the speed and position of the particle, the individual and global optimal values of the particle are updated to determine whether the maximum number of iterations is reached. If the maximum number of iterations has been reached, the obtained optimal SVM parameter value is returned; otherwise the data and position of the particle as well as the individual and global optimal value are iteratively updated.

3 Core Algorithm The neighborhood rough set forward greedy attribute reduction algorithm and the particle swarm optimization based SVM model parameter optimization algorithm are the core algorithms in the fatigue life prediction model based on fatigue characteristic domain. Among them, the forward greedy attribute reduction algorithm can realize the attribute reduction of the fatigue decision system, and thus determine the key factor set that affects the fatigue life of the welded joint; It can improve the accuracy of model prediction by using the SVM parameter optimization algorithm based on particle swarm optimization. The algorithm can find the global optimal solution, and can also optimize the parameters of SVM model. The main steps of the two core algorithms are outlined below. 3.1

Forward Greedy Attribute Reduction Algorithm

Define the fatigue decision system as a five-tuple: (U, C, D, V, f), where, U is a finite non-empty object set {x1, x2, x3,…, xn}, called domain; C is a collection of non-empty attributes {a1, a2,…, am}, called conditional attribute; D is a collection of non-empty attributes {d}, called decision attribute; V ¼ [ a2C [ D Va, Va represents the value range of the attribute a; f : U  ðC [ DÞ ! V is information function, specify the attribute value of each object x in U, which is x 2 U, a 2 ðC [ DÞ, f ðx; aÞ 2 Va. The main steps of the forward greedy attribute reduction algorithm include: Step1. Input welded joint fatigue life decision system and attribute importance threshold e, e is a positive number with a value greater than 0;

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Step2. For the condition attribute set, that is, each condition attribute ai of the welding joint fatigue life influencing factor concentration, the neighborhood radius of the attribute ai is calculated by the formula (1); dðaiÞ ¼ STDðaiÞ=k

ð1Þ

Where, STD(ai) represents the average value of the attribute ai, and k is the neighborhood radius calculation parameter, and its value range is usually: 2–4; Step3. Set the attribute reduction result set Red initial value to null; Step4. For each condition attribute in the condition attribute set ai 2 C  Red, calculate its attribute importance by formula (2); SIGðai; Red; DÞ ¼ cRed [ ai ðDÞ  cRed ðDÞ

ð2Þ

Where, cRed ðDÞ ¼ jNRedDj=jUj is attribute dependency; N Red D ¼ fxijdRed ðxiÞD; xi 2 Ug is the lower approximation; Step5. Select the attribute ak with the highest attribute importance value in all condition attribute sets; Step6. Determine whether the importance value of the attribute ak is greater than a given threshold e, then go to Step4, otherwise continue to Step7; Step7. Returns the attribute reduction result set Red, gets the result and ends. 3.2

SVM Parameter Optimization Based on Particle Swarm Optimization

The SVM parameter optimization based on particle swarm optimization includes the following five steps: Step1. Set the search range of the SVM model parameters and the population size, learning factor, inertia weight, maximum iteration number, and maximum speed of the PSO; Step2. Initialize the particle swarm, randomly generate the initial position of each particle, and randomly initialize the initial velocity of each particle; Step3. Set the fitness function as the standard deviation of the fatigue test data distribution, calculate the fitness value of each particle, and initialize the individual and global optimal position of the particle; Step4. Update the velocity and position of all particles and update the individual and global optimal positions of the particles; Step5. Determine whether the given maximum number of iterations is satisfied. If it is satisfied, stop the optimization and return the current optimal SVM model parameters, and the algorithm ends; otherwise, go to Step 4.

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4 Simulation Experiment Results 4.1

Fatigue Decision System

According to the collected data of fatigue test samples of aluminum alloy welded joints [19, 20], the decision-making system for the analysis of the factors affecting the fatigue life of aluminum alloy welded joints was established. The number of samples in the established decision-making system database is 64, and the main factors affecting the fatigue life of welded joints include a1 (Material type), a2 (Welding method), a3 (Thickness), a4 (Ratio), a5 (Load type), a6 (Joint type) and a7 (Equivalent structural stress range). Some of the data in the database table is shown in Table 1 below. Table 1. Fatigue test samples of aluminum alloy welded joints Welding method

Thickness Ratio Load t/(mm) type

5083 H11 5083 H11 5083 H11 AlMg4MnCr AlMg4MnCr AlMgSi1 (6082) AlMgSi1 (6082) NP5/6

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The greedy attribute reduction algorithm in 3.1 was used to conduct attribute reduction and feature extraction for the established fatigue database, and the attribute reduction result is {a1 (Material type), a4 (Ratio), a7 (Equivalent structural stress range)}. From the results of neighborhood rough set feature extraction in this test it can be seen, among the many factors affecting fatigue life of aluminum alloy welded joints, material type, stress ratio and equivalent structural stress range are the key influencing factor sets. The test sample points with the same value on the key impact factor set are distributed in a relatively independent area, which is called the fatigue characteristic domain. Therefore, based on the neighborhood rough set feature extraction results, the

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fatigue characteristic domain is delineated, and six fatigue characteristic domains are obtained: S1* S6. The determined fatigue characteristic domain is shown in Fig. 2. Fatigue Fatigue Fatigue Fatigue Fatigue Fatigue

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S1: {X2U∣XC1 = 5083H11 and XC4 = 0.1}; S2: {X2U∣XC1 = 5083H11 and XC4 = 0.5}; S3: {X2U∣XC1 = AlMg4MnCr and XC4 = 0.1}; S4: {X2U∣XC1 = AlMgSi1 and XC4 = 0}; S5: {X2U∣XC1 = NP5/6 and XC4 = 0}; S6: {X2U∣XC1 = HP30 and XC4 = 0};

Taking the fatigue characteristic domain1 as an example, in the fatigue test of aluminum alloy welded joints, all the fatigue test specimens that the material type is 5083H11 and the stress ratio is 0.1 distribute in relatively independent regions, called fatigue characteristic domain 1. The definition of fatigue samples in other fatigue characteristic domains (S2–S6) is similar. The determine of the fatigue characteristic domain can further refine the fatigue samples space in the coordinate system characterized by the equivalent structural stress range and fatigue life, so that all aluminum alloy welded joint fatigue test sample points are distributed in relatively independent sample subspaces. Thereby, the dispersion level of the fatigue test sample points is further reduced, and the accuracy of the fatigue life prediction of the welded joint is improved.

Fig. 2. Determine of fatigue characteristics domains

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The PSO-SVM model for fatigue life prediction of welded joints of aluminum alloy welded joints was established in the determined fatigue characteristics domain. The comparison of the life prediction value of the SVM model and the life prediction value of the least squares fit in each fatigue characteristic domain and the actual life value obtained during the test are shown in Fig. 3(a)–(f).

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(a) Fatigue characteristic domain 1

(b) Fatigue characteristic domain 2

(c) Fatigue characteristic domain 3 Fig. 3. Comparison of fatigue life prediction by SVM and least square method

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(a) Fatigue characteristic domain 1

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As could be seen from Fig. 3, the abscissa indicates the fatigue test piece of the aluminum alloy welded joint obtained by the fatigue test in each fatigue characteristic domain; the ordinate indicates the fatigue life of each fatigue test sample. The blue ‘○’ indicates the actual fatigue life of the aluminum alloy welded joint obtained during the test, the red ‘□’ indicates the fatigue life prediction value of the SVM model, and the black ‘*’ indicates the predicted value of fatigue life of the least squares fitting method. From fatigue characteristic domain 1-domain 6 we could find that compared with the least square method, fatigue life prediction by using SVM is much closer to the actual fatigue life of the aluminum alloy welded joints. In the PSO algorithm, the value of the local search capability related parameter c1 is 1.5, the value of the global search capability related parameter c2 is 1.7, the maximum number of iterations of the algorithm is 200, the maximum number of populations is set to 20, and the initial value of k is 0.6, the initial value of x is 1. Set the SVM parameter c to [0.1, 100], and the parameter g to [0.01, 1000]. Then optimize the SVM parameters c and g to get the value of the best parameters c and g, and based on the obtained optimal parameter values by using the PSO algorithm. Thus, the SVM model is established to realize the construction of the fatigue life prediction model for welded joints. In each fatigue characteristic domain, the absolute error comparison between the SVM model and the least squares fitting model for fatigue life prediction is shown in Fig. 4(a)–(f). As is shown in Fig. 4, the red ‘□’ indicates the absolute error value of the fatigue life prediction of the SVM model, and the black ‘*’ indicates the absolute error value of the fatigue life prediction of the least squares fitting method. From Figs. 3 and 4, we could find that in the characteristic domain 2 and the characteristic domain 3, the maximum error of the fatigue life prediction value of the welded joint of the SVM model is slightly higher than that of the least squares fitting method. In other characteristic domains, the maximum error of SVM model decreases to a greater extent. In fatigue domain 1, 4, 5 and 6, the prediction accuracy of SVM model is further improved. The comparison of prediction results shows that the fatigue life prediction model of welded joints based on PSO-SVM is more accurate than the traditional least square method.

5 Conclusion (1) The SVM model optimized by PSO algorithm can be used to predict the fatigue life of aluminum alloy welded joints. (2) Compared with the least squares fitting method, the SVM model has stronger antinoise ability and higher prediction accuracy. (3) In the case of delineating the fatigue characteristic domain, the prediction accuracy of the SVM model is further improved within the specific fatigue characteristic domain.

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References 1. Hobbacher, A.F.: Recommendations for Fatigue Design of Welded Joints and Components. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-23757-2 2. Niemi, E., Tanskanen, P.: Hot spot stress determination for welded edge gussets. Weld. World 44(5), 31–37 (2000) 3. Niemi, E., Fricke, W., Madox, S.J.: Fatigue Analysis of Welded Components: Designer’s Guide to the Structural Hot-Spot Stress Approach (IIW-1430-00). CRC, Cambridge, Boca Raton (2006) 4. Dong, P.: A structural stress definition and numerical implementation for fatigue analysis of welded joints. Int. J. Fatigue 23(10), 865–876 (2001) 5. Dong, P., Hong, J.K., Osage, D.A., et al.: Master S-N curve method for fatigue evaluation of welded components. Weld. Res. Counc. Bull. 474, 1–44 (2002) 6. Dong, P., Hong, J.K.: The master S-N curve approach to fatigue of piping and vessel welds. Weld. World 48(1–2), 28–36 (2013). Le Soudage Dans Le Monde 7. Yaghoubshahi, M., Alinia, M.M., Milani, A.S.: Master S-N curve approach to fatigue prediction of breathing web panels. J. Constr. Steel Res. 128, 789–799 (2017) 8. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982) 9. Chen, L.F., Tsai, C.T.: Data mining framework based on rough set theory to improve location selection decisions: a case study of a restaurant chain. Tourism Manag. 53, 197–206 (2016) 10. Hu, Q.H., Yu, D.R., Xie, Z.X.: Numerical attribute reduction based on neighborhood granulation and rough approximation. J. Softw. 19(3), 640–649 (2008) 11. Li, W.H., Chen, S.B., Lin, T., et al.: The comparison of discretization method in rough set based modeling method for welding. J. Shanghai Jiaotong Univ. 40, 1094–1097 (2006). (in Chinese) 12. Li, W.H., Chen, S.B., Lin, T., et al.: A generalized rough set modeling method for welding process. J. Shanghai Jiaotong Univ. 12, 319–322 (2007) 13. Li, W., Huang, Z., Jia, X., et al.: Neighborhood based decision-theoretic rough set models. Int. J. Approximate Reasoning 69, 1–17 (2016) 14. Boser, B.E., Guyon, I.M., Vapnik, V.N.: A training algorithm for optimal margin classifiers. In: Proceedings of Annual ACM Workshop on Computational Learning Theory, vol. 5, pp. 144–152 (1996) 15. Bai, P., Zhang, X.B., Zhang, B., et al.: Support Vector Machine Theory and Engineering Application Examples. Xi’an University of Electronic Science and Technology Press, Xi’an (2008). (in Chinese) 16. Ding, S.F., Qi, B.J., Tan, H.Y.: A survey of support vector machine theory and algorithms. J. Univ. Electron. Sci. Technol. China 40(1), 2–10 (2011). (in Chinese) 17. Zou, L., Yang, X.H., Sun, Y.B., et al.: Fatigue life prediction of aluminum alloy welded joints based on variable precision rough sets. Trans. China Weld. Inst. 34(04), 65–68+116 (2013). (in Chinese) 18. Zou, L., Yang, X.H., Sun, Y.B., et al.: Fatigue life prediction of titanium alloy welded joint based on RS_RBFNN. Trans. China Weld. Inst. 36(04), 25–29+78+114 (2015). (in Chinese) 19. Sidhom, N., Laamouri, A., Fathallah, R., et al.: Fatigue strength improvement of 5083 H11 Al-alloy T-welded joints by shot peening: experimental characterization and predictive approach. Int. J. Fatigue 27(7), 729–745 (2005) 20. Beretta, S., Sala, G.: A Model for Fatigue Strength of Welded Lap Joints[J]. Fatigue Fract. Eng. Mater. Struct. 28(1–2), 257–264 (2010)

Optimum Design of Radiation Well Horizontal Drilling Rig Based on TRIZ and Bionics Chenghao Liu1, Changqing Gao1(&), Bo Yang1, and Zhenghe Xu2 1

School of Mechanical Engineering, University of Jinan, Jinan 250022, China [email protected], [email protected] 2 School of Water Conservancy and Environment, University of Jinan, Jinan 250022, China

Abstract. In order to play the role of TRIZ and bionics in innovative design better, assisting designers in product development is the focus of current research. In this paper, the expression model of TRIZ and biological examples was proposed based on the case-based reasoning expression, and a biological knowledge base was established to support product innovation design. The knowledge base includes biological instance information, TRIZ, functional information, etc. The biological instance information includes biological living environment information, biological behavior, biological materials, biological structure. This paper proposed three retrieval methods: keyword retrieval, functional retrieval and conflict retrieval on the basis of the attribute characteristics of the knowledge base. The similarity judgment model of biological instances and functional requirements was established. The multiple similar bionic instances were retrieved to determine the optimal bionic examples, and the exact search of bionic sources was realized. The innovation design is supported by biological knowledge base which can be seen from the optimized design of the horizontal rig’s shell structure. Keywords: TRIZ theory  Case-based reasoning  Knowledge base Innovative design  Radiation well horizontal drilling rig



1 Introduction Conceptual design stage is the key stage to produce innovative ideas [1]. In this stage, there are fewer constraints on designers, which can enable designers to develop their creativity to design products [2]. The essence of innovative design is that it can put forward innovative ideas different from conventional or ordinary people in the process of design, which is novel and unique compared with the previous one [3]. Bionics is a discipline that uses the excellent evolutionary results of nature to solve engineering design problems [4]. TRIZ is a theory to solve the problem of invention based on the analysis of 2.5 million high-level patents worldwide [5]. The principle of TRIZ solving This project is supported by National Science and Technology Support Program (Grant No. 2015BAD20B02-05), National Natural Science Foundation Project (Grant No. 51775239, 50905074). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 990–1001, 2020. https://doi.org/10.1007/978-981-32-9941-2_82

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conflicts is similar to that of natural organisms. Therefore, it is reasonable and feasible to combine some biological mechanisms with TRIZ innovation principle in product design [6, 7]. The organic combination of bionics and TRIZ innovation principle can not only expand the application of TRIZ innovation principle in the field of design, but also help to overcome the drawbacks of bionics examples which are difficult to find [8]. It is of great significance to expand the application of Bionics in the field of engineering design [9]. In this paper, case-based reasoning (CBR) was used to express TRIZ theory and biological cases, and to construct a bionic knowledge base. The TRIZ problem analysis tool was used to analyze the problems of the horizontal well of the radiation well, and the search for similar biological examples was completed with the support of the bionic knowledge base.

2 Case-Based Reasoning Case based reasoning (CBR) is a similar method for solving problems, and it is also a hotspot in the field of artificial intelligence in recent years. CBR relies on the experience and methods that accumulated in past practice to solve the new problems in real life, avoids the bottleneck of knowledge acquisition, more in line with people’s way of thinking, and has been widely used in the field of design, and has become an important means of knowledge expression in the application of CAD technology. CBR applications generally include four steps: retrieval, reuse, revision and preservation [10]. The case-based reasoning process was shown in Fig. 1. Problem

New instance Similar instance

Retrieve

New instance

Instance of learning

Reuse

Previous instance

Retain Instance of modifications Verification scheme

Revise

Instance of solutions Proposed programme

Fig. 1. Case-based reasoning

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3 Construction of Bionic Knowledge Base 3.1

Structure Model of Bionic Knowledge Base

In the product design process, in order to design the product better, it requires knowledge from various fields. Nature is a natural knowledge base, which contains abundant knowledge and provides infinite inspiration for designers. TRIZ is a very mature theoretical system of innovative methods. Combining biology with TRIZ invention theory to construct a knowledge base is one of the main contents of this paper. The knowledge base of this study includes biological case information, TRIZ theory information, functional information and so on. The biological instance information includes biological living environment information, biological behaviors, biological materials, biological structure models and so on. TRIZ theory mainly includes information of invention principle, conflict matrix, standard engineering parameters, scientific effect and standard solution. The tree structure of the knowledge base is shown in Fig. 2. Principle Number Invention Principle Library Principle Explanation TRIZ Tool Library

Scientific Effect Library Principle Name Biological Structure

Standard Solution Library Biological Example

Biological Behavior TRIZ Tool Library Bionic Knowledge Base

Biological Case Library

Biological Example

Function Library

Biological Materials

Biological Environment

Biological Effect

Fig. 2. Tree structure diagram of bionic knowledge base

3.2

Main Contents of Bionic Knowledge Base

The creatures in nature have a wide range of functions that provide a constant source of inspiration for designers to engaging in innovative design processes. Through careful analysis, the process of realizing some functions or solving certain conflicts of various organisms has a certain correspondence with the principle of TRIZ invention. By

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browsing and reviewing relevant biological data, literature and websites, the typical biological examples were carefully analyzed and the TRIZ invention principles were integrated to form a biological instance library based on the inventive principle. As shown in Table 1.

Table 1. Principle of invention and corresponding biological examples (part content) Number 1

Name of principle of invention Division

2 3

Separate Local quality

4

Asymmetric

Biological example Grasshopper breaking foot, gecko tail, crab claw, animal vertebrae Woodpecker head, animal heart position distribution Flaps, honeycombs, leaves of the king lotus and toucans Pareas iwasakii teeth, molecular asymmetric structure

4 Biological Case Retrieval According to the characteristics of the knowledge composition in the bionic knowledge base, this paper used three different retrieval methods, such as the function retrieval method, the keyword retrieval method and the conflict type retrieval method. When the design requirement is a brand-new design, it is in the conceptual design stage, and there are relatively few constraints on the engineering designer. At this time, it is suitable to adopt a relatively fuzzy function retrieval method. When the design is in the improved design phase, optimization of one engineering parameter often leads to deteriorated one or more engineering parameters. The purpose of innovative design is to resolve conflicts, and it is appropriate to use conflict type retrieval. This type of retrieval was granular and the engineer can accurately match the biological instances that was solved the problem. However, the biological knowledge obtained in this way was more specific, which was not conducive to the principle innovation of designers. According to the actual situation, engineering designers can choose different search methods. The system matches the corresponding TRIZ information and biological instance information according to the input content. Then the output results were evaluated to determine whether meet the requirements. If not, the requirement problems were redefined and retrieved until the required biological instance information was retrieved. The retrieval process was shown in Fig. 3.

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Selection of Retrieval Methods

Re-analysis of Demand Problem

Functional Retrieval

Keyword Retrieval

Conflict Question Retrieval

Function Matching

Domain Keywords

Matching of Invention Principles

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N

Does It Meet the Requirements? Y Biological Example Browse in Detail

Fig. 3. Biological case retrieval process

5 Similarity Judgment of Engineering Case and Biological Case Setting up biological system A consists of N elements, A = {a1, a2, a3aN}. Technical system B consists of M elements, B = {b1, b2, b3bM}. The number of similar elements between biological system A and technical function system B is L. Let the similar elements between biological system A and technology B be represented by U, U = {u1, u2, u3uL}. Let the similarity be Q (A, B), whose value reflects the similarity (between 0 and 1). The formulas for calculating similarity are follows: QðA;BÞ ¼

L X L ðb qðu1 Þ þ b2 qðu2 Þ þ    þ bL qðuL ÞÞ M þ N  L i¼1 1

L X L ¼ b qðui Þ M þ N  L i¼1 i

In formula, b-weight coefficient, 0  bi  1,

PL i¼1

bi ¼ 1

ð1Þ

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Table 2. The value of judgment matrix and its meaning Value of uij 1 3 5 7 9 2, 4, 6, 8 Reciprocal

Meaning Two similar elements are of equal importance when compared with each other Comparing two similar elements, one is slightly more important than the other Comparing two similar elements, one is more important than the other The two features are very similar. Comparing two similar elements, one is more strongly important than the other Comparing two similar elements, one is more important than the other Represents the median values of the two adjacent judgements 1 − 3, 3 − 5, 5 − 7, 7 − 9 If factor xij is judged by comparing with factor xj, then factor xj is judged by comparing factor xi with factor xi as xji = 1/xij

q(ui) - Similarity of Similar Elements. M, N - Number of units in biological functional system A and technical functional system B. L - Number of similar elements in biological functional system A and technical functional system B. The uij was supposed represents the importance of similar element ui relative to uj. Then the judgment matrix P can be expressed as (2), The values of uij are shown in Table 2. 2

u11 6 u21 6 6 .. 6 . P¼6 6 ui1 6 6 . 4 .. ul1

u12 u22 .. .

   u1j    u2j .. .

ui2 .. .

uij .. .

ul2

 

ulj

   

3 u1l u1l 7 7 .. 7 . 7 7 uil 7 7 .. 7 . 5 ull

ð2Þ

Solving the Maximum Eigenvalue of Matrix P (kmax) and the Eigenvector Corresponding to the Maximum Eigenvalue G = {x1, x2, x3xn}. Normalizing eigenvectors (G) to get vectors bi = {b1, b2, b3bl}. Vectors were the weights of similar elements. In order to avoid the phenomenon that element A is more important than element B, element B is more important than element C, and element C is more important than element A, the consistency of judgement matrix is checked. The consistency checking formulas are shown in Formulas 3 and 4. CI ¼

kmax  n n1

ð3Þ

CI RI

ð4Þ

CR ¼

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In the formula, kmax is the largest characteristic root of matrix P, CI is the consistency test index of matrix P, CR is the random consistency ratio, RI is the random average consistency test index of matrix P, and RI is the value shown in Table 3. Table 3. Values of RI n 1 2 3 4 5 6 7 8 9 RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45

There are many features in the similarity elements between the biological function system and the technical system. The similarity of any one of the features can form the similarity between the two system elements. The gather (a) consists of features of similar elements (ai). The gather (b) consists of features of similar elements (bi). When the characteristics of similar elements were analysed and evaluated, similarity of similarity features of similar elements is recorded as ri1, ri2,, ril. The values of rij were shown in Table 4.

Table 4. Value of rij Value of rij [0, 0.2) [0.2, 0.4) [0.4, 0.6) [0.6, 0.8) [0.8, 1.0)

Meaning The two features The two features The two features The two features The two features

are are are are are

basically not similar slightly similar obviously similar very similar extremely similar

The formulas for calculating similar elements are as follows. qðui Þ ¼

l X l dj rij m þ n  l j¼1

ð5Þ

P In formula, dj-weight coefficient, 0  dj  1, li¼1 dj ¼ 1 m, n - Number of features of similar elements, l - Number of similar features between similar features, rij - Similarity between two similar features.

6 Engineering Application Radiation well horizontal drilling rig is the main tool for excavation of radiation well. It can be seen from the analysis that the base of the horizontal well of the radiation well needs to reduce the weight as much as possible, but the load capacity of the base will decrease as the weight is reduced, resulting in a decrease in the overall operational

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reliability of the horizontal well of the radiation well, that is, a technical conflict. Engineering problems were transformed into standard TRIZ contradictions using 39 standard engineering parameters. The engineering parameters for optimization and deterioration were the weight and reliability of moving objects, respectively. The principle of invention recommended by the conflict matrix were segmentation (principle 1), local mass (principle 3), pre-compensation (principle 11), and replacing expensive and durable objects with low-cost, non-durable objects (principle 27). According to the interpretation of the principle of invention and a large number of analyses, local quality (Principle 3) was chosen as the original understanding of the conflicts in the horizontal drilling rig technology of radiation wells. After querying the bionic knowledge base, examples of biological functions corresponding to the original understanding were cicada wing, victoria amazonica, honeycombs and toucans. The pictures were shown in Figs. 4, 5, 6 and 7.

Fig. 4. Cicada wing

Fig. 6. Honeycombs

Fig. 5. Victoria amazonica

Fig. 7. Toucans

The similarity analysis of the radiation rig horizontal rig base structure and cicada wing was carried out from four aspects function, structure, load and constraint. (1) In terms of function, the main function of the cicada wing was supported to carry the function during the flight. The radiant well horizontal rig base was used as the structure to mainly carry the radiation rig horizontal rig main body and the operation workers to ensure the horizontal rig works normally. Therefore, there was similarity in terms of function. (2) In terms of structure, the whole cicada wing has a plate-shell structure, and the surface of the cicada wing has a radial wing vein structure. The distribution of wing vein structure is conducive to improving the carrying capacity of the cicada

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wing in unit area, and the weight of the cicada wing increases relatively less. The distribution of wing vein structure of cicada wing was similar to that of reinforcement bar of horizontal drilling rig base structure of radiation well. The distribution of reinforcement bar was used to improve the unit bearing capacity of horizontal drilling rig base of radiation well. (3) In terms of load, the cicada wing load was mainly manifested in two aspects. On the one hand, the cicada wing mainly bears its own gravity and lift during gliding, which can be approximated to uniform load. On the other hand, it needs to bear strong vibration during flight, and the instantaneous load was several times higher than gliding state. The base structure of horizontal drilling rig in radial wells mainly bears the gravity of the rig and the worker themselves. It also needs to bear strong vibration and certain impact load in the working process, so there is a certain similarity in load between them. (4) In terms of constraints, there were some similarities between the constraints of cicada wings and the base structure of horizontal drilling rigs in radiation wells. The similarity of the radiation well horizontal drilling rig and flaps was analysed as an example. The similarity between the cicada wing and the radiation well horizontal rig base plate shell structure was assumed Q. Similar elements are function, structure, load, and constraint, respectively. The gather of similar elements is U, U = {u1, u2, u3, u4} = {function, structure, load, constraint}. Therefore, the values of M, N and L were 4. Known by formula 1, Q¼ ¼

L X L ðb qðu1 Þ þ b2 qðu2 Þ þ    þ bL qðuL ÞÞ M þ N  L i¼1 1 4 X

bi qðui Þ

i¼1

Taking the weight value of each similar element gather U = {u1, u2, u3, u4} as b, b = {b1, b2, b3, b4}. According to formula 2, the judgement matrix of relative weight value were established. 2

1 6 1=3 P¼6 4 1=3 1=2

3 1 1 1=2

3 1 1 1=2

3 2 27 7 25 1

After calculation, the maximum eigenvalue of matrix P was kmax = 4.1545. Feature vector corresponding to the largest eigenvalue G = {0.8298, 0.3549, 0.3549, 0.2440}. The weighted value of each similar element was b = {0.47, 0.2, 0.2, 0.13} after normalization

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Bring the results into consistency test formulas 3 and 4 CI ¼

kmax  n 4:1545  4 ¼ ¼ 0:0515 n1 41 CR ¼

CI 0:0515 ¼ ¼ 0:057 RI 0:9

According to the analysis of calculation data, CR = 0.057 < 10% the calculation result is credible. For feature of similar feature functions, structures, loads, and constraints, they were no longer subdivided. Therefore, in the Eq. (5) of this paper, the values of m, n, l, and dj were all 1, then qðui Þ ¼ rij Similarity was calculated based on similarity characteristics between cicada wing and base of horizontal drilling rig in radiation well. The similarity of each similar element between the shell structure of horizontal drilling rig of cicada wing and radiation well was q = {0.8, 0.8, 0.6, 0.4}. The similarity between cicada wing and shell structure of horizontal drilling rig base can be expressed as follows, Q ¼ 0:47  0:8 þ 0:2  0:8 þ 0:2  0:6 þ 0:13  0:4 ¼ 0:75 Similarity of the radiation well horizontal drilling rig with victoria amazonica, honeycombs and toucans were analysed. The similarity calculation process is the same as the similarity calculation between the flap and the radiation well horizontal rig. Similarity was analysed from four aspects: function, structure, load and constraint, and calculation process such as formula 1. First, determine the weight value of each similar element, and using Eq. (2) to calculate the weight value. The weight value calculation process was not described here. The similar weight values of victoria amazonica, honeycombs and toucans were shown in the Table 5. Table 5. Similar weight values Biological instance Similar element Function Structure Victoria amazonica 0.45 0.20 Honeycombs 0.46 0.14 Toucans 0.39 0.25

Load 0.20 0.26 0.11

Constraint 0.15 0.14 0.25

The characteristics of the similar elements of victoria amazonica, honeycombs and toucans were no longer subdivided, and they all were taken their own. Therefore, in the Eq. (5) of this paper, the values of m, n, l, and dj were all 1, the similarity value of similar features was rij. According to the analysis, the similar values of victoria

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amazonica, honeycombs and toucans and radiation well horizontal drilling rig were shown in Table 6. The value of the similar characteristics of the victoria amazonica, honeycombs and toucans were based on the expression in Table 6. Table 6. Similarity of two similar features Biological instance Similar element Function Structure Victoria amazonica 0.6 0.4 Honeycombs 0.3 0.5 Toucans 0.5 0.2

Load 0.6 0.1 0.5

Constraint 0.5 0.2 0.3

According to calculation, the similarities of victoria amazonica, honeycomb and toucans were 0.545, 0.304 and 0.375, respectively. Through comparison, the cicada wing was selected as a bionic source to optimize the design of the horizontal structure of the radiation well horizontal drilling rig.

