Vehicle Technology: Technical foundations of current and future motor vehicles 9783110595703, 9783110595697

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Dieter Schramm, Benjamin Hesse, Niko Maas, Michael Unterreiner Vehicle Technology

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Dieter Schramm, Benjamin Hesse, Niko Maas, Michael Unterreiner

Vehicle Technology Technical Foundations of Current and Future Motor Vehicles

Authors Prof. Dr.-Ing. Dr. h.c. Dieter Schramm Universität Duisburg-Essen Fakultät für Ingenieurwissenschaften Lotharstr. 1 47057 Duisburg www.imech.de/vehicle_technology Dr.-Ing. Benjamin Hesse Ford Werke GmbH 50735 Köln

Dr.-Ing. Niko Maas Universität Duisburg-Essen Fakultät für Ingenieurwissenschaften Lotharstr. 1 47057 Duisburg

Dr.-Ing. Michael Unterreiner Porsche AG Porschestr. 911 71287 Weissach

ISBN 978-3-11-059569-7 e-ISBN (PDF) 978-3-11-059570-3 e-ISBN (EPUB) 978-3-11-059346-4 Library of Congress Control Number: 2020931121 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2020 Walter de Gruyter GmbH, Berlin/Boston Cover image: metamorworks / iStock / Getty Images Plus Typesetting: Integra Software Services Pvt. Ltd. Printing and binding: CPI books GmbH, Leck www.degruyter.com

Contents Preface 1 1.1 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.1.6 1.2 1.2.1 1.2.2 1.2.3 1.3 1.3.1 1.3.2 1.4 1.5 2 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.3 2.3.1 2.3.2 2.3.3

XVII Introduction and overview 1 Basic terminology 1 Definition of the term motor vehicle 1 Life cycle of a vehicle 2 Motor vehicles as part of the energy chain 3 Vehicle categories and segments 4 Vehicle types according to drive type 5 Registration and production figures 5 Configuration of a vehicle 7 Vehicle assembly groups and component configuration 9 Important dimensions and vehicle packaging 11 The vehicle as part of the transport system 12 Product and technology development process in the automotive industry 13 New product development process 13 Automotive industry’s share of technical innovation 18 Automotive standards and conventions 19 Historic development of selected parameters 22 Wheels and tires 25 Tire structure 25 Structure of the radial tire 25 Avoidance of punctures and tires with emergency running properties 27 Comments on the manufacturing process of a tire 28 Tire labeling 29 Basic tire characteristics 30 Viscoelastic behavior 30 Rubber friction 32 Rolling resistance 35 Transmission of vertical forces 36 Influence of tire inflation pressure on tire properties 38 Influence of temperature on tire properties 42 Conflicting goals of tire development 43 Mathematical description of tire forces 44 Classification of tire forces 44 Tires under the influence of vertical forces 45 Tires under the influence of longitudinal and lateral forces

46

VI

2.3.4 2.3.5 2.3.6 2.3.7 2.3.8 2.3.9 2.4 2.4.1 2.4.2 3 3.1 3.2 3.3 3.4 3.4.1 3.4.2 3.4.3 3.5 3.5.1 3.5.2 3.5.3 3.5.4 3.5.5 3.5.6 3.5.7 3.6 3.6.1 3.6.2 3.7 3.7.1 3.7.2 3.7.3 3.7.4 3.8 3.8.1 3.8.2 3.8.3 3.8.4 3.9

Contents

Impact of the tire’s normal forces 54 Influence of the camber on the lateral tire force Mathematical tire models 56 Superposition of horizontal forces 59 Instationary tire forces 61 Dynamics of the braked and driven wheel 63 Monitoring of the tire pressure 65 Direct tire pressure monitoring 65 Indirect tire pressure monitoring 69

56

Vehicle dynamics and suspension system 73 General definitions of vehicle motion 73 Coordinate systems 75 Structure and components of the chassis 77 Axle kinematic properties 79 Toe in angle 80 Camber angle 82 Steering axis 83 Fundamentals of vehicle dynamics 85 Description of the planar vehicle dynamics using the linear single track model 85 Equations of motion of the linear single track model 86 Stationary steering behavior and circular drive 92 Transient steering behavior and driving stability 96 Influence of vehicle body roll 97 Quasistatic calculation of dynamic wheel loads 103 Effect of wheel load transfer on cornering behavior 104 Description of fundamental properties of dynamics in the general case 106 Stationary driving behavior 107 Instationary driving behavior 112 Standard driving maneuvers 116 Maneuver steady-state circular drive 117 Frequency response 118 Step-steer input 119 Double lane change 119 Chassis systems and suspensions 120 Overview of the characteristics of wheel suspensions 120 MacPherson spring-strut axle suspension 123 Multilink wheel suspension 124 Examination of the wheel suspension motion 126 Three-dimensional modeling of wheel suspensions 130

Contents

3.9.1 3.9.2 3.9.3 3.10 3.10.1 3.10.2 3.10.3 3.10.4 3.10.5 3.10.6 3.10.7 3.10.8 3.10.9 4 4.1 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.3 4.4 4.4.1 4.4.2 4.5 4.5.1 4.5.2 4.5.3 4.6 4.6.1 4.6.2 4.7 4.7.1 4.7.2 4.8 4.8.1 4.8.2 4.8.3 4.8.4 4.8.5 4.9

Kinematic models 131 Dynamic models 132 Elastokinematic models 133 Vertical dynamics 134 Vertical dynamic requirements of the chassis Roadway excitation 134 Wheel vertical dynamics 138 Body springs 138 Body damper 144 Stabilizers 145 Description of vertical dynamics 147 Objectification of vibration comfort 151 Oscillation frequency of wheel, seat, and body

134

155

Vehicle steering 157 Technical requirements of vehicle steering systems 158 Driver–vehicle interaction and steering feel 159 Basic requirements for steering systems 159 Assessment criteria for steering systems 161 Subject study and press analysis 162 Results of the press analysis on steering systems 163 Common designs of steering systems 164 Interpreting steering kinematics 166 Ackermann steering kinematics 166 Dynamic approach to steering kinematics 168 Components of the steering system 170 Steering wheel 170 Steering column and intermediate steering shaft 171 Steering rack 173 Parameters of the steered wheels 174 Definition of geometric parameters of the wheel 175 Changes in geometric parameters during cornering 177 Steering transmission 179 Ratio of the steering gear 181 Ratio of the steering linkages 181 Steering torques for conventional steering systems 186 Steering rack forces 186 Drilling torque 186 Drilling torque during stationary steering 188 Steering rack forces for large steering angles 190 Steering rack force during parking 190 Simplified model of rack and pinion steering 191

VII

VIII

4.10 4.10.1 4.10.2 4.10.3 4.11 4.11.1 4.12 4.12.1 4.12.2 4.12.3

Contents

Power steering assistance systems 195 Hydraulic power steering 196 Electrohydraulic power steering 197 Electromechanical power steering 198 Use of test benches for the development of steering systems 207 Example: test bench for electromechanical steering systems 208 Innovative approaches to vehicle steering 211 Superimposed Steering 211 All-wheel steering 212 Steer-by-wire 213

5 5.1 5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6 5.3.7 5.3.8 5.4 5.5 5.5.1 5.5.2 5.6 5.6.1 5.6.2

Braking systems 217 Structure of the braking system 217 Different implementations of braking systems 217 Design types 218 Functionality 219 Ideal brake force distribution 220 Failure of a brake circuit 225 Assembly components of the braking system 226 Overview and functionality 226 Brake pedal and master brake cylinder 231 Brake booster 232 Drum brakes 234 Disc brakes 236 Brake discs 237 Brake pads 237 Thermal behavior of brakes 238 Brake circuit layout 239 Braking process 240 Reaction and response times 240 Braking distances 241 Servo brakes 243 Electrohydraulic brakes (EHB) 243 Electromechanical brakes (EMB) and brake-by-wire systems

6 6.1 6.2 6.2.1 6.2.2

Propulsion systems 247 Basic types of powertrains 247 Propulsion requirements for motorized vehicles Driving resistance 249 Wheel resistance 251

