Transmissions and Drivetrain Design [2nd ed. 2023] 3662658593, 9783662658598

Table of contents :
Front Cover
Title Page
© Page
Preface
Contents
1 Transmissions and Drivetrain Design
1.1 Design of the Drivetrain
1.1.1 Driving Resistance
1.1.2 Transmission and Final Drive are Torque—and Rotational Speed Converters
1.1.3 The Real Engine and the Transmission Ratio
1.1.3.1 Overall Transmission Spread
1.1.3.2 The Upper Speed Range and the Axle Ratio
1.1.3.3 Maneuvering Speed
1.1.3.4 Real Torque Curve and the Tractive Force Hyperbola
1.1.4 Traction Limit
1.1.5 Drivetrain Design for Braking
1.2 Drivetrain Design for Electric Trucks
2 Transmission
2.1 Main Transmission
2.1.1 Internal Gearshift System
2.1.1.1 Synchronized Gearshift System
2.1.1.2 Unsynchronized Gearshift System
2.1.2 Reverse Gear
2.1.3 The Wheel Diagram
2.1.4 Design Concept of the Spur Gear System
2.1.5 The Gear Ratio
2.1.6 Losses in the Transmission
2.2 The Split Group
2.3 Planetary Transmission or Epicyclic Gear System
2.4 The Range Group
2.5 Range-Splitter Gearbox
2.6 External Gearshift System
2.6.1 Automated Manual Transmissions
2.7 Automatic Transmission
2.8 Power Take-Offs
2.9 The Transfer Case
3 The Clutch
3.1 The Friction Clutch
3.2 Hydrodynamic Clutches and Converters
3.2.1 Clutch Concepts for Heavy Goods Transportation
4 Propeller Shaft(s)
5 Retarders
5.1 Secondary and Primary Retarder
5.2 Hydrodynamic Retarders
5.2.1 Coolant Retarders
5.3 Inductive Retarders
5.3.1 Retarders with Permanent Magnets
5.3.2 Retarders with Electromagnets
Comprehension Questions
Abbreviation and Symbols
References
Index

Citation preview

Commercial Vehicle Technology

Michael Hilgers

Transmissions and Drivetrain Design Second Edition

Commercial Vehicle Technology Series Editor Michael Hilgers, Weinstadt, Baden-Württemberg, Germany

Michael Hilgers

Transmissions and Drivetrain Design Second Edition

Michael Hilgers Daimler Truck Stuttgart, Germany

ISSN 2747-4046 ISSN 2747-4054  (electronic) Commercial Vehicle Technology ISBN 978-3-662-65859-8 ISBN 978-3-662-65860-4  (eBook) https://doi.org/10.1007/978-3-662-65860-4 © Springer-Verlag GmbH Germany, part of Springer Nature 2021, 2023 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Responsible Editor: Markus Braun This Springer Vieweg imprint is published by the registered company Springer-Verlag GmbH, DE, part of Springer Nature. The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany

Preface

For my children Paul, David and Julia, who derive just as much pleasure from trucks as I do, and for my wife, Simone Hilgers-Bach, who indulges us.

I have worked in the commercial vehicle industry for many years. Time and again I am asked, “So you work on the development of trucks?” Or words to that effect. “That’s a young boy’s dream!” Indeed it is! Inspired by this enthusiasm, I have tried to learn as much as I possibly could about the technology of trucks. In the process, I have discovered that one has not really grasped the subject matter until one can explain it convincingly. Or to put it more succinctly, “In order to really learn, you must teach.” Accordingly, as time went on I began to write down as many technical aspects of commercial vehicle technology as I could in my own words. This booklet takes a look at the transmission and the drivetrain. While writing the text, my overriding intention was to describe the technical solutions that are commonly used at the time of printing in a way that can be clearly understood. Readers who are studying this subject (students and technicians) will find this booklet to be a good entry point and as a result, may discover that commercial vehicle technology is also a fascinating field of work for them. I further believe that this booklet will also be of value to technical specialists in related disciplines, who are interested in applications beyond their area of expertise, and are looking for a concise, easily comprehensible overview. In this second edition of this booklet some improvements were made to the text and some extensions have been made to make the text even more valuable for the readers. The most important objective of the text is to convey the fascination of truck technology to the reader and to make it an enjoyable exercise. With this in mind, I hope that you, dear readers, have much pleasure reading, skimming and browsing this booklet. Finally, I have a personal favor to ask. It is important to me that this work should continue to be expanded and refined. Dear reader, I would greatly welcome your help in v

vi

Preface

this regard. Please send any technical comments and suggestions for improvements to the following email address: [email protected]. The more specific your comments are, the easier it will be for me to grasp their implications, and possibly incorporate them in future editions. If you discover any inconsistencies in the content or you would like to express your praise, please let me know via the same email address. And now I wish you much enjoyment reading about transmissions. Weinstadt-Beutelsbach Beijing Aachen June 2022

Michael Hilgers

Contents

1 Transmissions and Drivetrain Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Design of the Drivetrain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Driving Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Transmission and Final Drive are Torque—and Rotational Speed Converters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 The Real Engine and the Transmission Ratio . . . . . . . . . . . . . . . . . 1.1.4 Traction Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.5 Drivetrain Design for Braking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Drivetrain Design for Electric Trucks. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 2

2 Transmission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Main Transmission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Internal Gearshift System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Reverse Gear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 The Wheel Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Design Concept of the Spur Gear System. . . . . . . . . . . . . . . . . . . . 2.1.5 The Gear Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.6 Losses in the Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Split Group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Planetary Transmission or Epicyclic Gear System . . . . . . . . . . . . . . . . . . . 2.4 The Range Group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Range-Splitter Gearbox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 External Gearshift System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Automated Manual Transmissions. . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Automatic Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Power Take-Offs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 The Transfer Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 13 14 17 17 17 19 20 21 22 24 25 29 29 32 32 33

4 4 8 8 9

vii

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Contents

3 The Clutch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Friction Clutch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Hydrodynamic Clutches and Converters. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Clutch Concepts for Heavy Goods Transportation . . . . . . . . . . . . .

37 37 39 41

4 Propeller Shaft(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

5 Retarders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Secondary and Primary Retarder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Hydrodynamic Retarders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Coolant Retarders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Inductive Retarders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Retarders with Permanent Magnets. . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Retarders with Electromagnets . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 45 46 47 47 47 48

Comprehension Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

Abbreviation and Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

1

Transmissions and Drivetrain Design

The task of the transmission, clutch and propeller shaft is to transmit the mechanical motion of the engine to the axle and the wheels. These components also perform other essential functions. The motion of the engine must be converted. The rotating speed of the combustion engine, at any given time is usually not the same as the desired rotating speed of the wheel; and the engine torque must be converted to supply the propulsive force required at the wheel. This task of converting the rotational speed and torque is carried out by the transmission. The transmission also makes it possible to reverse the direction of rotation of the wheels, which means the transmission enables the vehicle to travel forwards and backwards. Power take-offs and wear-free continuous brakes—also called retarders—often engage with the transmission as well to receive drive force (in the case of the power takeoff) or to deliver brake force to the wheels (in the case of the retarder). The transmission also has a neutral position in which the engine and the drivetrain are mechanically decoupled in the transmission. The clutch is positioned between the engine and the transmission. The clutch disconnects and connects (couples) the engine from/to the transmission. This disconnection is necessary for starting the engine, the stopping operation and for shifting gears in the transmission. Upon startup, the combustion engine has great difficulty keeping itself running, so the rest of the drivetrain that offers resistance to the rotation of the engine is uncoupled by the clutch. When the vehicle comes to a standstill, the engine continues running at idle speed. So in order to actually bring the vehicle to a standstill, the engine must be disconnected by the clutch. The clutch is also needed for shifting gears in the conventional transmission. Because in order to change gears while driving, there must be no load on the transmission gears. The engine torque must be decoupled so that the gear wheels can be disengaged from each other; for this, the clutch must be opened.

© Springer-Verlag GmbH Germany, part of Springer Nature 2023 M. Hilgers, Transmissions and Drivetrain Design, Commercial Vehicle Technology, https://doi.org/10.1007/978-3-662-65860-4_1

1

2

1  Transmissions and Drivetrain Design

The propeller shaft is flange-mounted on the transmission output. It transmits the rotating motion to the axle. It also allows the engine-transmission unit to move relative to the axle. The engine, transmission and clutch typically form a permanently bolted block that is suspended within the vehicle frame. Apart from the small amount of play the elastomer mounts for the engine and transmission have, the engine and transmission are fixed on the frame. But the axle moves significantly relative to the vehicle frame as part of the suspension process. This results in a relative motion between the axle and the transmission, which is compensated by the propeller shaft. In the conventional vehicle (without a transfer case), the second flange of the propeller shaft is attached to the final drive input. The purpose of the final drive is to rotate the axis of rotation of the rotating parts by 90°. In trucks, the engine crankshaft, the transmission shafts and propeller shaft rotate about axes that extend approximately in line with the longitudinal direction of the vehicle—the longitudinal axis of the vehicle is usually referred to as the x-axis. On the other hand, the wheels rotate about an axis perpendicular to the direction of travel, which is referred to in the industry as the y-axis. The functions of the axle with the final drive and the differential are described in detail in [3]. Depending on the vehicle design, the drivetrain also includes other elements, such as the transfer case, the other drive shafts required by the transfer case, power take-offs and wear-free brake elements. Figure 2.18 illustrates the components of a complex drivetrain in an 8 × 8 vehicle.

1.1 Design of the Drivetrain An immense variety of requirements are considered when configuring the drivetrain such as service life, weight and so on. But above all, the drivetrain must be designed so that it satisfies the basic requirement of enabling the vehicle to overcome driving resistance.

1.1.1 Driving Resistance The force required to overcome total driving resistance:

FDriving resistance = FAir + FRoll + FHill

(1.1)

Driving resistance comprises a weight-dependent component that is required to overcome the gradient, weight-dependent rolling resistance and it comprises the speed-dependent aerodynamic drag. If the corresponding mathematical terms are inserted, the following formula is obtained for motion resistance:

3

1.1  Design of the Drivetrain

FDriving resistance =1/2 · ρ · v2 · A · cd

+ mTotal · g · cRoll · cos(α)

(1.2)

+ mTotal · g · sin(α) Figure 1.1 illustrates the driving resistance of a 40-t tractor semitrailer combination with A ·cd -value of 5 m2 as a function of the speed of the vehicle and for various gradients. The increase in driving resistance as speed increases is visible. But for heavy commercial vehicles, the gradient the vehicle must climb is of much greater importance. The maximum force Fmax,theoretical theoretically available to the vehicle for overcoming driving resistance is derived from the maximum engine output Pmax. The maximum forces depends on the speed:

Fmax,theoretical = Pmax,engine / v

(1.3)

The maximum force Fmax,theoretical increases at low speeds. The plot of the vehicle’s maximum force as derived from the maximum engine output, according to Eq. 1.3, is called traction hyperbola, or curve. Figure 1.1 shows the plots of three traction hyperbola, or curves for 240 kW, 350 kW and 450 kW. The areas above and to the right of the respective traction hyperbola cannot be achieved by a vehicle equipped with the corresponding engine. If the force available to the vehicle is equal to the driving resistance, the vehicle can travel at constant speed. If the maximum force available from the engine is less then the

Fig. 1.1   Driving resistance of a fully loaded tractor/semitrailer combination with total weight of 40 tons. Here, A·cd is assumed to be 10 m2 · 0.5 = 5 m2 and the coefficient of rolling resistance cRoll has been given a value of 0.005. The maximum force theoretically available at the wheels (traction hyperbola, or curve) is plotted for a vehicle with maximum engine output of 240 kW (327 hp), a vehicle with maximum engine output of 350 kW (476 hp) and a vehicle with 450 kW (612 hp)

4

1  Transmissions and Drivetrain Design

driving resistance, the vehicle loses speed. If the vehicle has an excess of tractive force— i.e. the maximum possible force at the wheels is greater than the driving resistance—the vehicle can accelerate.