7 Conclusions (1) The case-based reasoning was used to describing the biological example and TRIZ innovation principle, and the construction of the bionic knowledge base was completed. The establishment of the bionic knowledge base not only facilitated the storage and update of biological knowledge by managers, but also facilitated the designer to search for biological instances. (2) The similarity judgment model between biological case and engineering case was constructed, and the selection of bionic case was realized by using the similarity judgment model. (3) The bionic knowledge base was used to complete the bionic instance of the horizontal drilling rig in the radiation well, which lays a foundation for the bionic design of the horizontal drilling rig. This process verifies the usefulness of the bionic knowledge base.

References 1. Zheng, H., Feng, Y.X., Gao, Y.C.: The solving process of conceptual design for complex product based on performance evolution. J. Mech. Eng. 54(9), 214–223 (2017) 2. Ren, L.Q.: Progress in the bionic study on anti-adhesion and resistance reduction of terrain machines. Sci. China Ser. E: Technol. Sci. 52(2), 273–284 (2009) 3. Wang, P., Ni, H., Wang, X., et al.: Research on the characteristics of earthworm-like vibration drilling. J. Pet. Sci. Eng. 160, 60–71 (2018) 4. Lu, M.Z., Wang, X.T., Zhang, J.X.: Research on mechanical equipment concept design based on FBS model and primitive model. J. Mach. Des. 35(5), 111–115 (2018)

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5. Belski, I., Belski, I.: Application of TRIZ in improving the creativity of engineering experts. Procedia Eng. 131, 792–797 (2015). (Complete) 6. Mastura, M.T., Sapuan, S.M., Mansor, M.R., et al.: Design strategy for concept design of hybrid bio-composite automotive anti-roll bar using TRIZ. Mech. Res. Day 60–61 (2016) 7. Ekmekci, I., Koksal, M.: Triz methodology and an application example for product development. Procedia-Soc. Behav. Sci. 195, 2689–2698 (2015) 8. Ma, R., Liu, L., Yu, T.: Innovative design of heat dissipation structure for LED street lamp based on AD and TRIZ. WIT Trans. Eng. Sci. 113, 159–170 (2016) 9. Yan, J.H., Shi, P.J., Zhang, X.B.: Review of biomimetic mechanism, actuation, modeling and control in soft manipulators. J. Mech. Eng. 54(15), 1–14 (2015) 10. Yu, Y.Z., Wang, Y., et al.: Pile foundation optimization design based on knowledge reasoning and second-order oscillating particle swarm optimization. J. Dalian Univ. Technol. 57(4), 383–389 (2017)

Innovative Design of Reversing Device and Rod Loading Device of Horizontal Drilling Rig Based on TRIZ Shifeng Sun1, Changqing Gao1(&), Bo Yang1, and Zhenghe Xu2 1

School of Mechanical Engineering, University of Jinan, Jinan 250022, China [email protected], [email protected] 2 School of Water Conservancy and Environment, University of Jinan, Jinan 250022, China

Abstract. Aiming at the problems of low automation level of horizontal drilling rigs and high construction intensity of constructors in China, innovative design of horizontal drilling rigs was carried out to improve the automation level of drilling rigs. However, improving the automation level of the horizontal drilling rig will increase the difficulty of manufacturing the horizontal drilling rig and the difficulty of maintenance. Therefore, TRIZ theory was used to solve the contradiction. Firstly, the functional model of the horizontal drilling rig was established through functional analysis to clarify the functional structure of the drilling rig and provide assistance for subsequent design. The main functions of the reversing device are the carrying rig, the rotary drilling rig and the positioning drilling rig. The main functions of the loading device are storing the drill pipe, conveying the drill pipe and positioning the drill pipe. The conflict analysis was used to solve the contradiction between the automation degree of the optimization device and the deterioration of manufacturability and maintainability. After the design, the automation of the drilling rig was greatly improved. Keywords: Horizontal drilling rig  TRIZ Conflict analysis  Innovative design

 Functional analysis 

1 Introduction Theory of the Solution of Inventive Problems (TRIZ) is a theoretical system established on the basis of analyzing a large number of high-level invention patents in the world, refining the knowledge involved, and integrating the principles and rules of multidisciplinary fields, and it can guide the latecomers to clarify the methods and ways of invention and creation, thus breaking the limitations of the inventors’ understanding and avoiding the blindness brought by trial and error in the traditional invention and creation process [1, 2]. The process of using TRIZ theory to solve problems is to first select the problem analysis tool according to the problem type, abstract the specific problem into a standard or general problem according to the problem analysis tool, and then use the corresponding problem solving tool to obtain the standard or general solution, and finally convert A solution to a specific problem [3, 4]. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1002–1009, 2020. https://doi.org/10.1007/978-981-32-9941-2_83

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Product function analysis is an important part of the conceptual design process, and it plays an important role in transmitting and generating design information and leading innovation principles. Yang conducted component analysis on the mechanical structure of the track inspection car, established a functional model, and found the weak points of the technical system in combination with the problems in the use of the track inspection car and the results of the functional analysis, and applied the TRIZ theory method to the functional model. Solve and efficiently generate innovative solutions [5]. Tian conducted functional analysis on the various components and functions of the traditional water mixer, and obtains the links that affect the heat transfer effect and cause pressure loss,and the conflict matrix tool was used to determine the principle of the invention to solve the problem [6]. In order to solve the problems of knotter disassembly and assembly after damage and difficult to repair and replace, Ma found a preliminary solution through functional analysis method, and further applied contradiction analysis method to get the final solution of the problem [7]. Conflict analysis is an analysis method that achieves innovative goals by solving contradictions in the system. It can help to solve the contradictions between the characteristics of negative related technologies. The basic process of conflict analysis is to use engineering parameters to describe conflicts, to find conflict matrix tables to obtain recommended inventive principles, and to analyze and obtain design schemes based on inventive principles [8]. Wang used QFD method to construct HOQ, clarified the key direction of product improvement in the early stage of design, described its contradictions with TRIZ theory, and solved the conflicts in the innovative design of heat-permeable moxibustion physiotherapy instrument by using corresponding inventive principles [9]. In view of the shortcomings in the innovative design of the museum tourism commemorative market, Liu analyzed and researched the user needs of museum souvenir consumers from the perspective of industrial design, constructed a user demand quality house, and proposed a design contradiction solution based on TRIZ theory [10]. At present, there are some problems in horizontal drilling rigs of excavated radial wells, such as low automation, bad working environment and high working intensity of workers. This paper applies TRIZ theoretical function analysis and conflict analysis to the innovative design of the horizontal rig automatic loading device and automatic reversing device, which improves the automation degree of the drilling rig and reduces the working time and working intensity of the workers. The function model of the horizontal drilling rig is obtained through functional analysis and the conceptual design information of the loading device and the reversing device is generated. Through the conflict analysis, the design of the reversing device and the loading device is obtained by solving the conflict between the manufacturing difficulty and the maintenance difficulty caused by the addition of the automatic reversing device, the addition of the automatic loading device and the addition of the two devices.

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2 Functional Analysis Horizontal drilling rig breaks gravels through drill pipe and forms drilling holes. Therefore, the general function of horizontal drilling rig was defined as breaking gravels. According to the total function of horizontal drilling rig, the total function of horizontal drilling rig was analyzed from three aspects: material flow, energy flow and information flow. The total function model of horizontal drilling rig in this paper is shown in Fig. 1. Drill pipe, water, dinas

Drill pipe, water, dinas control signal

control signal Broken Dinas

Hydraulic pressure

Cutting force, vibration, Sound, heat, machinery

Fig. 1. Total function model of horizontal drilling rig

The drilling rig crushes the whole sand and gravel through the drill pipe, and discharges the gravel through the drill hole under the action of water. According to this, the input material flow includes the drill pipe, water and gravel, and the output material flow includes the drill pipe, water and gravel. Usually, the working location of the drilling rig is relatively remote, and the working environment of the drilling rig is bad. Considering the safety factors of the downhole workers and the ease of energy, the mobile hydraulic pumping station is selected to provide energy. Therefore the input energy flow is hydraulic. The drilling rig connects the drill pipe through the power head to crush the sand stone. In the process, part of the hydraulic energy is converted into the cutting force of the drill bit, and partly converted into vibration, heat, sound and other energy, and the mechanical energy of the movement of each device of the drilling machine, so the output energy flow includes cutting force, vibration, heat, sound, machinery. The staff controls the hydraulic switch to start and stop in an orderly manner through the control signal, so that each device cooperates to complete the work of crushing sand and gravel, so the input and output information flows are both control signals. For a product with complex functions, it is impossible to clarify its internal functional structure only through the analysis of its total functions. It is necessary to decompose the complex total functions into simple sub-functions. The first level of decomposition: In order to achieve the total function of the drilling rig, the drilling rig should have three sub-functions: cutting rock, providing the energy needed for cutting and various auxiliary measures for easy operation. Therefore, this level can be divided into three

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aspects: providing energy, cutting rock, and using convenience. In the next layer, the three functions are further decomposed. The second level of decomposition: In order to complete the operation of cutting rock by drilling rig, the drilling rig should include the function of separating the whole rock and removing the separated rock. In order to provide the energy required for rig operation, the rig should include the function of converting the supplied hydraulic pressure into pressure and torque. Among the accessory measures for easy operation, in order to adapt to different geological environments, the power components of drilling rigs should include the functions of adjusting pressure and torque; in order to facilitate the installation of drill pipes, the drilling rigs should include the functions of installing drill pipes and fixing drill pipes; in order to lay drill pipes in different directions, the drilling rigs should include the functions of turning. Therefore, the level can be divided into nine aspects: supply energy can be decomposed into supply hydraulic pressure, pressure and torque; cutting rock can be decomposed into separating rock and removing gravel; using convenience can be decomposed into adjusting pressure and torque, fixing drill pipe, changing direction and installing drill pipe. The third level of decomposition: In order to generate pressure, the drilling rig should convert hydraulic pressure to pressure and transfer pressure to the power components of the drilling rig. In order to form the torque, the drilling rig should convert the hydraulic pressure to the torque and transfer the torque to the power components of the drilling rig. In order to achieve the function of removing gravel, the drilling rig impacts gravel by water and transports gravel through drilling holes. For the reversing function of the drilling rig, the parts or the whole rig that need to be reversed should be supported first, and then the parts or the whole rig that need to be reversed should be reversed and positioned. For the installation of drill pipe, the drill pipe should be released from the drill pipe storage device and then transported to the drill pipe positioning device to locate the drill pipe. Therefore, this level can be divided into 12 aspects: forming pressure can be decomposed into transforming hydraulic pressure into pressure and transferring pressure; forming torque can be decomposed into transforming hydraulic pressure into torque and transferring torque; removing gravel can be decomposed into impact gravel and transporting gravel; changing direction can be decomposed into rotary drilling rig, positioning drilling rig and supporting drilling rig; installing drill pipe can be decomposed into storing drill pipe and transporting drill pipe and positioning drill pipe. The functional chains are combined according to the logical relationship between functions and the duplicated parts are deleted to obtain the horizontal drilling rig functional model. The functional model of horizontal drilling rig in this paper is shown in Fig. 2. The conceptual design information of products can be obtained through functional analysis, but the contradictions in products have not been solved. The contradictions in products can be solved through the analysis of inventive principles obtained from conflict analysis. Finally, the design scheme of products can be obtained through the analysis of conceptual design information and inventive principles.

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Supporting rig

Turning rig

Rig for changing direction

Positioning rig

Mechanical energy

Hydraulic pressure Control signal Drill pipe Dinas, Water, Drill pipe

Mechanical Energy, Vibration, Sound

Mechanical energy

Releasing drill pipe

Control signal

Drill pipe

Mechanical energy Drill pipe

Transporting drill pipe

Hydraulic pressure Control signal

Hydraulic pressure

Mechanical energy Locating drill pipe

Control signal Hydraulic pressure

Drill pipe Thermal, Noise, Vibration Drill pipe

Fixed drill pipe

Dinas Control signal

Dinas, Drill pipe

Separation of dinas

spall,w ater

Impact spall

Water

spall,w ater Conveying spall

spall,w ater

Cutting force

Control signal

Control signal

Input hydraulic pressure

Converting Hydraulic Pressure to Pressure Converting Hydraulic Pressure to Torque

Pressure

Transfer pressure

Torqu

Transfer torque

Control signal

Regulating pressure and torque

Hydraulic pressure

Heat, vibration, sound

Fig. 2. Functional model of horizontal drilling rig

3 Conflict Analysis Adding automatic reversing device and automatic rod loading device will increase the difficulty of manufacture and maintenance of horizontal drilling rig. Therefore, there are four pairs of technical conflicts. The conflicts of these specific problems cannot be solved directly through functional analysis, and should be transformed into standard descriptions. The conflict is described by standardization of engineering parameters as shown in Table 1.

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Table 1. Conflict table Serial number Optimized parameter 1 Degree of automation 2 3 Degree of automation 4

Deteriorated parameter Manufacturability Maintainability Manufacturability Maintainability

The invention principle is obtained by finding the conflict matrix table and the invention principle table: division principle, reverse action principle, replication principle, and parameter change principle. Through the analysis, we can see that the principle of partition can solve the contradiction in the conceptual design of commutation device. Combining with the conceptual design information obtained through functional analysis, the design scheme of commutation device was finally obtained. Through the analysis, we can see that the principle of segmentation can solve the contradiction in the conceptual design of the rod-loading device. Combining with the conceptual design information obtained through functional analysis, the design scheme of the rod-loading device was finally obtained. The conceptual design model of horizontal drilling rig was as shown in Fig. 3. Circular rod accumulator Power head Frame Rotary platform Base

Servo Hydraulic Motor System Drill pipe chuck Pole holder Drill pipe holder

Fig. 3. Total function model of horizontal drilling rig

When the horizontal drilling rig performs the pipe laying operation at a certain level in the shaft, the base is suspended by the suspension device in the height of the pipe laying in the shaft, the base supporting cylinder is used to support the fixed wall of the well wall, and the frame supporting cylinder is used to support the wall of the well Fix the rack and wait for the base and the rack to stabilize before pipe laying. During the turning operation, the frame support cylinder is firstly contracted so that the frame can be rotated and reversed with the rotary platform, and then the servo hydraulic motor under the base is driven to rotate the rotary platform to complete the turning action of the drilling machine.

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During the rod loading operation, the power head of the drilling rig returns to the back end of the rack, the drill pipe clamp at the clamp end of the drill pipe holder opens, and the rod holder rises to the bottom of the circular rod holder. The starting servo hydraulic motor drives the rod holder to rotate slowly by 36 degrees through rubber friction wheel. Two drill pipe clamps open and release the drill pipe at the same time, and the drill pipe falls into the rod holder. The rod holder drops to the horizontal height of the main shaft of the power bit, and the drill pipe of the drill pipe holder clamps the drill pipe so that it cannot move. The hydraulic power head is started to rotate the main shaft slowly,and the feed cylinder is started to cooperate with the power head to complete the threaded connection with the drill pipe. The rod holder falls down to the bottom of the rig rack, and the drill pipe clamp at the clamping end of the drill pipe holder is opened to relax the drill pipe and complete the installation of the drill pipe. The design scheme of reversing device and rod loading device obtained by conflict analysis solves the contradiction in the product, and reduces the difficulty of manufacture and maintenance of horizontal drill while adding new reversing device and rod loading device for horizontal drill. At present, the constraints of research and future work are to build physical prototypes and carry out analysis and experiments, which is also the focus and difficulty of the next step.

4 Conclusions (1) The functional model of horizontal drilling rig was established through functional analysis, and the conceptual design information of commutation device and rod loading device was generated. The reversing function of drilling rig includes three main sub-functions: supporting drill rig, rotary drill rig and positioning drill rig. The drilling rig assembly function includes three main sub-functions: releasing drill pipe, transporting drill pipe and positioning drill pipe. (2) The conflict analysis was used to solve the conflict between adding automatic reversing device, adding automatic rod-loading device and manufacturability and maintainability, and innovative design of reversing device and rod-loading device was carried out. The recommended items of invention principle were obtained by searching engineering parameter table, conflict matrix table and invention principle table. The principle of division principle was used to analyse the design scheme of rod loading device was obtained by dividing an object into several independent parts and combining conceptual design information. The principle of division principle was used to analyse the design scheme of rod loading device was obtained by dividing an object into several independent parts and combining conceptual design information.

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References 1. Belski, I., Belski, I.: Application of TRIZ in improving the creativity of engineering experts. Procedia Eng. 131, 792–797 (2015). (Complete) 2. Mastura, M.T., Sapuan, S.M., Mansor, M.R., et al.: Design strategy for concept design of hybrid bio-composite automotive anti-roll bar using TRIZ. Mech. Res. Day, 60–61 (2016) 3. Ekmekci, I., Koksal, M.: Triz methodology and an application example for product development. Procedia-Soc. Behav. Sci. 195, 2689–2698 (2015) 4. Ma, R., Liu, L., Yu, T.: Innovative design of heat dissipation structure for LED street lamp based on AD and TRIZ. WIT Trans. Eng. Sci. 113, 159–170 (2016) 5. Yang, X.R., Meng, H., Yao, L.J., et al.: Mechanical structural innovation design of track inspection instrument based on TRIZ. Packag. Eng. 37(14), 16–20 (2016) 6. Tian, H., Wang, W.C.: Structural design of thermostatic mixing device based on the TRIZ theory. Times Agric. Mach. 44(05), 106–108 (2017) 7. Ma, S., Li, F.M., Qian, W.: Design of D-type knotter based on TRIZ theory. Trans. Chin. Soc. Agric. Mach. 49(S1), 327–331 (2018) 8. Gao, Y., Yu, B., Wang, X., et al.: Orthogonal test design to optimize products and to characterize heavy oil via biomass hydrothermal treatment. Energy 88, 139–148 (2015) 9. Wang, N.W., Wang, J.: Innovative design of hot moxibustion therapy apparatus based on QFD/TRIZ. Packag. Eng. 39(22), 218–224 (2018) 10. Liu, M.Y., Wu, T., Chen, D.K., et al.: Research on design method of museum tourist souvenirs based on QFD and TRIZ. J. Northwest. Polytechnical Univ. (Soc. Sci.) 37(04), 106–109 (2017)

AGV Trolley Tray Based on Honeycomb Paper-Based New Material Jingjing Yang, Xiaoyi Jin(&), and Anran Wang Shanghai University of Engineering Science, Shanghai, China [email protected] Abstract. In order to realize Green and Environmental Protection and sustainable development, a particular emphasis is put on NOMEX (aromatic polymer fiber) honeycomb paper based material, which replaces the metal tray of AGV car. With the results of the related finite element simulation analysis of ABAQUS, the mechanical properties and the carrying capacity of NOMEX honeycomb paper-based new material trays are analyzed. It is effectively to reduce costs for the purpose of green environmental protection and this design is also referenced for further research in this area. Keywords: AGV trolley tray

 NOMEX honeycomb paper base  ABAQUS

1 Introduction The AGV trolley is called the automatic guided transport vehicle, which is also a material handling tool. Compared with other material handling tools, it has great reliability, high material transportation efficiency and low labor cost. It can also be used in complex factory workshops. In industrial production, trays are vehicles that transform static cargo into dynamic cargo, a cargo platform, an active platform, or a movable ground. Tray is the most basic assembly unit and handling tool in the logistics industry, and has a wide application value in commodity circulation. Foreign trays implement the main mode of recycling, establishing a reasonable recycling mechanism, promoting the orderly circulation of trays between supply chain entities, realizing the mechanization of logistics operations, consistent use of trays, and having a wide economic value. However, China has not established an effective recycling mechanism [1] to ensure the cooperation and circulation of trays in enterprises and the reusability of materials. At present, China’s wooden trays account for about 90% of the total number of trays and plastic trays account for about 8% while steel trays and other materials only account for about 2%. Traditional AGV trolleys are usually made of metal trays and expensive. This paper replaces steel tray materials with NOMEX honeycomb paper-based material trays in order to reduce costs, protect the environment and achieve sustainable green development, which is in line with the theme of today’s social green development. In this research, the AGV trolley required for 3C automated production line transportation is taken as an example [2]. Under the premise of meeting the normal transportation of AGV trolleys, the AGV trolley tray material is replaced, which is based on NOMEX (aromatic polymer fiber) honeycomb paper-based materials. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1010–1017, 2020. https://doi.org/10.1007/978-981-32-9941-2_84

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The related finite element simulation analysis of ABAQUS is carried out, and the strain nephotograph and stress curve of the load are analyzed, which is also a reference for further research in this aspect.

2 Agv Trolley Structure The AGV trolley consists of the body, battery, charging system, drive unit, steering unit, precision stop unit, motion controller, communication unit, transmission system and navigation system. The device that used to transport cargo over the AGV body is called a tray and is usually made of metal. Although the metal material tray has the characteristics of large weight and long service life, the NOMEX honeycomb paper-based material can also achieve a certain load-bearing capacity and has good bending performance and load-bearing performance. What’s more, this material is environmentally friendly, degradable and lightweight, which also conforms to the current theme of the world’s green and environmental development. NOMEX honeycomb paper base is made of aromatic polymer fiber NOMEX and aramid pulp [3], which is made into paper by oblique mesh forming technology and then hot pressed. NOMEX honeycomb paper base is a kind of polymer flexible fiber material. As this shape structure is similar to the natural honeycomb shape, it is also referred to as aramid paper honeycomb. In this research, the main material of the honeycomb paper base is NOMEX honeycomb paper-based material, which is a three-layer sandwich structure. As is shown in Fig. 1, the sandwich structure generally has three layers. The middle of it is a soft lightweight honeycomb core material and the upper and lower layers are thin and strong plates. The supporting force of the honeycomb core material greatly increases the moment of inertia formed by the side plates. Honeycomb paper-based materials also have good bending and load-bearing properties and are environmentally friendly and degradable. Compared with Metal honeycomb and glass cloth honeycomb, NOMEX honeycomb paper-based material has high specific strength, excellent chemical inertia, excellent isolation, good electromagnetic transmission characteristics and good selfextinguishing performance.

Fig. 1. Schematic diagram of honeycomb paper base structure

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The honeycomb core material is a porous thin-walled structure. This shape of the honeycomb hole is mostly hexagonal, and the wall thickness is only 0.05 mm–0.1 mm. The model of this paper is 0.1 mm, the side length of the hole is 2 mm–5 mm, and 5 mm is used in this paper. The honeycomb has a high strength along the axial direction of the cells, but its lateral flexibility is large and its strength is low.

3 Nomex Honeycomb Paper-Based Tray Structure Modeling What we want to get is that whether the new material tray NEMOX honeycomb paper base can bear the load during transportation and can quickly transport the goods. In order to achieve get this force analysis, we have to create a model by ABAQUS. 3.1

Modeling Process

In the ABAQUS simulation of the NOMEX honeycomb model, the shell element is used for modeling, and the ABAQUS finite element software is used because the honeycomb core is a thin-walled material. Take the AGV trolley required for the 3C automated production line transportation as an example, and the design index and basic of the AGV. In the parameters, the body size is required to be 1100 mm  677 mm  660 mm. Therefore, the size of the tray is 1100 mm  677 mm. To begin with, the model parameters are obtained. The geometry of the commonly used honeycomb core is a regular hexagon. As described above, this paper selects a regular hexagon with a wall thickness of 0.1 mm and a hole length of 5 mm mold. Then, a single regular hexagonal cell is created in ABAQUS, as shown in Fig. 2. Besides, arraying multiple regular hexagons in the assembly to create the entire model, as shown in Fig. 3, which uses “interaction” instruction that integrates the three layers into one whole through the inter-layer contact instruction. This modeling method is faster and easier than modeling the “shell” instruction. During the simulation process, the tray is subjected to a uniform static load. Therefore, in the ABAQUS simulation, the size of the model does not affect the calculation result. To facilitate the simulation and reduce the time for simulating the generation of the cloud image, the model size of the model simulated in this paper is 60 mm  40 mm.

Fig. 2. Single hexagon model

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Finally, 3D solid honeycomb paper base model has been created to analyze the force bearing.

Fig. 3. 3D solid honeycomb paper base model

3.2

Finite Element Simulation of NOMEX Honeycomb Paper-Based Tray Structure

From the model built above, 100 kg uniform static load is set in the parameter table. Since the carrying capacity of the AGV trolley is in the range of 20 kg–100 kg, 100 kg uniform static load is applied here and simulation analysis is carried out. Figure 4 is a diagram of the total stress nephogram, containing stresses in three directions. From the x-direction normal stress nephogram, as shown in Fig. 5, it can be found that the x-direction displacement stress nephogram has the largest value, which is the main load direction. According to Fig. 7, the z direction is second, and finally the y direction, which is shown in Fig. 6. It can also be seen that the displacements in all three directions have negative values, indicating that the model is mainly subjected to compressive stress.

Fig. 4. Total stress nephotograph

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Fig. 5. X-direction normal stress nephogram

Fig. 6. Y-direction normal stress nephogram

Fig. 7. Z-direction normal stress nephogram

3.3

Mechanical Performance Analysis

The sandwich beam theory is usually adopted when analyzing the mechanical properties of honeycomb paper. The premise of the theory is to make sure that the panel is only subjected to the plane force and the effect of the bending strength is ignored. The sandwich model is only bears the shear stress for it is soft. The above 3D model is only subjected to a uniform static load and the analysis can be based on this theory.

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According to this hypothesis and related references [15], it can be known that the stress distribution of the honeycomb paper substrate when it is subjected to a bending load is shown in Fig. 8. The honeycomb paper base bears shear stress and compressive stress in bending.

Fig. 8. Stress of honeycomb paper base

To begin with, the shear stress on the honeycomb core can be got and Eq. (1) gives the expression: sc ¼

V bH

ð1Þ

Where sc is shear stress of honeycomb paper core, V is Stress on honeycomb paper base, b is Honeycomb paper base width, and H is honeycomb paper base thickness. When the shear strength at the adhesive is less than the shear stress on the honeycomb core, the adhesive fails at this time and causes structural damage between the honeycomb core and the honeycomb panel. Then the stress in the panel is also changed. The shear stress of honeycomb paper core should be within the honeycomb paper core allowable shear stress range and Eq. (2) gives the expression: sc ¼

V  ½scr  bH

ð2Þ

In the Eq. (2), ½scr  is honeycomb paper core allowable shear stress. The shear strength of the honeycomb paper base mainly depends on the strength of the adhesive layer of the adhesive used between the face paper and the honeycomb core paper according to the concept of uniform body, so Eq. (3) gives the strength of the glue layer: 8 dc ½scr   pffiffiffi ½rr  3 3a

ð3Þ

Where ½rr  is allowable shear stress of adhesive layer, a is honeycomb paper core length, and dc is honeycomb core thickness.

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According to the honeycomb paper-based torque balance and Eq. (4) gives the torque’s expression: M ¼ rf tf h

ð4Þ

Where rf is compressive stress on honeycomb paper base during bending deformation and M is torque. rf ¼

M  ½rr  tf hb

ð5Þ

Equation (5) is the formula of compressive stress on honeycomb paper base during bending deformation and within in the allowable shear stress of adhesive laye. The bending condition of the honeycomb paper base obtained by Eq. (5) is: rf ¼

M  ½r tf hb

ð6Þ

In Eq. (6), where ½r is critical stress of honeycomb paper base wrinkles, tf is honeycomb paper base thickness, h is honeycomb core thickness, b is Honeycomb core width. To make sure that the compressive stress on honeycomb paper base during bending deformation is within the critical stress range of honeycomb paper base wrinkling and deforming, the AGV trolley can be used to transport goods normally.

4 Conclusions (1) According to the stress nephotograph simulated by ABAQUS, the NOMEX honeycomb paper-based tray can still transport goods normally under the condition of 100 kg uniform static load. In addition, the cost of the honeycomb paper base is lower than that of the metal material, which is more in line with the maximum resource saving and the purpose of green development. (2) Since this paper does not consider the influence of the adhesive bond coefficient on the load-bearing capacity, it is possible to further explore the loading situation and further improvement of the NOMEX honeycomb paper-based tray from the perspective of modifying the adhesive bond coefficient. (3) Because the honeycomb paper base is easy to get wet, the life is short, which is a major defect. However, the surface of the honeycomb paper is coated with a waterproof and moisture-proof coating, such as emulsifying wax, which can effectively protect the surface of the honeycomb paper. The NOMEX honeycomb paper tray studied in this paper has been coated with emulsified wax waterproof coating, but its improvement content can be further studied.