248

244

Contents

6.2.3 6.2.4 6.2.5 6.2.6 6.2.7 6.3 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5 6.5 6.5.1 6.5.2 6.6 6.6.1 6.6.2 6.6.3 6.6.4 6.7 6.7.1 6.7.2 6.7.3 7 7.1 7.1.1 7.1.2 7.1.3 7.1.4 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.3 7.3.1 7.3.2 7.4 7.4.1 7.4.2

Air resistance (Drag) 253 Gravitational resistance (inclines) 254 Inertial resistance 255 The traction force equation 255 Ideal drive- and output mapping 259 Tangential force transfer tire-road contact 260 Power sources 262 Combustion engines 262 Electric traction drives 274 Power electronics 279 Hybrid drives 281 Implementing powertrains in the vehicle 288 Transmissions and shafts 288 Gears 288 Power losses in the drivetrain 290 Energy consumption 291 Determining energy consumption 292 WILLANS curves 293 Identification of different driving states 294 Driving cycles 295 Energy sources and storage 303 Fossil fuels 303 Alternative fuels 305 Electrical energy storage 306 Vehicle safety 317 Areas of vehicle safety 317 Definitions 317 Systems of active safety 319 Systems of passive safety 320 Legal rules and regulations 322 The role of the vehicle structure 325 Example frontal crash 328 AZT/RCAR test 328 FF (full frontal) 329 ODB (offset deformable barrier) 329 Basic course of a frontal collision 330 Physical considerations concerning the frontal crash Parameters for accident severity 332 Restraint systems 333 Seat belts and pretensioners 334 Airbag systems 336

330

IX

X

7.4.3 7.5 7.6 7.6.1

Contents

Trigger sensors and algorithms 341 Passenger detection 344 Vehicle roll-over 344 Physical considerations concerning the tipping of vehicles 346

8 Automotive electrical system 349 8.1 Energy powernet 350 8.1.1 History 350 8.1.2 Structure and mode of operation of today’s powernets 353 8.2 Energy storage 362 8.2.1 Starter batteries 363 8.2.2 Characteristics and guidelines for lead-acid batteries 368 8.3 Modeling of the battery behavior 373 8.4 Alternators in motor vehicles 378 8.4.1 Design of vehicle alternators 379 8.4.2 Efficiencies of vehicle alternators 380 8.5 Simplified model of a vehicle alternator 381 8.5.1 Electrical machine 382 8.5.2 Rectifier 385 8.5.3 Voltage regulators 386 8.5.4 Alternator load torque 387 8.6 Electrical consumers of the powernet 387 8.7 Approaches for an energy management 389 8.8 Electrical signal transmission 391 8.8.1 Overview of bus systems in motor vehicles 392 8.8.2 Fundamental terms 394 8.8.3 Analog signal transmission 394 8.8.4 Bus topologies 395 8.8.5 Structure of a bus system 396 8.8.6 The bus protocol 397 8.8.7 The data frame 400 8.8.8 The bit stream 404 8.8.9 Bus media – physical layer 405 8.8.10 Examples of bus systems in motor vehicles other than CAN 407 9 9.1 9.2 9.2.1

Driving dynamics control systems and driver assistance systems 411 Definition of the term “driver assistance system” 412 Vehicle automation concepts 416 Classification according to the degree of automation 416

Contents

9.2.2 9.2.3 9.2.4 9.3 9.4 9.4.1 9.4.2 9.5 9.5.1 9.5.2 9.5.3 9.6 9.6.1 9.6.2 9.6.3 9.6.4 9.6.5 9.6.6 9.7 9.8 9.9

Semi-automated systems 417 Highly automated systems 419 Fully automated vehicles 420 Driver assistance systems vs. driving dynamics control systems 421 Human–machine interface 422 Sensory channels 422 Warning levels 424 Driving dynamics control systems 425 Anti-lock braking system 425 Traction control system 432 Electronic stability program 432 Driver assistance systems 435 Adaptive cruise control 435 Lane keeping assistant 443 Lane changing assistance (LCA) 446 Highway driving assistant 447 Pedestrian assistance 448 Parking assistance 452 Adapted design of vehicles for assisted driving 454 Future development trends 454 Legal possibilities and limits for autonomous driving 456

10 Driving simulators 459 10.1 Basic requirements for driving simulators 461 10.1.1 Perception and distinction when driving a car 463 10.1.2 Vehicle guidance and requirements to information sources in driving simulators 463 10.2 Classification and basic structure of driving simulators 464 10.2.1 Simulation 465 10.2.2 Driver’s workplace 466 10.2.3 Environment depiction 467 10.2.4 The motion system 468 10.3 Simulator experiment 470 10.3.1 Reasons for the use of simulators 471 10.3.2 Study design and implementation 472 10.3.3 Possible values from simulator experiments 473 10.3.4 The phenomenon of simulator sickness 474 10.4 Exemplary implementation of a driving simulator 476 10.4.1 Desktop simulator 477

XI

XII

10.4.2 10.4.3 10.4.4

Contents

Simulator with cockpit 478 Static driving simulator with full vehicle Dynamic driving simulators 480

Literature Index

489 505

479

Preface In the 125 years of its history, automobile technology has become extremely complex in many areas. This includes the development and production of technology, as well as methods of quality assurance. It has become an exemplary field of expertise, not only limited to pure engineering sciences. This development has significantly contributed to the fact that vehicle technology poses highly functional reliability and safety requirements on its products. This means that motor vehicles must always remain operational even under harsh environmental conditions. and in the event of a malfunction, it must in many cases be possible for inexperienced operators to restore them to a safe condition. In addition, the car is mass-produced to produce millions of units at comparatively low cost. Decades of improvement processes, as triggered by these requirements, have resulted in an extremely mature product group. As such, it is considered the model for many other products in terms of cost, function, and quality. Nevertheless, there are fields that are currently undergoing major changes in the area of vehicle technology. This applies, on the one hand, to the field of vehicle drive. The combustion engine, which is used for over 120 years, is, though not nearly completely, replaced in short and medium terms, but at least supplemented by electric drives. The technical reasoning behind this is part of a detailed discussion in Chapter 6. On the other hand, there is a continuing development driven by processes in electronics and sensor technology since the past decades: connected cars and (advanced) driver assistance systems, which include purely supportive systems, further to systems that allow highly automated and, in the long term, fully automated driving. This topic is covered in Chapter 9. As a result of the discussed developments, changes in the vehicle industry have become apparent in ways they have not been observed in the past (Dudenhöffer 2016) but also delivers new opportunities for the future (Schramm 2017). In addition to these specialized topics, the book also introduces basic topics within current vehicle technology. The basis of this book is a lecture series on automotive technology, which runs at the University of Duisburg-Essen for many years. Furthermore, some of the authors have contributed current research results from their dissertations and research projects as well as discussions of their experience from working with vehicle manufacturers. Furthermore, results of the dissertations and research work of Dr.-Ing. Jeannette Kerkhoff, née Heide, Dr.-Ing. Mira Schüller, Dr.-Ing. Michael Ried, Dr.-Ing. M. Koppers, Dr.-Ing. Frederic Kracht, Dr.-Ing. Dario Düsterloh, M. Sc. Georg Burkhard and Dipl.-Ing. Stephan Schweig are included in the book. We would also like to thank Dr. jur. Schneider for his contribution to the topic “legal boundary conditions of automated driving”. In addition, many other persons were involved in the preparation of the book; a special mention of which goes to Dr.-Ing. Frederic Kracht, based on his significant contribution to the organization of the book and coordination of the creation of https://doi.org/10.1515/9783110595703-203

XIV

Preface

illustrations. We would also like to thank Messrs. Neuhaus and Golovko for their thorough production of the illustrations and Mr. M. Sc. Driesch for his support in obtaining printing permissions. Duisburg, February 2020 Dieter Schramm, Niko Maas, Benjamin Hesse, and Michael Unterreiner

1 Introduction and overview In the 125 years of its history, automobile technology has become extremely complex in many areas. This includes the development and production of technology as well as methods of quality assurance. It has become an exemplary field of expertise, not only limited to pure engineering sciences. This development has significantly contributed to the fact that vehicle technology poses highly functional reliability and safety requirements on its products. In that sense, motor vehicles must remain operational under harsh environmental conditions. In addition, in case of fault, vehicles must be able to be brought back in a safe state by inexperienced operators. In addition, the car is made in mass production to produce quantities of millions of units at extremely low cost. Decades of improvement processes, as triggered by these requirements, have resulted in an extremely mature product group. As such, it is considered the model for many other products in terms of cost, function, and quality. Nevertheless, there are fields that are currently undergoing major changes in the area of vehicle technology. This applies, on the one hand, to the field of vehicle drive. The combustion engine, which is used for over 120 years, is though not nearly completely replaced in short and medium terms, but at least supplemented by electric and semielectric drives. The technical reasoning behind this is part of a detailed discussion in Chapter 6. On the other hand, there is a continuing development, driven by processes in electronics and sensor technology since the past decades: connected cars and the development of (advanced) driver assistance systems, which include purely supportive systems, further to systems that allow highly automated and, in the long term, fully automated driving. This topic is covered in Chapter 9. In addition to these specialized topics, the book also introduces the basic topics within current vehicle technology.

