Computational Design and Digital Manufacturing 3031211669, 9783031211669

Table of contents :
Preface
Contents
Generative Design in Architecture: From Mathematical Optimization to Grammatical Customization
1 Introduction
1.1 Navigation and Mapping
1.2 Generative Design Systems
2 Theoretical Background
3 Framework
3.1 Discrete Design
3.2 Gradients for Disaggregated Design Evaluation
3.3 Design Space Navigation
4 Generative Design Methodologies
4.1 Mathematical Generative Design
4.2 Grammatical Generative Design
4.3 Gamified Generative Design
4.4 Generative Models for Data-Driven Generative
5 Conclusion
References
Augmented Reality-Driven Prototyping for Error Elimination During Computational Design and Digital Fabrication
1 Introduction
2 Relevant Works
3 Methodology
3.1 Computational Design to Digital Fabrication
3.2 Manual Formwork Adjustment Results Evaluation
3.3 AR-Driven Formwork Adjustment Results Evaluation
4 Results and Discussion
4.1 Results Based on Manual Adjustment of Formworks
4.2 Results Based on AR-Driven Adjustment of Formworks
5 Conclusions
References
Design of Gesture-Controlled Interface for Mechatronic Systems: A Computational Approach
1 Introduction
2 State of the Art
3 Methodology
3.1 Raw Data Video Capturing
3.2 Gesture Recognition
3.3 Feature Extraction
3.4 Commands Define—Feature Combination
4 Application
4.1 Human Mechatronic System Interface
5 Conclusions
References
Topology Optimization Utilizing Density-Based Approach for Additive Manufactured Components: A Case Study of an Automotive Brake Caliper
1 Introduction
2 Topology Optimization Processes
2.1 Density-Based Approach
2.2 Discrete/Truss-Based Approach
3 Use Case: Topology Optimization of Brake Caliper
3.1 Original Design of the Brake Caliper
3.2 Topology Optimization of Brake Caliper via Density-Based Approach
4 Conclusions
References
Rethinking the Brick: Developing a File to Fabrication Framework for Mortar-Free, Robotic Masonry Wall Assembly
1 Introduction
2 Background and Literature
3 Materials and Methods
4 Verification Through Design Experiments
4.1 Design Experiment 1
4.2 Design Experiment 2
4.3 Design Experiment 3
5 Findings
6 Conclusions
References
Knowledge-Based Design: A Function-Knowledge Reasoning Model for Product Conceptual Design
1 Introduction and Definition
1.1 Product Conceptual Design
1.2 User Requirement
1.3 Product Function
1.4 Knowledge
1.5 KBS and KBD
2 Product Conceptual Design with Knowledge and Methods
2.1 Knowledge in Product Conceptual Design
2.2 Some Design Methods Support Product Conceptual Design
3 A Function-Knowledge Reasoning Model
3.1 The Process of Function-Knowledge Reasoning Model
3.2 The Similarity Algorithm of Function-Knowledge Reasoning Model
4 A Knowledge-Based Product Conceptual Design System
4.1 Architecture of the System
4.2 Knowledge Management Platform
4.3 Function Modules and Relationships
4.4 Operation Process of the System
4.5 Interface of the System
5 Conclusion
References
Equation Driven Micro-Milling of 2D Free Form Models and Off-Line G-code Generation for Variable Feed Machining
1 Introduction
2 Equation Driven Designs and G-code Creation
2.1 Micro-Impeller Model
2.2 Spur Micro- Gear Model
2.3 Methodology for Equation Driven Free-Form Part Design and Offline G-code Generation for Variable Feed Rate Machining
2.4 Automated Design and G-code Generation for Parametrically Represented Curved Toolpaths for Curvature-Based Variation of Machining Feed Rate
3 Application of the Developed Methodology
3.1 Constant Feed CNC Micromachining Using CAM Software
3.2 Variable Feed CNC Machining of Curved Toolpaths
4 Results of Variable Feed Methodology Performance in Micro-Milling
5 Discussion
6 Conclusions
References
Study of the Topography of Face Milled Surfaces Using CAD-Based Simulation
1 Introduction
2 Face Milling Simulation
3 Validation
4 Parameter Investigation
5 Conclusions
References
Study on Design and Manufacturing of an Engine Block Using Digital Tools
1 Introduction
2 Design for Manufacturability and Assembly
3 Design for Disassembly
4 Virtual Assembling of Engine Block
5 Digital Collision Check
6 Tool Accessibility
7 Virtual Engineering Used for the Engine Block
8 Additive Manufacturing of the Engine Block
9 Conclusions
References
Automatization of CAD Model Development of Slewing Bearing Using Solid EdgeTM
1 Introduction
2 Methodology
3 Development of Application
4 Conclusions
References
CAD-Based Application in VBA for Tool’s Profiling
1 Surface Generation by Enwrapping
1.1 Introduction
1.2 Theoretical Fundaments
1.3 Modelling of Enwrapping Process
2 The Virtual Pole Method for Tool’s Profiling
2.1 Method’s Theoretical Fundaments
2.2 Advantage of Virtual Pole Method
2.3 Tools Profiling, Using the Virtual Pole Method
2.4 Tools Profiling with CATIA™ VBA Programming.
3 Conclusions
References
Index

Citation preview

Management and Industrial Engineering

Panagiotis Kyratsis Athanasios Manavis J. Paulo Davim   Editors

Computational Design and Digital Manufacturing

Management and Industrial Engineering Series Editor J. Paulo Davim, Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal

This series fosters information exchange and discussion on management and industrial engineering and related aspects, namely global management, organizational development and change, strategic management, lean production, performance management, production management, quality engineering, maintenance management, productivity improvement, materials management, human resource management, workforce behavior, innovation and change, technological and organizational flexibility, self-directed work teams, knowledge management, organizational learning, learning organizations, entrepreneurship, sustainable management, etc. The series provides discussion and the exchange of information on principles, strategies, models, techniques, methodologies and applications of management and industrial engineering in the field of the different types of organizational activities. It aims to communicate the latest developments and thinking in what concerns the latest research activity relating to new organizational challenges and changes world-wide. Contributions to this book series are welcome on all subjects related with management and industrial engineering. To submit a proposal or request further information, please contact Professor J. Paulo Davim, Book Series Editor, [email protected]

Panagiotis Kyratsis · Athanasios Manavis · J. Paulo Davim Editors

Computational Design and Digital Manufacturing

Editors Panagiotis Kyratsis Department of Products and Systems Design Engineering University of Western Macedonia Kozani, Greece

Athanasios Manavis Department of Products and Systems Design Engineering University of Western Macedonia Kozani, Greece

J. Paulo Davim Department of Mechanical Engineering University of Aveiro Aveiro, Portugal

ISSN 2365-0532 ISSN 2365-0540 (electronic) Management and Industrial Engineering ISBN 978-3-031-21166-9 ISBN 978-3-031-21167-6 (eBook) https://doi.org/10.1007/978-3-031-21167-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The present book intents to cover a variety of topics that deal with computational design and digital fabrication. We aimed in following an approach that combines both the design process using high end digital tools and the manufacturing with new technologies that are based on new technologies. We have managed to incorporate a number of directions, i.e., CAD-based design automation and applications, parametric and algorithmic design, generative design, additive manufacturing and prototyping, product design applications and methodologies, modern machining, materials, manufacturing automation, topology optimization, augmented reality, and mechatronics. A series of state-of-the-art chapters were gathered and deal with the following eras. The first chapter “Generative Design in Architecture: From Mathematical Optimization to Grammatical Customization” provides a methodological overview of generative design in architecture. It highlights the commonalities among the mathematical optimization methods for topology optimization, the shape optimization and the agent-based design games. The second chapter “Augmented Reality-Driven Prototyping for Error Elimination During Computational Design and Digital Fabrication” proposes a methodology for small-scale prototyping using computational design and digital fabrication by applying augmented reality. Its aim is to eliminate the errors that appear in each case. The third chapter “Design of Gesture-Controlled Interface for Mechatronic Systems: A Computational Approach” focuses on applying a computational approach when designing and developing an interface for interacting with a mechatronic system through gestures. Machine vision techniques are used for recording and locating the gesture through an image capture system. The fourth chapter “Topology Optimization Utilizing Density-Based Approach for Additive Manufactured Components: A Case Study of an Automotive Brake Caliper” applies the principles and methods of topology optimization, when analyzing a novel case study dealing with the design of a topology optimized brake caliper, when intended to be manufactured using additive manufacturing (design for additive manufacturing). The fifth chapter “Rethinking the Brick: Developing a File to Fabrication Framework for Mortar-Free, Robotic Masonry Wall Assembly” deals with the creation of a file-to-fabrication framework for mortar-free robotic assembly of masonry walls. It v

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focuses on the relationship between the individual brick geometry and the complete structure under consideration. The sixth chapter “Knowledge-Based Design: A Function-Knowledge Reasoning Model for Product Conceptual Design” uses a functionknowledge reasoning model for product conceptual design that constructs a mapping relationship between subfunctions after decomposition and granular clustered knowledge. It focuses on knowledge-based product conceptual design that helps identify critical issues and generates new conceptual solutions through configuration. The seventh chapter “Equation Driven Micro-Milling of 2D Free Form Models and Off-Line G-code Generation for Variable Feed Machining” deals with parametrically designed and machined out of brass spiral type and micro-gear 2D freeform models. The result is achieving improved surface quality, machining time and process efficiency. The eighth chapter “Study of the Topography of Face Milled Surfaces Using CAD-Based Simulation” presents a simulation model that is able to deal with improved machining in a CAD-based simulation platform. The outcome includes the resulting surface topography as well as the surface roughness metrics. The ninth chapter “Study on Design and Manufacturing of an Engine Block Using Digital Tools” offers access to the implementation of digital tools, when designing and manufacturing a lightweight four stroke engine block for kart competition. The tenth chapter “Automatization of CAD Model Development of Slewing Bearing Using Solid EdgeTM ” presents a novel approach in CAD-based automated development of slewing bearings. 2D sketches and their dimensions are linked to a lookup table and thus resulting in the automatic creation of the 3D solid models. All the appropriate operations are linked to the application developed for this purpose. The eleventh chapter “CAD-Based Application in VBA for Tool’s Profiling” allows profiling of tools such as rack-gear tool, gear shaped cutting tool or rotary cutter via visual basic for applications (VBA) and the implementation of the “virtual pole” method. The editors acknowledge the aid of Springer Publications and express their gratitude for this opportunity and for their professional support. The editors also express their gratitude to all the chapter authors for their availability and for delivering their high-quality research work. Kozani, Greece Kozani, Greece Aveiro, Portugal October 2022

Panagiotis Kyratsis Athanasios Manavis J. Paulo Davim

Contents

Generative Design in Architecture: From Mathematical Optimization to Grammatical Customization . . . . . . . . . . . . . . . . . . . . . . . . Pirouz Nourian, Shervin Azadi, and Robin Oval

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Augmented Reality-Driven Prototyping for Error Elimination During Computational Design and Digital Fabrication . . . . . . . . . . . . . . . . Odysseas Kontovourkis

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Design of Gesture-Controlled Interface for Mechatronic Systems: A Computational Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Apostolos Tsagaris, Maria Economou, Athanasios Manavis, and Panagiotis Kyratsis Topology Optimization Utilizing Density-Based Approach for Additive Manufactured Components: A Case Study of an Automotive Brake Caliper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nikolaos Kladovasilakis, Georgios Kosmidis, Panagiotis Kyratsis, and Dimitrios Tzetzis

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Rethinking the Brick: Developing a File to Fabrication Framework for Mortar-Free, Robotic Masonry Wall Assembly . . . . . . . . . . . . . . . . . . . . 107 Asterios Agkathidis, Yang Song, and Jiangyang Zhao Knowledge-Based Design: A Function-Knowledge Reasoning Model for Product Conceptual Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Yiwei Jiang, Xin Guo, Ying Liu, and Wu Zhao Equation Driven Micro-Milling of 2D Free Form Models and Off-Line G-code Generation for Variable Feed Machining . . . . . . . . . 141 Ch. Tzivelekis and A. A. Krimpenis

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Study of the Topography of Face Milled Surfaces Using CAD-Based Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Nikolaos Tapoglou, Chara Efstathiou, Anastasios Tzotzis, and Panagiotis Kyratsis Study on Design and Manufacturing of an Engine Block Using Digital Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Sever-Alexandru Haba and Gheorghe Oancea Automatization of CAD Model Development of Slewing Bearing Using Solid EdgeTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Rafael Gella-Marín, César García-Hernández, and José-Luis Huertas-Talón CAD-Based Application in VBA for Tool’s Profiling . . . . . . . . . . . . . . . . . . 217 Virgil Gabriel Teodor, Georgiana Alexandra Moro¸sanu, and R˘azvan Sebastian Cr˘aciun Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Generative Design in Architecture: From Mathematical Optimization to Grammatical Customization Pirouz Nourian, Shervin Azadi, and Robin Oval

This chapter provides a methodological overview of generative design in architecture, especially highlighting the commonalities between three separate lineages of generative approaches in architectural design, namely the mathematical optimization methods for topology optimization and shape optimization, generative grammars (shape grammars and graph grammars), and [agent-based] design games. A comprehensive definition of generative design is provided as an umbrella term referring to the mathematical, grammatical, or gamified methodologies for systematic synthesis, i.e. derivation, itemization, or exploration of configurations. Among other points, it is shown that generative design methods are not necessarily meant to automate design but rather provide structured mechanisms to facilitate participatory design or creative mass customization. Effectively, the chapter provides the theoretical minimum for understanding generative design as a paradigm in computational design; demystifies the term generative design as a technological hype; shows a precis of the history of the generative approaches in architectural design; provides a minimalist methodological framework summarising lessons from the three lineages of generative design; and deepens the technological discourse on generative design methods by reflecting on the topological constructs and techniques required for devising generative systems or design machines, including those equipped with Artificial Intelligence. Moreover, the notions of discrete design and design for discrete assembly are discussed as P. Nourian (B) · S. Azadi Research Group Urbanism and Urban Architecture, Department of Built Environment, Eindhoven University of Technology, Het Kranenveld 8, 5612 AZ Eindhoven, The Netherlands e-mail: [email protected] S. Azadi e-mail: [email protected] R. Oval Form Finding Lab, Department of Civil and Environmental Engineering, Princeton University, 59 Olden St, Princeton, NJ 08540, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6_1

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precursors to the core concept of design as decision-making in generative design, thus hinting to avenues of future research in manufacturing-informed combinatorial mass customization and discrete architecture in tandem with generative design methods.

1 Introduction What is generative design and why does it matter? What problem can it solve for society? This book chapter is to answer these questions in addition to providing a technical overview of the most important generative design processes right ahead of the frontier of the state of the art of generative design technologies. Here, we provide a brief definition of generative design processes given their applications. As shall be illustrated, contrary to the common belief, generative design processes are not necessarily meant to automate design processes, albeit except for generative models used for [procedural] content generation in the games and entertainment industry. One of the main contributions of this piece is to show the commonalities of three distinct sorts of generative design processes (mathematical derivation, grammatical itemization, and gamified exploration) in terms of similarities in their methodologies (algorithms) and representations (data structures). However, the clear distinction between applications of generative design to design derivation, design customization, and participatory design problems is key for avoiding the commonplace reduction of computational design to design automation. In what follows, we start with a brief introduction to the generative design spectrum; revisit three types of computational design problems (optimization, diversification, and consensus-building) and their inherent complexities; take a glance at the key role of discrete design representation in generative design; revisit some basic definitions and terminological matters essential to understanding the generative design paradigm, and then present three types of generative design methodologies, illustrated in Fig. 1, in-depth:

Fig. 1 Spectrum of archetypal generative design processes

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• Generative design in the sense of form finding or design discovery through mathematical derivation (topology optimization and shape optimization); • Generative design in the sense of writing in a pattern language or design customization through grammatical itemization (generative grammars); • Generative design in the sense of co-creating or participatory design through gamified exploration (cellular automata, serious gaming and multi-actor spatial decision support systems). The theoretical underpinnings of practice in these three lines of work can be traced to the core concepts of design sciences [1] and the paradigm of design as a matter of “rational problem solving” [2, 3]. The mathematical derivation methods can be traced back to topology optimization [4] and algebraic shape optimization (e.g. through the Force Density Method introduced by Schek [5]). Grammatical itemization methodologies can be traced back to the linguistic analogy in space syntax [6], pattern language [7], and shape grammars [8], all of which seem to have been inspired by Chomsky’s seminal book on syntax and formal grammars [9]. Later, Lindenmayer systems [10] and cellular automata of Von Neumann, especially those in the style of the [Solitaire] Game of Life of John H. Conway (see a recent compendium [11]) and Stephen Wolfram [12] as well as the ideas of William J. Mitchel [13], Jonathan Cagan [14], and Kristina Shea [15, 16] enhanced the grammatical generative design literature and emboldened it as an approach for promoting combinatorial design creativity. The idea of gamified exploration as a form of generative design can be traced back to multiple ideas, namely using multi-actor systems in search of a satisfactory equilibrium through group decision-making and multi-criteria decision analysis introduced by Herbert A. Simon [17], the notion of generative sciences put forward by Joshua Epstein [18] (i.e. complexity sciences driven by simulations), and the idea of Markovian design machines introduced by Michael Batty [19]. The particular ideas of building “design games” and “configurators” can be traced back, respectively, to the works of Henry Sanoff [20] and Yona Friedmann [21]. Generative design is a paradigm in computational design rooted in the paradigm of design as rational problem solving based on the ideas of Herbert a. Simon, q.v., the theoretical discussion on design paradigms by Kees Dorst on this matter [2, 22]. As an adjective, the term “generative” historically originates from the idea of generative grammars by Chomsky, on the one hand, and the notion of generating (deriving or discovering) a definite spatial design (typically for a mechanical structure) from given design requirements using topology optimization or shape optimization (a.k.a. form-finding) on the other hand. While the former sense (the grammatical definition of generative design) has been well-known in the context of architecture since at least the 1980s, the latter (i.e. the derivational definition of generative design based on gradients or partial differentials a.k.a. sensitivities, particularly in topology optimization) has been known in mechanical and structural engineering since the late 1990s (while differential/numerical shape optimization can be traced back to the 1970s, e.g. the force density method by Schek [5] or even much earlier, actually to the nineteenth century if we consider physical or geometric shape optimization methods

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of Gaudi or the graphic statics method as formulated by James Clerk Maxwell). However, the new surge of popularity of the term generative is mainly due to the more recent popularity of the topology optimization approach since the 2010s for large-scale architectural/structural applications. The idea of formulating discrete and multi-player design games as generative design systems is particularly our proposition as a mathematical formulation of multiple ideas such as those of Henry Sanoff for design games [20] and Yona Friedman for design configurators [21]. Additionally, another recent motivation for formulating design games has been the use of artificial intelligence (especially reinforcement learning) for playing games (see e.g. the use of RL for spatial configuration [23]), or more specifically multi-agent systems and cellular automata for playing simulation games similar to the MAS + CA system proposed by Ligtenberg et al. [24] and König [25] for urban planning and design as well as the “GoDesign” generative design framework for architectural design [26]. Here, we propose a comprehensive definition that encompasses the three approaches mentioned above: generative design processes are simulation-driven, feed-forward, gradual, discrete design processes that can generate a navigable artificial design space of valid, optimal, consensual, or idiomatic design alternatives respectively through design equations, design games, or design grammars (see Fig. 1). All generative design methodologies in our definition start from an explicitly “navigable” representation of the design problems (constraints, moves, objectives, and the structure of the state-space and/or the design space). What distinguishes generative design approaches from genetic evolutionary searches, mistakenly referred to as generative design, is this very explicit nature of the design space exploration and the explainable navigability of the design spaces in the generative design approaches, except for the “genetic programming” approach of Harding and Shepherd [27] due to its explicit formulation of design spaces based on discrete design variables.

1.1 Navigation and Mapping Inter alia, the importance of having an explicitly navigable picture of the design space (and its dual performance space a.k.a. performance landscape) is key to the ability of a designer for explaining and justifying design decisions. Two dual problems can be identified in this regard, which can reveal the complexity of design endeavours from a mathematical stance: the problem of mapping the multiplex associations of many design choices to their few integral consequences (dubbed here as the primal evaluation problem or the mapping problem in a manner of speaking) and the more challenging problem of figuring out what choices must be made to attain a specific multitude of performances or quality levels that can be regarded as the eventual consequences of the design choices (dubbed here as the dual design problem or the navigating problem in a manner of speaking) (see Fig. 2). The navigability of the design spaces requires the explicit modelling of the relations between one design alternative and another. Such relations can be referred to as design updates (based on gradient descent), design rules (as in grammatical rules)

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Fig. 2 Duality of mapping and navigation problems in generative design

or design moves (as in moves of a game) defining how one can get from one design alternative to another. Navigability also implies that we can have a rigorous sense of topology in our design space as to which we can measure similarity or dissimilarity between designs, depending on the number of operations, rules, or moves that set them apart. In other words, generative design processes are inherently topological workflows. The importance of this explicit notion of similarity can be understood by considering the key role of two sorts of similarities between designs that would provide for clustering or manifold mapping of design spaces for simplifying cognitive decision-making for human designers: similarity between designs in the highdimensional design [decision] space and similarity between designs in terms of the outcomes of interest in the performance space (referred to as the vectors of choices and consequences in Fig. 2).

1.2 Generative Design Systems Three archetypical generative design systems are identified here to define the poles of a broad spectrum (as introduced in Fig. 1): • Design Equations: Design optimization through mathematical derivation, in search of optima, exemplified in topology optimization and shape optimization processes; • Design Grammars: Design customization through grammatical itemization, in search of idiomata, exemplified in formal grammars, L-systems, and generative grammars (for shape rewriting or graph rewriting); • Design Games: Participatory design through gamified exploration, in search of [Nash] equilibria or another notion of satisfaction of multi-actor multi-criteria decision analysis problems.

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While all of these approaches are feed-forward and gradual as compared to blackbox feedback optimization, it can be noted that the method of reasoning in grammatical design itemization is akin to forward induction and that the method of reasoning in mathematical design derivation is akin to backward induction (i.e. working our way backwards from the target objective(s) converging to a particular vector of decision variables as opposed to the divergent expansion the design catalogue in the grammatical or rule-based itemization methods). A similar comparison can be made in terms of the depth-first-search and breadthfirst-search methods being analogous respectively to the design space navigation methods in mathematical design derivation and grammatical design itemization. In our proposed framework, gamified design exploration methods can exploit both types of navigation mechanisms (hereinafter referring to search and induction processes). Even though these three types of generative design methods cover the main applications of generative design, there is a much newer technology that is rapidly developing with excellent potential for the performance-based generative design that is yet to be explored: generative models. Towards the end of the chapter, we shall reflect on the utility of generative models for augmenting performance-based generative design with artificial intelligence.

2 Theoretical Background As stated by Batty [19], if any progress is to be made in systematic design, it will require to be based on an explicit and unambiguous statement of the design framework (states, goals/objectives, moves, constraints). We argue that it is necessary to have a framework for formulating design problems to be able to provide for rigorous progress in computational design, systemic change in practice and pedagogy of computational design for the betterment of methods in terms of explainability of processes and justifiability of the results in terms of the triad of sustainable development goals (balanced social-economic equity, social-environmental comfort, and environmental-economic resource efficiency of solutions). Furthermore, as has been extensively argued in the design research literature, one can quickly identify the difficulty of design as a matter of decision-making in that the designer is supposed to arrive at a detailed conclusion about the definite geometry of a building (colloquially referred to as the “form” of a building/structure) while they are only given an abstract and often vague description of the requirements, wishes, and objectives (collectively referred to as the “function” of a building/structure in the jargon of AEC). The typical characterization of design problems as ill-defined or even wicked is well-known and rather overstated [2, 3]. Revisiting these difficulties in terms of the complexity of decision-making, we can identify four types of complexities that make architectural design problems especially hard (see Fig. 3). The history-old difficulty of transiting from abstract functions to concrete forms has led to a design culture that is arguably over-reliant on intuition and the socalled tacit knowledge of the designers, which can be characterized by the so-called

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Fig. 3 Doubly complex nature of design problems

logical leap of design [28]. This leap refers to the difficult, unexplainable, and often unjustifiable transition that can be considered as the intuitive or creative synthesis process that appears to an external observer as jumping to a conclusion or solution without even explicitly formulating the problem. This gap of reasoning, concerning the dichotomy of the form and function of a design, can also be seen in the descriptive function-behaviour-structure (FBS) design framework by John Gero et. al. [29]. This ontological framework identifies some typical representations starting from the most abstract design requirements (R) to the most concrete eventual design description (D) and the typical actions leading back and forth to four intermediary representations of a design process: a process of “formulation” of the function (F) and the expected behaviour [performance] (Be) of the system, a process of “synthesis” leading to the proposed/designed structure [form] (S), a process of “analysis” revealing the actual behaviour of the structure (Bs), and a process of “evaluation” for comparing the expected behaviour with the actual behaviour analysed (simulated) on the structure to assess how appropriate is the particular structure proposed in a design iteration, followed by a process of “documentation” detailing the proposed structure [Form] into a design description (D). The description also contains three “reformulation” processes as to which design processes are sometimes referred to as “co-evolution of problems and solutions” [30]. Echoing the genuine appeal of Yona Friedman’s “Towards a Scientific Architecture”, we argue that the “Sciences of the Artificial” [31] in their plurality, as the decision sciences focused on how to change the current state of things and environments towards better states, are key to such a scientific transition. Contrary to the reductionist connotation of the term scientific, the non-reductionist notion of “generative sciences”[18] takes it for granted that the matter of mapping a myriad of choices to a few consequences is an endeavour in the realm of complexity sciences that can be dealt with through utilizing simulations, be it simulations based on first principles often encapsulated in partial differential equations, stochastic or deterministic simulations of design moves on a decision tree of grammatical rules (exhaustiveenumerative search for cataloguing or probabilistic approaches such as the wave function collapse [32]), agent-based simulations, Markov chains, or Markov decision

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processes, as well as simulation games that can reveal the emergence of “collective intelligence” [33].

3 Framework While there is no general way of proving that a design is the best it could possibly be, generative design can at least bridge the logical leap of design by methodically structuring and mapping the design space and its dual performance space, starting with defining the requirements, defining valid or meaningful design moves (decisions leading to an identifiable change in the discrete state of a design from one to another), setting explicit quality criteria, and identifying alternatives in the design space through a systematic navigation process to satisfy the set quality criteria in three distinct problem settings (optimization, customization, or participation problems as explained in the Introduction). A generative design framework must explicitly identify the “purpose” of design or the nature of the design problem, as to which we have identified three types of purposes, namely: reaching a unique optimum, producing a plethoric catalogue of idiomatic designs, or reaching a fair/equitable equilibrium in a multi-actor participatory design process. The framework presented here is an extension and elaboration of the GoDesign framework for generative design [26]. However, one can trace back the roots of this inherently discrete generative design framework to the configurational studies of pioneers of computational design such as Lionel March, Philip Steadman and Raymond Matela on discrete design and configurations with Polyominos and William J. Mitchel’s discrete grammatical approach [34, 35].

3.1 Discrete Design The most obvious common feature of the three types of generative processes reintroduced here is their discretized design spaces. While this discreteness is not necessarily carried over to the actual construction of the designed objects (e.g. in topology optimization of small objects), in the relatively large scale of buildings, the discrete design variables can correspond one to one to the actual building blocks. Observe that buildings are too large to be made as really monolithic objects and as such their construction design most probably requires some sort of segmentation (polygonization and polyhedralization). In the discrete architecture paradigm [36], discreteness or jaggedness of the results is not regarded as a limitation but embraced as a digital way of building as an aggregation of discrete modules. Discretization not only brings about advantages for the construction process but also, as a mathematical proviso, provides a discrete notion of an array of design variables that is key to generative design. As can be seen in the context of the three archetypical generative design processes, such

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a discretization of design variables makes the mathematical, computational, and play processes very straightforward: 1. In topology optimization, the discrete material design variables make a vector of design variables x ∈ (0, 1]n , as to which the sensitivities (encapsulated in a gradient vector) can be efficiently computed. Similarly, in shape optimization, a discrete mesh or network model allows for the straightforward characterization of the decision variables as the coordinates of a number of distinct vertices, given a constant topology for the mesh or the network, as well as the discretization of differential operators required for shape optimization (e.g. the gradient, divergence, and Laplacian operators). 2. In grammatical design, the grammar is effectively a system of graph-rewriting or mesh-rewriting that depends on the identification of distinct topological conditions (antecedent) on the graph neighbourhoods or mesh cells that should lead to their rewriting (consequent) based on a discrete set of topological-geometrical rules. Similar to mesh subdivision and graph simplification procedures, the topological (and thus discrete) identification of predicates and functions make implementing “if this then that” “pattern languages” very straightforward. 3. In gamified design, the discretization of the design space and design moves makes designing as structured, teachable, and score-able as playing board games like Go & Checkers, tile-based games like Dominoes & Anagrams, or construction sets/toys like LEGO & Lincoln Logs. Discrete design moves and game pieces lower the participation threshold for non-expert human players for partaking in decision-making and facilitates the attainment of valid designs and their scores. Additionally, a discrete state space for the game also provides for teaching machines to play these games through reinforcement learning, multiagent systems, or Markovian design machines, all of which require the discrete setup of board games or cellular automata to work. The remarkable success of artificial intelligence (reinforcement learning in particular) in playing retro Atari games [37] and the game Go should provide a convincing motivation in that regard. In summary, generative design is about discrete decision-making. Note that in mathematics, decision problems are binary decision problems. When we formulate the design space as a discrete space we can enumerate design alternatives, and this, inter alia, can allow for measuring the likelihood of one configuration of decisions (a design) or another, and this, in turn, allows for measuring information content based on a measure of entropy as in Shannon entropy, which pertains to the number of questions, e.g. binary questions, that need to be answered to determine the exact state of a design configuration. In other words, even though the design space can still contain infinitely many decisions, at least, in this discrete setting, we have a navigable and countable plethora of designs. Moreover, the similarity of designs can be rigorously modelled in discrete generative design, provided the designs are represented with decision vectors or multiple criteria as performance vectors. While designs can be compared easily in terms of the similarity of their measurable performance/quality consequences, describing the

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similarity of designs in terms of their inner structure, i.e. the similarity of their combinations of choices, is typically harder and depends on the extent of explication of a design space. In the mathematical sense of topology optimization, the similarity between decision variables will be a matter of defining a similarity metric as to an inner product between high-dimensional arrays of density-like decision variables (typically in the form of x ∈ (0, 1]n ). In the most abstract case, when the decisions are all completely discrete, i.e. in the grammatical design sense, the notion of similarity between graphs or meshes is purely discrete and pertains to the number of rules that need to be applied to get from one design to another (the number of design moves or operations in a decision graph). Describing similarity between design states in tile-based design games is similarly explained in [38].

3.2 Gradients for Disaggregated Design Evaluation Evaluation is the backbone of decision-making; it allows one to compare various options for design moves and decide based on the projected consequences. In the general sense, computational performance evaluation mechanisms have existed and been applied in mainstream practices since the 1980s or even since the 1950s (if we take into account the history of the finite element method). However, the specific idea here is to define and formulate evaluations that are disaggregated at the level of discrete design moves. The kind of evaluations that can inform generative design moves are those that can be derived as sensitivities or gradients of the aggregate objective functions with respect to the density of the discrete decision variables determining the relative or absolute existence of some parts in the aggregate design, i.e. if a single objective function can be formulated as a scalar function of a vector decision variable in the form of f (x) in which x := [xi ]n×1 ∈ (0, 1]n , then its gradient vector denoted as ∇ f (x) can be expected to contain relevant information content at the level of each design variable revealing the sensitivity or partial differential of the objective function in question to an infinitesimal change in each one of the design variables corresponding to density (or [the relative existence) of the discrete ] . In the more general case of cells in the design space, i.e. σ := ∇ f (x) = ∂∂xfi n×1 the multi-objective design [problem setting, i.e. a vector objective function of vector ] decision variables f (x) = f q o×1 , the gradient or the vector of sensitivities is gener[ ] [[ ] ] ∂f alized to the Jacobian of the system: J := ∇ f (x) = ∂ xqi = ∇ T f q 1×n . o×n

o×1

Note that also for constrained optimization problems, the method of Lagrange multipliers require one to compute the gradient of the explicitly formulated (equality or inequality) constraints as functions of vector decision variables. Gradual feed-forward progression in design is the hallmark of generative design that is most explicitly achieved by utilizing such gradients in topology optimization and shape optimization (either for making design moves in a manner like the gradient descent or quasi-analytic solutions characterizing the state of equilibrium which

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incorporate the gradients in their formulation, such as the force density method [39]). However, not all the qualities and constraints are easy to formulate explicitly as analytical functions of decision variables. The frontier challenges in the art and science of generative design can be directly bordered by the extent to which one can formulate the objectives and constraints as functions of the decision variables. In other words, emblematically speaking, the central question of generative design is how to navigate in the realm of decision variables with a compass informed by the polarities in the realm of objectives and constraints. In cases where subjective opinions, intangible cultural values, and aesthetics, are to be considered, we eventually have to rely on human judgement for the evaluation process, whether directly by involving humans in the loop or by training neural networks as “function approximators” using AI. Architectural design is almost always concerned with multiple validity constraints and quality criteria as to which the alternatives need to be assessed. Often, such criteria are not commensurate due to their different physical dimensions. Before jumping to the conclusion that architectural design is about multi-objective optimization, we need to observe that in the mathematical sense, speaking of the optimum beyond a single objective can be rather absurd in most cases. Instead, in the general case, the endeavour is directed at finding a satisfactory design that can be characterized either as a hierarchically dissected chain of multiple optimization problems, a diversification problem concerned with the enumeration of valid designs for customization (that is not at all about optimization), or satisfaction of decisionmaking criteria in a multi-actor and/or multi-criteria setting using multi-criteria decision analysis (MCDA).

3.3 Design Space Navigation As stated in our definition, generative design is all about confidently navigating design spaces based on a possibly partial but explainable map of the associations between design choices and their performance consequences. Specifically, however, the navigation strategies differ from one type of generative design to another, primarily because the nature of the design spaces can be very different from one type to another. Considering the most general purpose of design processes in architecture and structural design as forming a particular material distribution or spatial arrangement, we can observe that discrete design is practically about making changes in some meshes (hyper-graphs containing 0D vertices, 1D edges, 2D faces, and possibly 3D cells) in the general form of M = (V , E, F ) for discrete 2D manifolds or M = (V , E, F, C) for discrete 3D manifolds. Without loss of generality, in the most common cases, the faces and cells are respectively triangular–tetrahedral or quadrilateral–hexahedral. Generative design can be described in terms of changes that can be made on such meshes in terms of the positions of vertices or “shape changes”, attributes of

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Fig. 4 Design space navigation for a mesh: changing shape (form), connectivity (topology), and colour (data)

vertices/hyper-edges (edges, faces, cells) or “colouring changes”, or the very set of hyper-edges and possibly the set of vertices or “topology changes”. 0. Shape Space is the space of possible coordinate positions for the vertices of a mesh V = [vi ]n×3 (shape optimization or grammatical design as in shape grammars, protein folding game FoldIt [40]). 1. Colour Space is the discrete material design domain corresponding to the vector/array of decision variables x = [xi ]n×1 , , which is either about integer colours or ambient colours indicating relative density levels (see Fig. 4). 2. Topology Space is the space of possible meshes M = (V , E, F, C), possibly attributed (grammatical design or construction games as a matter of mesh rewriting regulates how one possible design can be changed to another possible design with a distinct topology). The so-called state space of design games in which the design moves are defined could be in the form of the 1st or the 2nd or rarely the 0th type of design spaces defined above, depending on the application. Once the nature of the data points in a design space is explicitly specified, one can think of effective and efficient methods for navigating within a vast design space, considering the nature of informed and directed design moves that can take one design as a data point in a decision space to another. The navigation strategies are later introduced in the specific context of the archetypical generative design methods. This idea of informing design moves in the case of mathematical derivation of designs can be simply understood in terms of gradient descent moves in the decision space. In the case of grammatical design, however, as explained before, the mode of reasoning is forward induction, as to which the idea of evaluation is present at a meta-level informing the design moves in terms of guaranteeing that the grammatical rules result in valid designs. While these categories encompass the most common approaches, there are specific hybrid approaches to design space navigation that do not fit into a single one of such categories, a notable example of which is the Shape Annealing Method by Kristina Shea and Johnatan Cagan (shape annealing = shape grammars + simulated annealing by [16, 41]). However, in the general case, the purpose of grammatical design methods is to produce a navigable catalogue of designs and so, the more explicit use of evaluation is in the feed-forward formulation of design rules that can be guaranteed to result in valid designs. See a spectrum of design space navigation approaches in Fig. 5.

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Fig. 5 Spectrum of design space navigation methodologies and the essential mathematics of generative design

4 Generative Design Methodologies Up to this point, we have discussed the common features of generative design processes in terms of their discreteness, the idea of gradual progression or informed navigation in design spaces, and the key role of simulations (solving partial differential equations using numerical methods, deterministic or stochastic simulation of grammatical rewriting logic, modelling finite-state machines or automata, or simulation games). In what follows, we go into the specifics of each of the mathematical, grammatical, and gamified generative design methodologies as introduced in the generative design spectrum (see Fig. 1). In the last part of this section, we briefly review the potential of generative models in artificial intelligence for performance-aware architectural design applications.