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References 1. An, Y., Xu, Y.: Application status of logistics tray and its application analysis in finished cigarette logistics. Logistics Technol. 37(05), 21–24 (2018). (in Chinese) 2. Xiao, Q.: Research on AGV Structure Design and Control for 3C Automated Production Line, pp. 1–101. Guangdong University of Technology, Guangzhou (2018). (in Chinese) 3. Ke, Y., Jin, C., Liu, G.: Optimization of NOMEX honeycomb core high speed milling process. China Mech. Eng. 12, 1299–1302 (2006). (in Chinese) 4. Zhang, Y., Fan, X., Jutian, B.: Optimization method of quantity configuration for multiple types of AGV based on simulation optimization. China Mech. Eng. 22(14), 1680–1685 (2011). (in Chinese) 5. He, Y.-L., Davim, J.-P., Xue, H.-Q.: 3D progressive damage based macro-mechanical FE simulation of machining unidirectional FRP composite. Chin. J. Mech. Eng. 31(03), 128– 143 (2018) 6. Lu, Y., Sun, S., Zhang, K.: Research on the development strategy of innovative design. Mech. Des. 36(02), 1–4 (2019). (in Chinese) 7. Zhang, Y., Cai, M.: Overall life cycle comprehensive assessment of pneumatic and electric actuator. Chin. J. Mech. Eng. 27(03), 584–594 (2014) 8. Sun, Y., Cai, Z.-B., Wu, S.-B., et al.: Effect of cycling low velocity impact on mechanical and wear properties of CFRP laminate composites. Chin. J. Mech. Eng. 31(06), 45–54 (2018) 9. Fang, X., Liu, Z., Tan, J., et al.: Multi-scale simulation method with coupled finite/discrete element model and its application. Chin. J. Mech. Eng. 26(04), 659–667 (2013) 10. Qiong, Y., Xue, J., Chen, S., et al.: Three-dimensional finite element analysis of delamination buckling of composite laminates considering interface contact effect. Mech. Strength 41(02), 377–382 (2019). (in Chinese) 11. Li, M., Deng, Z., Guo, H., et al.: Crashworthiness analysis on alternative square honeycomb structure under axial loading. Chin. J. Mech. Eng. 26(04), 784–792 (2013) 12. He, F., Zhang, M., Zhang, S.: Aramid fiber/pulp surface energy and its composite paper properties. J. Compos. Mater. 04, 62–67 (2008). (in Chinese) 13. Smail, B., Blandine, A., Omar, B., et al.: Investigating automation and AGV in healthcare logistics: a case study based approach. Int. J. Logistics Res. Appl. 22(3), 273–293 (2019) 14. Yan, R., Dunnett, S.J., Jackson, L.M.: Novel methodology for optimising the design, operation and maintenance of a multi-AGV system. Reliab. Eng. Syst. Saf. 178, 130–139 (2018) 15. Wang, X., Yang, F., Zeng, J., et al.: The Sandwich Structure Conforms to the Material Design Principle and its Application. Chemical Industry Press, Beijing (2007). (in Chinese)

The Study of Electric Field Distribution on Small Holes in Pulse Electrochemical Machining Zhaolong Li(&) School of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin 150080, Heilongjiang, China [email protected]

Abstract. The application of tube electrode for electrochemical machining (ECM) holes in the surface of nickle based alloy was investigated in this paper. The distribution of interstitial electric field in electrochemical machining of tube electrode and the effect of interstitial electric field on hole size and hole depth were obtained via analysising electric field distribution on small holes forming, thus the reasons affecting the stability of electrochemical machining of small holes with tube electrode were obtained. Keywords: Electrochemical machining Electric field distribution  Feed speed

 Machining gap 

1 Introduction By general mechanical machining or other methods, it is difficult to produce cooling holes on turbine blades of gas turbine engines with a diameter of 1–4 mm, a depth-todiameter ratio of 40–150 and even higher than 500. Nowadays, the tube electrode is mainly used for ECM [1–5] due to the relatively high shape accuracy and surface quality. There is a major problem that the machining stability of tube electrode is highly poor in the electrolytic processing. Generally, the machining gap is narrowed to ensure the shape and size accuracy of the small holes in the ECM with tube electrode. The narrower the gap, the higher the machining accuracy [6–9], and the control of the electric field distribution contributes to the machining gap. The effect of electric field distribution on the deep machining of small holes in the process of tube electrode electrochemical machining was studied. The effect of different electrode feed rate on small holes forming was studied as well. The interstitial electric field distribution in electrochemical machining of tube electrode and the effect of interstitial electric field on hole diameter and hole depth were obtained. The reasons affecting the stability of electrochemical machining of small holes with tube electrode were obtained at the same time. This project is supported by Research Special Fund Project of Harbin Science and Technology Innovation Talent (Grant No. RC2017QN006016). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1018–1029, 2020. https://doi.org/10.1007/978-981-32-9941-2_85

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2 Experiment The experiment was conducted under the conditions including: initial gap between the tube electrode and the workpiece of 1 mm, feed rate of the tube electrode was set to be zero, the gap current was collected and turned to be zero in 4 min later. It was until the electrochemical machining finished that small holes were formed on the surface of workpiece. Covering with an insulating layer, the electrolytic reaction only occurred on the front surface of the tube electrode. With a pressure of 2.4 Mpa, the electrolyte was sprayed to the surface of the workpiece from the inner of the tube electrode. The effect of the gap electric field on the radius and depth of the small holes was studied, and the effects of the pulse width and pulse interval on the machining of the small holes was studied as well. The electric current sampling of ECM was shown in Fig. 1. As can be seen, it has the highest pulse current in 2 min, at 5 A. The whole process lasts for 4 min, after which the collecting current turned to be zero, with the gap between the tool and the workpiece of 2.1 mm. Besides, the tube electrode maintained a certain speed and the relevant electrical machining parameters were used to ensure the effect of electrode feed rate on the machining accuracy of small holes.

Current / A

5 4 3 2 1 0 0

1

2 Time / min

3

4

Fig. 1. Electric current sampling of ECM

3 Experimental Equipment The experiment was conducted on a self-made pulsed ECM equipment, which was pictorially presented in Fig. 2. The experimental equipment includes a working table, a flow system of electrolyte, a pulse power supply, etc. As was shown in Fig. 3, the tube electrode (with a diameter of 2.1 mm) was externally covered with an insulating layer.

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Fig. 2. Structure diagram of ECM equipment

Fig. 3. Schematic diagram of stirnelektrode

4 Results and Discussion

Radius and depth of hole / mm

As was shown in Fig. 4, the diameter of holes increased fastest during the 0–1 min and reached a maximum at 3 min; the depth of the small holes varied a lot during the 0– 3 min and remained unchanged at 4 min. In the whole process of ECM, the maximum radial electrolysis speed to the depth direction electrolysis speed occurred at about 1 min, at about 5. 3.5 3.0

Radius of hole Depth of hole

2.5 2.0 1.5 1.0 0.5 0.0 0

1

2 3 Time / min

4

Fig. 4. Influence of processing time on the semidiameter and depth of the hole

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It can be seen from Fig. 5 that the gap electric current patterns were similar at different pulse width. The collecting peak current increased with the increasing pulse width, rising from 2.9 A to 3.7 A. It was mainly because that the electrolytic machining effect in per unit increased when the pulse width increased, thus leading to a higher gap current.

Time-on 1900µs Time-on 1950µs Time-on 2000µs Time-on 2050µs

7

Current / A

6 5 4 3 2 1 0 0

1

2 3 Time / min

4

Fig. 5. Electric current sampling of ECM

As was shown in Fig. 6, with a specific pulse interval of 500 ls, the pulse width increased from 1900 ls to 2100 ls and the diameter increased from 2.9 mm to 3.1 mm. The influence of pulse width on the processing depth of ECM was showned in Fig. 7. It can be seen clearly that the depth increased from 1 mm to 3 mm. With the increasing pulse width, the diameter of the electrolysis hole increased by 22% and the depth of the electrolysis hole increased by 35%.

Diameter of holes / mm

3.4 3.2 3.0 2.8 2.6

1900

1950 2000 2050 Time-on / us

2100

Fig. 6. Influence of pulse width on the semidiameter of the hole

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Depth of holes / mm

1.4 1.3 1.2 1.1 1.0 0.9 0.8 1850 1900 1950 2000 2050 2100 Time-on / us

Fig. 7. Influence of pulse width on the processing depth of ECM

The influence of pulse interval on the semidiameter of the hole was presented in Fig. 8. As was shown in Fig. 8, with a specific pulse width of 2100 ls, the pulse interval increased from 200 ls to 500 ls and the diameter of the electrolysis holes decreased from 3.1 mm to 2.9 mm. The influence of pulse interval on the processing depth of ECM was shown in Fig. 9, the depth of electrolytic holes decreased from 1.1 mm to 0.9 mm. With the increasing pulse interval, the diameter of the electrolysis holes decreased by 6% and the depth of the electrolysis hole decreased by 18%.

Diameter of holes / mm

3.2

3.0

2.8

2.6

200

300

400

Time-off / us

500

Fig. 8. Influence of pulse interval on the semidiameter of the hole

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Depth of holes / mm

1.2 1.1 1.0 0.9 0.8

200

300 400 Time-off / us

500

Fig. 9. Influence of pulse interval on the processing depth of ECM

Diameter of holes /mm

As was shown in Figs. 10 and 11, when the tube electrode maintained a constant speed, the unilateral space of processed hole was inversely proportional to the electrode feed rate during the specific working cycle, while the gap current was proportional to the electrode feed rate. It was mainly because the average dissolution rate of the workpiece remained unchanged under a specific working cycle, and the electrolysis effect in per unit time was shortened with an increasing tube electrode feed rate, thus leading to a narrower singled-sided gap on the side of processed holes. However, with the increasing tube electrode feed rate, the machining gap in the front narrowed, resulting in the increasing of the front machining current If and the increasing of total machining current I.

2.65 2.60

Duty cycle 0.64 Duty cycle 0.72 Duty cycle 0.81

2.55 2.50 2.45 2.40 2.35 2.30 0.95 1.00 1.05 1.10 1.15 1.20 Tool feed rate / mm/min

Fig. 10. Influence of tool electrode feed rate on the unilateral space of processed hole

Z. Li

Current (A)

1024

20 19 18 17 16 15 14 13 12 11 10 0.60

Duty cycle 0.64 Duty cycle 0.72 Duty cycle 0.81

0.64

0.68

0.72

0.76

0.80

Tool feed rate (mm/min)

Fig. 11. Influence of tool electrode feed rate on the electric current in the gap

5 Stability of the ECM Analysis The workpiece was electrolytically etched in the ECM of the tube electrode. Since the material of the workpiece was a high-temperature nickel-based alloy including nonmetallic materials such as carbon and silicon, thus a quantity of the metal and nonmetal ions are oxidized to form ions at the anode according to the following equations. C ! C2 þ þ 2e

ð1Þ

Si ! Si2 þ þ 2e

ð2Þ

Ni ! Ni3 þ þ 3e

ð3Þ

Mo ! Mo3 þ þ 3e

ð4Þ

Ti ! Ti3 þ þ 3e

ð5Þ

When these ions entered the electrolyte in the machining gap, they were continuously diffused towards the stirnelektrode of the tube electrode under the effect of strong electric field and flow field. They were oxidized on the surface of the cathode and formed a non-metallic non-conductive layer after adsorption and deposition. At the same time, there was a large amount of NO 3 with strong oxidation near the end of the tube electrode where the metal titanium nearby was oxidized under the effect of electric field, thus leading to a decreased flatness of the end face of the tube electrode, the chemical equation was as follows: The internal voltage in the machining gap was relatively low and the micromorphology of the end surface of the tube electrode had a ups and downs shape during a certain period when the pulse was turned off. Therefore, in the end surface of tube electrode, there was such an area which was presented in Fig. 12. As was shown, the voltage of point B was lower than that of point A at the moment of the low voltage due

The Study of Electric Field Distribution on Small Holes

1025

Pulse Width U

1 2 t n Pulse interval

Low Voltage

Electrode

B O-

A

2

H2O2

Fig. 12. Oxidation film formation of tool electrode end face processed by low voltage power in instant

to the height difference between the two points of AB, resulting in an electric field. Then oxygen adsorption was formed at point A and non-metal particles nearby were oxidated. In the electrolysis process of tube electrode, pulse power supply was adopted so that such a low voltage appeared periodically in instant. What was moore, countless electric field like AB appeared in the end face of the tube electrode, accelerating the formation of non-metallic material layer and increasing the frequency of short circuit. By means of scanning electron microscope and EDX spectrum analysis, the morphology of the end face of the tool electrode was studied. As was shown in Fig. 13, there were a large amount of non-metallic materials in the end face of tube electrode.

Fig. 13. EDX spectrum of tool electrode end face after short circuit

1026

Z. Li

Therefore, it can be concluded that non-metal particles on the end surface of the tube electrode generated various oxides to form a surface layer which was shown in Fig. 13. It can be seen from Fig. 14 that the gap electric field of electrolytic machining of tube electrode was affected by the layer formed by non-metallic materials such as carbon and silicon, thus leading to the frequent occurrence of short circuit.

Fig. 14. Oxidation film formation of tool electrode end face

6 Effect of Electrolyte Pressure on ECM Electric Field Analysis There were bubbles depositing in the end face of the tool electrode during the ECM of deep small holes. After depositing, these bubbles were not exist in the electrolyte nearby but tightly adsorbed on the end face of the tool electrode. It was mainly because that the pressure of these bubbles was uneven in the electrolyte nearby the tube electrode, and these bubbles were tightly pressed in the end face of the tube electrode, which was shown in Fig. 15.

Tool electrode

bubble

pressure

Fig. 15. The bubble adsorption in the processing gap

The Study of Electric Field Distribution on Small Holes

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Due to the poor conductivity of the bubbles, these bubbles were firmly pressed in the end surface of the tube electrode, which greatly affected the electric field strength in the electrolytic processing circuit and weakened the current in the processing gap. As a result, the conductivity in the processing gap was decreased and the gap electric field of the electrolytically small holes was affected. Meanwhile, as was shown in Figs. 16 and 17, the results showed that the lateral pressure distribution of the straight front hole of AB section was M-shaped and the gap pressure distribution was symmetrically uniform and decreased by simulation analysis of the machining gap pressure. The symmetry electrolyte pressure distribution guaranteed the stability of the tool electrode when the electrolyte pressure was continuously increased, which further guaranteed the stability of the electric field in the machining gap.

Internal pressure of electrode Gap pressure of side Gap pressure of front-end

Fig. 16. Simulation of pressure of machining gap

p r e s s u r e

Sampling point

Fig. 17. Influence of electrolyte pressure on the unilateral space of processed hole

1028

Z. Li

Depth-averaged radial overcut /mm

The experiment was conducted under conditions including pulse width ranged from 500 to 1000 ls, the pulse voltage of 24 V and the electrolyte pressure ranged from 1.9 to 3.0 Mpa. As was shown in Fig. 18, It can be seen clearly that the singled-gap narrowed when the electrolyte pressure increased at a certain ton. This was mainly because the timely removal of bubbles, reaction products and reaction heat in the electrochemical machining gap when the electrolyte pressure increased, renewaling the electrolyte in the machining gap and improving the localization in the electrolysis process of the deep small holes.

0.40

Ton 500μs Ton 750μs Ton1000μs

0.35 0.30 0.25 0.20 0.15 2.0

2.2 2.4 2.6 2.8 3.0 Pressue of electrolyte / MPa

Fig. 18. Influence of electrolyte pressure on the unilateral space of processed hole

7 Conclusions The following conclusions were obtained via the influence of electric distribution on the deep small holes of tube electrode: (1) The diameter of the machining hole was parabolic distribution in the static electrolytic process of tube electrode, and the maximum radial electrolysis speed to the depth direction electrolysis speed occurred at about 1 min, at about 5. (2) When the pulse power supply was used for the deep machining of small holes, the machining aperture was inversely proportional to the electrode feed rate during a specific working cycle, while the gap current was proportional to the electrode feed rate when the tube electrode maintained a constant speed. The electrode feed rate was inversely proportional to the singled-gap on the side of the holes and it was proportional to the gap current. (3) By qualitative analysis of the tube electrode in ECM, the reason of the frequent occurence of short circuit was that: with the increasing working time, a nonmetallic layer would be formed on the end face of tube electrode, and the layer forming mechanism of the end face of tube electrode was analyzed.

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(4) The influence of electrolyte pressure on the electric field in ECM was studied. Within a certain range, increasing the electrolyte pressure would not affect the stability of the gap electric field through simulation analysis. At the same time, it was believed that increasing the electrolyte pressure could greatly renew the electrolyte in the machining gap and improve the localization in the electrolysis process of the deep small holes, which further improving the shape accuracy of the deep small holes in ECM.

Appendix Appendix and supplement both mean material added at the end of a book. An appendix gives useful additional information, but even without it the rest of the book is complete: In the appendix are eighteen detailed charts. A supplement, bound in the book or published separately, is given for comparison, as an enhancement, to provide corrections, to present later information, and the like: A yearly supplement is issue.

References 1. Buckney, N., Pirrera, A., Green, S.D., Weaver, P.M.: Structural efficiency of a wind turbine blade. Thin-Walled Struct. 67, 144–154 (2013) 2. Geest, M.V.D., Polinder, H., Ferreira, J.A.: Design and testing of a high-speed aerospace permanent magnet starter/generator. In: International Conference on Electrical Systems for Aircraft (2015) 3. Ismagilov, F.R., Khairullin, I.K., Vavilov, V.E., et al.: A high-temperature frameless startergenerator integrated into an aircraft engine. Russ. Aeronaut. (Iz VUZ) 59(1), 107–111 (2016) 4. Kozak, J., Rajurkar, K.P., Balkrishna, R.: Study of electrochemical jet machining process. Tr ASME J. Manuf. Sci. Eng. 118, 490–498 (1996) 5. Sharma, S., Jain, V.K., Shekhar, R.: Electrochemical drilling of Inconel super alloy with acidified NaCl electrolyte. Int. J. Adv. Manuf. Technol. 19, 492–500 (2002) 6. Baker, G.E.: Hole drilling processes experiences, applications, and selections. In: Proceedings of the SME Non-traditional Machining Symposium, Orlando, pp. l–12 (1991) 7. McGeough, J.A., Pajak, P.T., de Silva, A.K.M., Harrison, D.K.: Recent research and developments in electrochemical machining. Int. J. Electr. Mach. 8, 1–14 (2003) 8. Jain, V.K., Kanetkar, Y., Lal, G.K.: Stray current attack and stagnation zones in electrochemical drilling. Int. J. Adv. Manuf. Technol. 26, 527–536 (2005) 9. Kozak, J., Rajurkar, K.P., Wof, R.: Modeling and analysis of pulse electrochemical machining. Trans. ASME 116(8), 316–323 (1994)

Reliability Optimization Design of New Automatic Tensioning Belt-Gear Transmission Chengyi Pan(&), Guanqun Cao, and Yuanqi Tong School of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin, China [email protected], [email protected], [email protected] Abstract. Automatic tensioning belt-gear transmission is a new type of transmission mechanism. The reliability optimization design of the device is carried out to meet the working reliability and optimize structural parameters. The design is based on the force balance equation, with the belt transmission reliability as the main constraint condition and the minimum number of belt and the minimum volume of gear as aimed function. The reliability and stability of the design are verified by simulation analysis based on the design results. This design method can ensure the reliability of belt transmission and quickly obtain a set of optimal structural parameters. The advanced design method greatly improves the design speed and quality, and provides an effective design method for the new transmission. Keywords: Automatic tensioning  Belt-gear transmission  Numerical integration  Reliability optimization design  Simulation analysis

1 Introduction The tensioning method of the belt drive has regular tensioning and automatic tensioning. In the automatic tensioning belt transmission, the tensioning method with automatic adjustment of the belt tension with the change of the load size is the best [1]. In literature [2], the method of automatic tensioning of the belt drive by gear is introduced. The pulley and the gear are integrated, and the sleeve is placed on the tie rod, which can swing around the motor shaft. When the transmission power increases, the tension is increased. And vice versa. The bearing shaft force generated on the motor shaft is much smaller than that generated by other tensioning methods, and the bearing and belt have a longer life and higher efficiency. With the advancement of manufacturing technology and the wide application of computers, the use of such excellent automatic tensioning devices has attracted more and more attention [3, 4]. How to improve the working performance of the automatic tensioning of the belt drive has always been the subject of research [5]. However, the theoretical analysis and design basis in this aspect are still very scarce. For this reason, the literature [1] proposes a new type of automatic tensioning belt-gear transmission combination. Compared with the method of the literature [2], it is more suitable for occasions with large bearing capacity, high speed and shock vibration. In the literature [1], the device is deeply analyzed and researched, and the literature gives computer programming methods. © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1030–1043, 2020. https://doi.org/10.1007/978-981-32-9941-2_86

Reliability Optimization Design

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However, for the design method, the algorithm is rough, the design speed is slow, and it is difficult to achieve the best design results. Therefore, based on this, the reliability optimization design of the device is proposed. This paper introduces the driving principle of a new type of automatic tensioning belt-gear transmission and the force balance equation of large belt wheel. Furthermore, taking the balance condition of big belt pulley, reliability of belt transmission, gear strength and structural parameters as constraints, and taking the minimum root number of belt and the minimum gear volume as objective function, the reliability optimization design is carried out and carry on the simulation verification, which can quickly obtain the best design results while meeting the reliability requirements. Compared with the traditional design method and the design method in literature [1], the design is of higher quality, faster and more advanced.

2 Transmission Principle and Large Pulley Force Balance Equation 2.1

Transmission Principle

Figure 1 shows the automatic tension belt-gear transmission diagram, 1 a small pulley, 2 a large pulley, 3 a small gear, 4 a large gear, 5 a frame, 6 a pendulum. The pinion gear 3 is coaxially fixed with the large pulley 2 and suspended from the frame by the swing rod 6. When the small pulley transmits the torque T1 and rotates at the rotation speed n1, the large pulley and the pinion rotate together by the belt drive, the large pulley torque T2, the pinion torque T3, T3 = T2, and then the large gear is driven. When the gear rotates, the torque is output by the large gear. At this time, the tension of the tight side of the belt is F1, and the pulling force of the loose side is F2. The belt is automatically tensioned by the circular gear’s circumferential force, the weight of the large pulley and pinion. The greater the circumferential force on the pinion, the greater the tension, and vice versa, so that the tension of the belt can be automatically adjusted according to the magnitude of the transmitted load. 4 d4 O2

5

6

F1

F1 F36t

1

D1

T1 O1 5 n1

FQ

F2

F2

Ft3

TQ

d3

D2

3 2

Fig. 1. Automatic tension belt-gear transmission schematic

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C. Pan et al.

Designing the power P1 of the small pulley transmit, speed n1 and belt transmission ratio i1 are generally given according to the work requirements, according to the conventional design method can determine the diameter of the small pulley D1, the diameter of the large pulley D2 and the center distance of the belt drive a1. The determination of the diameter of the pinion index circle d3 needs to consider two aspects, namely: not only to meet the requirements of the belt drive tension, but also to meet the requirements of the gear strength, so as to ensure that the belt drive neither fatigue damage and no slip. 2.2

Large Pulley Force Balance Equation

As shown in Fig. 1, it is assumed that the circumferential force of the gear teeth on the pinion 3 is Ft3, and the force of the free end of the pendulum (the large pulley and the axis O2 of the gear 3) is F36t, and the tight side of the belt. The force generated by the tension and the loose side tension on the shaft is simplified to the axial center O2 as the axial force FQ and the torque TQ, and then the total pulley and the pinion total gravity G are considered. When running smoothly, the large pulley is subjected to the balance and the force balance equation of the Large pulley is [1]. Ft3 þ G sin c  FQ cosðc þ bÞ ¼ 0

ð1Þ

Where: c is the angle between the center line of the two gears and the vertical line; b is the angle between the connection line of the two pulleys’ center and the horizontal line.

3 Building a Mathematical Model The transmission design of the known conditions are generally given small wheeled transmission power speed n1, P1 and small pulleys with i1, i2 of gear transmission ratio of the transmission ratio and the performance of the transmission device, when running meet the big belt wheel force equilibrium condition, the requirement with the model, with the root of the number, and the main dimensions of the pulley and gear. According to the power P1 transmitted by the belt, the speed n1 of the small pulley and the working condition of the belt drive, the model of the belt can be easily determined by the mechanical design manual, and then the main geometrical dimensions of the transmission are determined by the reliability optimization method. 3.1

Establishing the Objective Function

For the V-belt drive, select the small pulley diameter D1 and the belt length L as the design variables; for the gear transmission, the gear modulus m, the pinion gear number z3 and the tooth width coefficient Wd are selected for the design variable; the total

Reliability Optimization Design

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weight G of the large pulley and pinion, the installation angles c and b are the design variables for the balance state of the pendulum, that is the design variables. X ¼ ½x1 ; x2 ; x3 ; x4 ; x5 ; x6 ; x7 ; x8 T

ð2Þ

¼ ½D1 ; L; m; z3 ; wd ; G; c; bT

For the V-belt drive, when the model of the belt has been determined, under the condition of satisfying the same bearing capacity, the fewer the number of belts Zb, the lower the cost, and the problem of uneven force between the belts in situation of multiple belt drives are reduced. And it can reduce the axial dimension of the pulley; for gear transmission, the smaller the total volume VP of the two gears, the lower the cost. From the literature [2], the following objective function is established: FðXÞ ¼

h

f1 ðXÞ f2 ðXÞ

i

9 > > > > > =

KA P1 ðP0 þ DP0 ÞKa KL > > > > p 2 > 2 ; minf2 ðXÞ ¼ minVR ¼ min ðd3 þ d4 Þb 4 minf1 ðXÞ ¼ minZb ¼ min

ð3Þ

Where: Pc is the calculated power of the belt drive; KA is the operating coefficient; Ps is the power that can be transmitted by a single belt; P0 is the power that can be transmitted by a single belt under certain conditions; DP0 is the power transmitted by a single belt Increment; Ka is the wrap angle coefficient; KL is the band length coefficient; d3 is the index circle diameter of the pinion gear, d3 = mz3; d4 is the index circle diameter of the large gear, d4 = d3i2; b is the width of the two gears, b = d3Wd. The above equation pursues two objective functions with the least number of belts and the smallest gear volume. The main objective function method is used to transform the multi-objective optimization problem into a single-objective optimization problem [6, 7], that is, minf1(x) is used as a better goal of search, and the minf2(x) as a constraint is reflected in the mathematical model, then the above equation is transformed into: 9 KA P1 > = ðP0 þ DP0 ÞKa KL p > g1 ðXÞ ¼ ½VRmin   ð1 þ i22 Þðx3 x4 Þ3 x5  0 ; 4

minFðXÞ ¼ minf1 ðXÞ ¼ min

ð4Þ

In the equation, [VPmin] is the preset minimum volume of two gears, which can be determined by heuristic method. P0 can be calculated by the following equation [8]. P0 ¼ ðK1 v0:91  K2 =D1  K3 v2 Þv

ð5Þ

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Where K1, K2, and K3 are the coefficients associated with the belt type, see Table 1 [8]. v is the belt speed, which can be expressed as v¼

pD1 n1 px1 n1 ¼ 60  1000 60  1000

ð6Þ

ΔP0 in Eq. (4) can be expressed as DP0 ¼ Kb n1 ð1 

1 Þ Ki

ð7Þ

Where: Kb is the bending influence coefficient, Kb = K2/19100; Ki is the trans 5:31 mission ratio coefficient of the belt drive; Ki ¼ i1 1 þ2i5:3 ; i1 is the transmission ratio 1

of the belt. In the Eq. (4), Ka can be expressed as Ka ¼ 1:25ð1  5

a1 Þ p

ð8Þ

In the equation, a1 is a small wheel wrap angle. a1 ¼ p  D 1 ð

i1 1 i1 1 Þ ¼ p  x1 ð Þ a a

ð9Þ

Equations (7) to (9) can be found in literature [8], where a in the Eq. (9) is the center distance of the belt drive, and the calculation equation is derived from literature [2].  a ¼ 14 L  p2 ð1 þ i1 ÞD1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ ðL  p2 ð1 þ i1 ÞD1 Þ2  2ði1  1Þ2 D21 which is  a ¼ 14 x2  p2 ð1 þ i1 Þx1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ ðx2  p2 ð1 þ i1 Þx1 Þ2  2ði1  1Þ2 x21

ð10Þ

KL in the Eq. (4) is a belt’s length coefficient, and its calculation equation is [8] KL ¼ 1 þ 0:195435  ðln L  ln Lt Þ which is KL ¼ 1 þ 0:195435  ðln x2  ln Lt Þ Where Lt is the experimental length of the belt, see Table 1.