1.1.2 Transmission and Final Drive are Torque—and Rotational Speed Converters The transmission and final drive bring about conversion of the torque. We are ignoring the energy losses in the transmission and the final drive (these are in fact small, but in other contexts must not be disregarded—see [5] for example). It is important to note that the energy that is input to the transmission and subsequently the axle is also output. Since we assume a lossless condition, this results from the principle of conservation of energy. Since neither the transmission nor the axle store energy, the mechanical energy is passed on instantaneously, which means that the power input into the transmission and the axle is output again immediately:

Pin = Pout

(1.4)

Pin = Min · ωin = Pout = Mout · ωout

(1.5)

which yields a torque and rotation speed conversion:

Mout ωin = ωout Min

(1.6)

If the rotation speed is reduced, the torque is increased, and vice versa. The ratio between the rotating speeds at output and at input is called the transmission ratio i1:

i=

ωin ωout

(1.7)

1.1.3 The Real Engine and the Transmission Ratio A typical characteristic for a modern diesel engine such as is used in a heavy goods vehicle is shown in Fig. 1.2. This shows the curve of the maximum possible mechanical output of the engine plotted against the rotating speed of the engine. Figure 1.2 shows the characteristic for four power variants of one engine type.

1 Strictly

speaking, the transmission ratio is a signed variable: If the rotating speed of output shaft is in the opposite direction to the input shaft, the transmission ratio is negative. If both shafts rotate in the same direction, the transmission ratio is positive. For the sake of simplicity, we usually dispense with the prefix and concentrate solely on the value.

1.1  Design of the Drivetrain

5

Output [kW]

Engine speed [revolutions per minute]

Fig. 1.2   Maximum output curve or full-load curve of the OM471 diesel engine built by MercedesBenz. In 2012, the engine was available in four power levels [6]

The usable engine speed range is roughly between 800 and 2000 revolutions per minute (rpm). In maneuvering mode, it is also possible to run the engine at close to the idle speed of 500 rpm. The rotating speed of the engine is converted to the rotating speed of the wheels and, consequently, the travel speed of the vehicle by the transmission and the axle. Engine speed and vehicle speed are correlated as follows: the transmission ratio iTransmission, the axle ratio iAxle and the radius of the wheel rdyn can be used to find the vehicle speed v as a function of the engine rotating speed nEngine with:

vVehicle = 2 · π · nEngine · rdyn ·

1 1 · iTransmission iAxle

(1.8)

1.1.3.1 Overall Transmission Spread The overall spread iSpread of the transmission describes the ratio between lowest gear and the highest gears: iSpread =

ilowest gear of the transmission ihighest gear of the transmission

(1.9)

In direct drive gearboxes the ratio of the highest gear is equal to 1, which means that the overall transmission spread is the same as the transmission ratio of the lowest gear. In the following passage, we will explain how the desired spread of a transmission is defined based on the considerations for a long-haul commercial vehicle. The specific numerical values chosen here correspond roughly to the drivetrain design of modern European long-haul commercial vehicles, which are used with a light to moderately heavy driving profile.

6

1  Transmissions and Drivetrain Design

1.1.3.2 The Upper Speed Range and the Axle Ratio Diesel engines are operated particularly efficiently in terms of fuel consumption at low rotation speeds. Therefore, it is most beneficial to run the engine at speeds of about 1100–1200 rpm.2 For our example, we will assume an engine speed of 1170 rpm, that is to say 19.5 revolutions per second. A further aim is to operate the transmission in the direct gear in the vehicle’s main operating point, as this is efficient with regard to fuel consumption—more about this later. The direct gear means iTransmission = 1. If one assumes that the vehicle’s main operating point on the freeway is about 55.3 mph (89 km/h), corresponding to 24.7 m per second, with a tire radius of 0.53 m, a practical axle ratio can be deduced for the long-haul commercial vehicle: iAxle = 2 · π · nEngine · rdyn ·

1 iTransmission

= 2 · 3.1415 · 19.5 s

−1

·

1 vVehicle

· 0.53 m · 1 ·

1 24.7 ms

(1.10)

= 2.63

1.1.3.3 Maneuvering Speed In order to represent a vehicle that is easily drivable—that is to say easily maneuverable—in the lower speed range too, the requirements are calculated for the lowest gear. If one assumes a desired maneuvering speed of 1.5 mph (about 0.7 m per second/2.5 km/h) and an intended engine idle speed of 500 rpm (8.33 revolutions per second), the requirements derived for the lowest gear return a transmission ratio of: iTransmission = 2 · π · nEngine · rdyn ·

1 1 · iAxle vVehicle

= 2 · 3.1415 · 8.33 s−1 · 0.53 m ·

1 1 · 2.63 0.7 ms

(1.11)

=15

1.1.3.4 Real Torque Curve and the Tractive Force Hyperbola The real torque curve of the engine according to Fig. 1.2 shows that the engine only delivers maximum engine output in a narrow rev range. The tractive force curve shown in Fig. 1.1 is therefore only available if the engine speed associated with the maximum engine output can be “set” for all travel speeds of the vehicle. In order to run the engine at the point of maximum engine output at all times with a continuous speed profile, according to Eq. 1.8 it would be necessary to use a transmission with an infinite number of gears. This is called a continuously variable transmission. But in commercial vehicles,

2 For

engine speeds lower than this, the available engine power is low—see Fig. 1.2—which would consequently make it necessary to downshift even for very small increases in driving resistance.

1.1  Design of the Drivetrain

7

stepped transmissions are used because these kinds of transmission are associated with very little power loss besides being particularly inexpensive and hard-wearing. So the problem that now has to be solved is to get the actually available tractive force to approximate the tractive force curve as closely as possible using a suitable number of gears. The force actually available at the wheels is calculated for each gear with the speed-dependent engine torque MEngine(v):

1

FDrive = MEngine (v) · iGear · iAxle ·

(1.12)

rdyn

In the case of a 12-gear transmission with direct drive in the highest gear and a transmission spread of 15, the drive force curves shown in Fig. 1.3 are obtained for each gear individually. If the gears are close enough together, it is quite possible to obtain an adequate approximation of the curve for the maximum possible drive force. Reserve Force and Climbing Capability of the Vehicle If the rolling resistance FRoll and the aerodynamic drag FAir is subtracted from the maximum force F max,theoretical (Eq. 1.2), what remains is the reserve force FReserve. (1.13)

FReserve = Fmax,theoretical − FAir − FRoll

This reserve force is a type of surplus that can be used to accelerate the vehicle or to climb a gradient. The maximum climbing capability of the vehicle is: 200,000

Tractive force at the wheels

Traction hyperbola 350 kW

160,000

1. gear 2. gear

120,000

3. gear 4. gear

80,000

5. gear 6. gear 7. gear

40,000

0

0

10

20

30

40

8. gear

10. gear

9. gear

50

60

12. gear

11. gear

70

80

90

Speed in km/h

Fig. 1.3   Plot of the drive force for the drivetrain of a vehicle with an axle ratio of iAxle = 2.62, an engine torque curve similar to Fig. 1.2 and an evenly stepped direct drive gearbox with 12 gears and a transmission spread of about 15. The wheel radius of rdyn = 0.53 m as used earlier is used again here

8

1  Transmissions and Drivetrain Design

sin(αMaximum gradient ) =

FReserve mTotal · g

(1.14)

FReserve and αMaximum gradient are dependent on the current speed of the vehicle. From the graph of the available drive force (compare Fig. 1.3), it can be seen that the maximum gradient climbing capability is reached when the vehicle begins driving up the gradient with the speed at which the force at the wheels is maximal. Driving off on a slope is only possible for gradual gradients.

1.1.4 Traction Limit In order to calculate the actual usable force of a vehicle, besides the traction hyperbola force curve (which results from the engine power) it is also essential to bear in mind that the vehicle’s force must be transmitted to the ground via the wheels. If the vehicle reaches its traction limit, a more powerful engine does not give any benefit, which is a discovery practically everyone who has ever driven on wintry roads has probably made at one time or another. The maximum force that is transmissible to the road by one of the tires is given by the coefficient of friction µ and the wheel load—that is to say the force by which the tire is pressed onto the road surface:

Fmax,Traction limit = FWheel load · µ

(1.15)

The traction limit may be imagined as a horizontal line in Fig. 1.3. If a force above this line is transmitted to the tires, they will slip.

1.1.5 Drivetrain Design for Braking The vehicle’s braking ability is also taken into account in the design of the drivetrain. The service brake (see also [4]) ensures that the vehicle is decelerated safely. However, it is not designed to be applied for prolonged periods on long downhill stretches, because this will cause the service brake to overheat. For prolonged braking, the engine brake and, if available, permanent brake systems (see Chap. 5) are used. The brake force required to maintain a constant vehicle speed when traveling downhill is calculated similarly to Eq. 1.1:

FInertia = FDownhill force − FAir − FRoll

(1.16)

1.2  Drivetrain Design for Electric Trucks

9

1.2 Drivetrain Design for Electric Trucks The parameters for the drivetrain design for an electric truck are basically the same as for a conventional drive with combustion engine. Top speed vmax, maximal gradeability and the gradeability required at a certain speed are the parameters to start with when designing an electric vehicle [16]. E-motor characteristics and transmission ratios must be chosen according to those requirements. There are different layouts for the drivetrain of the electric truck: The central drive layout resemble the conventional truck. The e-motor is sitting in the front and is driving a conventional axle through a propeller shaft [18]. The conventional drive train layout needs a change in orientation of the axis of rotation. This normally is done by a bevel gear (pinion) and a hypoid gear (crown wheel). From an efficiency standpoint it is better to place the e-motor in line with the axis of rotation of the axle and the wheels. This results in better efficiency for the electric drive. So called e-axles have one or more electric motors sitting in parallel to the axle. To find the best compromise between efficiency, size (and costs) of the e-motors and the space required, e-axles are designed with a transmission with two to four gears [16, 17]. An additional advantage of the e-axle is, that the space inside the frame that is taken by the engine and the propshaft in a conventional truck is freed up and can be used to accommodate other electrical components (battery, inverter etc.). As efficiency and packaging space are extremely important in tractors for long haul applications, future long haul trucks will probably opt for an e-axle. Another space efficient solution for an electric drive system are the wheel hub motors: At each hub of the axle an electric motor is sitting. This option is very attractive for example for low-floor busses. One disadvantage are the high unsprung masses at the wheels.  Figure 1.4 illustrates the central drive motor, the e-axle and the axle with wheel hub motors. For durability considerations the additional load coming from regenerative braking must be considered in an electric drivetrain (similar to the engine/retarder braking in a conventional truck).