1.1 Basic terminology 1.1.1 Definition of the term motor vehicle According to Bundesministerium für Verkehr (2011)1 motor vehicles are “Non-permanent track-guided land vehicles moved by machine power.”

To keep the volume of the book manageable, only four-wheeled passenger cars will be considered. The book does not cover bikes, trucks, and buses. Nevertheless, some of the topics addressed are also applicable to these vehicle classes. 1 German Federal Ministry of Transport and Digital Infrastructure. https://doi.org/10.1515/9783110595703-001

2

1 Introduction and overview

1.1.2 Life cycle of a vehicle A vehicle is a product that is produced by an original equipment manufacturer (OEM) and is traditionally sold via a car dealer to a consumer. However, there are indications of change in this area as even as of today more and more new and used vehicles are being sold over the Internet. A large number of suppliers are usually involved in the manufacturing process. They are classified according to their position in the supplier pyramid in tier 1, tier 2, and so on and raw material supplier (Figure 1.1). However, this hierarchy is not always strictly preserved. Instead, for example, for electrical contacts, connecting parts and of course raw materials direct deliveries from tier 2, tier 3, and so on to OEMs are common.

Direct delivery OEM Tier 1 System and module suppliers Tier 2 Component and assembly suppliers Tier 3 Parts manufacturer

Figure 1.1: Supplier pyramid.

After a period of use, which is typically between 8 and 15 years, the vehicle is scrapped, or rather recycled to a large extent. Figure 1.2 illustrates this development and life cycle.

Concept definition

Development

Production

Figure 1.2: Development and life cycle of a vehicle.

Useful life

Recycling

1.1 Basic terminology

3

1.1.3 Motor vehicles as part of the energy chain Motor vehicles account for a considerable part of the world’s energy consumption of transport systems.2 In 2012, about 82% of the total energy consumption of transportation systems in Germany was due to road traffic (Figure 1.3).

Energy consumption/peta joule

3,000

2,500

2,000 Road traffic

1,500

Air traffic

1,000

Rail transport Coastal and inland navigation

500

0

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012 Year

Figure 1.3: Distribution of energy consumption for transport systems in Germany 1990–2012 (Umweltbundesamt 2015).

For the analysis of energy consumption, it has to be considered that only a small part of energy consumed is actually converted into kinetic energy. The process illustrated in Figure 1.4 uses several terms, which will be used repeatedly: – Well-to-tank: Energy supply. The book does not cover this topic in detail. – Tank-to-wheel: Energy consumption of the vehicle. This field of energy conversion chain is more relevant than ever before in the history of automobiles and therefore is included in much detail in several chapters of the book. – Well-to-wheel: Total energy consumption during vehicle use. Figure 1.4 describes the process of converting chemical primary energy into mechanical energy, which may be required several times to move the vehicle. In principle, this illustration may also apply to electrically driven vehicles. However, in this case, a possibility exists of replacing primary energy source with renewable

2 The proportion of total energy consumption (including, e.g., also industry and households) is much lower.

4

1 Introduction and overview

Usage–well-to-wheel

Primary energy source

Well-totank

Energy stored in the car

Tank-towheel

Wheel available energy

Figure 1.4: Energy consumption chain of a vehicle.

energies, at least in the long term. Furthermore, electric powertrains prove to be significantly superior in terms of their efficiency to all internal combustion engine drives. This will be explained in Chapter 6. In addition, the field of energy and raw material consumption, which is not considered yet, is essential in the production of the vehicle.

1.1.4 Vehicle categories and segments Even when focusing on passenger cars, the variety of vehicles to be considered is difficult to overview. In that sense, a classification into vehicle segments is usually carried out. This can be done according to different criteria. Hence, the KBA,3 as an example, does not follow a single formula for segment formation, but a combination of criteria: – external dimensions (length, height), – weight (maximum authorized mass), – engine (displacement), – power (maximum speed and acceleration), – luggage compartment (indicated load, variability), – seats (quantity), – seat height (front), – all-wheel drive (driven axles), – tail shape (variants), – vehicle category (for mobile homes), and – basic price. This results for Germany in the 10 segments listed in Figure 1.5. The graph shows that there is a strong trend toward the sports utility vehicles (SUV) segment, which is at the expense of the other vehicle segments.

3 KBA: German Federal Motor Transport Authority.

1.1 Basic terminology

23.8%

SUVs

15.7%

23.3% 25.6%

Compact class 14.5% 16.3%

Sub compact cars

11.9% 12.6%

Middle class 7.2%

VANs Mini Utilities Upper middle class

5

10.9%

6.7% 6.9% 4.9% 4.0% 4.0% 4.5%

2.7% Other (*) 2.5% 0.8% Luxury class 0.8% 0% 5%

10%

2017 2013

15%

20%

25% 30% Registration shares

Figure 1.5: Registration sharesa of passenger cars segments in Germany according to/as cited by KBA classification (*: including sports cars) in 2013 and 2017 (Radke 2018). a Rounded values.

1.1.5 Vehicle types according to drive type Due to the emergence of partially or fully electrically driven vehicles, a more detailed classification of vehicles according to the drive type is required (Table 1.1). Another distinction concerns the design of new vehicles with modified powertrains (see also Chapter 6). One refers to “Purpose Design” if a completely new vehicle is developed based on powertrain structures. Examples include the Nissan Leaf, the vehicle models by Tesla or BMW models i3 and i8. If a new drive train is integrated into an already existing design, one refers to “Conversion Design.” Examples include Daimler B-class, Volkswagen e-up, and e-Golf.

1.1.6 Registration and production figures To be able to assess the importance of the automotive industry and thus of motor vehicle technology, exploration of some key data sets is helpful. For example, in 2018, approximately 70.5 million passenger vehicles were produced worldwide (Figure 1.6), 18.71 million in the whole European Union, and thereof 5.12 million in Germany (OICA 2019). The development of the motor vehicle stock in Germany during the last decades is shown in Figure 1.8. The strong decline in 2008/2009 is attributable to the economic weakness at that time.

6

1 Introduction and overview

Table 1.1: Classification of motor vehicles according to the drive system used (see also Chapter 6). Designation

Acronym

Description

Internal combustion engine vehicle

ICEV

Motor vehicle conventionally powered by a combustion engine

Battery electric vehicle

BEV

Electric vehicle with batteries as energy storage

Range extended electric vehicle

REX

Electric vehicle with additional combustion engine for range extension

Hybrid electric vehicle

HEV

Vehicles with combustion engine drives and, simultaneously, electromotive drives. Charging of battery via combustion engine

Plug-in hybrid electric vehicle

PHEV

Similar to HEV, but battery is rechargeable via power grid

Fuel cell hybrid electric vehicle

FCHEV

Electric vehicle with fuel cells for energy supply

80 72.1 67.8

70 63.1 58.3

60 53.2 49.9

50 41.2

40

39.8 41.4

42

44.6

68.5

73.5 70.5

65.7

59.9

52.7 47.8

46.9

30 20 10 0

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Figure 1.6: Development of global automobile production in the years 2000 to 2018 (in millions) (OICA 2019).