ð11Þ

Reliability Optimization Design

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Table 1. V-type belt related parameters Parameter K1 K2 K3  10-4 Lt q(N/m)

Z 0.246 7.44 0.441 800 0.588

A 0.449 19.62 0.765 1700 0.98

B 0.794 50.6 1.31 2240 1.666

C 1.48 143.2 2.34 3750 2.94

D 3.15 507.3 4.77 6300 6.076

E 4.57 951.5 7.06 7100 8.82

When the values of the variables x1, x2, x3, x4 and x5 are given, and the Eqs. (5) to (11) are substituted into the Eq. (4), the values of the functions f1(x) and f2(x) can be obtained. 3.2

Establish Constraints

3.2.1 Pendulum Force Balance Constraint In order to make the automatic tension belt-gear transmission run smoothly, it must be ensured that the Large pulley is under stress. The axial force FQ in Eq. (1) is calculated by the following equation [2]: FQ ¼ 2Zb F0 sin

a1 2

ð12Þ

In the equation, F0 is the initial tension when the single belt is installed, and the calculation equation is [2]: F0 ¼ 500

  Pc 2:5  Ka þ qv2 Zb v Ka

ð13Þ

Where q is the long mass per meter, see Table 1. Substituting Eq. (13) into Eq. (12), sin (a1/2) is approximated to one. FQ ¼ 1000

  Pc 2:5  Ka þ 2Zb qv2 v Ka

ð14Þ

Let K be the load factor of the gear transmission, and take the Eq. (14) and 6 1 i1 Ft3 ¼ 2KT d3 ¼ 2  9:55  10 ðKP1 =n1 Þi1 =d3 into Eq. (1). 2  9:55  106 KP1 i1 þ G sin c d3 n1    1000Pc 2:5  Ka 2  þ 2Zb qv cosðc þ bÞ ¼ 0 v Ka

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Then the large pulley with force balance constraint is 2  9:55  106 KP1 i1 þ x6 sin x7 x 3 n1    1000Pc 2:5  Ka  þ 2Zb qv2 cosðx7 þ x8 Þ ¼ 0 v Ka

h1 ðxÞ ¼

ð15Þ

Ka is still calculated according to Eqs. (8)–(10). In order to facilitate the calculation of the computer, the Eq. (15) is rewritten into the following constraint form, i.e. 2  9:55  106 KP1 i1 þ x6 sin x7 x 3 n1    1000Pc 2:5  Ka 2  þ 2Zb qv cosðx7 þ x8 Þ  0 v Ka

g2 ðxÞ ¼

2  9:55  106 KP1 i1 g3 ðxÞ ¼  þ x6 sin x7 x 3 n1    1000Pc 2:5  Ka 2  þ 2Zb qv cosðx7 þ x8 Þ  0 v Ka

ð16Þ

ð17Þ

3.2.2 V Belt Drive Reliability Constraints In order to calculate the reliability of the V-belt drive, the quantile ZR is first obtained [8]. Ps  Pc =Zb ZR ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðCk Ps Þ2 þ ðSk Pc =Zb Þ2

ð18Þ

Where: Ps is the mathematical expectation of the power transferable by a single band; Pc/Zb is the mathematical expectation of the calculated power delivered by a single band; Ck is the coefficient of variation of Ps; and Sk is the coefficient of variation of Pc/Zb. It can take Ck = 0.51, Sk = 0.56 [8]. Equation (18) is the connection equation. Through this equation, and then with the reliability as the constraint, it can be related to the optimization design, which constitutes the reliability design calculation. From the ZR, the reliability R can be obtained by the following equation [8], i.e. 1 R ¼ pffiffiffiffiffiffi 2p

Z

1

ZR

t2

e 2 dt

ð19Þ

Equation (19) is a importer integral. It is very difficult to calculate by hand. For this reason, the parabola method in the numerical integration of Simpson is used. When any

Reliability Optimization Design

1037

quantile is given, the computer can quickly obtain the corresponding reliability. The calculation accuracy and calculation range are better than the table look-up method, and it is convenient to optimize the dynamic observation of the process, which creates favorable conditions for reliability optimization design [9]. Bringing the Eq. (18) into the Eq. (19), the V belt drive reliability R can be obtained. 1 R ¼ pffiffiffiffiffiffi 2p

Z

1

t2

s c b pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðCk Ps Þ2 þ ðSk Pc =Zb Þ2 P P =Z

e 2 dt

ð20Þ

Obviously, the reliability of the V-belt drive should be greater than its allowable reliability [R], so the V-belt drive reliability constraint is 1 g4 ðxÞ ¼ pffiffiffiffiffiffi 2p

Z

1

t2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ps Pc =Zb ðCk Ps Þ2 þ ðSk Pc =Zb Þ2

e 2 dt  ½R  0

ð21Þ

3.2.3 Gear Transmission Contact Fatigue Strength Constraint The gear transmission can adopt closed transmission. The main failure mode is contact fatigue failure. The design experience shows that the gear contact strength has a large margin. Therefore, the contact stress rH of the control gear is less than its allowable contact stress [rH]. By literature [10], there is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KT2 ði2 þ 1Þ rH ¼ 673 d33 wd i2 Then the gear contact fatigue strength constraint is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KT2 ði2 þ 1Þ ½rH   673 0 d33 wd i2

ð22Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KT2 ði2 þ 1Þ g5 ðxÞ ¼ ½rH   673 0 d33 wd i2

ð23Þ

Scilicet

3.2.4 Structural Parameter Constraint The structural parameter design conditions are determined based on design experience and include the following conditions:

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C. Pan et al.

(1) Small pulley diameter limit conditions. Take D1min  D1  D1max, then there is g6 ðxÞ ¼ x1  D1min  0

ð24Þ

g7 ðxÞ ¼ D1max  x1  0

ð25Þ

(2) Small belt wheel wrap angle restriction conditions. The small pulley wrap angle a1 should be larger than the specified small pulley wrap angle [a1], and the small pulley wrap angle limitation condition of Eqs. (9) and (10) is  g8 ðxÞ ¼ p  4x1 ði1  1Þ= x2  p2 ð1 þ i1 Þx 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 p þ ðx2  2 ð1 þ i1 Þx1 Þ  2ði1  1Þ x1  ½a1   0

ð26Þ

(3) Belt drive center distance limit conditions. Take amin  a  amax, then there is g9 ðxÞ ¼ x2  p2 ð1 þ i1 Þx1 : qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ ðx2  p2 ð1 þ i1 Þx1 Þ2  2ði1  1Þ2 x21  amin  0 1 4

g10 ðxÞ ¼ amax  x2  p2 ð1 þ i1 Þx1 : qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ ðx2  p2 ð1 þ i1 Þx1 Þ2  2ði1  1Þ2 x21  0 1 4

ð27Þ

ð28Þ

(4) Restrictions on the length of the V-belt. Take Lmin  L  Lmax, then there is g11 ðxÞ ¼ x2  Lmin  0

ð29Þ

g12 ðxÞ ¼ Lmax  x2  0

ð30Þ

(5) Limitation of V-belt speed. Take vmin  v  vmax, then there is g13 ðxÞ ¼

px1 n1  vmin  0 60000

ð31Þ

px1 n1 0 60000

ð32Þ

g14 ðxÞ ¼ vmax 

(6) The total weight limit of the large pulley and pinion. Take Gmin  G  Gmax, then there is g15 ðxÞ ¼ x6  Gmin  0

ð33Þ

g16 ðxÞ ¼ Gmax  x6  0

ð34Þ

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(7) Mounting angle c and b constraints g17 ðxÞ ¼ x7  cmin  0

ð35Þ

g18 ðxÞ ¼ cmax  x7  0

ð36Þ

g19 ðxÞ ¼ x8  bmin  0

ð37Þ

g20 ðxÞ ¼ bmax  x8  0

ð38Þ

(8) Gear modulus limit conditions. Take mmin  m  mmax, then there is g21 ðxÞ ¼ x3  mmin  0

ð39Þ

g22 ðxÞ ¼ mmax  x3  0

ð40Þ

(9) Pinion gear limit conditions. Take Z3min  Z3  Z3max, then there is g23 ðxÞ ¼ x4  Z3min  0

ð41Þ

g24 ðxÞ ¼ Z3max  x4  0

ð42Þ

(10) Tooth width factor limit condition take. wdmin  wd  wdmax, then there is g25 ðxÞ ¼ x5  wdmin  0

ð43Þ

g26 ðxÞ ¼ wdmax  x5  0

ð44Þ

The calculation results show that the calculation method proposed in literature [1] can reduce the number of belts from the original 5 to 4, and the total gear volume is reduced from 3.2  106 mm3 to 2.7  106 mm3. Obviously, the calculation result is better than the algorithm of literature [1], and the calculation speed is fast and the quality is high, which is more conducive to practical application.

4 Simulation Analysis According to the result of optimization design, the ADAMS software is used to build the simulation model and carry on the simulation. The simulation model is shown in Fig. 2.

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Fig. 2. Adams simulation model

Firstly, according to the requirements in literature [1], n1 = 24 r/s for small pulley speed, D1 = 125 mm for small pulley diameter, D2 = 280 mm for large pulley diameter, and i = 3 for gear transmission ratio are set as the initial conditions, and the simulation model is established according to the results of optimal design. Then, in order to verify the stability and reliability of transmission, the center distance of two belt wheels (Distance), the rotation speed of the large gear (Rotation speed) and the radial force of the small belt wheel (Radial force) are selected as the analysis parameters for analysis. Finally, in order to verify the performance of automatic tensioning with gear transmission, different torques (0 N.mm, 5000 N.mm, 10000 N.mm, 15000 N.mm) are applied on the output big gear as loads to obtain multiple sets of simulation results. The four groups of simulation data obtained are shown in Figs. 3, 4, 5 and 6.

Fig. 3. 0 N. mm load analysis diagram

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Fig. 4. 5000 N. mm load analysis diagram

Fig. 5. 10000 N. mm load analysis diagram

As shown in this figure, at the initial stage of transmission (about 0–1.5 s), the Rotation speed rises steadily, and the Distance keeps changing and the amplitude gradually decreases, and the maximum amplitude is 1 mm (about 0.1% of the Distance under stable conditions). At this time, there may be slippage in the belt drive, and the change of Distance causes the change of the Radial force, and the maximum peak value of the Radial force can reach 105% of the stable value of the Radial force. In the middle stage of transmission (about 1.5 s–2.5 s), the Rotation speed is stable, and the Distance vibrates at a center slightly larger than the average value of the initial transmission, and the amplitude gradually decreases and the maximum value is less than the maximum value of the initial transmission. The change of Radial force is similar to that on the Distance, and the peak value is less than initial stage. At the stabilization stage (after 2.5 s), the Rotation speed is stable, the Distance is stable, and the Radial force is stable.

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Fig. 6. 15000 N. mm load analysis diagram

At this time, the automatic tensioning process has been completed, and the belt-gear transmission can stabilize the output speed and torque according to the preset requirements. Through the comparative analysis of the four groups of simulation, it can be found that with the increase of load, the amplitude of Radial force and the Distance decreases with increases speed, and the time to reach the stability stage gradually decreases, and when the load is 0 N.mm, the stability time is the longest, which is 2.5 s. Through the above analysis, the following conclusions are obtained. (1) According to the new automatic tensioning belt-gear transmission design method, the structure can achieve stable speed in a short time (1.5 s in the simulation) and stable operation in 2.5 s. (2) According to the new automatic tensioning belt-gear transmission design method, the radial force on the structure motor shaft fluctuates from start-up to smooth operation, and the fluctuation peak of the radial force is about 105% of the stable value of the radial force. The axial force on the motor shaft is obviously smaller than that on the conventional structure.

5 Conclusions (1) The automatic tension belt-gear transmission proposed in this paper is a new type of transmission mechanism. During tensioning the axial force is small, and the bearing and the belt have a long service life, high efficiency and easy maintenance, and the effect is best compared with other tensioning methods. (2) The design of the new automatic tensioning belt-gear transmission, reliability optimization design, which provides a theoretical basis for the practical application and in-depth study of the new transmission mechanism is deduced. (3) The design method proposed in this paper, under the condition of satisfying certain reliability, miniming the number of belts and minimizing the volume of the

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gears, and at the same time obtaining a set of optimal structural parameters. The design speed is fast and the quality is high, which is convenient for promotion and application.

References 1. Chengyi, P.: Design of combination of automatic tension belt drive and toothed gearing. Mach. Des. Res. 30(1), 17–19 (2014) 2. Xuanhuai, Q.: Mechanical Design, 4th edn, p. 198. Higher Education Press, Beijing (2003). (in Chinese) 3. Joseph, F.L.: Belt and chain tensioners. Plant Eng. 56(8), 39–43 (2002) 4. Maier, M.: Introduction of an automatic belt tensioning device for the belt conveyors in the indent opencast mine. World Min. Surf. Undergr. 61(1), 14–22 (2009) 5. Clark, R.B., Larry, R.O., William, F.B.: Dynamic analysis of belt drive tension forces during rapid engine acceleration. SAE (Soc. Automot. Eng.) Trans. 100(6), 898–913 (1991) 6. Xiaojing, L.I., Qingbo, L.U.: Multi-objective optimization design of V-belt transmission based on differential evolution algorithm. J. Mech. Transm. 37(10), 86–90 (2013) 7. Li, S., Fengtao, W., Wei, L.: Multi-object fuzzy optimization design of belt drive based on improved genetic algorithm. J. Mech. Transm. 30(5), 28–30 (2006) 8. Qi, W., Wenbo, W.: Reliability Design of Common Mechanical Parts, pp. 166–176. China Machine Press, Beijing (1996). (in Chinese) 9. Chengyi, P., Yan, M.: Optimal design of strength reliability of screw joints for micron woodfiber mould products. Mech. Sci. Technol. Aerosp. Eng. 27(2), 162–164 (2008) 10. Jinsong, T.: Concise Mechanical Design Manual, pp. 268–273. Shanghai Scientific and Technical Publishers, Shanghai (2009)

Design and Simulation Analyses of a Five-Wheeled Stair-Climbing Mechanism Based on TRIZ Theory Chengyi Pan(&) and Yuanqi Tong School of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin 150080, China [email protected], [email protected] Abstract. Based on TRIZ theory, a five-wheeled stair-climbing mechanism is designed. Its function and structure of the system are analyzed, and the contradiction analyses are made on the problem existing in the design process. The ideal final result is found by combining 40 inventive principles. Then, the fivewheeled stair-climbing mechanism is simulated and analyzed to verify the rationality and stability of its structure. The mechanism is small in size and simple in structure. It is suitable for general stairs and has a good practical value. Keywords: Five-wheeled stair-climbing mechanism Simulation analysis  Innovative design

 TRIZ theory 

1 Introduction At present, there are many kinds of stair-climbing mechanisms and stair-climbing robots in the market, which can be mainly divided into two types: crawler and tripod [1]. The center of gravity of tripod jumps greatly, which will produce impact on the moving objects. So it is not suitable for carrying sophisticated equipments. The crawler has small fluctuation of center of gravity, smooth movement but large weight, and its movement is not flexible enough. It causes tremendous pressure on the edge of stairs when climbing, which has certain damage to the stairs. In view of the optimization of the stair-climbing mechanisms, many domestic scholars have carried out researches on it. Because of the particularity of the motion environment, the stair-climbing mechanisms should not only have a simple and compact structure, but also have extremely high stability, which makes the design particularly difficult. SI has designed a five-wheeled rotating stair-climbing cart, which can save strength by reducing the rotation angle of the wheels’ center when going upstairs [2]. But its power can only come from people, unable achieve automatic stairclimbing. Wei, Yang, et al., research a kind of eight-wheeled stair-climbing robot, which verifies the rationality of its structure, but it is more suitable for the field with complex terrain [3]. Liu and Ma establish a kinematic model of a five-wheel articulated lunar robot traveling on rough terrain, laying a foundation for the motion control of the robots in three-dimensional terrain [4]. In recent years, the popularity and continuous improvement of the theory of solving inventive problems provides a powerful auxiliary tool for the solution of design © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1044–1053, 2020. https://doi.org/10.1007/978-981-32-9941-2_87

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problems. In view of the above problems, this paper applies TRIZ tools to analyze the existing contradictions, solving the problems in the design process, and obtaining the optimal solution.

2 Analyses Based on TRIZ Theory TRIZ (The Theory of Inventive Problem Solving) is a set of systematized and practical theories, methods and systems for solving inventive problems, which was established in 1946 by a group of scholars led by Altshuller, an inventor of the former Soviet Union [5]. The TRIZ theory is efficient. It uses systematic methods and tools to solve problems that are often unsolvable or difficult to solve, especially for designers to break the traditional inertia and get inspiration [6]. In this paper, the TRIZ theory are used to analyze the contradictions in the design process, and a five-wheeled stair-climbing mechanism is designed. 2.1

Basic Structure Design and System Completeness Analysis

The purpose of this design is using the principle of mechanical transmission to make the mechanism climb up stairs. Through the analyses of the current situation of the stairclimbing mechanisms, it can be seen that the small stair-climbing mechanisms mostly have two rows which are added three or five wheels in a flat plane. Its movement is unstable and unsafe. The six-wheeled and eight-wheeled stair-climbing mechanisms are stable but complex in control and structure. Too few wheels will reduce the stability accordingly, and too many wheels will make the control complicated and consume materials. Therefore, the stair-climbing mechanism of this design uses five wheels to make the structure as simple as possible under the premise of high stability. Instead of following the previous five-wheeled structure, a new five-wheeled stair-climbing mechanism with space movement is innovated. The distribution of the five wheels is shown in Fig. 1. The two front wheels are driven by motors, which provide the power source for the whole moving forward. The two rear wheels are connected by a rod. This is only a general idea, the power source of the auxiliary wheel and how to move, as well as its specific transmission mode need to be solved by using TRIZ tools.

Fig. 1. The basic structure of five-wheeled mechanism

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In order to achieve the function of the system, the complete structure of technical system usually includes at least four parts: power device, transmission device, actuator and control device, without which part of the system can not be established [7]. Table 1 shows the system completeness analysis of the five-wheeled stair-climbing mechanism. Table 1. System completeness analysis Energy source Power device Transmission device Actuator Product Control device External control

2.2

Electricity Motors Rods Front wheels, auxiliary wheel, rear wheels Five-wheeled stair-climbing mechanism PLC circuit control system Operator

Functional Analysis and Working Principle

Product is the carrier of function, and function is the core and essence of product. Analyzing product function is an important and practical activity [8]. The function of the stairclimbing mechanism is to replace the manual climbing action and save labor. The stairclimbing mechanism designed in this paper intends to let two front wheels climb up the stairs firstly and then two rear wheels climb up the steps, so as to achieve the goal of climbing up the steps as a whole. Therefore, the mechanism should have the function of pulling up the wheels. If the lifting part is set on the front wheels, it is unrealistic and will add redundant devices, which violates the principle of simple structure. Therefore, this design adds the front rod to the connecting rod of the auxiliary wheel, and the front wheels are lifted by stretching the front rod. After the front wheels are lifted, the mechanism loses the power source to move forward, so an additional motor is added to the auxiliary wheel. The lifting of the rear wheels are also accomplished by the rear rods. In this process, in order to ensure its stability, the auxiliary wheel forms a stable triangular structure with the front wheels and the rear wheels respectively, so the auxiliary wheel is an important transitional part for the front and rear wheels to climb up the steps. The designed transmission structure is shown in Fig. 2. The force direction of front and rear rods are marked respectively, and their other ends are attached to the fixed frame.

Fig. 2. Schematic diagram of the transmission structure

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Technical Contradictions

A contradiction happens when an improvement of one of the system parameters will then lead to deterioration of other parameters [9]. The contradiction matrix is used to analyze the problems in the design process. (1) In order to reach the purpose of pulling up the front wheels and rear wheels, the front rod and rear rods are required to be able to stretch. Since the force direction and analyses are determined, so flexible connectors such as springs cannot be used. Only the rods with certain stiffness can be used. The rods should be long enough to lift the front and rear wheels higher and the range of application is bigger. If the lengths of the front and rear rods are increased, the greater work done during the movement, which will cause energy loss. So there is a technical contradiction. The technical parameters of the system were abstracted into the 39 general parameters of TRIZ, and the technical contradiction is as follows. Improving parameter: No. 3 the length of a moving object. Deteriorating parameter: No. 22 energy loss. Looking up the Altshuller contradiction matrix table, it can be found that available invention principles are 7, 2, 35, 39. Through comparison and analyses, the contradiction is solved by the invention principle No. 7, that is nesting method. The front and rear rods are replaced by hydraulic cylinders and rods. When climbing a step, the hydraulic rods connected to the auxiliary wheel and the rear wheels are automatically stretched in turn, so that the whole device climbs up the steps, and then recovers in turn after climbing the steps. It converts the hydraulic energy of the hydraulic cylinder into mechanical energy and realizes the stair-climbing action. The hydraulic rods are stretched out when working and retracted when not working, which not only reduces the lengths of the rods, but also reduces the energy loss. Figure 3 shows the application of nesting method.

Fig. 3. The schematic diagram of improved structure

(2) Because of the limitation of stair steps width, it is required that the base area of the five-wheeled stair-climbing mechanism should not be too large, otherwise it

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cannot be parked on the steps. However, the five-wheeled stair-climbing mechanism has a certain weight. If the area is reduced, the volume of the mechanism will decrease accordingly, which will lead to poor stability. So there is a technical contradiction. The technical contradiction is as follows. Improving parameter: No. 13 stability. Deteriorating parameter: No. 5 the area of a moving object. Looking up the Altshuller contradiction matrix table, it can be found that available invention principles are 11, 2, 13, 39. Through comparison and analyses, the contradiction is solved by the invention principle No. 11, that is preset defense method. After the head of the mechanism is lifted up, it is inclined and easy to turn over. The hydraulic cylinder connected to the rear wheel is controlled by the PLC circuit system. After the front wheels climb up the step, the hydraulic rod is immediately stretched out to lift the tail, so that the head and tail of the mechanism are on the same horizontal plane to prevent the mechanism from turning and ensure its stability. Figure 4 shows the application of preset defense method.

Fig. 4. The preventing process

2.4

Ideal Final Result Analysis

Ideal final result: the mechanism can automatically and smoothly go up and down the stairs, without any fluctuation, without any damage to the stairs. Small in size and light in weight. Ideal result: The mechanism can go up and down stairs as smoothly and automatically as possible without great vibration and damage to stairs. The volume is within the range that general staircases can accommodate. The obstacles to the ideal result mainly include the width of stair steps, the weight of materials, and the collision between wheels and stairs. Conditions for the absence of such obstacles: the volume of the device is not larger than the limit of the general staircases, and its movement is smooth. Resources available to create these conditions: PLC control systems, motors, hydraulic systems, wheel shafting components, hydraulic cylinders, hydraulic rods. According to the ideal result analysis, the scheme is as follows: the mechanism is designed with small volume, simple and compact structure, saving materials and reducing weight. By installing infrared sensor to accurately sense the distance between

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the mechanism and the stairs. The head of the device is raised before the collision occurs, and there is no collision with the stairs in the process of movement, so that the device can work smoothly and the stairs can not be damaged. The length of the device is 280 mm, and the lifting height of hydraulic rod is 180 mm. It can climb steps with width more than 280 mm and height less than 180 mm. It’s suitable for stairs in most places. The installation position of infrared distance sensor is shown in Fig. 5.

Fig. 5. Installation position of infrared sensor

3 Motion Simulation of the Five-Wheeled Stair-Climbing Mechanism In the UG NX simulation software, the three-dimensional solid model is established, and the motion pair, drivers, motion function and contact condition are added in the motion simulation interface. The motion process of the five-wheeled stair-climbing mechanism is simulated to verify the rationality of its structure. Before the motion simulation, the STEP function, which is an important part of controlling the stair-climbing motion, is introduced briefly. Because the stair-climbing movement is variable, there is a strict time sequence relationship between the movements. In order to control the movements accurately in time, the motion control function of UG NX - STEP function is needed [10]. The format is as follows: STEPðx; x0 ; h0 ; x1 ; h1 Þ

ð1Þ

Where x is independent variable, x0 is the initial value of the independent variable, x1 is the terminal value of the independent variable, h0 is the initial value of the function, h1 is the terminal value of the function. The meaning of STEP function is shown in formula (2). 8 h0ðtime  t0Þ > > <  2 stepðtime; t0; h0; t1; h1Þ ¼ h0 þ timet0 :ðh1  h0Þðt0  time  t1Þ t1t0 > > : h1ðtime  t1Þ

ð2Þ

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The specific meaning expressed by STEP function needs to be determined according to the type of motion pairs. If it is a rotary pair, it can represent angle, angular velocity and angular acceleration. If it is a sliding pair, it can represent displacement, velocity and acceleration. In this simulation environment, the steps width is 300 mm, the height is 100 mm. Three rotating pairs drives and two sliding pairs drives are defined in the ‘Joints’ interface, and the 3D contact friction coefficient of five wheels and the stair is 0.3. The specific motion pairs and contact conditions are shown in Fig. 6.

Fig. 6. The specific motion pairs and contact conditions

The simulation of the stair-climbing process is shown in Fig. 7. The five-wheeled stair-climbing mechanism goes straight as shown in (a). After the head of the mechanism is about to touch the vertical surface of the stairs, the hydraulic cylinder connected to the auxiliary wheel is pressurized, and the hydraulic rod is stretched out to lift the head of the mechanism as shown in (b). The whole device is driven by the motor connected to the auxiliary wheel to continue straight ahead. When the front wheels reach the level of the stairs as shown in Figure (c), the hydraulic cylinders connected to the rear wheels are pressurized, and the hydraulic rods are immediately stretching to lift the tail of the mechanism until the whole device is horizontal as shown in (d). Then the device continues to move forward powered by the motors connected to the front wheels. At this time, the auxiliary wheel starts to retract to just touch the horizontal plane of the step as shown in (e), forming a triangular structure with two front wheels to maintain the device stable. When the rear wheels are about to touch the vertical surface of the stairs, the hydraulic rods connected to the rear wheels are retracted as shown in (f). At the moment, the entire stair-climbing process is completed, and the device

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returns to the initial state. Repeat this process, and the reciprocating stair-climbing motion is achieved. The device goes downstairs following the opposite route of going upstairs. The movement feasibility and structure rationality of the five-wheeled stairclimbing mechanism can be obtained through the simulation.

Fig. 7. Simulation of the stair-climbing process

Figure 8 shows the displacement of the barycenter of the five-wheeled stairclimbing mechanism in the Y-axis direction during the stair-climbing process. From the figure, we can see that the displacement curve of the barycenter in the vertical direction basically coincides with the shape of staircases. Although there are fluctuations, there is no large displacement mutation, and overall, it is still rising steadily.

Fig. 8. The displacement curve of the barycenter in Y-axis

Figures 9 and 10 are respectively the torque curves of the motors connected to the front wheels and the auxiliary wheel in the stair-climbing process. The peak value of the motor connected to the front wheel is caused by driving the whole device forward before and after climbing the stairs, and the torque value is 0.14 Nm–2.12 Nm, with a few exceeding 2.12 Nm; The peak value of the motor connected to the auxiliary wheel is caused by the excessive load when lifting the head of the mechanism, and the torque

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value is 0.89 Nm–3.88 Nm, with a few exceeding 3.88 Nm. The two peaks do not appear at the same time, which indicates that the wheels work alternately to support the loads in the stair-climbing process. It implies the structure of the five-wheeled stairclimbing mechanism. The torque value is within the allowable range, which proves that the motion is relative stable.

Fig. 9. Torque curve of the motor connected to front wheel

Fig. 10. Torque curve of motor connected to auxiliary wheel

Figure 11 shows the acceleration of the device in X-axis during the stair-climbing process. From the figure, it can be seen that the overall acceleration tends to be stable, but there is a big sudden change when the device is about to touch the steps. The acceleration reflects the inertia force of the device and the impact of the device on the steps. Obviously, the impulse of the device in the X direction has little effect to the steps, which can completely satisfy the purpose of not damaging the steps.

Fig. 11. Acceleration curve of the device in X-axis

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4 Conclusions (1) A five-wheeled stair-climbing mechanism is designed by using TRIZ theory and relevant inventive tools. The contradictions in the design process are analyzed and the final ideal result is found. Through the ingenious structural design of the five wheels and the coordinated control of the movement time, the steady stairclimbing movement can be realized, and the mechanism can freely go up and down steps. It is convenient, safe and reliable. (2) The virtual prototype is used to simulate the stair-climbing process of the mechanism. The result shows that the moving trajectory of the centre of mass is similar to the shape of the stair steps. The five-wheeled structure designed is reasonable, which provides a reference for the practical application and in-depth study of the stair-climbing device. (3) The specific control parameters of the five-wheeled stair-climbing mechanism can be determined by the main performance indicators of the site. The best structural parameters needs further theoretical and experimental research.