10

1  Transmissions and Drivetrain Design

Fig. 1.4   Different drivetrain configurations for an electric truck. From left to right: Central drive, e-axle and axles with wheel hub motors. Wheel hub motors allow a very space efficient layout for portal axles in low-floor urban busses. (Fotos: ZF a) and c), Allison b))

2

Transmission

Many different types of transmissions exist in motor vehicle construction. The torque can be converted hydraulically or mechanically. Hydraulic variants are usually associated with greater power loss than the mechanical ones. Mechanical solutions are based on the principle of transmitting movement between two wheels of different sizes. In this process, the shaft of the larger wheel is subjected to less angular velocity and more torque. The mechanical solutions are categorized according to the way the force is transmitted between two shafts (with wheels of different sizes). In continuously variable transmissions or belt drive transmissions, the force is transmitted via a traction means which passes around the two wheels—see Fig. 2.1, top diagram. The traction component may be a belt (very old vehicles), or a chain (as used on bicycles, for example) or also a toothed belt. One exotic variant of the mechanical transmission is the friction drive, in which the force is transmitted between an input shaft and an output shaft by a friction disc, for example. Transmissions of this kind enable interesting gearing ranges, but they have not gained meaningful popularity in automotive construction. The same applies for cone ring transmissions [11], in which a displaceable friction ring transmits the force between two cones; these have also gained little acceptance in the field. When directly meshing gear wheels are used—as in the bottom diagram of Fig. 2.1— we talk of gear drives. In commercial vehicles, in which very high torques and forces are transmitted, gear drives are used. The direct gearing reverses the rotating direction. A distinction is made between stationary transmissions, that is to say transmissions in which the axes of the rotating parts are fixed with regard to the transmission housing, and epicyclic transmissions, in which the axes of the wheels move within the transmission housing. The planetary transmission explained in Sect. 2.3 is an epicyclic gear system, because the axes of the planetary gears travel in orbits in it.

© Springer-Verlag GmbH Germany, part of Springer Nature 2023 M. Hilgers, Transmissions and Drivetrain Design, Commercial Vehicle Technology, https://doi.org/10.1007/978-3-662-65860-4_2

11

2 Transmission

12

Angular velocity faster

Co-rotating Angular velocity slower

Angular velocity slower

Direction reversal Angular velocity faster

Fig. 2.1   Basic principle of the mechanical transmission: Two wheels of different sizes drive each other. This is how rotating speed and torque are converted. If the wheels are coupled to each other via a chain or belt, they both rotate in the same direction. In gear drives, the direction of rotation is reversed

The Transmission and the Entire Vehicle The transmission affects many important properties of the vehicle. As was explained earlier, the maneuvering speed, the rotating speed of the engine at traveling speed, and the vehicle’s climbing and acceleration capabilities are determined substantially by the drivetrain design and the transmission. Other vehicle properties in which the transmission is involved include, for example, the vehicle’s fuel consumption and the noise it makes. The transmission affects the engine brake performance and, in the case of the primary retarder, the retarder brake performance. The ease of gear change contributes to general driving comfort. The installation space the transmission is allowed to occupy as part of the entire vehicle concept is limited: The transmission should not protrude beyond the frame, so that the installation space for the body the vehicle will support can be kept simple and cuboid to the extent possible. The volume for the transmission is limited downwards because the vehicle’s ground clearance must be maintained. Furthermore, additional clearance must be maintained laterally between the transmission and the frame to allow pneumatic lines and cables to be installed. Of course, the transmission is also a factor in the ever-present main design targets of a truck, that is to say cost and weight. Of course, the transmission is an element of the

2.1  Main Transmission

13

manufacturing costs, and also of repair and servicing costs; in this context, oil change intervals should be mentioned in particular. Synthetic oils and a transmission oil cooler help to extend the intervals at which the transmission oil must be changed.

2.1 Main Transmission Two engaging gear wheels engaged on different shafts—as shown in the bottom part of Fig. 2.1—form a gear wheel pair. This gear wheel pair is a gear. Multiple gear wheels are mounted on the two parallel shafts of a vehicle transmission. The diameters of the gear wheels on one shaft differ, thereby making different gear ratios available, in other words, different gears. Figure 2.2 shows this. All of the gear wheels on one of the two shafts are fixed to the shaft. The shaft and all of the gear wheels attached to it rotate with the same angular velocity. These are called fixed wheels. On the other shaft, the gear wheels can rotate freely about the shaft. This is essential, otherwise nothing would turn because of the different gear ratios. The gear wheels, which can rotate freely about the shaft, are called idler gears. In all cases, only one of the idler gears is attached non-rotatably to the shaft. When this connection is made, a gear is engaged. a

Drive shaft = Input shaft

Single-stage transmission

Power take-off = Output shaft

Gear wheels

b

Drive shaft = Input shaft

Two-stage transmission

Power take-off = Output shaft

Center distance Countershaft

Fig. 2.2   The single-stage transmission and the two-stage transmission

14

2 Transmission

In modern commercial vehicle transmissions, the gear pairs are permanently in contact (this is called meshing). This means that all gear wheels turn. But only the gear pair whose idler gear is connected non-rotatably to the shaft (Sect. 2.1.1) transmits torque from one shaft to the other and determines the rotating speed of the shaft with the idler gears. The distance between the two shafts, also called the center distance, is one of the important parameters which define the transmission. The larger the center distance is, the larger the gear ratios that can be represented, which in turn means that greater torques can be transmitted. Consequently, the center distance in the transmissions of heavy trucks is larger than the center distance in transmissions for medium-size trucks, and this in turn is larger than the center distance in van and car transmissions. But of course, as the center distance increases the diameter of the gear wheels and consequently the weight as well increase. In Fig. 2.2, the center distance is marked in the bottom diagram. The simplest transmission construction is the single-stage transmission: In this form, one gear wheel of each gear pair is mounted on the input shaft or drive shaft and the other gear wheel of the gear pair is mounted on the output or power take-off shaft. The simplest construction after this is the transmission with countershaft: From the drive shaft, the force is transmitted to the countershaft and from there it is then passed on again to the output shaft. Figure 2.2 shows the principles of a single-stage and a twostage transmission. In each gear pair the transmission ratio is changed, so two-stage transmissions enable a larger overall gear ratio between the transmission input and the transmission output than is possible with a single-stage transmission. The two-stage type also enables simple, efficient realization of a split group (see below). The main transmission of a commercial vehicle generally consists of a two-stage gearbox with countershaft. The disadvantage of multi-stage gear transmissions is that each gear system through which the force flows in the transmission leads to losses, so it is advisable to have the smallest number of gearing stages in the transmission. Precisely this is the advantage of the direct drive gear (see below Sect. 2.1.5 and Fig. 2.7): no gear systems through which the force flows and hence reduced losses.

2.1.1 Internal Gearshift System Connecting the idler wheel and the shaft then disengaging them again is the task of the internal gearshift system. In the main transmission, this consists essentially of a shift rod, a sliding sleeve, and in the case of a synchronized gearbox, the synchronizer unit as well. The function of the sliding sleeve is to connect the idler wheel to its shaft. The sliding sleeve is in toothed engagement with the shaft and therefore rotates permanently with the shaft. The sliding sleeve is displaced axially along the shaft during the shifting process. It engages in a side contour of the idler wheel. In this way, the idler wheel is fixed mechanically to the shaft so that it rotates with exactly the same angular velocity as the shaft. This process of moving the sliding sleeve is the gearshift. Figure 2.3 illustrates the

2.1  Main Transmission

Drive shaft = Input shaft

15

Passage selection (Shift rods)

Shift rods Idler wheels

Shift rods Power take-off = Output shaft Idler gear (for reversing)

Fixed wheels

Sliding sleeves

Countershaft

Gear selected!

Fig. 2.3   Selection of a gear: The fixed wheels are connected fixedly to the shaft, the idler wheels are initially mounted on the shaft so as to be freely rotatable. The sliding sleeve connects ONE idler wheel with the shaft and so makes it possible to select individual gears

principle of shifting gears with the sliding sleeve.1 In the illustration depicted here, all of the idler wheels are mounted on the output shaft. However, the idler wheels and the gearshift system can just as well be positioned on the countershaft. The sliding sleeves that connect the idler wheels individually to the shaft are moved within the gearbox by the shift rods. One shift rod moves exactly one sliding sleeve. One sliding sleeve can be used to engage two gears if—as shown in Fig. 2.3—two adjacent idler wheels can be reached by one slider sleeve. Therefore, selecting a gear in a manual gearbox consists of two movements: first the driver selects the shift rod that is to be moved (typically with a sidewards movement), and with a second movement the shift rod and sliding sleeve are moved.

1 There

are also other principles, such as displaceable gear wheels. The gearshift system with sliding sleeve as described here is used in modern commercial vehicle transmissions. For more esoteric or historical solutions, the reader is referred to the specialist literature on transmissions [1].

16

2 Transmission

In order to be able to connect the idler wheel to the carrier shaft via the sliding sleeve, the speeds of the idler wheel and the support shaft must be matched. This matching of the rotating speeds can be carried out by various mechanisms. A distinction is therefore made between synchronized transmissions and non-synchronized transmissions. Gears can only be shifted in the spur gear transmission if the flow of force across the gear system is interrupted. This is why the clutch is opened when shifting gears. During this interruption of the flow of forces, the vehicle’s speed changes. When it is traveling downhill, it picks up speed; when traveling uphill it slows down, regardless of the engine speed. To reduce this effect, it is recommended to keep the interruption as short as possible and shift gears very swiftly.

2.1.1.1 Synchronized Gearshift System In order to match the rotating speeds of the shaft and the sliding sleeve with the rotating speed of the idler speed, transmissions are equipped with a synchronizer. Roughly speaking, this is a ring-shaped friction element that is located between the sliding sleeve and the idler wheel. It speeds up or slows down the idler wheel to the necessary speed so that the sliding sleeve can engage in the idler wheel. The use of a synchronizer (often also called a synchromesh kit) means that additional parts have to be fitted in the transmission, and these parts have very strict requirements in terms of material and machining quality. 2.1.1.2 Unsynchronized Gearshift System The unsynchronized transmission or constant mesh transmission dispenses with the synchronizing components. In the unsynchronized transmission, the rotating speeds are adjusted in other ways. Synchronization by the Driver During Manual Gearshift without Synchronizing Components in the Transmission In the case of a manually shifted transmission, in order to downshift the driver, must first shift into neutral and then, with the clutch closed, with a throttle blip speed up the engine, the countershaft and the idler wheel up to (approximately) the right rotational speed, so that the idler wheel is rotating at a speed matching that of the output shaft. Then the idler wheel can be connected to the output shaft with the aid of the sliding sleeve. The rotating speed of the output shaft is defined by the rotating speed of the wheels when the vehicle is moving. Automated Unsynchronized Constant Mesh Transmissions With the latest state of the art, the automated constant mesh transmission, the entire process of shifting gears is automated. The complex manual synchronization, which requires much practice, is carried out automatically and under electronic control. Automated constant mesh transmissions may also be equipped with a countershaft brake to slow the countershaft speed down in a controlled manner, making faster gear shifting processes

2.1  Main Transmission

17

possible. [7] describes an unsynchronized automated constant mesh transmission and explains the sequence of operations for shifting up and down the gears. Advantages of the Constant Mesh Transmission The constant-mesh transmission has several advantages over synchromesh transmissions: The synchronizing components, which are expensive and complex for modern, well-synchronized transmissions, are not needed. Because these synchronizing components are no longer present, the gear wheels can also be made wider in the same transmission housing. This in turn means that a constant mesh transmission using the same installation space can be designed for higher torques. As engines become relentlessly more powerful, this is a very welcome effect.

2.1.2 Reverse Gear The transmission must also ensure that the wheels can be driven in both directions of rotation even though the combustion engine always turns in the same direction. This reversal of rotating direction takes place in the main transmission by the provision of a gear system with an additional intermediate gear wheel between the main shaft and the countershaft. The intermediate gear wheel drives the output shaft in the opposite direction to the other gears. Reverse gear with the intermediate gear wheel is illustrated in Figs. 2.3 and 2.4.