4.1 Mathematical Generative Design In this section, we explain the foundations of the generative design processes that can be categorized as being mathematical as to their commonalities in terms of derivation of forms (topologies and geometries, a.k.a. configurations and shapes). These methodologies are known as topology optimization and shape optimization in the computational design literature. In this sense, however, the implication of the term optimization goes beyond fine-tuning a design or haphazardly generating combinations of parameters to create forms in a genetic or evolutionary fashion. Instead,

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the search processes characterized as shape and topology optimization are directly navigated by the gradients (a.k.a. sensitivities) of the cost (or benefit/utility) functions for converging to forms that have some measurable and differentiable minimal or maximal properties, and so it is fair to call such approaches as form-finding approaches. Even though the terms shape optimization and topology optimization originate from structural engineering and refer to notions of performance related to minimal compliance or minimal materialization of structures under certain load cases, we can see that it is possible to generalize their definitions to other domainsspecific notions of performance, e.g. passive climatic design principles (governing equations from geometric optics) or even environmental psychology (insofar as the governing equations can be formulated in terms of the decision variables). We shall see in detail that these approaches are most suitable for convergent search in a design space equipped with a clear notion of performance or quality. Here, we provide two compact and general definitions of these processes: Shape Optimization Problem: Given a network (graph) or a mesh (hyper-graph) with fixed topology, it is desired to find a valid embedding (i.e. 3D vertex positions) for the network/mesh that would minimize a cost function describing how costly (uncomfortable) the shape is, possibly subject to multiple constraints of validity. The general idea is to formulate a so-called [virtual] energy function (typically explainable as a Dirichlet energy functional) that measures the extent to which a shape is far from being relaxed, optimal, or desirable. Topology Optimization Problem: The core idea of topology optimization is about solving a problem in this general form to find a [black & white] colouring of a tessellated cell space that would minimize a cost function. The cell colours are eventually supposed to be integer labels determining whether a cell is in or out of the ultimate form. The white-coloured cells are effectively removed from the final configuration. So, the topology of the final configuration effectively alters as compared to the initial super-graph that is dual to the cellular tessellation of the design domain, hence the name topology optimization.

4.1.1

Existing Work

The history of structural shape and topology optimization can arguably be traced back some 150 years (see this literature review [42]) but providing an exact timeline or a comprehensive literature review in this regard falls out of the scope of this book chapter. In this section, we briefly introduce some critical references to the existing works on [mostly] structural shape optimization and topology optimization, specifically those of particular interest in terms of generality and applicability in the AEC. The generalization of structural optimization approaches to architectural design remains a challenge that would go beyond the scope of this summary. For the sake of brevity, as well as our focus on explainability, scalability, reproducibility, and justifiability of generative design methods, we shall restrict our attention to the form-finding or mathematical design derivation approaches that are explicitly

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and rigorously led by gradients and the only hint to alternative approaches such as metaheuristic methods or integer programming, namely topology optimization than shape optimization. Shape Optimization In the context of discrete generative design, shape optimization refers to methods for optimizing (typically minimizing) an energy function that takes the shape of a mesh as the input function. Thus, the objective function is often in the form of a Dirichlet energy integral. Such an integral functional, which is typically based on a partial differential equation governing the dynamics of the movement of the mesh vertices, can be written as a discrete integral or the sum of magnitudes of the very forces that could be considered as the gradients of the input function (mostly the positions of vertices) over the mesh elements (edges, faces, or cells). This generalized definition points to two types of approaches for solving the shape optimization problem: those concerned with analytically solving the governing equations in the strong form (differential form) and thus characterizing the optimality criteria, in which typically the Laplacian (see two prominent introductions by Olga Sorkine [43] and Bruno Levy [44]) or generally the Kirchhoff Stiffness matrix operators (see a thorough mathematical introduction [45]) are used to discretize the governing equations, the classical example of which is the force density method by Hans-Jörg Schek [39]; and those approaches that can be described loosely as being based on the weak form (integral form) focused on numerical integration of the energy functional and updating the discrete differentials alternatively, the classical example of which is the dynamic relaxation method by Barnes [46, 47]. While the former has the elegance and appeal of a purely mathematical method, the latter has the flexibility of dealing with nonlinear optimization problems. For a more detailed comparison of these two approaches in a broader sense, see a comprehensive literature review [48] with a thorough mathematical formulation and collation of the methods. While the force density method already refers to generalizations for possibly nonlinear constrained problems, it is noteworthy that general methods such as the shape-up method of constraint projections by Bouaziz et al. [49–51] or the thrust network analysis by Block and Ochsendorf [52] have been introduced for interactive and constrained form-finding. Additionally, a class of interactive methods for confidently navigating the space of optimal shapes (networks) in equilibrium have been proposed based on graphic statics, e.g. an exemplary compendium [53]. Topology Optimization A generalized problem formulation for topology optimization problems can lead to new frontiers of research in computational design that go much beyond the famous structural design applications, cf., the formulation of massing and zoning problems in architectural configuration inspired by structural topology optimization problems in the GoDesign framework [26]. Referring to the three types of design moves in generative design as mesh editing procedures (for modification of shape, colour, and topology), it must be noted that contrary to what the name suggests, the most common and the most scalable approaches to topology optimization do not work with altering

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the topology (by using binary decision variables x = [xe ]n×1 ∈ {0, 1}n ) throughout the optimization process. Even though the ultimate aim of the topology optimization process is to end with a particular combination of binary decision variables defining a distinct topology of a cellular material domain, the ambient colours typically indicate float density-like variables corresponding to the possibility/probability of having a cell or not. Thus, it is common to consider an array of float density variables corresponding to the cellular finite elements in the tessellation in the form of x = [xe ]n×1 ∈ (0, 1]n . This change of decision variable x presents two relaxations to the theoretical topology optimization problem. One relaxation concerning the change of a Boolean decision variable to a float variable brings about straightforward differentiability, thus resolving the need to compute a topological derivative, q.v. [54]. Another relaxation is about changing the infimum from zero to a small nonzero value (e.g. 10E-3) to avoid singularities in the stiffness matrix (as well as to avoid division by zero in the smoothing/filtering step [55]). The most crucial step of any analytical topology optimization process is the simulation of the cost function and its gradient as a function of the decision variable. In the case of structural topology optimization, this is performed in these steps:[re]computing the Stiffness Matrix with the current density variables based on the current density distribution; computing a numerical solution to the governing equations using the finite element method; computing a gradient vector showing the sensitivity of the cost function to the perturbations of density variables; iteratively seeking a Lagrange multiplier (in the optimality criteria method) for solving the volume constraint; multiplying the sensitivities by the Lagrange multiplier; applying some distance based filtering or smoothing on the gradient vector, and lastly multiplying the next-iteration density vector by the smoothened gradient in a heuristic fashion assuming that where there is higher sensitivity, there should be more material. The most common approaches to structural topology optimization, to this date, are either directly based on or inspired by the Solid Isotropic Microstructure with Penalization (SIMP) methodology [4, 56, 57]. Notably, several pieces of vectorized MATLAB code have been published for topology optimization based on the SIMP methodology including the famous 99 Lines [4] and 88 Lines [58] for the 2D structural optimization or 3D structural optimization [55]. Rozvany and Zhou [59] explain in depth why the intuitively appealing and bioinspired approaches known as soft-kill, hard-kill, evolutionary structural optimization (ESO), or bidirectional evolutionary structural optimization(BESO) that were popularized by Mattheck [60, 61] and Yi Min (Mike) Xie [62, 63] are not guaranteed to find optimal solutions. Thus, due to the mathematical orientation of the proposed approaches in this book chapter, we shall skip these methodologies in favour of those directly working with the gradients of the objective function. While the use of a numerical simulation is the core of the methodology, it does not have to be based on the finite element method; there are alternative formulations based on other numerical methods such as the discrete element method [64].

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Navigation Strategies

Here, the basic concepts of topology optimization methodologies are explained with a view towards generalization, from the structure of the design space to the different design space navigation methods. Tessellation of a Spatial Material Domain A material domain is modelled as a topological space, technically tessellated into some regular or irregular cells, e.g. without loss of generality, some triangles or quadrilaterals in 2D or tetrahedra or hexahedra in 3D. Together, these cells form an algebraic topology (a [combinatorial] cell complex) that can be represented as a graph whose vertices are dual to the cells of the cell complex. A Vector Design Variable To every cell of the cell complex, a virtual density-like parameter is attributed, making up an n-vector of [binary] decision variables for n cells in the tessellation. The ultimate goal can be described as figuring out for every cell if it should exist as a materialized domain in the final design or not for some minimization or maximization goal to be achieved. However, the most prominent approaches to solving this problem tend to deviate from defining binary decision variables at least for the duration of the topology optimization process for multiple reasons that can be summarized as differentiability and preservation of topology. Formulating a Cost Function A virtual energy function or a cost function is typically formulated as a function of the vector decision variable to be minimized (hence the term optimization), which represents something that conceptually defines the extent to which a design can be assumed to be tense or unsatisfactory (opposite of relaxed or satisfactory); this is usually a form of the Dirichlet energy, such as the strain energy of a structure known as the compliance of the structure under a particular load case given some boundary conditions (supports). More generally, any cost or benefit function that is explicitly a function of the vector decision variable can be sought to be minimized or maximized in this regard. Correspondingly, the argmin or argmax will be the optimum design effectively describing a foggy picture of the minimal or maximal material distribution over the design domain that is typically snapped to a binary density vector at the end of the process. Topology Optimization Problem-Solving Method From the very description of the design variable, it must be noted that even in the case of the binary decision variables, the search space expands exponentially in the order of O(2n ) and thus, a naive brute-force search quickly becomes intractable. Furthermore, even after introducing the float variables and the common SIMP heuristic (the penalization scheme) that makes the cost function easily differentiable, the problem is almost always non-convex and generally difficult to solve with thousands or hundreds of thousands of decision variables. The approaches for solving topology optimization

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problems bifurcate with respect to at least two major questions: (a) binary decision variables or float decision variables, and (b) analytical or metaheuristic. As explained earlier, the metaheuristic approaches fall out of the scope of this summary. The approach of using binary decision variables is perhaps interesting or appealing for small educational examples such as LayOpt [65] but is not scalable to be applicable in high-resolution applications [54]. As for the analytical approaches, in addition to the most common optimality criteria method introduced briefly earlier, a notable alternative is a method of moving asymptotes (MMA) [66] and its newer variant, the generally convergent method of moving asymptotes (GCMMA) [67] by Krister Svanberg. However, the optimality criteria method generally remains more accessible and thus more prevalent in mathematical topology optimization. Architectural Layout Methods The GoDesign framework [26] explains how the problem of 2D/3D space layout in architecture can be broken down into three sub-problems of massing (binary colouring) [68], zoning (multi-colour spatial allocation or space planning), and routing (corridor generation) [69]. The problem of architectural space planning, especially the 3D layout, is arguably the hardest in computer-aided architectural design especially because it is ill-defined and over-constrained [70, 71], and so to keep the discussion contained we refer the reader to a few literature reviews [72– 74] and restrict our attention to explicitly discrete problem formulations such as space allocation [75] or mesh colouring [76], most of which propose mathematical integer programming (linear or quadratic optimization with integer variables using operations research solvers) [77, 78].

4.1.3

Illustrative Example

Applications of the topology optimization (TO) methodology in domain areas other than structural optimization are quite rare; see a range of applications in a recent review by Mike Xie [79]. However, there is at least one other prominent application of TO other than SO in engineering for designing heat sinks [55] and at least one application for the design of a complete building structure [80]. Thus, here we show only two architectural applications of topology optimization which differ significantly from the mainstream structural applications. The first illustrative example [81], shown in Fig. 6: Is a topology optimization process for finding a compressiononly structure with large-scale cells whose self-weights are not negligible, and thus, the example has a few additional constraints of validity on the stress, self-weights, and the supports. The second illustrative example [82], shown in Fig. 7 is a topology optimization process for finding an optimal climate-adaptive shape for the envelope of a building with a mathematical formulation of the cost function and gradient both explicitly formulated in terms of a discrete opacity (density-like) decision variable. These examples help in illustrating the bigger picture of topology optimization. in that

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the general idea of defining a simulation-driven differentiable cost function as a function of a vector of density-like decision variables corresponding to a cellular tessellation of a design space provides for solving a mathematical optimization problem for deriving an optimal bicolouring of the lattice graph dual to the cellular tessellation based on its analytical gradients. Such a problem can be formulated in this compact form: ⎧ n : decision variable ⎪ ⎪ x := [xe ]n×1 ∈ (0, 1] ⎪ ⎨ minc(x) : cost function s.t.g(x) = 0 : constraint function ⎪ ⎪ ⎪ ⎩ H (x ∗ ), x ∗ = arg min L(x, λ) = c(x) − λg(x) : solution x

where H (x ∗ ) denotes the Heaviside step function at an arbitrary threshold and L(x, λ), denotes the Lagrangian functional. In summary, as long as the costs and the constraints are differentiable functions of a density vector variable corresponding to the cellular elements of a tessellated region, the above problem can be regarded as a topology optimization problem.

Fig. 6 Structural topology optimization for designing a discrete compression-only structure, image credit: Dijk [81]; a a 2D toy problem showing the proposed method as compared to the common isotropic formulation obtained from the Ansys Topology Optimization package; b a 3D toy problem showing the discrete results of the topology optimization process for a compression-only/funicular structure to be built out of discrete blocks

Fig. 7 Climatic topology optimization for deriving a building mass/envelope of optimum solar potential, mage credit: Florou [82], a a hypothetical binary mass configuration and the changes in performance from one configuration to another, b the proposed analytical solution to the topology optimization problem for maximizing the solar potential as a level set in the design space

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4.2 Grammatical Generative Design Grammatical approaches to generative design can be traced back to the figurative work of Chomsky on Formal Grammars [9, 83]. Additionally, to the historical example of shape grammars initiated by Stiny [8, 84], there is a congruent framework to discuss modern grammatical approaches to design based on graph grammars or graph rewriting systems from a mathematical and computational point of view. Practically, grammatical approaches can be implemented either computationally or as a system of rules for [pen & paper or physical] games. These processes allow a designer to explore a vast range of topological designs, especially because they let the designer systematically change the topology of the design space directly. Such exploration processes are typically not bound to or directed by an explicit definition of performance. The introductory example in Fig. 8 uses a simple two-rule grammar to evolve fractal squares designs. The marker in pink is positioned with a MOVE rule to choose which square to subdivide with the SPLIT rule. The SPLIT rule has an optional Boolean parameter: whether the subdivision goes across all squares. The MOVE rule has two discrete parameters to choose the number of squares to traverse in the X and Y directions. We first present existing work on the development of grammars for generative design, from formal to shape and finally to graphs. Then we discuss the navigation strategies and illustrate them on an example.

4.2.1

Existing Work

The rule-based design encapsulates different applications with design grammars that can apply to language, form and structure through different levels of complexity, starting with formal grammars. Formal Grammars Chomsky introduced in the 1950s generative design applied to language using formal grammars [9, 83]. A finite set of formal grammar rules apply modifications to a finite set of words, enabling the generation of an infinite set of sentences. The design rules define the language—or design space—to which these sentences—or designs— belong.

Fig. 8 Introducing grammatical generative design: fractal square subdivision of squares by moving a marker (in pink)

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L-Systems L-systems extend formal grammars for the generation of geometries. In 1968, Lindenmayer introduces L-systems as a type of formal grammars to algorithmically describe the growth of plants [10, 85]. A set of rules applies to a string of characters that come from an alphabet. The interpretation of the string generates the corresponding shape in the manner of turtle graphics [86]. The rules are applied iteratively to generate different levels of growth of the shape. The shape depends on the starting string axiom and the different parameters in the case of parametric rules. L-systems can also describe the generation of patterns such as fractals. L-systems can apply to architectural and structural design as parametrization strategies for the generation of designs. The combination of L-systems and genetic algorithms provides a means for topology optimization for the search for statics-optimized designs [87, 88]. Shape Grammars Shape grammar does not only modify a chain of characters, as formal grammars do but a geometrical design and found many applications for exploration and design of general geometries. Stiny and Gips introduce in 1971 shape grammars for the generation of shapes in painting and sculpting [8]. A classification can be found in [89]. Subsequently, shape grammars found a large set of applications in many fields of design, architecture, and engineering [14, 84, 90]. Architectural Grammars Architectural grammars include a variety of applications, such as Palladian villas [91], Frank Lloyd Wright’s prairie houses [92], Queen Anne Houses [93], Yingazo Fashi Chinese buildings [94], or Siza’s houses in Malagueira [95]. The grammar decodes each architectural style or building typology, formalized and structured into a set of rules to generate multiple other designs that share the same characteristics. Design grammars also apply at other scales than the building. Urban shape grammars tackle the district, like the Medina of Marrakesh [96], or the city, like Praia in Cabo Verde [97]. Product shape grammars tackle specific styles of chairs [98], coffeemakers [99], cars [100], or tableware [101], for instance, allowing mass customization. An architectural grammar for housing rehabilitation takes into account the varied information like new usage, among others, instead of decoding a design style [102]. Functional, Structural and Force Grammars Even though architectural grammars focus on the arrangement of shapes, grammars can include functional aspects other than geometry. Shape grammars evolve into functional and structural grammars to include non-geometrical data related to structures. This data can include structural-behaviour and construction-technology requirements. Engineering applications include houses [13], towers [103, 104], halls [105], bridges, [106], trusses [41], or geodesic domes [15, 16]. Some applications are specific to a fabrication technology, like CNC machines [107, 108], instead of a structural system. Force grammars describe the organization between forces, as

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opposed to the one between spaces or elements, which can later materialize into a structure. Force grammars for graphic statics are introduced by Lee et al. and applied to 2D edge networks [109] and 3D cell decompositions [110]. Mesh and Graph Grammars The exploration of the topology of patterns and meshes resulted in the development of several operations, sometimes also framed as grammar rules, which are not specific to architecture and structures, which abstract a design and generalize the range of applications. Considering [polygon] meshes as hyper-graphs that can contain higherdimensional topological entities known as hyper-edges (more commonly known as faces and cells), mesh grammars are also considered graph grammars. The extensive range of applications of meshes sparked the design of very different sets of rules tuned for specific objectives, mainly for aesthetic purposes. Hansmeyer and Dillenburger [111] introduce a mesh grammar following a formal grammar approach that modifies the density and the geometry of meshes to generate highly detailed ornamental shapes. This grammar focuses on shape. Indeed the pattern and its singularities are not modified. In computer graphics, quad-mesh grammars modify the topology to improve the regularity of dense and unstructured meshes [112–115]. This regularity for modelling and representation concerns both geometry and topology. These quadmesh grammars consist of a set of local rules that preserve the quad-mesh constraint, unlike other grammars for triangulated meshes. Another family of quad-mesh grammars does not consist of rules, but different patterns [116–118]. The patterns feature different singularities to patch N-sided polygons with a prescribed number of subdivisions on each side. Combining these patterns allows for completing the mesh of different shapes. These rules apply to meshes for the field of computer graphics, animation and rendering. These rules have little use in the context of architectural and structural design, where design does not start with a dense unstructured mesh and where many more objectives come into play. The Conway operators constitute a grammar developed by John H. Conway for the description of polyhedra [119]. Conway operators can be applied to translate one tessellation into another, already applied for optimising space frame structures [120, 121]. Indeed, tessellations present different structural and fabrication properties worth investigating [122–124]. The design of a pattern is a trade-off between topological regularity and irregularity. Oval et al. [125] provide a grammar tailored for the topological design of vertex singularities in quad meshes. Heisserman [126] presents a grammar on the boundary of solids represented by meshes for modelling architectural spaces or volumetric objects. Modifications of the topology result from modifications of the geometry. The topology is updated when a movement modifies the adjacency or creates an overlap. This grammar explores the topology of the shape, the underlying mesh being only a representation for computation.

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Of course, such processes can be coupled with aggregate performance evaluators, but incorporating disaggregated performance gradients with respect to the discrete design moves (graph-rewriting actions) would require much more sophisticated mathematics than multi-variate calculus. For the sake of brevity, we shall restrict our attention to the use of grammatical approaches for exploration (and rewriting of) design spaces as a matter of itemization, i.e. itemising a wide range of distinct design options. We can easily observe that the act of itemization does not require a notion of performance to guide the process. It is mainly the definition of the graph-rewriting actions (the proposed graph grammar) that defines how a design space can change to another while itemising distinct design topologies. Design Space Creation: Granularity, Distance, Similarity The grammar defines the design space, its extent and its granularity. The constraints on the design are directly embedded in the definition of the grammar rules. These constraints can relate to organization, feasibility, constructibility, etc. Therefore, it is crucial to design the grammar rules to provide the desired level of granularity. Lowlevel rules apply atomic changes and allow a comprehensive description of design variations at the expense of applying many rules to obtain designs of significant differences. High-level rules make more substantial changes in a design, allowing to produce of a large variety of designs with a few rules, though missing intermediary hybrid designs. This opposition between low-level and high-level rules may be understood as local search versus global search. The most relevant ones depend on the application and approach as they have different pros and cons and can be combined for efficient design space search, including creating intermediary-level rules. In the example of the quad-mesh grammar by Oval et al. [125], the grammar consists of two rules only. These rules ever add or delete a strip of quad faces, which are the fundamental object in quad meshes. As such, the grammar is constrained to generating quad meshes, not generic polygonal meshes, and all quad meshes. The design space has the aimed level of granularity: all and only quad meshes. A grammar adding or deleting edges would generate meshes with any combination of polygonal faces. A grammar modifying other mesh elements would not guarantee the possibility of obtaining any quad-mesh topology. Performance Search: Evaluation, Navigation, Decision Originally, the grammatical generative design relies on the user to evaluate the suitability of the design and choose which rules to apply. Indeed, if the grammar is properly designed, all the generated designs should be pertinent. Every design generated by Stiny’s Palladian-villa grammar [91] should look like a Palladian villa! The designer can evaluate qualitatively or quantitatively the design options generated during an open-ended search. However, this combinatorial space can be daunting or under-explored by a designer if not provided with search aids, mainly when the grammar consists of

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numerous rules. Therefore, combinatorial algorithmic search, with different levels of machine-user interaction, from gamification to automation, including AI and data-driven search, can contribute to grammatical generative design.

4.2.3

Illustrative Example

We illustrate grammatical generative design with the example of a truss in Fig. 9. The proposed grammar consists of two types of rules: shape rules that modify the geometry of the truss and connectivity rules that modify its topology. Additional rules could consider the materials and the cross sections of the truss elements. The shape rules consider two truss profiles: a BOX with a straight bottom and top chords or a quadratic profile with a curved top chord. They have parameters to control the length and the heights of the truss directly. More complex shapes could be considered though, probably resulting in designs that are harder to build with little gain in structural efficiency. The BOX rule can be considered redundant as such designs are exceptional cases of the quadratic designs. However, the designer may want to limit design exploration to standard BOX profiles, maybe using automated optimization of the height parameter, hence the interest in this rule. The connectivity rules control the number and type of vertical and diagonal bars between the two chords. The SWAP rule could also be considered redundant, as the diagonal rule has parameters allowing to choose any or both directions for the diagonal bars. However, the SWAP rule enables the designer to change their mind about that aspect of the design without starting over and further navigating the design space by applying more grammar rules. The last design in Fig. 9 results from the following sequence of rules: BOX(10.0,3.0)—VERTICAL(4)—DIAGONAL(0,1)—SWAP(0)— BOX(10.0,2.0)—VERTICAL(5)—QUADRATIC(10.0,1.0,2.5). It could have been produced in an infinite number of rule combinations. The shortest number of combinations, also called design path, consist of three rules only:

Fig. 9 Illustrating grammatical generative design: combining shape and connectivity rules to evolve a series of truss designs

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QUADRATIC(10.0,1.0,2.5)—VERTICAL(5)—DIAGONAL(1,0). However, the redundancy provided by this choice of grammar allows the designer to navigate the tree of possibilities without being constrained by early decisions. While applying a chain of rules, the designer can, in the first instance, visually and qualitatively assess the suitability of the design based on their intuition and experience. Additionally, this design process can be enhanced by informing the designer regarding the performance of the design on one or multiple metrics after an analysis at each step or at key steps only. Here, structural analysis can provide results about the load path for structural efficiency, for example. The algorithmic search could aim at finding the combination of rules, including their continuous (e.g. height), discrete (e.g. vertical subdivisions), and Boolean (e.g. orientation of diagonals) parameters, that minimize a performance objective, like the total load path for structural efficiency, respecting to some constraints, like a fixed length and a maximum height to respect integration in a building or landscape. Other requirements are by design embedded by the generation grammar, like the limited shape and connectivity complexity for construction simplicity. The redundancy provided by the grammar can make automated exploration more difficult because of the high number of rules that increase the combinatorial complexity of the design space without enriching it with new designs. Indeed, several chains of rules yield the same designs, also known as a problem of isomorphism between the description (genotype) and the design (phenotype), making algorithmic learning more complex. Therefore, a sub-grammar limited to the rules quadratic, vertical, and diagonal, which are independent of each other and make the rules BOX and SWAP redundant, would potentially be more suitable for automated optimization.

4.3 Gamified Generative Design In the middle of the spectrum of generative design methods lies the simulationdriven games where the interactivity of the grammatical methods meets the robust evaluation and assessment capabilities of mathematical methods. In a broad sense, the gamified generative design processes are design processes where a gamified environment allows the players to navigate the design space in a structured way while the alternatives are being evaluated and the corresponding scores are reported back to the player; hence emblematically dubbed play & score mechanisms. The first element, play, refers to serious gaming, which is individual or collective activities for making decisions with high utility based on conflicting objectives and limiting resources [127]. The second element, score, pertains to the inherent capability of evaluating different alternatives based on their integral performance as a design and consequences as a decision vector combining many choices. Thus we require simulation models that represent the states and dynamic behaviours of realworld phenomena [128], so we can predict the functional performance and consequences of choices (design moves). To recapitulate, a gamified generative design process is a serious game that has an incorporated simulation model of the real world,

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which interactively informs the players about the consequences of their actions. Such games provide exploration and experimentation environments for the players to take actions, learn, and design through formal simulations based on logic, rules, first principles, and statistical co-relations [129]; and role-play in [group decision] simulation (games) based on experience, negotiation, and intuition [130]. The main challenge of the simulation game designer is to (1) formulate the main objective of the game, (2) capture the essential dynamics of the real phenomena in the simulation engine, and (3) provide the proper interaction channels so players can understand decision dynamics. These three aspects have been named: meaning, reality and play by Harteveled [131]. One of the key characteristics of a game is the level of abstraction which has major consequences on the ease of reasoning about the system [132] and the focus of the reasoning in the game. For illustration, board games often have a higher level of abstraction than computer games, as their medium is more constraining. The degree of abstraction and simplification is essential in the modelling and design processes; however, in the gamified approach, it is specifically consequential. Games provide an artificial environment for exploration, assessment, and discussion of decisions. A highly abstracted game has the risk of omitting the complexities of the original problem, and the lowly abstracted game has the risk of losing the focus on the main problem. Therefore, the gamified environment needs to have an adequately abstract representation of the complexity of the real problem. In Fig. 3, we have elaborated on different types of complexities present in a built environment design problem. These complexities demonstrate numerous inputs and outputs with high levels of inter-dependencies which can impede human cognition in grasping the details of the problem and taking action accordingly [133]. Simulation games facilitate the decision makers in understanding, assessing, and exploring these complex problems; hence, their utilization can also be understood as an approach for augmenting human cognition.

4.3.1

Existing Work

The earliest use of serious games in urban planning and architectural design goes back to Abt [127] and Sanoff [20]. During the last decades, the use of games in design and decision-making has increased. Initially, the main driving force was integrating the simulation in an interactive environment, but later, designers and planners started to focus on the participatory potential of games as well [134]. In this section, we provide an overview of different gamification approaches and applications in generative design. Games for Education One of the main advantages of serious games is that they provide a safe environment to explore a model and learn about its dynamics. The majority of the research body in serious gaming aims to exploit this pedagogical potential of games by educating the players through interaction in simulation-driven game sessions [135].

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For instance, researchers have utilized simulation games to explore the complex interdependencies of sustainable development of the built environment [135] to allow first-year architectural students to learn by interacting with such systems [136]. The foundations of how games can contribute have been established in Constructivist learning theories since they highlight interaction, curiosity, and social negotiation as the main driving force of internalizing knowledge [137]. Furthermore, it is key to note that other games that do not have a primarily educational goal exploit this potential for familiarizing the players with the topics and establishing a common language for discussions and negotiations. First Principle Simulations Beyond the educational case, other applications of serious games, such as decisionmaking and planning support, have received relatively little attention [138]. However, these applications are central to the gamified generative design approach, as they support evidence-based navigation of the design space. The most prominent way to provide evidence for the comparison of alternatives is first principle simulations and evaluations. In these approaches, a formal model that is rooted in previously established scientific and theoretical work is used to assess the alternatives. A classic example of this is the original SimCity game [139], in which the authors used Forrester’s model to replicate urban dynamics. This helped them predict the population increase or decrease based on education, unemployment, and growth rates [140]. More recently, Sanchez focused on the ecological aspect of urban development through Block’hood: a simulation-driven voxel placement game that resembles sand-boxes such as Minecraft and Simcity for neighbourhood development [141]. Specific to urban infrastructure, SimPort-MV2 focuses on land allocation in portplanning [142]; MATRICES in the ProRail games focuses on the scheduling and rail infrastructure to predict the consequences of different scenarios [143]; the Train Fever game utilizes an integrated transportation and land-use model to predict population and employment flow based on the rail networks [140]. More recently, there is increasing interest in games that aim to integrate different domains to achieve a more holistic representation of the urban planning complexities, such as waterenergy-food-land-climate nexus serious game [144] where the authors embed statistical correlation from different domains to make an integrated inference engine for assessment of scenarios. Another interactive multi-player game is the Sustainable Infrastructure Planning Game (SIPG) which focuses on the inter-dependencies of different sectors in strategic planning exercises [145]. On the architectural scale, Moloney proposes a serious game for integral sustainable design [136]. They provide a set of spatial quality measures based on the rule of thumb and a peer review mechanism that capture the qualitative views of the players as a collective. Savov proposes a block-based assembly game for facade design with a setup similar to Jenga. They conduct light and structural analyses to provide live feedback to the players about the performance of the design [146]. Lin suggests integrating VR and BIM to communicate the qualitative requirements of healthcare buildings to the players [147].

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Agent-Based Models and Cellular Automata Spatial systems are integrated with various aspects of human life, many of which cannot be represented formally with first principles. This is especially true in the case of human behaviour within the built environment. In such cases, agent-based models (ABM) can be constructive, as they allow the game designers to embed complex relationships between agents and their environment in the simulation model (see Fig. 12 as an example). A recent example is the work of Raghothama et al., where the authors utilize the SUMO simulation model for gamifying the operation of the transport system in two cities of Rome and Haifa [148] within the ProtoWorld framework [149]. At the architectural scale, crowd simulation ABM has been used to assess the accessibility of spatial configuration in standard, and emergencies [150]. A particular category of the ABM is cellular automata (CA), which consists of spatially fixed agents. These models are explicitly valuable for design and planning as the agents defined in them have a fixed topology (relation network) that can encapsulate context-specific spatial relations. In an urban case of flood mitigation policy development, Khoury et al. embed a CA in a serious game to educate the participants and reach a consensual policy. They utilize the CADDIES open-source framework, which is 2D CA developed explicitly for urban flood modelling [151]. On an architectural scale, CA has also been used to represent spatial design’s horizontal and vertical constraints to generate spatial configurations [152]. Beyond evaluation, ABM can also be used for exploration. Epstein very well establishes the foundations of such approaches as the generative social sciences [18]. A recent example is using artificial agents for exhausting and mapping all possible scenarios in a serious game environment to achieve a holistic picture of the design space [144]. This approach has also been applied for design configurations in the GoDesign framework [26] where the authors propose using ABM to allocate the program of requirement in the predefined envelope (see Fig. 12 [153].) Similar to the ABM, artificial agents can be defined in the simulation environment to explore the design space and learn about dynamics of it under the reinforcement learning framework, for example, for configuring architectural spaces [154]. Grammar Based Games Some games utilize explicit grammar formalisms to structure the exploratory process of the game. Most of these games are focused on the morphological aspect of the built environment. In the architectural scale, the exploration of complex spatial configuration can be structured as a voxel-based grammar in [155] or a shape grammar with structural verification routines in [156]. On the urban scale, rule-based systems have been used extensively to describe the morphological relations of the city [157]. These rule-based morphological systems are the basis of the procedural generation of cityscapes [158]. Furthermore, such procedural methods can be used to optimize the urban configuration by integrating assessments to evaluate the alternatives [159]. In a recent example, authors integrate a prediction model for population density to evaluate the procedurally generated alternative and guide the exploration [140].

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Games for Consensus Serious games can provide the medium for a common language for structured discussions and comparisons that can potentially facilitate the process of reaching a consensus. This potential is mainly the result of the interactive environment of the games that allows an engaging experience and a transparent relationship between decisions and their consequences. The foundations of this potential of games can be traced to social cognition studies where the dynamics of the individuals’ opinion concerning their interaction with the group is studied [160]. For example, in [161], the authors propose an online game for mass participation of the neighbourhood inhabitants to focus on the “Not In My Backyard” phenomena. Another example is presented in [150], where the researchers utilize crowd-sourcing for floor plan generation. They provide an implicit peer review mechanism by allowing players to access the design of other players [150]. Similarly, Fumarola and Verbraeck suggest constructing a decision tree of the game to map how the player interactively makes decisions. Providing additional abilities to navigate this decision tree allows the player to explore multiple what-if scenarios, understand their relations, and draw a conclusion about the potential trade-offs [162].

4.3.2

Navigation Strategies

The simulation games sit in-between the mathematical derivation and grammatical itemization mainly as their navigation of the design space is a merger of the two ends of this spectrum. In this segment, we first elaborate on the similarities and differences of the gamified approach with each of the mathematical and grammatical approaches and then explain how they make it a unique methodology in generative design. The common thread between grammatical and gamified approaches is twofold. Firstly, they both limit the navigation to a rule-set. In simulation games, the player’s actions are predefined based on the game rules. In the grammatical approach, the rules define what the possible design changes that can be made are. Often, the game rules are more forgiving than grammar structures as they provide for the players’ exploration. However, in both approaches, decisions/actions are defined based on the rule sets and the grammar structures, which determine the possible changes that can be made in the decisions/actions. Thus, the grammar creates pathways in the design space that make it navigable for human agents. This brings us to the second similarity between gamified and grammatical approaches: they both rely on the human agency as the principal controller of the navigation process. This means that the decision to apply a rule primary lies in the control of the human agents. In some examples, game actions can be delegated to artificial agents or might be based on the system’s recommendation, but the human player remains the authority in the navigation process. On the other hand, gamified and mathematical approaches are similar as they both incorporate evaluation mechanisms that can provide a basis for comparison of alternative actions/decisions. In simulation games, these evaluations are generally

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introduced as indicators that allow the players to have a basis for their comparison. Performing the evaluation relies on formal or role-play simulations that essentially project the consequences of actions and decisions to the identified indicators. The formal simulations can be embedded in the game as analogue mechanisms in card games or digital simulations similar to objective functions in the mathematical approach. Role-play simulations are normally introduced to represent the societal and organizational complexities of the problem. Thus, they are closely related to the consensus-building capabilities of games. In all cases, the overlap of the gamified and mathematical approach is that given two decisions, it is possible to differentiate them by evaluating indicators. In the mathematical approach, this differentiation is performed formally through the gradient-based approaches that also help the process identify the new potential decisions. However, in the gamified approach, the comparison of the alternatives and the specification of the new decisions are performed purely by the human agent.