To date (2019), only production figures for electrically powered motor vehicles have been reported that are well below the figures specified or targeted by individual governments. This applies in particular to the major automotive markets in China, the USA, and Germany (see Chapter 6). Therefore, while the number of conventionally powered vehicles registered worldwide has increased drastically over the past few years, driven among other things by the strong increase in motorization in China, the

7

1.2 Configuration of a vehicle

number of electrically powered vehicles in stock has lagged far behind the expectations (see Figure 1.7). This is mainly due to the high cost of batteries and the unusually low range of these vehicles for customers. However, a strong increase is expected in the future due to government measures in many countries and the strategic orientation of major vehicle manufacturers, not least due to the expected cost reductions for batteries. The latter will also result in larger batteries eliminating or at least greatly reducing the well-known range restrictions of BEVs, which will lead to improved market acceptance. Figure 1.8 shows an exemplary overview of the development of the stock of vehicles with conventional drive systems in Germany.

7,000,000 Number of electric cars worldwide

6,000,000

5,610,860

5,000,000 4,000,000

3,416,680

3,000,000 2,157,760 2,000,000

1,404,030 845,210

1,000,000 205,380

422,870

0 2012

2013

2014

2015

2016

2017

2018

Figure 1.7: Stock development of electric cars worldwide between 2012 and 2018 (ZSW 2019).

Of course, the total numbers are reflected in one of the major economic factors in consumer spending on passenger cars. In addition, the automotive industry is one of the most important sources of employment, especially in Germany. Conversely, a large proportion of consumer spending by German households, notwithstanding a stagnation in recent years, accounts for traffic, and an even greater part to motorized individual transport (Figure 1.9).

1.2 Configuration of a vehicle The entire vehicle is usually divided into assemblies, which are described in Section 1.2.1. Moreover, a common terminology for the dimensions and the socalled packaging of a vehicle exists, which provides a uniform language for technical descriptions of vehicles. Section 1.2.2 describes the most important and common measurement variables.

2004

13,352

15,473

9,338

6,860

45,023

< 1,399 ccm

2005

13,384

15,377

9,602

7,013

45,376

2006

13,460

15,325

9,918

7,387

46,090

Stock in thousands of pieces

2008

12,315

13,219

9,231

6,419

41,184

1,400–1,700 ccm

2007

13,604

15,219

10,282

7,464

46,570

2009

12,511

13,066

9,302

6,432

41,311

2011

13,412

12,681

9,613

6,587

42,292

1,800–1,999 ccm

2010

13,009

12,708

9,470

6,542

41,729

2012

13,841

12,699

9,752

6,625

42,917

2014

14,570

12,514

10,058

6,692

43,833

> 2,000 ccm

2013

14,206

12,638

9,916

6,658

43,418

Figure 1.8: Stock of motor vehicles in Germany (KBA). As of 2008 only registered vehicles without temporary shutdowns/decommissioning broken down by engine displacement ranges.

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000

2015

14,974

12,405

10,230

6,770

44,379

Total

2016

15,404

12,350

10,426

6,861

45,041

8 1 Introduction and overview

1.2 Configuration of a vehicle

9

Billion € 200 180 160 140

Purchase of vehicles

120 100 Goods and services for operation 80 60 Fuels and lubricants 40 20 Transport services 0 1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

Figure 1.9: Consumer spending for traffic in Germany, according to Kunert, Radke et al. (2012).

1.2.1 Vehicle assembly groups and component configuration 1.2.1.1 Vehicle assembly groups The essential assemblies for a vehicle are – chassis and wheels (see Chapters 2–4), – powertrain with engine and transmission gear (see Chapters 5 and 6), – vehicle body and safety systems (see Chapters 7 and 8), and – vehicle electrics and electronics (see Chapter 9). These assemblies can be assigned to the individual subassemblies and components of a vehicle. An overview of the allocation of individual components of a vehicle to the assemblies is given in Table 1.2. In terms of added value, there has been a steady shift away from mechanics to electrics and electronics over the past two decades. This trend is further intensified by electrification of vehicles as well as networking and massive sensory upgrades of new vehicles. 1.2.1.2 Topologic arrangement of components The vehicle topology describes the arrangement of essential components of the vehicle. Due to its significance and its structural scope, this includes, in particular,

10

1 Introduction and overview

Table 1.2: Typical assembly groups of a vehicle. Chassis and wheels

Powertrain

Vehicle body and safety systems

Vehicle electrics and electronics

Wheels and tires

Engine with auxiliary units

Frame, chassis

Battery, generator, starter

Wheel suspension Transmission gear, clutch, converter

Doors, hoods, roof

Wiring harnesses for power and information

Springs and dampers

Propeller shaft

Glazing

Lighting

Braking system

Differential

Seats

Servomotors

Steering system

Driveshafts

Pedals

Sensors and actuators

Antiroll bars

Restraint systems

Infotainment

Active elements

Instrumentation

Bearings

Bumper Vehicle fairing Air conditioning

the powertrain. The powertrain includes, in case of purely combustion engine drives, the combustion engine with its auxiliary units and the fuel reservoir (tank), the transmission gear as well as central and wheel-specific driveshafts. In case of HEVs, electric drive and storage systems are added. In case of a combination of both propulsion systems, a multitude of possible combinations for vehicles with more than one power source exists. This will be discussed in detail in Chapter 6. In recent decades, the combustion engine has been used almost exclusively as the sole driving source for traction in private transport. In essence, drive topologies have been established. They are depicted in Figure 1.10 (Braess and Seiffert 2011). In 75% of vehicles, the combustion engine is installed transversely at the front and the front axle is powered. This topology has benefits for the integration process as the motor is positioned exactly on the driven axle. Accordingly, there is no need for an additional drive shaft. The second most popular drive topology is the standard drive (16%). The front of the engine is installed longitudinally and powers the rear axle. This variant allows the installation of larger engines and allows for advantageous driving dynamics due to drive on the rear axle. With 3% and 4% market share, respectively, the all-wheel drive variants use the two presented drive topologies. Vehicles with rear or center engine have a small market share and together only make up about 1% of vehicles.

11

1.2 Configuration of a vehicle

Front-longitudinal

Front-lateral Front

Four-wheel

Front

Rear

Four-wheel

75%

3%

1%

16%

4%

Figure 1.10: Essential combustion engine powertrain topologies with corresponding market sharesa in Germany, according to Ried (2014) and Grote and Feldhusen (2012). a Rounded figures.

1.2.2 Important dimensions and vehicle packaging Regulations and definitions of main dimensions and the so-called packaging in vehicles are summarized under “vehicle dimension concept,” which defines essential characteristics of a vehicle (Roschinski, Hansis et al. 2008). The vehicle dimension concept includes the dimensions describing a vehicle with lengths (L), widths (W), heights (H), and angles (A) based on the nomenclature of (SAE 2009). The German Automobile Industry Association (VDA4) describes a dimensional exchange plan that contains all the basic vehicle dimensions of a model. The international variant is referred to as the GCIE5 (GCIE 2011). Figures 1.11 and 1.12 show the main dimensions of a vehicle of the exterior and interior (Braess and Seiffert 2011). The classification of vehicles in vehicle classes is based on the main dimensions of the exterior. However, due to the panoply of new vehicle concepts that have emerged in recent years and the resulting variety of models, the differences between vehicle classes are sometimes blurred, complicating a precise classification. Table 1.3 lists a possible classification into vehicle classes based on average values of the principal dimensions of the exterior and interior. For each vehicle class, a corresponding

4 VDA: Verband Der Automobilindustrie (Automotive Industry Association). 5 GCIE: Global Car Manufacturer’s Information Exchange Group.

12

1 Introduction and overview

Figure 1.11: Main dimensions of the exterior (Ried 2014), (Braess and Seiffert 2011).

Figure 1.12: Main dimensions of the interior (Ried 2014), (Braess and Seiffert 2011).

vehicle is given as an example. A commonly used reference mark is the seat reference point (SRP) of the manikin6 (Braess and Seiffert 2011).

1.2.3 The vehicle as part of the transport system The vehicle is an important part of the transport system, which consists of – private transport, – public transport, – public long-distance transport, and – nonmotorized private transport.

6 Manikin: CAD model of the human being which is mainly used in the automotive industry for anthropometric purposes and examinations.