2.1.3 The Wheel Diagram Wheel diagrams or transmission diagrams are often used to simplify understanding and the discussion of a transmission. Gear wheels, shafts and other functionally critical components of the transmission are illustrated in line drawings. The simple transmission of Fig. 2.3 is represented in Fig. 2.4 as a wheel diagram. If the wheel diagram is expanded to include the tooth numbers of the individual gear wheels, the various gear ratios also become apparent.

2.1.4 Design Concept of the Spur Gear System The usual configuration of the spur gear system is the two-shaft transmission presented in diagram form in Fig. 2.3 or the three shaft transmission with two countershafts. The position of the shafts relative to each other is a distinguishing feature of several transmission variants—see Fig. 2.5. When the output shaft and the countershaft are aligned side by side, this is described as a flat arrangement, if one is on top of the other,

2 Transmission

18 Idler wheels

Power take-off = Output shaft

Drive shaft = Input shaft

Intermediate gear wheel (for reverse gear)

Countershaft

Fixed wheels

Sliding sleeves

Fig. 2.4   Representation of a simple transmission in the wheel or transmission diagram. This is a twostage transmission with three forward gears and one reverse gear

a

Upright arrangement

b

Flat arrangement

c

Offset arrangement

d

Three shaft transmission

Fig. 2.5   Various arrangements of the shafts in the transmission. a to c show two-shaft transmissions and d illustrates the three shaft transmission

it is called an upright arrangement. According to a third variant, the shafts are offset with respect to one another. In the three-shaft transmission (see [12]), the input shaft drives two countershafts, and these two countershafts in turn drive one common output shaft. The advantage of this configuration is that the force always acts on two gear systems at the same time. Consequently, either the teeth can be made thinner than for a two-shaft transmission or if the tooth width is unchanged more torque can be transmitted. It is logical for all shafts to lie in the same plane so that the main shaft is loaded symmetrically. Most importantly, this construction solves the problem of shaft deflection very elegantly. On the other hand, the transmission structure is quite wide.

2.1  Main Transmission

19

2.1.5 The Gear Ratio The gear ratio between the various gears is directly related to the numbers of teeth on the gear wheels through which the flow of force passes. In the two-stage transmission shown in Fig. 2.2, the transmission ratio of the gear is calculated as follows: if zi is the number of teeth of the gear wheel on the input shaft, zCountershaft 1 is the number of teeth of the gear wheel on the countershaft engaging with the input shaft, zCountershaft 2 is the number of teeth on the gear wheel of the countershaft that drives the output shaft and zo is the number of teeth of the gear wheel on the output shaft which is currently selected, the transmission ratio of the gear is obtained as follows (see Eq. 2.1):

iGear =

zCountershaft 1 zo ωInput shaft = · zi ωOutput shaft zCountershaft 2

(2.1)

In Fig. 2.6, the transmission ratios for a main transmission based on the tooth numbers are presented by way of example. In this example, all gears with the exception of the highest gear have a transmission ratio greater than 1. This means that the input shaft always rotates faster than the output shaft of  the transmission. Particularly older transmissions also have gear ranges in which the rotating speed is sped up. The output shaft rotates faster than the input shaft. These are then called overdrive transmissions.

First stage

Teeth on input shaft (Zi) Teeth on countershaft (Zv)

Second stage

29 34

27

21

16

21

Intermediate gearwheel (reversing) Teeth on main shaft (Zo) Ratio ω(engine) / ω(countershaft) = Zv/Zi

Reversal of rotation direction 16

34

39

44

40

1.259

1.857

2.750

2.500

Total transmission ratio of the main transmission

Ratio ω(engine) / ω(propshaft)

Gear

Stage increment i(n) / i(n+1)

3.224

A

1.48

2.177

B

1.47

1.476

C

1.48

1.000

D

2.931

R

1.172

Ratio ω(countershaft) / ω(main shaft) = Zo/Zv

1.172 1.172 1.172 Direct drive 1.172

2.750 1.857 1.259 2.500

Fig. 2.6   Derivation of gearing stage steps from the number of teeth in a spur gear system with four forward gears and one reverse gear. This is a two-stage transmission. The numbers of teeth on the gear wheels are listed in the top part of the table. The bottom part shows the transmission ratios resulting therefrom. The highest gear in the transmission is a direct drive. The gears are not numbered here, since a main transmission of this kind with equidistant stage increment creates a sub-transmission of a group transmission. As such, the main transmission shown here is incorporated in Fig. 2.12 in a range-change transmission (group transmission) with a split group and a range group

2 Transmission

20

In our example, the highest gear has a transmission ratio of exactly 1. In the attempt to achieve the greatest possible fuel efficiency, much effort is invested in designing the highest gear (the gear used predominantly for driving on the highway) as the direct drive gear. Each gear system in the flow of force is exposed to considerably more friction than the gear systems that are entrained under no load (it may be remembered that all gear pairs are meshed permanently). Now direct drive is a gear in which the input shaft and the output shaft are mechanically connected to one another directly. This capability is only available with the two-stage transmission when the input shaft and the output shaft are arranged in line. The principle of direct drive is illustrated in Fig. 2.7. The Stage Increment Figure 1.3 illustrates very effectively how important the increments between the gears are for the drivability of the vehicle. The relationship between the transmission ratios of two adjacent gears is called the stage increment φ:

φ=

in+1 in

(2.2)

The smaller the gear steps, the closer the transmission ratios of two gears are to each other.

2.1.6 Losses in the Transmission By its nature, the transmission causes losses due to the inescapable effects of friction. We try to keep these losses as low as possible in order to create a fuel-efficient drivetrain. A distinction is made between losses that increase with the transmitted load, called Direct drive: Direct connection of input shaft and output shaft

Drive shaft = Input shaft

Power take-off = Output shaft

Fig. 2.7   Principle of the direct drive: input shaft and output shaft are connected directly. The flow of force is not diverted through the gear systems and is therefore highly efficient. The technical construction for enabling connection of the input shaft and the output shaft is shown in Fig. 2.8

2.2  The Split Group

21

Table 2.1  Losses in the transmission Gear system

Bearing friction

Gasket friction Splashed oil losses

Oil pump drive

Non-load related

X

X

X

X

Load-related

X

X

X

load-related losses, and non-load related losses, which remain constant. Friction and the losses associated with friction occur at various points in the transmission, and these can be categorized as gear system losses, bearing friction, gasket friction, oil splash losses and losses due to the oil pump. Table 2.1 lists the loss types. The gear system losses arise due to the friction of the gear wheels rotating past each other. The direct drive mentioned in the previous section is an effective way to reduce losses relating to the gear systems. But even in direct drive, all the gear wheels rotate into each other and produce—albeit very small—gear system losses. Bearing friction occurs because the shafts generate friction with the bearings on which they are supported. The gaskets which are essential on the input shaft and the output shaft of the transmission also generate friction. Rotating shafts and gear wheels encounter the oil mist that forms in the transmission, and the lowest gear wheels may even spin through the oil in the oil pan at the bottom of the housing. On the one hand, this splashed oil is very useful, ensuring that the oil is spread everywhere in the transmission, but it is also associated with losses. Transmissions are equipped with an oil pump to spread the oil to all important areas of the transmission. The pump may be mounted on the end of the countershaft, for example. The power consumption of the pump adds to the power loss from the transmission. Ultimately, all of the losses in the transmission are friction-related. Consequently, mechanical work is converted into heat; the thermal output heats the transmission. Some heating of the transmission and the transmission oil is welcome, because it improves the oil’s viscosity and thus reduces the effects of friction. But if the transmission becomes too warm, the transmission oil ages prematurely. This is why transmissions that must sustain heavy loads have a transmission oil cooler. This serves to cool the transmission oil and dissipate the power loss to the ambient air. Transmissions without a separate transmission oil cooler discharge the heat to the outside via the housing.

2.2 The Split Group The function of the split group is to provide intermediate gears between the gearing stages of the main transmission. This is why they are sometimes referred to colloquially as half-gears. The smaller separation of the stages enabled by the split group are particularly useful when the vehicle is heavily loaded or climbing a gradient. A gear ratio can

2 Transmission

22 Fig. 2.8   The wheel diagram for the split group. The four different ways to use the split group are shown

a

c

Via constant 1 to the countershaft

Constant 1 and constant 2 form one gear

b

Via constant 2

d

Direct drive

to the countershaft

be selected more precisely to match a given driving situation. The gear step provided by the split group is typically equal to half the value of a gear step in the main transmission. One way to realize the split functionality is shown in the wheel diagram in Fig. 2.8. In principle, it is based on the idea of enabling the countershaft to be driven by two different gear systems. The gear system from the input shaft that drives the countershaft is also called the constant. In this case, the split functionality is provided by the fact that there are two constants. Different transmission ratios can be selected depending on whether the countershaft is driven by constant 1 (see Fig. 2.8a) or constant 2 (see Fig. 2.8b). In direct drive mode, both constants are bypassed—Fig. 2.8d. Figure 2.8c shows how the two constants are used to create one gear of the main transmission. In this design, the split functionality is integrated in the main transmission. So in this smart solution it is impossible to distinguish clearly between the split transmission and the main transmission.

2.3 Planetary Transmission or Epicyclic Gear System The basic form of a planetary transmission or epicyclic gear system consists of a sun gear, a carrier which carries planetary gears, and the ring gear. The sun gear is positioned in the middle of the transmission. The sun, the carrier and the ring gear are aligned coaxially. The carrier supports the planetary gears, which rotate around and roll over the sun.

2.3  Planetary Transmission or Epicyclic Gear System

23

Typically there are three to five planetary gears. If there are more planetary gears, the load is spread among those gears, so three planetary gears may usually be encountered in lighter transmissions. The planets are surrounded by a ring gear whose internal toothing meshes with the planetary gears. Figure 2.9 is a schematic representation of the simplest form of an epicyclic gear system. Planetary gears are very compact and can transmit high torques because several gear wheels are engaged at the same time. If z stands for the number of teeth of the various gear wheels, the basic equation for the simple planetary gear set (the Willis equation) is as follows: | | zRing gear zRing gear · ωRing gear − 1 + · ωCarrier = 0 ωSun + (2.3) zSun zSun Figure 2.10 explains how Eq. 2.3 is derived. We consider the speeds at the point of contact between sun and (one of the) planets: When the sun is turning but the carrier is rotating at a different speed, the relative speeds of the sun and the carrier result in a rolling movement of the planets. If the carrier rotates more slowly than the sun, the planets rotate in the opposite direction to the sun. The translational speed at the contact point can be looked at from the sun  and from the planet. Both ways must give the same result (equal sign in our equation). Considering that the translational speed is defined by the angular velocity and the radius (being proportional to the number of teeth) we obtain (see a in Fig 2.10):

ωSun · zSun = ωCarrier · (zSun + zPlanet ) − ωPlanet · zPlanet

(2.4)

Figure 2.10b shows the relationships between the planetary gears and the ring gear. Here too, we consider the translational speed at the contact point. Again we look at it from two different point of views: from the ring gear and from the planet that has two contributors to the movement: the rotation of the carrier and the rotation of the planet. Those two

Planetary gears

Ring gear Sun gear

Carrier

Fig. 2.9   The planetary gear set consists of the sun, the ring gear and the carrier with the planetary gears

2 Transmission

24 a

b

ωPlanetary gear ω Planetary gear ωCarrier ωSun

ωCarrier ωRing gear

Fig. 2.10   Illustration of Eqs. 2.4 and 2.5

approaches must give the same result (equal sign in the equation). Keep in mind that we consider the number of teeth proportional to the radius. The following equation results: ) ( ωRing gear · zRing gear = ωCarrier · zRing gear − zPlanet + ωPlanet · zPlanet (2.5)

If Eqs. 2.4 and 2.5 are added a simple transformation yields the basic equation for the epicyclic gear system: Eq. 2.3. If two angular velocities are equalized in the equation Eq. 2.3 the third angular velocity also assumes the same value. For technical purposes, this means that if two elements of the planetary gear set are connected to each other, the entire planetary gear set revolves as a block. If one of the elements of the planetary gear set is selected as the frame, i.e. it does not rotate (ω = 0), the transmission ratios for the rotation figures of the other two elements are returned as listed in Table 2.2. The number of teeth on the planetary gears does not appear in the table—it is not significant for the gear transmission ratio. It must simply be selected so that the tooth geometry of the planetary gears matches the tooth geometries of the ring gear and the sun.