4.3.3

Illustrative Example

In this segment, we elaborate on the EquiCity design game to dive deeper into the potential of spatial simulation-driven games as generative design methodologies. EquiCity is a spatial game for planning the redevelopment of a neighbourhood in Delft, the Netherlands. The existing site was a historical factory that has been an economic attraction of Delft in the last century. As the factory has stopped working, the municipality is aiming to redevelop the area with a mixture of functionalities such as residential, commercial, cultural, and public spaces. The main objectives of the redevelopment consist of three main categories: (1) environmental such as light and visibility; (2) social such as accessibility; and (3) economic concerning the intervention extent. The main planning measures pertain to allocating different functions in various sites within the district. As the game is a multi-player game, the participants from various backgrounds were involved in deciding about this district. On the methodological level, the problem has been formulated based on the introduced framework. As indicated in Fig. 10, the decisions of the players were structured (t) . Players would specify their decisions individually at as the interest matrix X n×m×o the beginning of each round. Then the game engine would gather all of the decisions, construct the interest matrix, and perform opinion pooling, and proportional fitting (t) . As the decito achieve a consensual decision on the allocation of functions Vn×o sions are on the planning level, the spatial decision on the configuration of each site is degated { { } } to the agent-based massing process, which produces the prospective massing k (t) . In the next step, the game engine evaluates the corresponding massing k (t) j j based on the predefined economic, social, and environmental objective functions. Finally, individual utility values are combined through multi-criteria decision analysis (MCDA) to produce the group score, individual score, and achievement badges. At this point, one iteration of the game is complete; and players can explore their

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scores, previous decisions, and extra analytical information to be able to negotiate for the next round of decisions. The gaming platform of EquiCity is a web-based interface that players can individually access to participate in the game (see Fig. 11). Authentications are embedded to ensure that only dedicated players can access the decision-making interface, while the gameplay and the analytical information are openly accessible for everyone else to follow the flow of the game. EquiCity is inherently a multi-player game that aims to structure the negotiations of the stakeholders by providing feedback on the performance of their decisions. The stakeholders in EquiCity are represented with predefined roles that are described by the corresponding Interest X and Control C matrices. The predefined interest X (0) of

Fig. 10 Schematic formulation of a gamification problem in EquiCity game as a combination of an MCDA problem, a generative massing problem, a consensus-building problem, and the creation of extra scores for the encouragement of competitive or cooperative play styles

Fig. 11 Screenshots of two iterations of game-play in the EquiCity game, the case of the redevelopment of a former factory into an urban district featuring a mix of residential, commercial, and cultural spaces in addition to communal/public spaces. The overlaid screenshots show the information on individual and collective scores (right) and the control, interest, and power difference matrices (left) shown to the players

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the stakeholders identifies their individual agenda and how their individual score is computed. The control matrix of the stakeholders specifies how influential they are in each site-function pair. With these two matrices, we can conduct the opinion pooling and iterative proportional fitting process to achieve a consensual decision about the district. However, this decision might not perform the best for the environmental and social indicators. Therefore, the stakeholders are motivated to deviate from their initial interest X (0) and produce new decisions X (t) to reach a better performance. The translation of this approach in the gameplay is an iterative process where the stakeholders will negotiate with their peers about their agenda and performance of the area as a whole and try to form new decisions. At the end of each round, after submitting their decision, they will get the evaluation of their decision which is the basis for comparison with the previous decision and is potentially constructive in guiding them towards a new decision. EquiCity embodies the principles of gamified generative design as it (1) structures the design space by defining decision variables (planning measures); (2) establishes a robust evaluation system for differentiating the alternatives based on evidence from the simulations; (3) incorporates the participatory nature of the problem in the game and facilitates them in reaching consensus; and finally, (4) provides an interactive environment where the relevant information is accessible to the stakeholder to support their decision-making process (see Fig. 11). Nevertheless, EquiCity is just a detailed example of this approach. As it has been established in the previous subsections, the gamified generative design can (1) have various sets of decision variables to address different application areas in the spatial domain; (2) benefit from various evaluation methods such as first principles, ABM, statistical inference, and even participatory evaluation such as peer review; (3) incorporate various levels multi-actor complexity to undertake the societal and organizational challenges of the spatial problem; and finally (4) utilize various technological infrastructure such as web-based interfaces, game engines, VR, etc. to provide an interactive environment for the participants (Fig. 12).

4.4 Generative Models for Data-Driven Generative Here, we juxtapose the so-called generative models in artificial intelligence with the three archetypical generative design processes and reflect on their potential for augmenting generative design processes. Before proceeding, it is necessary to note that an ambiguous notion of performance can lead to misunderstandings and unrealistic expectations from such models. The notion of performance as in the realistic look of generated designs is important in applications related to the entertainment industries (computer graphics, especially in generative arts, game-level design and procedural content generation); however, in architectural design, we need to work with a multi-faceted and much more constrained notion of performance. Producing valid designs that meet spatial constraints is already a significant challenge in most architectural applications,

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Fig. 12 Top rows show the application of the Technique for Oder of Preference by Similarity to Ideal Solution (TOPSIS) for solving the massing configuration problem, and the bottom row shows the application of the method of Multi-Actor Multi-Attribute Gradient-Driven Mass Aggregation (MAGMA) Method, a participatory zoning algorithm based on Fuzzy Aggregation in Configraphics [153, 164]

let alone generating designs of high quality with respect to multiple quality criteria. Thus, it is somewhat pointless to discuss the performance of the generative capabilities of generative models for generating realistic pictures in the styles learnt from a corpus of humans (such as the 2D or 3D images typically generated with generative adversarial networks or DALL.E). Regardless of whether it is a utopian or dystopian future for AI models to generate architectural designs, the technological possibility for generating a design is already available. The more critical question of interest regards the capability of AI for solving hard problems of performance-based generative design [165] where mapping or navigating the design space is intractable due to the difficulty of formulating the associations of choices and consequences, see a comprehensive review of the applications of deep generative models in design [166]. One particular class of models of interest are thus the models that can help make these high-dimensional “bipartite design spaces” intuitively understandable and tractable for humans; a particularly, relevant example is a one-layer deep Bayesian belief network [167] that can be trained to work in both directions, i.e. both from the design space to the performance space and from the performance space to the design space. Considering the difficulty of simulating some aspects of performance related to subjective and cognitive matters such as ergonomics, the need for building function approximators capable of associating performance levels with spatial configurations can be fulfilled with trainable neural networks, provided a systematic data collection campaign is conducted; see a connective perspective on spatial computing for design [168]. In general, however, there are two major types of problems that can be meaningfully addressed with AI: mapping or associating low-dimensional performance data points with high-dimensional input design variables (encoding spatial

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configurations) and the inverse or dual problem of navigating this bipartite space in the opposite direction (see Fig. 2: Duality of mapping and navigation problems in generative design). Two major lines of work can be identified as relevant in this regard: one that uses neural networks as function approximators for regression aimed at Interpolation and Extrapolation between data points; and another that is concerned with manifold learning, dimensionality reduction (encoding), signal reconstruction (decoding), and sampling (as in design of experiments), see a recent example for making an explainable encoder–decoder network architecture [169]. A particular class of generative models with special relevance to the dual problems of mapping and navigation are probabilistic graphical models (PGM), which are of two general types [170, 171]: Bayesian (directed acyclic graphs) and Markovian (bidirected or undirected). Examples of such models include Bayesian belief networks, restricted Boltzmann machines [171], flow-based models, Markov random fields, and diffusion models. In short, generative models equipped with AI can augment the three types of generative design processes where there is a complication related to the difficulty of navigation or mapping in high-dimensional bipartite design spaces. However, the use of generative models for content generation, no matter how interesting for the entertainment industry, does not introduce a new type of generative design relevant to AEC, unless one adopts a reductionist approach to GD as design automation (automating the task of a human, not necessarily supposed to produce better results than those made by humans).

5 Conclusion Here, we look back at the rhetorical questions posed at the beginning and provide succinct answers. Cedric Price in 1966 expressed the provocation “Technology is the answer, but what was the question?”. When it comes to the application of digital technologies in AEC, sadly, this rhetorical question seems to be relevant more than ever before. The AEC industry as a whole has yet to learn from other Sciences of the Artificial for forming a transparent culture of listing and formulating problems. Before claiming to have invented yet another solution, one needs to ask rigorously what the problem is. The most pressing confusion about “the problem of the design problem” seems to be about the notion of automated design. We hope to have presented compelling reasons to think beyond automation, optimization, or even problem solving by presenting the essentially different problem settings where the purpose of the design process can be the gradual and explainable derivation of design, participation in design for the sake of ensuring inclusivity and equity, or mass customization and formation of rich design languages capable of forming diverse designs, not only for the sake of comprehensively reaching better performance levels but also for enriching design cultures as integral parts of human cultures. In this sense, we hope to have adequately shown that it is time to think beyond the cliched wicked problem mind-set and go about formulating design problems rigorously. The following paragraphs summarize the moral of the paradigm of generative design.

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Methodological Commonalities As we have illustrated in the “three plus one” methodologies, generative design is not an agglomeration of isolated and distinct approaches but a coherent spectrum of methodologies that surround the principles of formulating the problem, structuring the design space, and navigating the design space based on evidence, knowledge, rules (design principles), or policies (control or game-playing strategies). Despite the differences in the three approaches, there are commonalities in these methodologies, most importantly, they all have explicit discrete decision variables on which the design space and an explicit formulation of the problem are based. This discreteness allows the design solutions to be countable, whether finite in the case of mathematical optimization or infinite in the grammatical approach. The enumerability of the design space is a prerequisite of a structured navigation strategy. The three methodologies have explicit and explainable navigation strategies. In the grammatical approach, the grammar describes the applicability of the rule-set alternatives, which in total exhibits pathways through the idiomatic expansion of the design space. In the gamified approach, the navigation pathways are looser to allow for the creative exploration of the players. Nevertheless, the scoring mechanism facilitates the players to learn about the dynamics of the game and reach a consensus collectively. In the mathematical approach, navigation is delegated to the gradient-based search to have the utmost objectivity in the design derivation process. The last common theme is explicit validation and evaluation which appears in all of the methods. In the mathematical approach, constraints ensure the validation and objective function will be an evaluation of the performance of the design that we aim to maximize. In the grammatical approach, the validation is ensured by the limitations of the grammar and the evaluation is based on the subjective opinion of the designer. In the gamified approach, the game rules ensure the validity of the design and the feedback provided by the simulations enables evaluation. Customization Versus Automation More unfortunate than the prevailing false dichotomy of automation and customization is the preconception that automation is integral to generative design. The mapping of the generative design methodologies in this paper clearly illustrates how generative design ultimately provides for customization of solutions; customization through itemization in the rule-based grammatical approach; customization through the informed exploration to reach consensus in gamified approaches; and customization for the satisfaction of the specific needs of a particular problem in mathematical approach. The generative design paradigm aims to formulate the problem, structure the design space, and devise navigation strategies to facilitate the customization of the design to the requirements and preferences of the future inhabitants. Future Research We can envisage two main directions for future research in generative design: development of methodologies and rigorous evaluation of methodologies. The existing methodologies under the umbrella of generative design are rooted in disparate fields

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and subjects, thus bringing incompatible terminologies and notations. As an example, the term decision variable in decision theory is equivalent to control vector in control theory, planning measures in urban planning, and design parameters in architectural design. This lack of a common terminology fundamentally impedes the formation of a rigorous discourse that is necessary for any structured discipline. In addition, much work is needed for meaningfully mapping mathematical methods and connecting them to appropriate applications in AEC. Currently, various methodologies are borrowed and applied based on the individual expertise of researchers and practitioners. Although enriching, it is unclear how effective each method has been for the corresponding problem. In other words, it is impossible to benchmark, compare and validate the application of methods in problem categories. This is because a collective culture of sharply defining, formulating, and benchmarking problems is practically non-existent in the AEC disciplines. For this, the generative design paradigm requires a unified way of evaluating the methodologies based on explicitly mathematical design frameworks. Specifically, we need to evaluate the formulated design space based on size (number of alternatives), evaluate the problem-solving methods based on their informed navigation potential for a human designer, explainability, reach/coverage, and reproducibility, as well as the justifiability of solutions.

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Augmented Reality-Driven Prototyping for Error Elimination During Computational Design and Digital Fabrication Odysseas Kontovourkis

This chapter proposes a methodology for small-scale prototyping using computational design and digital fabrication by incorporating Augmented Reality (AR), aiming at eliminating errors during the process. In the first stage, the chapter presents an algorithm for evaluating the accuracy of physical prototypes against digital design results, which have been developed in the context of an undergraduate course in computational design and digital fabrication. The errors that arise in each case are indicated based on quantitative and qualitative criteria. In the second stage, the process of fabricating corresponding structures by users with the participation of AR technology is proposed, providing a real-time correlation of the digital results with the physical outcomes throughout the fabrication process. Then, initial and new errors, which are occurred during computational design and fabrication, are compared, presented and discussed. Ultimate aim is the application of AR for eliminating errors in cases where computational design and digital fabrication incorporate human intervention.

1 Introduction While the well-established process of computational design to fabrication has been widely considered and its contribution has been recognized in many industries, it often appears to operate partially during the prototyping process. As a consequence, results are often unexpected and unsatisfactory in terms of required time or geometrical accuracy as well as costly as regard the required steps of the process. Moreover, specific design and fabrication processes cannot solely be carried out by using digital media, since the contribution of the human factor is inevitable. All the above often O. Kontovourkis (B) Department of Architecture, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6_2

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lead to major geometrical errors in the execution phase of the process and production of physical prototypes. Augmented Reality (AR) technology has been increasingly applied in the fields of architecture and construction industry the last few decades, especially in the context of the transition to Industry 4.0, which refers to the introduction of advanced technology and the digitization in the construction sector. The ability of AR technology to allow real-time interaction between the physical and digital environment and in particular its ability to project digital information that is visible to the users in the physical space [1] allows the emergence of a range of advantages in terms of architectural design and construction processes. Along with the other advantages that this technology can bring in the construction industry is the easy and low-cost use in the fabrication of complex shapes, an issue under consideration in the modern integrative processes from digital design to automated construction. More specifically, AR technology offers an alternative way of using digital construction media towards more efficient, low-cost and faster processing of complex structures. This might offer an alternative and productive integration of computational design and digital fabrication tools and at the same time might allow the active and efficient contribution of users during the process. Within this context, the next section of this chapter provides a literature review as regard the latest advances in this area of investigation and more specifically discusses the integration of AR technology within the framework of computational design to digital fabrication, which can be expanded into different directions and objectives. The theoretical investigation provides a generic overview regarding the latest developments in this direction of research and assist in the formulation of the methodology together with its application in the specific case study scenario of an undergraduate course.

2 Relevant Works The importance of Augmented Reality (AR) as a constantly evolving and emerging technology that can bring multiple benefits to the Architectural, Engineering and Construction (AEC) industry has been widely discussed in the last few decades with different works being presented both at the level of theoretical review and at the level of practical applications. Dunston and Wang [2] discussed the development of AR systems for digital content manipulation and human-to-human interaction as well as for planning, operation and inspection in job sites through superimposing digital info onto the user’s view in the real-world environment. In similar direction, Wang and Dunston [3] introduced an AR CAD platform, an augmented reality assisted viewer, that can reduce the time required for simple conflict detection tasks, providing spatial cognition benefits in comparison with a standard CAD tool. In the work by Chi et al. [1], almost ten years ago, the discussion has been focused on four technologies that have the potential to influence the development of AR applications in complex environments. Specifically, reference was made to technologies focusing on localization,

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natural user interface (NUI), cloud computing and mobile devices, aiming to assist AR technology towards specific architectural, engineering and construction tasks. Since then, significant advances have been made as regard the introduction of AR tools and technologies in AEC direction with applications to be mainly focused on visualization, inspection and monitoring in job sites, allowing decisions to be made [4], but without neglecting other implementations like 3D exterior and interior environment perception of space, collaborative and users centric design in various scales. Recently, significant work has been done towards the implementation of AR technology to enhance manufacturing and construction activities, which might allow a more productive and efficient involvement of unskilled users/workers in various constructions tasks. This was due to the maturity of AR technology that has reached a stage where digital platforms linked with AR devices have been widely available and open to the public for investigation. Special focus has been given to complex and non-standards designs, where the accuracy in the implementation of predefined tasks and the processing of the large amount of information often lead to errors and deviations during fabrication. In a recent work by Song et al. [5], the application of AR for digital fabrication in architecture has been examined based on literature review and analysis of respective works and publications. Briefly, in this work, AR applications were classified into three main categories: AR 3D holographic instruction, AR data sharing and AR for human–computer interaction. The first category, that of 3D holographic instruction was found to be the most widely published the last years with two sub-categories to be distinguished: AR 3D holographic instruction for assembly and AR 3D holographic instruction for fabrication. As regard the assembly process, several works attempt to apply AR for brick laying procedures, especially in case of complex wall structures that can be implemented by unskilled workers. Fazel and Izadi [6] introduced an affordable AR procedure for constructing free-form modular surfaces based on accessible devices, which included two cameras, two markets and one Head Mounted Display (HMD) based on Google Cardboard model. Several real-scale walls and columns were used as case studies for experimental execution, that included projection of virtual guidelines augmented on the HMD screen and user’s adjustment and bonding of bricks. These experimentations showed that the majority of errors were smaller than 6 mm and less than 2° for orientation. Similarly, Jahn et al. [7] demonstrated an AR approach for the holographic construction of a parametric wall in the form of a double-curved geometry based on the parametric environment of Grasshopper [8] with the use of Fologram [9], a plug-in for Grasshopper that allows viewing and sharing of information in the mixed reality environment, and the Microsoft HoloLens [10], a commercially available HMD. In this case, various planar courses of bricks were created and information related to the outline of the top face of each brick was overlaid on the construction site in order for the bricklayers to view each course separately, making the necessary corrections as regard the brick placement. The physical wall result showed that the use of the holographic model reduced construction time if comparison was made with time-consuming manual methods of measuring and setting out brick locations.

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Also, in terms of accuracy, the result was scanned and compared with the digital model, showing average deviations according to brick courses ranged from 21 to 5 mm due to the dimension differences of bricks. In similar directions, which involve the implementation of AR technology for the assembly of structural parts and modules through the projection of digital information or guidelines for their accurate placement, other examples using different components and materials can be found. In the work by Jahn et al. [11, 12], a method for steam bent timber elements was introduced, assisted by the application of AR technology and specifically the Fologram plug-in for Grasshopper with the use of HoloLens HMD. According to the suggested approach, temporary formworks were placed and an approximate method of forming timber was conducted based on AR. The results show that the use of AR for forming and assembling was a fast and reliable method for fabricating the bending elements due to the ability of the specific technology to allow easy positioning of formworks, eliminating, in parallel, their cost production. Similarly, in the work by Jahn et al. [13], AR plug-in Fologram with HoloLens hardware was applied for bending and then assembling, in this case, using mild steel tubes. In both cases, although deviations and errors might occur due to the available materials and the skills of the workers, the great importance and benefits of the method applied in cases of construction of complex structures were recognized. Examples of digital information and sequence of instructions that drive assembly with the application of AR can also be observed in the literature. In the work by Lharchi et al. [14], a framework in architectural applications was demonstrated based on an augmented assembly process using AR devices. In particular, a proposed Assembly Digital Model (ADM) was accessed by different stakeholders through a web-based platform with a 3D viewer for mobile, smartphone and tablet onsite usage. The users were able to assemble complex structures without previous knowledge or experience, only by extracting step by step information and guidelines regarding the assembly process, again through the HoloLens. Also, the work of Wu et al. [15] presented a method for bamboo material analysis, machine learning and augmented reality application. In this case, the system allowed the users to interactively create their own space, and after scanning available bamboo poles, it teaches them how to assemble the bamboo component in a sequence of steps using smartphone devices, resulting in an effective and fast construction of complex structures. The application of AR technology as information-driven mechanism that direct assembly sequence can be also observed in the work by Kontovourkis et al. [16]. In this work, an AR-driven methodology for assembling a modular shading device was presented stressing the necessity for specific application especially in cases where structures consist of a large number of elements and complex assembly tasks. In this work, construction time issues were investigated by measuring the time required by skilled and unskilled users/workers, showing that their assembly time performance can be improved with the use of AR, especially during the first layers of assembly. A large part of AR applications in digital fabrication is associated with the integration of AR technology into robotic manufacturing processes [17], which can be classified under the category of AR for human–computer interaction according to the work by Song et al. [5]. In this case, the need for seamless processes that incorporate

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AR and robotic technology for fabrication might help towards a fully automated and enhanced manufacturing process. An example in this direction was presented in the work by Johns [18], where the user was able to draw on the floor the trace of a complex wall, which was then projected in front of him using custom-made augmented reality glasses. The digital information could then be transferred to an industrial robot to build the wall by picking and placing brick components. The increased cost of using robotic mechanisms in digital manufacturing processes, and on the other hand, the need of introducing new and economically beneficial technologies, that reduce manufacturing costs, leading to AR application solutions, have been stressed and demonstrated in several works [15]. But beyond the cost of automated mechanisms, an important reason that has influenced the application of AR technology and has been discussed in many research examples is the ability of AR technology to achieve precision in the construction of complex structures. Also, the easy and effective guidance provided to unskilled users, workers, bricklayers, etc. towards the development of those structures. Furthermore, the available AR technology can provide a fast and reliable platform for parametric design and control, visualization and inspection, eliminating in this way the time require for programming and control of digital structures before their actual fabrication. Nowadays, the literature emphasizes that the rapid development and application of AR technology has been achieved due to the development of widely available tools but also due to the development of cloud computing and smartphones. In addition, parametric associative design environments like Grasshopper, a plug-in for Rhino and the ability of developers to introduce and make AR technology plug-ins available to the broader community, like the Fologram plug-in [9], have helped in this direction. Finally, the rapid development of HMDs for AR, such as HoloLens [10] has also benefited this direction of research as well. The above-mentioned literature review as regard the application of AR technology in several examples of computational design and digital fabrication but also the currently available technologies reveal their great potential as mechanisms to enhance users’ intervention in the workflow, offering advantages over processes where the user operates without the aid of technology. However, its implementation is still at an early stage of adoption in the AEC industry with a number of issues still unresolved, requiring their further exploration and consideration. An important aspect is the accuracy of the physical results obtained based on the available AR technology, which in the future might lead to widely adoption for application in real-scale construction scenarios. Towards this direction, the current research work proposes a specific computational design and fabrication workflow by integrating AR technology, as mechanism to increase the accuracy of physical prototypes produced when users/workers are involved. The integration of AR technology into a specific digital design and construction workflow aims to demonstrate the advantages that this technology can bring in terms of geometrical accuracy based on quantitative and qualitative criteria and discusses advantages and disadvantages over the users’ intervention without AR-assisted technology.

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The following section describes the methodology adopted for this research work by describing the two basic steps undertaken, the computational design and digital fabrication process based on manual users/workers intervention and the AR-assisted one. In both cases, the parametric design and control algorithms introduced are explicitly analysed and discussed further, together with their mechanism of comparison. Then, results are analysed and discussed, and finally, concluding remarks are provided.

3 Methodology In order to achieve this, initially the study refers to the analysis of results obtained based on a computational design to digital fabrication workflow as regard their geometrical accuracy. The development of the design results and physical prototypes was carried out as part of an undergraduate course taught by the author in the Department of Architecture at the University of Cyprus during Fall 2021. Within the framework of the above-mentioned course, although in fabrication stage a CNC router was introduced for formwork development, the human involvement was an indispensable part of the process towards the physical execution of prototypes. Inevitably, this has led to numerous deviations of the physical outcomes compared to the digital ones. The results were analysed using an algorithm that compares the digital design prototypes with the physical ones after their scanning using a structured light scanner. The deviations occurred due to the difference between digital and physical prototypes are presented and comparatively discussed. Then, same digital prototypes are selected according to quantitative and qualitative criteria for the second part of the process, that of physical prototyping with the application of Augmented Realty (AR) technology. In order to achieve this, initially the formworks produced through CNC milling are incorporated in a custom-made mechanism for AR implementation in order to achieve the accurate specification of formworks position for casting. Final part of the process includes the scanning of physical prototypes that are developed based on AR and their comparison as regard deviations and error measurements, which are occurred during physical production. The aim is to provide an indication of the differences occurred between the two fabrication approaches, the manually driven one, where formworks are positioned by students without the assistance of AR technology and the AR-driven physical prototyping one, where the application of AR technology is introduced as part of the fabrication process.

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3.1 Computational Design to Digital Fabrication The current study begins with the development of a series of 3D digital models and their physical implementation, a process that took place in the context of the undergraduate course, which was focused on introducing students to computational design and digital fabrication during the Fall 2021. The procedure referred to specific and distinct implementation steps, which the students were aware of and followed in order to implement their design solutions as well as their physical prototypes. Briefly, the steps of the proposed process were distinguished into two main stages, the computational design and the digital fabrication. In the first stage, that of computational design, the following steps were undertaken: . Topology Optimization diagrams Diagrammatic results of analysis based on Topology Optimization (TO) principles were provided to 28 students enrolled in this course. A structural beam was used as the case study under investigation, which was subjected to one specific boundary and six different loading conditions. These diagrams were produced using the plug-in TopOpt [19], a TO plug-in for Grasshopper plug-in [8] in Rhino 3D NURBS modelling software [20], which was developed based on the work by Sigmund [21]. The diagrams have been initially produced for developing similar concept as part of the same course held during Fall 2019 and has been presented in previous work done by the author [22]. The respective TO diagrams, together with grids consisting of 100 cells and 2D domains, were provided as the starting point for the development of the free-form beam shapes, following the suggested computational design to digital fabrication process. The TO analysis is not presented in this chapter since it is out of the scope of the current research work. However, the analytical description of the geometrical boundary conditions, input loading conditions and parameters used for TO analysis can be found in a previous work published by the author [22]. Figure 1 demonstrates the six diagrams developed through TO analysis in the form of contour curves.

Fig. 1 Six diagrams of TO analysis of case studies (CSs), demonstrating the material distribution according to different conditions and parameters

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. Variable values According to the number of participants in the course held during Fall 2021, 28 digital 3D models in the form of design cases (DC) were expected to be produced. As it has been already mentioned, the objective of this computational design exercise was to provide an understanding on parametric design principles by defining design variations according to the distance of each cell from the contour lines of TO diagrams. Thus, the mass generated and distributed in the overall shape is alternated according to the distance of cells from the contour curves. Specifically, cells in further distance from the contour curves are minimizing their mass, while cells in closer distance from the contour curves are maximizing their mass. The accumulated distribution of mass according to the distance leads to the generation of the overall shape and hence the development of the freeform beam structures. This process refers to respective alternated distribution of material in areas that is needed and according to the analysis results of TO, similar to functional graded structures [23–25]. The allocation of the loading and mass distribution diagrams to the students was followed by the three-dimensional development of their structures by defining a list of variable values in order to achieve design variety in accordance with the 100 cells grid and the specific 2D domain provided. Further or closer perpendicular distances between cells centre and contour curves in XY plane were recorded and presented in the form of tables (Fig. 2). In a subsequent stage, the data provided, through an inversely proportional relationship determined by simple mathematical equations based on each design case, is converted into a height value in Z direction in order to achieve the increase and decrease of the mass, depending on the corresponding closer and further distance. Finally, points are created with a distance from the centres of the cells equal to the Z height values.

Fig. 2 Diagram indicating the initial measurements as regard the distance between cells centres and contour curves (Student Alina Neophytou)

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Fig. 3 Design of basic lines or curves based on the height values (Students David Pereira, Christos Anthimou and Rafail Sarmallis)

. Curves configuration The introduction of intuitive design criteria by each student was considered as an important step in the design development stage together with more objective ones. Specifically, the main design objective was to achieve a design balance between the free-form shape of structure and the formwork in order to reduce material, while at the same time, maintain structural and construction efficiency. In this stage, initiation of the design process through the definition of basic lines or curves was achieved, with a view to the subsequent development of the three-dimensional structure. Figure 3 demonstrates different basic lines or curves proposals. . Main and secondary surfaces configuration In this step, the lines or curves are integrated to develop the main surface of the structure at the top as well as the side surfaces, defining the overall threedimensional shape in the form of a closed solid polysurface (Fig. 4). . Final three-dimensional free-form beam and formworks The final configuration of the free-form beam structure is achieved through mirroring of the three-dimensional shape resulting on a joint polysurface. Subsequently, the negative shapes of the two formworks are generated through Boolean difference applied to polysurfaces and their bounding box. Figure 5 presents selected DCs.

Fig. 4 Main closed polysurface development (Students Styliani Ioakeim and Ana Maria Ioannou)

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Fig. 5 a Final digital prototypes and b respective formworks (Students Alina Neophytou and Christos Anthimou)

In the second stage, that of digital fabrication, the following steps were undertaken: . CNC toolpath generation In order to produce the physical prototypes through the gypsum casting process, the two free-form formworks that were designed in each design case (DC) were proceeded to the production process using a CNC milling machine. In order to calculate the toolpaths for formworks CNC milling, the software DeskProto Version 7.1 [26] was used. The formworks were milled at scale 1:20 and based on the parameters indicated in Table 1. Also, Fig. 6a shows toolpaths and Fig. 6b simulation results throughout the process. The parameters and calculation process lead to the creation of a NC-Program file (.iso) that is sent to the CNC machine for execution. Table 1 CNC milling machine settings for formwork production Machine

Cutter

Precision

Speeds

ISO plain G-codes -mm

Flat tip, radius 3

Distance between toolpaths

Feed rate

Spindle speed

Diameter 6 mm

0.67 (d/9)

2000 mm/min

2000 rpm

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Fig. 6 CNC milling calculation toolpaths and simulation of a characteristic DC (Student Alina Neophytou)

. CNC milling execution Polystyrene material with 5 cm thickness is used for the production of formworks through the CNC milling procedure. Figure 7 demonstrates results during CNC milling execution and formwork production. . Formwork manual adjustment and material casting In the final step, the placement and manual adjustment of the distance between the two polystyrene formworks are conducted using a wooden base as guideline. Subsequently, casting and production of physical prototypes in 1:20 scale are achieved using gypsum as the material of implementation (Fig. 8). Based on this approach, 28 manually driven Fabrication Studies (M-FSs) are physically produced with a variety in their free-form shape that is the results of both specific computational design steps but also subjective design decisions taken by each student individually. Through the above-mentioned design exercise, it is expected that students will acquire knowledge as regard basic method of parametric design, that lead to free-form shape generation. At the same time, the specific exercise aims to raise awareness as regard the development of design solutions that are driven by material usage minimization principles. Figure 9 demonstrates selected physical prototypes. The limitation occurred during computational design to digital fabrication process and the drawbacks observed during the production of prototypes, that are mainly due to the manual adjustment of the two formworks, prevent the establishment of a fully automated production process. Inevitably, this leads to geometrical deviations of prototypes from the ones produced during the computational design stage.

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Fig. 7 CNC milling procedure and formwork results (Students Christos Anthimou and Styliani Ioakeim)

Fig. 8 Formworks adjustment and gypsum casting (Students Styliani Ioakeim and Katerina Pavlou)

3.2 Manual Formwork Adjustment Results Evaluation In order to detect the geometric deviations and errors that arise in the fabrication process of M-FSs, this part of the methodology describes an accuracy evaluation approach in the production of their physical prototypes by comparing the results obtained with the digital ones. Initially, the physical prototypes are scanned by using a structured light scanner. The process refers to placing the physical prototype on a turn table at a set distance

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Fig. 9 Selected physical prototypes based on manually driven fabrication (Students Christos Anthimou, Rafail Sarmallis, Panayiotis Anastasiou)

Fig. 10 3D scanning of physical prototypes using the structured light scanning procedure

from the projector and cameras, which capture consecutive images of the prototype. The main settings refer to 20 segments that make up a complete rotation around the axis of the prototype, which are then integrated with the help of the software and create the final 3D prototype in mesh form (Fig. 10). For the accuracy evaluation of results, a visual algorithm that is developed in the parametric design environment of Grasshopper plug-in is proposed. The purpose of the algorithm is to mainly provide quantitative and qualitative results as regard the geometrical differences between the mesh model of the physical prototype and the polysurface model of the digital one. Specifically, the digital file of each physical prototype is imported into the parametric environment as mesh geometry and checked in terms of its total volume (mm3 ). Also, in the same algorithm, the digital file of each generated model, through the computational design procedure in the form of a polysurface, is imported and checked as regard its total volume (mm3 ). The two volumes can be checked and compared, indicating the physical/digital percentage of volume differentiation (%). Regarding the calculation of the deviation of all surfaces resulting from the physical and digital prototypes, the algorithmic steps are as follows. Firstly, due to the arbitrary positioning of scanned mesh file on the digital environment in relation to

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Fig. 11 Colour gradation of the minimum and maximum distance deviation between the physical and the digital prototype of M-FS 10

the digital one, an accurate correlation of the mesh model of the physical prototype with the polysurface model of digital one is necessary. In order to achieve this, a single-objective Genetic Algorithm (GA) is introduced, that calculates the exact transformation (rotation) angles in the three axes (X, Y and Z) of a bounding box that encloses the mesh geometry. The minimum box volume is used as fitness value in the Galapagos evolutionary solver in Grasshopper plug-in [8]. The optimized rotation angle of mesh bounding box and the orientation of digital model bounding box are used for re-orienting the mesh geometry in order to accurately align with the digital prototype. Secondly, the centre points of faces of each mesh geometry are extracted by using a parametric component that finds the closest point on a BREP geometry. As a result, the distance (mm) between the centre points and the closest point on polysurface is calculated. Due to the large number of faces in each mesh, and hence, the large number of distance values obtained, the calculation achieves the extraction of high-resolution results over the entire extent of the surface coverage of the models. Also, the algorithm provides measurable information regarding the minimum and maximum distance (mm) of each face centre from the digital surface, as well as the average distance value (mm) obtained from all surfaces. Finally, through the colour gradation of the minimum to the maximum distances, it is possible to qualitatively investigate the results and detect the areas with the least and the greatest error (Fig. 11).

3.3 AR-Driven Formwork Adjustment Results Evaluation In the next step, a number of AR-driven Fabrication Studies (AR-FSs) are selected to repeat the fabrication process, this time by applying AR technology. The difference between this process and the previous one lies in the change in the way the two formworks of each prototype are set up for gypsum casting. The steps regarding the computational design and digital fabrication of formworks using CNC milling process remain the same. The errors occurred in the phase of adjusting the position of formworks for casting, and for this reason, this step is taken into further consideration.

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As it has been mentioned in the second part of this chapter, the latest developments as regard Augmented Reality (AR) technology with open source and plug-ins widely available for use in well know parametric design platforms, for instance, the Fologram plug-in, allows seamless and uninterrupted workflows to emerge within the same digital environment. Together with the flexibility offered for real-time modification of parametric variables, through parametric design platforms, for instance, Grasshopper plug-in in Rhino 3D NURBS modelling software offers new opportunities to consider alternative solutions using AR technology. Also, the possibility of using the Fologram plug-in allows the projection and viewing of digital/parametric results through simple devices such as mobile phones and tablets. This demonstrates additional advantages such as the reduction of the cost of purchasing specific devices and their replacement with widely available devices mostly used on a daily basis. The cost of purchasing HMDs could be a deterrent to the application of the technology in some cases. The present study refers to the use of the above-mentioned software, due to the possibilities of their integration within a unified parametric design framework, which is based on the previous investigation regarding the evaluation of the geometric accuracy in the production of the physical prototypes. Hence, in the digital environment of Grasshopper and based on the algorithm developed above, Fologram components are incorporated to handle the AR process. Specifically, the goal is to place the digital hologram in the real space and overlay it within a proposed mechanism for the highest possible accuracy of setting the position of the formwork in each case. The already existing algorithm incorporates additional parametric components for AR-driven formwork adjustment. More specifically, the polysurface file produced during computational design is used as the starting point. This prototype is appropriately rotated to facilitate the casting of the material as well as the projection of the hologram in the physical environment based on the specific structure and function of the proposed formwork mechanism. Two main surfaces of the prototype appear as holograms, the upper and lower surfaces in order to overlap and align them with the boundaries of the formworks produced through CNC milling. For the projection of the two surfaces, the parametric component of Fologram that deals with synchronized geometry is used, which is controlled by a number slider according to the surface selected for holographic projection. In order for the users/workers to select and control which of the two surfaces are used during the fabrication process, the number slider controlling the projection of upper or lower surface is connected with the Fologram plugin through the use of sync parameters component. The surface holograms can be viewed using the Fologram application in Smartphone or iPhone devices. Initially, a QR code is generated in Rhino software that is scanned by the mobile device. Then, through the Fologram app, the surface for projection is scanned and a specific position for hologram placement is defined by the users/workers. Then, the mobile is placed on a specially designed support system that together with the formwork containers consists the basic structure of the proposed mechanism. This system allows easy adjustment of formworks position according to the holographic projection of prototypes surface (Fig. 12). This is followed by formworks position locking and

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gypsum casting that results in the hardening of the material and its removal from the formworks (Fig. 13). As final step in the AR-driven fabrication process, the physical prototypes are scanned using the structured light scanner and importer to the previously presented algorithm for the new accuracy evaluation. The results obtained from the accuracy evaluation based on manual adjustment and the results obtained based on AR-driven adjustment are compared and discussed.

Fig. 12 AR-driven formwork positioning

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Fig. 13 Gypsum casting and hardening of prototype

4 Results and Discussion In this section, the results from both the first phase of experimentation, i.e. the analysis of the accuracy in the production of the prototypes by the manual adjustment of formworks, and the results from the second phase, i.e. the analysis of the accuracy of the produced results with the application of AR technology, are presented and discussed. Specifically, the first part presents the results obtained from the analysis of 10 out of 28 physical prototypes produced. The second part presents the results obtained from the analysis of 3 selected examples based on the 10 prototypes examined in the first phase. The listing and comparison of the results leads to important conclusions regarding the usefulness of the proposed process to be incorporated in the suggested computational design to digital fabrication workflow. Undoubtedly, the results are based on a number of assumptions, which can be volatile and change from case to case. Thus, the evaluation of the process requires consideration of the parameters and criteria set in each case.