References 1. Gu, Y., Wang, S., Liu, Z., et al.: Light-load stair climbing machine driven by electricity. J. Mech. Transm. 42(9), 160–163+167 (2018) 2. Si, C.: Design of a five-wheel rotating stroller. Equip. Manuf. Technol. 9, 67–68+76 (2018) 3. Wei, J., Yang, S., Wang, J., et al.: Design and simulation analysis of eight-wheeled climbing obstacles. Mech. Sci. Technol. 38(1), 1–7 (2019) 4. Liu, F., Ma, P., Cao, Z., et al.: Kinematics modeling of five-wheeled articulated lunar robot. Robot 23(6), 481–485 (2001) 5. Shi, J.: Innovative design of noise improvement bushing for rack and pinion mechanical steering gear based on TRIZ theory. Pioneer. Sci. Technol. Mon. 4, 116–118 (2015) 6. Pan, C., Wang, J., Zhao, J., et al.: Creative design of self-return conveying vehicle based on TRIZ. Forest. Mach. Woodworking Equip. 7, 40–42 (2009) 7. Liu, J., Wang, Y.: Intelligent product design based on TRIZ theory. Control Instrum. Chem. Ind. 45(1), 73–76+86 (2018) 8. Qi, Y., Yao, G.: Application research of functional analysis and tailoring based on TRIZ theory. Mech. Res. Appl. 31(5), 27–29 (2018) 9. Rosli, M.U., Ariffin, M.K.A., Sapuan, S.M., et al.: Integrated AHP-TRIZ innovation method for automotive door panel design. Int. J. Eng. Technol. 5(3), 3158–3167 (2013) 10. Guo, J., Sun, G., Zhang, Y., et al.: Dynamic simulation of punch manipulator based on UG. Exp. Technol. Manag. 36(3), 65–68 (2005)

Extensible Innovation Design of Globoidal Cam Deceleration Mechanism Based on Knowledge Shengyang Tian1, Qingshan Gong1,2(&), Guangguo Zhang1, Mingmao Hu1, and Yuemin Wu1 1

2

Hubei University of Automotive Technology, Shiyan 442002, China [email protected] Wuhan University of Science and Technology, Wuhan 430081, China

Abstract. In order to increase the innovation and design efficiency of deceleration mechanism design, a knowledge-based product extension innovative design method was proposed. Extracting the characteristic knowledge of the product, constructing the knowledge model of the product, and combining the matter-element thought of the extension theory, transforming the knowledge model of the product into the extension matter-element model. Resolving the contradictions encountered in the product design process is realized through matter-element transformation. Using the correlation function in the extension theory, the correlation degree between the product design feature parameters and the corresponding design parameters in the existing product design knowledge base was calculated, and the design feature parameters with high correlation degree are selected to improve the efficiency of product design, extension design was used to improve the innovation of products, and the knowledge solving process of product design was given. Finally, a globoidal cam deceleration mechanism was taken as an example for verification. Keywords: Knowledge model Extension design

 Deceleration mechanism  Globoidal cam 

1 Introduction Deceleration mechanism is an important aspect of mechanical transmission equipment. It increases output torque by reducing movement speed and is commonly used in lifting, transportation, metallurgy, construction, aviation, military and other fields. With the rapid development of modern industrial technology, the traditional deceleration mechanism has been impossible to meet the requirements of various fields for high precision, high efficiency and high reliability of the deceleration mechanism. Research on the globoidal cam deceleration mechanism solves this problem. Compared with the traditional deceleration mechanism, the globoidal cam deceleration mechanism has the advantages of high precision, high reliability and high transmission efficiency, which meets the requirements of modern manufacturing industry for the deceleration mechanism. Research on the globoidal cam deceleration mechanism has high practical and economic value. Liu [1] has been developing a complete set of knowledge service © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1054–1069, 2020. https://doi.org/10.1007/978-981-32-9941-2_88

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methods and technologies to more effectively achieve knowledge acquisition, retrieval and matching of products. Gao et al. [2], have constructed a knowledge base framework model based on knowledge elements, improved the representation of the knowledge base model, and improved the relevance between knowledge bases. Lv et al. [3], put forward a knowledge model of the product design process based on graphical semantic cognition, and combined with extensive theory to realize knowledge representation of product design. Liao et al. [4], established product models with different characteristics by extensive innovation methods, and obtained new product designs through extensive transformation. Yang et al. [5], have studied the extensive innovation method in product design. Wang et al. [6], put forward an extensive configuration model for complex product scheme design based on axiomatic design and extension theory. Zhang et al. [7], proposed an evaluation model for conceptual design of customized automotive products based on extensive theory. Feng et al. [8], proposed a globoidal cam reducer with multi-roller contact, gave its working principle and threedimensional modeling, and carried out dynamic analysis and finite element analysis on the globoidal cam reducer. Cao et al. [9], studied modeling of globoidal cam deceleration mechanism and optimized the mechanism. Qi [10] has carried out a detailed study on the design theory of globoidal cam reducer, and has carried out a series design for it, thus realizing the development of a CAD system for globoidal cam reducer. This paper studies the acquisition of knowledge, proposes a method of acquisition and application of product knowledge, constructs an extension matter-element model of product knowledge based on extension theory, proposes a method of constructing correlation function, and establishes a product design evaluation scheme based on extensive theory. This method is applied to the design and evaluation of the globoidal cam deceleration mechanism, completing each step of the extensive design evaluation scheme, obtaining the ideal design scheme and carrying out extensive design and implementation.

2 Extraction and Application of Product Knowledge The acquisition of product knowledge is the acquisition of feature information of each component part of the product. The most important parts of globoidal cam deceleration mechanism include globoidal cam and cylindrical roller driven plate. From the structural point of view, the globoidal cam consists of a spatial cam ridge and a rotary matrix, and the cylindrical roller drove turntable consists of a cylindrical roller, a needle roller bearing and a connecting turntable. The characteristic information of these parts is used as a knowledge module to form a knowledge model of the globoidal cam deceleration mechanism. No matter what product, its knowledge acquisition is similar to the knowledge acquisition of globoidal cam deceleration mechanism, which is mainly to extract and model the feature information of parts of the product. The acquisition of product knowledge represents the characteristic information of each part of the product. In product design, product knowledge model plays an important reference role. The most important thing about product knowledge model is that it includes past design experience and design ideas, which can provide the design basis for

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new product design, and is also helpful to solve contradictions in product design. The flow chart of product knowledge extraction and application is shown in Fig. 1.

Existing product knowledge base be put in storage

New Product Knowledge Model

Extract

Knowledge Model of Similar Products

Calculation

obtain

Correlation degree of relevant knowledge

Matching

Product design requirements

Feedback

Given

New design scheme

Fig. 1. Flow chart of product knowledge extraction and application

3 Application of Extension Theory in Product Design Extension theory is a theory for intelligent design put forward by Cai Wen, the founder of extensive science, which is used to solve the design contradictions encountered in the design process. Extension design knowledge is the knowledge to describe the contradictory problems in the design process. Through the application of extension theory, the matter-element model of the design product is established, and the characteristics of the product are corresponding to the specific values, making the design problems clear at a glance. Extension design is a new intelligent design method. In establishing an extensive model of a product, the design process is modeled, making it easier for designers to develop creativity. In the aspect of information integration expression, extension theory improves the integration level of design models and improves the product evolution ability, which can provide design reference for subsequent product design. At the same time, extension theory can also be applied to multi-objective design problems. 3.1

Matter Element

When the design variables are expressed in the form of matter elements, they are called information matter elements [11]. The extension model based on this is matter element model. Let the object to be Or be the object, cr be the feature, vr be the magnitude of Or with respect to cr , and the ordered triplet formed is: R ¼ ðOr ; cr ; vr Þ

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As the basic matter element of the design, it is called one-dimensional matter element model. Among them, Or , cr , and vr are the three elements of matter element R, cr and vr constitute the feature element Or of matter ðcr ; vr Þ. When there are n features, the n features cr1 ; cr2 ;    ; crn of the object Or and the corresponding feature values vr1 ; vr2 ;    ; vrn form an n-dimensional matter element model, and an array can be obtained R: 2 R ¼ ð O r ; cr ;

6 6 vr Þ ¼ 6 4

Or ;

3 vr1 vr2 7 7 .. 7 . 5

cr1 ; cr2 ; .. . crn ;

3.2

vrn

Establishment of Correlation Function

To establish the correlation function, the distance and bit value between design feature information elements must be calculated first, and a quantitative calculation must be made. Let x0 be any point in the real number domain and X0 ¼ ha; bi be any interval in the real number domain, and call qðx0 ; X0 Þ the distance [7] between point x0 and interval X0 ¼ ha; bi, namely:    a þ b b  a   ð1Þ qð x 0 ; X 0 Þ ¼  x 0  2  2 Set X0 ¼ ha; bi, X ¼ hc; d i, and X0  X, the location is:  Dðx; X0 ; X Þ ¼

qðx; X Þ  qðx; X0 Þ; x 62 X0 ; 1; x 2 X0 ;

Right distance, given interval X ¼ ha; bi, x0 2 q¼

a þ b

 ; b , then:

8
m. The friction along the spiral groove are respectively f, f1, f2. The exciting force are respectively F, F1, F2. According to the geometric relationship, if the cylindrical roller is keeps moving along the spiral groove without departing from the inclined surface, it needs to satisfy F = mga, F1 = m1gcosa, F2 = m2gcosa. If the cylindrical roller keeps moving uniformly along the inclined surface, it needs to satisfy f = mgsina, f1 = m1gsina, f2 = m2gsina. Be known to vector relationships: f2> f1> f, F2> F1> F. When the speed of the cylindrical rollers

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of different specifications is same, the cylindrical roller with large diameter needs more exciting force and the sliding friction is greater [8].

m2 g sin F1

m1 g sin y

F

mg sin

o m1

o f m

o m2

f1

f2

x o

mg cos

m2 g cos

m1 g cos

mg

m1g

m2g

Fig. 3. Stress analysis on the screw groove of cylindrical roller with different specifications

3 Dynamic Simulation of Feeding Mechanism 3.1

Establishment of Simulation Model of Feeding Mechanism

The four cylindrical rollers of the feeding mechanism are placed in four different positions in the trough,and the top of the spiral track is connected with the adjustable track, which is used to transport the cylindrical rollers of different diameters, and finally convey the cylindrical rollers through metal hoses. According to the revised Kutzbach-Grubler formula [9], and according to Fig. 4, the formula for the freedom of the space mechanism of the electromagnetic vibrating hopper is: 5

6

M

N

4 L K

3

H G

E O F

2

D C

1 A

B

Fig. 4. Electromagnetic vibration hopper space mechanism movement diagram

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M ¼ 6ð n  g  1Þ þ

g X

fi þ v  f

i¼1

ð16Þ

M ¼ 6ð15  17  1Þ þ 21 ¼ 3 Where: fi is the freedom degree of the ith pair of Kinematic pair. M is the degree of freedom of spatial mechanism. g is the total number of Kinematic pairs. n is the total number of all components. f is the local degree of freedom in the mechanism. According to the analysis and calculation, the degree of freedom of the electromagnetic vibration hopper of the whole feeding mechanism is 3. As shown in Fig. 4, the motion sketch of the spatial mechanism of the electromagnetic vibration hopper simulation model is given. The degree of freedom of spatial mechanism which is obtained from formula (16) is 3 and it is consistent with the degree of freedom of theoretical dynamic model established in Sect. 2.1. Therefore, the multi-rigid-body mechanism simulation model of the feeding mechanism meets the design requirements. The complex model of flexible body and rigid body mechanism is simplified to the complex motion of multi-rigidbody for simulation analysis, which improves the reliability of simulation data and verifies the reliability of simulation model [10]. 3.2

Simulation of Feeding Process of Cylindrical Rollers with Different Diameters

As shown in Fig. 5, it is the electromagnetic vibration hopper adding constraint and driving force diagram. The motion state of the whole feeding process is simulated. The motion state of the cylindrical roller is observed by bringing four cylindrical rollers to four different positions of the feeding trough. Due to the different sizes and specification of cylindrical rollers, this simulation is grouped by serializing cylindrical rollers, and finally simulates 35 times, and debugs the electromagnetic excitation force, including the vibration frequency and amplitude. To ensure that each kind of cylindrical roller can be normally fed to the adjustable track, and ultimately through the metal hose to transport the cylindrical roller. As shown in Table 1, the cylindrical rollers of different specifications have different qualities, and the vibration frequencies required in electromagnetic vibration hoppers are different. The minimum roller diameter is 10 mm, the length is 15 mm, the maximum roller diameter is 35 mm, the length is 50 mm, the vibration frequency fluctuates in the range of 44.586–143.312 times/s, the angular velocity fluctuates in the range of 280–900 rad/s, and the amplitude fluctuates in the range of 0.3–0.6 mm. According to the difference in cylindrical roller size of different diameters, the matched excitation frequencies and amplitudes are different. Therefore, according to the relationship between simulation results and parameters, the functional equation of average speed in the feeding process of cylindrical roller can be obtained: v ¼ pfAk

ð17Þ

Study on Contact Dynamics of Cylindrical Roller Feeding Mechanism 7

6

8 9

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5 4 3

10 2 1

1. base 2. plate spring 3. roller 3 4.roller 4 5. spiral groove 6. adjustable track 7. triangular chuck 8. roller 1 9. roller 2 10. hose Fig. 5. Electromagnetic vibration hopper to add constraints and driving force diagram Table 1. The simulation results of cylindrical roller technical parameters Parameter

Serial number 1 2 Diameter  length (mm) 10  15 35  50 Quality (kg) 0.09196 0.3755 Amplitude (mm) 0.6 0.3 Angular velocity (rad/s) 280 900 Vibration frequency (times/s) 44.586 143.312

Where f is the exciting force frequency HZ, A is the amplitude, K is the velocity loss coefficient, and is usually take k = 0.6 * 0.82. Taking a cylindrical roller with a diameter of 32 mm, a length of 50 mm and a mass of 0.32 kg as an example. Analyzing the motion state of cylindrical rollers on spiral grooves with different amplitudes and different vibration frequencies. In the Fig. 6a, the amplitude is 0.5 mm and the angular velocity is 500 rad/s. The calculated vibration frequency is 79.618 Hz. At 2.44 s, the cylindrical roller begins to enter the spiral groove at the bottom end of the trough. At 2.44–4.3 s, the speed of the cylindrical roller is significantly decelerated. At 4.3–5 s, the cylindrical roller tends to be stationary on the spiral groove and cannot be feed normally. In Fig. 6b, the amplitude is 0.3 mm, the angular velocity is 900 rad/s, and the calculated frequency is 143.312 times/s. At 1.83 s, the cylindrical roller begins to enter the spiral groove at the bottom end of the trough. Due to the large vibration frequency, the roller is greatly affected by contact, friction and collision, and the inertial force is large, and the speed changes are also large. At 1.83–3.3 s, the cylindrical roller completes the feeding process of spiral groove. Therefore, if the normal feeding of cylindrical roller is achieved, the vibration frequency of hopper should be adjusted and the amplitude should be reduced at the same time.

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speed(mm/s)

1500.0

amplitude0.5 mm angular velocity500 rad/s

1000.0 500.0

0.0 0.0

1.0

2.0

Time/s

3.0

4.0

5.0

a.Cylindrical roller spiral groove can not feed simulation curve

Speed(mm/s)

1500.0 1000.0

amplitude0.3 mm angular velocity900 rad/s

500.0 0.0 0.0

0.5

1.0

1.5 2.0 Time/s

2.5

3.0

3.5

b.Simulation Curve of Cylindrical Roller Feeding Normally in Spiral Groove Fig. 6. Cylindrical roller in the spiral groove on the two state of motion curve

Adjusting the matching relationship between the amplitude, vibration frequency and angular velocity of the electromagnetic vibrating hopper, the data shown in Table 2 is the result of the simulation of 35 sets of data. Table 2. Electromagnetic vibration hopper series of dynamic parameters matching Experiment number 1# 2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12# 13# 14# 15#

Angular velocity (rad/s) 280 302 313 336 349 358 369 377 389 412 439 471 495 518 559

Vibration frequency (times/s) 44.586 48.089 49.841 53.503 55.573 57.006 58.758 60.032 61.943 65.605 69.904 75.000 78.722 82.484 89.013

Amplitude (mm) 0.6 0.57 0.55 0.53 0.51 0.495 0.49 0.485 0.48 0.467 0.465 0.46 0.45 0.45 0.43 (continued)

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Table 2. (continued) Experiment number 16# 17# 18# 19# 20# 21# 22# 23# 24# 25# 26# 27# 28# 29# 30# 31# 32# 33# 34# 35#

Angular velocity (rad/s) 582 613 642 670 682 687 702 728 759 775 795 801 815 819 828 830 845 850 870 900

Vibration frequency (times/s) 92.675 97.611 102.229 106.688 108.599 109.395 111.783 115.924 120.860 123.408 126.592 127.548 129.777 130.414 131.847 132.166 134.554 135.350 138.535 143.312

Amplitude (mm) 0.42 0.40 0.39 0.39 0.385 0.385 0.38 0.38 0.38 0.37 0.37 0.37 0.37 0.37 0.36 0.36 0.34 0.34 0.32 0.30

4 Conclusions (1) This paper analyzed the feeding mechanism of the cylindrical roller dimensional sorting system. According to the working principle of electromagnetic vibration hopper, a dynamic model is established to determine the dynamic parameters which affected the feeding process. (2) In this paper, the dynamic simulation of the feeding process of the cylindrical roller sorting system is carried out. The dynamic parameters of the dimensional sorting system are determined, and the specific dynamic parameters of the feeding mechanism are determined. The correctness of the model is verified by calculating the degree of freedom in the spatial mechanism.

References 1. Zhang, Y.: Modeling of Multi-body Dynamic Contact and Collision. Huazhong University of Science and Technology, Wuhan (2007) 2. Zhang, H., Zhuang, F., Qu, Z., et al.: Research on the fast analysis method of non-smooth dynamics in the guiding stage of space separation device. J. Peking Univ. (Nat. Sci. Ed.) 04, 717–721 (2016)

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3. Xie, Y.: Systematic theory research and modeling of tribological systems. J. Tribol. 01, 1–8 (2013) 4. Rooth, E.K.: Dynamics of a System of Rigid Bodies. Dover Publications Inc., New York (1960) 5. Keller, J.B.: Impact with friction. J. Appl. Mech. 53, 1–4 (1986) 6. Wosle, M., Pfeiffer, F.: Dynamics of multibody systems containing dependent unilateral constraints with friction. J. Vib. Control 2(1), 161–192 (1996) 7. Konieczny, Ł., Burdzik, R., Folęga, P.: Multibody system software used for research of car suspension system dynamics. Adv. Mater. Res. 3483(1036), 794–799 (2014) 8. Wang, J.: Dynamic Characteristics of Parallel Mechanism Based on Multi-flexible Body Dynamics. Shenyang Architectural University, Shenyang (2015) 9. Yang, D.: Dynamic Simulation of Multi-joint Robots Based on RecurDyn. Shanghai Normal University, Shanghai (2016) 10. He, B., Wang, S.: Study on the dynamic model and simulation of a flexible mechanical arm considering its random parameters. J. Mech. Sci. Technol. 19(1), 265–267 (2005)

Trajectory Planning for Winding Process of Small-Sized Motor Stator Winding Robot Yanling Zhao1,2, Linqiang Wang2, Jingzhong Xiang2(&), and Yudong Bao2 1

State Key Laboratory of Robotics and Systems, Harbin, China [email protected] 2 Harbin University of Science and Technology, Harbin, China [email protected], [email protected], [email protected]

Abstract. Aiming at the phenomena of overlap, bulge and uneven arrangement in the winding process and ensuring the smooth motion of the winding robot without impact in the working process, the trajectory planning of the winding process of the winding robot is studied. Firstly, the winding principle of the winding process is analyzed, the winding model of the end is established, and the trajectory equation of the end winding is established according to the matching relationship between the rotary motion and the feed motion in the winding process. Secondly, according to the principle of trajectory smoothness, the quintic polynomial programming algorithm in joint space is selected for trajectory planning. Finally, the software simulation is used to obtain the end winding trajectories of three different winding angles, as well as the smooth curves of joint velocity and acceleration with respect to time. The results show that the joint and end coordinate curves are basically continuous and smooth without mutation, which proves that the winding robot can carry the line according to the planned trajectory, and the movement is stable, basically no impact and vibration. This research lays a foundation for realizing high efficiency, high precision and high reliability of small stator winding. Keywords: Winding robot End winding model

 Trajectory equation  Planning algorithm 

1 Introduction The winding of the motor is an important component of energy conversion, and the performance of the motor is closely related to the quality of its winding. At present, there are problems such as low winding efficiency and low winding quality, and low winding precision. The correct planning of the winding path is an important guarantee for the successful winding of the coil. In terms of trajectory planning, Niku [1] studied various methods of robot trajectory planning. One of them is the cubic polynomial trajectory planning method. Using this method to find the trajectory of the manipulator, two points, namely the initial point and the ending point, are determined. However, this

© Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1093–1108, 2020. https://doi.org/10.1007/978-981-32-9941-2_91

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method has limitations. The scope of its application is limited to the trajectory planning between two points. The stability of the manipulator during the movement process is easily affected by the sudden change of the initial point acceleration. Bazaz [2] et al. used cubic spline interpolation method in joint space for trajectory planning. This method needs to solve the multivariate matrix equation when applied, which involves a large amount of calculation and also causes a rectangular mutation of the acceleration curve. Chettibi and Constantinescu et al. conducted separate studies on the principle of minimum consumption [3] and shortest time [4]. To make the acceleration curve smooth, Wang [5] et al. used the cubic triangular Bezier line to plan the motion trajectory of the manipulator. It is proved that an ideal acceleration smoothing curve can be obtained. Later, Gasparettol [6] and others studied the characteristics of the objective function and used it obtained a smooth curve. Xu, Yang [7] and others studied the geodesic winding trajectory of a six-degree-of-freedom compound elbow industrial robot. The factors affecting the stability of the robot winding bending motion are analyzed. The development of the domestic motor coil automatic winding machine started late. Ning, Pan [8] and others have planned the joint space trajectory based on kinematics and dynamics, used quintic interpolation polynomials to fit the motion trajectory in the joint space, and applied the dynamic model to the trajectory planning. Final, a continuously steerable displacement, velocity, acceleration, and jerk curve are generated. Gao [9] used the bionics principle to plan the trajectory of a quadruped robot’s jumping gait with one leg, and deduced the driving functions of the joints of the hydraulic cylinder. In summary, researchers at home and abroad have done a lot of research on robot trajectory planning, but it has not been applied in the study of winding process of winding robot [10, 11]. To ensure that the winding robot works according to the actual task requirements, it must be trajectory planning. The trajectory planning discussed in this paper is divided into two parts: one is the trajectory planning of the winding in the winding process, and the other is the trajectory planning of the robot arm during the wire feeding process.

2 End Winding Process Trajectory Planning 2.1

Analysis of Winding Principle of Winding Process

In the process of winding the enameled wire at the end of the robot, the enameled wire is wound on the rectangular mold in the shape of a spiral coil. To ensure uniform and non-overlapping parallel arrangement of the winding, a close cooperation between the end rotary motion and the up and down feed motion is required. That is, when the endeffector bypasses one turn, the distance it moves upward must not be less than the length of one wire diameter. In this way, not only can the angle between the enameled wire coils wound at the end of the robot be consistent, the appearance is maintained,

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but the coil size irregularity caused by the improper length of the payout line can be avoided, and the theoretical basis for the size of the payout line is provided. The defects in the winding process are shown in Fig. 1.

a)

b)

c)

Fig. 1. Winding defect at the end

The defect shown in Fig. 1(a) is that the end-feeding speed of the end-effector is too fast to form an uneven gap between the coil and the coil, causing the coil to be disordered. The defect shown in Fig. 1(b) is that when the end-effector makes an upward feed motion, it deviates from the original set path, causing the turns to overlap with the turns. The defect shown in Fig. 1(c) is that the up and down feed motion of the end-effector does not cooperate with the swivel motion during the winding process, resulting in a convex and redundant phenomenon of the wound coil. For the problems that occur during the winding process, the winding principle of the winding robot is analyzed. In order to correctly plan the end winding trajectory later. In the initial position, the end-effector of the winding robot is aligned with the enameled wire of the pay-off mechanism, and the enameled wire is wound by the guide pin to the corresponding square end-effector in a certain regularity. Then the various joints of the robot coordinate. And the wrapped enameled wire is sent to the stator frame, and the enameled wire is pushed side by side to the stator wire through the up and down movement of the push-wire mechanism to complete a winding task. At the end of the winding robot, the enameled wire is connected to the end effector via a guide pin, on the one hand, the end-effector performs a circumferential rotational motion, and on the other hand, an upward feed motion. The two are combined to ensure that the enameled wire does not overlap or align when it is entangled. This requires setting the rotational speed and the upward feed speed of the robot. The winding process of the end actuator is shown in Fig. 2.

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x 3 2

4

1

6

7

8

5

y 9

1.Machine hand 2. Stop dog 3. Push plate 4. Leads 5. Enameled wire 6. Wire clamping device 7. Connecting rod 8.Column 9. Workbench

Fig. 2. Schematic diagram of the end actuator winding process

2.2

End Winding Model Establishment

In order to complete the above principle, it is necessary to rationally plan the winding of the end wires. The established end winding trajectory model is shown in Fig. 3.

L1 L2

d

L0

θ

a

Fig. 3. Schematic diagram of the winding trajectory at the end

As can be seen from Fig. 3. L0 is the vertical distance from the starting position of the first lap to the end position of the last lap. L1 is the position between the centers of

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adjacent two turns of the coil. L2 is the gap between two adjacent turns of the coil. d is the diameter of the enameled wire. h is the spiral angle of the winding. a and b are the two side lengths of the rectangular end winding mold, respectively. Because 10 turns and one side length are to be wound in one winding process, the relationship between the parameters is obtained without considering the bending radius: L0 ¼ 10L2 þ 11d þ a tan h

ð1Þ

L1 ¼ L2 þ d

ð2Þ

When L2 is zero, that is, there is no gap between a coil and an adjacent one when winding, then the value of L0 will change, namely: L0 ¼ 11d þ a tan h

ð3Þ

The distance the actuator has traveled through during the entire process is:  s¼

 11 20b 10 þ aþ cos h cos h

ð4Þ

In the winding process, because the two movements are required to mutual cooperate, the feed speed is v1, and the movement speed of the guide needle relative to the actuator is v2, then there is the following relationship: L0 ¼ v 1 t

ð5Þ

s ¼ v2 t

ð6Þ

Therefore the relationship between the speeds of the two can be obtained as follows: v1 ¼ v2 10 þ

L0  11 20b cos h a þ cos h

ð7Þ

And according to the geometric relationship, we can know: L2 ¼ a tan h 2

ð8Þ

So formula (7) can be written as: v1 21a tan h þ 11d  ¼ 11 20b v2 10 þ cos h a þ cos h

ð9Þ

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It can be known from formulas (1) and (8): h ¼ arctan

L0  11d 21a

ð10Þ

The mold selected in this paper is a = 10 mm, b = 12 mm, and H = 40 mm. From this, it can be known that the range of h is [2.8624°, 9.3303°]. According to the above analysis, in the process of winding the rectangular end actuator, as long as the value of L0 is set, the relationship between v1 and v2 can be obtained correspondingly. The range of L0 can be determined by the wire diameter of the enameled wire and the height of the end-effector. That is, 11d + atanh  L0  H, where H is the height of the end effector. 2.3

Winding Trajectory Equation Establishment

In the winding process, the end-effector movement needs to follow a certain rule to ensure a reasonable trajectory, and it is more convenient to wrap the enameled wire around the stator in the subsequent process. According to the previous analysis, the position of the end of the enameled wire, that is, the position of the guide pin, is a combination of the rotary motion and the feed motion. So the trajectory is a square spiral, as shown in Fig. 4. According to the spiral line that has been wound out, a corresponding coordinate system is established at the center of the bottom surface, and then the size of each side length is set according to the size of the mold, thereby further solving the winding trajectory equation.

z

x

y

Fig. 4. Spiral winding trajectory under compound motion

It can be seen from Fig. 4 that the trajectory is divided into four groups of trajectory line segments according to the end square mold, and the equations are respectively established for the four groups of trajectory line segments. Since the two side lengths of

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the winding mold are a = 10 mm and b = 12 mm, the coordinates of the partial inflection point can be listed as: (6, −5, 44 tanh);(6, 5, 54 tanh);(−6, 5, 66 tanh);(−6, −5, 76 tanh); Solve four sets of straight line equations separately. Let the direction vector of the four sets of trajectory lines be (m, n, p), then the parametric equation of the line is: 8 > < x ¼ x0 þ mt y ¼ y0 þ nt > : z ¼ z0 þ pt

ð11Þ

According to the above coordinate values, the direction vectors of the four sets of trajectory segments can be written as (0, 10, 10 tan h), (−12, 0, 12 tan h), (0, −10, 10 tan h), (12, 0, 12 tan h). According to equation (11) and direction vector, the parameter equations of four sets of trajectory lines can be listed. The first set of trajectory parameter equations: 8 >

: z ¼ 44k tan h þ 10 tan ht The second set of trajectory parameter equations: 8 > < x ¼ 6  12t y¼5 > : z ¼ ð10 þ 44kÞ tan h þ 12 tan ht

ð13Þ

The third set of trajectory parameter equations: 8 > < x ¼ 6 y ¼ 5  10t > : z ¼ ð22 þ 44kÞ tan h þ 10 tan ht The fourth set of trajectory parameter equations: 8 > < x ¼ 6 þ 12t y ¼ 5 > : z ¼ ð32 þ 44kÞ tan h þ 12 tan ht

ð14Þ

ð15Þ

Where k = 0, 1, 2, 3… 10, t is a parameter constant. From Eqs. (12), (13), (14) and (15), it can be seen that the degree of density of the end winding trajectory is determined by the h angle, and h is related to v1 and v2. Therefore, the trajectory of different degrees of density can be obtained by the cooperation of the two speeds.