2.4 The Range Group The task of the range group is to make the transmission spread larger. This requires the use of a sub-transmission with a very large gear step. In order to be able to create a useful spacing between the transmission gears, the range group must have a gear step that is equal to the spread of the main transmission plus one gear step of the main transmission—see Sect. 2.5. A common form of the range group is a planetary gear. The sun is the input which is connected to the main transmission, and the carrier is the output rotating at the speed of

2.5  Range-Splitter Gearbox

25

Table 2.2  Gear transmission ratios in a simple epicyclic gear system when one of the elements is fixed in position (frame) Input

Output

Frame (stationary)

Gear ratio

Comment

ωInput ωOutput zRing gear zSun

a)

Sun

Carrier

Ring gear

i =1+

b)

Sun

Ring gear

Carrier

i=−

c)

Carrier

Sun

Ring gear

i=

d)

Carrier

Ring gear

Sun

i=

e)

Ring gear

Sun

Carrier

zSun i = − zRing gear

f)

Ring gear

Carrier

Sun

i =1+

zRing gear zSun 1

1+

zRing gear zSun

Inverse of a)

1

zSun Ring gear

1+ z

zSun zRing gear

Inverse of b) Inverse of d)

the transmission output to drive the propeller shaft. If the carrier and the ring gear are connected, for example, the planetary gear set revolves as a block and does not generate a gearing, so the contribution of the range group to the transmission ratio is 1. If the ring gear is immobilized (attached to the transmission housing), a transmission ratio as shown in Table 2.2 a) is obtained, resulting from the number of teeth on the ring gear and the sun:

iPlanet = 1 +

zRing gear zSun

(2.6)

Since the ring gear has many more teeth than the sun, the transmission ratio is very large. Figure 2.12 shows the example of 85 teeth on the ring gear and lists 25 teeth for the sun. This results in a transmission ratio of 4.4. However the range group does not necessarily have to be an epicyclic gear system. It can also be constructed as a conventional spur gear system in the same way as the main transmission.

2.5 Range-Splitter Gearbox In light trucks, a transmission consisting only of the main transmission is often sufficient. This transmission design is typically able to provide up to six gears (as in the case of the passenger car with manual gearshift). The single group transmission represents a solution for realizing progressive gradation of the gears. This means that the step to the next higher gear becomes progressively smaller. If more than six gears are available, a range-change transmission is called for. In this case, two or three transmission (groups) are arranged in a cascade. The advantage of this construction is that the number of gears possible is a multiple of the number of gearing stages of the individual sub-transmissions. In Europe, the range-splitter gearbox with

26

2 Transmission

split group (two gearing stages), main transmission (with three or four gears) and the range group (two gearing stages) is the most popularly used. This configuration provides twelve or sixteen gears. These range-change transmissions are typically designed in geometric gear steps—in contrast to the progressive gear steps of the single group transmission. With geometric stepping, the gear steps between two adjacent gears are always the same size. Geometric stepping makes it easier to combine three sub-transmissions to create a range-splitter gearbox. Many range-splitter transmissions are built so that the split group offers a gear step half the size of the main transmission. The range provides a large step which is equal to the transmission spread of the main transmission plus one gear step. With strict geometric stepping, the stage increment φ between two adjacent speeds is derived from the overall transmission spread iOverall of a transmission with z speeds according to: [ φ = z−1 iOverall (2.7)

iOverall = φ z−1

(2.8)

Figure 2.11 shows the relationship between engine speed and vehicle speed for a geometrically stepped 12-speed range-change transmission. Figure 2.12 shows an example of the transmission ratios (and the tooth numbers) of a 16-speed range-splitter transmission with a split group, a planetary gear set as the range, and four gears in the main transmission. When the individual sub-transmissions are cascaded to form a range-splitter transmission, the reverse gear is also multiplied. The reversal of the rotation direction in the main transmission (see Sect. 2.1) can be combined with the two gearing stages of the split group to produce two reverse gears. In theory, it should also be possible to use the two transmission ratios of the range group and so enable a total of 4 reverse gears. Although two of them would lead to very high traveling speeds, which is why the fast transmission ratio in the range group is not usually used when reversing. 2000

1st gear

1800 Engine speed [rpm]

Fig. 2.11   Diagram of the engine speed over vehicle speed for each gear of a 12-gear transmission. A direct drive gearbox with 12 gears and a transmission spread of about 15 is represented. The plot is based on a final drive ratio of iAxle = 2.62, and a wheel radius of rdyn = 0.53 m is assumed. The highest gears are designed such that at the rated engine speed the vehicle’s traveling speed is well above 90 km/h

6th gear 7th gear

2nd gear

1600

8th gear 9th gear

3rd gear

1400

10th gear

4th gear

11th gear

1200 5th gear

12th gear

1000 800 600

0

10

20

30

40

50

Speed in km/h

60

70

80

90

2.5  Range-Splitter Gearbox

27

Split group

Teeth on input shaft (Zi)

Constant 1 27

Constant 2 29

Teeth on countershaft (Zv)

38

34

Main transmission

27

21

16

Intermediate gearwheel (for reversing)

Teeth on main shaft (Zo) Ratio ω(engine) / ω(countershaft) = Zv/Zi

1.407

28

40

25

1.259

1.857

2.750

2.500

4.400

2.750 2.750

1.172

4.400 4.400 4.400

1.857 1.857 1.259

1.172 1.407 0.853 Direct drive

1.259

1.857 1.857

1.172 1.407

1.259

1.172 1.407 0.853 Direct drive

1.259

1.172

4.400 4.400 4.400 4.400 4.400 2.750 2.750

1.172

1.407

1.407

21 44

1.172

K1 -- K2

85

39

1.407

1.407

16

34

1.407

K1 -- K2

Complete transmission

Teeth on ring gear Teeth on planetary gear Teeth on sun

Ratio ω(engine) / ω(propshaft)

Gear

Gear steps i(n) / i(n+1)

1.172

Ratio ω(countershaft) / ω(main shaft) = Zo/Zv

1.407

Range

Reverse gear

2.500 2.500

4.400 4.400

Transmission ratio of planetary gear set 17.030 14.186 11.501 9.580 7.798 6.496 5.282 4.400

1 2 3

1.20 1.23 1.20

4 5 6 7 8

1.23 1.20 1.23 1.20 1.14

3.870 3.224 2.614

9 10 11

1.20 1.23 1.20

2.177 1.772

12 13

1.23 1.20

1.476 1.200 1.000

14 15 16

1.23 1.20

15.481 12.897

R R

Fig. 2.12   Derivation of gearing stages from the numbers of teeth in a 16-speed range-splitter transmission. The top part of the table lists the numbers of teeth on the gear wheels belonging to each gearing stage. The bottom part shows the transmission ratios resulting therefrom. The highest gear of the transmission is a direct drive gear. In the example shown, only the reverse gears of the slow group are used. The gear steps generally conform to a geometric progression

The wheel diagram for a European, 16-speed transmission is shown in Fig. 2.13. Figure 2.14 shows what the transmission will look like when it is actually built. It is most sensible to place the range group that downshifts to slow speed with its large gear step at the end of the transmission. The reduction to slow speed generates a considerable increase in torque. If the range group is positioned at the transmission output, the other transmission components will not be exposed to the increased torque. There are also design variants of a group transmission in which two spur gear systems are arranged one behind the other. [12] shows an example of a transmission in which a main transmission with five speeds (four gear systems and direct drive) is combined with a second spur gear system that has another four gears. These four shift positions include two gears in close proximity to each other and provide a split functionality, a very large transmission ratio which is used to provide a crawler with high transmission ratio, and a direct drive. Arithmetically, this produces 20 gearing stages, although not all of these can be used in any practical way. Other double group transmissions combine the main transmission with a second gearbox, in which the split functionality provides three gearing

2 Transmission

28

Reverse gear

Split group

Main transmission

Range group

Fig. 2.13   The wheel diagram for a 16-speed range-splitter transmission for heavy trucks. The tooth numbers added correspond to the numbers in Fig. 2.12

Split group

Main transmission

Planetary gear set (range group)

Shift rods

Input shaft

Oil pump

Countershaft

Sliding sleeve

Reverse gear

(reversing gear wheel not shown)

Fig. 2.14   Sketch of a 16-speed range-change transmission with synchronization for heavy trucks (older design type). (Illustration: Daimler)

2.6  External Gearshift System

29

stages. In this case the main transmission includes very substantial stage increments, which are divided into three sub-gears by the splitter. Some transmissions are equipped with the so called crawler gear. This is a gear with a very high transmission ratio.

2.6 External Gearshift System The internal gearshift system (Sect. 2.1.1) consists of the components for shifting gears inside the transmission. The external gearshift system is the control element by which the driver’s intention to change gears is registered and conveyed to the transmission, precisely to the internal gearshift system of the transmission. In vehicles with manual gearboxes, the driver operates the gear selector lever (or shiftstick) to change gears. There are various ways to transfer the shiftstick signal into the transmission. If it is positioned immediately above the transmission and engages it directly, this is called a direct gearshift system. If the transmission and the shiftstick are not located together—this is usually the case in cab-over-engine designs—the shift request is passed on. It can be passed on mechanically by means of a linkage or by cable (cable shift). Means for transmitting the shift request hydraulically are also known. The movement of the gear stick is converted into hydraulic pressures which convey the shift request to the actuators on the transmission via hydraulic lines. One challenge in the development of these systems lies in the fact that the cab moves relative to the transmission: It bounces relative to the frame and is equipped with a tilting mechanism. Any shift linkage must therefore be designed telescopically—see Fig. 2.15 for an illustration of the problem. With cable and hydraulic solutions, the lines must be routed so as to ensure that the cab can still be tilted (routing through the tilt axis of the cab). The force applied with cable and linkage systems may optionally be further amplified by pneumatic cylinders, for example. Then, the driver does not have to apply high force himself, and the gear shifting operation is made more comfortable and requires less force.

2.6.1 Automated Manual Transmissions In the automated manual transmission, an electronic unit calculates whether a shift change is appropriate and specifies which gear is to be engaged. To do this, the electronic unit actuates solenoid valves that introduce air into pneumatic cylinders (and let it out again) to operate the transmission’s inner gearshift system. Usually, a display shows the driver which gear is currently engaged.

30

2 Transmission

Fig. 2.15   Tilted cab of a cab-over-engine vehicle from the 1970s. The telescopic linkage of the manual gear shift is clearly visible. (Photo: Daimler)

Mechanical automated manual transmissions (AMT)2 launched in the European market in 2000 [8], and in less than a decade have gained a dominant position in the long-distance haulage industry. A few years later, a similar market success occurred in the US. AMTs represent a substantial contribution to driver comfort, and they affect fuel consumption positively (see also [5]) and improve the vehicle’s resale value. Starting around the year 2020 AMTs are now on the rise in markets like China. In the AMT, a control unit determines start-off gear and also decides when to change gears. The vehicle speed, rolling resistance and total weight of the tractor trailer combination are all incorporated in the process in order to define optimum gearshift strategies. The total weight is estimated by an algorithm based on the dynamic behavior of the vehicle. The electronic unit knows how much engine power is currently available and what speed and acceleration values can be achieved with it. This data is sufficient to allow an adequate estimate of the total weight of the tractor trailer combination. If the vehicle has been parked, of course the vehicle weight must be recalculated because it might have been loaded or unloaded. The weight calculation algorithm normally assumes a heavy weight as the initial value and adjusts this initial value close to the actual weight value in the course of the journey.