4.1 Results Based on Manual Adjustment of Formworks From the 28 case studies that were originally produced during the undergraduate course based on the suggested computational design to digital fabrication by integrating manual adjustment of formworks, 10 samples of M-FSs are selected to be studied further by checking their accuracy according to their geometry, in an effort to cover solutions with different design criteria. Following paragraphs summarize the quantitative and qualitative results of this comparison based on the algorithm presented in the previous sections of the chapter. Table 2 summarizes the results obtained from the first evaluation phase. As it can be observed, the 10 M-FSs together with measurable information regarding deviations

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of the physical versus digital prototypes is provided as well as information regarding the increase or decrease in the total volume of the free-form shapes. Figure 14 presents in the form of a graph the percentage of volume change of the physical prototypes that have been produced by the students based on the manual adjustment procedure. Results of percentages less than 100% indicate that the volume of physical prototypes is smaller than the digital ones, while percentages greater than 100% indicate an increase in the mass of the physical prototypes compared to the digital ones. Based on the evaluation conducted, only 2 out of 10 prototypes have smaller volume as regard their physical prototypes compared to the digital ones, the M-FS 6 and M-FS 9. In contrast, the physical/digital volume deviation percentage for the remaining 8 M-FSs ranges from 101.32 to 150.25%. The first percentage is the smallest and refers to the M-FS 10, which by extension is closest to its faithful reproduction, while the second percentage appears to be the largest deviation in relation to the volume and is reported in M-FS 8. Figure 15 demonstrates the deviation tendency of each digital model against its physical/digital volume deviation percentage. The graph indicates that in high volume design examples such as M-FS 4, M-FS 6 and M-FS 10, small values of physical/digital volume deviation percentage are observed, namely 107.74, 96.26 and 101.32%, respectively. On the contrary, in cases of design development of small and medium volume prototypes, greater percentages of physical/digital volume deviation are observed, as for example, in the cases of M-FS 1, M-FS 3, M-FS 5 and M-FS 8, where values are 135.76, 133.04, 118.99 and 150.25%, respectively. Figure 16 shows the average distance deviation of each M-FS in relation to the physical/digital volume deviation. As it can be logically extracted from this graph, MFS prototypes with minimum physical/digital volume deviations have also minimum average distance deviation between the surfaces of physical and digital prototypes. Specifically, M-FS 4, M-FS 6 and M-FS 10 have the minimum average distance deviation with values 1.11, 1.54 and 1.74 mm, respectively. Figure 17 shows qualitative results obtained through distance deviation measurements. Specifically, the colour gradations of all surfaces based on the minimum and maximum distance deviation values between digital and physical prototypes are presented. Figure 17a presents the results in the case of M-FS 10, where a minimum distance deviation of 2.5E-5 mm, a maximum deviation of 7.45 mm and an average value of deviation of 1.74 mm appear. Figure 17b presents the results in the case of M-FS 8, where a minimum distance deviation of 2.61E − 6 mm, a maximum deviation of 11.36 mm and an average deviation value of 3.6 mm appear. Also, the diagrams show the colour intensity as regard the distance deviation on each side of the free-form shapes. The colour intensity shows that in the case of M-FS 10, large distance deviations appear on the surfaces located at the edges of the shape, while on the surfaces processed through CNC milling, very small distance deviations are shown. On the contrary, in the case of M-FS 8, the CNC milled surfaces show larger deviations compared to those of M-FS 10 due to possible errors during manual adjustment of formworks distance by the student. Finally, as in the case of M-FS 10, the comparatively larger distance deviations of the surfaces of M-FS 8 appear on the surfaces located at the edges of the free-form shape.

7.37758

7.451217

3.41E−06

0.000025

9

10

6.75294

11.36906

6.17E−07

2.61E−06

6.516711

7.845024

5.319592

9.319831

7

1.43E−06

6

6.810303

8.051121

8

5.13E−07

1.12E−06

4

1.27E−06

3

5

7.98E−07

2.92E−07

1

2

1.964195

1.742442

2.098001

3.604892

1.882264

1.546748

1.480337

1.117282

2.061577

2.654631

186080.84

334113.72

202074.62

247651.52

251616.87

260979.44

203255.06

294598.54

181793.46

229943.50

338526.79

148315.63

372097.32

319620.25

251234.40

241870.66

317403.59

241870.66

321994.14

252631.90

Physical

Volume deviation (mm3) Aver

Digital

Max

Distance deviation (mm)

Min

M-FSs

A/A

Table 2 Accuracy evaluation results of the 10 M-FSs

101.32

73.39

150.25

127.02

96.26

118.99

107.74

133.04

140.03

135.76

Physical/Digital (%)

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Fig. 14 Physical/digital percentage of volume deviation

Fig. 15 Volume deviation tendency. Digital prototypes with large volume have smallest percentage of physical/digital volume deviation

4.2 Results Based on AR-Driven Adjustment of Formworks The deviations observed in the above results of the 10 prototypes are re-examined through their re-fabrication by using AR technology. From the 10 M-FSs examined in the previous phase, 3 are selected for further processing. The 3 new results shall be called AR-driven Fabrication Studies (AR-FSs). The specific examples are selected based on quantitative and qualitative deviation results observed during the previous investigation. Specifically, the samples selected are the M-FS 3, the M-FS 5 and the M-FS 8, in an attempt to explore the possibility of reducing their relatively large deviations in relation to other examples.

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Fig. 16 Comparison between distance and physical/digital volume deviations of the 10 M-FSs

Fig. 17 Colour intensity of distance deviation between physical and digital surfaces in the samples of the M-FS 10 and M-FS 8

As it has been mentioned in previous section, the 3 selected cases go through the same CNC milling procedure for formwork development but with the only difference being the formwork adjustment that involves AR technology by the user/worker. The physical prototypes produced through the AR-driven approach are scanned again based on the settings of structured light scanner introduced in previous part. Then, by using the accuracy evaluation algorithm already introduced in the methodology part of the chapter, deviation results are obtained. Table 3 provides the deviation results of the selected M-FSs occurred in the previous phase of the research and the results of respective AR-MSs prototypes occurred during AR-driven fabrication procedure. Figure 18 demonstrates the percentage physical/digital volume deviation of the AR-MSs that have been produced based on AR-driven adjustment of formworks in comparison with the results of volume deviation obtained in the previous phase

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Table 3 Accuracy evaluation results of the 3 AR-FSs in comparison with the results of respective M-FSs AR-FSs

Distance deviation (mm)

A/A

Min

1

Digital

Physical

Physical/Digital (%)

7.944864 1.346931 181793.46

178605.87

98.24

M-FS 5 1.1165E−06 7.845024 1.480337 203255.06 241870.665 118.99 AR-FS 2.61E−06 2

3

Aver

M-FS 3 1.2707E−06 9.319831 2.061577 181793.46 241870.665 133.04 AR-FS 4.81E−07 1

2

Max

Volume deviation (mm3 )

5.582048 0.940000 203255.06

208350.12

102.5

M-FS 8 2.6095E−06 11.36906 3.604892 247651.52 372097.324 150.25 AR-FS 4.13E−06 3

9979.444 2.154686 247651.52

284182.24 114.75

of investigation. As it is shown, in the case of AR-MS 1 and AR-MS 2, the physical/digital percentage of volume deviation reaches the values of 98.24 and 102.5%, respectively, improving significantly the deviation results of respective M-FSs. More specifically, in the case of AR-MS 1, there is a reduction in the deviation at 34.8% and in the case of AR-MS 2 at 16.49%. Similarly, in the case of AR-MS 3, reduction of the physical/digital volume deviation at 35.5% is achieved compared to respective M-FS 8. This indicates that the application of AR technology can improve the process of adjusting the position of formworks towards the accurate production of physical prototypes. Figure 19 demonstrates comparative results as regard the average distance deviation for both, selected M-FSs and AR-MSs. It is observed that similar to the reduction of physical/digital volume percentage, a significant reduction of average distance deviations in all cases can be achieved with the application of AR. In the AR-MS 1,

Fig. 18 Physical/digital volume deviation in percentage and comparison between M-FSs and ARFSs

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Fig. 19 Comparison between average distance deviation of selected M-FSs and AR-M-FS

while the average distance deviation value was 2.06 mm, this has been reduced to 1.34 mm. Similarly, in AR-MS 2 and AR-MS 3, the average distance deviation values were 1.48 and 3.6 mm and have been reduced to 0.94 and 2.25 mm, respectively. Figure 20 demonstrates the qualitative results obtained from the comparison between physical prototypes developed through manually driven formworks adjustment and AR-driven ones. Specifically, the qualitative results are related to the colour gradations of the perpendicular distance deviations between the surfaces of physical and digital prototypes. Figure 20a shows the distance deviations occurred in the case of M-FS 3 and AR-FS 1. In this case, the minimum deviation is 1.27E − 6 and 4.81E − 07 mm, respectively. The maximum distance deviation is 9.31 and 7.94 mm, respectively, with the average deviation to be 2.06 and 1.34 mm, respectively. Figure 20b demonstrates the distance deviation for M-FS 5 and AR-FS 2. In this case, the minimum deviation is 1.16E − 6 and 2.61E − 07 mm, respectively. The maximum distance deviation is 7.84 and 5.58 mm, respectively, with the average deviation at 1.48 and at 0.94 mm, respectively. Figure 20c compares the deviations of cases M-FS 8 and AR-FS 3. It is observed that minimum, maximum and average distance deviation for M-FS 8 is 2.6E − 6 mm, 11.36 and 3.6 mm, respectively, while for AR-FS 3 is 4.13E − 6, 9.97 and 2.15 mm, respectively. The colour intensity ranges between green, showing areas with minimum distance deviation, to red, showing areas with maximum distance deviation. The comparison between the pairs of cases examined above shows an improvement in the deviation measurement indicators in the second column, where the prototypes are the result of adjusting the position of formworks using AR technology. This indicates the usefulness of the proposed procedure, even though the results do not achieve 100% correlation of the physical with the digital prototypes.

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Fig. 20 Qualitative results of geometrical deviations occurred in the case of physical prototypes production based on manually driven and AR-driven adjustment of formworks. The colour intensity shows minimum and maximum perpendicular distance between the surfaces of physical and digital prototypes

5 Conclusions The research presented in this chapter has focused on the development of a methodology for the production of small-scale prototypes using a computational design to digital fabrication process. Emphasis has been given on evaluating the accuracy of physical prototypes versus digital ones based on produced formworks through the CNC milling process, and subsequently based on their adjustment for material casting. In the last part of the process, two different production methods are proposed. Initially, prototypes are produced based on manual positioning of formworks by the

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users/workers, specifically the students of an undergraduate course. Then, the adjustment of formworks is achieved using AR technology. The research proposes specific algorithms, both for the accuracy evaluation and for the interoperability of the parametric design part with the AR technology. Nowadays, the rapid increase in the possibilities offered by AR technology allows a seamless connection between digital and digital world in a dynamic and flexible manner. The purpose of introducing AR technology is to achieve a reduction in distance and volume deviations between physical and digital prototypes. The goal of the proposed methodology is the formation of a research framework that allows an uninterrupted workflow from computational design to digital fabrication of free-form shapes to be established. Despite the rapid and recent developments in this area of research, in cases where human involvement is necessary, further investigation is required. In the event that the human factor is an important part of the process, the enhancement of the digital fabrication with AR technology can help reducing deviations and errors during the production phase and, by extension, improve the production process. The evaluation of the results is divided into two categories. Firstly, the results of accuracy evaluation in case of physical prototypes that have been produced manually, which are called manually driven Fabrication Studies (M-FSs), are demonstrated. Examples with large deviations are observed and reproduced through the AR process, which are called AR-driven Fabrication Studies (AR-FSs). Then, the results from both studies are evaluated and compared. The accuracy assessment indicates that the use of AR can greatly enhance and improve the results obtained in the fabrication phase. In particular, the evaluation of AR-FSs indicates that the method can lead to a reduction of the average deviation value of the prototypes, which ranges from 0.5 to 1.45 mm. Also, it can reduce the physical/digital volume deviation, which range from 16.49 to 35.5%. Despite the advantages that the application of AR technology can bring to the fabrication of free-form shapes, it is important to consider the advantages and disadvantages in the selection of hardware (mobile phone, tablet, HMDs, etc.), depending on the task to be performed. For example, in the case of the fabrication of free-form structures in scale, such as the work presented in this chapter, this can be implemented through the use of a mobile phone or tablet. In other cases, such as the construction of free-form structures in real scale, the use of HMDs can provide more freedom to involve users in the process since it frees their hands and leaves them undistracted in the construction process. In any case, the cost of each device and its availability should be taken under consideration. The present research has the potential to be improved through future actions such as increasing the samples for examination, both at the level of the manually driven formwork positioning control process and at the level of AR-driven process. Also, by increasing the quantitative and qualitative evaluation criteria introduced, further results and conclusions regarding the manufacturing accuracy of the studies under investigation will be drawn. Also, issues concerning other steps in the process, for instance, the CNC milling settings applied, could be discussed and re-evaluated. Future goals are the holistic control and evaluation of all steps undertaken throughout the computational design and digital fabrication process that incorporates human

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intervention, and the application of AR technology to other examples of free-form shapes production, both in small and large scales. Acknowledgements The results of the manually driven Fabrication Studies (M-FSs), which were presented in this chapter, were developed within the context of the undergraduate course ARH-220 Digital Architectural Communication Media, taught by the author during the Fall semester of 2021. The results of AR-driven Fabrication Studies (AR-FSs) have been produced at a later stage by the author. I would like to sincerely thank all the students who attended the course and their works are presented in this paper. Also, I would like to sincerely thank George Vessiaris and Dimitris Stylianou from the FabLab UCY of the Department of Architecture, UCY, for their great help and support during all phases of the process.

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Design of Gesture-Controlled Interface for Mechatronic Systems: A Computational Approach Apostolos Tsagaris, Maria Economou, Athanasios Manavis, and Panagiotis Kyratsis

The paper focuses on designing and developing an interface for interacting with a mechatronic system through gestures. Using machine vision techniques, a methodology is developed that aims to record and locate the gesture through an image capture system. Once the gesture is isolated and gesture recognition is possible, the appropriate control commands of the system are determined. This makes it possible to control the mechatronic system through a dictionary of movements, called gesture vocabulary. The results of the methodology were applied to a real mechatronic system and showed significant results. The efficiency and effectiveness of the interface emerged from a satisfactory sample of users. It appeared quite easy to use, but also presented some basic difficulties in its application. The conclusion of the research is that controlling mechatronic systems through gestures can be a very important interaction interface.

A. Tsagaris (B) · M. Economou Department of Industrial Engineering and Management, International Hellenic University, 57400 Sindos, Thessaloniki, Greece e-mail: [email protected] M. Economou e-mail: [email protected] A. Manavis · P. Kyratsis Department of Product and Systems Design Engineering, University of Western Macedonia, 50100 Kila Kozani, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6_3

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1 Introduction Due to the evolution of technology in the field of computer system development, the modern era allows the interaction of the human factor with computers. This fact contributes to the most efficient service of the daily life of the person, providing the best possible solution to each of his problems. From time to time, research is carried out with the main concern of collecting and processing such problems and with the ultimate goal of identifying easy-to-use applications, thus solving human– computer interaction problems. The algorithm formulated by the computer systems, in combination with the engineering, provides a basis for a more enhanced experience for the users of these systems, through the concept of robotics. Computational vision is used in several applications, making extensive use of the integration of this technology in mobile phones. It is the field of study that describes how computers view and understand digital images and videos and also covers all the work performed by biological vision systems, understanding complex visual stimuli and exporting complex information in a form that can be used by other procedures [1]. In order to understand digital images and videos, it is first important to identify their area of interest, which can be found through the analysis of color space, i.e., the range of colors that a particular device can produce or record [2]. The retrieval of the binary mask, the digital image that separates the background pixels from the pixels of the area of interest in the form of logical bits ‘0’ and ‘1’, respectively [3], is an important step in retrieving the area of interest. Thus, later, using appropriate algorithms, commands for human–computer interaction can be defined. To complete an application or a product, it is necessary to study its usability, the degree to which a system can be used by specific users to achieve specific objectives under defined conditions of use with efficiency and effectiveness, providing subjective capacity to end users [4]. The designers of the application need to penetrate the way of thinking of the end users and anticipate points that should be paid attention to, in order to provide them with the most positive experience possible. The purpose of this work is to develop an interaction system for navigating a robotic vehicle through gesture interaction. A one input-one output interface is created, where at the input the development of artificial vision for the recognition of the gesture is allowed. Then, while the system has collected all the necessary information needed, such as the color of the hand, the areas where the fingers are detected and the distance between the fingers, it performs the recognition of the shape of the hand, and accordingly with its position in space, it perceives the movement that be transferred to the robotic vehicle each time (right, left or straight), so that it in turn can move accordingly. The conclusion that emerges from the information collected is transmitted to the robot’s engines in the form of motion commands, the combination of which brings its self-direction in the desired direction.

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2 State of the Art The human–computer interaction in the context of computational vision is a field that has occupied much research and development of various methods of object recognition. Such methods are widely used in areas such as education, medicine, industry, entertainment and applications designed for home use. In the field of education, MATLAB™ is, perhaps, the most widespread environment for the development of a computer vision system. This is due to the fact that this software provides the ability to add and customize special libraries, which have the appropriate tools to create such applications. In the literature, there is a report on how to implement a mathematical model using the Fuzzy Logic toolkit, which aims to identify the skin through the Mamdani method for the YCbCr color space [5]. OpenCV™ is a very popular library for real-time computing that is used in industry and other areas. This library is based on artificial intelligence and provides programmable image processing methods for recognizing gestures for human– computer interaction [6]. OpenCV™ is written in C++ and can be integrated into the MATLAB™ environment. Computational object recognition can be performed by methods such as detecting the color area, determining the size of the object, calculating the parameter of the depth of the object in space or a combination of these methods. The Kinect™ camera, found on motion recognition consoles such as the Xbox, has two sensors, one of which inserts the recorded image in RGB, while the other calculates the depth of the objects contained in the image [7]. There is frequent reference in the literature for computational vision in service applications, such as earthquake rescue services. In this context, special robots have been programmed, for the purpose of patrolling, locating and rescuing people after seismic disasters [8]. These robots can approach demolished areas from where they collect information in the form of images, which are then processed to detect any victims. The development of the Internet of Things has led to the integration of computational vision into applications designed for smart homes. This allows you to operate any home appliance connected to the Internet, just by recognizing hand gestures [9]. Another example of such an application are security cameras that recognize the human characteristics of the members of the house and issue an alarm signal for an intruder or an unwanted person.

3 Methodology The implementation of the system requires the use of a simple computer video camera and a suitable toolbox and library of robotic functions for driving the robotic equipment. The creation of the interface for the wheeled vehicle was carried out in the environment of the MATLAB™ application, using the GUIDE tool, while the

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Fig. 1 Fingertip detection methodology

software was programmed in the C++ programming language. In addition, an open library ‘RWTH—Mindstorms™ NXT Toolbox’ offered by Aachen University was used to link the software to the wheeled vehicle [10]. The steps of the fingertip recognition methodology are described in the Fig. 1. The methodology includes four basic steps: capturing the gesture, recognizing the gesture, extracting its characteristics and, finally, defining the commands of the movements that are exported according to these characteristics.

3.1 Raw Data Video Capturing When testing various values for video resolution, it was observed that the higher the value of the resolution, the lower the performance of the system, in terms of computing power, resulting in a noticeable delay in the response of the graphical environment. For this reason, the resolution of 320 × 240 pixels was preferred.

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3.2 Gesture Recognition After the video recording is completed, the recorded video is split into the individual digital images of which it is composed, each of which is then subjected to multiple processing steps until the hand shape recognition is successfully performed. The first step in recognizing the shape is to successfully identify the skin area. Later, the extraction of the object that constitutes the handpiece is required, while finally, according to the previous analysis and with the help of an appropriate algorithm, the areas of the object that correspond to fingertips are located (Fig. 2).

3.2.1

Detection of the Skin Area

The skin color model looks simple visually, but can become quite complicated when it comes to programming it in machine language. Important factors to consider in this process are: a) the device used for video recording, b) the lighting, which often distorts the colors of the images, c) the movement of objects in an image, which can cause blurring of the area of interest, d) the fact that skin color differs between people and e) the color space used for analysis. Below are the characteristics of the RGB and normalized rg color spaces tested, with full reference to the technique chosen for skin detection.

Fig. 2 Implementation stages for the recognition of the handicraft

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Fig. 3 RGB color model

RGB Color Model The RGB color model consists of a combination of three color regions: red, green and blue. These three components are combined to reproduce more colors. RGB includes the brightness component, which depending on the intensity at which it exists, causes the corresponding color alteration. In fact, the blue component does not provide any valuable information in the case of hand recognition, as the skin color area is made up of red and green components, mixed with brightness information. To study the RGB color space [11] (Fig. 3), the SIdb (Skin Image Database) library from the Cobris website was used, consisting of 357 images with differentiated skin colors [12]. Based on this, a relevant model was extracted to separate the elements of an image that constitute a skin area from the areas that constitute its background (Kovac model). This model is divided into four sub-rules [12]: 1. 2. 3. 4.

R > 95 and G > 40 and B > 20 Max(R,G,B)–Min(R,G,B) > 15 |R–G|>15 R > G and R > B.

This model was later used to create a new method based on mixing and creating new colors. The rule of this method is characterized by the equation [11]. 0.0 ≤

B R−G ≤ 0.5 and ≤ 0.5 R+G R+G

RG Normalized Model This model is a variant of RGB. The theory behind it is to simplify the components of the colors red, green and blue, in order to eliminate the component of brightness that

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Fig. 4 Mathematical equation as a function of the components of colors

affects their true value. The mathematical model that describes the normalization of RGB space is understood from the following relations. The normalization of the blue component is not particularly important, as it is not used by this model (Fig. 4). To determine the area of interest of the rg shot, a ready-made image library consisting of skin parts was used [3]. The conclusion from the library study is that the color components occupy a very small area of color with little scattered points that could geometrically look like a rectangle. Based on this geometric shape, the block of the spaces for the r and g axes is determined in order to extract the mathematical reference needed in the writing of the code. Having defined the area of interest, the maximum and minimum intervals of the red and green components for rg can now be determined [3]: r = [0.34, 0.62], g = [0.25, 0.42] In practice, the normalized model is more complex than RGB, as rg encoding acts as a filter, smoothing the colors and removing existing brightness and shading. According to research by Tsagaris et al., it has been shown that the use of the normalized RGB color space (rg) has many advantages in gesture recognition applications [13] with image scale and rotation invariance. Therefore, it makes the application even more robust and efficient [14, 15].

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3.2.2

Hand Segmentation

Binary Mask Calculation Having determined the appropriate skin model for the detection of the gesture, the next step is to isolate the parts of the image that constitute the area of interest, from the parts that constitute the surrounding space. This is achieved by applying a binary mask to the normalized image, which acts as a filter by coating the pixels of the area of interest in white—logic 1—and the pixels in the background in black—logic 0. The binary mask δ_λ is divided into basic components θ_λ and χ_λ, according to the relation [3]: δλ = θλ + χλ , where: • δλ , the binary mask resulting from the frame through skin detection, • χλ , the binary mask that includes only the hand figure, • θλ , the noise included in δλ . Therefore, the hand figure component can be modeled as the difference function [3]: χλ = δλ − θλ . Noise Reduction The noise encountered in such applications is often in the form of white areas or spots that do not belong to the gesture, or black spots that appear on the skin and are recognized as non-dermal areas. Also, the ‘trembling’ that is often created around the figure of the hand is a form of noise. For effective recovery of the shape, noise removal is necessary. This is achieved by adding special filters that correct the mathematical morphology of the binary mask. The combination of the following four morphological filters, applied in serial alternation, effectively isolates the noise [3]: • Dilation—Expansion of objects, • Erosion—Contraction of objects, • Opening—Smooths the closed line (border) of an object, breaks narrow channels and eliminates fine areas, • Closing—Merges narrow fractures and long thin cavities, eliminates small holes and fills gaps. The choice of filters to use is related to the way the user chose to locate the fingertips. In the present work, the K-Curvature method was used, which aims to detect the fingertips using overlapping vectors. This method is explained in the next chapter. The morphological filters selected and related to the K-Curvature method are the zoom in and out. Their combination results in the recovery of the hand figure just as it was previously captured by the digital camera, without any distortion. Finally, the binary filler was used. As mentioned earlier, there is a possibility of black spots appearing on the gesture. This indication is incorrect, if the case of bare

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Fig. 5 Algorithm for gesture recovery

skin is examined. The filtration filter, in effect, ‘fills’ the black areas that are points of noise. After editing and simplifying an image, it is possible to retrieve more than one object, which is not actually a gesture. This is because of the presence of objects of the same color area of interest in the background. The process of disposing of unnecessary objects is carried out taking into account that the shape of the hand prevails in most of the image. Therefore, using appropriate commands, the objects in the image are detected, and then, by comparing the area of these objects, the object with the largest area is selected, while the rest are deleted. In this way, the image under study is freed from the extra noise. Gesture Contour Recovery In a digital image, to retrieve the contour of the hand, the purpose is to calculate the value threshold resulting from the binary mask of a pixel with its neighbors. The algorithm for retrieving the contour of the gesture includes the following steps: Initially, the image under study is scanned vertically until an element whose value is equal to 1. A coordinate value of the current pixel is stored in a variable A. Retrieving the point corresponding to this variable means that a point belonging to the outline of the hand was found. The scan continues, and all elements after A change their value from 1 to 0, as they are a point of the handform. The algorithm then looks for the point where the pixels cease to be displayed in white—logic 1—where it stops displaying the skin area. This last point is assigned to a second variable B. This completes the scan for the first column of the image elements, and the algorithm is repeated for the remaining columns [3] (Fig. 5).

3.2.3

Fingertip Detection

Finding the fingertips requires the use of an appropriate geometric algorithm. Thus, two fundamental methods of Euclidean geometry are used, the Convex Hull method and the K-Curvature method. Assuming that in a random space S there is a set of scattered points, the Convex Hull of S is the smallest convex polygon containing all the points of this space

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[16]. In the case of locating the fingertips, all the points that make up the outline of the hand figure are considered as points of random space and the Convex Hull is drawn around it, so that all the points of the outline are inside it, forming a closed polygon (Fig. 6). The corners of this convex polygon are the fingertips. The Convex Hull algorithm gives reliable results in case the chin is extended, while in the case where the fingertips are gathered or some of them are extended, detection errors are observed. As the Convex Hull method does not prove to be completely reliable for the needs of this work, the K-Curvature method was chosen (Fig. 6). The K-Curvature method is based on the calculation of the vector product between the points that make up the outline of the gesture, in order to locate curves on the contour line (Fig. 7). First, it is necessary to take into account the fact that the outline of the gesture is represented by a set of infinite points, even [16]. P(i ) = (x(i ), y(i )), where P(i) is a random point and (x(i), y(i)) its coordinates at the Cartesian coordinate system. Fig. 6 Convex Hull of the points of a random space S

Fig. 7 Convex Hull of the hand figure

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Each point P(i) emits two vectors that start from it and end at other points that are at a distance k from point P(i) and are to its right and left, forming an angle, the value of which is taken into account later. The design of these vectors in the Cartesian space is calculated as follows: [P(i − k), P(i)] and [P(i), P(i + k)] [16], where k is a selected integer. In areas where the angle between these two two-dimensional vectors is sharper and at the same time the vector product of the angle is positive, the fingertips are detected. During the calculation of the outline of the hand figure, an appropriate table is created with all the coordinates that make up the outline of the area of interest. Due to the large volume of data stored in this table and, at the same time, taking into account the best performance of the K-Curvature algorithm, it was decided to select seventy-five elements from the contour of the area of interest, which are equidistant from each other, to save computing power. Starting from the first point and working in the 3D space, the vectors are created that start from this point and end up in other points that are four points apart before and after the reference point. Following this procedure, the smallest angle formed between the two vectors is calculated. At this point, it should be noted that it is necessary to define a threshold for the angle. Since sharper angles are more likely to be a fingertip, based on this threshold, a check is made on whether the angle is sharp enough so that it is not absorbed by the algorithm. Forty degrees (40°) was chosen as the maximum value for the threshold. Therefore, any angles measured greater than forty degrees are discarded (Fig. 8). Then, the product of the two vectors is calculated. The algorithm that runs to locate the fingertips checks the product of the vectors, and if it turns out to be positive, it concludes that it is a vertex, while if it turns out to be negative, it turns out to be a valley and is rejected. The coordinates of the points with a positive vector product are stored in a new table, which contains only those points that were detected to be the fingertips.

Fig. 8 Fingertip detection

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3.3 Feature Extraction Extracting the fingertips in an image provides information about the position of the gesture at a specific time. This position translates into a kind of hand movement, having defined an appropriate dictionary of commands, through which the controlled movement of the robotic vehicle can be performed by an operator. For this purpose, it is initially necessary to determine the position of the hand. In this work, the position of the hand in front of the digital camera was defined, with the palm facing the ground and the fingers slightly bent downwards. Next, four different commands were defined, which are translated into motion by the following gestures: • • • •

The hand is in a straight position—the vehicle is moving straight. The hand turns to the right—the vehicle turns to the right. The hand turns to the left—the vehicle turns to the left. The fingers of the hand are gathered in the form of a fist—the vehicle stops moving on the spot, waiting for the assignment of a new command.

In movements intended to turn the vehicle, three speed change commands were added to the speed at which the vehicle performs the turn. From the previously detected fingertips, four vectors were defined, as well as the fingers to be used, which start at the center of the object representing the handicraft and end at each of these fingers. Finally, all the angles were measured and compared with each other, in order to find the angle with the largest opening, which corresponds to the angle formed by the two extreme fingers. Once the control for the extraction of the distal fingers is completed, their distances from the centroid are stored in two variables, Ay and By, respectively (Fig. 9). The next step is to define a threshold, which will be a boundary between the various movements. Because the user’s wrist rotates, values are set on the vertical axis so that the vehicle understands when to move in a straight line and when to turn. In fact, what happens is that the distances Ay and By from the center of the hand figure are compared. The rules for defining the threshold are as follows: • If the difference between the two distances is less than 30 (Ay-By < 30), the wheeled vehicle moves in a straight line.

Fig. 9 Define of movements

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Fig. 10 Velocity rules

Table 1 Velocity rules

For left-hand drive: • 0–29° → Fast speed • 30–59° → Normal speed • 60–89° → Slow speed For right-hand drive: • 90–119° → Slow speed • 120–149° → Normal speed • 150–179° → Fast speed

• If the difference between Ay and By is greater than 30 and the distance Ay is less than the distance By (Ay-By > 30 and Ay < By), then the vehicle is turning right. • If the difference between Ay and By is greater than 30 and the distance Ay is greater than By (Ay-By > 30 and Ay > By), then the vehicle is turning left. To define the rules representing the velocities of these two movements, it is assumed that the fingers A and B are joined by an imaginary line. For each rotational movement, the hand needs to move with a maximum of 90°, with the left movement in the range 0–89° and the right movement in the range 90–179°. By relating the vector belonging to the fingertips to the vector of the first vertical column of the image and then measuring the angle formed between the two vectors (Fig. 10), the velocity rules for the intervals of left and right motion are defined, as shown in Table 1.

3.4 Commands Define—Feature Combination A wheeled vehicle made with the help of Lego components was used for the application. The wheeled vehicle consists of two engines—MOTOR A and MOTOR B—located at the rear, an engine at the front—MOTOR C—and the NXT™ Brick, which is the computing unit of the vehicle, and its purpose is to convert incoming commands to the corresponding actions assigned to it. The morphology allows the vehicle to move in all directions (straight, right turn, left turn, reverse). Figure 11 shows the parts of the vehicle, according to the corresponding legend.

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Fig. 11 Robotic vehicle parts

Writing commands for the performance of movements provides a defined structure. The first part includes the activation of the serial line to which the device will be connected and the initialization of the motors that will be put into use. The main part of the code defines the commands for the movement of the vehicle in combination with the traffic rules previously defined. Finally, the process ends by turning off the motors and emptying the connection line. In the present work, the motors A (MOTOR_A) and B (MOTOR_B) were used to control the right and left wheel, respectively. The code section explained in this section includes fourteen initializations, of which the first seven refer to motor A and the rest to motor B. In addition, for each motor, the speed for straight-line driving is initialized, as well as the speeds of the left and right turns of the vehicle. The following example gives the command to initialize motor A. Move = NXTMotor(MOTORA ); [10]. Motor B is initialized in a similar way, replacing MOTOR_A with MOTOR_B. Before giving instructions for moving the vehicle, it is necessary to determine the speeds associated with its behavior. For this purpose, different values were given for the velocity of the motion in a straight line and for the rotational motions. Speed is defined in the form of energy. In fact, the value given to a variable determines the energy that the vehicle must consume to move, and which exits the engines in the form of speed. The maximum value that can be given to a value for the definition of energy to be used is equal to one hundred, while the minimum limit is zero. The command to set the amount of energy to use is as follows: Move.Power = 10; [10]. The sign is used to determine engine rotation. Its predetermined direction of rotation is represented by a positive number, while a negative number contributes to

Design of Gesture-Controlled Interface for Mechatronic Systems: … Table 2 Motor speed values for straight, left and right drive of the vehicle

Type of movement

Speed / Motor

87 Left

Right

Straight

Normal

− 30

− 30

Left

Slow

−8

− 80

Right

Normal

−5

− 90

Fast

−3

− 100

Slow

− 80

−8

Normal

− 90

−5

Fast

− 100

−3

the reverse motion of the motor. Because the construction of the vehicle provides for the connection of the engines opposite to the time we want the vehicle to move, the gear variables were given negative values. The values given to the engines for the three types of drives are shown in detail in Table 2. Having completed the task, before the user exits the application, the code snippet is executed to shut down the interface. This part is performed in two parts. Initially, the motors are instructed to stop any work they ( are )currently performing. The engines are shut down with the command: Move.Stop ' off' ; [10]. While all motors have been switched off, the interface connection line remains off.

4 Application 4.1 Human Mechatronic System Interface A prerequisite for the user’s interaction with the robotic vehicle is the creation of a graphical environment, which offers an interactive experience. The interface created (Fig. 12) consists of a suitable virtual field, which captures the recording of live video, so that the operator can control the movements of his hand while using the application. At this point, it was possible to start and end the video recording, with the help of a mode toggle button. In addition, an appropriate field was added to the interface which captures the state of the binary mask of the gesture in video format, so that through it the possible incorrect recognition of the movement due to non-ideal lighting conditions can be perceived. A table of Cartesian coordinates of the detected fingers was created, which consists of two columns, x and y, corresponding to specific points on the Cartesian plane, and 4 rows, as well as the fingers that are detected. Also included were indications of coordinates corresponding to the two distal fingers of the hand detected, points A and B. The interface also included a real-time display of the gesture, enriched with dots where the fingertips are detected. Finally, the application contains appropriate fields

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Fig. 12 Human mechatronic system interface

showing the number of fingers detected at any given time and the corresponding movement status of the vehicle. The control of the mechatronic system through the interface described above was tested and evaluated in three cases of movement. Users were asked to perform the following three movements with the help of gestures (Fig. 13). In all three cases of control, it was proved that an effective control can be performed. The application was tested by 20 people, 10 men and 10 women. Initially, it is suggested to introduce the participants to the functions of the application and to familiarize them for a few minutes with the application they are going to use. Each

Fig. 13 Mechatronic system movements

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user is then asked to perform a series of tasks as described in Fig. 13 and record the results of their actions.

5 Conclusions During the execution of the participants, some unconscious mistakes were observed, which were made quite often by the users. The majority of the participants had difficulty in the movements concerning the two turns (right and left movement), due to the fact that as they twisted the palm of their hand, they hid the distal fingers, as a result of which the movement was not visible and is recognized by the system as unspecified. The cause of this problem, in some cases, may be due to the fact that users had to watch the video recording and the movement of the robotic vehicle at the same time, resulting in detuning and losing control of their movement. This portion of people recognized this mistake and corrected it in time, while with the passage of work the movements they performed showed improvement. A second part of the participants who made this mistake showed that there was difficulty in understanding the realization of the movement. Although the proportion of these individuals was very small, they did not show improvement in movements even after their explanation by the mediator of the evaluation. Another problem that has been observed is the differences that are observed between those users who have their right hand as their main hand and those who use their left hand more. This problem was observed to apply to almost all participants in the study and is addressed to the same degree in both categories of individuals. More specifically, it was observed that users who used their right hand had difficulty making the right turn, while, on the contrary, those who used their left hand had difficulty with the left movement. This resulted in a negative rating of the respective movements in terms of their degree of difficulty and the intensity of the feeling of fatigue. There were also times when the difficulty of the corresponding movement led the participants to use the right hand exclusively to make the left turn and the left hand to make the right turn. However, the result was not satisfactory, as users noticed more fatigue and therefore returned to the original way of moving. This research, of course, did not lack those who found it difficult to accept the system in terms of how the recognition of movements is carried out, either because they had difficulty performing the movements or because they had used a similar application in the past, thus adopting a preference of their own as to how to use the application.