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3 Joint Space Trajectory Planning During Wire Feeding To ensure that the winding robot successfully completes the wire feeding task, it must plan the joint space trajectory for it. During the space motion of the robot, the points on the trajectory are generally represented by the position in the space. Accordingly, some points on the trajectory will be represented by the angle value of the robot connecting rod before the trajectory planning in the joint space, and then fitted. The fitted function curve should be smooth and pass through the pre-set points as far as possible, and finally complete the required tasks. Because it is a real-time planning between the connecting rods, it is necessary to ensure that each connecting rod reaches the target point in the same time. Accordingly, the time for each connecting rod to complete one variation is the same, that is, each connecting rod must move at the same time. In this way, the robot can fulfill the expected requirements in terms of speed and acceleration, and ensure the completion of the winding task. When trajectory planning is performed on the robot in the joint space, the polynomial interpolation method is used to interpolate the points, and finally the curve of the angular velocity and the acceleration of each joint during the time change are obtained. When using the interpolation method to trajectory planning the robot in the joint space, there are commonly used cubic polynomial interpolation method, quintic polynomial interpolation method and parabolic linear interpolation method. When trajectory planning is performed with different functions, the resulting trajectory curves are different. When using cubic polynomial trajectory planning, the overall calculation process is relatively simple, but the resulting velocity and acceleration function curves may have problems such as sudden changes, sharp corners, and unsmoothness. The above problem can be solved by using a quintic polynomial, and the resulting trajectory is a smooth trajectory. The relational expression of the quintic polynomial interpolation can be written as: hðtÞ ¼ a0 þ a1 t þ a2 t2 þ a3 t3 þ a4 t4 þ a5 t5

ð16Þ

Similarly, the speed and acceleration functions when using the quintic polynomial interpolation are: (

_ ¼ a1 þ 2a2 t þ 3a3 t2 þ 4a4 t3 þ 5a5 t4 hðtÞ € ¼ 2a2 þ 6a3 t þ 12a4 t2 þ 20a5 t3 hðtÞ

ð17Þ

According to the constraint conditions of the starting point and the ending point, the following relational expression can be listed: 8 h0 ¼ a0 > > > > > hf ¼ a0 þ a1 tf þ a2 tf2 þ a3 tf3 þ a4 tf4 þ a5 tf5 > > > > < h_ 0 ¼ a1 > h_ f ¼ a1 þ 2a2 tf þ 3a3 tf2 þ 4a4 tf3 þ 5a5 t4 > > > > > > h€0 ¼ 2a2 > > :€ hf ¼ 2a2 þ 6a3 tf þ 12a4 tf2 þ 20a5 tf3

ð18Þ

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Similarly,solving the Eqs. (16), (17) and (18) simultaneously can obtain the coefficients of the function: 8 a0 ¼ h0 > > > > > a1 ¼ h_ 0 > > > > € > > a2 ¼ h20 > > > < 20hf 20h0 ð80h_ f þ 12h_ 0 Þtf ð3€h0 2€hf Þtf2 a3 ¼ ð19Þ 2tf3 > > > > 30h0 30hf ð14h_ f þ 16h_ 0 Þtf ð3€h0 2€hf Þtf2 > > a3 ¼ > > 2tf4 > > > > > 12h 12h0 ð6h_ f þ 6h_ 0 Þtf ð€h0 €hf Þtf2 > : a3 ¼ f 2t5 f

h0 and hf are respectively the joint angles of the starting and ending points of the winding robot in relational expression. Since the function of h about the time t in the quintic polynomial is second order continuous derivable, the velocity and acceleration at the junction of the two segments can be continuously smoothed by the quintic polynomial interpolation.

4 Simulation Analysis of Trajectory Planning of Winding Robot The content of this chapter is the simulation of end winding and wire feeding process of winding robot. The simulation logic diagram in this paper is shown in the Fig. 5.

Fig. 5. Logic diagram of trajectory planning simulation

4.1

Simulation Analysis of End Winding Trajectory

The trajectory curve of the end winding can be drawn in MATLAB. Figure 6 shows the end winding trajectory at different winding angles,which are 3°, 6°, and 9°, respectively.

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a) Winding angle is 3º

b) Winding angle is 6º

c) Winding angle is 9º Fig. 6. Winding curve simulation curve at different angles

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It can be seen from Fig. 6(a), (b) and (c) that the end winding trajectory is a square spiral. At different winding angles, the density of the trajectory is different, that is, the speed of the slewing motion and the feeding motion are different, and the range of winding on the square mold is different. Therefore only let the two speeds Cooperate reasonably to get a uniform and precise trajectory. 4.2

Simulation Analysis of Wire Feeding Trajectory

The trajectory planning of the winding robot is carried out in the Robotics Toolbox in MATLAB. It is a toolbox developed by Peter Corke, an Australian professor of robotic vision, specializing in robotic modeling and simulation. The Robot Toolbox contains various functions and codes for trajectory planning, which correspond to different functions. It includes the analysis and planning of robot model, kinematics and dynamics. It can analyze various parameters of the robot and achieve the purpose of simulation. It plays an important role in trajectory planning and Simulation of robots. To trajectory planning a winding robot, we must first create a 3D model of the robot in the toolbox. The first is to model each link and joint. Modeling robots in MATLAB is accomplished by calling the Link function and the Serilink function. When the single link is modeled, the Link function is called. When the connected link model needs to be established, the Serilink function is called. And finally the robot’s model can be fully rendered. The call format of the Link function is: L = LINK([alpha A theta D sigma of set], CONVENTION) Each parameter in the function represents different meanings. Among them, ‘alpha’ refers to torsion angle, ‘A’ refers to the length of connecting rod, theta refers to the joint angle, ‘D’ refers to the offset of connecting rod, ‘sigma’ refers to the type of joint: rotating joint is represented by 0, moving joint is represented by non-zero, all of the robots used in this paper are rotating joints. CONVENTION can take two values: standard and modified. Standard represents the standard D-H parameter. It indicates that the length of connecting rod A is the distance between the common perpendicular line of connecting rod i and i + 1, and modified means using the D-H parameter as shown in Table 1. The length of connecting rod A is the common perpendicular line between connecting rod i -1 and i. Table 1. winding robot connecting rod D-H parameter i 1 2 3 4 5 6

关节变量 h1 h2 h3 h4 h5 h6

ai 0 a2 a3 0 0 0

ɑi −90° 0° 90° −90° 90° 0°

di 0 d2 0 d4 0 d6

hi −160°–160° −225°–45° −45°–225° −110°–170° −100°–100° −266°–266°

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According to the parameters listed in the table above, a2 = 86.36 mm, a3 = 4.064 mm, d2 = 29.818 mm, d4 = 86.614 mm and d6 = 11.25 mm, the model of winding robot can be built in Robotics Toolbox as shown in the Fig. 7.

Fig. 7. winding robot model diagram

The joint angle and coordinate values shown on the left side of Fig. 6 are adjusted by the teach function in the robot toolbox. X,Y,Z and R, P and Y are the positions and postures of the relative base coordinates of the end effector. q1, q2, q3, q4 and q5 represent the joint angles of each joint of the winding robot. According to the structure of the winding robot and the wire-feeding task to be achieved, we specify five postures to be achieved as shown in Fig. 8.

Fig. 8. Schematic diagram of each line of the wire feeding process

Through the Robotics Toolbox in MATLAB, the pose effects that the winding robot needs to achieve during the wire feeding process are obtained, as shown in Fig. 9.

Trajectory Planning for Winding Process

Fig. 9. Simulation attitude diagram of the wire feeding process

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This paper uses the quintic polynomial trajectory planning. We set the starting point position as(0.030,−0.082,−0.098,180,0,−90),(0.184,0.030,−0.004,0,90,0). meanwhile, set the exercise time to 5.5 s according to the task requirements. The angular velocity of each joint and the angular acceleration curve of each joint are shown in Fig. 9.

Fig. 10. Curve of velocity and acceleration of joint variables with time

It can be seen from Fig. 10 that the velocity curve of each joint variable has not been abrupt, and the Junction between the attitudes has also been basically smooth. Similarly, it can be seen from the acceleration curve of the joint variable that the acceleration curve of the joint one is basically stable. There were spikes between joints 2 and 3 in 2 – 4 s, but there was no mutation. Overall, the first three joints are the main moving joints throughout the workspace, and the last three joints are on the end effector, so the change in the joint space is 0 s. At the same time as planning each joint, the trajectory curve at the end should also be considered, and the smoothness of the end trajectory can also bears on the smoothness of the entire mechanism. By matching the joint angle of the joint space to the Cartesian space, we can get the velocity and acceleration curve of the end coordinate system with time, as shown in Fig. 11.

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Fig. 11. Three coordinate speeds, acceleration versus time curve of the end effector

As can be seen from Fig. 11, the end effector has a relatively smooth curve of speed and acceleration with time in the process of wire feeding according to a given joint angle, without sudden changes and fluctuations, and the overall operation of the end is stable.

5 Conclusions The trajectory planning is performed on the end winding process and the wire feeding process respectively. The end winding model is established, and the relationship between the end rotation and the feed motion is obtained, and the trajectory equation of the end winding is derived. The relationship between the rotary motion and the feed motion is obtained. According to the trajectories of the two, the corresponding winding equations are established and simulated at different angles. During the wire feeding process, five attitudes on the path are determined and the trajectory planning is performed using the quantic polynomial trajectory planning of the joint space. The speed and acceleration of each joint of the winding robot were simulated using the Robotics Toolbox of MATLAB software. In the trajectory planning of the joint space of the winding robot, the trajectory planning of the whole feeding process is carried out by using the quintic polynomial trajectory planning algorithm. The speed and acceleration curve of each joint and end coordinate may have some spikes in some places, but the whole process is smooth and without sudden change, which proves that the winding robot can follow the planned trajectory and move smoothly without impact and vibration.

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References 1. Niku, S.B.: Introduction to Robotics: Analysis, Systems, Applications. Prentice Hall, New Jersey (2001) 2. Nadir, B., Mohammed, O., Abdessalam, K.: A new method for time-jerk optimal trajectory planning under kino-dynamic constraint of robot manipulators in pick and place operations. IAES Int. J. Rob. Autom. (IJRA) 3(3), 184–190 (2014) 3. Chettibi, T., Lehtihet, H.E., Haddad, M., et al.: Minimum cost trajectory planning for industrial robots. Eur. J. Mech.-A/Solids 23(4), 703–715 (2004) 4. Constantinescu, D.: Smooth and time-optimal trajectory planning for industrial manipulators along specified paths. J. Rob. Syst. 17(5), 223–249 (2000) 5. Wang, Y., Xu, W., Sun, N.: Manipulator trajectory planning based on the cubic triangular bezier spline. In: 2010 8th World Congress on Intelligent Control and Automation (WCICA), pp. 6485–6488. IEEE (2010) 6. Gasparetto, A., Zanotto, V.: A new method for smooth trajectory planning of robot manipulators. Mech. Mach. Theory 42(4), 455–471 (2007) 7. Xu, J., Yang, H, Liu, M, Tian, J., Liu, B.: Research on winding trajectory planning for elbow pipe based on industrial robot. Int. J. Adv. Manuf., 1–9 (2017) 8. Ning, X., Pan, Y., Yang, Y., Huang, W.: Joint space trajectory planning based on kinematics and dynamics. Comput. Simul. 32(2), 409–413 (2015) 9. Gao, Y.: Hydraulic Four-Legged Robot Single Leg Jumping Gait Planning. Harbin University of Science and Technology, Harbin (2017) 10. Herrmann, P., Gerngors, M., Endisch, C.: NURBS based trajectory generation for an industrial five axis needle winding robot. In: International Conference on Control, Automation and Robotics (ICCAR). IEEE (2018) 11. Qian, Q.: Research on automatic stacking system of stator core of turbo generator based on industrial robot. Electric Motor Technology (2014)

Experimental Study of a Solid-Liquid Mixing and Conveying Pump with Variable Flow and Proportion Wei Liu1, Qian Tang1(&), Wenzhe Cai2, Pinghua Liang1, Zongmin Liu1, and Xiaojie Fan1 1

State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China [email protected] 2 Beijing Institute of Power Machinery, Beijing 100074, China

Abstract. To achieve the mixing and conveying of solids and liquids and meet the requirements of variable flow, proportion, and uniform mixing, a novel twophase flow pump was designed, built, and investigated in this research. The spiral conveyor was used to convey solid powder and transfer volume was controlled using the rotation speed of the spiral conveyor. The twin screw pump conveyed liquid and mixture, and the transfer volume of the liquid was controlled using rotation speed and the outlet pressure of the twin screw pump. The gear transmission chamber drove the mixing impeller to achieve uniform mixing of solid and liquid so the different transfer volumes of powder and liquid could achieve variable solid-liquid proportions. The experiment demonstrated the transfer volume and rotation speed curve of the powder with the motor speed of the spiral conveyor ranging from 0 to 100 r/min, and the rotation speed and outlet pressure curve of liquid when the liquid flow rate was 4 L/min, 6 L/min, 8 L/min, and 10 L/min, respectively. The performance curve was used to guide the mixing test. Finally, the mixing proportion was set to 5% and 10%, and the outlet pressure was set to 100 kPa and 400 kPa. Then four sets of mixing tests were conducted, and the results were evaluated. The two-phase flow pump designed in this paper achieved mixing and conveying of solid-liquid two-phase materials and meets the requirements of variable flow, proportion, and uniform mixing. Keywords: Variable flow  Variable proportion  Solid-liquid two-phase flow pump  Experimental study

1 Introduction In recent years, the requirements for solid-liquid mixing and conveying equipment in the market have become greater, especially in industries such as chemical, pharmaceutical, food, and aerospace. Taking the aerospace industry as an example, a large Supported by the National Natural Science Foundation of China (Grant No. 51575069). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1109–1123, 2020. https://doi.org/10.1007/978-981-32-9941-2_92

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number of solid-liquid hybrid propulsion flight projects [1] have demonstrated the advantages of safety, environmental friendliness, low cost, adjustable thrust, and simple structures. These flight projects improved the technical maturity of solid-liquid hybrid propulsion. The solid-liquid hybrid rocket engine combined the advantages of solid engines and liquid engines to store solid fuel and liquid oxidant separately in their respective propulsion systems [2, 3]. The specific impulse of the HTPB-LOX solidliquid hybrid rocket was comparable to that of the RP-1-LOX liquid rocket, which was significantly higher than the solid rocket. The theoretical specific impulse could reach 340 s, but the density was 17% higher than kerosene [4]. Therefore, solid-liquid mixing and conveying will play an important role in the future. The twin-screw pump is a type of positive displacement pump. The screw rotor does not have the unilateral wear but does have the listed advantages of low leakage, high pump efficiency, multiphase transportation suitability, auxiliary stirring function, stable delivery, small hydraulic pulsation, and strong pressurization performance. Xu and Qu of Xi’an Jiaotong University analyzed the multi-mixing technology of oil and gas in the twin-screw pump and the pressurization performance of the downhole twinscrew pump [5–8]. Dolan et al. discussed the limitations of traditional multiphase transmission systems. To obtain good gas-liquid two-phase mixing and transmission performance, the twin-screw multiphase pump system was designed and developed, and passed the experimental test. The results showed the system could transport the two-phase flow with different gas content (GVF) [9]. In 2004, Prang and Cooper proposed a calculation model to predict the performance of a two-phase pump, and compared it with experimental data under different fluid viscosities and gas content (0– 100%) [10]. Mewes established a one-dimensional model for calculating the performance of the multiphase pump based on cavity mass and energy conservation equations, and carried out experimental comparisons to verify the feasibility of the method [11]. Chan and Patil of Texas A&M University in the United States conducted numerical simulations and experimental studies on the steady-state and transient characteristics of the two-phase screw pump under different working conditions and analyzed the compression process of gas in multiphase mixing. The effects of the viscosity of the sealing fluid and different gas content on the performance of the screw pump were discussed and provided a reference for multiphase flow research of the screw pump [12, 13]. Rabiger established the performance and working process calculation model of the multiphase screw pump, and the thermodynamic model of the multiphase pump chamber. The performance of the multiphase screw pump for gasliquid mixing and transportation, especially in the case of high gas content (90%–99%), was numerically simulated and experimentally studied, and the leakage flow of radial clearance was visualized [14, 15]. Ruschel studied the volumetric efficiency and multiphase mixing characteristics of the screw pump, built a test bench for performance observation, examined the flow field in the pump chamber of the three-screw pump using transparent pump shell material and a high-speed camera, compared the flow situation of the transparent medium with different viscosities, analyzed the flow situation and the cavitation phenomenon in the clearance, and discussed how to reduce rotor wear and improve multiphase mixing efficiency [16, 17]. In the field of multiphase conveying of the screw pump, most scholars focus on gas-liquid transportation,

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which is passive transportation. There is little research and application in solid-liquid two-phase active mixing and conveying. In addition to the study of solid-liquid active mixing, the active addition of solid particles must be considered. The spiral conveyor is a common conveying machine mainly used to convey powder and granular materials and has a simple structure, small cross-section, good sealing, reliable work, low manufacturing cost, and other characteristics. Considering the layout and filling efficiency of the spiral conveyor shaft, the working efficiency of the spiral conveyor was calculated theoretically, which could provide a reference for the selection of the motor [18]. The design and calculation formula of key components such as spiral shaft, the spiral blade, and intermediate bearing of the LS-type spiral conveyor were given [19]. The DEM model of viscous particle flow in the spiral conveyor was established and the experimental study was carried out. A continuous charging of solid particles into the bin or hopper was adopted, and the effect of the cohesive force on the performance of the screw feeder and the underlying mechanism were investigated [20]. To improve the transportation performance and increase the transmission efficiency of a coal auger, the spiral conveyor device’s parameters were optimized by taking the spiral conveyor device’s diameter, pitch, helix angle, strength of center axis, and speed of non-clogging as design variables, choosing maximum productivity and minimum energy consumption of a spiral conveyor device as the optimal objective, and using the GAAA algorithm [21]. The above literature on the spiral conveyor was mainly concerned with the design of structural parameters, as well as the impact of the parameters on performance and efficiency. There is little research on how to use the spiral conveyor to realize variable transmission. Multiphase conveying of the screw pump is mainly used in gas-liquid mixing and conveying, and it is passive conveying. There is no case of actively adding solid-liquid and conveying it. In view of this, and supported by the National Natural Science Foundation of China, the State Key Laboratory of Mechanical Transmission at Chongqing University has carried out research on the solid-liquid two-phase pump. Consider as there is no precedent for a solid-liquid two-phase pump in China, and it is rare in the world, we plan to begin with testing, combining theory with practice, and guiding practice with theory.

2 Model Design 2.1

Overall Design Concept

Even while achieving solid-liquid mixing and variable transport as the solid-liquid proportion changes, the pump must still have high efficiency and supercharging capacity. The following problems must be addressed: first, achieve a variable volume of solid powder; second, achieve a variable volume of liquid; and third, achieve uniform mixing. Because the measurement method of two-phase mixing is not mature, the method of measuring solid and liquid separately can be adopted to avoid the problem. The stability of solid and liquid transportation is important to the homogeneity of solidliquid mixing, and measures should be taken to ensure it occurs. In addition, a highspeed data acquisition and processing system should be used due to the dynamic nature

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of the test signal. To test the effect of friction speed on the boosting capacity of the twophase pump, the speed of the power conveying shaft should be adjustable. After comparing all types of conveying equipment synthetically, the spiral conveyor is selected to convey solid materials and achieve variable force conveying. At the same time, only the positive displacement pump achieved accurate variable delivery. The screw pump has continuous transmission, small pulsation, and auxiliary mixing functionality, making it the best choice for mixing transportation. The mixing method uses a propeller-type impeller with good mixing effect (not described in detail here). The overall system composition is shown in the following Fig. 1: Drive system 1

Drive system 2

Gear transmission system

Powder conveying system

Mixing Liquid system conveying system

Functions of mixing and transportation with variable flow and variable proportion Fig. 1. Composition system

2.2

Solid Conveying System

The design considerations for the spiral conveyor are: first, the basic conditions of powder conveying, the quantity and properties of powder are determined; second, according to the conditions, the relevant parameters are defined and key parameters such as screw conveying diameter, limit speed, and conveying capacity are obtained; third, according to the above design, a series of parameters are calculated theoretically to explore the one-to-one correlation among the parameters, particularly the relationship between the delivery volume and the rotation speed. The following are related formulas. The calculation formula of the delivery amount: Q ¼ 60

pD2 Snuqs C 4

ð1Þ

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where Q is the conveying mass, D is the screw diameter, S is the pitch, n is the rotation speed, u is the fill factor of the conveyed powder, qs is the bulk density of the conveyed powder, and C is the correction factor. The relationship between rotation speed and screw diameter can be obtained by determining the conveying volume. In this work, the minimum diameter of the screw conveying shaft is determined according to the maximum conveying volume: sffiffiffiffiffiffiffiffiffi Q DK cC

ð2Þ

2:5

where K is the comprehensive coefficient of the materiel and c is the material density. Before a certain rotation speed, the influence of additional material flow on material movement is not significant. When the rotation speed exceeds a certain value, the material will roll perpendicular to the conveying direction, stirring instead of axial driving. Therefore, the minimum screw diameter is substituted to determine the limit speed: A n\nmax ¼ pffiffiffiffi D

ð3Þ

where nmax is the permissible maximum speed and A is the empirical coefficient. Based on the above calculation, the basic parameters of the screw powder feeder are calculated as follows (Table 1): Table 1. Parameters of the spiral conveyor Parameters Spiral blade diameter Pitch Inlet length Inlet width Spiral shaft diameter

Value/(mm) 40 32 66 40 10

The three-dimensional model is built using the above parameters (Fig. 2): Bearing

Motor

Coupling

Sealing

Inlet

Screw blade Outlet

Fig. 2. The structure of the spiral conveyor

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Liquid Conveying System

The 2–3 type screw line (the number of main and slave screw teeth is 2 and 3, respectively) is designed using the volumetric efficiency, processing cost and mixing performance, adopting the cycloidal tooth shape design. Then, a 2–3 screw profile is designed using the cycloidal tooth profile design (the number of male and female screw teeth is 2 and 3, respectively). The end profile is shown in Fig. 3.

Fig. 3. The profile of cycloidal screw pump

The main-slave screw end profile equation is expressed as a matrix equation as follows: The cycloid of the male rotor (normal cycloid): 3 2 x11 cos t 4 y11 5 ¼ 4 sin t 0 1 2

 cosð1 þ i21 Þt  sinð1 þ i21 Þt 0

3 2 3 0 a 0 5 ¼ 4 Rt 5 1 1

ð4Þ

The cycloid of the female rotor (elongated cycloid): 3 2 cos t x21 4 y21 5 ¼ 4 sin t 0 1 2

 cosð1 þ i12 Þt  sinð1 þ i12 Þt 0

3 2 3 0 a 0 5 ¼ 4 Rt 5 1 1

ð5Þ

where a is the center distance, Rt is the radius of the top circle, n1 is the rotation speed of the male rotor, and n2 is the rotation speed of the female rotor. In this research, the corresponding screw parameter design is given with the maximum outlet pressure of 0.6 Mpa and the maximum flow rate of 10 L/min. The geometric parameters are as follows (Table 2):

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Table 2. Parameters of the screw pump rotors Parameters Addendum circle diameter Root circle diameter Pitch circle diameter of the male rotor Pitch circle diameter of the female rotor Center distance Lead of the male rotor Lead of the female rotor Pitch Length of pump sleeve Length-lead ratio

Value/(mm) 36 24 24 36 30 50 75 25 130 1.73

According to the above design parameters, the corresponding three-dimensional model is established as shown in the Fig. 4 below. The left side is the female rotor and the right side is the male rotor. Other parts such as bearings, seals, and gears are selected according to the twin-screw rotors.

Fig. 4. The twin screw pump rotors

3 Mechanism and Hydraulic System 3.1

Mechanical System Layout

Through the design of each independent system, the device (Fig. 5) consists of three parts: the spiral conveyor mechanism, the impeller stirring mechanism, and the twinscrew mechanism, which realize the powder feeding, solid-liquid mixing, and flow control, respectively, with all three parts integrated into one. The entire machine is in a sealed state. The screw feeding conveying mechanism is located at the top and motor 1 drives the screw shaft to transport the solid powder in the storage chamber to the mixing chamber through the spiral cavity; the liquid inlet is on the side of the mixing chamber and motor 2 drives the rotor of the twin screw pump, thereby generating negative pressure. The liquid is drawn into the mixing chamber. The mixing shaft is driven by motor 2 through the gear transmission chamber to achieve solid-liquid mixing. It is mixed in the mixing chamber and discharged from the outlet through the twin screw. The safety valve behind the valve body acts as pressure protection. In the figure the solid

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line is the flow path of the liquid and the dotted line is the flow path of solid powder. Both are evenly mixed in the mixing chamber and output through the twin screw pump chamber. At the same time, a throttle valve is connected to the outlet of the pump to control the outlet pressure, which is reflected in the hydraulic circuit in the next section. Liquid flow path Powder conveying path

Powder storage chamber

Powder transfer chamber

Motor 1

Mixing chamber Motor 2

Solid-liquid conveying chamber

Fig. 5. Structure of the entire machine

3.2

Hydraulic Circuit Setting

According to the model structure, the hydraulic circuit is connected and a test bench is built. The test platform primarily includes two parts, the test instrument and the test panel. The test instrument is comprised of the pressure gauge and the flowmeter. The test panel is used to display measurement data in real time. At the same time, it is also equipped with an infrared sensor to detect the speed of the motor and a throttle valve to adjust the outlet pressure. Pressure gauge Flowmeter

Throttle valve

Safety valve Pump

M

Intake tank

Return tank

Fig. 6. Principle diagram of hydraulic experiments on the test bed

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b

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(a) Integral test bench (b) Test panel (c) Pump Fig. 7. Test platform

Figure 6 is a schematic diagram of the hydraulic test equipment connection circuit, and Fig. 7 is the physical diagram of the test. Figure 7(a) is the overall diagram of the entire mechanical system and test platform, and Fig. 7(b) is the test panel and operation interface. Adjustment of the mechanism is achieved using the control button, and the display panel shows performance parameters such as rotation speed, pressure, flow, and power. Figure 7(c) is the actual situation of the mechanical system.

4 Experimental Study 4.1

Solid Conveying Experiment

In this experiment, powder 1 and powder 2 were selected as materials to test their transport properties, as shown in Table 3 and Fig. 8. In addition to the spiral conveyor, this experiment also requires a container of powder, an electronic scale, and a timer. The purpose is to measure the relationship between powder delivery and motor speed.

Table 3. Physical properties of the experiment powder Average particle size/(lm) Density/(kg  m3 ) Color Calcium carbonate 5 398 white Kaolin 2 627 yellow brown

No. Powder 1 2

Calcium carbonate

Kaolin

Fig. 8. Two conveying materials

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By adjusting the motor speed, the powder delivery at the corresponding time and speed was recorded, as shown in Fig. 9. The mass rate or volume rate at the speed was calculated and recorded as v1 and v2 (Tables 4 and 5).

Outlet

Powder

Container Electronic scale

Fig. 9. The spiral conveyor experiment

Table 4. Conveyance-rotation speed table for calcium carbonate Speed/(r/min) 10 10 10 . . . 100 100 100

Weight/(g) 57.4 57.7 57.7 . . . 266.1 259.5 274.1

Time/(s) 45.61 40.76 40.71 . . . 20.61 20.72 20.53

v1/(g/s) 1.2585 1.4156 1.4173 . . . 12.9112 12.5241 13.3512

v2/(L/min) 0.1204 0.1355 0.1357 . . . 1.2357 1.1987 1.2778

Table 5. Conveyance-rotation speed table for kaolin Speed/(r/min) 10 10 10 . . . 100 100 100

Weight/(g) 59.4 49.2 43 . . . 35.5 64.7 51.2

Time/(s) 51.00 45.70 40.46 . . . 5.11 8.69 6.45

v1/(g/s) 1.1647 1.0766 1.0628 . . . 6.9472 7.4453 7.9380

v2/(L/min) 0.1756 0.1623 0.1602 . . . 1.0473 1.1224 1.1967

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By sorting the above data and calculating the average value, the change in the two types of powder conveyance with motor speed was achieved. To intuitively observe the relationship between motor speed and blanking volume rate of the spiral conveyor, the curve of the rotation speed-volume rate was drawn, and the delivery volume and speed are were found to be proportional (Fig. 10). 1.4

Volume rate / (L/min)

1.2 1 0.8 0.6 0.4

Calcium carbonate

0.2

Kaolin

0 0

20

40 60 80 rotation speed / (r/min)

100

120

Fig. 10. The relationship curve between rotation speed and volume rate

Through the above work, the transport performance formulas of the two powders were fitted to prepare for the follow-up experiments. In the formula y1 ¼ 0:011x1 þ 0:0252 y2 ¼ 0:104x2 þ 0:0724

ð6Þ

x1 and x2 are the rotation speeds of calcium carbonate and kaolin, respectively. The values y1 and y2 are the conveyance volume rate of calcium carbonate and kaolin, respectively. According to the formula, the conveying capacity can be calculated at a given speed. 4.2

Liquid Transport Experiment

In the previous section, the relationship between the conveying volume and the rotation speed of the spiral conveyor was obtained. The relationship curve of the liquid conveying amount is relatively complicated, related not only to the rotation speed but also to the outlet pressure. The conveying flow designed in this research is up to 10 L/min, so four flow values of 4 L/min, 6 L/min, 8 L/min and 10 L/min were selected. Under the premise of constant flow, the relationship between speed and pressure is measured. The rotation speed is achieved by the stepless speed change of the motor, and the pressure is controlled by the size of the throttle valve switch at the outlet. The pressure is adjusted to suit different working conditions. The liquid transported is aviation kerosene (density 1 g/cm3, viscosity 25  10−4 Ns/m2), and the liquid is transparent.