1.3 Product and technology development process in the automotive industry

13

Table 1.3: Vehicle classification with example vehicles of main dimensions of the exterior and interior according to (Braess and Seiffert 2011). Subcompact Compact Lower middle class

Middle class

Upper middle class

Luxury class

Van

SUV

Example

Fiat 

Opel Corsa

VW Golf

BMW Audi A  series

MB VW BMW S-class Sharan X

Length L/mm

,

,

,

,

,

,

,

,

Width W/mm

,

,

,

,

,

,

,

,

Hight H-B/mm

,

,

,

,

,

,

,

,

Wheelbase L/mm

,

,

,

,

,

,

,

,

Distance SRP road surface H-/mm

















Distance SRP heel flat front H-/mm

















This book deals exclusively with passenger cars. However, regarding the importance of assistance systems, not only the behavior of the vehicle on the road but also the interaction between the driver and the vehicle must be considered as well as future developments, such as the communication between vehicles and the infrastructure. Therefore, there is a strong interaction between vehicle, driver, and environment (infrastructure; see Figure 1.13).

1.3 Product and technology development process in the automotive industry 1.3.1 New product development process In the automotive industry, every manufacturer typically runs its own process for developing a new vehicle. However, this proprietary process usually follows a typical pattern. The following exemplary presentation follows the procedure described in Düsterloh (2018). There also new approaches for a further optimization of the product development process and the complexity management can be found.

14

1 Introduction and overview

Perception

Driver Behavioral

Environment

• Navigation • Anticipation • Stability

Position

Motion

Velocity

Steering wheel

Forces

Friction

Communication Brake pedal

Acceleration

Road inclination

Drive pedal Wind

Vehicle Dynamics Figure 1.13: Interaction between vehicle, driver, and environment.

The development process for new products (NPD) can be divided into three basic phases (Figure 1.14). 1.3.1.1 Concept development During this phase, the vehicle concept is defined, developed, analyzed, and agreed upon. This phase normally lasts from 18 to 24 months. This timeframe suits a completely new vehicle. In case a new vehicle is based on a predecessor, the concept phase can dramatically shrink. This is true for all of the generic development phases. The concept phase often already sets ground for the market success of a vehicle. Considering that this phase starts about 4–5 years prior to production start, it is not an easy task to define what kind of vehicle will meet the future customers’ demands. 1.3.1.2 Series development In the phase of series development, the vehicle is developed from concept to series maturity and its function is validated. The duration of this phase is between 24 and 30 months.

Project Phase

Key Milestones

Functional Safety

Vehicle Phase

ProjectDefinition

ConceptDefinition

Design Specification

Procurement Release

Testing

Design Approval

Testing

Virtual methods have proven design readiness for prototype build

Parts Availability Preproduction Production Series Series for Production

Procurement Build-Up

Building Steps Release

Project Scheduling

Simulation (digital twin), virtual validation and optimization

Testing

Danger and Risk Analysis - D&R

Failure Mode and Effect Analysis - FMEA

Procurement Build-up

ProjectFeasability

24–30 months

18–24 months

Project Scheduling

Project Fact Sheet

Serial development

Figure 1.14: Simplified representation of a product development process.

Full System Release

Concept development

SOP Market Launch

4–6 months

Production start-up

1.3 Product and technology development process in the automotive industry

15

16

1 Introduction and overview

The series development starts after the concept development if all the concepts have proven to meet future demands and the intended vehicle promises return on invest (ROI). The development phase itself is often subdivided into several parallel and serial tasks. Figure 1.14 shows building and testing phases that are used to build up prototype vehicles and then use them to validate the system behavior. Today’s development cycles of the automotive industry vastly use virtual methods to build virtual prototypes (digital twins). These simulation models are then used to validate the system behavior prior to availability of physical prototypes. This method enables the developers to save time and cost but also to check more possible designs and therefore optimize the entire vehicle. The development phase could be subdivided into virtual and physical phases. Often the physical prototype phase will only be entered if the virtual methods have proven that no major issues exist. The goal today is to increase the product maturity as much as possible only using virtual methods before building few prototypes to finally sign off the vehicle. 1.3.1.3 Production start-up In the last 4–6 months of the development process, the production start-up phase begins, and the first vehicles are already produced with series tools. Key milestones are defined within the product development process. These key milestones represent a binding framework for the timely and technical objectives for all company stakeholders. In particular, the technical and economic objectives defined for each of the following main milestone must be met. Project fact sheet The key milestone set up of the project fact sheet defines the strategic and technical product positioning. In addition to defining the target vehicle segment, this includes the estimation of sales figures. It is becoming increasingly important to exploit synergies concerning the configuration variants in order to achieve economic goals in particular. However, it is also important to differentiate the new vehicle from other vehicles in the same modular building blocks. Project definition In order to achieve this key milestone, the desired characteristics of the vehicle as well as the financial target values must be defined in the project definition. In addition, a first version of the specifications must be available here at the latest. The requirement specification contains a technical product description of the target vehicle.

1.3 Product and technology development process in the automotive industry

17

Project feasibility Both the technical and the economic feasibility of the development project must be confirmed here by all the relevant business units. The location of the planned production and the first suppliers for front-loading volumes will also be determined here. Front-loading volumes are components or assemblies that, due to their high complexity of content or innovative functional concepts, require an advanced, intensive concept validation to achieve a quality suitable for testing in the series phase. Concept definition The key milestone concept definition concludes the concept phase. This assumes that the vehicle concept can be confirmed. In particular, the interior and exterior dimensions must be defined. In addition, estimates of the equipment ratios of optional extras must be available. An important and indispensable point is that the manufacturability of the vehicle can be confirmed by production. Design specification The existence of an exterior and interior design with the package and the technical feasibility both for the development and the production are the prerequisite for the successful achievement of the milestone design definition. In addition, the specification sheet, which contains all requirements for the vehicle, is confirmed. Parts availability for production The key milestone parts availability for production confirms the required availability and quality of parts to manufacture the product in terms of market launch planning. Preproduction series The prerequisite for reaching this key milestone is the availability of a first preseries vehicle. In order to optimize manufacturing facilities and production processes, the construction for high-priority volumes is to be carried out using the manufacturing facilities for series production. In this way, problems in production or dimensional accuracy can be identified and eliminated at an early stage. Production series This is where the production processes are coordinated and optimized. Components and parts with series properties are installed in the vehicles. In addition, the function of operating resources and systems under production conditions on concatenated lines have to be tested and confirmed.

18

1 Introduction and overview

Start of production (SOP) When this key milestone is reached, the vehicles can be manufactured for press events, trade fairs, and dealers. The series ramp-up will end approximately 3 months after the SOP. Market launch This is the latest time at which the vehicle is presented to the trade and to customers. Some of the new vehicles can even be ordered before they go into series production. The time for the presentation to the public depends on when there are, for example, big fairs.

1.3.2 Automotive industry’s share of technical innovation Already at the introduction of this chapter, reference was made to the economic importance of the automotive industry. However, the automotive industry also plays a significant role in technical innovation. One way to measure innovation performance is to count the number of patent applications filed in a particular area of industry. Figure 1.15 shows an overview of the number of patent applications in

4038

Robert Bosch GmbH Schaeffler Technologies AG & Co. KG

2383

Ford Global Technologies LLC

2047

Bayerische Motoren Werke AG

1776

Daimler AG

1588

Audi AG

1266

ZF Friedrichshafen AG GM Global Technology Operations LLC Volkswagen AG

1157 1128 1077

Siemens AG

972

Continental Automotive GmbH BSH Hausgeräte GmbH

542 533

FANUC Corporation

527

Toyota Jidosha K.K.

520

Dr. Ing. h.c. F. Porsche AG

503 0

500

1,000

1,500

2,000 2,500

3,000 3,500

4,000

4,500

Figure 1.15: Most important companies by number of patent applications filed with the German Patent and Trade Mark Office in 2017, (DPMA 2019).

1.4 Automotive standards and conventions

19

Germany for 2017. This illustration immediately shows that the vast majority of patent applications at least in Germany are filed by companies that are either directly active in the automotive industry or have at least a large part of their business in this sector.