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References 1. DeepAI (2020) Computer vision. Retrieved from https://deepai.org/machine-learning-glo ssary-and-terms/computer-vision 2. Tι ε´ιναι o χρωματικ´oς χωρoς ´ (n.d.) BenQ. Retrieved from https://www.benq.eu/el-gr/kno wledge-center/knowledge/color-gamut-monitor.html 3. Manitsaris S (2010). Computer vision for movement rcognition: analysis of stochastic model for musical interaction. Ph. D., Retrieved from https://www.didaktorika.gr/eadd/handle/10442/ 30856 4. Spiliotopoulos, A. (2007). Methodological Framework for the development of easy-touse computing systems - national and kapodistrian university of Athens school of positive sciences department of information and telecommunications. In: Docplayer. Retrieved from https://docplayer.gr/2383818-Methodologiko-plaisio-gia-tin-anaptyxi-eyhriston-ypolog istikon-systimaton.html 5. Iraji MS, Yavari A (2011) Skin color segmentation in fuzzy YCBCR color space with the mamdani inference. Am J Sci Res 2011(7):131–137. https://doi.org/10.5815/ijigsp.2012.04.05 6. Gurav RM, Kadbe PK (2015) Real time finger tracking and contour detection for gesture recognition using OpenCV. In: 2015 International conference on industrial instrumentation and control (ICIC). IEEE, pp 974–977. https://doi.org/10.1109/IIC.2015.7150886 7. Ren Z, Meng J, Yuan J (2011) Depth camera based hand gesture recognition and its applications in human-computer-interaction. In: 2011 8th International conference on information, communications & signal processing. IEEE, pp 1–5. https://doi.org/10.1109/ICICS.2011.617 3545 8. Yanco HA, Drury JL, Scholtz J (2004) Beyond usability evaluation: analysis of human-robot interaction at a major robotics competition. Hum Comput Interact 19(1–2):117–149. https:// doi.org/10.1207/s15327051hci1901&2_6 9. Bhuiyan M, Picking R (2011) A gesture controlled user interface for inclusive design and evaluative study of its usability. J Softw Eng Appl 4(09):513. https://doi.org/10.4236/jsea. 2011.49059 10. RWTH - Mindstorms NXT Toolbox (2011) RWTH - Mindstorms NXT Toolbox - File Exchange - MATLAB Central. Retrieved from https://www.mathworks.com/matlabcentral/fileexchange/ 18646-rwth-mindstorms-nxt-toolbox 11. Wikipedia Contributors (2021) RGB color model. In: Wikipedia. Retrieved from https://en.wik ipedia.org/wiki/RGB_color_model 12. Osman G, Hitam MS, Ismail MN (2012) Enhanced skin colour classifier using RGB ratio model. arXiv preprint arXiv:1212.2692. https://doi.org/10.5121/ijsc.2012.3401 13. Tsagaris A, Manitsaris S (2013) Color space comparison for skin detection in finger gesture recognition. Int J Adv Eng Technol (IJAET) 6(4):1431–1441 14. Tsagaris A, Manitsaris S, Dimitropoulos K, Manitsaris A (2011) Intelligent invariance techniques for music gesture recognition based on skin modelling. In: 12th IEEE International symposium on computational intelligence and informatics (CINTI), pp 219–223, Budapest, Hungary 15. Tsagaris A, Manitsaris S, Dimitropoulos K, Manitsaris A (2011) Scale and rotation invariance for the recognition of finger musical gestures performed in space. Eur Workshop Vis Inform Process (EUVIP), pp 4–6, Paris, France 16. Farooq J, Ali MB (2014) Real time hand gesture recognition for computer interaction. In: 2014 International conference on robotics and emerging allied technologies in engineering (iCREATE). IEEE, pp 73–77. https://doi.org/10.1109/iCREATE.2014.6828342

Topology Optimization Utilizing Density-Based Approach for Additive Manufactured Components: A Case Study of an Automotive Brake Caliper Nikolaos Kladovasilakis, Georgios Kosmidis, Panagiotis Kyratsis, and Dimitrios Tzetzis

The recent developments in additive manufacturing technologies lead to rapid production of fully functional customized parts with high geometric complexity and without the limitations of the traditional manufacturing methods, such as machining. Hence, in the last decade, the structural optimization of the existing products has gained increased scientific interest, especially in form of topology optimization. In the current chapter, the basic principles and the main methods of the topology optimization processes are described and analyzed coupled with a novel case study presentation of the topology optimization procedure of a brake caliper designed for additive manufacturing (DfAM). More specifically, the case study focused on the topology optimization of a brake caliper for the automotive industry, in order to reduce the overall weight and enhance the performance of the vehicle. Firstly, an original design of the brake caliper was studied via finite element analyses (FEA) under realistic static loads and the need for the topology optimization of the part was pointed out. Through the topology optimization process, the maximum mass reduction from the original design was achieved by holding the mechanical response of the part on the desired levels, i.e., maintaining the factor of safety above one. To conclude, the topologically optimized design of the brake had a weight of almost 2173 gr compared to the original design of 3195 gr achieving a mass reduction of 32%. It is worth mentioning that the factor of safety for the final design was calculated at 1.325.

N. Kladovasilakis · G. Kosmidis · D. Tzetzis (B) School of Science and Technology, Digital Manufacturing and Materials Characterization Laboratory, International Hellenic University, 57001 Thessaloniki, Greece e-mail: [email protected] P. Kyratsis Department of Product and Systems Design Engineering, University of Western Macedonia, 50100 Kila Kozani, Greece © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6_4

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1 Introduction In the last decade, additive manufacturing (AM) technologies concentrated increased scientific interest and were rapidly researched and developed. In detail, AM methods are the fabrication techniques that produce the desired parts directly from the raw material building them layer by layer with the corresponding cross-sections of the part for each layer [1, 2]. Hence, AM techniques are radically differentiated from traditional manufacturing techniques, such as machining. Nowadays, there are 8 different categories in which the AM methods are classified, according to international standards [2, 3], and they are listed in Table 1 coupled with a short definition for each one. AM technologies offer a plethora of advantages both in terms of manufacturability and in terms of productivity. The main advantages of AM process are the rapid fabrication of prototypes and even functional parts, the relatively low cost of the process for customized parts, and the ability to produce objects with high geometrical complexity [4]. These advances in additive manufacturing processes led to the rapid development of topology optimization procedures [5]. Thus, there is a necessity to establish a process map that describes the different approaches of topology optimization coupled with their advantages and disadvantages. Hence, the purpose of the current chapter is to present an in-depth analysis of the topology optimization processes coupled with a real industrial application in order to facilitate the commercialization process of the topology optimization procedures. More specifically, in this study, the two major approaches, namely the density-based and the discrete/truss-based, were presented and analyzed [6]. In detail, the most widespread algorithms for the density-based approach are listed coupled with their Table 1 Additive manufacturing categories [2]

AM category

Definition

Material extrusion

The material is extruded for a heated nozzle

Material jetting

The material is jetted through an inkjet print-head

Binder jetting

Deposition of bonding agent droplets to material’s powder

Sheet lamination

Sheets of material are bonded/welded together

Vat photopolymerization

Selectively curing liquid photopolymer

Powder bed fusion

Selective thermal fusion of material’s powder

Directed energy deposition Melting of material that deposited through a nozzle Cold spraying

Material’s powder is blown at high speed to adhere to the part

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mathematical formulation of the optimization problem. On the other hand, for the discrete/truss-based approach, the architected materials were introduced accompanied by their detailed classification. In addition, the unique properties of the architected materials were presented coupled with the most promising and cutting-edge applications. Finally, in the last section of this chapter, a case study of topology optimization was conducted for an automotive application and more specifically for a Brembo® F 50 224 brake caliper, showing the significant mass reduction that could be occurred in order to achieve lightweight final objects.

2 Topology Optimization Processes The objective of topology optimization is to find the minimum required material’s mass with the optimal distribution in the predefined design volume, in order to fulfill certain design or engineering criteria, i.e., maximum stress, for given operating loads [7, 8]. As a result, a weight reduction is achieved and the specific strength of the object is increased. A fundamental tool for the topology optimization process is the finite element analyses (FEA). During the topology optimization procedure, the volume domain of the part is divided into voxels (finite elements). Each finite element possesses a specific conditional density value from zero to one. The value of this density is controlled by the contribution of each element to the total strength of the designed part. The elements with a major role in the structural integrity of the part have values of one in contrast with elements with a negligible contribution which have values of zero. All the other elements have intermediate values of conditional densities. Various functions (and their combinations), such as flexibility or potential deformation energy, volume, displacement, and strength characteristics, can be defined as criteria and constraints for topology optimization procedures. Currently, topology optimization is performed via two main approaches: the density-based approach (density, topological derivatives, level set, phase field, etc.) and the discrete/truss approach or lattice structures approach (evolutionary-based algorithms), and their combined approaches [6]. The following section presents the most common density-based topology optimization methods, i.e., Solid Isotropic Material with Penalization (SIMP) and Evolutionary Structural Optimization (ESO) or Bidirectional Evolutionary Structural Optimization (BESO) [9, 10]. Furthermore, a short description of lattice structures is also listed coupled with their advantages and the potential applications. Figure 1 depicts the logical flowchart of a topology optimization process.

2.1 Density-Based Approach The density-based approach, also known as generative design, employs the aforementioned conditional density method in order to remove material from a designed

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Fig. 1 Flowchart of the topology optimization process

object. The three most widespread algorithms for topology optimization via densitybased are the SIMP, the ESO, and BESO. The algorithms of ESO and BESO have been both studied and developed intensively in recent years. ESO is based on the simple concept of gradually removing inefficient material from the structure’s volume domain. The resulting structure of the ESO method evolves toward its optimal shape and topology. Although it is not guaranteed that such an evolutionary procedure would always produce the best solution. However, the ESO technique provides a useful tool for engineers who are interested in exploring structurally efficient forms and shapes during the conceptual design stage of a project [11]. This optimization algorithm can be utilized to optimize both large-scale structures but also to optimize the design of micro-scale and nano-scale structures. The first appearance of the ESO method was in 1992 by Professors Huang and Mike Xie [12]. The ESO technique is called a hard destruction technique that repeatedly removes or adds a finite amount of material. Heuristic criteria are used that can be based on well-defined sensitivity information. Thus, ESO is relatively easy to implement, which is an advantage for topology optimization problems involving complex physical processes. Utilizing FEA, the ESO evaluates the load level in an arbitrary section of the object [9]. Inefficient use of the material is determined by a low level of load (or deformation) in the individual section of the object. Ideally, the load level in the object should be the same all over the object, close to the limit but at a safe value. According to the above condition arises the principle of material removal in which insufficiently loaded material is removed, resulting in the removal of individual elements from the finite element model. Comparing the stress σ e vm element with the critical or maximum value σ max vm of the object determines the stress level of that element. If, as a result of finite element analysis, the element satisfies the following condition σevm vm < RRi σmax0 where RR is the limit value (subtraction rate) then this element is removed and the control process starts a new control cycle. The test of the individual components is performed into iterations until a steady state is reached, i.e., the state in which there are no other components that meet this subtraction limit. According to the specific evolution rate H i, the subtraction rate can then be increased by the equation: R R(i+1) = RRi + Hi

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The above procedure can be performed with an increased subtraction ratio, and the analysis is performed until a new steady state is reached. The iterative procedure is performed until the required result is achieved, for example, until all the material is removed from those areas where the stress level does not exceed 20% of the maximum material stress. A quantitative estimate of the change of stiffness of the structure as a result of the subtraction of i-th finite element is the elasticity index, defined for the mean elasticity as shown in the following equation [5], where ui is the node displacement vector of element i and K i is the element’s stiffness matrix. αie =

1 ∗ u iT K i u i 2

The sensitivity function shows the decrease of the mean stiffness as a result of the removal of the i-th element, which is equal to the elemental deformation energy of the i-th element. To maintain the stiffness by removing the elements, it is necessary to remove elements with the minimum value of the sensitivity factor [5]. The mathematical formulation of the ESO algorithm is equally applicable for two-dimensional (2D) and three-dimensional (3D) problems as it is quite simple and clear; at the same time, the application of the software does not require complex programming. The subtraction of elements is performed by assigning a zero value to their coefficient of the equation, and as a result, they are ignored during the subsequent repetitions. This iterative process of removing data leads to a reduction in the number of equations, thus reducing the computational demands of the problem, which is particularly important for 3D problems. A major disadvantage of the ESO method is that it does not allow the removed material to be recovered while this material may be efficient in subsequent ones. Summarizing the above, it is obvious that the ESO method in some cases does not provide the optimal solution and this disadvantage is eliminated with the BESO method. The BESO algorithm allows the simultaneous removal and addition of material to the design volume. The fundamental difference between these two methods is that the sensitivity index of the blank elements is determined by linear extrapolation of the displacement field obtained as a result of finite element analysis [13]. After that, the full elements with the lowest sensitivity index values are removed from the structure and the empty elements with the highest sensitivity values are filled with material. The numbers of elements removed and added at each iteration are determined by two independent parameters: the RR subtraction ratio and the RI inclusion ratio [14]. Although the ESO/BESO methods are quite simple to implement, there is virtually no application of the ESO method to solve production-oriented topology optimization problems [5]. The third and most widespread method is Solid Isotropic Material with Penalization or simply SIMP algorithm. It is worth mentioning that the majority of commercial design software utilizes this algorithm of topology optimization, and it was also employed in this research for the purpose of the brake caliper case study. The fundamental idea of the SIMP method is to create a virtual density field that is proportional to the actual characteristics of the understudy object [15]. This method aims to reduce

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the flexibility of the structure due to the redistribution of the material in the examination area under specific limit conditions. The result of using the SIMP method is that the object maintains the same stiffness values within the under-consideration problem. This method is widely used in studies for additive manufacturing constructions, as additive manufacturing enables the creation of objects with high complexity shapes and geometries. The material density is utilized as a designed variable when calculating the optimization. Thus, the optimal structure, within the planned area, is achieved by redistributing the material based on the criteria given during the optimization. The SIMP method is again based on dividing the examined volume into voxels (finite elements), as it was above-mentioned. The properties of the material are constant in each of these elements and depend on the relative density x i . After completion of the optimization, the relative density of each element must be equal to one or zero. To limit the intermediate relative density is used the rejection factor p. As designed variables are taken the relative densities of the elements, and the mean correspondence is chosen as the objective function. The problem of topology optimization for minimum correspondence can be written as follows: Find : X = {x1 , x2 , . . . , xi }T , i = 1, 2, . . . , n ↓ n n Σ Σ Min : C(X ) = F T U = U T K U = u iT ki u i = (xi ) P u iT k0 u i ↓

i=1

Subj. to : K U = F, V = f 0 V0 =

i=1

n Σ

xi vi

i=1

↓ with : 0 < xmin ≤ xi ≤ xmax ≤ 1 where • • • • • • •

C is the objective function and is defined as the mean correspondence. X is the vector of construction variables. F is the loading vector. U is the total displacement vector. K is the total stiffness strain. V is the material’s volume. F 0 is the volumetric ratio.

The final and the most effective density-based algorithm is the ESO-SIMP method which is a combination of the ESO and SIMP methods and aims to compensate for the disadvantages of these two topology optimization methods [16]. To solve the optimization problem, the relative densities are used as the designed variables and the mean correspondence is selected as the objective function. The optimization problem for the minimum mean correspondence based on the ESO-SIMP algorithm is as follows:

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⎧ ⎪ Find : X = {x1 , x2 , . . . , xi }T , i = 1, 2, . . . , n ⎪ ⎪ ⎪ ⎪ ↓ ⎪ ⎪ ⎪ n n Σ Σ ⎪ ⎪ T T ⎪ Min : C(X = U K U = u k u = ) (xi ) P u iT k0 u i i i ⎪ i ⎪ ⎨ i=1 i=1 . ↓ ⎪ n ⎪ Σ ⎪ ⎪ Subj. to : K U = F, V = xi vi ≤ f 0 V0 ⎪ ⎪ ⎪ i=1 ⎪ ⎪ ⎪ ⎪ ↓ ⎪ ⎪ ⎩ with : 0 < xmin ≤ xi ≤ xmax ≤ 1 The difference between the ESO-SIMP and SIMP methods is the volume limitation. During each iteration, elements whose relative density is less or equal to the ejection factor are removed from the design volume, and all other elements are inserted into the next iteration. In practice, this combination method proves to be more suitable than ESO and SIMP separately in terms of efficiency and reliability.

2.2 Discrete/Truss-Based Approach The lattice structures concentrate the scientific interest from the ancient times when humans observed cellular materials in nature and in structures such as corals and foams and tried to imitate them in artificial structures, such as honeycombs [17]. Nowadays, the interest in artificial lattices has been revived due to additive manufacturing techniques that allow the production of complex lattices in relatively small sizes. All lattice structures consisted of architected materials with numerous shapes and topology characteristics. Currently, there are a vast number of different architected materials with their main physical characteristic the applied relative density [18–20]. The applied relative density is the percentage of the volume that is filled with the employed architected material, which is defined by the designer/engineer and the ratio of structure thickness to unit cell length. Due to the ability to modify the relative density of architected materials, therefore their mass and mechanical properties, the architected materials are employed in topology optimization processes via the discrete/truss-based approach. It is worth mentioning that when the relative density of an architected material is ultra-low ( 0.3re zS

(15)

where f feed rate in mm/min, z number of teeth (cutting flutes), S spindle speed in rpm and re cutting edge radius in mm. In the developed application, the maximum allowed feed was calculated for each linear segment of the variable feed toolpath, tested against maximum and minimum allowed feed values, and implemented in the G-code. User-defined chord error, sampling time and tool tip radius were set as 0.0001 mm, 10–3 s and 0.0005 mm, respectively. Under these conditions the resultant feed rate value ranged at 50–58 mm/min.

3 Application of the Developed Methodology In order to assess and compare machining results for constant and variable feed machining, as proposed in Sect. 2, two workflows were implemented. The first workflow utilizes a well know CAM software, proven to work well on any 2D or 3D machining process, which applies constant feed for G-code creation. The second workflow involves the creation of variable feed G-code through the methodology presented in Sect. 2.3, which makes use of part coordinates and minimum chord error for feed calculations.

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Fig. 5 For extracting the G-code from the CAM software, the two models, micro-impeller and micro-gear, where combined. a Micro-impeller after CAM simulation, b Micro-gear after CAM simulation (not shown in proportion to a, but in detail). Stock material for the micro-gear was the cylinder left in the center of the micro-impeller, as seen in a

3.1 Constant Feed CNC Micromachining Using CAM Software According to the first workflow, a combined demonstration 3D CAD model of the micro-gear and micro-impeller parts presented in Sect. 2 was imported in CAM software to plan the machining process. For all toolpaths, feed per tooth value was monitored, for violation of minimum chip thickness criterion of 30% of cuttingedge radius [19–21]. Cutting width values (maximum) were selected as 40% of cutting tool’s diameter. In every toolpath, a 0.01 mm layer of material was left after roughing as allowance for finishing. The combined model (Fig. 5) was machined out of a cylindrical block of brass of 15 mm height and 24 mm diameter. A twoflute 0.5 mm diameter uncoated carbide flat end mill was used for the microgear feature and a similar tool of 1 mm diameter for the micro-impeller feature. The feed rates were set according to recommended cutting velocities for brass. Roughing and finishing toolpaths for the micro-gear and micro-impeller features were programmed in CAM software and compiled to NC programs as ISO G-codes. Toolpaths were simulated prior to actual machining. The micromachining experiments were performed on a 3-axis Nanowave MTS5R CNC micro- mill. This machine has three stepper motors of 100 nm positioning accuracy. The tool is mounted on air bearings and maximum spindle speed is 100 krpm. The machining parameter values, and respective machining time, are presented in Table 1.

3.2 Variable Feed CNC Machining of Curved Toolpaths After applying the methodology in Sect. 2.3, we obtained variable feed toolpaths (Fig. 6) and created the respective ISO G-codes for execution in the same machine as before. This model was machined out of a cylindrical brass block of 25 mm diameter and 15 mm height (Fig. 7). The same tools were used, as in the constant

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Table 1 Machining Time and parameter values for constant feed micromachining of combined demonstration model. Legend: MT = Machining Time in hh:mm:ss, D = Cutting Tool Diameter in mm, F = Cutting Feed rate in mm/min, S = Spindle speed in 1000 rpm, ap = Cutting depth in mm, ae = Cutting width in mm, ft = feed per tooth in 10–3 mm/tooth, Vc = Cutting Velocity in m/min Combined model A: micro-gear B: micro-impeller

MT

D

F

S

ap

ae

ft

Vc

Roughing A

01:32:58

0.5

80

30

0.15

0.2

1.33

47.1

Finishing A

00:02:03

0.5

60

40

0.1

0.15

0.75

62.8

Roughing B

01:59:48

1

120

25

0.2

0.4

2.4

78.5

Finishing B

00:30:53

1

80

35

0.1

0.4

1.43

109.9

Total

04:05:42

Retract rate: 400 mm/min, Plunge rate: 40 mm/min, cutting tools are uncoated carbide flat end mills, Part material: brass

feed machining method. Figure 6 shows the correlation between the local radius of the part and the feed adaptation, calculated by the developed application. By comparing Tables 1 and 2, we can see that the application of variable feed rate methodology leads to a significant reduction in machining time values. Specifically, there is a reduction of 15.7 and 8.9% in roughing and finishing time, respectively, of the micro-gear feature, while roughing and finishing time of the micro-impeller feature was reduced 14.4% and 15.0% respectively. This is significant improvement in productivity, since the feed rate values calculated by the proposed methodology are in the same vicinity with the constant feed runs. What remains is to compare surface quality of the produced parts with the two workflows. This is presented in Sect. 4. Fig. 6 Curvature adapted cutting feedrate

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Fig. 7 Variable feed micro-machining of the combined demonstration model of micro-gear and micro-impeller out of brass

Table 2 Machining Time and parameter values and for variable feed micromachining of the combined demonstration model, based on proposed methodology. Legend: MT = Machining Time in hh:mm:ss, D = Cut-ting Tool Diameter in mm, F = Cutting Feed rate in mm/min, S = Spin-dle speed in 1000 rpm, ap = Cutting depth in mm, ae = Cutting width in mm, ft = feed per tooth in 10–3 mm/tooth, Vc = Cutting Velocity in m/min Combined model A: micro-gear B: micro-impeller

MT

D

F

S

ap

ae

ft

Roughing A

01:18:25

0.5

71–82

30

0.15

0.2

1.18–1.37

47.1

Finishing A

00:01:52

0.5

49–63

40

0.1

0.15

0.61–0.79

62.8

Roughing B

01:42:36

1

99–125

25

0.2

0.4

1.98–2.50

78.5

Finishing B

00:26:15

1

73–84

35

0.1

0.4

1.04–1.20

109.9

Total

03:29:48

Vc

Retract rate: 400 mm/min, Plunge rate: 40 mm/min, cutting tools are uncoated carbide flat end mills, Part Material: Brass

4 Results of Variable Feed Methodology Performance in Micro-Milling No contact white light interferometry and focus variation microscopy was used for evaluating the surface quality of the machined features. Combined measurements were performed on a Zyngo Newview 5000 and an Alicona Infinite Focus SL. To compare constant to variable feed workflows, both MRR and surface quality were addressed. Table 4 depicts the obtained values for the two workflows on the demonstration part. The Ra values presented in the table are average values obtained at ten different areas of the part.

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Table 3 Micromilling performance: MRR and surface quality Combined model

Machining time

Mean roughing MRR (mm3 /sec)

Side machined surface Ra

Bottom machined surface Ra

Constant feed

04:05:42

0.04

1.25 um

1.08 um

Variable feed

03:29:48

0.045

1.12 um

0.98 um

From Table 3, Figs. 8 and 9, two basic conclusions can be drawn regarding the proposed methodology: 1. The machining time for the demonstration part micromachining was improved both for each separate single machining phase (about 9– 15%) and as a total (14.6%). 2. The measured average Ra for both the side and the bottom micro-machined surfaces, when the proposed variable feed methodology was implemented, led to an improvement of about 10%. The average surface roughness as measured in the bottom of the machined surface of the combined model was measured with white light interferometry a little better than the one measured on the sides. Analysis on the individual micro-parts that

Fig. 8 Aa Micro-gear and micro-impeller combined model machined out of brass. b Height map and c respective magnified surface image as acquired in Zyngo white light interferometer for the side milled blades’ surface

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Fig. 9 a Height map and b respective optical microscopy image as acquired in Zyngo white light interferometer for the side-milled gear’s surface

comprise the combined part reveals that although higher cutting velocities values were used in the micro-impeller, similar average surface roughness but rougher texture was obtained for the finished surface of the spur micro-gear part, which was machined at lower cutting velocity values. This level of surface quality for micro-components addressed to several applications and is achieved at a decent productivity rate. Surface quality of the bottom traces of machining of the curved toolpaths under constant and variable feed was evaluated on Alicona. Overall surface texture and average roughness value was affected by varying the feed according to curvature at this specific experiment; however it is a matter of further processing of the results and conducting more extensive experimentation in order to verify that the 10% improvement of Ra is a significant one for this type of micro-parts. For more complicated toolpaths and high-volume production, such level of machining time reduction significantly improves productivity.

5 Discussion The application of the proposed methodology for obtaining variable feed G-code based on the parametric equations of parts can be summarized in the following: (A). Reduced time from design to manufacturing with equation-derived designs. Equation-derived designs can be instantly modified according to userdefined parameters, by exploiting built-in routines in CAD software or custom routines developed through CAD API in generic programming languages. Reducing design times through automation can accelerate and improve experimentation, eliminate design errors and ultimately improve both quality and productivity for various manufacturing methods and particularly CNC applications.

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(B). Cutting conditions for parametrically designed models and their impact on surface quality and MRR. Cutting conditions clearly play the most important role in determining machining time and surface quality levels of the produced parts. The spur gear and micro-impeller combined model was machined out of brass using two individual finishing toolpaths initially computed in CAM software with constant feed rates. The former was machined at significantly lower cutting velocity values from the latter (63 m/min and 110 m/min respectively). This resulted in the improvement of MRR, but also surface smoothness for the impeller model. Obviously, specific speeds and feeds and consequently MRR values corresponds to an optimum level of achievable surface quality at a given setup. Machining outside recommended feeds and speeds boundaries for each material, machining can become unstable resulting in low surface quality, excessive tool wear, energy and material waste and additional computational times. Variable feed machining according to curvature was successfully implemented computationally for a set of simple parametric parts and ISO NC code was programmatically generated and modified for feed variation using VB.NET. A set of curved toolpaths were machined out of brass using curvaturebased feed variation. The same computationally derived curved toolpaths were machined using constant feed. The Ra values obtained using focus variation microscopy for the variable and constant feed machined curves were different, improved with variable feed rate philosophy. Different curve shapes that result in a wider range of curvature values and increase in curve thickness could help for better evaluation of this method in terms of surface quality. Curvature-based feed variation resulted to a reduction of machining time for a short toolpath, fact that hints that such methods can practically impact very significantly machining time in highly curved models. The variable feed rate method can be implemented with success for all toolpaths that can be parametrically described. The overall performance of machining is satisfying with an indicative average Ra value not exceeding 1.3 μm in the case of brass micro-milling. Higher spindle speed values and therefore cutting velocity values could have resulted in an even greater increase of surface quality It is noticed that decrease in cutting tool diameter should be compensated by an increase in spindle speed values which justifies the need of high-speed spindle for micro-machining. Machining time can be greatly affected by the cutting tool diameter and machining strategy, along with the significant effect of machining feed rate. A constant machining feed-rate as set according to the material hardness and geometry typically lower than the maximum possible within a defined tolerance value or the allowable the deviation of the actual toolpath. Varying the feed rate according to curvature can slow down the feed when a highly curved surface is machined and increase it when machining occurs in a linear trajectory. For highly curved components, curvature-based feed variation may result in improved surface quality and smoother machining. Varying the feed within a range determined by the material and cutting tool may further reduce machining

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time compared to a constant feed approach for specific geometries aiming at the same level of surface quality. Newly developed CAM software use feed rate variation according to curvature and/or different objectives, such as constant cutting width/ depth, MRR and cutting force, although this cannot be manipulated by the users. Such optimization methods can have a significant impact in micro-machining applications where increased tolerances and low tool radiuses impose increased machining time.

6 Conclusions Parametric mechanical design is a necessary tool in modern engineering, as it can be manipulated directly by the modern CAM systems or by developing custom applications for specific design and manufacturing purposes. Models that can be parametrically described can reduce costs related to product development and have particularly useful extensions in interfacing with manufacturing operations. In this study, a methodology and the respective VB application for creating 3D CAD models based on parametric curves was developed and implemented for parts consisting of 2D free-form curves. Also, off-line G-code generation for parametrically designed features through application programming interface of CAD programs can have important practical applications in machining operations for production or research purposes, as it minimizes the need for extensive work in CAM software and directly produce G-codes based on parametric G-codes for similar parts or parts that share geometric features even with variations. Optimization techniques, such as the variable cutting feedrate along curved toolpaths proposed in this study, can be easily implemented for offline G-code extraction, implying only limited computational costs. The developed methodology involved the direct production of G-code based only on the parametric curves and the minimization of geometric error by using variable feed rates for micro-parts. Particularly in micro-machining, adaptive feedrate appears capable to noticeably reduce machining time, improve surface quality and increase productivity for curved features in 2D and 2.5D models, while it can contribute to a wider multiobjective optimization strategy which includes both economical, managerial, and technical objectives.

References 1. Dhanorker A, Liu X, Özel T (2007) Micromilling process planning and modeling for micromold manufacturing. In: Proceedings of the ASME 2007 international manufacturing science and engineering conference. Atlanta, Georgia, USA. October 15–18, pp 759–769. https://doi.org/ 10.1115/MSEC2007-31070. 2. Filiz S, Xie L, Weiss L, Ozdoganlar O (2008) Micromilling of microbarbs for medical implants. Int J Mach Tools Manuf 48:459–472

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3. Guckenberger D, De Groot T, Wan A, Beebe D, Young E (2015) Micromilling: a method for ultra-rapid prototyping of plastic microfluidic devices. Lab Chip 15(11):2364–2378 4. Wilson ME, Kota N, Kim YT, Wang Y, Stolz DB, Ozdoganlar OB (2011) Fabrication of circular microfluidic channels by combining mechanical micro-milling and soft-lithography. Lab Chip 11:1550–1555 5. Ducobu F, Filippi E, Riviere-Lorphevre E (2009) Chip formation and minimum chip thickness in micro-milling. In: Proceedings of the 12th CIRP conference on modeling of machining operations, 1:339–346. 6. Davim JP, Jackson MJ (2008) Nano and micromachining. Wiley 7. Kim C, Mayor JR, Ni J (2005) A static model of chip formation in microscale milling. ASME J Manuf Sci Eng 126(4):710–718 8. Peng F, Wu J, Fang Z, Yuan S, Yan R, Bai Q (2013) Modeling and controlling of surface micro-topography feature in micro-ball-end milling. Int J Adv Manuf Technol 67:2657–2670 9. Chen PC, Pan CW, Lee WC, Li KM (2014) An experimental study of micromilling parameters to manufacture microchannels on a PMMA substrate. Int J Adv Manuf Technol 71:1623–1630 10. Alsayyed B, Hamdan MO, Aldajah S. (2012) Vortex tube impact on cooling milling machining. In: Proceedings of the ASME 2012 international mechanical engineering congress and exposition. Volume 3: Design, Materials and Manufacturing, Parts A, B, and C. Houston, Texas, USA. November 9–15, pp. 773–776. 11. Hinduja S, Ma YS, Barrow G (1995) Determination of the radial width of cut and cutting modes in milling. Int J Mach Tools Manufact 35(5):689–699 12. Sun Y, Wang J, Guo D (2006) Guide curve based interpolation scheme of parametric curves for precision CNC machining. Int J Mach Tools Manuf 46:235–242 13. Sodemann AA, Mayor JR (2011) Experimental evaluation of the variable-feedrate intelligent segmentation method for high-speed, high-precision micromilling. ASME J Manuf Sci Eng 133(2):1–12 14. Yeh SS, Hsu PL (2002) Adaptive-feedrate Interpolation for parametric curves with a confined chord error. Comput Aided Design 34(3):229–237 15. Elkeran A, El-Baz M (2014) NURBS Feedrate Adaptation for 3-axis CNC machining. http:// www.maintenanceresources.com/referencelibrary/ezine/nurbs.htm. [Accessed 20 June 2014]. 16. Tzivelekis CA, Yiotis LS, Fountas NA, Krimpenis AA (2015) Parametrically automated 3D design and manufacturing for spiral-type free-form models in an interactive CAD/CAM environment. Int J Interact Des Manuf 11:223–232 17. Tzitzis A, Garcia-Hernandez C, Huertas-Talon JL, Kyratsis P (2020) CAD-based automated design of FEA-ready cutting tools. J. Manuf Mater Process 4(4):1–14 18. Razfar MR, Zinati RF, Haghshenas M (2011) Optimum surface roughness prediction in face milling by using neural network and harmony search algorithm. Int J Adv Manuf Technol 52(5):487–495 19. Özel T, Liu X (2009) Investigations on mechanics-based process planning of micro-end milling. Mater Manuf Process 24(12):1274–1281 20. Wu T, Cheng K (2013) Micro milling: the state-of-the-art approach towards applications. in Micro-cutting: fundamentals and applications, John Wiley & Sons, Ltd. 21. Mayor JR, Sodemann AA (2008) Intelligent tool path segmentation for improved stability and reduced machining time in micro-milling. J Manuf Sci Eng 130(3):031121

Study of the Topography of Face Milled Surfaces Using CAD-Based Simulation Nikolaos Tapoglou, Chara Efstathiou, Anastasios Tzotzis, and Panagiotis Kyratsis

The generation of high-quality machined surfaces is of great importance for a series of applications. Face milling is one of the most common processes for machining such surfaces; the process is influenced by a series of factors that if not taken into consideration would result in poorly machined surfaces. The cutting parameters, the cutting tool design and the setup of the cutter and the workpiece play a pivotal role in the success of the machining process. In order to understand the effect of each parameter on the resulting surface quality of face milled surfaces, the current research presents a simulation model that is able to incorporate all the factors mentioned above in a CAD-based simulation platform. The results of the model include the resulting surface topography as well as surface roughness metrics. The results of the simulation approach were validated with experimental results.

1 Introduction The quality of machined surfaces plays an instrumental role in the functional performance of manufactured components. Face milling is one of the processes used to reference surfaces in order to allow for high accuracy assemblies. Establishing N. Tapoglou (B) Department of Industrial Engineering and Management, International Hellenic University, Sindos, 57400 Thessaloniki, Greece e-mail: [email protected] C. Efstathiou Department of Production Engineering and Management, Technical University of Crete, Chania, Greece A. Tzotzis · P. Kyratsis Department of Product and Systems Design Engineering, University of Western Macedonia, Kila, 50100 Kozani, Greece © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6_8

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process models offers a means to analyse, visualize, and optimize the cutting process in order to achieve the best balance between time, cost, and quality of the manufacturing process investigated. Simulation models offer a cost-effective means to perform such optimization tasks as they avoid lengthy experimental trials. The simulation of manufacturing processes, therefore, has gained a lot of traction in industry. Researchers have used a series of techniques in order to predict key performance indicators of manufacturing processes. Analytical, geometrical, experimental and machine learning approaches have been used in order to simulate the cutting process and predict metrics of the process such as the surface roughness, cutting forces, tool wear and residual stresses on the component [1–4]. In the field of face milling simulation researchers have performed machining trials and developed robust simulation models in order to optimize the process. Kim and Ehmann [5] were amongst the first to introduce a cutting force model for the face milling operation. Their model was based on the analytical description of the cutting edge and all the motions of the process and the results included verified cutting forces. Felho et al. [6] developed a method for predicting surface roughness values of face milled components using the analytical description of the cutting edge. Franco et al. [7] focused on the role of tool runout on the resulting surface quality characteristics. Their model used analytical equations in order to simulate the effect of runout on surface roughness. Tapoglou and Antoniadis [8] presented a CAD-based approach on the simulation of face milling. Their model included the calculation of cutting forces and the resulting surface quality metrics. Arizmendi and Jimenez [9] used a combination of analytical equations and a regularly spaced grid of points in order to model the cutting process and predict the surface characteristics, including multi pass cutting. Extending the research presented above the model presented in this research focuses on the integration of runout errors, both axial and radial, in a CAD-based simulation approach. In an effort to further understand the issues that result from runout, the model developed is used to generate process capability maps in which the acceptable limits for tool runout are presented. The remainder of the paper is structured as follows; Sect. 2 presents the architecture of the developed simulation platform as well as the structure and results of the algorithms implemented. Section 3 presents the validation of the simulation platform while Sect. 4 presents the development of the process maps. Section 5 introduces the concluding remarks and future work.

2 Face Milling Simulation The kinematics of face milling is well established and has been analysed in detail by many researchers. The primary cutting motion is the rotation of the cutting tool around its axis. The primary feed motion is along a vector that sits on the plane normal to the axis of rotation. The axial and radial depth of cut are defined in relation to the axis of rotation of the tool The kinematics of the process is presented in Fig. 1.

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Fig. 1 Face Milling kinematics

In multi insert tools, that are commonly used in industry due to the high productivity they offer, the position of the cutting edges with respect to each other can introduce deviations in the final surface generated and contribute to the deterioration of the cutting edge and the decrease in the final surface quality. These deviations can occur in the axial and radial directions. The so-called axial and radial runout of the tool are also presented in Fig. 1. In order to simulate the cutting process a novel simulation platform was developed. The simulation platform is based on a CADmodelling kernel in order to leverage the best-in-class accuracy of such platforms. The flowchart of the simulation process is presented in Fig. 2. The inputs to the simulation platform include geometrical as well as numerical data. One of the primary inputs is the geometric definition of the cutting edge that is imported by the user as a 2D profile. The numerical data of the process can be divided into three categories, namely, cutting tool data, workpiece data and process parameter data. Once all the input variables have been correctly defined the simulation algorithm uses the geometrical core to generate the trajectory of each cutting edge during machining. The surfaces created are used to split the volume of the initial workpiece into two solids, the chip and the workpiece after that machining step. The process is repeated until all the teeth machine fully the surface. After the end of the simulation, the final topography of the workpiece can be further analysed to obtain the surface roughness values and the profile on section planes along or perpendicular to the federate direction. Moreover, the chip geometry can be further analysed to extract the cutting forces expected during machining. Figure 3 presents in more detail the tooth trajectory calculation algorithm. As can be observed the first step in the process is the location of the axis of rotation of the tool

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Fig. 2 Face milling simulation algorithm

in the 3D space. As the tool rotates the centre of the tool also advances with a value proportional to the feedrate used. The axis of the tool is used to position the cutting edge profile in 3D space with the tool rake and side rake angles that are defined by the user. At this stage, the axial and radial runout values for each individual tooth are applied to the tooth profile by adjusting its position. As the tool rotates a series of profiles in 3D space are created and are used to create a 3D surface that includes the full kinematic chain of the process as well as the tool axial and radial runouts.