2 Automated

manual transmissions are also called clutchless manual transmissions to indicate that their internal mechanisms still resemble conventional manually operated spur gear systems and to differentiate the automated manual transmissions from the fully automatic versions. Clutchless here means that there is no clutch pedal anymore to be operated by the driver. Technically the AMT still needs and still has a clutch.

2.6  External Gearshift System

31

Automated manual transmissions often offer the driver additional functions designed to simplify vehicle operation: • Maneuvering mode makes it easier to maneuver the vehicle at low speeds. In maneuvering mode, the full range of the accelerator pedal is provided over a narrow engine speed band e.g. from 500 to 1000 rpm. This enables the driver to control the vehicle at low speed more precisely. • Rocking mode is a function intended specifically for construction site vehicles and all-terrain vehicles. It can be used to switch rapidly between forward and reverse gears (initiated by the driver). This function can help to rock a vehicle free if it becomes stuck in soft ground. • Some automated transmissions offer a power mode. In Power mode, the vehicle is able to access more of the engine’s output, which means that it shifts gear at higher engine speeds. Consequently, more power is available to the driver, as the name Power mode suggests. The disadvantage of power mode is that by its nature it entails increased fuel consumption. • The kickdown function works similarly to the power mode. When the driver depresses the accelerator pedal strongly, the electronic unit interprets this as a desire for maximum engine output and lets the engine rotate faster before shifting to the next higher gear. So more engine power is available. • Economy mode is the opposite of power mode. The gearshift points are selected so that the vehicle travels as economically as possible—meaning shifting up to next gear happens at relatively low engine speed. • Another function of the transmission and drivetrain control which assists with fuel efficiency is the EcoRoll function. EcoRoll is active when the vehicle is in a rolling phase. During a rolling phase, the transmission is switched to neutral. The energy that is needed to overcome the engine’s drag torque does not slow-down the rolling vehicle. The engine is decoupled from the rest of the drivetrain and runs freely without any load. As a result, the vehicle’s momentum is not slowed as quickly and the rolling phase is prolonged. However the engine consumes the fuel needed for the idle running in this phase. A peculiarity of automated manual transmissions is that the vehicle must not be left in gear when switched off—this is different from vehicles with a manual gear stick, which are often left in gear for parking. A vehicle with automated manual transmission must be parked with the transmission in neutral to make sure that the engine can be started. For engine start the transmission must be shifted to neutral or the clutch must be open. In a vehicle with AMT compressed air is required to open the clutch or to shift to neutral. But if the vehicle is left for a prolonged period, there is no guarantee that there will be enough air in the air reservoirs to shift the transmission into neutral or to open the clutch, because after an extended inactive period the vehicle may lose air from the compressed air system. If the transmission is switched to neutral when the vehicle is parked,

32

2 Transmission

the engine is disconnected from the powertrain and the engine can be started. The engine drives the compressor, which in turn fills the reservoirs with the requisite amount of air so that clutch operations and gearshifts are then possible again. The conventional manual transmission with gear stick and clutch pedal does not have this problem because the drive can uncouple the engine from the drivetrain by pressing the clutch pedal, so there is nothing to prevent the engine from being restarted.

2.7 Automatic Transmission The classic automatic transmission consists of planetary gear set transmissions with multi-disc brakes and a hydrodynamic torque converter clutch as coupling element. In the passenger car field, this form of transmission predominates in many markets, but among trucks it is a rather unusual solution found mainly in niche applications. In buses, particularly city buses, the automatic transmission with torque converter clutch is very widespread. An automated spur gear system is NOT an automatic transmission in this sense, even though it shifts gears automatically. The advantages of the automatic transmission are the high degree of driving comfort and the shift operations without interruptions in the tractive force. The converter helps to make launch procedures very smooth, which is particularly attractive in the city bus (standing passengers!). The converter is also responsible for a portion of the desired overall driveline spread (torque multiplication—see Sect. 3.2), so the spread between highest and lowest gear of the transmission does not have to be as large, and consequently a transmission with fewer gears can be used. On the other hand, multiplate clutches need oil pressure all the time, resulting in noticeably higher consumption—in the order of about 5%—in drivetrains with automatic transmissions compared with automated manual spur gear systems.

2.8 Power Take-Offs To drive other major assemblies on the truck with the mechanical energy of the engine, devices called power take-offs are provided. For example, the following functions may be powered: the tilt function for the dump box on a construction vehicle, crane functions, drives for concrete pumps, street sweepers, winches, drives for garbage collection trucks, water pumps and much more. The mechanical power take-off often powers up a hydraulic pump first. One (or more) of the functions listed is/are then powered with the aid of the hydraulic energy. A distinction is often made between engine-dependent power take-offs, which are driven directly by the engine, and power take-offs which are flange-mounted on the transmission behind the clutch.

2.9  The Transfer Case

33

Power take-offs

Power take-offs, driven by the transmission

Engine-dependent power take-offs

Engine power take-off via crankshaft

Power take-off on the side of the transmission

Power take-off at the rear of the transmission

Engine power take-off via gear wheel drive/camshaft

Engine power take-off in front

Engine power take-off behind

Fig. 2.16   Classification of power take-offs

Engine-dependent power take-offs can be driven directly by the crankshaft or branched off via the gear wheel drive/the camshaft. They are not dependent on the transmission. If the power take-off is branched off in the transmission, there are several possibilities. In the transmission the power take-off can be driven by a special wheel on the countershaft, or a shaft extension can be made to protrude out of the transmission at the end of the countershaft. Figure 2.16 shows a classification of power take-offs.

2.9 The Transfer Case As their name suggests, the purpose of transfer cases is to transfer driving force. In this sense, axle differentials and drive-through axles are also transfer cases, but will not be discussed here (see [3]). On trucks with front axle drive, the transfer case is a separate assembly which is mounted to the frame. The transfer case is driven by a propeller shaft coming from the transmission and distributes the force. Some of the force is transferred to the front axle(s), another part of the force is transferred to the rear axle(s). The distribution of force can be symmetrical (50:50), or it may be transmitted in different proportions. Transfer cases for heavy trucks often offer a switching option. This may consist of a means for switching the flow of force to the front axle on and off, which effectively lends the vehicle switchable front wheel drive capability. Some transfer cases

2 Transmission

34

also offer an additional gearing stage. In normal mode, the transfer case has a transmission ratio of 1; on difficult terrain, the transfer case can be switched into slow mode. The wheel speed (vehicle speed) is reduced, the tractive force at the wheels is increased. Figure 2.17 shows the diagrams for various functions that can be found in the transfer case. Figure 2.18 shows the installation position of a transfer case in the vehicle. Figure 2.19 shows a cross-sectional drawing of a complex three-shaft transfer case. The transmission-side flange through which the driving power is transferred appears in the top left of the drawing. The bottom part shows the two output flanges for the front axle(s) and the rear axle(s). The upper shaft includes the gearshift system which enables two transmission ratios to be selected in the transfer case.

a

Input

Rigid connection with front axle

c

Input

b VA

HA

Input

Switchable front axle

d

Two transmission ratios on the transfer case

VA

Input

Asymmetrical distribution of torque to the front and rear axles VA

VA

HA

HA

HA

Fig. 2.17   Various functions of the transfer case shown as a wheel diagram. VA stands for front axle and HA stands for rear axle. a shows the simplest transfer case. Diagram b shows that the front axle can be engaged by switching. Diagram c shows the wheel diagram for a transfer case with two gearing stages, while diagram d shows a possible design in which the torque is split asymmetrically between the front axle and the rear axle

35

2.9  The Transfer Case

Transfer case

Propeller shafts Fig. 2.18   Installation position of the transfer case in an 8 × 8 vehicle. (Illustration: Daimler)

Fig. 2.19   Complex three-shaft transfer case. (Illustration: Daimler)

3

The Clutch

The clutch has the task of connecting and disconnecting the engine and the transmission (plus the drivetrain elements attached to the transmission). This ability to disconnect the engine from the rest of the drivetrain is essential to enable the engine to be started, gears to be changed in the transmission and to stop the vehicle. The clutch also smooths out the engine’s rotational irregularities and torsional vibrations.

3.1 The Friction Clutch With the friction clutch or dry clutch, the coupling function is performed by pressing two surfaces against each other with a diaphragm spring. One of these two clutch faces is permanently attached to the transmission input shaft, the other is permanently attached to the engine crankshaft. Figure 3.1 illustrates the working principle of the dry clutch. If a force is applied to the diaphragm spring, the two surfaces are disengaged from one another. In heavy trucks, the opening of the clutch against the (very strong) diaphragm spring is carried out with the assistance of a pneumatic cylinder. With a standard clutch pedal, the pneumatic cylinder is activated when the pedal is depressed. In automated manual transmissions the electronic unit actuates a solenoid valve, which fills the pneumatic cylinder with air, thus opening the clutch. One distinguishes between pushtype clutches and pull-type clutches depending on whether it is necessary to push or to pull the diaphragm spring to open the clutch. The geometry of the diaphragm spring and how the diaphragm spring is connected to the clutch cover determines whether we have a pull or a push clutch. Figure 3.2 shows a foto of a clutch disc and clutch cover with diaphragm spring for a commercial vehicle. The outer friction area of the clutch disc and the hub of the clutch

© Springer-Verlag GmbH Germany, part of Springer Nature 2023 M. Hilgers, Transmissions and Drivetrain Design, Commercial Vehicle Technology, https://doi.org/10.1007/978-3-662-65860-4_3

37

38

3  The Clutch

Fig. 3.1   a) Function of a dry clutch: The diaphragm spring presses the pressure plate and the clutch disc against the flywheel. The flywheel is connected to the crankshaft of the engine whereas the clutch disc is connected to the input shaft of the transmission. Depending on how the diaphragm spring is connected to the clutch cover (not shown here) the clutch is opened either by pulling or by pushing the spring. b) The clutch might be actuated by a central clutch actuator sitting in the clutch bell of the transmission housing or by an external cylinder that is moving a lever, the so called clutch fork

Fig. 3.2   Picture of a clutch plate and the clutch cover with diaphragm spring for a commercial vehicle. Foto: ZF

3.2  Hydrodynamic Clutches and Converters

39

disc can be slightly twisted against each other. This twisting movement is dampened by springs. These spring elements act as a damper to reduce the transfer of torsional vibrations between the engine and the transmission. In the coupled state (clutch engaged), the friction force between the two clutch faces must be large enough to ensure that the faces do not slide (slip) against each other. The maximum torque transferable by the clutch must be equal to the maximum torque of the engine plus a safety factor. The amount of torque the clutch is capable of transferring is determined by the effective area of the clutch, the coefficient of friction and the pressing force applied by the diaphragm spring. Clutches with different diameters are available depending on the necessary torque transfer. The performance capability of the clutch can be increased by using double-disc clutches. Here the effective area is increased as the clutch consists of two clutch plates. The dimensions of the housing for spring-loaded friction clutches for trucks and buses are standardized in ISO 7649 [9]. The engine-side connection of the clutch housing, that is to say the flywheel housing, is standardized in ISO 7648 [10]. This way, a transmission with unified clutch bell can be installed in vehicles built by different manufacturers. Since the two plates rub against each other as part of the coupling process, a large amount of heat is generated in a short period of time. This heat energy is absorbed by the thermal mass of the clutch and the flywheel and gradually given off to the surrounding air. The clutch must therefore be of a certain minimum size in order to be able to absorb this heat. If the clutch becomes too hot, it can be damaged or even destroyed. When heavy loads are involved (heavy gross combination weight, high torque), incorrect handling of the clutch can very quickly lead to clutch damage. In this context, another advantage of the AMT (Sect. 2.6.1) is evident: The clutch is operated in automated mode, so it cannot become worn prematurely due to improper action on the part of the driver.