1.4 Automotive standards and conventions For the development, production, and operation of motor vehicles, a large number of standards and legal regulations that are subject to both international and national specifications exist. The following sections only list a selection of these regulations that play an important role for the topics covered in this book. A selection of the automotive standards cited in the book is listed in Table 1.4. For more selected references to standards in the individual automotive disciplines, please refer to the corresponding chapters of the book. Table 1.4: Selected standards in the field of automotive engineering. Topic

Standard

Life cycle of vehicles

EN ISO 

Development processes

ISO 

Functional safety

ISO  (ISO )

Environmental management

ISO  (ISO ) RL //EWG

Vehicle dynamics

DIN  (DIN ) SAE J  (SAE )

Determination of unloaded mass

DIN  (DIN )

EN ISO: standard adopted as European standard. ISO: International Organization for Standardization. DIN: Deutsches Institut für Normung (German Institute for Standardization). SAE: SAE International; former denomination Society of Automotive Engineers.

Motor vehicles are, as mentioned, subject to a number of additional and specific standards due to specific operating conditions and threats arising from their use. Vehicle standards regulate and structure, among other things, the quality processes in the development and construction of vehicles. This has become increasingly important, especially because of the massive use of electrical and electronic systems and increasing variety and complexity of vehicle functions over the last decades. Thus, for example, ISO 26262 regulates functional safety of motor vehicles. The idea of this standard bases on the assumption that especially safety of electrical and

20

1 Introduction and overview

electronic systems of a vehicle must be an integral part of the system. For this purpose, the standard defines the necessary activities, as well as the methods to be used for the development and production of electric and electronic systems, in a so-called procedure mode. The requirements are structured and classified by the so-called security requirement levels. From these, corresponding quality goals are derived. Safety requirement levels start with nonsafety-related requirements and are divided into the so-called ASI-levels (automotive safety integrity level) in the safety-relevant area. The ASI levels are divided into the levels QM (quality management) and A to D. The QM class describes the lowest risk rating and the D class the highest rating. The higher the risk classification of a system, the more comprehensive the validation must be. To determine the risk class, a system must be assessed against three different criteria. The first criterion is the severity (designated with “S” in Figure 1.17) of a system error (“E” in Figure 1.17) or the resulting threat to the user or the environment. The second criterion to be assessed is the probability of exposure. The last criterion describes the controllability (“E” in Figure 1.17) of the vehicle when the fault occurs. Defined evaluation categories exist for the three criteria, which are listed below (ISO 2011): – Severity – S (severity of the fault, danger to the user or the environment) – S0: no injuries (unharmed) – S1: minor to moderate injuries – S2: severe injuries (survival very likely) – S3: most severe injuries (survival unlikely) – Probability of exposure – E (probability of occurrence, connection of malfunction and operating condition, taking into account the duration and frequency of the occurrence of the situation) – E0: impossible occurrence – E1: rare occurrence (e.g., lying on a level crossing) – E2: occasional occurrence (1% of service life, e.g., driving with trailer or roof rack) – E3: frequent occurrence (1–10% of the service life, e.g., refueling of the vehicle or driving on a wet road) – E4: constant occurrence (10% of service life, e.g., acceleration/deceleration, brakes/steering) – Controllability C (controllability of situation) – C0: safe control (all drivers control this situation, e.g., unwanted increase of the radio volume) – C1: easy controllability (more than 99% of the drivers can handle the situation (e.g., steering column engaged when starting the vehicle)) – C2: normal controllability (more than 90% of drivers are able to control the situation; e.g., failure of the ABS during emergency braking) – C3: difficult controllability (less than 90% of drivers can control the situation; e.g., suddenly occurring high steering forces)

1.4 Automotive standards and conventions

21

The basis of this classification into safety requirement levels is an assessment of system risk without consideration of safety measures through hazard and risk analysis. Subsequently, a safety concept is to be developed, which reduces the existing system risk to a permissible level. The effectiveness of the created safety concept must be documented by means of a safety certificate and its scope is determined by the safety requirement level. Figure 1.16 shows the evaluation criteria and the resulting ASIL classification (ISO 2011). Accordingly, the highest risk level ASIL-D is only assigned if the highest criticality level occurs for all three evaluation criteria. If one of the criteria is evaluated with class 0, the system is classified with QM. In automotive engineering, there are currently two systems, the braking system and the steering system, which are classified in accordance with ASIL-D.

Figure 1.16: Risk graph for ASIL classification according to ISO (2011).

Within the framework of a hazard and risk analysis, a system evaluation is carried out with the help of the ASIL classification. For this purpose, an evaluation of the risk when an error occurs is performed for different safety-relevant driving situations. In doing so, all theoretically conceivable errors, their consequences, the reaction of the driver, and their impact on the assessment must be included. For the evaluation of the probability of occurrence E of a driving situation both the location, the road type, the road condition, the traffic situation, and the driving maneuvers are of importance. The assessment of the controllability C of the vehicle during the fault occurrence can be prevented by means of driving tests under safe conditions on a test site.

22

1 Introduction and overview

To evaluate the severity of error S, the following must be taken into consideration of the driving situation estimates of the possible effects can be made. The system is evaluated according to the highest risk class occurring within the hazard and risk analysis in the first place. The described ASIL classification procedure is shown in Figure 1.17. Driving situation

ISO 26262

E Fail

C

Reaction

Impact

ASIL

Consequence

S

Figure 1.17: ASIL-classification process (Düsterloh 2018).

1.5 Historic development of selected parameters In the following, important developmental trends of two selected vehicle parameters for newly registered passenger cars in Germany between 1985 and 2012 are presented in their temporal development. For this, total vehicle mass and fuel consumption per 100 km were selected as parameters. Data were deduced empirically from corresponding vehicle data of vehicles available on the market for small and compact cars, middle class, upper middle class, and luxury class. Figure 1.18 shows a steady increase in total vehicle mass, which was largely caused by massive growth in comfort and safety

2100 Segment 1900

Mass / kg

1500

+

+

+

+

+

+

+

+

+

+

+

Upper middle class

+

+

+

1300

+

Luxury

+

1700

+

+

+

+

+

Middle class +

1100

+

+ +

Compact

+

+

+

900

+

+

Subcompact

+ +

700 1985

1990

1995

2000

2005

2010

Figure 1.18: Development of masses of passenger cars in Germany 1985–2012 (Schramm 2012).

1.5 Historic development of selected parameters

23

systems and has only recently grind to halt. Nowadays, a downward trend due to requirements for CO2 emissions and fuel consumption of vehicles powered by internal combustion engines (ICE) can be observed. An example of significant reduction in vehicle mass for a vehicle of upper middle class is shown in Figure 1.19. Following a steady increase in the last three generations of vehicles, a reduction in the total mass of a comparable vehicle version of about 80 kg in the model change (2016) was recorded.

+20 kg +95 kg

+120 kg

1.620

1.640

1.760

–80 kg 1.680

1.525

Type series

W124

W210

W211

W212

W213

Market launch

1985

1995

2002

2009

2016

E 300 TD (1987)

E 220 CDI (1999)

E 220 CDI (2004)

E 220 Blue (2015)

E 220 d

Performance [KW]

105

105

110

125

143

Unladen weight ff EG

1525

1620

1640

1760

1680

Type (year of manufacture)

Figure 1.19: Development of overall mass of Mercedes E-Class in years 1985 to 2016 © Daimler AG.

Figure 1.20 shows the relationship between vehicle mass and fuel consumption in the formerly used driving cycle NEDC7 using the example of DIESEL vehicles. Data show values for vehicles that were on the market in Germany in 2012. A proportional increase in fuel consumption with the vehicle mass (0,5 l fuel per 100 kg vehicle mass) is observed. However, this relationship in combination with the development of vehicle masses is not reflected in the development of average fuel consumption. On the contrary, Figure 1.21 shows that despite increasing vehicle mass, the average fuel consumption according to NEDC was reduced by about 20% between 1985 and 2012. This can be substantially attributed to the optimization of the powertrain as well as to measures, which are further discussed in Chapter 6. The important technicalphysical contexts are discussed there.

7 NEDC: New European Drive Cycle (see Chapter 6).

24

1 Introduction and overview

Fuel consumption / (l/100 km)

12 11 10 9 8 7 6 5 4 3 1,000

1,500

2,000

2,500 Mass/kg

Figure 1.20: Development of fuel consumption in NEDC taking into account mass using the example of DIESEL vehicles (Schramm 2012).

14 Segment

Fuel consumption / (l/100 km)

13 12

+

Luxury

+

11 +

10 9

+ + +

Middle class

+

8

+

6

+ + + +

+

7

+

+

Upper middle class

+ +

Compact

+

+

+ +

+

+

Subcompact

+

+

5 4 1985

1990

1995

2000

2005

2010

Figure 1.21: Development of masses of passenger cars in Germany 1985 to 2012 (Schramm 2012).