Fig. 3 Cutting edge calculation algorithm

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3 Validation After the development of the algorithm, several cases were simulated in order to test the robustness of the developed approach. The first step of the validation process included trials in which only one insert was used. This was selected in order to validate the results of the simulation process before runout errors are integrated into the process. The simulation results were compared with experimental trials performed by Franco et al. [7]. The results of this validation step are presented in Fig. 4. As can be observed there is good agreement between the machined and simulated surfaces with the lowest error observed in lower cutting feeds. This deviation has been reported by other researchers and is attributed to the stochastic phenomena during the machining process. The second step of the validation included cases where multiple inserts were employed in machining a surface. The simulation results were compared with experimental results from Arizmendi and Jimenez [9]. The cutting parameters as well as the axial and radial runout were identical to the machining trials performed. The validation results are presented in Fig. 5. As can be observed the simulation results

Fig. 4 Single insert validation

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Fig. 5 Multi-insert validation

closely follow the experimental results. The effect of the runout can be observed in all three cases investigated.

4 Parameter Investigation The understanding of the effect of runout on the resulting surface quality is of paramount importance in the successful generation of features in final parts. In order to map the deviation of the final surface and provide an understanding of the effect of runout on the final gear topography the simulation framework developed were used to investigate this effect. A series of simulation cases were executed looking at variable levels of axial and radial runout and the effect they have on the resulting surface quality. It was observed that the effect of the radial runout did not have a dominant effect on the resulting surface roughness and topography of the resulting surface. On the other hand, even a small axial runout value on the insert resulted in considerable deviations in the final surface quality. Figure 6 depicts the influence of the two runout parameters on the final surface topography. Based on the findings above, the impact of axial runout was further investigated. Different levels of axial runout across a range of feedrates was investigated, and a number of process maps were developed. Figure 7 summarises the developed process maps by presenting the expected average surface roughness and the Rz roughness. As can be observed the axial runout does not have a strong influence on the surface roughness at the low and medium feedrates examined. However, the surface quality

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Fig. 6 Effect of radial (top) and axial (bottom) runout on surface topography

Fig. 7 Developed process maps

deteriorates at higher, more productive feedrates. At the highest federate the surface roughness increases sevenfold when the runout of the tool is increased by 12um.

5 Conclusions Face milling is one of the most commonly employed methods for referencing large surfaces. Its use in automotive aerospace and general manufacturing is of key importance in the success of any manufacturing of engineering components. In an effort to provide an increased understanding into the process, a simulation platform was developed that is in a position to model the movement of the tool and incorporate

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the axial and radial runout of the tool. The simulation model was validated with the use of experimental data both for single insert trials, where runout is not applicable and for multi insert trials incorporating the tool runout values. The simulation model was used to develop a series of process maps that provide an understanding of the effect of runout on the final surface characteristics.

References 1. Karpuschewski B, Kundrák J, Felh˝o C, Varga G, Sztankovics I, Makkai T, Borysenko D (2018) Preliminary investigations for the effect of cutting tool edge geometry in high-feed face milling. In: Vehicle and automotive engineering (pp. 241–254). Springer, Cham. 2. Tapoglou N, Antoniadis A (2012). CAD-based calculation of cutting force components in gear hobbing. J Manuf Sci Eng 134(3) 3. Kyratsis P, Tzotzis A, Markopoulos A, Tapoglou N (2021) Cad-based 3d-fe modelling of aisi-d3 turning with ceramic tooling. Machines 9(1):4 4. Tapoglou N (2021) Development of cutting force model and process maps for power skiving using CAD-based modelling. Machines 9(5):95 5. Kim HS, Ehmann KF (1993) A cutting force model for face milling operations. Int J Mach Tools Manuf 33(5):651–673 6. Felh˝o C, Karpuschewski B, Kundrák J (2015) Surface roughness modelling in face milling. Procedia CIRP 31:136–141 7. Franco P, Estrems M, Faura F (2004) Influence of radial and axial runouts on surface roughness in face milling with round insert cutting tools. Int J Mach Tools Manuf 44(15):1555–1565 8. Tapoglou N, Antoniadis A (2012) 3-Dimensional kinematics simulation of face milling. Measurement 45(6):1396–1405 9. Arizmendi M, Jiménez A (2019) Modelling and analysis of surface topography generated in face milling operations. Int J Mech Sci 163:105061

Study on Design and Manufacturing of an Engine Block Using Digital Tools Sever-Alexandru Haba and Gheorghe Oancea

Abstract The chapter presents the using mode of some digital tools in the process of design and manufacturing of an engine block used from lightweight four-stroke engine system for competition kart. The combustion engine from automotive industry has the enlarged future because in the green world is grooving the combustion solution with Liquefied Natural Gas (LNG) and, in the last time, Hydrogen. Different digital environments, including CATIA™, provide a large number of tools for design in order to obtain the best constructive solution for a product and later to manufacture it. The design for disassembling is implemented starting with the concept level of the engine block. For the collision check is used the CATIA™ DMU Space analysis applied on the 3D engine block model. All parts for engine assembly are moved in functional position using the digital tool from Assembly Design module. Another possible issue, the wrong access for assembly tools is validated using the 3D models for the tools safety spaces. To check the most important designed parts in real world are generated the 3D files and are manufactured the real parts using two additive manufacturing systems. The G code for multi-axis machining of the engine block is generated from CATIA™ Machining module and the CNC files are also simulated to be validated in virtual environment.

1 Introduction Industrial development is synchronized with the evolution of human society. Nowadays, the industrial environment is situated in front of new level, the Industry 4.0 capabilities and challenges. Gradually, new generations of goods, products and services appear. Also, there is a transformation of human life, particularly workers in different environments, including industrial companies [1]. S.-A. Haba · G. Oancea (B) Department of Manufacturing Engineering, Transilvania University of Brasov, Mihai Viteazul 5, Brasov, Romania e-mail: [email protected] S.-A. Haba e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6_9

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According to actual industrial environments, the terms like design for manufacturability, design for manufacturing and assembly, design for additive manufacturing, design for disassembly, digital manufacturing and so on [2, 3] are currently used. The design and manufacturing of automotive parts are directly changed by the digital tools’ era. These digital tools are also implemented in many other domains, including motorsport industry. This book chapter allows to the reader to find out how the digital tools are used in the process of design and manufacturing of an engine block from a lightweight four-stroke engine. It is a multi-purpose four-stroke lightweight engine; the engine design is accommodated with the green environment and the digital tools assure the updating of construction parameters in real time. Gradually, the main stages of work are described, as well as the concepts and digital tools used: design for manufacturability, design for assembly and disassembly, virtual assembling of engine block, digital collision check tools, tool accessibility stage, virtual engineering for engine block and the additive manufacturing systems used like a bridge between the digital environment and real life.

2 Design for Manufacturability and Assembly The subchapter is dedicated to the design for manufacturability concept applying in the engine design process. The design for manufacturability (DfM) assures the design parts for optimal manufacturability and compatibility with factory processes and design for assembly (DfA) taking into account the assembling process [3, 5]. In order to assure the best accommodation with the consumer market price, for designing the engine parts is used the general DfM guidelines for part design [4]. Generally, it is used the parts from common engines (standard parts), the geometrical constructions with symmetry are implemented at large scale and for low-volumes production are used the multi-axis CNC machining. The core of this lightweight engine is the external engine block, made of aluminium alloy (Fig. 1), or simply engine block (1) assembled with the cylinder casing (1). This assembly is presented in Fig. 1 and the cylinder casing (2) is made of cast iron. The engine block assembled with the engine casing in fact is an interference fit, to create a perfect contact, in the assembly process, the external engine block is heated at about 500 °C degrees, and the temperature of cylinder casing is 20 °C degrees. After the insertion of the cylinder casing in the engine block, the obtained assembly is cooled down in the environment for which the standard temperature is considered 20 °C degrees. According to the design for assembly, Fig. 2a shows the details of self-locating features form the top of the cylinder casing. The top area, named the cylinder casing collar, has the inner assembling chamfers as follows: (1)—is used to assure an easily insert procedure for engine piston, and

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Fig. 1 Engine block assembly [2]

Fig. 2 Cylinder casing, specific features used for DfA

the outer chamfer (2)—is used to assure simply assembling the cylinder casing with corresponding engine block hole. In the bottom area of cylinder casing, Fig. 2b, there are the inner assembling chamfer (1) which is used to assure the insert procedure for engine maintenance and the outer chamfer (2) used for the assembly of the base of cylinder casing in the corresponded hole from crankcase. Similarly, the engine block is designed with self-centring chamfers (Fig. 3), here are inner chamfer (1), outer chamfer (2) and guide holes with chamfers (3) and (4). The semi-finished engine block is manufactured through the under-pressure mould injection process from lightweight alloys. In order to assure the optimal manufacturing process for this engine block, several radii are provided (Fig. 4). The (1) and (4) radii are designed to assure the uniform

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Fig. 3 Engine block, specific features for DfA

Fig. 4 Engine block, specific features for DfM

flow of molten material in mould tool, and the (2) and (3) radii have the role in the assuring of easy extraction of the part form the mould tool. The engine block and the cylinder casing cutting procedures are grouped in two main groups, in this way is reduced the fixing errors. All the standard added geometry for engine block (assembly base for exhaust manifold, intake-manifold added surfaces for seal trip and so on) are included in external parts, in this way is reduced the auxiliary tools in manufacturing process.

3 Design for Disassembly The main design objective for all modern systems is the embedded maximum functionality properties in minimum space (minimum box for maximum features). This modern concept is implemented due to reduce the dimensions and the weight of the devices. This concept leads to the following technical issue. . disassembly procedures become too complicated; . increasing the times resource allocated for disassembly; . increasing the price for dedicated tools;

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. increasing the risk of does not access tools in service procedures. From this point of view, it is necessary to use the design for disassembly as a tool to obtain a product according to the objective mentioned above. It can be also mentioned that contrary to common opinion, assembly process and disassembly process are not exact opposite one of one. The assembly process is not exact opposite of disassembly, due of the presence of several products and process parameters [5]. For example, in the case presented in this chapter, the factory devices are not identically with the service devices. The engine assembly is divided in 3 main areas (Fig. 5), and all areas are designed using the design for disassembly concept: . 1—engine block area; . 2—gear box area; . 3—air intake and fuel admission area. For the total engine maintenance, the air intake and fuel admission area (3) are dismounted trough a translation movement along OX axis, due to the digital tools is possible to check the real movement without any collision (Fig. 6). In order to check the possibility of clash between the engine parts is used the CATIA™ Clash detection digital tool. Because exist a lot of parts in the engine structure, it is used multiple selections from selection tree. The interferences are coloured in red [6]. In opposite position is the exhaust manifold (Fig. 7). For increasing the dismounting possibility, this exhaust manifold is designed with detour geometry Fig. 5 Engine assembly

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Fig. 6 Air intake and fuel admission dismounting direction

around the gearbox components. The dismounting movement is a translation along OY axis. To assure a correct design, it is preferable to perform a checking procedure with the chassis environment and with the engine in the functioning position. There are not special tools required for both systems dismounting, although the maintenance disassembly in service is made in a different way that the mounting procedure in the construction factory. In Fig. 8, it can be seen the exploded detail for engine block area with the following parts: . . . .

engine block (1) with its corresponding casing (2) and gasket; crankshaft and conrod; piston assembly; cylinder head assembly;

Fig. 7 Exhaust manifold dismounting direction

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Fig. 8 Exploded detail for engine block area

. assembling set of screws and nuts; . four mounting long studs (mounted in crankshaft cases). In order to assure an easy and cheap dismounting process for the engine block is implemented only three disassembly directions along OX, OY and OZ axis, in any other case, the disassembly direction increases the effort of the human operator in service. For assuring the extract of the engine block from engine assembly, is established from the design stage the safety space for dismounting the nuts from cylinder head; the dismounting direction is along OZ axis (Fig. 9). From the designed stage, according to the principle of disassembling, it is needed to be implemented the following facilities: . . . .

safety space between the engine wiring and dismounting tools; safety space for extract the engine ignition spark; the extraction pockets for tools; reducing residual engine oil losses when the cylinder head assemble is moved along OZ direction (Fig. 10); . eliminating the possibility of screws and nuts escaping from tools to falling in inaccessible places of the engine; . the dismounting trajectory for dismounting tools must be simple and easy to be made by the human operators; . occupational safety and health for human operators.

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Fig. 10 Dismounting direction for cylinder head

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Because the piston bolt is in the bottom position of the engine assembly (Fig. 11) from design stage is necessary to have the external bolt surface position over the cylinder base level. The dismounting direction is established form a translation along OY axis, and the bolt has no possibilities to drop under the piston area. The green parts (1) presented Fig. 12 are designed with groove to position the extract tools without the possibility of its accidentally moving. An important aspect is that accidentally moving of dismounting tools can generate the injury of the human operator. Figure 13 shows the area in left and right positions (rounded in red) for two dismounting tools. It is visible the differences between the diameters of cylinder head and engine block in order to create two steps. These two steps are used for positioning the extraction tools and for disassemble step is necessary only for rotating the tools with a small rotation angle. Fig. 11 Dismounting direction for piston bolt

Fig. 12 Grooves for position the extract tools

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Fig. 13 Steps for dismounting tools

4 Virtual Assembling of Engine Block In order to assure the correct assembling process in factory and the corresponding assembling time, similarly with plastic parts, all the parts from engine must be designed using the rules of the Design for Assembly (DfA) [7]: . decrease the number of parts of an assembly; . design parts from optimum automatic or manual handling; . decrease the assembling time spent. Virtual assembling of engine block is done in CATIA™ digital environment, and it is used the 3D models of engine parts, at 1:1 scale. The assembling is governed by a complete set of geometric constraints imposed by the functional roles [8]. To realize the digital assembling of complex systems, the digital tools are the best solution, because it is possible to move all the components in functional positions, using real mounting trajectories. In this case, CATIA™ provides the Smart Move digital tool, it is included in Assembly Design module. In the development process of a complex project, the assembly stages are grouped in a document generally called assembly concept. Finally, using this assembly concept, the manufacturing process design team creates the assembly frameworks. For this engine block assembly created in the digital environment, the next steps to be followed are briefly described below: . . . .

pressing the guides for engine block base; inserting the piston assembly; pressing the piston bolt; screwing up the four mounting long studs;

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. positioning the engine block; . pressing the guides for cylinder head; . positioning the cylinder head. After the virtual assembling of engine block stage is checked using the digital tools (in this case CATIA™ V5 Assembly Design module), the next stage in checking the all-product assembling process is the assembling of all 3D printed parts. It is recommended to assembly all real parts because engineers have the opportunity to observe the real correspondence between the engine parts. Possible solutions for obtaining the 3D printed parts for the engine block are shown in the end of this chapter. Figure 14 shows the first step of virtual assembling of engine block with its adjacency parts, pressing the guides for engine block base (the two parts coloured in green in Fig. 14). For virtual positioning for the guides, it is used a translation down to OZ axis. The descendent digital trajectory is marked with the green arrow. Figure 15 is marked the piston surface used for translation along OZ axis. For parts with complex surface, it is necessary to select a base surface for the manipulation tool. The base surface selected is automated marked by the system. Figure 16 is marked the piston bolt surface used for translation along OY axis. Position of the moving digital tool is represented by the axis system mark, rounded in circle in the figure. It is very important to mention that at this stage, the engineers have not possibility to check the assembling tools clash with engine parts because does not exist the digital model for assembling tools. The feedback will create in the accessing tools check stage. The digital moving tools can work with groups of components, for example, it is possible to move down along mounting trajectory the screwing up the four mounting Fig. 14 Direction to pressing the guides for engine block base

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Fig. 15 Selected piston’s surface

Fig. 16 Selected piston bolt surface used for translation and associated direction

long studs (Fig. 17). This action is done at the step of screwing up the four mounting long studs. In order to move more parts together, exist the following possibilities: . . . .

creating the selection sets; creating the groups; selecting all the parts together; moving the entire product with its environment.

The next step of digital assembling is positioning the engine block (Fig. 18), in this case is moved down the product of engine block (the product consists of engine block and cylinder casing).

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Fig. 17 Creating the selection set for long studs

The digital moving tool allows to select and move down along the necessary mounting trajectory the parts without common area or without contact between (Fig. 19). For example, in CATIA™ environment, the property named check connectivity is not checked by the user. The last step of digital assembling is positioning the cylinder head assembly (Fig. 20), for moving down along OZ axis, the digital tool uses the enlarge flat surface marked by the axis system. The engine assembly that is studied in digital tools context in this chapter is designed to be used on a competition lightweight kart. Figure 21 shows the engine assembly positioned in the kart chassis in virtual assembling. This competition kart is designed according with the green environment and is used a four-stroke engine with high-speed rotation and exhaust filtering system, not a two-stroke engine, to decrease the exhaust gases toxicity. The kart chassis components are numbered follow: . 1—rear bumper (from body kit);

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Fig. 18 Positioning the engine block

. . . . .

2—middle deflector (engine area); 3—engine assemble; 4—chassis (made by the steel pipes welded); 5—front bumper (from body kit); 6.—seat.

In the end, it is studied in virtual environment entire the engine block, and this action is extremely useful because, for example, in engine service stage, on chassis, the engine block dismounting service procedure can be easily made.

5 Digital Collision Check To complete verification procedure for performing a complex system in digital environment, in this case, an engine assembly involves checking the digital prototype to determine the collisions and safety spaces.

Study on Design and Manufacturing of an Engine Block Using Digital … Fig. 19 Digital moving tool for non-contact parts

Fig. 20 Positioning the cylinder head assembly using the enlarge flat surface

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Fig. 21 Engine assembly positioned in the kart chassis

The digital environment aided engineers in activity to validate assembly solutions using digital prototypes technologies and kinematic simulation set-up using digital media [9]. From the kinematic point of view, it is noted that there are three categories of digital collision check: . between the static engine components, for example: engine block and cylinder casing; engine block and cylinder head; engine block and four mounting long studs; . between moving (or rotating components), for example: conrod and crankshaft; crankshaft and its fuse bearings seat; . between moving and stating components, for example: conrod and cylinder casing. With the applied digital tools, the engineers have a large number of collision check tools, with important options [10]: . ignoring complex surfaces (collision are only detected on the surface type); . highlighting faces (the faces are highlighted); . sound (the system beeps when a collision is detected)—very useful in the analysis; From the kinematic point of view near the engine block, there are several areas of interest: . conrod and crankshaft movement; . piston assembles and conrod.

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Fig. 22 Base of the engine block

As it is known, some engineering software systems mark the threaded assembly as collision, for example, in CATIA™ digital check procedure, the threaded assembly is marked along the entire length of thread. At the base of the engine block, it is found an interest zone, here it is the safety space for rotation of the conrod assembly (Fig. 22), and the following items are marked: . . . .

1—cylinder casing base; 2—crankshaft assembly; 3—crankshaft case; 4—area of possibility of collision;

In this case of digital collision check, in CATIA™ digital environment, the user applied the analysis in kinematic mode, with active option for collision detecting. The system, in real time, generates the swept spaces, using the 3D models for previously maintained parts combined with functional joints. This swept space is checked with statics parts from immediate vicinity. For example, another area to study against collision or wrong safety space for movement is the joint between piston assembly and conrod (Fig. 23, the area of interest is rounded). The possibility of clash exists between the small end of conrod and the piston barrel. Here is an interesting analysis because the conrod describes a rotation movement and the piston describes a linear movement, and the digital collision check has possibility to perform the analysis between the components in movement with different trajectory. The digital tools for collision and wrong distances analysis have no possibility to detect the difference between the collision classes. For assembling point of view, the collisions have three possibilities: . collisions corresponding to interference fits—technological collisions;

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Fig. 23 Safety space for conrod movement

. collisions corresponding to erroneous part dimensions—wrong collisions; . collisions corresponding to threaded parts—collisions due the design system, collisions only in 3D model. Figure 24 detailed the resultant analysis report generated by the digital check clash tool from CATIA™. This tool performs three types of check items: . contact: in order to check the interference fits; . clash: in order to check the erroneous part dimensions; . clearance: in order to check the clearance fits. This report shows a long clash between two static components (presented in Fig. 24), after the study of situation, is established this clash is correct interference fits, because between the engine casing and its engine block is a shrunk fit. Finally, these collision analysis reports are attached to the digital project in project Product Lifecycle Management (PLM) database. The report of clash analysis digital tool is not enough in order to identify the situation from 3D digital prototype, and the system assure attached to each analysed entity a detailed image. For example, in clash line between the engine block and cylinder casing, the correct clash for interference fit is shown a direction mark with common distance and the common surfaces are highlighted (Fig. 25). The complete rules of digital collision check are shown in Fig. 26. It is presented all category of the situations with relevant status (relevant item means the item was verified by the user): . clearance (3 mm imposed safety space for analyses); . clash (for interference fits);

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Fig. 24 Resultant analysis report

Fig. 25 Clash line between the engine block and cylinder casing

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Fig. 26 Status of the collisions in list by conflict from report

. contact (for guide, centring parts, seals). The collision checks digital tools have also the role of validating the assembly concept. In assembly, concept parts with contact and tightening are provided. Figure 27 detailed the items from check clash report: . clash—interference fit: between the engine block (2) and its cylinder casing (3); . contact—in the top area: Fig. 27 Detailed items from check clash report

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between the guides for cylinder head (highlight rounded) and engine block (2); between the engine block (2) and top seal (1); . contact—in the bottom area: between the guides for crankshaft case (highlight by rounded) and engine block (2).

6 Tool Accessibility The tools accessibility is the bridge between the Design for Manufacturing/Design for Manufacturing and Assembly (DfM/DfMA) and Design for Disassembly (DfD). To assure this procedure, the engineers have two possibilities: . analogic procedures—using real tools (embarrassing procedures and time consuming); . digital procedures—using digital environment (it works in real time, with low costs and high-performance results). The tools accessibility check procedure is an important section in performing project database. To perform this extremely important stage of work in the engine digital prototypes, the following three main items are needed: . digitized 3D models for all used tools (tools set for factory, and tools set from services); . digital prototype for studied system (in this case for engine system); . digital environment (with 3D moving capabilities). All the digitized 3D models for used tools must be accompanied by the necessary spaces for work when the tools are in position, the so-called safety space. For this stage, the designers must collaborate with the tool makers to obtain the information about dimensions and safety spaces associated to each tool. From safety spaces point of view, the industrial rotary tools require less space than standard tools. For example, a solid wrench needs more safety space for works that an electric screwing tool. In the tool’s accessibility check procedures, it is extremely important to have all possibilities for simulation: . industrial assembling process by robotics arm; . industrial assembling process by human operator; . service disassembling by human operator (in services and repair shops, there are still workers nowadays, and the disassembling/assembling time is too long than robotics systems from factories). Figure 28 shows the safety space for tools (1). The model for tools is marked in 3D environment as cons because these cons included the all-tool wiring area, and the assembling tools have four mounting long studs and engine piston in the vicinity.

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The following remark is made regarding this figure, the differences between the assembling procedure and disassembling procedure: . industrial assembling process (by robotics arm or by human operators)—pressing the engine block guides in their corresponding hole: assembling tool type: pneumatic pressing tool; electromechanical device; . services disassembling process by human operators—hanging and pulling out the guides form their corresponding hole: disassembling tool type: manually extraction grip. Figure 29 shows the safety space for tools (1). The model for tools is marked in 3D environment as cons, the level of access it upper than in figure above and the trajectory of the assembling tools is easier. Figure 30 shows another task for digital simulation, the assembling of complex system in its mechanical environment, there are the following items to check: . tool accessibility in mechanical environment (in this case a competition kart chassis); . mounting trajectory (in this case is a translation along OY axis, if change the trajectory along OZ, it involves mounting the kart chassis on a rotating table); . human hands safety space (in order to assure the health and safety work conditions); Fig. 28 Safety space for tools—bottom area

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Fig. 29 Safety space for tools—top area

Fig. 30 Tool accessibility in mechanical environment—base screws

. mounting points with or without direct visibility for human operators; . fail results in case of the screw fells from screwing tool (the screw dropped from the assembling tool must be easily retrievable by the human operators); . importance of using battery-powered tools (there is no need to have space for the powered cord). Assembly and disassembly procedures involve two stages (whether is done in the factory or in service location):

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Fig. 31 Tool accessibility in mechanical environment—tool in work movements

. approaching assembling tool stage; . effective assembly stage. From the framework point of view, the approaching assembling tool phase is vital to generate in the virtual media the swept space by the assembling/disassembling tool. The swept spaces by the assembling tool are made using the 3D model for tool and the assembly path. The 3D model for tool is displaced along the assembly path, and all the intermediate positions for tool are added in a resultant body named swept space. Figure 31 presents the swept space by the battery-powered screwing tool, and the different intermediate positions are rounded highlighted. In assembly path, the designers must consider the human operator capacity: assembling tool weight, work position, direct visibly degree, including simulation in digital media for workplace lighting quality, etc. As it is known, in many situations, the so-called pockets for tolls accessing are used. Figure 32 shows the digital simulation for tools accessing, and the access pockets involve the comparation between the end effector of the assembling tool and the effectively access space for assembly element. In this case of screw heads with a drowned profile, the size of the screw may be larger than the tool head. The combined 3D models for safety space measurement are rounded highlighted.

7 Virtual Engineering Used for the Engine Block Virtual engineering (VE) has an important role in sustainable manufacturing, global decreases the CO2 emissions and allows to create environment-friendly products. It plays a key position in the mechanical design, control design and process design

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Fig. 32 Tool accessibility in mechanical environment—the access pockets

[11]. The engine manufacturing trends are accommodated with the VE strategy in order to perform high-tech goals: . . . . .

create environment-friendly products; decrease the time spent to manufacturing; reduce the energy consumption; cost cut for engineering; reduced the technological fails.

In order to assure the virtual engineering goals, the machining processes are the big challenge in nowadays industrial environment governed by the Industry 4.0. The machining process is one of the most important components of virtual engineering, and for the complete and correct 3D prototypes of complex systems, it has to be used. Machining process is described by complex and nonlinear relationship between input and output parameters, for example, in the case of cutting process, the input variables include cutting tool material, workpiece material, speed, feed rate, depth of cut, etc. and the output parameters are tool life, tool wear, tool wear rate, cutting forces, material removal rate, etc. [12]. Virtual manufacturing (VM) technology could be considered one of the most important parts in the manufacturing systems [12, 13]. The main components of machining error are from clamping error and machine error, from this reason are done the studies of simulation model of machining process based of virtual modelling technologies [13]. Digital model used for engineering and manufacturing simulations at the engine block used three main entities: . digital prototype for engine block; . digital machining environment (tools and trajectories); . clamping devices.

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Figure 33 shows the 3D prototype for engine block ready for manufacturing simulations. The prototype is characterized by the following items: . . . .

part body—3D model for engine block; material—aluminium alloy; design table—for parametric changes; construction—geometrical set for surfaces construction.

In order to assure a properly cutting cost for the manufacturing process in case of small and unique production, the main rule is to group and performed machining phases in minimum operations to reduce the number of machine tools and clamping devices. From this reason, the engine block is machined in two machining operations: . engine block in functionary position: machining top and inner areas; . engine block rotated with 180 degrees: machining bottom surfaces and long holes. CATIA™ digital environment allows the manufacturing simulation using a digital assembly composed of the two major parts (Fig. 34): . semi-finished 3D model for engine block (1); . 3D model for modular clamping device (2). Virtual machining simulation is done using a modular clamping device. The modular clamping systems are commonly used because systems like this could adapted for many groups of dimensions.

Fig. 33 3D prototype for engine block—manufacturing tree components

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Fig. 34 Digital assembly used for manufacturing simulation

The time to change the production type is also short because of the modular clamping devices assure a quick reconfiguration. The modular devices are designed in contextual environment, the digital prototype for part is the core of input data and the minimum and maximum overall dimensions of the parts family are also considered [14]. The digital tools dedicated to surface machining have many tasks for performing the complex bodies using milling or lathe machining. Figure 35 shows the assembly composed by the engine block semi-finished part and the clamping devices. It is shown the collision check sequences and is used the digital tool surface machining from CATIA™ V5. This is an example of virtual simulation for combined clamping systems (base one and second on the top area at semi-finished part in working position). It is also simulated the tool clamping dimension against collision with environment. In highlight, rounded area is shown the upper modular clamping segment, and the tools approach trajectories and the working trajectories which are without any collisions. To perform collision check task, the user must set the resource list: . machine type (including the postprocessor emulator); . home point for system; . tools list (generally imported from the software tools databases). The digital environment provides to the user on demand the intermediate positions for milling tool to obtain a visual information about the safety level compared to the clamping device (Fig. 36). The approach trajectory and the direction along OZ component are shown in Fig. 37. At this level of simulation, the main task is to determine the cutting path

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Fig. 35 Engine block semi-finished part and the clamping devices

Fig. 36 Intermediate positions for milling tool

to reduce the machining shock, because it decreases the shock and protects guide to reduce the machine wear and to increase the tool life. Another situation for machining simulation is shown in Fig. 38, where the assembly is composed by the following components: . semi-finished part (1), general settings opacity 50%; . final part (2), general settings opacity 100%; . clamping device (3), general settings opacity 100%.

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Fig. 37 Approach trajectory for machining tool

Fig. 38 Digital assembly used for manufacturing simulation–bottom area

The area for machining is free from clamping devices, and it used the central engine block hole for an elastic auto-centred device.

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The machining simulation in digital environment (Fig. 39) assures to the user a detailed representation about the tool for current step (1) and the no-machining surfaces (2). Figure 40 shows an intermediate stage, after the milling process, the long drill (1) is shown in working position, the first two fully machined holes are rounded. It is important to note that the user possibility to direct check the cutting depth with a digital measurement tool. Similarly, the user can check by measurement on the virtual model the final diameter of the pre-drilled holes.

Fig. 39 Tool in the current step—milling tool

Fig. 40 Long drill in working position

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8 Additive Manufacturing of the Engine Block As mentioned above, the first contact between the designers and the result of their digital work is to have real projected parts, obtained by using additive manufacturing systems. The additive manufacturing systems create the bridge between the digital world and real world. The parts from project under construction manufactured using additive processes allow to the designer to perform: . . . . . .

general shape analyse; surfaces design comparison; assembling test; embedding request spaces test; tool access check (with rapid prototypes of used tools); human operators’ position (for real test of mounting trajectories).

It is well known that the main additive manufacturing standard processes are the following (grouped by the principle of works) [15, 16]: . sheet lamination: sheets of material are bonded to form an object; the processes are: ultrasonic additive manufacturing (UAM) and laminated object manufacturing (LOM); . binder jetting: a liquid bonding agent acts as an adhesive between layers to join powder material; . material extrusion: the material is distributed through a nozzle where it is heated and then it is deposited layer-by-layer (Fused Deposition Modelling—FDM or Fused Filament Fabrication-FFF process; . material jetting: droplets of build material (photopolymer and wax) are selectively deposited in a similar manner of a two-dimensional ink jet printer; . directed energy deposition: different energy sources like laser, electron beam or plasma arc are used to melt the materials; . vat photopolymerization—liquid photopolymer in a vat is selectively cured by UV light polymerization; . powder bed fusion: thermal energy selectively fuses regions of a powder bed; the processes are: Direct metal laser sintering (DMLS), Electron beam melting (EBM), Selective heat sintering (SHS), Selective laser melting (SLM) and Selective laser sintering (SLS). Nowadays, fused deposition modelling (FDM) is used at large scale in different industries, including automotive, with more and more applications such as [17] testing models, lightweight tools and final functional components. The powder bed fusion processes produce 3D complex shapes from the powder material, including metal powder, in a layer-by-layer manner. The processes have the potential to be more flexible, to obtain a wider range of shapes with different working parameters, and use more challenging materials [18, 19]. All additive manufacturing systems work according to the following principles:

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. 3D model is sliced in layers by OZ direction; . layers are digitized in a controlled face tress mesh; . using mesh, the software generates the transfer file (common format for transfer files is STL); . additive manufacturing systems import the transfer file and perform the command file with trajectories and process parameters; . hardware component of the additive manufacturing systems builds the physical prototype. Figure 41 presented the application of digital tools for processing the transfer STL file for the engine block prototype. The 3D model is imported in CATIA™ STL rapid prototyping tool with roughness of tessellation set to 0.001 mm. In this case, it is necessary to set the tessellation so fine because the 3D model has more rounded areas. The considered engine block used two types of additive manufacturing processes: . SLM—selective laser melting, in order to visualize the engine block made by metal; . FDM—fused deposition modelling, to study the engine block assembly and for obtaining the physical engine block in a sectioned mode. Figure 42 presented the engine block main body made by the iron alloy powder using the SLM250 machine and the model was scaled at 1:4 dimension. It is easy to observe the difference between the Oz axis roughness and the OXY planar roughness. Figure 43 presented the result of using the FDM process in manufacturing of the engine block from an ABS filament. This process assures to create the solid part

Fig. 41 Engine block imported for additive manufacturing

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Fig. 42 Engine block made by the iron alloy, scaled at 1:4 [2, 9]

with solid external surface and low-density honeycomb core, in order to obtain the low consumption of allocated resources, in this case is strong reduced the printing process time. Figure 44 presented the cylinder casing obtained by using the FDM process and ABS filament. Another task for the designer was the cycle closing alignment, in presented case, this linear deformation along OZ axis was eliminated using the digital option to circle closing in helical path. In order to perform the real section trough, the engine block and cylinder casing, several parts were made in different configurations (Fig. 45): engine block sectioned in OZY plane (1), entire cylinder block (2) used for assembly testing and cylinder casing (3). The real sectioned assembly between the engine block assembly and its cylinder casing is shown in Fig. 46.

Fig. 43 Engine block obtained by using the FDM process [2]

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Fig. 44 Cylinder casing obtained by using the FDM process [2]

Fig. 45 Engine block and cylinder casing—parts were made in different configurations Fig. 46 Real sectioned assembly—made by FDM process [2]

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Fig. 47 Final assembly—manufacturing by FDM process [2]

Figure 47 presented the final assembly between the engine block and its cylinder casing; it can be said that this is the first physical result of the development of the considered digital project. Referring to the assembly between the parts made from FDM process, it has to be pay attention to perform the 3D models dedicated to additive manufacturing, and these parts have to be designed with geometrical allowance equals or bigger than the FDM system processing tolerances (in other case, in 3D, all assembly allowances are checked, but the printed models cannot be assembled).

9 Conclusions This chapter presents the applications of digital technologies in the design and manufacture of an engine block from construction of competition kart, four-stroke engine. Parallel to the use of large-scale digitization in design and manufacturing, other activities are also presented: industrial frameworks, tools accessing and possible issues, mounting concept, assembling trajectories, safety and health at work and some differences between robotics assembly systems and human workers. All these are implemented using specific tools from CATIA™ environment and the concepts: design for manufacturability, design for assembly and disassembly, virtual assembling of engine block, digital collision check tools, tools accessibility, virtual engineering for engine block and the additive manufacturing. First section presented how the main rules of design for manufacturability and assembly are applied in the engine design process and in the second section is showed the using of the design for disassembly tool to obtain a product according to the objective of decreasing the service technical requests. The third section presents the application of the digital environment in order to assure the virtual assembling of the engine block. Virtual assembling is done in CATIA™ digital environment, and it is used the 3D models of engine parts. There are

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also presented the digital features for moving all the components in the functioning positions and the simulation for all real mounting trajectories. In digital environment, using the CATIA™ kinematic mode, the fourth section showed the complete procedure to check the digital prototype, determine the collisions and safety spaces for the engine assembly. The fifth section allows to the readers to see the check procedure associated to the tools accessibility for complex 3D models (in this case the engine assembled on the chassis). The sixth section presented the virtual engineering used for the engine block, focused to the manufacturing simulation. For these activities is used the three main entities: the digital prototype for the engine block, digital machining environment and the clamping devices. The last section, the section seven, presents how, in this case, the additive processes are used to obtain the real prototypes for the engine block and its associated cylinder casing, in different scales to check the designed shapes and the assembling details.