3.2 Hydrodynamic Clutches and Converters Hydrodynamics uses the mass inertia of a fluid flow to transmit forces.1 In the drivetrain, the hydrodynamic clutch, the converter and the fluid retarder (for the retarder see Sect. 5.1) serve as hydrodynamic elements. The basic principle is the same for all three major assemblies: an impeller accelerates the fluid, the fluid is forced against the turbine wheel and the turbine wheel is driven round by the fluid. This system involves two energy transformations. First, the mechanical energy of the pump wheel and the parts rigidly connected to the pump wheel is converted into kinetic energy of the fluid. Then, the kinetic energy of the fluid is converted back into mechanical energy at the turbine wheel. This double conversion is inefficient. Inefficiency of this kind is unfavorable in

1 Whereas

hydrostatics works with pressure propagation and displacement.

40

3  The Clutch

clutches and converters. This is why hydrodynamic clutches and converters are equipped with lock-up clutches: If the properties of the hydrodynamic elements are not needed, the pump wheel side and the turbine wheel side are joined mechanically. The hydrodynamic element is bypassed. The advantage of the hydrodynamic clutch is that it enables a continuous, smooth launch action. This extra comfort is very welcome on city buses, for example (standing passengers) and private cars. The torque that is transmitted can be varied continuously by adjusting the fill level of hydraulic fluid in the blade space. Since the engine and the drivetrain are not joined by a rigid mechanical connection, the torsional vibration of the engine is also damped. And the engine cannot stall. If the hydrodynamic system only includes a pump wheel and a turbine, it is a clutch. If a stator is also installed between the pump and the turbine, the stator can be used to convert the torque. Figure 3.3 is a diagrammatic representation of a converter and its most important components. The pump can rotate considerably faster than the turbine. In this case torque at the turbine wheel is higher than on the pump wheel. This effect is called torque multiplication. This can be used to make more torque available to the wheels, when launching, for example. However, torque rise can also result in the traction limit between the tires and the road surface being reached frequently. Given the constant increase in engine power and torque, the practice of installing converters with torque multiplication in trucks is steadily losing its appeal. The hydrodynamic clutch, particularly with lock-up clutch, is more expensive than a standard dry clutch, so most trucks are equipped with a dry clutch.

Fig. 3.3   Diagram of a torque converter with pump wheel, turbine wheel and stator

Turbine wheel

Pump wheel

Stator Input shaft

Output shaft

3.2  Hydrodynamic Clutches and Converters

41

3.2.1 Clutch Concepts for Heavy Goods Transportation Heavy goods transportation involves the movement of large, bulky and heavy loads. The loads may be, for example, large engines, turbines, machinery, transformers, finished steel and concrete parts or (rail) vehicles and typically cannot be broken down into smaller units. The unique feature of heavy goods vehicles is that they are able to launch under heavy loads and can maneuver for extended periods at very low speeds (bulky cargo!). This application places a very large thermal load on the clutch. Conventional dry clutches are not capable of performing this function. This is why hydrodynamic clutches or hydrodynamic converters are used for transporting very heavy cargos. The engine and the hydrodynamic element, which absorbs an enormous quantity of thermal energy, are cooled by a rear-mounted cooling system located behind the cab. [13] Illustrates the drivetrain in a heavy duty tractor unit with particular emphasis on explaining the hydrodynamic element.

4

Propeller Shaft(s)

The function of the propeller shaft is to transmit torque between the transmission, the transfer case and the driving axles. The propeller shaft makes it possible to connect two axes of rotation which are not exactly in the same plane. Since the transmission and the axles move relative to each other as part of the suspension process, the propeller shaft must be able to balance out this relative movement. The relative movement can alter the positioning of major assemblies with respect to each other and the distance between the assemblies. The propeller shaft must therefore be able to compensate for both (small) angular and (small) longitudinal offsets according to the geometrical environment. In order to satisfy these requirements, the propeller shaft typically includes universal joints or cardan joints, and possibly a length adapter, as well as the actual shaft tube. Flanges at the end of the propeller shaft enable the shaft to be connected to the output or input shaft of the respective major assemblies. The angle between the axis of rotation of the propeller shaft and the axis of rotation of the assembly is called the deflection angle. When the major assemblies are placed with respect to each other, care must be taken to minimize the deflection angles. Larger deflection angles cause the universal joint to transmit variable rotational movement and leads to increased component stress, higher vibration and noise generation. The angular velocity at the output end of the universal joint is momentary not identical to the angular velocity at the input end. In order to minimize the deflection angle, the design engineer can install the major assemblies in the vehicle like engine, transmission and axle (slightly) tilted. Figure 4.1a is a photo of a propeller shaft. Figure 4.1b illustrates some of the geometrical conditions mentioned in the text. Long propeller shafts are supported by an intermediate shaft bearing. Long propeller shafts may also be designed as multipart shafts which are separated in the middle by another joint—Fig. 4.1a shows a multipart propeller shaft with intermediate shaft bearing. © Springer-Verlag GmbH Germany, part of Springer Nature 2023 M. Hilgers, Transmissions and Drivetrain Design, Commercial Vehicle Technology, https://doi.org/10.1007/978-3-662-65860-4_4

43

44

4  Propeller Shaft(s)

a Intermediate shaft bearing

Length adapter

Universal joint (cardan joint)

Flange

b

Major assembly tilted for installation

Suspension movement of the axle Longitudinal compensation

Deflection angle

Assembly axes in different planes

Deflect angle

Fig. 4.1   a Propeller shaft for heavy trucks with three universal joints, longitudinal compensation and intermediate shaft bearing. (Photo: Daimler). b Geometry of the propeller shaft and its installation in the vehicle

If the vehicle is equipped with an axle through-drive (two driven rear axles) or a transfer case (driven front axle), several propeller shafts are required—see Fig. 2.18.

5

Retarders

Retarders are wear-free brakes that can be fitted in the vehicle besides the normal disc brake and the engine brake. The braking effect of the retarder depends on the rotating speed of the component that is to be braked: the faster this component is rotating, the more powerful the braking effect is.

5.1 Secondary and Primary Retarder The retarder is often located at the transmission output or on the propeller shaft. If the retarder is located behind the transmission it is called a secondary retarder. This location enables a higher braking effect when the wheels and the transmission output are turning rapidly. At low speeds the braking effect is lower. The currently selected transmission gear does not influence the braking effect of the secondary retarder. The braking effect is also preserved while shifting gears. Another benefit of secondary retarders is that the braking torque of the secondary retarder does not burden the transmission. Besides the secondary retarder, primary retarders also exist. These are located before the transmission. The braking effect does not depend on the wheel speed only, but on the wheel speed multiplied with the selected gear ratio of the transmission (this is basically the engine speed). Primary retarders only contribute to braking when the clutch is closed, a gear has been selected and hence the retarder is connected to the rear axle(s). As a result, the braking effect of the primary retarder can be changed by gear changes. So the primary retarder is able to provide good braking effect in the lower speed range if a low gear with high transmission ratio is selected.

© Springer-Verlag GmbH Germany, part of Springer Nature 2023 M. Hilgers, Transmissions and Drivetrain Design, Commercial Vehicle Technology, https://doi.org/10.1007/978-3-662-65860-4_5

45

46

5 Retarders

Fig. 5.1   a) Left side: (Secondary) oil retarder for HD trucks (Foto: Voith 2018). b) Right side: Assembly of a HD truck transmission with a retarder flanged to it (Foto: Scania 2010). The two pictures show different retarder brands. Heat exchanger and coolant connection can be seen on both pictures

5.2 Hydrodynamic Retarders Figure 5.1 shows hydrodynamic retarders. The principle of the hydrodynamic retarder is as follows: The retarder has a rotating impeller, the rotor. The rotor rotates inside a housing. If the braking effect is needed, the housing is flooded with a fluid so that the rotor rotates in the fluid and accelerates it. In standard hydrodynamic retarders, the fluid used is oil. The retarder also houses a stator, against which the fluid is thrown and which directs the fluid stream. The fluid is slowed down in the stator. The rotor transmits its kinetic energy to the fluid, the movement of the rotor encounters strong resistance and slows down. In order to achieve the most effective design possible for the retarder, its internal geometry is shaped according to its intended purpose. The rotor is also shaped to achieve the maximum braking effect. Finally, the kinetic energy of the rotor is converted into thermal energy. As the rotor (and the vehicle) brakes, the retarder fluid and the retarder housing heat up. This heat must be dissipated. When braking, conventional retarders pump the retarder fluid through a heat exchanger, which transfers heat to the engine cooling system.1 Various retarder stages are controlled by incremental regulation of the amount of fluid that is fed into the active retarder volume. The permanent braking performance of the retarder is limited by the capacity of the cooling system. When the cooling system is unable to absorb any more heat because the refrigerant water has reached its maximum temperature, the retarder braking effect must be reduced to avoid damaging the vehicle.

1 There

are also secondary retarders which are integrated in the oil circuit of the transmission. They are marketed under the brand name Intarder (MAN), for example.

5.3  Inductive Retarders

47

When the braking action is completed, the fluid is expelled from the rotor–stator chamber of the retarder again. This pumping action is performed by the scooping effect of the rotor itself. When the retarder is freewheeling (no braking action is requested), the rotor rotates through the air in the retarder housing. This movement too has a slight (undesirable) braking effect. In order to keep this effect as small as possible, low power-loss retarders are available in which the rotor is pushed away from the stator by a spring. So the air can circulate in the chamber almost entirely unobstructed. Unwanted power-loss can be further reduced if the retarder is decoupled when not needed for braking.

5.2.1 Coolant Retarders Weight optimized retarder concepts work directly with the refrigerant water from the engine’s cooling circuit as working medium. There is no dedicated oil circuit for the retarder. The heat exchanger between the oil circuit and the engine’s refrigerant water circuit is no longer needed. Furthermore, the retarder oil and the oil reservoir are not needed anymore. This saves weight and costs and the costs of maintaining the retarder oil. [15] shows an example of a primary retarder with water as the working medium.

5.3 Inductive Retarders The inductive brake uses so called eddy currents for braking. Those inductive currents are produced in conductors (metal parts) that move through magnetic fields. The principle of induction is as follows: If an electrical conductor moves perpendicular to a magnetic field a voltage difference is induced in this metal (induction). As a result of this voltage, eddy currents flow through the conducting material. According to Lenz’ rule the emerging eddy currents generate their own magnetic field that brakes the movement of the conductor in the external magnetic field. The electrical resistance of the conductor forms an ohmic load for the eddy currents and the conductor will heat up. So the kinetic energy of the moving parts is converted into heat. The heat is dissipated into the environment. Eddy current brakes are widely used in railway technology as well.