2 Wheels and tires An essential part of the development of modern vehicles is the complex coordination and tuning of the chassis as well as the tires held by the chassis, which significantly contribute to the required safe and comfortable handling of the vehicle. The tires act as a link between the vehicle and the road and take on the wheel loads in the vertical direction. At the same time, the tires transmit forces in the longitudinal and lateral directions that inevitably result from braking, accelerating, and cornering (Mitschke and Wallentowitz 2014), (Schramm et al. 2018). The development of the chassis components aims mainly to achieve the optimal usage of the tires’ potential. For this purpose, for example, the kinematic of the chassis is designed to assure that in diverse driving situations the tires are always oriented in a way enabling them to transmit the largest possible forces and ensure vehicle stability (see Chapter 3). Today, however, semiactive and active suspension components, such as devices for roll stabilization or steerable rear axles, are used to positively influence the wheel contact force, the wheel positioning and thus the vehicle lateral balance. Concerning the implementation and the operation of the tire, compromises must nevertheless be made. Desirable are properties such as high wet grip, low rolling resistance, a long service life, and a good comfort behavior of the tires. In this chapter, in addition to comments on the general manufacturing process of the tires, the structure of the tire, the basic mechanisms, and dependencies of the power transmission through the tire are described. Finally, Section 2.4 deals with direct and indirect tire pressure monitoring systems (TPMS).

2.1 Tire structure The most widely used tire in the automobile industry today is the tubeless radial tire. The tire with radial carcass was patented in 1946 by the company Michelin and was sold from 1949 onward under the name “X” (Michelin 2016). It combines a radially arranged carcass layer, which allows for good vertical deflection, with a belt ply above the carcass ply giving the tire its stability and designation.

2.1.1 Structure of the radial tire Figure 2.1 shows a sectional view of a radial tire. The tire consists of two bead rings (6), which are connected to each other via the carcass layers (10) radially. This construction forms the load-bearing substructure and is hermetically sealed on the inside by an inner liner (9). The tire carcass (10) forms the supporting frame of the tire and is arranged radially. It consists of layers of cord, rayon, polyamide fibers, and steel, each separated https://doi.org/10.1515/9783110595703-002

26

2 Wheels and tires

1

2

3

12 11

4 10 9 5

9 8

14

7

8 7

13 6

1 2 3 4 5

Tread Tread block Tread groove Tire shoulder Sidewall

6 7 8 9 10

Bead ring Apex strip Chafer Inner liner Carcass layers

11 12 13 14

Belt layers Under tread Rim star Rim flange

Figure 2.1: Components and zones of a passenger car radial tire, cross section through a wheel.

by rubber layers. Each carcass layer extends from one tire bead to the other and transmits, via internal pressure, which tensions the carcass, the forces arising between the tire and the road surface onto the rim. The sidewall influences the lateral stiffness of the tire and thus effects the overall stiffness of the vehicle axle, the vertical drive comfort, and the rolling resistance significantly. Above the carcass are the belt layers (11) that give the tire its necessary rigidity and stiffness at high speed. The tread (1), consisting of different rubber compounds, is in touch with the road and, apart from the material properties, is significantly characterized by the tread pattern. The tire tread pattern consists of the tread blocks (2) and the tread grooves (3). Laterally, the carcass is protected from damage and weather by the sidewall (5) (Nüssle 2002) Hereafter, the individual components and zones of the tire and their function are described in more detail. The tread (1) contains the tire profile (tread blocks (2), tread grooves (3), and lamellas). It varies depending on the application area of the tire (e.g., summer, winter, allseason, or racing tires). The tread consists of different rubber compounds (Sperling 2005), which should give the tire a high grip in dry conditions and a good grip in wet conditions. In addition, a smooth running, a low rolling resistance, and a low noise level must be ensured while being in use. The tire tread pattern must allow the drainage of water in wet conditions, so that the contact to the road of the tire is maintained even at higher speeds and a floating of the tire on the water film is avoided. Given a certain degree of road wetness and driving speed, the tire is eventually going to start floating anyway, which gives rise to aquaplaning. The tread should maintain the

2.1 Tire structure

27

mentioned properties as constant as possible even under different operating conditions (e.g., varying temperatures, different road properties, and aging). The tire shoulder (4) is located in the area between the outer tire tread and the edge of the side wall (5). The shoulder area of the tire plays a crucial role for the necessary dissipation of heat. The sidewall (5) is the area between the tire shoulder (4) and tire bead containing the bead core (6) and the bead filling (apex strip) (7). It consists of a thin rubber layer intended to protect the lateral carcass layers from chafing at the edge of the roadway and to avoid the intrusion of foreign matter. Likewise, the sidewall protects the tire from UV radiation and chemicals such as gasoline and oil. On the sidewall, the tire label (e.g., tire size, tire design, load capacity, speed index, fabrication, and location date) is applied in the vulcanization process using the baking mold. The tire bead makes use of the bead core (6) for clamping the tire carcass on the rim flange (14) air tightly. The tire bead consists, among other things, of the core of the bead, the bead filling (7), and the chafer (8). The bead filling (7) and the chafer stiffen the tire bead and thus influence the lateral stiffness of the tire. The bead core prevents undesired movement of the tire in relation to the rim and secures the tire even under high lateral forces on the rim. For the tire assembling and disassembling, the bead core must be very resistant and strong, but it also has to allow sufficient elasticity and be as light as possible. The bead core consists of a rubber-coated, ring-shaped steel cable. The steel cable can consist of several twisted steel wires. The strength of the bead core is designed to match the inflation pressure, tire size, and rotational speed. The belt layers (11) are located under the tread and above the tire carcass (10). They stabilize the tread and provide the necessary resistance to a possible impact, which protects the tire from damage when driving over edges and blow bars. The forces that arise while braking, accelerating, and cornering are transmitted to the carcass via the belt layers. Furthermore, the belt layers have to ensure an even distribution of ground pressure in the footprint. In addition, the belt ply absorbs high lateral forces at high speeds, thus ensuring the integrity of the tire. The tire belt width and the angle (between 18° and 28°) under which the steel or cord threads are arranged largely determine the tire’s stiffness and thus to a large extent the driving behavior of a vehicle. The tire innerliner (9) is an air- and waterproof membrane that seals the tire on the rim flange (Heisler 2002).

2.1.2 Avoidance of punctures and tires with emergency running properties If a tire is damaged, for example, by nails or broken pieces, it either loses air suddenly or slowly over a longer duration of time. The tire sidewall is compressed by the lack of internal pressure between road surface and rim. The resulting flexing work heats up the tire strongly while driving. Already after a very short distance this leads to a tearing of the side wall and thus to the complete destruction of the tire.

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2 Wheels and tires

Today, many newly registered vehicles do not employ a spare wheel anymore, in order to save payload space and reduce the overall mass of the vehicle. If a pressure loss is detected in time, for example, by direct measurement (by means of sensor) or indirect measurement (calculation from the wheel speeds; see Section 2.4), the tire may be sealed by a tire sealant. A compressor pumps the sealant into the tire via the filling valve that temporarily seals the damage. Furthermore, radial tires with emergency running properties known as run-flat tires are available on the market. An additional reinforcement of the side wall by rubber (Figure 2.2) ensures that the vertical force can be carried even in the absence of internal pressure. Through this emergency-running property of the tires, a safe drive over a certain distance to the next car workshop (at reduced speed) is enabled. For the strengthening a special rubber compound is used, which has a lower heat sensitivity. The disadvantages of the run-flat tire compared to the conventional radial tire are: worse comfort behavior, increased rolling resistance, and a slightly higher weight.

Reinforcement elements Figure 2.2: Transverse section through a run-flat tire.

There are also radial tires, which are self-sealing, thanks to an additional sealing layer on the innerliner.