References 1. Cevikcan E, Ustundag A (2018) Industry 4.0 managing the digital transformation, Series: Springer series in advanced manufacturing, Springer, ISBN: 978-3-319-57870-5, 3319578707, 978-3-319-57869-9 2. Haba SA (2013) Digital manufacturing of single-cylinder engine block. PhD thesis, Transylvania University of Brasov, Romania 3. Andersn D (2014) Design for manufacturability: how to use concurrent engineering to rapidly develop low-cost, high-quality products for lean production. Taylor & Francis Group. https:// doi.org/10.1201/b16501, ISBN: 9780429255588 4. Anderson D (2020) Design for manufacturability: how to use concurrent engineering to rapidly develop low-cost, high-quality products for lean production, 2nd ed. Taylor & Francis Group. https://doi.org/10.4324/9780429285981, eBook ISBN9780429285981 5. Mital A, Desai A, Subramanian A, Mital A (2014) Design for assembly and disassembly, in book product development, pp 159–202. Elsevier. https://doi.org/10.1016/B978-0-12-7999456.00007-7 6. Ghionea IG, Tarba IC, Cukovic S (2021) CATIA V5 parametric design and programming applications. Printech Publishing, Bucharest 7. Kent R (2016) Design quality management in book: quality management in plastics processing, pp 227–262. Elsevier. https://doi.org/10.1016/B978-0-08-102082-1.50008-3 8. Haba SA, Oancea G (2012) Virtual assembling of an engine block using CATIA environment. Acad J Manuf Eng 10(3):74–79 9. Haba SA, Oancea G (2015) Digital manufacturing of air-cooled single-cylinder engine block. Int J Adv Manuf Technol 80(5):747–759. https://doi.org/10.1007/s00170-015-7038-x 10. *** (2021) Solidworks—collision detection. https://solidworks.com/2021/English/SWConn ected 11. Assad F, Konstantinov S, Rushforth EJ, Vera D, Harrison R (2021) Virtual engineering in the support of sustainable assembly systems. Proc CIRP 97(202):367–372. https://doi.org/10. 1016/j.procir.2020.05.252 12. Adane TF, Nicolescu M (2018) Towards a generic framework for the performance evaluation of manufacturing strategy: an innovative approach. J Manuf Mater Process 2(2):23. https://doi. org/10.3390/jmmp2020023

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13. Liu Y, Peng F, Liu H (2017) Final machining of large-scale engine block with modularized fixture and virtual manufacturing technologies. Hindawi J Eng 3648954. https://doi.org/10. 1155/2017/3648954 14. Panc N (2021) Devices—conception and design. Publishing U.T. Press, Romania. ISBN 978606-737-515-2 15. *** (2015) Standard ISO/ASTM 52900—additive manufacturing. General Principles—Terminology 16. *** (2022) https://www.lboro.ac.uk/research/amrg/about/the7categoriesofadditivemanufactu ring/, Accessed on 9 Jul 2022 17. Gao X, Yu N, Li J (2020) Influence of printing parameters and filament quality on structure and properties of polymer composite components used in the fields of automotive. Woodhead Publ Ser Compos Sci Eng 2:303–330. https://doi.org/10.1016/B978-0-12-819535-2.00010-7 18. Buican GR, Oancea G, Lancea C, Pop MA (2015) Influence of layer thickness on internal structure of parts manufactured from 316-L steel using SLM technology. Appl Mech Mater 809:369–374. https://doi.org/10.4028/www.scientific.net/AMM.809-810.369 19. Nandy J, Sarangi H, Sahoo S (2019) A review on direct metal laser sintering: process features and microstructure modelling, lasers in manufacturing and materials processing, Vol 6, pp 280–316. https://doi.org/10.1007/s40516-019-00094

Automatization of CAD Model Development of Slewing Bearing Using Solid EdgeTM Rafael Gella-Marín, César García-Hernández, and José-Luis Huertas-Talón

The use of CAD models is a fundamental part of components development in modern industry. Not only it provides a 3D representation of the piece but it also allows performing simulations to evaluate how it behaves under working conditions. The development of a CAD model involves the use of several operations. The starting point is usually the creation of a 2D sketch. Then, using extrusions and cuts, a 3D model will be created. This process is valid for models where no previous CAD model is available. In this case, the model has to be developed from scratch. However, the industrial brochures where the workpieces are modifications of a ground model present an opportunity to use the programming features of CAD programmes to automate the model development. Each of the operations in the CAD software is in fact code lines using the model coordinate system, the part dimensions and the operation that have to be performed. This is the reason why the CAD model operations lend themselves to be automated either creating a Visual Studio™ application or a lookup table. In this chapter, an approach for the automation of CAD development for slewing bearings is presented. First, a 2D sketch is created. Then, all the dimensions in the sketch will be linked to a lookup table, allowing modifying the sketch. Finally, all the operations will be linked to a variable table in Solid Edge.

R. Gella-Marín (B) · C. García-Hernández · J.-L. Huertas-Talón Department of Design and Manufacturing Engineering, University of Zaragoza, Campus Rio Ebro, C/ Maria de Luna 3, 50018 Zaragoza, Spain e-mail: [email protected] C. García-Hernández e-mail: [email protected] J.-L. Huertas-Talón e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6_10

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1 Introduction The manufacturing of new products involves a development phase which includes creating 2D or 3D models. These models can give the designers an insight in how the new product can interact with other components and make sure that the assembly can be successful. Physical simulations can also be necessary to evaluate how the product behaves under operation conditions, thus making it necessary to develop an accurate geometry model of the component. To develop these 2D and 3D models, CAD software is the standard tool in industry. In the case of 2D drawings, the designer uses the CAD software Graphical User Interface (GUI) and develops a drawing using 2D operations. If a 3D model is needed, the designer has two choices. He can use the 2D model previously created as a sketch and expand it to 3D. However, the CAD software developers have been recently presenting another choice. They give the users the choice to develop their models in a 3D environment, skipping the previous 2D step. No matter which procedure is used, designers have to create their models following several steps. That involves using operations which define the model geometry and linking them to the desired dimensions. This can be a repetitive process if the designer must develop different models. Companies are under pressure to develop proposal documents and drawings as fast as possible for the customers. Thus, the engineering teams must create, update, and check each detail of the model. This can lead to errors and delays in presenting the documents. This is the reason why the automation of the CAD model development can be a powerful tool to reduce mistakes and improve the workflow. It allows customization to avoid repetitive modelling tasks and standardize the model design. CAD automation means creating a parametric model where, if a dimension is changed, the whole model is updated. Anderl and Mendgen [6] Discusses the basics behind parametric design. Gujarathi and Ma [1] Uses a “Common Data Model” (CDM), with all the required parametric information for CAD modelling and CAE analysis. Roller [2] Discusses a method that uses automatic storage of geometric constraints for the generation of parametric models. Myung and Han [3] Applies parametric modelling for machine tool assembly. Monedero [4] extends this methodology to architectural design tools. Nahm and Ishikawa [5] Presents a set-based parametric design (SBPD) for parametric modelling. Sanchez et al., Benaouali and Kachel [7, 13] Discuss parametric modelling methods for CAD/CAE in the aeronautic industry. Machado et al. [8] Compares two open-source scripting tools for parametric modelling. [9] Describes a multibody approach for part environment in parametric CAD programmes and presents example models. [10] Presents solutions for constraint-based modelling. Mathur et al. [11] Explains how to implement Graphical User Interfaces (GUI Graphical User Interface (GUI)) in CAD systems with programming to create sub-programmes and develop automated modelling operations. Gomes et al. [12] Shows how to automatically generate optimized CAD models. Kim et al. [14] Presents a methodology to maintain the parameters, constraints,

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features, and other elements in Standard for Exchange of Product (STEP) files. Li et al. [15] Proposes a method to exchange design data between shipyards and equipment suppliers who use different CAD systems. Reddy and Rangadu [16] Presents a parametric CAD modelling system for Spur Gear Design using the AGMA standards. This provides a faster and simpler gear design system compared to conventional design systems. This chapter proposes a methodology for the parametrization of slewing bearing CAD design. Using the 2D dimensions set in a fictitious commercial brochure for a wide arrange of models, a 2D sketch is created. Next, the sketch dimensions are linked to a spreadsheet. Then, the 2D sketch is transformed to a 3D model. When the dimensions in the spreadsheet are changed, using the brochure dimensions to create another slewing bearing, the CAD model is updated. Using this methodology, the designer can create CAD models focusing on the dimensions and not on manually updating the model, providing a faster answer to the customer and minimizing errors in the CAD development.

2 Methodology Parametric CAD design involves creating a model where the model dimensions are linked to constraints. If the value of the constrained dimensions is changed, the model auto updates and it is not necessary to change the design manually. This allows to automate repetitive tasks, which usually take place in families of products. As we can see, parametrization is a very useful tool when the designer must perform slight variations on a core design. This supports design teams that must modify models on a regular basis. It also makes easier to see how the model will behave when something is changed. There are several benefits when developing a parametric model. The first one is that it provides an easy definition and automatic creation of families of products. It also allows for integration with manufacturing processes, resulting in a decrease of the production time. The main drawback is that the development of the 3D CAD parametric model takes longer, as the designer must link the constraints to the models. He must be also sure that the constraints do not interfere with the model when they are changed, creating an incorrect model. In this chapter, we will present the methodology to develop a parametric model of a slewing bearing for a commercial company. We will show how to create a 2D sketch with a slewing bearing profile. We will link the dimensions to constraints. Then, we will extrude the 2D sketch to create the 3D model. Next, we will create the bore holes in the outer and inner rings, and finally, we will link them to constraints. This will generate a parametric 3D model. To show its benefits, we will show how modifying the constraints using the bearings dimensions taken from a brochure of a commercial company creates a 3D model equal to the one from the brochure.

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3 Development of Application Commercial components in brochures are usually made from a template, where one or several dimensions are changed from one reference to another. The example that we are going to consider in this chapter is a slewing bearing from a fictional brochure. A slewing bearing withstands axial, radial, and tilting loads and rotates at a comparatively slower rotational speed than a typical bearing. Some of their applications are wind turbines, cranes, excavators, tunnel boring machines, and trains. A slewing bearing is formed by an inner ring and an outer ring which are assembled. In each ring, bolt holes are drilled to attach the slewing bearing to the supporting structure of the application. In Fig. 1, a template for a slewing bearing is presented. Table 1 gives the slewing bearing variables to be considered in the design of a single row four point contact ball slewing bearing. In Table 2, a fictional slewing bearing brochure is presented. By changing the variables value, seven different slewing bearing references are created. In this chapter, we will show how to create a CAD slewing bearing template in Solid Edge™ and link it to a spreadsheet, so the user can select different references and the CAD model will auto update itself, adapting the dimensions. We will create a spreadsheet (Fig. 2) using a dropdown list to select one of the seven different types of bearing. “Brochure” contains the dimensions from the different slewing bearing models. “Brochure import” contains the dimensions of the selected

Fig. 1 Slewing bearing template

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Table. 1 Slewing bearing variables Variable

Description

Dimension

Dl

Raceway diameter

mm

Da

Outer diameter of outer ring

mm

Ra

Outer radius of outer ring

mm

Di

Inner diameter of inner ring

mm

Ri

Inner radius of inner ring

mm

H

Total slewing bearing height

mm

O

Outer diameter of inner ring

mm

Ro

Outer radius of inner ring

mm

U

Inner diameter of outer ring

mm

Ru

Inner radius of outer ring

mm

H1

Outer ring height

mm

H2

Inner ring height

mm

Hu

Lower gap between inner ring and outer ring

mm

Ho

Upper gap between inner ring and outer ring

mm

La

Bolt holes circle diameter in outer ring

mm

Rla

Bolt holes circle radius in outer ring

mm

Li

Bolt holes circle diameter in inner ring

mm

Rli

Bolt holes circle radius in inner ring

mm

na

Bolt holes number in outer ring

ni

Bolt holes number in inner ring

Ba

Bolt hole size in outer ring

mm

Bi

Bolt hole size in inner ring

mm

Ma

Bolt metric in outer ring

Mi

Bolt metric in inner ring

bearing from the brochure. “Solid Edge™ 2D sketch input variables” are the table that we will link to the CAD model. Using the VLOOKUP function in Excel™, we will select each one of the variables from the “Brochure” spreadsheet and copy it to the “Brochure import” spreadsheet (Fig. 3). Since the dimensions in the table are diameters, we will change them to radius because the 2D Solid Edge™ sketch works with them. These values will be copied to the “Solid Edge™ 2D sketch input variables” spreadsheet and will be linked to the Solid Edge™ model. First, we will create a 2D sketch with the slewing bearing profile. Since we will revolve the 2D sketch to create the slewing bearing, we must create a symmetry axis. All the radial dimensions will be linked to this axis (Fig. 4). After linking all the radial dimensions to the axis of revolution, we will extrude the 2D sketch around this axis to create the 3D model of the two rings.

1213.5

1328.5

1443.5

1558.5

1673.5

3

4

5

6

7

983.5

1098.5

1

Dl

2

Slewing bearing

1788.5

1673.5

1558.5

1443.5

1328.5

1213.5

1098.5

Da

1558.5

1443.5

1328.5

1213.5

1098.5

983.5

868.5

Di

Table. 2 Fictitious slewing bearing brochure

71.1

71.1

71.1

71.1

71.1

71.1

71.1

H

1674.4

1559.4

1444.4

1329.4

1214.4

1099.4

984.4

O

1672.1

1557.1

1442.1

1327.1

1212.1

1097.1

982.1

U

62.1

62.1

62.1

62.1

62.1

62.1

62.1

H1

62.1

62.1

62.1

62.1

62.1

62.1

62.1

H2

9

9

9

9

9

9

9

Hu

9

9

9

9

9

9

9

Ho

1742.5

1627.5

1512.5

1397.5

1282.5

1167.5

1052.5

La

1604.5

1489.5

1374.5

1259.5

1144.5

1029.5

914.5

Li

48

42

42

36

30

30

28

na

48

42

42

36

30

30

28

ni

22

22

22

22

22

22

22

Ba

22

22

22

22

22

22

22

Bi

20

20

20

20

20

20

20

Ma

20

20

20

20

20

20

20

Mi

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Fig. 2 Spreadsheet to export the brochure data to Solid Edge™

Fig. 3 Dropdown list to select the slewing bearing from the brochure

Next, we will create a sketch of a bolt hole in the inner ring and in the outer ring. We will include the bolts diameters and bolts circle diameter. Then, we will create the holes by extruding the bolt holes sketches. Next, we will create a circular pattern for the bolt holes in the inner ring and in the outer ring. We have created a full 3D model. Now, we have to link the slewing bearing components dimensions to the spreadsheet. If we right click, we can select “Variables”. This opens a spreadsheet within Solid Edge™ showing all the variables in the 3D model (Figs. 5 and 6). After this, we can copy each dimension value from the fictitious brochure spreadsheet and paste them to the Solid Edge™ spreadsheet. This also pastes the fictitious brochure spreadsheet file path (Fig. 7). The process is copying the value of each variable in the brochure spreadsheet (Fig. 8) and pasting as link in the Solid Edge™ spreadsheet (Fig. 9).

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Fig. 4 2D sketch

Fig. 5 Selection of the “Variables” menu

Now, we have linked the variables from the fictitious brochure spreadsheet to the CAD model. If we select a different model from the dropdown list, the CAD will auto update. We can see how the CAD model is updated in Figs. 10 and 11 when each of the different slewing bearings is selected from the brochure. .

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Fig. 6 CAD model variables spreadsheet in Solid Edge

Fig. 7 Copy of the dimension variables to the Solid Edge™ spreadsheet

4 Conclusions This chapter shows how to link the dimensions of a CAD model to a spreadsheet. This allows the designers to create CAD models of different slewing bearings from a brochure faster than creating each model from scratch. This methodology can also be extended to CAD models of other products. The process will start with the creation

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Fig. 8 Copy of a variable value in the brochure

Fig. 9 Paste as link of the variable value in the Solid Edge™ variables spreadsheet

of a CAD model template. Then, we will develop a spreadsheet with the dimensions of the different models that will be available in the brochure. Finally, we will link the dimensions from the spreadsheet to the CAD model. This method automates the CAD model development and reduces errors that can happen when developing a new model.

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Fig. 10 CAD model of the slewing bearing model 1

Fig. 11 CAD model of the slewing bearing model 7

References 1. Gujarathi GP, Ma YS (2011) Parametric CAD/CAE integration using a common data model. J Manuf Syst 30(3):118–132 2. Roller D (1991) An approach to computer-aided parametric design. Comput Aided Des 23(5):385–391 3. Myung S, Han S (2001) Knowledge-based parametric design of mechanical products based on

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configuration design method. Expert Syst Appl 21(2):99–107 4. Monedero J (2000) Parametric design: a review and some experiences. Autom Constr 9(4):369– 377 5. Nahm YE, Ishikawa H (2006) A new 3D-CAD system for set-based parametric design. Int J Adv Manuf Technol 29(1):137–150 6. Anderl R, Mendgen R (1995) Parametric design and its impact on solid modeling applications. In: Proceedings of the third ACM symposium on Solid modeling and applications, pp 1–12 7. Sanchez F, Liscouët-Hanke S, Tfaily A (2021) Improving aircraft conceptual design through parametric CAD modellers–a case study for thermal analysis of aircraft systems. Comput Ind 130:103467 8. Machado F, Malpica N, Borromeo S (2019) Parametric CAD modeling for open source scientific hardware: comparing OpenSCAD and FreeCAD python scripts. PLoS ONE 14(12):e0225795 9. Łukaszewicz A (2009) Modelling of solid part using multibody techniques in parametric CAD systems. In: Solid state phenomena (vol 147, pp 924–929). Trans Tech Publications Ltd. 10. Solano L, Brunet P (1994) Constructive constraint-based model for parametric CAD systems. Comput Aided Des 26(8):614–621 11. Mathur A, Pirron M, Zufferey D (2020). Interactive programming for parametric CAD. In: Computer graphics forum (vol 39, no 6, pp 408–425). 12. Gomes S, Varret A, Bluntzer JB, Sagot JC (2009) Functional design and optimisation of parametric CAD models in a knowledge-based PLM environment. Int J Prod Dev 9(1–3):60–77 13. Benaouali A, Kachel S (2017) An automated CAD/CAE integration system for the parametric design of aircraft wing structures. J Theor Appl Mech 55(2):447–459 14. Kim J, Iyer R, Kim J, Pratt MJ, Sriram R (2007) Data exchange of parametric CAD models using ISO 10303–108. US Department of Commerce, National Institute of Standards and Technology. 15. Li J, Kim BC, Han S (2012) Parametric exchange of round shapes between a mechanical CAD system and a ship CAD system. Comput Aided Des 44(2):154–161 16. Reddy EJ, Rangadu VP (2018) Development of knowledge based parametric CAD modeling system for spur gear: an approach. Alex Eng J 57(4):3139–3149

CAD-Based Application in VBA for Tool’s Profiling Virgil Gabriel Teodor, Georgiana Alexandra Moro¸sanu, and R˘azvan Sebastian Cr˘aciun

The issue of generating surfaces which are ordered curl of surfaces, using profiled tools, is a current concern of the international research teams. The performance of the generating by machining depends by the cutting tool’s geometry, and the 3D modelling allows a simple and rigorous analysis of the actual geometry of tool’s cutting edges. Initially, the issue of surface generating by enwrapping has a graphical approach and subsequently an analytical one. This analytical way to study the generating by enwrapping processes is yet frequently used by researchers. A fundamental contribution had F. Litvin which approaches the modelling of the teethed wheel, in analytical form, as base of the general issue of design for this type of parts [1]. Obviously, the analytical approach of the surface generation is very important in this domain, but this can and has to be completed or, where the methodology allows, replaced with alternative methods. Sometimes, these methods are easy to use and induce minimum errors from technical point of view. The continuous development of the graphical design environment allows returning to the graphical or grapho-analytical approach for the surface’s enwrapping problems, using capabilities offered by AutoCAD, CATIA, Solid Edge or other graphical design programs. At “Dun˘area de Jos” University of Galat, i, in the department of Manufacturing Engineering, a research team, of which the authors of this chapter are also part, developed applications in the graphical design environment, solving problems of the tool’s profiling for the generation of: ordered curl of surfaces associated with V. G. Teodor (B) · G. A. Moro¸sanu · R. S. Cr˘aciun Department of Manufacturing Engineering, Dun˘area de Jos, University of Galat, i, Domneasc˘a Street, No. 21, Galati, Romania e-mail: [email protected] G. A. Moro¸sanu e-mail: [email protected] R. S. Cr˘aciun e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6_11

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a couple of rolling centrodes and tools bounded by revolution surfaces, generating helical cylindrical surfaces with constant pitch. All these approaches give solutions based on enwrapping fundamental theorem, like the Olivier or Gohman theorems, for enwrapping problems. In the frame of the same research team, an alternative method was developed based on the simplification of the Willis theorem, method published as method of “virtual pole”. During the elaboration of previous works, it was observed that it is possible the elaboration of some scripts which allows automatizing the process of tool’s profiling, in the frame of previously mentioned graphical design environments. In the present chapter, the method of “virtual pole” is presented and a program for profiling the generating tool was developed for the first time. The programs were written in Visual Basic for Applications (VBA), which allows profiling of tools like: rack-gear tool, gear shaped cutting tool or rotary cutter.

1 Surface Generation by Enwrapping 1.1 Introduction For generating pieces with symmetry as ordered curl of surfaces, in both cases of manufacturing by plastic deformation or by machining, it is largely used the enwrapping surface generation. This generating method has some considerably advantages as: increased productivity; dimensional precision for obtained surfaces; and correctness of obtained shape. These two last advantages are in closed connection with the surface obtaining way, this surface not being a merely copy of the counterfort of tools but being obtained as a large number of cutting or positioning of generating tool. However, this way to obtain the surface also has a disadvantage, due to the necessity to calculate with increased precision the shape of the active surface of generating tool. Often, the needed calculations for tool’s profiling are difficult and significantly use the available computing resources. Over the years, some methods were established for surface generating by enwrapping, from these being able to be mentioned [2]: the Olivier theorems, which allows the study of linear and single-point contact between the enwrapping surfaces; the Willis theorem also known as the “theorem of normal” for study of in-plane enwrapping between profiles; and finally, the Nikolaev method for study of reciprocally enwrapping between revolution or cylindrical surfaces with cylindrical helical surface with constant pitch. Subsequent, in order to simplify the calculus effort for profiling the tools previously mentioned, some complementary methods were developed, characterized by a limited applicability, but having the advantage of a simplest form for the enwrapping condition, keeping the mathematical rigour [3]. Among the complementary theorems, developed at “Dun˘area de Jos” University of Galat, i, by a research team

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conducted by the respected professor Ph.D. eng. Nicolae Oancea, we can mention [4]: the method of “minimum distance”; the method of “trajectories”; the method of “substituting circles”; the method of “in-plane generating trajectories”; etc. Using at large scale, the techniques for computer-assisted design, determining the development of some methods, which allows to the user to take the advantage of this techniques, when is necessary to determine profiles of tools which generate by enwrapping. For this, were imagined and published profiling algorithms which can be utilized for various CAD programs, as: AutoCAD™ , CATIA™ , Solid Edge™ , etc. [5–10]. The script presented at the end of this chapter is part of this effort. It was developed in VBA language and takes advantage of the CATIA™ design environment to profiling tools of type: reach-gear, gear shaped cutter or rotary cutter, designed to generate by enwrapping, using the rolling method, profiles known in analytical or discrete form.

1.2 Theoretical Fundaments Generating of helical surfaces or of ordered surface curl needs determining the active surface of tool. A particularity of generation by enwrapping is that, both the generated surface and the generating one, are moving surfaces and, more, each of them is envelope for the family generated by the other surface, in time of relative movement regarding the envelope. For this reason, it is possible to imagine some specific methods for determining the geometrical place of the contact points between the two mentioned surfaces. In the established vocabulary, this geometrical place of the contact points is named “characteristic curve” and constitutes the starting element for identifying the form of the enveloping surface. As we previously mentioned, both considered surfaces must be in situation of reciprocally enwrapping. This allows determining the mathematical expression of a relation between surfaces and determining of a kinematical enwrapping condition between the generated and generating surface. Regarding the analytical expression of the generated surface and the movement between the two surfaces, determining the kinematical enwrapping condition assumes three approaches: for case when the surface’s family to be generated depends by one parameter; for the case when the surface’s family to be generated depends by two independent parameters; and the third case, when the movement between the two surfaces is a complex motion.

1.2.1

The Generated Family Depends by One Parameter

If it is denoted with Σ the generated surface and it is analysed its movement regarding a global reference system, it is possible to demonstrate that the movement equation has form:

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x = α T · X + A,

(1)

⎛ ⎞ x where x = ⎝ y ⎠ represents the matrix obtained with coordinates of a point, M, z ⎛ ⎞ X belonging to the Σ surface in a global reference system xyz; X = ⎝ Y ⎠ is the Z matrix obtained with the coordinate of the same point in a mobile reference systems, XYZ, joined with the Σ surface; α = (αik (τ )) is the orthogonal transforming matrix between the unitary vectors of the two systems, XYZ and xyz; and A = (ai (τ )) is the matrix associated with the position vector of the point O, the vector →r O see Fig. 1. Presuming known the analytical equation of the Σ surface in the reference system joined with this: F(X, Y, Z ) = 0,

(2)

we can write the surface’s family generated in the movement given by the τ parameter: F(x, y, z, τ ) = 0.

Fig. 1 Reference systems. Note The τ parametenr may represent the “time” parameter or another similar parameter, associated with time. The movement given by the τ parameter regarding a global reference system (e.g. xyz) is named the absolute movement

(3)

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Definition The geometrical place of the contact points between the enveloping of the Σ surface’s family, generated in the movement (3), and the envelope of this family is named “characteristic curve”. The characteristic curve, C, onto the Σ surface is given by the equation system: ⎧ ⎨ F(x, y, z, τ ) = 0; C : Fτ' = Fx' · ddτx + Fy' · ⎩ τ = const.

dy dτ

+ Fz' ·

dz dτ

= 0;

(4)

The condition (4) may be regarded as the scalar product of a two vectors, the normal to the Σ surface, drawn from the M point: ] [ → Σ = Fx' , Fy' , Fz' , N

(5)

and the velocity vector of the M point, in the absolute motion of the Σ surface: [ v→ =

] d x dy dz , , . dτ dτ dτ

(6)

In this way, we get the Gohman theorem according to which: “from the kinematic point of view, a point onto the Σ surface belongs to the characteristic curve only if, in this point, the normal to the Σ surface is perpendicular to the velocity vector, in the absolute movement of the surface”. Regarding (5) and (6), the equation system (4) can be written as: ⎧ ⎨ F(x, y, z, τ ) = 0; → · v→ = 0; C: N ⎩ Σ τ = const.

1.2.2

(7)

The Generated Surface’s Family Depends by Two Parameters

The case is characteristic for a surface obtained by moving a generatrix curve following a trajectory established by the directrix curve. In this way, the surface’s family depends by two independent parameters and has the form: F(x, y, α, β) = 0.

(8)

In Eq. (8), the two independent parameters from which the surface’s family depends are α and β. Similarly with the previous case, the enveloping of the surface’s family described by (8) is given by the equation system:

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⎧ ⎪ ⎨ F(x, y, α, β) = 0; dx + Fα' y · P : Fα' = Fα' x · dα ⎪ ⎩ F' = F' · dx + F' · β βx dβ βy

dy dα dy dβ

dz + Fα' z · dα = 0; dz ' + Fβz · dβ = 0.

(9)

If we made the analogy with the Eqs. (5) and (6), the system (9) can be brought to the form: ⎧ ⎨ F(x, y, α, β) = 0; → · v→ = 0; P: N (10) ⎩ →Σ α N Σ · v→ β = 0. In Eq. (10), v→ α and v→ β represent the absolute velocity in the movements determined by the parameters α and β. In these two movements, onto the Σ surface are determined two characteristic curves and their intersection point is called characteristic point. In the characteristic point, the normal to the Σ surface is common with the normal to the surface’s family envelope.

1.2.3

Case of Composed Movement

If in one of the ( two ) previously presented motions the Σ surface is self-generated, for example Σβ ≡ Σ, then exists the relation: → Σ · v→ β = 0. N

(11)

In this case, the surface’s characteristic curve can be determined from the equation system: ⎧ ⎨ F(x, y, α, β) = 0; → · v→ = 0; C: N ⎩ Σ α α = const.

(12)

The relation (12) represents, in principle, a dependency as β = β(α). This particular situation can be stated as: “The characteristic curve of the Σ surface does not depend by the component of movement in which the surface is self-generated”.

1.3 Modelling of Enwrapping Process The case of generation by enwrapping presents practical interest because the absolute movements of the two surfaces are rotations around two axes joined with these surfaces. In practice are known the surface to be generated, Σ, and the absolute

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movements by which it is generated following the determination of the generating surface. Regarding the absolute movements by which the surface Σ is generated, the contact between the two surfaces can be done along a curve or at a single point. So, if the relative motion between the two surfaces can be described by a single parameter, the contact along a curve, meaning that the Σ and S surfaces are tangents along this curve named characteristic curve. Each of the surfaces represents the enveloping of the family generated in the relative motion of another one, and they are called conjugated surfaces. If the relative motion of the surfaces is described by two parameters, the contact between them is at a single point. In this chapter, the case of reciprocally enwrapping surfaces with contact along a curve will be analysed. This case is characterized by the fact that the enwrapping surfaces are joined with axodes which have rotational movements around axes, see Fig. 2. The ratio: i=

ϕ2 , ϕ1

(13)

is called transmission ratio. For the study of the two conjugated surfaces, it is used three reference systems: xyz is defined a global reference system; XYZ—mobile reference system, joined with the surface to be generated Σ; and ξ ηζ —mobile reference system, joined with generating surface S. → 1 the unitary vector of the rotational axis regarding In Fig. 2 was denoted with n → 2 the unitary vector of rotational axis regarding the XYZ reference system and with n the ξ ηζ reference system. Furthermore, were used the notations: a→ for the position vector of the origin of mobile reference system XYZ in the global reference system Fig. 2 Conjugated surfaces with contact along a curve

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(point O1 ), b→ for the position vector of the origin of the mobile reference system ξ ηζ in the global reference system (the point O2 ) and →c1 and →c2 normal drawn from the origin of the fixed reference system (point O) to the rotation axes I and, respectively, II. → →c1 and →c2 (the projections of these The matrix expressions of the vectors a→ , b, vectors onto the axes of global reference system) are: ⎛

⎛ ⎞ ⎛ ⎞ ⎞ ⎛ ⎞ a1 c11 c21 b1 a→ = ⎝ a2 ⎠, →b = ⎝ b2 ⎠,→c1 = ⎝ c12 ⎠, →c2 = ⎝ c22 ⎠. a3 b3 c13 c23

(14)

If it is denoted with α the orthogonal transformation matrix between the unitary vectors of the axes of mobile reference system XYZ and the unitary vectors of the global reference system xyz and with β the orthogonal transformation matrix between the unitary vectors of the axes of mobile reference system ξ ηζ and the unitary vectors of the global reference system, we can define the coordinates transformation: X = α · (x − a),

(15)

ξ = β · (x − b),

(16)

X, ξ and x being the matrix obtained with coordinates of the current point in the corresponding reference systems: ⎛

⎞ ⎛ ⎞ ⎛ ⎞ X ξ x X = ⎝ Y ⎠, ξ = ⎝ η ⎠, x = ⎝ y ⎠. Z ζ z

(17)

The absolute movement of the Σ surface joined with the XYZ system moving can be described by the transformation: X = ω n1 (ϕ1 ) · α · (x − c1 ) + α · (c1 − a),

(18)

→ 1 unitary ω n1 (ϕ1 ) being the notation for the rotation matrix around the axis with n vector, rotation with the angle ϕ 1 . Similarly, the absolute movement of the S surface can be defined, joined with the reference system ξ ηζ: ξ = ω n2 (ϕ2 ) · β · (x − c2 ) + β · (c2 − b),

(19)

the significance of the ω n2 (ϕ2 ) matrix being like this of the ω n1 (ϕ1 ) matrix. From Eqs. (18) and (19), the relative motions between the mobile reference system can be deduced. These movements represent the movement of the Σ surface regarding the S surface:

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} { ξ = ω n2 (ϕ2 ) · β · α −1 · ω−1 n1 (ϕ1 ) · [X − α · (c1 − a)] + c1 − c2 + β · (c2 − b),

(20)

and the reverse of this movement, the movement of the S regarding Σ: ] } { [ X = ω n1 (ϕ1 ) · α · β −1 · ω−1 n2 (ϕ2 ) · ξ − β · (c2 − b) + c2 − c1 + α · (c1 − a).

(21)

−1 In Eqs. (20) and (21) was denoted with α −1 , β −1 , ω−1 n1 and ω n2 the inverse of the matrix α, β, ω and ω. The Eq. (20) represents the equation of the family generated by the Σ surface in its relative motion regarding the S surface. Admitting that the parametrical equations of the Σ surface have the following form: | | X = X (u); | | (22) Σ : | Y = Y (u); | | Z = Z (u),

with u variable parameter, the surface’s family will have, in principle, the form:

(Σ)ϕ1

| | ξ = ξ (u, ϕ1 ); | | : | η = η(u, ϕ1 ); | | ζ = ζ (u, ϕ1 ).

(23)

In Eq. (23), u and ϕ 1 are independent parameters. Determining the enveloping of surface family assumes finding of the enwrapping condition which, in principle, represents a link between the two independent parameters. According to the Gohman theorem [3], the enwrapping condition can be written as: → ϕ1 = 0. →Σ · R N

(24)

→ Σ represents the normal to the Σ surface, drawn in the current In the Eq. (24), N → point, and Rϕ1 represents the direction of the tangent to the trajectory of this current point, in its relative motion regarding the ξ ηζ reference system. By identification of the enwrapping condition, the equations of the S surface can be written. In this case, the equations will have form:

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| | ξ = ξ (u, ϕ1 ); | | η = η(u, ϕ ); 1 | S:| | ζ = ζ (u, ϕ1 ); | | ϕ = ϕ (u). 1

(25)

1

The contact surface [3] can be defined as: “the geometrical place, in the global reference system, of contact points between the two conjugated surfaces, in the movement assembly of these”. The contact surface’s equations can be identified if the enwrapping condition is associated with the absolute movement of the Σ surface: x = α −1 · ω−1 n1 (ϕ1 ) · [X − α · (c1 − a)] + c1 .

(26)

2 The Virtual Pole Method for Tool’s Profiling Machining through generating for ordered curls of surfaces may be done using tools as: rack-gear, gear shaped cutter or rotary cutter. All these three types of tools generate by method of rolling, which make that their profiling can be regarded as an inplane enwrapping issue. In specialized literature for solving this type of issues, are presented various methods as: method of “minimum distance”; method of “in-plane generating trajectories”; method of “substitutive circles family”; the Willis method also known as “theorem of normal”; etc. Each of these methods is based on determining the enwrapping condition using one of the properties of curves in reciprocally enwrapping as they were defined in the previous section. Regardless of the used method, the profiling algorithms presented in literature assume to follow the stages: writing the equations for the profile to be generated; writing equations for the absolute movements of piece and tool; determining the relative motions between piece and tool, based on the previous determined absolute movements; finding the curve’s family generated in this relative motion; and identifying the enwrapping condition, which allows selecting the points belonging to the enveloping curve, from the multitude of points belonging to the family. Generally, beside the conjugated curve identifying (curve which is the profile of the generating tool) interests the finding of the contact curve between the two enwrapping profiles. Definition: The contact curve represents the geometrical place, in a fixed reference system, of the tangency points, established in the movement assembly of two reciprocally enwrapping curves [4].

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2.1 Method’s Theoretical Fundaments The method of “virtual pole” represents a reinterpretation for the method of normal and uses the propriety of reciprocally enwrapping curves to admit, in the contact point, a common normal which passes through the gearing pole. According to the proposed method, corresponding to each point onto the profile to be generated is identified one “virtual pole”, defined as intersection point between the normal to profile, drawn in the current point, and the centrode associated with this profile, see Fig. 3. In certain conditions, the virtual pole may become gearing pole. Considering this observation, the enwrapping condition can be found identifying the conditions under which the virtual pole becomes actual gearing pole. These conditions can be identified founding the position vector of the virtual pole (the point Pv in Fig. 3), which allows establishing the movement which brings the virtual pole in the gearing pole. Once established this condition, and applied to the generated profile, it is obtained the position when the current point onto this profile is in contact with the generating tool. If the two conjugated profiles are in contact, their tangency point belongs to the contact curve too, according to definition. Therefore, applying the absolute motion necessary for the virtual pole to overlap the gear pole, the current point on the generated profile is brought onto the contact curve. Being known also the absolute motion of the generating profile means that the coordinates of the contact point belonging to this profile can be identified too. This approach for the in-plane issue allows elusion necessity to write the relative motions between the generate and generating profiles, as so as the equations of the profile’s Fig. 3 Principle of “virtual pole” method

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family generated in these relative motions. In this way, is avoided a major source of errors and the calculus effort is reduced significantly. In Fig. 3, are represented the C 1 and C 2 centrodes, associated with the two profiles, Σ, profile to be generated and S, generating profile. The absolute motions of the two centrodes and consequently of their associated profiles are given by the rotations ϕ 1 and ϕ 2 , carried around the points O1 and, respectively, O2 . The virtual pole is represented by the point Pv , in its initial position and, respectively, P’v in rotate position, when it is overlapped to the gearing pole (point P in Fig. 3). The vector r→ represents the position vector of the current point M, and the vector N→Σ is the normal to the generated profile, drawn through the current point. The position vector of the virtual pole was denoted in Fig. 3 with r→Pv . In Fig. 3, the positions of elements after the motions carried on to bring the virtual pole in the gearing pole were represented with dash line and the notations of these elements were indicated with symbol ' (prime).

2.2 Advantage of Virtual Pole Method The comparison between the “virtual pole” method and a classical method (in this case the Willis theorem) is presented in Table 1. The comparison is made for profiling the rack-gear designed to generate a shaft-type piece, with squared section, see Fig. 4. In Table 1, were used the following notations: – – – – –

–

– – – – – – – – –

Σ—profile to be generated (piece); a—half side of the squared section; u—variable parameter which describes the piece’s profile; ϕ—rotation angle of the reference system joined with the profile to be generated; ϕ u —particular value of the ϕ rotation angle, for which, in the absolute motion of the piece, the virtual pole becomes the gearing pole. The value depends by the considered point onto the profile; M—current point onto the piece’s profile (profile to be generated) which by intersecting with the centrode associated with piece (the circle with Rrp radius) defines the gearing pole, P; X(u), Y(u)—parametrial equations of the profile, which for a certain value of u give the coordinates of current point, M; ξ , η—axes of mobile reference system joined with the tool’s profile; x, y—axes of the global (fixed) reference system; X,Y —axes of the mobile reference system, joined with the piece’s profile; Rrp —rolling radius of piece; ω3 (ϕ)—rotation matrix; ω3T (ϕ)—transposed of the rotation matrix; A—translation matrix obtained with the coordinates of the mobile reference system’s origin, in the global reference system; ˙ λ —derivative of the translation matrix; A

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Table 1 Comparison between the “virtual pole” method and a classical method Crt. Method of “virtual pole” No. 1

Profile to be generate Σ [3] | | X (u) = −a; | Σ:| | Y (u) = u.