5.3.1 Retarders with Permanent Magnets In retarders with permanent magnets [14], powerful permanent magnets are located in the stator. The stator is also equipped with a collar of displaceable pole pieces—or the magnets are movable and the pole pieces are fixed in place. These can be moved to various positions relative to the permanent magnets. The magnetic field lines of the permanent magnets pass through the rotor or not, depending on the position of these pole

48

5 Retarders

pieces. If the field lines do pass through the rotor, according to Lenz’s law, a Lorentz force is induced in the rotor. This Lorentz force acts in the opposite direction to the direction of movement, meaning that it attempts to slow the movement of the rotor (see [2] or any other good physics textbook). Figure 5.2 illustrates the principle of this retarder. The rotor is heated by the current induced in the rotor. So the kinetic energy is converted into thermal energy. For this reason, the rotor has a ribbed structure so that it can discharge as much heat as possible to the ambient air. The construction of the permanent magnet retarder offers the following benefits: low weight and relatively simple integration in the vehicle.

5.3.2 Retarders with Electromagnets Powerful eddy current brakes are created with electromagnets. The braking principle is the same as for the permanent magnet retarder: when braking is initiated, the magnetic field lines pass through the rotor and generate a force in the opposite direction to the direction of movement of the rotor. In this case, however, the magnetic field is generated with coils (electromagnets). If the driver or the vehicle’s electronic brake management systems calls on the braking effect of the retarder, the coils are energized and the required magnetic field is generated. The brake force is switched off when the electric current to the coils is interrupted.

Fig. 5.2   Principle of the retarder with permanent magnets

Comprehension Questions

The comprehension questions serve to test how much the reader has learned. The answers to the questions can be found in the sections to which the respective question refers. If it is difficult to answer the questions, it is recommended that you read the relevant sections again. A.1 Driving Resistance (a) What forces contribute to driving resistance? (b) How are these forces related to speed? (c) How is the required engine output calculated from this relationship? A.2 Task of the Transmission Why does a vehicle need a transmission? A.3 Direct Drive Transmission (a) What is direct drive in a commercial vehicle transmission? (b) What advantage does a direct drive transmission offer? (c) Why is it recommended for the highest gear to be a direct drive gear (in long-distance haulage)? A.4 Reverse Gear (a) How does the reverse gear work? (b) How does the flow of force in Figs. 2.13 and 2.14 proceed when reverse gear is engaged? A.5 Spread (a) What is the spread of a transmission? (b) By what is the necessary total spread of transmission determined? (c) Why do torque converter transmissions function successfully with only a low spread in the transmission?

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Comprehension Questions

A.6 Losses in the Transmission (a) How is energy lost in the transmission? (b) Where does this energy go? A.7 Drivetrain (a) What additional components does a vehicle with driven front axle(s) need? (b) What movements must the propeller shaft compensate for? A.8 Torque and Engine Speed (a) Explain the conversion of torque in the transmission. (b) How are engine speed and travel speed related? A.9 Retarders (a) What advantages does a retarder provide? Are there also disadvantages? (b) What operating principles are used for retarders? A.10 Power Take-Off (a) What are power take-offs needed for? (b) What power take-offs are there? A.11 Terminology Explain the following terms: (a) Traction limit, (b) Traction hyperbola, (c) Synchronization.

Abbreviation and Symbols

The following is a list of the abbreviations used in this booklet series. The letters assigned to the physical variables are in conformity with the normal usage in engineering and natural sciences. The same letter can have different meanings depending on the context. For example, lower case c is a very busy letter. Some abbreviations and symbols have been subscripted to avoid confusion and improve the readability of formulas, etc. Lowercase Latin Letters a

acceleration

c

coefficient, proportionality constant

cd

coefficient of aerodynamic drag

f

coefficient or correction factor

g

gravitational acceleration (g = 9.81  m/s2)

g

gram—unit of mass

h

height (measure of length)

hp

horsepower, unit of power (not a SI unit); 1 hp = 735.5 W

i

transmission ratio, engine speed ratio

k

kilo = 103 = multiplication factor of 1000

kg

kilogram—unit of mass

km/h

kilometers per hour – unit of speed; 100 km/h = 27.78  m/s

kW

kilowatt—unit of power; 1000 watts

kWh

kilowatt-hour—unit of energy

l

length

l

liter, unit of volume; 1 l = 10–3 m3

m

mass

m

meter, unit of length

© Springer-Verlag GmbH Germany, part of Springer Nature 2023 M. Hilgers, Transmissions and Drivetrain Design, Commercial Vehicle Technology, https://doi.org/10.1007/978-3-662-65860-4

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Abbreviation and Symbols

m

milli = 10−3 = a thousandth part

n

rotational speed

r

radius (measure of length)

rpm

revolutions per minute; unit of angular velocity

s

route (linear measurement)

t

ton - unit of mass; 1 t = 1000  kg

v

speed

z

number of teeth (on a transmission gearwheel)

Uppercase Latin Letters A

area, particularly frontal face area

E

energy

F

force

FG

weight force

J

joule, unit of energy

M

torque

M

mega = 106 = Million

MJ

megajoule, unit of energy—one million joules

N

newton, unit of force

P

power

W

mechanical work or mechanical energy

Wkin

kinetic energy (motion energy)

W

watt, unit of power

Lowercase Greek Letters α

(alpha) angle

β

(beta) angle

λ

(lambda) angle

µ

(mu) coefficient of friction

µ

stands for micro = 10–6 = a millionth

ρ

(rho) density

φ

(phi) angle

φ

stage increment in the transmission difference between the transmission ratios of two adjacent gears

ω

(omega) angular velocity

ω

engine speed

References

General Reference Works 1. Lechner, G., Naunheimer, H.: Fahrzeuggetriebe – Grundlagen, Auswahl, Auslegung und Konstruktion. Springer, Berlin (1994) 2. Kneser, G.C.H.O., Vogel, H.: Physik – Ein Lehrbuch Zum Gebrauch neben Vorlesungen. Springer, Berlin (1989) 3. Hilgers, M.: Chassis and axles. Commercial vehicle technology. Springer, Berlin (2021) 4. Hilgers, M.: Electrical systems and mechatronics. Commercial vehicle technology. Springer, Berlin (2021) 5. Hilgers, M.: Fuel consumption and consumption optimization. Commercial vehicle technology. Springer, Berlin (2021)

Technical Articles 6. Mercedes-Benz: The new Antos, heavy-duty distribution. 18–44 tonnes GCW (2012). Technical data from product brochure 7. Vollmar, J., Köllermeyer, A., et al.: Mercedes Powershift – neue Generation automatisierter Schaltgetriebe. ATZ Automobiltechnische Zeitschrift 2008(January), 38 (2008) 8. Reichenbach, M.: Getriebeinnovationen auf der 58. IAA. ATZ Automobiltechnische Zeitschrift 2000(November), 934 (2000) 9. DIN ISO 7649: Clutch housings for reciprocating internal combustion engines – Nominal dimensions and tolerances (1992) 10. DIN ISO 7648: Flywheel housings for reciprocating internal combustion engines – Nominal dimensions and tolerances (1988) 11. Dräger, C., et al.: Das Kegelringgetriebe– Ein stufenloses Reibradgetriebe auf dem Prüfstand. ATZ Automobiltechnische Zeitschrift 1998(September), 640 (1998) 12. Eaton: Service Manual: Fuller Heavy-Duty Transmissions TRSM0670 EN-US (2013). http:// www.roadranger.com/rr/CustomerSupport/Support/LiteratureCenter. Accessed: Aug. 2013 13. Becke, M., et al.: Das Antriebskonzept des Mercedes-Benz Actros SLT. ATZoffhighway Special issue of ATZ 2009(March), 58 (2009) 14. Voith Turbo SMI Technologies GmbH & Co KG: Prospekt: Der neue Voith Magnetarder. So leicht kann besser bremsen sein (2010)

© Springer-Verlag GmbH Germany, part of Springer Nature 2023 M. Hilgers, Transmissions and Drivetrain Design, Commercial Vehicle Technology, https://doi.org/10.1007/978-3-662-65860-4

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References

15. Heilinger, P., et  al.: Bremsen mit Wasser – Der neue Aquatarder von Voith. Automobiltechnische Zeitschrift ATZ 105(4/2003), 354 (2003) 16. Tochtermann, J., et  al.: Integrierte elektrische Lkw-Achse für den innerstädtischen Verteilerverkehr. ATZ Automobiltechnische Zeitschrift 2017(November), 60 (2017) 17. Schey, A., Tryon E.: Compact electric axles for commercial vehicles. ATZ heavy duty worldwide 2021/04, 20 (2021) 18. Witzig, J. et al.: Electric central drive for commercial vehicles. MTZ worldwide 2018/10, 16

Index

A Aerodynamic drag, 2 Automated Manual Transmission (AMT), 30 Automatic transmission, 32 Axle ratio, 5

Direction of rotation, 1 Direction reversal, 11 Double-disc clutch, 39 Drivetrain of the electric truck, 9 Dry clutch, 37

B Bearing friction, 21 Brake, wear-free, 45

E E-axle, 9 Economy mode, 31 EcoRoll function, 31 Eddy current brake, 48 Electric Truck, 9 Elements, hydrodynamic, 39 Engine speed range, 5 Engine torque, 7 Epicyclic gear system, 22 Equalizing output hyperbola, 3 Excess tractive force, 4

C Cable, 29 Carrier, 22 Center distance, 14 Characteristic, 4 Climbing capability, 7 Clutch, 1 Coefficient of friction, 8 Constant, 22 Constant mesh transmission, 16 Control unit (ECU), 30 Converter rise, 40 Countershaft, 14 Crawler, 29 Crawler gear, 29

D Deflection angle, 43 Diaphragm spring, 37 Direct drive, 19, 20 Direct-drive transmission, 5

F Fixed wheel, 13 Friction, 20 Friction clutch, 37 Full load curve, 5

G Gear, 13 direct, 6 half, 21 Gear drive, 11 Gear ratios, 13

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Index

Gearshift system hydraulic, 29 internal, 14, 29 Gear stick, 29 Gear wheel pair, 13 Gradient, 3

P Planetary gears, 23 Power mode, 31 Power take-offs, 32 Primary retarder, 12, 45, 47 Propeller shaft, 43

H Heat, 21 Heavy goods transportation, 41 High-gear transmission, 5, 19

R Range-change transmission, 27 Range group, 24 Range-splitter gearbox, 25 Reserve force, 7 Retarder, 45 Retarder with permanent magnets, 47 Reversal of rotating direction, 17 Reverse gear, 17 Rev range, 6 Ring gear, 22 Rocking mode, 31 Rolling resistance, 2 Rotational speed converter, 4

I Idler gear, 13 Incrementing, geometric, 26 Incrementing, progressive, 26

K Kickdown function, 31

L Lenz’s law, 48 Lock-up clutch, 40 Lorentz force, 48 Loss, 20 Losses in the transmission, 21 Losses load-related, 21 non-load related, 21

M Main transmission, 13 Maneuvering mode, 5, 31 Maneuvering speed, 6 Motion resistance, 2

O Oil pump, 21 Overall transmission spread, 5 Overdrive transmission, 19

S Secondary coolant retarder, 47 Secondary retarder, 45, 46 Shift operations, without interruptions in tractive force, 32 Shift rod, 15 Sliding sleeve, 14 Split group, 21 Spur gear transmission, 17 Stage increment, 20 Sun, 22 Synchronizer, 16 Synchronizer unit, 14

T Telescopic gearshift system, 29 Three-shaft transmission, 18 Tooth numbers, 17 Torque converter, 4 Torque converter clutch, 32 Torque rise, 40 Traction limit, 8

Index Tractive force hyperbola, 3 Transfer case, 33 Transmission automated manual, 29 single-stage, 13 Transmission ratio, 5 Transmission ratio i, 4, 19

57 U Universal joint, 43

W Wheel diagram, 17, 28 Willis equation, 23