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The measurement results are shown in Table 6 with pressure recorded as P and speed recorded as n. Table 6. The relationship between outlet pressure (kPa) and speed (r/min) at a constant flow rate 4 L/min P 0 50 88 130 180 288 372 584 728 820

6 L/min P 0 65 102 235 350 520 600 650 700 859

n 196 248 272 297 331 392 430 520 574 611

n 270 328 353 437 486 553 575 611 642 675

8 L/min P 0 75 125 222 300 402 500 685 735 820

10 L/min p 5 80 155 219 295 406 553 646 720 820

n 382 451 482 545 576 623 657 715 759 765

n 478 545 592 628 675 724 780 811 841 887

To more intuitively observe the relationship between pressure and speed at a constant flow rate with pressure as the ordinate and rotational speed as the abscissa, the curve with the four flow values is as follows (Fig. 11): 1000 900

Outlet pressure / (kPa)

800 700 600 500 400

4L/min

300

6L/min

200

8L/min

100

10L/min

0 0

200

400 600 Rotation speed / (r/min)

800

1000

Fig. 11. The relationship curve between outlet pressure and rotation speed at a constant flow rate.

The analysis shows the outlet pressure is proportional to the rotation speed under the conditions of a constant flow rate. By adjusting the rotation speed and outlet pressure simultaneously, the target flow rate and the working conditions of a given pressure can be obtained.

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Mixing Experiment

Based on the above two independent tests, the relationship curve between solid powder and liquid conveyance are obtained. Given the total flow rate, solid-liquid proportion and outlet pressure, and the rotation speed of the powder motor, the rotation speed of the liquid motor and outlet pressure are determined to realize the target conveyance. Next, the mixing test is performed. The pressure and solid-liquid proportion of two groups were set and four groups of mixing tests were carried out. The experimental settings are shown in Table 7. The goal was to achieve flow rates of 4 L/min and 6 L/min and solid-liquid proportions of 5% and 10%. To observe the effect of the test, the flow at the outlet was intercepted by beakers. The liquid and solid powder at the outlet are observed to be mixed more evenly (Fig. 12).

Fig. 12. Mixture obtained by mixing tests Table 7. Experimental settings for the mixing tests Experiment no. Rotation speed of male rotor/(r/min) Speed of spiral conveyor/(r/min) Outlet pressure/(kPa) Total flow/(L/min) Powder conveying capacity/(L/min) Solid-liquid ratio

1 270 31 90 4 0.4 10%

2 452 31 400 4 0.4 10%

3 353 22 102 6 0.3 5%

4 452 22 400 6 0.3 5%

To further analyze the mixing effect, four groups of experiments were comprehensively compared. The four groups of experiments were arranged in chronological order from left to right, and the mixture in the beaker was the result of precipitation for a period of time. In the experiments the solid-liquid proportion of the first two cups in each group was relatively low, and the mixing proportion gradually stabilized with time. The reason for the low solid-liquid proportion of the first two cups was inadequate mixing at the beginning, which is consistent with the expected effect. In general, the mixing effect was good (Fig. 13).

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b

c

d

Fig. 13. Results of the four groups in the mixing tests

5 Conclusions A solid-liquid mixing pump was designed and developed. A three-dimensional model was established, and a hydraulic testing platform was set up. The related performance tests were completed. The following conclusions were drawn: (1) Through the solid powder conveying test, the conveying quantity is proportional to the rotation speed, and the conveying quantity of solid powder can be controlled by the rotation speed of the motor. (2) In the liquid conveying experiment, the performance curves of the four flow values were obtained. When the flow rate is constant, the rotation speed and outlet pressure are proportional. The liquid conveying capacity is controlled by the speed of the motor and the size of the throttle valve. (3) Through mixing tests, analysis and comparison of the mixture after mixing transportation was performed, and solid-liquid mixing uniformity was validated. The device can achieve solid-liquid mixing uniformity, and the flow rate and the solidliquid proportion can be adjusted. Acknowledgements. This paper is supported by the National Natural Science Foundation of China (Grant No. 51575069). We thank the State Key Laboratory of Mechanical Transmission at Chongqing University and the Beijing Institute of Power Machinery for their help.

References 1. Chiaverini, M.J.: Fundamentals of Hybrid Rocket Combustion and Propulsion. American Institute of Aeronautics and Astronautics, Reston (2000) 2. Cai, G.B.: Development and application of hybrid rocket motor technology: Overview and prospect. Tuijin Jishu/J. Propul. Technol. 33(6), 831–839 (2012). (in Chinese) 3. Tian, H., Wu, J., Yu, N., et al.: Experimental research of regression rate of N2O and metalized HTPB hybrid rock⁃et motor. J. Propul. Technol. 35(3), 413–421 (2014). (in Chinese)

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4. Cantwell, B., Karabeyoglu, A., Altman, D.: Recent advances in hybrid propulsion. Int. J. Energ. Mater. Chem. Propul. 9(4), 305–326 (2010) 5. Xu, J., Feng, Y., Qu, W., et al.: The theoretical study and its discussion about double-screw multiphase pump. Oil Field Equip. 35(6), 5–8 (2006). (in Chinese) 6. Qu, W., Xu, L., Xu, J.: A brief talk on oil-gas mixed transportation theory oftwin-screw pump. Drill. Prod. Technol. 30(3), 82–84 (2007). (in Chinese) 7. Qu, W., Xu, Z., Zhang, H.: Theoretical study on leakage model of submersible twin-screw pump. Petrol. Dril. Tech. 35(6), 76–78 (2007). (in Chinese) 8. Wang, J., Xu, J., Qu, W., et al.: Optimal design of clearance of submersible two-screw pump. Petrol. Mach. 36(8), 32–35 (2008). (in Chinese) 9. Dolan, P.J., Goodridge, R.A., Leggate, J.S.: Development of a twin-screw pump for multiphase duties. Spe Prod. Eng. 3(4), 629–632 (1988) 10. Prang, A.J., Cooper, P.: Enhanced multiphase flow predictions in twin-screw pump. In: Proceedings of the 21st International Pump User Symposium, Texas A&M University, Houston, pp. 69–76 (2004) 11. Mewes, D., Aleksieva, G., Scharf, A.: Luke modelling twin-screw multiphase pumps–a realistic approach to determine the entire performance behaviour. In: 2nd International EMBT Conference, Hannover, Germany, pp. 104–116, April 2008 12. Chan, E.: Wet-gas compression in twin-screw multiphase pumps. MS Thesis, Texas A&M University (2006) 13. Patil, A.: Performance evaluation and CFD simulation of multiphase twin-screw pumps. Ph. D. Thesis, Texas A&M University (2013) 14. Rabiger, K.: Fluid dynamic and thermodynamic behaviour of multiphase screw pumps handling gas-liquid mixtures with very high gas volume fractions. Ph.D. Thesis, Faculty of Advanced Technology, University of Glamorgan (2009) 15. Rabiger, K., Maksoud, T., Ward, J., et al.: Theoretical and experimental analysis of a multiphase screw pump, handling gas-liquid mixtures with very high gas volume fractions. Exp. Therm. Fluid Sci. 32(8), 1694–1701 (2008) 16. Ruschel, A., Schlücker, E.: Modelling flows for efficiency gains. World Pumps 2010(5), 29– 31 (2010) 17. Ruschel, A.: Fluiddynamische Effekte in Schraubenspindelpumpen bei der Multiphasenförderung (Fluiddynamic effects in screw pumps at multiphase operation). Shaker Verlag GmbH, PhD thesis, Erlangen-Nürnberg University (2014) 18. Salins, A.: Working efficiency of spiral conveyor in transportation of mixed feed. In: Engineering for Rural Development - International Scientific Conference, pp. 117–122 (2010) 19. Li, W., Qin, J., et al.: Design of key components on LS-type spiral conveyor body. In: AIP Conference Proceedings, vol. 1864(1) (2017) 20. Hou, Q.F., Dong, K.J., et al.: DEM study of the flow of cohesive particles in a screw feeder. Powder Technol. 256, 529–539 (2014) 21. Li, X., Lin, Q., He, Y.: Parameter optimization of spiral conveyor for coal auger based on GAAA algorithm. J. China Coal Soc. 35(3), 498–502 (2010). (in Chinese)

Effect of Pore Parameters on Lubrication Performance of Oil-Containing Cage Tingting Yin1, Yuanyuan Li2, Ke Yan1(&), Pan Zhang1, Yongsheng Zhu1, and Jun Hong1 1

Key Laboratory of Education Ministry for Modem Design and Rotor-Bearing System, Xi’an Jiaotong University, Xi’an 310027, China [email protected] 2 Luoyang Bearing Research Institute Co. Ltd., Luoyang 471039, China

Abstract. Under oil-free lubrication conditions, oil-containing cage becomes the only oil storage unit for bearing lubrication in aerospace equipment, therefore the performance of oil-containing cage directly determines the running state and operation life of rolling bearing. By X-ray CT technology, threedimensional reconstruction analysis of cage microporous structure was carried out. And the image segmentation method based a level set function was employed to characterize the pore parameters and micropore structure of the cage. Finally, operating temperature of bearing cage was monitored via quantum dots temperature sensor, which is an on-line and non-contact test method. Based on the theoretical and experimental analysis, the lubrication performance of the oil-containing cage was evaluated. Keywords: Oil-containing cage  Bearing lubrication performance Reconstruction analysis  Temperature measurement



1 Introduction The rapid development of aerospace technology, like space station equipment with extra-long service cycle, has made the demand for long-life oil-impregnated bearings increasingly urgent [1]. Due to the limitation of the space equipment, it is impossible to replenish lubricant for bearings during their service process. Owe to their unique porous structure, porous materials are widely used to make bearing cage store and release oil. The oil-containing cage with porous structure is not only an important rotating component of bearing, but also a carrier of lubricating oil, which obviously affects bearing service life [2]. Polyimide (PI), with excellent temperature resistance, mechanical and tribological properties, is widely used for oil-containing cage. During the rotation of bearing, the lubricating oil in micro-sized porous structure of bearing cage will overflow under the double effect of centrifugal force and the squeezing force generated by the thermal This project is supported by National Natural Science Foundation of China (Grant No. 51875439) and the National Key R&D Program of China (No. 2018YFB2000603). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1124–1135, 2020. https://doi.org/10.1007/978-981-32-9941-2_93

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expansion. As the rotating speed of bearing decrease, the lubricating oil can be inhaled into the micro-sized porous structure owing to the capillary effect. A self-lubricating bearing is formed in the process of oil being inhaled and released. Therefore, the microsized porous structure of oil-containing cage is crucial for bearing lubrication performance. Oil content rate, oil retention rate and porosity, which are main indicators of porous structure, closely related to the number of connected pores, pore diameter, porosity and other parameters, can greatly affect cage lubrication performance [3]. It is noted that the porosity refers to the ratio of the pore volume to the total volume of structure. However, it is difficult to balance the oil content rate and the oil retention rate of the porous cage. It is of great significance to study the porous structure, size and distribution law of the porous oil-containing cage for the optimization of bearing cage and lubrication mechanism of bearing. However, since the pore size and pore distribution of the cage mainly depend on the raw material and the sintering process, the generated structure can be hardly predicted. Meanwhile, it is difficult to reveal the flow feature of lubricating oil in the pores due to the internal pore size is micro-sized and complicated. Besides, the lack of direct experimental data makes it hard to evaluate cage lubrication performance with different pore parameters. Based on X-ray CT technology, this paper reconstructed a three-dimensional microporous structure of oil-containing cage. And the image segmentation method based on level set function was employed to characterize the porosity, number of connected pores and pore distribution of the cage. Furtherly operating temperature of bearing cage and outer ring were monitored via quantum dots temperature sensor which is an on-line and non-contact test method. Finally, the lubrication performance of the oil-containing cage was discussed and evaluated through theoretical and experimental analysis.

2 Pore Parameters Identification of Oil-Containing Cage 2.1

Three-Dimensional Reconstruction

The three-dimensional structure of the porous cage was scanned by X-ray CT, and the basic data such as internal porous structure and porosity were all obtained. The GE Nanotom M device was employed to perform three-dimensional layer-by-layer scanning inside the cage with a resolution of 670 nm. The test piece is a square body with a side length of 2 mm, and the material is a MPPI02 type of porous polyimide from Luoyang Bearing Research Institute Co. Ltd. Three views generated by CT scans of the test piece was shown in Fig. 1, in which the gray parts are polyimide material, the white parts are polytetrafluoroethylene, and the dark blue parts are micro pores. It can be seen from the Fig. 1 that the pore distribution of each section is non-uniformly. The pore distribution of the right view is denser than the main view which is caused by uneven lateral pressure. When the cage is manufactured by cold press sintering, the lateral pressures in the inner and outer portions of the press process are not the same, resulting in a difference in porosity between the internal and external parts.

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Fig. 1. Three view of pore distribution after CT scanning

Figure 2 shows the three-dimensional pore model of the reconstructed polyimide material of oil-containing cage. Due to the resolution accuracy, many pores with diameters less than 670 nm are not detected, which is the reason that some of the pores are not connected and the pore-connected structure cannot be seen clearly. But it can be seen the distribution of the pores and the shape of the internal pores, which enables a true and effective rebuilding of the internal pore structure.

Fig. 2. 3D pore model of reconstruction cage

2.2

Pore Parameter Identification

Scanning electron microscopy is widely used in the observation of material microstructure due to its high resolution [4]. In order to qualitatively analyze the pore parameters of porous oil-containing cage, scanning electron microscope (SEM) was used to scan samples 1# and 2#, which have a porosity of 15% and 21% monitored by

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mercury intrusion meter, respectively. After that, the image segmentation method based on level set function was carried out, obtaining the scanned SEM images, seen in Fig. 3. Based on the region-based active contour model, the cage pore parameters of the two different samples were extracted.

Fig. 3. SEM images of the samples

2.2.1 Image Segmentation Principle Based on Level Set Function If X  R2 is the image domain, then the grayscale image can be represented by I:X ! R2. Mumford and Shah [5] use a mathematical function to represent the regionbased active contour model of image segmentation problem, writes as Eq. (1): Z Z ðu  I Þ2 dx þ l ð1Þ F MS ðu; CÞ ¼ jruj2 dx þ vjC j X

X=C

|C| is the length of the contour C which divides the image domain into disjoint subregions. And u is an optimal function that fits the original image I and that is smooth within each of the subregions. When the contour C is closest to the segmentation edge of a given image I, the above objective function has a minimum value. For a given image I, the process of seeking the contour C of the target region can be obtained by minimizing Eq. (1) and fitting function u. However, it is difficult to minimize the objective function Eq. (1) in practical applications, and the algorithm operation efficiency is low. By assuming that u has a piecewise constant characteristic in the above objective function and u equals certain invariant value in different segmentation regions, Chan and Vese [6] design a famous model named C-V model. For image I, the above objective function can be simplified to Eq. (2). Z F

CV

Z 2

ðC; c1 ; c2 Þ ¼ k1

jI ð xÞc1 j2 dx þ vjCj

jI ð xÞc1 j dx þ k2 outsideðCÞ

ð2Þ

insideðCÞ

Where outside(C) and inside(C) represents the image regions of outside and inside of the pore boundary, respectively, and c1, c2 are approximately constant values for outside(C) and inside(C). However, the SEM image of the cross section of the porous cage is affected by the gradation imbalance, so that the gray values of some of the divided regions are far from the assumed approximations c1, c2. Then, the active

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contour with local binary fitting energy is used to accurately extract the intensity uneven image information. As a result, automatic initialization is achieved and the amount of calculation is reduced. We define each point x  X with the following energy as Eq. (3). Z ð C; f ð x Þ; f ð x Þ Þ ¼ k K ðx  yÞjI ð yÞ  f1 ð xÞj2 dy eLBF 1 2 1 x inðC Þ Z ð3Þ þ k2 K ðx  yÞjI ð yÞ  f2 ð xÞj2 dy outðC Þ

k1 and k2 are normal numbers, and K is kernel function with positioning properties where K(u) is decreasing or close to zero. And the values of f1 and f2 refers to image intensities near each x [7]. For each center point x, the local fitting energy eLBF can be x minimized when the contour C is just on the object boundary and the fitted values f1 and f2 are optimally selected. Therefore, the entire object boundary is found by minimizing LBF eLBF for all the center points x in the image domain X as Eq. (4): x . Integrating ex Z eðC; f1 ; f2 Þ ¼

X

eLBF x ðC; f1 ð xÞ; f2 ð xÞÞdx

ð4Þ

Convert the above equation to the equivalent level set formula, as Eq. (5): Z

2 eLBF x ðu; f1 ð xÞ; f2 ð xÞÞ ¼ k1 Kr ðx  yÞjI ð yÞ  f1 j H ðuð yÞÞdy Z

þ k2 Kr ðx  yÞjI ð yÞ  f2 j2 ð1  H ðuð yÞÞÞdy

ð5Þ

H is the Heaviside function, which is used to ensure the stable evolution of the level set function ф. At the same time, a distance regularization term of Eq. (6) is added to reduce the deviation of the level set function ф from the signed distance function. Z PðuÞ ¼

1 ðjruð xÞj  1Þ2 dx X2

ð6Þ

In order to standardize the zero-level contour of ф, the length of the zero-level curve (surface) is defined as Eq. (7). ð7Þ In summary, the definition of the entire energy function can be expressed as Eq. (8): ð8Þ l and m are non-negative constants. This energy function is a form of level set function expression. By minimizing the level set energy function, the point where u is zero is the segmentation result.

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2.2.2 Segmentation Result Analysis Sample 1# and sample 2# are porous structure from two oil-containing cage, whose porosity are 15% and 21%, respectively, measured by a mercury intrusion meter. Figure 4 shows the image segmentation results based on the image recognition method of the level set function, in which the red lines are zero-horizontal contour and the portion surrounded by the red curve are divided pores. From the segmented SEM image, it can be clearly seen that the pore segmentation achieved good result, exception for a few regions with insignificant gray distribution, further verifying the accuracy of the method. This image segmentation method provides a new direction for the analysis of the porous parameters of the bearing cage.

1#

2#

Fig. 4. Final contour of level set function image recognition

Figure 5 is a binary image for identifying the porous structure, in which the white portion refers to the pores and the black portion is polyimide material. It can be seen that the pore distribution is similar to the blue part of Fig. 1, which exists many nonconnected pores. Since the resolution of the scanning electron microscope is higher than that of the CT scan, the number of connected areas in Fig. 5 is more than that in Fig. 1, which also verifies the rationality of the scan analysis result. The grayscale image can be read into a two-dimensional planar matrix by MATLAB, in which the product of rows and columns represents the number of pixels

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Fig. 5. Binary image of cage pore structure

in the image, the size of the pixel is proportional to the area of the corresponding region in the image. Firstly, by marking the connected area in the image, the number of pixels in every connected area can be extracted. Then the area distribution of the interconnected regions of the porous material was characterized by the numbers of pixel points, shown in Fig. 6. At the same time, it is also found that the connected areas with less than 500 pixels of sample 1# account for 88.83% and for sample 2#, the connected areas of no more than 2000 pixels account for 87.97%. Compared with the results of the three-dimensional reconstruction, it is verified that the low porosity measured by the three-dimensional reconstruction is caused by insufficient resolution. The pore size of the sample 1# is smaller than that of sample2# but the pore numbers of both samples are close. The results indicate that the reason of the increase in cage porosity is because the increase of pores size instead of the increase of pores number. With the pore size increasing, the porous capillary force becomes small, causing the inhalation of lubricating oil and oil retention capacity become weak. On the contrary, the content of lubricating oil will decrease. By image segmentation program, the porosity of samples is 13.39%, 20.53%, respectively. Compared with the porosity measured by the mercury intrusion meter, the difference is 1.61% and 0.47%, respectively. The small differences verify the feasibility

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Fig. 6. Area distribution of connected areas

and accuracy of the method of extracting the cage porosity by the principle of a level set function image segmentation method.

3 Direct Monitoring of Cage Lubrication Performance 3.1

Experimental Platform

Oil-containing porous cages with different pore parameters were installed into 7008C bearings to test the lubrication performance. The PT100 temperature sensor and IMX100 data acquisition system were used to monitor the temperature of the outer ring and the non-contact monitoring method based on cadmium telluride quantum dots (CdTe QDs) was employed for temperature monitoring of the cage. Based the test data, this paper evaluates bearing lubrication performance in condition of different cage porous parameters and bearing rotation speed. MPPI02 type porous polyimide, used as the material of the cage, is provided by Luoyang Bearing Research Institute Co. Ltd. The experiment was designed as two groups for comparative testing. The porosity of the cage was 15% and 21%, respectively, and the other test parameters were consistent. For each group, three kinds of speed including 2000 rpm, 4000 rpm, and 6000 rpm were used to test. When the

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temperature of outer ring became stable, the rotation speed was directly raised to the next rotation speed. A three-times repeat test was carried out and the average of data was taken to avoid accidental errors. The test bench is built as shown in Fig. 7.

4 5 2 1

3

6 7

8

9

10

11

1-optical fiber 2-Transmitting and receiving probe 3-Support, 4-Temperature acquisition probe, 5-Bearing cage of PI, 6-Axis, 7-Laser, 8-QE Pro spectrograph, 9-IMX100 Temperature collector, 10-405nm laser, 11-PC.

Fig. 7. Testing bench for bearing outer ring and cage monitoring

3.2

The Test Principle of Cage Temperature

By non-contact testing method based on CdTe QDs [8, 9], as shown in Fig. 7, the cadmium telluride quantum dots are attached to the end face of the bearing cage, and it is irradiated by the laser emitter through the optical fiber. At the same time, the quantum dots can emit fluorescence in specific wavelength. Spectrometer is used to collect spectral information at the corresponding temperature. Finally, the spectral information is transmitted to the computer, and cage temperature of the bearing is calculated by the temperature characteristic calibration relationship of the quantum dots characteristic parameters. Figure 8 is a calibration curve which indicates the conversion relationship between the peak wavelength and temperature of the peak wavelength of the quantum dots with temperature. It can be seen that the peak wavelength has a good linear fit with temperature, and the fitting coefficient is above 99.5%, which indicates that temperature sensor of the quantum dots has a good thermal stability. Based on this, the calibration formula Eq. (9) can be got, and the sensitivity of the peak wavelength of the quantum dot sensor to temperature is 0.15 nm/°C. W = 0:14993t + 564:88727

3.3

ð9Þ

Discussion and Analysis

3.3.1 Temperature Monitoring of Bearing Outer Ring By punching holes in the bearing housing and setting a thermocouple probe through it, the fixing point temperature of bearing outer ring can be directly tested [10]. Three thermocouple probes were set at different positions on bearing outer ring, and the

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temperature change of the outer ring of the bearing was recorded by the IMX100 temperature collector. Finally, the average of the three temperature values were taken as the outer ring temperature. The temperature rise curves of outer ring are shown in Fig. 9, including collected samples 1# and 2#.

Fig. 8. Quantum dot temperature calibration curve

Fig. 9. Temperature rise curve of bearing outer ring

It can be seen from Fig. 9 that the temperature change trend of the outer ring increases rapidly firstly and then becomes stable. The temperature of sample 1# is uniformly changed at each rotation speed. The temperature change of sample 2# is not obvious at low speed, but becomes greater at high speed. This is because at low speed, the porosity and pore diameter of sample 2# are so large that the capillary force is weak, resulting in massive oil overflow from the cage, and the temperature rise of sample 2# is not as obvious as sample 1#. At high-speed, the sample 2# was excessively oiled causing the oil retention rate decreased. So, the temperature rise in highspeed was more obvious than it in the low-speed stage.

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For the sample 1#, the porosity and the pore diameter are small, and the oil overflow and the oil retention rate may maintain at a certain balance, so the temperature rise is uniformly increased when the rotational speed is changed. 3.3.2 Bearing Cage Temperature The spectrometer saved fluorescence spectrum reflected for every three minutes, and each group of tests was tested for approximately 270 min. The peak wavelength was obtained by using Gaussian fitting method. The peak wavelength was converted into temperature by Eq. (9). The initial temperature and the stable temperature under each rotational speed of cage was organized as Table 1. Table 1. Cage temperature at different speed R(r/min) 0 2000 4000 6000 1#(°C) 24.82 28.07 31.30 34.22 2#(°C) 21.44 23.28 36.65 35.55

It can be concluded from Table 1 that the temperature change of the cage of sample 1# corresponds to the temperature change of the outer ring. Due to the oil overflow of the cage and the oil retention rate are keeping balance, the temperature is evenly changing when the rotation speed is increased. However, when the rotation speed of sample 2# increases to 4000 and 6000 r/min, the temperature of cage rises sharply, and finally decreases slightly. When the temperature of cage rises sharply, the lubricating oil in the cage flows out quickly due to thermal expansion, so the temperature rise of the outer ring is not obvious.

4 Conclusions The lubrication performance of oil-containing cages with different pore parameters are evaluated by the combination of theoretical analysis with the X-ray CT technique and image segmentation method of level set function and experimental testing of temperature of bearing cage and outer ring, from which the conclusion is as follows. (1) According to the three-dimensional reconstruction result of the microporous structure of the oil-containing cage, the internal pore structure of the cage is rebuilt effectively and it provides reference comments for further study in the future. (2) A level set function method was employed for extracting pore contour of cage. As a result, pore size and porosity are in a one-to-one relationship and cannot be discussed separately. That is, the increase in porosity is due to the pore size increasing rather than the number of pores. (3) At certain low speed, porous oil-containing cage with large pore size and large porosity has better lubricating performance.

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(4) Compared with outer ring temperature of bearing, the temperature rise of the porous oil-containing cage is little, which indicating that the porous oil-containing cage of the polyimide material has a good lubrication performance.

References 1. Yang, Y.X.: Research on Preparation and Modification of Polyimide Based Porous Oilbearing Material, pp. 4–5. Harbin Institute of Technology, Harbin (2017) 2. Zhao, H.J.: Study on Improving the Performance of Rolling Bearing at Starved Lubrication by Porous PI, pp. 1–2. Nanjing Aerospace University, Nanjing (2017) 3. Wang, Y.L., Zhang, F.: Calculation of porous copper’s porosity by SEM method. Initiating Explos. Device 06, 49–53 (2012) 4. Deng, L.H., Wang, R., Chen, Y.Y.: Application of image processing system of image J based on electronic scanning in porous materials. Sens. Microsyst. 31(05), 150–152 (2012) 5. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577–685 (1989) 6. Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Imag. Proc. 10, 266–277 (2001) 7. Li, C., Xu, C, Gui, C.: Level set evolution without re-initialization: a new variational formulation. In: CVPR2005, vol. 1, pp. 430–436 (2005). Goertz, R.C., Thompson, R.C.: Electronically controlled manipulators. Nucleonics 12(11), 46–47 (1954) 8. Allison, S.W., Cates, M.R., Noel, B.W., et al.: Monitoring permanent-magnet motor heating with phosphor thermometry. IEEE Trans. Instr. Meas. 37(4), 637–641 (1988) 9. Yan, K., Yan, B., Li, B.Q., Hong, J.: Investigation of bearing inner ring-cage thermal characteristics based on CdTe quantum dots fluorescence thermometry. Appl. Therm. Eng. 114, 279–286 (2017) 10. Yan, K., Zhu, Y.S., Hong, J., Hang, Z.Y.: Experimental study on heat generation and heat transfer for rolling bearing subassembly. J. Huazhong Univ. Sci. Technol. (Nat. Sci. Ed.) 40 (S2), 31–34 (2012)

Defects Detection System for Fluorescent Coating of Metal Plate Based on Machine Vision Yujin Wu1, Fengxia Zhao1(&), Chuanfu Xin1, Jianshe Gao1, and Zhigao Chen2 1

2

School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China [email protected], [email protected] Henan Police Signage Production Center, Zhengzhou 450000, China

Abstract. Aiming to solve the defects detection problems of metal plate fluorescent coating in printing, a machine vision-based metal plate fluorescent coating printing quality online detection system was provided. According to the requirements of factory and measurement accuracy, the camera, lens and illumination mode in the image acquisition module are selected, which forms an imaging effect that is conducive to image processing, and the problem of highlight bright spots and the surrounding object reflections caused by the reflective surface of the coating surface has been solved. Using color space conversion technology, BLOB analysis technology, sub-pixel edge extraction technology and template matching technology to detect common defects that appear on the coating, such as color spots, uneven printing, pattern defects. Under VS2010 environment, based on C# and Halcon, the on-line inspection software system for the printing quality of fluorescent coatings on the metal plate was developed. This software is used to test examples online, the results show that the speed of the provided detection system is quickly and the detection results are reliable, it can meet the requirements of factory. Keywords: Machine vision  Fluorescent coating Sub-pixel  Template matching

 Defect detection 

1 Introduction To attract attention in daylight and night, the metal fluorescent coating products add fluorescent micro-powder to the coating to make it have various colors and strong surface reflection. At present, automatic printing equipment has been used in the printing of fluorescent coatings on metal plates in China, and the automatic assembly line work could be realized [1]. However, the monitoring of printing quality by these devices is still manual control method, this method has many disadvantages: This project is supported by the National Key R&D Program of China (Grant No. 2018YFB010 4101). © Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1136–1149, 2020. https://doi.org/10.1007/978-981-32-9941-2_94

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1. The detection standards are not uniform; 2. The detection process is prone to visual fatigue, leading to missed detection or false detection; 3. Slow detection speed; 4. High cost; 5. Working environment is not conducive to workers’ health; 6. Detect has to wait for drying which it is easy to appear as a batch; 7. The exposure to product testing could lead to the samples polluted by testers which resulted in damage to the surface of the coating. Therefore, it is urgent to research on-line detection method for the printing quality of metal fluorescent coatings. With the development of computer technology and digital image processing technology, researchers all over the world have applied machine vision technology and digital image processing technology in various fields [2–6], however, it is hard to find the report on the on-line detection of the printing quality of fluorescent coatings on metal. The main reasons are: the coating surface is highly reflective, which brings difficulties on image collection; various uncertain defects (such as color spots, uneven printing, and pattern defects) will occur randomly in fluorescent coatings processing; coating color is often changed according to demand, and the production process is dynamic; the production clock of the assembly line is very demanding, and the time delay for quality monitoring and processing is very short, if the printing quality is monitored by computer, it is necessary to match many printed images and to recognize uncertain images, which makes the development of image processing system very difficult. In order to realize automatic identification of coating defects on metal plate, we design an image acquisition system for double-sided diffuse illumination, and propose a method for detecting spots defect in the coating region based on colorimetric analysis, a method for detecting uneven defects based on sub-pixel edge extraction, and a method of pattern boundary defect detection based on shape template matching. Finally, those methods were verified by experiments.