2

Absolute movements of tool and piece [3]

Method of normals (Willis’ theorem) [3]

– for piece: ξ = x + A. – for tool: x = ω3T (ϕ) · X. 3

Relative motions between tool and piece –

– for piece regarding the tool [3]: ξ = ω3T (ϕ) · X − A; | | ξ = X (u) · cos ϕ − Y (u) · sin ϕ + R ; rp | | | η = X (u) · sin ϕ + Y (u) · cos ϕ + Rr p · ϕ.

4

–

– for tool regarding the piece [3]: [ ] X = ω3 (ϕ) · ξ − A .

Enwrapping condition [3] →r Pv = X (u) · →i + Y (u) · →j . ( ) → Σ = λ · Y˙u · →i − X˙ u · →j . N

− → N Σ : [X − X (u)] · X˙ u + [Y − Y (u)] · Y˙u = 0

| → Σ = X (u) · →i → Pv = →r Pv + N | X = −R · cos ϕ; N rp ( ) P : || | Y = Rr p · sin ϕ. → → → + Y (u) · j + +λ · Y˙u · i − X˙ u · j | | X = −R · cos ϕ; rp | C 1 :| | Y = Rr p · sin ϕ. → Σ ∩ C1 = PV N ϕu = arcsin

5

(

u Rr p

)

.

→Σ P∈N [ ] −Rr p · cos ϕ − X (u) · X˙ u [ ] + Rr p · sin ϕ − Y (u) · Y˙u = 0 ( ) ϕ = arcsin Rur p .

Coordinates of the current point, M – in the global reference system (onto the contact curve) [3]: | | x = −a · cos ϕ − u · sin ϕ ; u u | M M x y :| | y M = −a · sin ϕu + u · cos ϕu . (continued)

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Table 1 (continued) Crt. Method of “virtual pole” No.

Method of normals (Willis’ theorem) [3]

– in the tool’s reference system (rack-gear tool’s profile) [3]: | |ξ = x + R ; M rp | M Mξ η :| | η M = y M + Rr p · ϕu . 6

Tool’s profile, C S [3] | | | | | (CΣ ) || ξ = −a · cos ϕu − u · sin ϕu + Rr p ; ϕ | | η = −a · sin ϕu + u · cos ϕu + Rr p · ϕ. | Cs :| ( ) | | ϕ = arcsin u . | u Rr p

Fig. 4 Rack-gear for generating a shaft with squared section [11]

– – – –

−→ N Σ —normal vector to the Σ profile; − → Rϕ —velocity vector; r—position vector of the current point; −→ λ—scalar parameter representing the modulus of the normal vector, N Σ .

2.3 Tools Profiling, Using the Virtual Pole Method Next, will be presented the particular cases for profiling rack-gear, gear shaped cutter and rotary cutter.

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2.3.1

231

Profiling of the Rack-Gear Tool

The generation of surfaces by rolling, using rack-type tools, is a particular case for the application of the Willis theorem. According to this theorem: “profiles that transmit rotational motion between two parallel axes admit, at the point of contact, a common normal that passes through the gear pole” [3]. When using the rack tool, only one of the profiles has a rotational movement, respectively, the profile to be generated. The other, the generating profile, has a translational motion. However, the Willis theorem remains valid if we consider that the translational motion can be seen as a particular case of rotation, in which the centre of rotation is located at infinite distance. So, in the case of generation with the rack tool, it can be considered that the rolling radius of the tool is infinite, which causes its centroid to transform from a circle to a straight line. Usually, two mobile reference systems are used for profiling the rolling generating tools, one joined with the generated profile, Σ, the other joined with the generating profile, S, and a fixed reference system. The three reference systems, as well as the centroids associated with the studied profiles, are shown in Fig. 5. In this figure, the elements related to the piece were represented in red, those related to the tool in blue and those related to the fixed system in green. In connection with Fig. 5 are defined: the fixed reference system, xOy, whose origin coincides with the centre of the centroid of the generated profile, C 1 , which is a circle of radius Rrp ; the mobile reference system, XOY, having the same origin as the fixed system and which rotates with the generated profile, being joined with it; the angular parameter of rotation of the generated profile, ϕ; the mobile reference system joined with the generating profile, ξ O1 η, having, at the initial moment, the ξ axis overlapped on the x and X axes and the η axis being overlapped on the centrode of the generating profile, C 2 , which is a line; and the translation parameter of the generating profile, δ. In Fig. 5, the positions of the elements and of the axes after the execution of the movement that brings the virtual pole overlapped with the gear pole were represented with a dashed line. In figure was marked also the gearing pole, P, representing the tangency point between the two centrodes and the virtual pole, Pv , defined as intersection point → Σ , drawn through the current point between the normal to the generated profile, N M and the centrode associated with this profile, the circle C 1 . The position of the current point is given by the position vector →r . Admitting as known, in its own reference system, the parametrical equations of the generated profile, Σ, in form: | | X = X (u) : | Σ:| | Y = Y (u),

(27)

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Fig. 5 Reference systems. Conjugated centrodes

with u variable scalar parameter, it is possible to determine the position vector of the current point M, for a certain value of u: →r = X (u) · →i + Y (u) · →j .

(28)

The normal to the generated profile, drawn through the current point, will have →Σ: the direction given by the unitary vector n → Σ = Y˙u · →i − X˙ u · →j . n

(29)

In Eq. (29), X˙ u and Y˙u represent the partial derivatives of the X(u) and Y(u) functions relative to variable u. Denoting with λ the modulus of the normal vector, the expression of this becomes: ( ) → Σ = λ · Y˙u · →i − X˙ u · →j . N

(30)

→ Σ vector is in the current point and its We have to notice that the origin of the N end belongs to the C 1 centrode, but the modulus of this vector is not yet known.

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→ Σ , it is possible to determine the virtual pole position Summing the vectors →r and N vector expression: ] [ → Σ = X (u) + λ · Y˙u · →i →r Pv = →r + N ] [ + Y (u) − λ · X˙ u · →j .

(31)

Regarding the parametrical equations of the C 1 centrode: | | X = −R · cos ϕ; rp | C1 | | Y = Rr p · sin ϕ,

(32)

where ϕ represents the angular parameter which describes this circle, and putting the condition that the end of the →r Pv vector to belong to this centrode, it is obtained: ⎧

X = −Rr p · cos ϕ = X (u) + λ · Y˙u : Y = Rr p · sin ϕ = Y (u) − λ · X˙ u .

(33)

Now, it is possible to determine the modulus of the →r Pv vector, eliminating from the Eq. (33) the scalar parameter λ. We will obtain: λ=

−Rr p · cos ϕ − X (u) Rr p · sin ϕ − Y (u) = , − X˙ u Y˙u

(34)

or: [

] [ ] Rr p · cos ϕ + X (u) · X˙ u − Rr p · sin ϕ + Y (u) · Y˙u = 0.

(35)

The relation (35) represents a dependency between the u and ϕ parameters, meaning the enwrapping condition. In order to take advantage of the “virtual pole” method, it is necessary that for the known value of the u parameter, corresponding to a certain position of the M point onto the Σ curve, to determine the ϕ u value which satisfies the Eq. (35). Being known the position of the M current point, as a pair of coordinates X M , Y M and the value of the angular parameter which brings the virtual pole onto the gearing pole, can be determined the position of the current point in the global reference system at the moment of contact between this point and the generating profile. For this, we must keep in mind the rolling condition, meaning the condition that the C 1 and C 2 centrodes roll one to another without slipping: δ = Rr p · ϕ.

(36)

If, in relation (36), the ϕ angular parameter takes the particular value ϕ u , giving to the current point the absolute movements of the generated profile:

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x = ω3T (ϕ) · X,

(37)

the coordinates x M and yM can be determined. Now, the current point is in contact with the generating profile. Developing the relation (37) where the matrices x and X are matrix given by the coordinates of the M point in the corresponding reference systems, xOy and, respectively, XOY, and ω3T (ϕ) represents the matrix of orthogonal transformation between the unitary vectors of the above-mentioned reference systems, we will obtain: ( ) ( ) ( ) x XM cos ϕu − sin ϕu · , = sin ϕu cos ϕu YM y

(38)

resulting: | | x = X · cos ϕ − Y · sin ϕ ; M u M u | M | | y M = X M · sin ϕu + Y M · cos ϕu .

(39)

We have to mention that, in this position, the M point is also onto the contact curve. Keeping in mind the rolling condition, it is obtained the value of the δ parameter for which the generated profile is in tangency with the generating profile, in the M point, see Fig. 5: δu = Rr p · ϕu ,

(40)

which, also regarding the absolute motion of the generating tool: x = ξ + A,

(41)

allows identifying the coordinates of contact point between the two profiles, in the reference system of the rack-gear, ξ O1 η. In the relation (41), the meaning of the x matrix is identical to that from the (37) relation, the matrix ξ is given by the coordinates of the current point in the reference system joined with the rack-gear, ξ O1 η, and the matrix A is given by the coordinates of the tool reference system’s origin in the global reference system. Thus, developing the relation (41) it will be obtained: ( ) ( ) ( ) x ξ −Rr p , = + −δ y η

(42)

which allows finding the coordinates of the contact point between the two conjugated profiles in the reference system of the rack-gear tool, in form, sub forma:

CAD-Based Application in VBA for Tool’s Profiling

(

ξM ηM

)

( =

xM yM

)

235

( −

) −Rr p , −δu

(43)

namely: | |ξ = x + R ; M rp | M | | η M = y M + δu .

2.3.2

(44)

Profiling of the Gear Shaped Tool

Mainly, the gear shaped tools are intended to generate internal surfaces as: internal teeth; profiled holes, as K-type holes; polygonal bushes; etc. It is also not uncommon to use this type of tool to generate exterior surfaces. The use examples are similar to those presented above. Generation with gear shaped tools is characterized by the fact that the axes of the two axodes are parallel and at a finite distance from each other. This makes the absolute motions associated with both centrodes rotational motions. Unlike the previous case, this time is needed to use four reference systems, as are presented in Fig. 6: two fixed reference systems, xOy and x 1 O1 y1, and two mobile systems XOY and, respectively, ξ O1 η. As we mentioned before, the gear shaped-type tool can generate both external and internal surfaces, these cases being presented in Fig. 6.a and 6.b.

Fig. 6 Reference systems at generating with gear shaped tool. Conjugated centrodes

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The xOy reference system is selected in this way that its origin coincides with the centre of the C 1 centrode, the circle with radius Rrp . The XOY reference system, mobile, is joined with the piece and has, at the initial moment, the axes overlapped with the axes of xOy system. As we mentioned before, the piece has rotational movement, so the XOY will rotate with this. The generated profile is defined in this system. The rotation of the XOY system and, simultaneous, of piece, is described by the angular parameter ϕ 1. The x 1 O1 y1 reference system is fixed, chosen so its origin to coincide with the C 2 centrode, meaning the centrode joined with the generating profile. This centrode is also a circle, this radius being Rrt in Fig. 6. The A12 distance between the origins of the two reference systems depends by the values of the rolling radii by formula: A12 = Rr p ± Rr t ,

(45)

the sign “ + ” corresponding to the external surface’s generation and “-” corresponding to internal surfaces. The fourth reference system is the mobile system ξ O1 η where the generating profile is defined. It is chosen that its origin coincides with those of x 1 O1 y1 system and, initially, has axes overlapped to this system. Being joined with the generating profile, the system ξ O1 η rotating with this profile the angular parameter being ϕ 2 . The generated profile, Σ, is defined in system XOY by equations as (27). For a certain value of the u parameter, it is obtained a current point onto the Σ profile and the position vector of this point is given by the Eq. (28). When u go through all its definition domain, the point defined by this parameter becomes current point, describing the whole generated profile. The normal to the Σ profile is described by Eq. (30). → Σ it is obtained the position As in the previous case, summing the vectors →r and N vector of the virtual pole, →r Pv , with expression given by (31). From the condition that the end of the vector →r Pv belonging to the centrode joined with piece, it can be deduced the enwrapping condition according to the Eq. (35). Starting from the known position of the M current point, with the pair of coordinates X M , Y M and the value of angular parameter ϕ 1 which brings the virtual pole in the gearing pole, can be determined the position of point M, in the global reference system. For this, we have to keep in mind the rolling condition, meaning the condition that the C 1 and C 2 centrodes roll one to another without slipping: Rr p · ϕ1 = Rr t · ϕ2 ⇒ ϕ2 =

Rr p · ϕ1 . Rr t

(46)

/ Usually, it is used the notation Rr p Rr t = i, which bring the Eq. (46) at form: ϕ2 = i · ϕ1 .

(47)

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The ratio i is named “gearing ratio” or “transmission ratio”. If, in relation (36), the angular parameter ϕ 1 takes the particular value ϕ 1u , giving to the current point the absolute movement performed by the generated profile: x = ω3T (ϕ1 ) · X,

(48)

the coordinates x M and yM can be determined. At these coordinates, the current point is in contact with the generating profile. Developing the relation (48) where the matrices x and X are given by the coordinates of M point in the corresponding reference systems, xOy and, respectively, XOY, and ω3T (ϕ1 ) represents the orthogonal transformation matrix between the unitary vectors of the above-mentioned systems, it is obtained: ( ) ( ) ( ) x XM cos ϕ1u − sin ϕ1u · , (49) = sin ϕ1u cos ϕ1u YM y resulting: | | x = X · cos ϕ − Y · sin ϕ ; M 1u M 1u | M | | y M = X M · sin ϕ1u + Y M · cos ϕ1u .

(50)

We have to mention that, for various positions of the M point, the Eq. (50) represents the contact curve. Regarding the rolling condition, it is obtained the value of the ϕ 2 parameter, for which the generated profile is in tangency with the generating profile, in point M: ϕ2u = i · ϕ1u ,

(51)

which, considering the coordinates transformation between the x1 and x fixed reference systems: ( x 1 = x + A; A =

−A12 0

) (52)

and the absolute movement of the generating tool: x 1 = ω3T (∓ϕ2 ) · ξ ,

(53)

allows identifying the coordinates of the contact point between the two profiles, in the tool’s reference system, ξ O1 η. In relation (52), the meaning of the value A12 is given by the relation (45), the matrix ξ is given by the coordinates of the current point in the reference system joined with the tool, ξ O1 η, and the matrix A is given by the coordinates of the origin of the generating profile’s system in the fixed reference system x 1 O1 y1 . Hence, developing

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the relation (53) it is obtained: (

x1 y1

)

( =

cos(∓ϕ2 ) − sin(∓ϕ2 ) sin(∓ϕ2 ) cos(∓ϕ2 )

) ( ) ξ · , η

(54)

which allows finding the coordinates of contact point between the two conjugated profiles, in the reference system of the gear shaped tool, in form: (

ξM ηM

)

( =

cos ϕ2 ± sin ϕ2 ∓ sin ϕ2 cos ϕ2

)(

) ( ) ( ) ( ) x1M x1M xM −A12 ; = + , y1M y1M yM 0

(55)

meaning: | | ξ = x · cos ϕ ± y · sin ϕ ; 1M 2 1M 2 | M | | η M = ∓x1M · sin ϕ2 + y1M · cos ϕ2 .

(56)

As before, in Eq. (56) the sign “+” corresponds to external surfaces and the sign “−” to internal surfaces.

2.3.3

Profiling of Rotary Cutter Tool

Usage of the rotary cutter for generation by rolling of profiles can be regarded as being the inverse of generation with rack-gear tool. In this case, the tool has rotation movement, and the generated profile has translation movement. Mostly, the generated surface is a helical surface, and the translation of the generated profile is obtained from a helical movement around an axis parallel with the piece’s centrode. Usually, for profiling tools which generate by rolling are used two mobile reference systems, one joined with the generated profile, Σ, the other one joined with the generating profile, S, and a fixed reference system. The three reference systems as so as the centrodes joined with the studied profiles are presented in Fig. 7. In this figure, the elements linked with the tool were represented in red, those linked with piece in blue and those linked with fixed reference system in green. In connection with Fig. 7 are defined: fixed reference system, xOy, whose origin coincides with the centre of the generating profile’s centrode, C 2 , which is a circle with radius Rrt ; mobile reference system, XOY, where is defined the generated profile. The X axis of this system is initially overlapped to the x axis of the fixed reference system, and the Y axis coincides, throughout the entire movement with the centrode of the generated profile, the line C 1 , the translating parameter being δ.

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Fig. 7 Reference systems at generation with rotary cutter. Conjugated centrodes

A third reference system, ξ O1 η, is mobile joined with the generating profile and has, at initial moment, the axes overlapped to the fixed system. The movement parameter of this system is the angular parameter ϕ. As in previous cases, in figure were represented the gearing pole, point P, the → Σ , drawn through the current virtual pole, Pv , the normal to the generated profile, N point M, and the centrode joined with this profile, the line C 1 . The position of the current point is given by the position vector →r . Considered as known, in its own reference system, the parametrical equations of the profile to be generated, Σ has the form (27), with u variable scalar parameter, it is possible to determine the position of the current point M for a certain value of u. → Σ , whose mathematical expressions are given by Summing the vectors →r and N Eqs. (28) and (30) it is possible to determine the expression for the position vector of virtual pole: Considering the parametrical equations of C 1 centrode: | | X = δ; | C1 | | Y = 0,

(57)

where δ represents the linear parameter which describes the line, and putting the condition that the end of →r Pv vector belongs to this centrode, it is obtained:

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⎧

X = δ = X (u) + λ · Y˙u : Y = 0 = Y (u) − λ · X˙ u .

(58)

Now, it is possible determining the modulus of the →r Pv vector, eliminating from Eq. (58) the scalar parameter λ. We obtain: λ=

δ − X (u) Y (u) = , ˙ Yu X˙ u

(59)

or, keeping in mind the rolling condition: δ = Rr t · ϕ,

(60)

[Rr t · ϕ − X (u)] · X˙ u − Y (u) · Y˙u = 0.

(61)

The relation (61) represents a dependency between the parameters u and ϕ, meaning the enwrapping condition. Being known the position of the current point M[X M , Y M ] and the value of δ parameter which brings the virtual pole in the gearing pole, the position of the current point can be determined, in the fixed reference system, at the moment of contact between this point and the generating profile. For this, the rolling condition (60) must be taken into account, meaning the condition that the centrodes C 1 and C 2 roll one to another without slipping. If, in relation (60), the linear parameter δ takes the particular value δ u , giving to the current point the absolute movement performed by generated profile: x = X + A,

(62)

can be determined the coordinates x M and yM where the current point is in contact with the generating profile. Developing the relation (62) where the matrices x and X are given by the coordinates of the M point in the corresponding reference systems, xOy and, respectively, XOY, and A is given by the coordinates of the piece’s reference system’s origin in the fixed system: ( ) ( ) ( ) x −δ XM + , = YM y −Rr t

(63)

results: | | x = X − δ; M | M | | y M = Y M − Rr t .

(64)

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Taking into account the driving condition, it is obtained the value of the ϕ parameter, for which the generated profile is in tangency with the generating profile in the point M, see also Fig. 7: ϕu =

δu , Rr t

(65)

which, given also the absolute movement of the generating tool: x = ω3T (ϕ) · ξ ,

(66)

allows identifying the coordinates of the contact point between the two profiles, in the rack-gear’s system, ξ O1 η. In relation (66), the meaning of the x matrix is identical to those from relation (62), the matrix ξ is given by the coordinates of the current point in the reference system associated with the rack-gear, ξ O1 η, and the matrix ω3T (ϕ) represents the orthogonal transformation matrix between the unitary vectors of the reference systems x and ξ. Thus, developing the relation (66) it is obtained: ( ) ( ) ( ) x cos ϕ − sin ϕ ξ = · , y sin ϕ cos ϕ η

(67)

which allows finding the coordinates of the contact point between the two conjugated profiles, in the reference system of the rack-gear, in form: (

ξM ηM

)

( =

cos ϕu sin ϕu − sin ϕu cos ϕu

) ( ) xM · , yM

(68)

namely: | | ξ = x · cos ϕ + y · sin ϕ ; M u M u | M | | η M = −x M · sin ϕu + y M · cos ϕu .

(69)

2.4 Tools Profiling with CATIA™ VBA Programming. In the language Visual Basic for Applications (VBA), several modules have been developed to profile the types of tools mentioned above. The application was implemented in the CATIA™ program being structured in three stages: – input data; – calculation of the generating profile, depending on the profile to be obtained and the type of tool;

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– optionally, export the coordinates of the points calculated for the contact curve and for the generator profile, respectively. To simplify the use of the application, its commands have been entered in a toolbar called “Profiling”. The appearance of the toolbar is shown in Fig. 8 The data entry step is common to the three types of tools and consists of a form that allows you to choose the type of tool you want, set the generation parameters and the name of the working file. The form is shown in Fig. 9. After choosing the respective elements, the characteristic elements used for the generation are created: the reference systems, the origins of the reference systems (points O and O1 ), the centrodes of the part and, respectively, the tool and the gear pole (point P). The design tree after the creation of the respective elements is shown in Fig. 10. Part of the feature generation script is shown below. The real type variables are defined, which will be used further: Dim Dim Dim Dim Dim

A12 As Double Rrs As Double Rrp As Double semn As Integer reference As Reference

For the gear shaped tool, depending on the type of generation, external or internal, choose the sign needed to calculate the distance between the centres of the centroids, the size A12 . If cbTipGenerare Then sign = -1 Else sign = 1 End If Rrs = CDbl(tbRrs.Text) Rrp = CDbl(tbRrp.Text) A12 = Rrp + sign * Rrs

The origins of the reference systems are generated, positioned according to the selected tool type: ’Generation of origin points Dim origineFix As HybridShapePointCoord Set origineFix = elemente.AddNewPointCoord(0, 0, 0)

Fig. 8 Profiling toolbar

CAD-Based Application in VBA for Tool’s Profiling

Fig. 9 Input data form Fig. 10 Design tree after element creation

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origineFix.Name = origineFix.Name & ".O" corp.InsertHybridShape origineFix Dim origineMobil As HybridShapePointCoord If obCutitRotativ Then Set origineMobil=elemente.AddNewPointCoord(-Rrs,0,0) Else Set origineMobil=elemente.AddNewPointCoord(-A12,0,0) End If origineMobil.Name = origineMobil.Name & ".O1" corp.InsertHybridShape origineMobil

The reference systems are generated: ’Generating of reference systems Dim sistemeAxe As AxisSystems Set sistemeAxe = reper.AxisSystems Dim sistemFix, sistemPiesa, sistemScula As AxisSystem Set sistemFix = sistemeAxe.Add() sistemFix.OriginType = catAxisSystemOriginByPoint Dim formaPunct As HybridShapePointCoord Set formaPunct = forme.Item("Point.O") Set reference=reper.CreateReferenceFromObject(formaPunct) sistemFix.OriginPoint = reference sistemFix.Name = "Axis System.fix" sistemFix.IsCurrent = True Set sistemPiesa = sistemeAxe.Add() sistemPiesa.OriginType = catAxisSystemOriginByPoint If obCutitRotativ Then Set formaPunct = forme.Item("Point.O1") Else Set formaPunct = forme.Item("Point.O") End If Set reference=reper.CreateReferenceFromObject(formaPunct) sistemPiesa.OriginPoint = reference sistemPiesa.Name = "Axis System.piesa" Set sistemScula = sistemeAxe.Add() sistemScula.OriginType = catAxisSystemOriginByPoint If obCutitRotativ Then Set formaPunct = forme.Item("Point.O") Else Set formaPunct = forme.Item("Point.O1") End If Set reference=eper.CreateReferenceFromObject(formaPunct) sistemScula.OriginPoint = reference sistemScula.Name = "Axis System.scula"

It is generated the point representing the gearing pole: ’Generating of gearing pole Dim polAngrenare As HybridShapePointCoord If obCutitRotativ Then Set polAngrenare=elemente.AddNewPointCoord(-Rrs,0,0)

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Else Set polAngrenare=elemente.AddNewPointCoord(-Rrp,0,0) End If polAngrenare.Name = polAngrenare.Name & ".P" corp.InsertHybridShape polAngrenare

Depending on the type of tool chosen, the centrode is drawn. For the rack tool, the tool’s centrode is a line, and the workpiece centrode is a circle; for the gear shaped tool, both centrodes are circles; and for the rotary cutter tool, the tool’s centrode is a circle and the piece’s centrode is a line. The name of the respective elements in the CATIA™ file has been changed, keeping in name the type of the element (“line” or “circle”) and changing the code, respectively, C1 for the workpiece centroid and C2 for the tool centroid. Below is the script portion for drawing the piece, drawing the tool in a similar way. ’Centrodes drawing Dim reference1 As Reference Dim linii As HybridShapeFactory Set linii = reper.HybridShapeFactory Dim directie As HybridShapeDirection Set directie = linii.AddNewDirectionByCoord(0#, 1#, 0#) Dim cercuri As HybridShapeFactory Set cercuri = reper.HybridShapeFactory Dim plane As OriginElements Set plane = reper.OriginElements Dim planReferinta As HybridShapePlaneExplicit Set planReferinta = plane.PlaneXY Dim referinta2 As Reference Set reference2=reper.CreateReferenceFromObject(planReferinta) Dim startCentroida, endCentroida As Double Dim centroidaLinie As HybridShapeLinePtDir Dim centroidaCerc As HybridShapeCircleCtrRad ’Generating of piece’s centode If obCutitRotativ Then Set formaPunct = forme.Item("Point.O1") Set reference1=reper.CreateReferenceFromObject(formaPunct) startCentroida = -Rrs endCentroida = Rrs Set centroidaLinie=linii.AddNewLinePtDirOnSupport(refere nce1, directie, reference2, startCentroida, endCentroida, False) corp.InsertHybridShape centroidaLinie reper.InWorkObject = centroidaLinie centroidaLinie.Name = "Line.C1" Else Set formaPunct = forme.Item("Point.O") Set reference1=reper.CreateReferenceFromObject(formaPunc t)

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Set centroidaCerc=cercuri.AddNewCircleCtrRad(reference1, reference2, True, Rrp) corp.InsertHybridShape centroidaCerc reper.InWorkObject = centroidaCerc centroidaCerc.Name = "Circle.C1" End If .........

Some lines have been added at the end of the script that allows to change the file path and select the option to save it. If the path to that file is incorrect, a procedure has been introduced to resolve this error so that the application does not crash (FileInexistent). Dim cale As String cale = tbCale.Text Dim numeComplet As String numeComplet = cale + "Profilare.CATPart" If cbSaveFile Then On Error GoTo FisierInexistent fisier.SaveAs (numeComplet) End If frmDateIntrare.Hide FisierInexistent: Err.Clear End Sub .......

The calculation for the chosen tool type can then be made. The user must have created the profile to be generated so that in the next step he can select it. The application recognizes line profiles, arc of a circle and spline curve. An excerpt from the profile selection script is shown below. ... Set selection = fisierPiesa.Selection selection.Clear ReDim strArray(2) strArray(0) = "Line" strArray(1) = "HybridShapeCircle" strArray(2) = "HybridShapeCurveExplicit" Dim sStatus As String sStatus = selectie.SelectElement2(strArray, "Select piece’a profile", True) frmNrPctDisc.Show vbModal ...

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Fig. 11 Form for choosing the number of points

Note: It is important to note that the profile to be generated must have been previously created as a wireframe element. Especially in the case of a spline curve, introduced in the idea of profiling for known curves in discrete form, it must have been isolated before its selection. Immediately after selecting the profile, a form opens that allows the choice of the number of points in which the discretization of the profile to be generated is made, i.e. the number of points in which the calculation is made. The appearance of this form is shown in Fig. 11. By default, the discretization value is 10 points, but that number can be changed at the user’s request. However, it should be noted that as the number of points increases, the time required to calculate the tool profile will increase. After choosing the discretization value, the calculation for the chosen value starts. An area of the tool profile calculation script is shown below. The variables inc and poz, of real type, have the role of establishing the increment with which the current point moves on the profile curve to be generated. The current point was obtained as a point on the curve, positioned at a certain percentage of the length of the curve. ... Dim inc, poz As Double Dim numarPunct As Integer inc = 1 / frmNrPctDisc.tbNrPcte.Value poz = 0 numarPunct = 1 ’ Profile calculus Do While poz 0 Then For i = 1 To iCount If selectie.Item(i).Type = "Point" Then nrPunct = nrPunct + 1 Set punct = selectie.Item(i) punct.Value.GetCoordinates (coordonate) oExcel.Cells(i + 1, 1) = coordonate(0) oExcel.Cells(i + 1, 2) = coordonate(1) oExcel.Cells(i + 1, 3) = coordonate(2) End If Next oK = True Else MsgBox "No selected points!" oK = False End If selectie.Clear oExcel.Cells(i + 1, 1) = "End" End Sub

By command “ModuleExportCoord”, a display box is open, asking the user to select some 3D points. This box is presented in Fig. 15. If user fails to select some points, it is warning by a message, presented in Fig. 16. After the correct selection of 3D points, their coordinates are copied in an Excel file and can be saved. The appearance of the window for exporting coordinates is presented in Fig. 17.

Fig. 15 Result of “ModuleExportCoord”

CAD-Based Application in VBA for Tool’s Profiling

Fig. 16 Warning display box

Fig. 17 Window for export coordinates

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3 Conclusions In this chapter, a new complementary method for profiling tools like rack-gear, gear shaped or rotary cutter was presented. This method is called the method of “virtual pole”. For the above-mentioned types of tools, was imagined the method’s applicating algorithm and were developed in-house calculus programs, which allows numerical determining of profile. The “virtual pole” is defined as the intersection point between the normal to the profile to be generated and the centrode associated with the piece. The method can be applied for profiling tools which generate by enwrapping, by method of rolling and is based on a re-interpretation of the Willis theorem. This assumes that, for accomplishing the Willis theorem, when a normal to the generated profile passes through the gearing pole, that normal belongs both to the generated and generating profile. This variant for enwrapping condition determination has the advantage to allow the need to write, in explicit form, the equations of the relative movement of the piece. At the same time, the enwrapping condition remains rigorous from the mathematical point of view. Consequently, in the method of “virtual pole”, three curves are simultaneous in contact. These are: the generated profile, the generating profile and the contact curve. By definition, the contact curve is the geometrical locus of the tangency points between the two mentioned profiles. The coordinates of contact point depend by the absolute movements performed by the tool and piece. In this way, we can determine, in succession, the points onto the tool’s profile, which will generate, known points onto the piece’s profile. Using the method of “virtual pole”, they are simplified the calculus needed for profiling the above-mentioned tool’s types, keeping in mind that the determining of the relative movements between tool and piece can be a source of major errors. We must highlight that, in the profiling process, by the new algorithm, the influence of the relative motions is not eliminated, but only the need to write these movements is avoided.

References 1. Litvin FL (1992) Theory of gearing. Reference Publication, NASA, p 1212 2. Oancea N (2004) Generarea suprafetelor prin infasurare. Teoreme fundamentale (Surface generation trough winding. Fundamental theorems). Dunarea de Jos, University Publishing House, Galati 3. Oancea N (2004) Generarea suprafetelor prin infasurare. Teoreme complementare (Surface generation trough winding. Complementary theorems). Dunarea de Jos, University Publishing House 4. Oancea N, Baicu I, Dima M, Teodor VG (2005) Generarea suprafetelor prin infasurare. Complemente de teoria infasurarii suprafetelor (Surface generation trough winding. Complements). Dunarea de Jos, University Publishing House 5. Gella-Marín R, Tzotzis A, García-Hernández C, et al (2021) CAD Software Integration with Programming Tools for Modelling. In: Measurement and Verification of Surfaces

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6. Teodor VG, Baroiu N, Susac F, Oancea N (2016) The rack-gear tool generation modelling. Non-analytical method developed in CATIA, using the relative generating trajectories method. In: IOP conference series materials science engineering pp 1–6 7. Teodor VG, P˘aunoiu V, Berbinschi S et al (2015) The method of In-plane generating trajectories for tools which generate by enveloping-application in CATIA. J Mach Eng 69–80 8. Teodor VG, Berbinschi S, Baroiu N, Oancea N (2014) Study of the enwrapping profiles associated with rolling centrodes by the minimum distance method. Graphical solution developed in the CATIA design environment. Appl Mech Mater 181–191 9. Baroiu N, Teodor VG, Oancea N (2015) A new form of plane trajectories theorem. Generation with rotary cutter. Bull Polytech Inst Iasi 27–36 10. Nicus, or B, Silviu B, Gabriel TV, et al (2017) The complementary graphical method used for profiling side mill for generation of helical surface. In: IOP conference series: materials science and engineering. Sibiu 11. Costin GA, Teodor VG (2019) The virtual pole method—an alternative method for profiling tools which generate by enwrapping. Ann Dun˘area Jos Univ Gala¸ti 31–34

Index

A Additive Manufacturing (AM), 91, 92, 96, 97, 99, 167, 168, 197, 198, 201 Algorithm, 2, 21, 33, 45, 50, 57–61, 65, 69, 74, 77, 81–83, 92–96, 98, 103, 110, 111, 117, 119, 127, 137, 138, 160–163, 219, 226, 258 Augmented Reality (AR), 45–50, 58–61, 64–70

Design for Disassembly (DfD), 168, 171, 187, 201 Design for Manufacturing (DfM), 168, 170, 187 Detection, 46, 76, 77, 80–83, 171 Digital environment, 46, 57, 59, 167, 168, 176, 180, 182, 183, 187, 192, 193, 196, 201 Dismounting, 171–176, 180

C CAD-based, 159, 160 Caliper, 91, 93, 95, 99–104 CNC, 21, 50, 54–56, 58, 59, 62, 65, 68, 69, 110, 111, 141, 143, 149, 151, 155, 168 Collision, 167, 168, 171, 180, 182–184, 186, 193, 201, 202 Computational design, 1–3, 6, 8, 13, 15, 45, 46, 49–51, 55, 57–59, 61, 68, 69 Computer Aided Design (CAD), 46, 101, 143–146, 148, 149, 151, 155, 157, 161, 205–209, 212–215, 219 Customization, 1–3, 5, 8, 11, 21, 34, 35, 206

E Enwrapping, 217–219, 222, 223, 225–227, 229, 233, 236, 240, 258 Equation driven, 144, 146

D 2D model, 157, 206 3D model, 52, 143, 167, 176, 183, 184, 187, 190, 192, 198, 201, 202, 205–207, 209, 211 Design experiment, 107, 109, 111, 112, 114–117 Design for Assembly (DfA), 168–170, 176, 201

F Fabrication, 21, 22, 45–51, 54–57, 58–61, 64, 65, 68, 69, 92, 108–111, 113, 115, 117, 197 Fabrication framework, 107–111, 116 Feature fingertips, 84 Finite Element Analysis (FEA), 91, 93–95, 101–104 Freeform parts, 146

G Games, 2–5, 8–10, 12, 13, 20, 25–32, 35 Gamified design, 6, 9 Generative design, 2–6, 8–15, 20, 23–27, 29, 30, 32–36, 93 Gesture, 74–76, 79–82, 84, 87, 88 Grammatical design, 6, 9, 10, 12 Graphical User Interface (GUI), 206

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al. (eds.), Computational Design and Digital Manufacturing, Management and Industrial Engineering, https://doi.org/10.1007/978-3-031-21167-6

261

262 I Industry 4.0, 46, 167, 191 Interferences, 168, 171, 183, 184, 186 Interlocking, 107, 108, 110–112, 114–117

K Knowledge-Based Design (KBD), 122, 123, 137 Knowledge-Based System (KBS), 122, 123, 137 Knowledge management, 131–136, 138

M Machine vision, 73 Mechatronics, 73, 87, 88 Micro milling, 141–143, 154, 156 Milling, 50, 54–56, 58, 59, 62, 65, 68, 69, 142, 159–162, 165, 193, 194, 196

O Optimization, 1–3, 5, 6, 8–11, 13, 15–17, 19, 25, 34, 35, 91, 93, 94, 96, 97, 99, 102–104, 119, 125, 142, 157, 160

P Parametric curves, 144, 146, 147, 149, 157 Polysurface model, 57, 58 Product conceptual design, 119–134, 136–138 Prototyping, 45, 50, 198

Q Quality Function Deployment (QFD), 119, 124, 127, 137, 138

Index R Reasoning, 6, 7, 12, 26, 119, 123, 127–130, 132, 134, 137, 138 Robotic, 48, 49, 74, 75, 84, 86, 87, 89, 107–113, 115–117, 187, 188, 201 Roughness, 142, 154, 155, 160, 161, 164, 198

S Segmentation, 8, 80 Shape optimization, 1, 3, 5, 9, 10, 12–15 Simulation, 3, 4, 7, 8, 13, 16, 19, 25–30, 32, 35, 54, 55, 100, 102, 110–115, 151, 159–166, 182, 187, 188, 190–193, 195, 196, 202, 205, 206 Surface, 47, 53, 57–59, 62, 65, 67, 68, 98, 99, 101, 141–143, 149, 152–157, 159–161, 163–166, 170, 175, 177–179, 181, 182, 184, 192, 193, 196, 197, 199, 217–220, 223–226, 231, 235, 236, 238

T Tool profile, 247, 250, 251, 255 Topography, 159, 161, 164, 165 Topology, 1, 3–5, 8–10, 12–24, 28, 91–100, 102–104, 117, 127

V Variable feedrate, 143, 146, 147, 152, 156, 157 Virtual Engineering (VE), 168, 190, 191, 201, 202 Visual Basic (VB), 144, 146, 148 Visual Basic for Applications (VBA), 218, 219, 241 Visual Studio, 205