2 On-Line Coating Quality Detection System for Metal Plate The size of metal samples to be tested is 440 mm  140 mm, production speed is 150 mm/s. According to the actual production situation, the printed quality detection system of fluorescent coating on metal plate is designed as shown in Fig. 1. Machine vision box Conveyor belt Industrial Camera control station sensor

baffle plate lens light source

computer

Fig. 1. Printing quality detection system for fluorescent coating on metal plate

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The system includes a product transfer module consisting of a sensor and a conveyor belt, an image acquisition module consisting of a machine vision box, and an image processing module integrated with the control software. During the test, the product transfer module transports the product to the detection position, and the image acquisition module acquires image and transmits the image signal to the computer. Finally, the computer performs image processing and outputs the detection result. The machine vision box consists of a camera, a lens and two light sources. In order to adapt to the speed of production, the camera selects the color screen camera with global exposure to prevent the image from smearing. The model of industrial camera used in this paper is Daheng MER-503-GC-P color COMS industrial camera, the resolution of the camera is 2448 * 2048 and the frame rate is 20 fps. The screen size is set to 2000 * 2048 according to the field of vision in field detection. The screen size is set to 2000 * 2048 according to the visual field requirement of the filed detection, which aiming to reduce detection time and meeting the vision needs. The lens we chosen is Computar’s M0814-MP2 lens, the Specification is 2/3”, the focal length is 8 mm, which is matches the camera. The data transmission between camera and computer adopts Gigabit Ethernet GigE image interface technology, which can realize high-speed image transmission and meet real-time requirements. Since the surface of the coating is mirror, there are high brightness noise and interference of surrounding objects during the image capturing process. In order to eliminate these interferences, in this paper, a double-sided diffuse reflection illumination scheme is designed. A reflective baffle is designed on the plane of the lens to eliminate information interference on the surface of the coating. The optical path diagram is shown in Fig. 2. Among them, the light source is P-BL2-462-38-W strip light source (produced by RSEE company), the length is 462 mm, which is larger than the product length, ensuring uniform illumination of the product surface. The light source hangs slightly below the lower surface of the lens. In order to generate diffuse light, the inner surface of the metal case is white. The image acquisition module is used to acquire the image which is less disturbed by the outside world. We have used this image acquisition module to obtain images that are interfered by the external.

Fig. 2. Light path diagram of light source system

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3 Key Technologies in the Quality Inspection of Fluorescent Coatings After obtaining the product image, the image needs to be processed to detect the quality of the coating. In this paper, the acquired image is processed by computer based on C# and Halcon in VS2010 environment. 3.1

Image Preprocessing

Preprocessing can reduce interference and enhance useful information in images. Before performing defect detection, it is necessary to eliminate interference information such as conveyor belt image and noise. The process is shown in Fig. 3.

Fig. 3. Image preprocessing flowchart

Considering that the belt is worn and whitened during use and the grayscale value range of the whitening part is large, because of this, using traditional blob analysis methods to perform threshold analysis on grayscale images will be affected. Therefore, the image is processed in HSV color space. In the HSV color space, H represents hue, S represents saturation, and V represents value. The color coatings have high saturation and are quite different from the uncoated portion. Therefore, the image is segmented by threshold in S channel to eliminate the influence of conveyor belt. However, there is still noise in the image, so it is necessary to obtain region of interest (ROI) by threshold segmentation again in H channel for subsequent detection. The H, S, and V channel values are calculated by the following procedure based on the R, G and B channel values. Firstly, calculate the maximum and minimum values of R, G and B channels: Min ¼ minð½R; G; BÞ

ð1Þ

Max ¼ maxð½R; G; BÞ

ð2Þ

Then we can calculate the values: V ¼ Max  S¼

0 MaxMin Max

Max ¼ Min Max 6¼ Min

ð3Þ ð4Þ

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3.2

8 > >
MaxMin  rad ð60Þ > : RG 4 þ MaxMin  rad ð60Þ

Max  Min Max ¼ R Max ¼ G Max ¼ B

ð5Þ

Color Spot Defect Detection Based on Chromaticity Analysis

The main feature of the color spot defect is that dark or light ink spot appear in a relatively uniform area, as shown in Fig. 4. For such characteristics, Sun et al. [7] detected the back crack and side defects of the electrical contact, mainly used the closing top-hat operation and the gamma transformation to enhance the side image of the electrical contact, and used blob analysis technology to extract the defect. However, the grayscales of some ink spots on the coating are too close to the background grayscale (Fig. 5 (a)), and it is difficult to separate them using traditional blob analysis methods. Niu et al. [8] identified healthy and pest leaves of strawberry. Eight kinds of features (average gray level, standard deviation, third-order central moment, smoothness, uniformity, average information, maximum probability gray level, gray level range) obtained from gray histogram of strawberry leaves were trained based on SVM, and strawberry pest leaf classifier was obtained. In this paper, some small defects have little effect on the above features, and it is difficult to classify small area defects.

Color spot Color spot Color spots (a)

(b)

(c)

Fig. 4. Examples of color spot defect

Therefore, this paper uses chromaticity analysis method to extract the color spot defects, and the processing process is shown in Fig. 6.

Fig. 5. Grayscale diagrams of Fig. 4

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Fig. 6. Color spot defect detection flow chart

Thresholding the H channel image of the ROI, the chromaticity-qualified area is preserved, and the chromaticity abrupt area in the image will become holes. However, there may still be noise effects near the edge of the ROI (Fig. 7(c)), in which case the opening arithmetic is used to remove noise. The open operation process is shown in formula 4, and the processing result is shown in Fig. 8. A  S ¼ ð A  SÞ  S

ð6Þ

Where, A——Target image; S——Structural element; —Opening operation; ——Erosion operation; ⊕——Dilation operation;

(a)

(b)

(c)

Fig. 7. Results of the H channel threshold in Fig. 4.

Fig. 8. Results of the opening operation in Fig. 7

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In order to extract the defect region, the boundary of the region after opening operation is first obtained, and then select the feature (this paper uses the area feature and the ratio of the major axis to the minor axis of the of minimum circumscribed ellipse) to remove the boundary outside the coated regions. The final defect processing result is as follows (Fig. 9).

Fig. 9. Defect detection results for Fig. 4

3.3

Uneven Printing Detection Based on Subpixel Extraction

Due to the failure of the printing machine, it is easy to produce uneven printing of fluorescent ink in coating printing process, and the defects mainly reflected in dark or light stripes with a width of 0.5 mm and above (Fig. 10). The color of the stripe is very close to the qualified color, which is difficult to distinguish. If these defects cannot be found immediately, the defect area will increase in the following coating printing process, which will bring in a large number of defective products.

Fig. 10. Examples of uneven printing defect

Stripes produced by uneven printing are similar to image texture features. Xu et al. [9] did some research on the extraction of image texture and proposed a rectangular circumferential spectrum energy spectrum method based on Fourier transform. In this paper, the details of defects are less, and it is difficult to separate the corresponding high-frequency information by using Fourier transform in frequency domain. Nouri [10] evaluates Bread Storage nondestructively by calculating the energy, contrast, uniformity, correlation and entropy of gray level co-occurrence matrix. However, the method of gray level co-occurrence matrix is not suitable for the case of this paper. The main reason is that the different ink concentration directly affects the color of the

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coating. Different batches of products have different gray scale characteristics. It is difficult to obtain the characteristic parameters for all products suitably by using gray level co-occurrence matrix method; Tsai et al. [11] detected the surface defects of workpieces with circular tool-marks based on morphology and blob analysis. Morphological method with arc-shaped SE is proposed for machined surface inspection, but This method is suitable for the case where the surface texture has a sudden change, which is not applicable to the case of this paper. In this paper, the resolution of the image acquisition system is 1 pixel/mm on the product surface, but the width of some defect stripes is less than 1 mm. The resolution of the sampling system does not satisfy the sampling theorem, and causes image aliasing. To extract the defects, it needs higher accuracy than the image pixel resolution. Therefore, this paper calculates the sub-pixel accuracy data to obtain image defects. There are usually two methods to obtain sub-pixel data [12]: sub-pixel threshold segmentation and sub-pixel edge extraction. When segmenting an image, the threshold needs to be very accurate and adapt to changes in light. Fluorescent coating surface defect extraction algorithm requires robustness to light changes, so this paper selects sub-pixel edge extraction technology. To extract the sub-pixel edges of an image, the initial value of the edge should be calculated first at the pixel scale. This paper proposes Canny algorithm to calculate the initial value of the edge. The Canny algorithm has the advantages of unilateral response, low error rate, accurate edge location, sensitive to details, and good noise immunity. The processes of canny algorithm are as follows: (1) Firstly, two-dimensional smoothing mask is used to convolute the image to prevent noise from affecting the edge of the image and to preserve the original image features to the greatest extent. Choosing the appropriate mask is the key to improve the calculation speed and the accuracy of edge extraction. (2) Then, the gradient magnitude and direction of the image are calculated by the first-order partial derivative finite difference, and the obtained gradient amplitude is non-maximally suppressed to remove the random noise. (3) Finally, the edge of the image is extracted and closed using a bilateral threshold. In this paper, the smooth mask is constructed as a 55  55 Gaussian mask. There are three main methods to get sub-pixel edges: interpolation method, moment method, and fitting method. Among them, the interpolation method has the characteristics of high calculation efficiency and high speed, which is more suitable for online detection. In this paper, we use bilinear Interpolation to obtain sub-pixel precision edges. The bilinear interpolation method uses the gray values of four adjacent pixels around the position to interpolate. First, the horizontal and vertical distances from the center of the pixel to the position to be measured should be calculated, as shown in Fig. 11.

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Fig. 11. Bilinear interpolation

Because the center distance of two pixels is 1, the range of distance to be located in the center of adjacent pixels is [0,1]. Then, the weight of four adjacent pixels’ gray values is calculated according to the distance, and obtain the result of bilinear interpolation: f ðPÞ ¼ ð1  bÞ½f ðQ21 Þ  a þ f ðQ11 Þ  ð1  aÞ þ b  ½f ðQ22 Þ  a þ f ðQ12 Þ  ð1  aÞ

ð7Þ

For the experimental samples in this paper, we extract the edges on G channel in Fig. 10. The result is shown in Fig. 12.

Fig. 12. (a) Fig. 10(a) uses the canny algorithm to detect results at sub-pixel scale (Filter Width = 55, Low = 1, High = 4) (b) Fig. 10(a) uses the canny algorithm to detect results at pixel scale (Filter Width = 25, Low = 4, High = 8) (c) Fig. 10(b) uses the canny algorithm to detect results at sub-pixel scale (Filter Width = 55, Low = 1, High = 4) (d) Fig. 10(a) uses the canny algorithm to detect results at pixel scale (Filter Width = 25, Low = 4, High = 8)

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It can be seen from Fig. 12 that the canny algorithm at the pixel scale can only extract defects with wide stripes and large color variations, but the defects with small width and of color aliasing (Fig. 10 (b)) will lose the ability to extract. In the sub-pixel scale, the uneven defects can be detected with higher accuracy. 3.4

Pattern Defect Detection Based on Template Matching

Some fluorescent coating products have complex patterns on the coating, and complex patterns often have defects (Fig. 13). The biggest feature of this kind of defect is that the edge shape of defect pattern is quite different from that of qualified pattern. For regular patterns (such as rectangle and circle), some scholars use morphological analysis to extract edge defects [12]. But for complex patterns, morphological methods cannot extract image defects. Therefore, this paper uses template matching method to identify pattern defects.

(a)

(b)

(c)

Fig. 13. (a) Qualified product; (b), (c) Examples of pattern defect

Template matching technology mainly searches for the template in the image by moving the template in the image to be measured. This technology can quickly find the position of template in the image to be measured, so it is widely used in the field of target tracking and target detection. Template matching is usually based on the gray value of the model and the image. The similarity score between template and image is obtained by calculating the similarity of gray value between template and image. However, because this method is sensitive to the change of illumination [13], when detecting the pattern of fluorescent coatings, there may be the influence of uneven illumination and noise. According to calculate the similarity between template edge feature vectors and image edge feature vectors, this paper gets the defect location. Because the position of the product is not fixed when the image is taken. In the acquired image, the pose of the coating pattern has a rigid transformation, the rotation and translation transformation of the template should be considered in the detection (Fig. 14).

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Fig. 14. Pattern defect detection flow chart

(1) Create a shape model. Find the centroid of ROI where the model located in the qualified image. Get a set of points pi ¼ ðxi ; yi ÞT by extracting the edges of the template and a set of direction vector di ¼ ðti ; ui ÞT which is corresponding to pi and the centroid. (2) Create a variant model. Establish a homogeneous transformation matrix A: 2

1 A ¼ 40 0

0 1 0

3 0 05 1

ð8Þ

Add a rotation matrix R to A to get the transformation matrix B:  R¼ 2

cosðphiÞ sinðphiÞ

cosðphiÞ B ¼ 4 sinðphiÞ 0

sinðphiÞ cosðphiÞ



3 sinðphiÞ 0 cosðphiÞ 0 5 0 1

ð9Þ

ð10Þ

The transformed point and direction vectors can be expressed as: p0i ¼ Bpi

ð11Þ

di ¼ Bdi

ð12Þ

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(3) Calculate the similarity measure and find the model in the image. At the time of detection, the image to be tested is also converted into a direction  T corresponding to each point ðx; yÞ, and the transformed vector ex;y ¼ vx;y ; wx;y model is compared with a specific position of the image to be measured, and calculate the sum of the dot product of the direction vector of the transformed model and the direction vector of the image at all point positions in the image, then we get the similarity measurement of the point Q position. s¼

n D E 1X d0i ; e0p þ q n i¼1

n 1X ¼ t0 vx þ x0i ;y þ y0i þ u0i wx þ x0i ;y þ y0i n i¼1 i

ð13Þ

In order to resist the influence of uneven illumination, the above formula needs to be normalized: D E n d0i ; e0p þ q 1X     s¼ n i¼1 d0i   e0p þ q  n ti0 vx þ x0i ;y þ y0i þ u0i wx þ x0i ;y þ y0i 1X ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 n i¼1 t02 þ u02 þ v2 0 0 þw 0 0 i

i

x þ xi ;y þ yi

ð14Þ

x þ xi ;y þ yi

Graphic pyramids are used for hierarchical search to speed up the search process. In this paper, the number of pyramid layers is selected as 10. (4) Detecting pattern defects. To judge the defects in the image, a high threshold and a low threshold are added to the model to identify the bright and dark regions in the image. After the recognition is completed, the bright and dark regions are output as defects. The results of the pattern defect detection in Fig. 13 are shown in Fig. 15.

Fig. 15. (a) Test results for Fig. 13(b); (b) Test results for Fig. 13(c)

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4 Results In this paper, an experimental platform for printing quality detection of fluorescent coatings on metal plates is established. Based on C# and Halcon software, the corresponding detection program for license plate is developed under VS2010 environment. The experimental platform is shown in Fig. 16.

Fig. 16. (a) Machine vision box and conveyor (b) Internal structure of the machine vision box

The main interface of the test program is shown in Fig. 17.

Time of detection

defect

Fig. 17. The main interface of the test program

In Fig. 17, three picture boxes respectively display the image acquired by cameras, and the defect positions are marked with red lines in the image. The time in the system for defect detection is displayed in the upper right corner of the window. After many experiments, it is shown that the method proposed in this paper can accurately extract spots, uneven printing and pattern defects from the image of license plates, and the test results are stable and reliable. In addition, the computer processing time from the beginning of image acquisition to the completion of defect detection is about 1000 ms, which satisfies the requirements for online detection of license plates.

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5 Conclusions This paper designs a metal plate fluorescent coating detection system based on machine vision system, which can quickly and accurately identify three kinds of common defects of metal plate fluorescent coating: color spots, uneven printing, and pattern defects. The structure of machine vision system designed can reduce the influence of image reflection and high-brightness noise caused by coating reflections. Compared with traditional blob analysis method and gray histogram method, the proposed method based on chromaticity analysis can achieve higher detection accuracy, and has a good detection effect for the defects with small area and less color changes. The uneven printing detection method based on sub-pixel edge extraction has robustness to illumination and can detect the slim stripes whose image is difficult to satisfy the sampling theorem. The pattern defect detection method based on template matching can accurately match the position of the pattern in the image and detect the defects at the edge of the pattern. This method is not affected by illumination, grayscale changes, and noise. Moreover, the detection speed is fast. It has been proved that the system can detect the quality of the license plate in real time, and meet the detection requirements.

References 1. Yu, J.: Summary of patented screen printing technology. Screen Print. Ind. 02, 31–34 (2018) 2. Barjaktarovic, M., Petricevic, S., Radunovic, J.A.: Timely detection of a coated board streak defect in subsampling conditions using monochrome vision system. AEU - Int. J. Electron. Commun. 66(4), 313–321 (2012) 3. Sun, Z., He, C., Tang, P., Luo, H.: Fabric defect detection based on wavelet transformed textured characteristics. Comput. Meas. Contr. 18(09), 2060–2062 (2010) 4. Zhang, J., Zhang, H., Zhao, Y., Sima, Z.: Tile defects detection based on morphology and wavelet transformation. Comput. Simul. 36(01), 462–465 + 474 (2019) 5. Hai, C., Zhao, F., Sun, S.: Research on online detection for jujube surface defects based on blob analysis. Food Mach. 34(01), 126–129 (2018) 6. Li, J., Zhao, F., Jin, S.: the defect detection system for the glass fiber cloth base on machine vision. Mach.Des. Manuf. (01), 163–165 + 169 (2018) 7. Sun, T.H., Tseng, C.C., Chen, M.S.: Electric contacts inspection using machine vision. Image Vis. Comput. 28(6), 890–901 (2010) 8. Niu, C., Niu, Y., Li, H., et al.: Strawberry pest identification based on image gray histogram. Jiangsu Agric. Sci. 45(04), 169–172 (2017) 9. Xu, G., Mao, H.: A new method for extracting image texture features by Fourier transform. Opto-Electron. Eng. 11, 55–58 (2004) 10. Nouri, M., Nasehi, B., Goudarzi, M., et al.: No-destructive evaluation of bread staling using gray level co-occurrence matrices. Food Anal. Meth. 11(12), 3391–3395 (2018) 11. Tsai, D.-M., Molina, D.E.R.: Morphology-based defect detection in machined surfaces with circular tool-mark patterns. Measurement 134, 209–217 (2019) 12. Steger, C., Ulrich, M., Wiedemann, C.: Machine Vision Algorithms and Applications. Wiley-Vch, Weinheim (2017) 13. Steger, C.: Similarity measures for occlusion, clutter, and illumination invariant object recognition. In: 23rd DAGM Symposium (2191), p. 148 (2001)

Author Index

A An, Xianghua, 28 B Bao, Hong, 1 Bao, Yudong, 12, 518, 1070, 1082, 1093 Bu, Wanghui, 28 C Cai, Wenzhe, 1109 Cao, Guanqun, 1030 Chen, Bowen, 41 Chen, Chao, 394 Chen, Jianwu, 310 Chen, Jing, 28 Chen, Liang, 41 Chen, Long, 52 Chen, Shishi, 394 Chen, Tao, 615 Chen, Weifang, 592 Chen, Xiaojian, 12 Chen, Xingbin, 63 Chen, Yinping, 898 Chen, Yuliang, 477 Chen, Zhigao, 1136 Chen, Zhiya, 274 Cheng, Guanghua, 546 Cheng, Xianfu, 84 Cheng, Xiaole, 888 Chu, Xingpeng, 102 Cui, Lei, 371 Cui, Sihai, 518 Cui, Yan, 202

D Di Ke, Qing, 1 Dixit, Uday Shanker, 102 Dong, Changbin, 447 Dong, Yafan, 125 Dong, Yahong, 139 Dou, Hao, 41 Du, Chuanming, 151 Du, Jinfu, 162 F Fan, Qingrong, 918 Fan, Weipeng, 634 Fan, Xiaojie, 1109 Fang, Laixin, 28

G Gao, Changqing, 990, 1002 Gao, Jian, 380 Gao, Jianshe, 749, 1136 Gao, Xianming, 170 Gao, Yiteng, 162 Gao, Yu, 214 Ge, Chang, 785 Gong, Qingshan, 1054 Gu, Chao, 729 Gu, Peihua, 102 Gu, Xiaoshan, 508 Guo, Hong, 189 Guo, Huiqiang, 243 Guo, Shanshan, 877 Guo, Sheng, 1

© Springer Nature Singapore Pte Ltd. 2020 J. Tan (Ed.): ICMD 2019, MMS 77, pp. 1151–1154, 2020. https://doi.org/10.1007/978-981-32-9941-2

1152 H Han, Jianggui, 615 Hao, Pengyu, 170 Hao, Weina, 274 He, Bin, 847 He, Hongjun, 202 He, Liqun, 12 He, Yingbo, 310 Hong, Jun, 1124 Hou, Jiarui, 229 Hou, Yi, 888 Hu, Chengzhu, 952 Hu, Mingmao, 1054 Hu, Qingchun, 63 Hu, Qiu, 288 Huang, Haijun, 223 Huang, Jingkai, 28 Huang, Kang, 769 Huang, Ming, 288 Huang, Xin, 229, 602 Huo, Xiangyu, 456 J Ji, Xiaomin, 697, 864 Jiang, Chao, 424 Jiang, Fan, 253, 477 Jiang, Haixiang, 267 Jiang, Lanfang, 274 Jiang, Wei, 977 Jianwei, Wang, 669 Jin, Miao, 623 Jin, Xiaoyi, 1010 Jin, Zhenan, 811, 823 K Kong, Xiangzhan, 832 L Li, Li, Li, Li, Li, Li, Li, Li, Li, Li, Li, Li, Li, Li, Li, Li,

Chen, 546 Fuxing, 302 Hongxin, 977 Liansheng, 310 Lin, 325 Long, 708 Meng, 708 Mengli, 466 Mengru, 729 Mengyang, 288 Pengxiang, 214 Ronghua, 623 Ruizhen, 189 Shipei, 342 Tian, 354 Xia, 518

Author Index Li, Xiaopeng, 214 Li, Xiaozhen, 560 Li, Xiaozhou, 944 Li, Ying, 371 Li, Yuanyuan, 1124 Li, Zhaolong, 1018 Liang, Junlang, 380 Liang, Pinghua, 1109 Liang, Xichang, 602 Liao, Fulin, 447 Lin, Qizhang, 394 Lin, Wenzhou, 697, 944 Liu, Beibei, 466 Liu, Chao, 412 Liu, Chenghao, 990 Liu, Geng, 151 Liu, Guifeng, 93 Liu, Jihong, 310 Liu, Jingfei, 424 Liu, Junqi, 151 Liu, Kai, 162 Liu, Lu, 113 Liu, Nan, 546 Liu, PinKuan, 288 Liu, Wei, 125, 1109 Liu, Wen, 243 Liu, Wenguang, 412 Liu, Wenjin, 904 Liu, Xiaomin, 41 Liu, Xinyu, 647 Liu, Yang, 795 Liu, Yongping, 447 Liu, Zhanqiang, 52, 647 Liu, Zhuli, 456, 466 Liu, Ziruo, 602 Liu, Zongmin, 1109 Long, Xiangyun, 424 Lu, Chenhui, 202 Lu, Haoran, 477 Lu, Jiajie, 719 Lyu, Zhipeng, 493 M Ma, Ning, 499 Ma, Shangjun, 151 Mei, Zhiwu, 310 N Niu, Qichen, 877 P Pan, Chao, 508 Pan, Chengyi, 12, 518, 1030, 1044 Pan, Jianye, 243

Author Index Pan, Peidao, 769 Pei, Zijian, 170 Q Qi, Xiaolong, 477 Qiao, Zhi, 944 Qin, Deng, 354 Qu, Chenxi, 531 R Ren, Bing, 647 Ren, Xuezhuang, 546 Ren, Yun, 274 S Shang, Junzhi, 499 Shang, Yuejin, 139 Shen, Jiacheng, 686 Shen, Jian, 253 Shen, Xuehui, 804 Shen, Yusu, 592 Sheng, Dongping, 560 Shu, Xin, 274 Su, Chuan, 592 Su, Hua, 570 Su, Xiao, 971 Sun, Guan, 202 Sun, Peng, 592 Sun, Shifeng, 1002 Sun, Yao, 229, 602 T Tan, Runhua, 125 Tang, Dayong, 113 Tang, Dunbing, 342 Tang, Qian, 1109 Tao, Lei, 971 Tian, Maopeng, 623 Tian, Shengyang, 1054 Tian, Yingzhong, 708 Tong, Yuanqi, 1030, 1044 W Wan, Liyun, 84 Wan, Yi, 229, 602, 647 Wan, Zhiyuan, 898 Wang, Anran, 1010 Wang, Baolin, 804 Wang, Baosheng, 508 Wang, Chaowen, 223 Wang, Dameng, 634 Wang, Fenggang, 394 Wang, Hepeng, 518 Wang, Hongwei, 647

1153 Wang, Jianbin, 661 Wang, Lielong, 769 Wang, Linqiang, 1093 Wang, Mulan, 508 Wang, Qi, 342 Wang, Ruiqin, 125 Wang, Xiang, 729 Wang, Xinyue, 1082 Wang, Xupeng, 325, 697 Wang, Yaobin, 412 Wang, Yazhen, 686 Wang, Yiquan, 719 Wang, Yongfeng, 832 Wang, Yuan, 760 Wang, Zhengrong, 162 Wen, Jinfeng, 253 Wu, Chaoqun, 904, 918 Wu, Ningning, 189 Wu, Tong, 708 Wu, Xiaoguang, 456 Wu, Yangdong, 719 Wu, You, 795 Wu, Yuemin, 1054 Wu, Yujin, 749, 1136 X Xi, Ying, 729 Xia, Xie, 740 Xiang, Jingzhong, 518, 1070, 1093 Xiao, Bo-xin, 785 Xiao, Qian, 971 Xiao, Zhongmin, 477 Xin, Chuanfu, 749, 1136 Xiong, Fenfen, 394 Xu, Kelin, 760 Xu, Nan, 760 Xu, Rui, 769 Xu, Shi-yi, 785 Xu, Zhenghe, 990, 1002 Xue, Yan-min, 785 Xue, Yanmin, 795, 864 Xue, Yunna, 804 Y Yan, Ke, 1124 Yang, Bo, 499, 990, 1002 Yang, Hexu, 214 Yang, Jing, 832 Yang, Jingjing, 1010 Yang, Liang, 531 Yang, Lijun, 546 Yang, Peilin, 888 Yang, Qin, 669 Yang, Sen, 877

1154

Author Index

Yang, Shuai, 189 Yi, Guodong, 811, 823 Yin, Bichao, 223 Yin, Jishu, 661 Yin, Peng, 531 Yin, Tingting, 1124 You, Zhuan, 466 Yu, Mingzhi, 647 Yu, Qianyi, 847 Yu, Shuaihong, 686 Yuan, Chengren, 93 Yue, Deyu, 634 Yue, Huihui, 686 Yue, Yiling, 243 Z Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang,

Chunmei, 864 Chunqiang, 325, 697, 864 Gongxue, 170, 877 Guangguo, 1054 Hanxiao, 310 Jian, 102 Jianmin, 669 Jindi, 380 Jiye, 354 Lanyu, 380 Le, 354 Pan, 1124 Peng, 125 Shaoju, 811, 823

Zhang, Shuyou, 274 Zhang, Weihua, 354 Zhang, Wenqun, 93, 615 Zhang, Xiao, 647 Zhang, Xiujuan, 623, 634 Zhang, Xugang, 888 Zhang, Xu-yang, 785 Zhang, Zhao, 1070 Zhang, Zhe, 371 Zhao, Fengxia, 749, 1136 Zhao, Guangtong, 380 Zhao, Guoru, 832 Zhao, Xiaohua, 531 Zhao, Yanling, 12, 518, 1070, 1082, 1093 Zhong, Gengjun, 380 Zhou, Hao, 310, 456 Zhou, Jian, 84 Zhou, Qi, 904, 918 Zhou, Sizhu, 493 Zhou, Weiqi, 28 Zhou, Yihui, 795, 944 Zhu, Chune, 63 Zhu, Chunxia, 952 Zhu, Haihua, 342 Zhu, Haiyan, 223, 971 Zhu, Rupeng, 560 Zhu, Tao, 253 Zhu, Yongsheng, 1124 Zou, Li, 977 Zuo, Fuchang, 310