2.1.3 Comments on the manufacturing process of a tire The production of a tire is a complex process, since the tire consists of a mixture of different materials, is built up in several layers, and must undergo a thermal manufacturing process. This is colloquially referred to as “black magic” because it is extremely difficult to accurately predict how the tire must be designed to ensure fulfilling the requirements of a particular application at the end of a step in the development. To tune a tire so that it meets the required driving dynamics of car manufacturers, such as grip (maximum friction coefficient), vehicle balance, rolling resistance, and its behavior on a wet road, and also features such as

2.1 Tire structure

29

stiffness, abrasion, and durability (see Section 2.2.7), many iterative steps are usually necessary in the development process. The tire consists mostly of natural and synthetic rubber supplemented by additives. Among those are silicates, soot, chemical additives such as accelerators, retarders, activators, and mixing aids as well as sulfur. For the tire compound, every tire manufacturer has developed its own secret mixture. The individual tire components, such as treads, sidewalls, and other structural elements, are partly embedded in this mixture. The tire is then wound from the tailored components and strengthening layers of steel and synthetic fibers. The supporting layers give the tire its strength and resistance, influencing the transmission of the longitudinal and lateral forces, the vertical comfort, and thus the driving behavior of the vehicle as a whole. The tire is then “baked” under high pressure and at temperatures of 160 to 200 °C in a solid mold for 9 to 17 minutes (goodyear 2016). This baking process is called vulcanization. The vulcanization creates sulfur bridges, which connect the entire tire and link the components of the tire inseparably. During this process, elastic rubber is created from the plastic rubber mixture. This baking process as well as the mixture and construction of the tire have a great influence on the desired properties. After vulcanization, the tire quality is assessed. Thereby nondestructive testing processes, for example, X-ray analysis and holography procedures, are performed. During production, tires are tested randomly on outer-drum test stands for their high-speed and structural properties.

2.1.4 Tire labeling The dimensions and other properties of a tire are usually obtained directly from the label of the tire sidewall. For example, in Figure 2.3 this caption reads 255/35 R 19 94 W.

Figure 2.3: Tire labeling.

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2 Wheels and tires

Using the information from Table 2.1 the construction radius can be calculated: 1 mm r0 = bR qR + D · 25.4 . 2 inch

(2:1)

In this case the radius is r0 = 330.55 mm. Table 2.1: Tire labeling. Example

Value

Description

255

bR = 255

Tire width in mm



qR = 0.35

Height to width relation H=B in %

R

–

Radial tire



D = 19

Rim diameter in incha



–

Classification number for tire tonnage, see Michelin ()

–

Speed index, here “Y-” tire approved for max speed  km/h (other indices: S:  km/h, H:  km/h, W:  km/h)

–

calendar week , year 

V  a

inch equals 25.4 mm.

2.2 Basic tire characteristics The tire characteristics, such as longitudinal and transverse stiffness, maximum grip, slippage at maximum power transmission, intake and comfort behavior change with inflation pressure, tire temperature, tread depth, and age of the tire. To assess the influences on the tires’ behavior and thus on the overall vehicle behavior, the mechanisms for transmitting power from the tire to the roadway are described in the following sections. In relation to this, the friction theory for rubber, presented by Kummer and Meyer (1967), is considered. This differs fundamentally from the classical theory of friction and is therefore discussed in more detail below. From this it is derived how the tire’s force transmission takes place and which parameters are influenced by the tire inflation pressure and temperature.

2.2.1 Viscoelastic behavior Tires mostly consist of raw rubber, which is made through the vulcanization of caoutchouc. The viscoelastic behavior of rubber is comparable to a spring in parallel connection (corresponds to the elasticity) and a damper (corresponds to the viscosity). When rubber is deformed, it returns to its original form due to its spring

2.2 Basic tire characteristics

31

component after removal of the impacting force. This requires a certain amount of time due to the damping component. This phenomenon is also called hysteresis and is associated with the creation of energy in the form of heat due to the damping friction (Michelin 2005, Trzesniowski 2014). Rubber changes its properties based on its temperature and load frequency (Figure 2.4; “analogy between temperature and period/load frequency”). At low temperatures or high load frequencies, rubber is in a “glassy” state. The stiffness is high in this state, so that it is hard to deform the material. At higher temperatures or low frequencies, rubber behaves elastically. The stiffness is then low, and the material behaves flexibly. Around the glass transition temperature, rubber reaches its maximum viscosity (Michelin 2005).

E-module energy dissipation

Main working area of tread rubber

Glass behavior

Area of hysteresis maximum

Rubber behavior

E-module Hysteresis

Glass transitiontemperature (Tg)

Temperature/period length

Figure 2.4: Dependence of the rubber properties, modulus and hysteresis on temperature and load frequency or period length (Michelin 2005).

The occurring load frequency depends among others on the rolling speed of the tire. As already mentioned, this influence behaves in exactly the opposite way as temperature influence (Figure 2.4 right). At low load frequencies, the material thus behaves elastically; at high load frequencies, however, glass behavior occurs. In a different frequency range depending on the rubber compound, the rubber behaves viscoelastic (Michelin 2005). The relationship between load frequency and glass transition temperature can be explained by the temperature-dependent molecular velocity and the load frequency-

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2 Wheels and tires

dependent strain rate. If the rate of deformation is greater than the rate at which the molecules move, the material will show glass-like behavior. On the other hand, if the rate of deformation is below the molecular velocity, the material behaves like rubber. This equivalence of load frequency and temperature is described by the WLF law (Williams–Landel–Ferry equation) (Williams et al.). For example, in the low frequency range (10–100,000 Hz), a frequency increase by a factor of 10 has the same effect as a temperature decrease of 7 to 8 °C (Michelin 2005).

2.2.2 Rubber friction The classic friction laws, according to which the frictional force is only proportional to the normal force and independent of the size of the contact area and the relative sliding velocity (FR = μFN ) (Schramm 1986), no longer apply for rubber. In contrast to classical friction, the friction coefficient μ of the rubber friction is not constant, but depends on dynamic processes as well as on other parameters (Kummer and Meyer 1967). Due to the viscoelastic properties of the rubber occurring hysteresis acts through two main mechanisms: adhesion friction (also called molecular adhesion) and hysteresis friction (also called interlocking effect) (Michelin 2005). The cohesive and the viscous friction play a minor role in this process. Adhesive friction provides the majority of frictional force on smooth, dry, and even surfaces (Bachmann 1999). It arises from the fact that external atoms of the chain molecules of the rubber form a connection while in direct contact with the road surface. The relative velocities between rubber and road stretch certain chain molecules and tear apart other already existing links. After the dissolution of the compound, the molecular chains return to their initial form. The process of periodic tensioning and relaxation converts kinetic energy into heat energy and, as shown on the right in Figure 2.5, gives rise to a frictional force opposite to the direction of movement (Haken 1993).

V

V

Rubber

Road surface FH

FA

Figure 2.5: Mechanisms of hysteresis (left) and adhesion rubber friction (right) according to Heißing and Ersoy (2011).

2.2 Basic tire characteristics

33

Since these compounds form only in direct contact of the rubber with the friction element, the adhesion FA is directly dependent on the contact surface. It maximizes with increasing size of the footprint and increasing smoothness of the surface. In addition, the material properties of the friction element as well as the temperature and the relative sliding velocity of the rubber on the contact area influence the adhesion (Bachmann 1999). The adhesion builds up in steps of hundredths of a micron and starts at 0.0001 km=h relative speed between the tire and the road surface, reaching its maximum at about 0.1 km=h (Heißing and Ersoy 2011). The hysteresis portion FH of the frictional force is caused by the deformation of the rubber element during friction. The hysteresis friction takes place in the centimeter to micrometer range. It is effective in the frequency range of 102 and 106 Hz (Michelin 2005). In the contact area, an asymmetry of pressure arises due to damping losses of the rubber element that acts opposite to the driving direction (Figure 2.5, left). In contrast to adhesion, hysteresis reaches its maximum only at very high relative sliding velocities. The magnitude of the hysteresis is furthermore dependent on the composition of the rubber, the surface structure, but relatively independent of a thin medium (Bachmann 1999). If the road is humid, the importance of the hysteresis friction therefore increases proportionally, since almost no adhesion forces can arise between the rubber and the road. However, if the water level on the road and the driving speed rise, the tire can begin to float (aquaplaning). In this case, the power transmission between road and tire breaks down almost completely. The force components FH from the hysteresis and FA from the adhesive effects account for the majority of the total frictional force that results from rubber friction FR = FH + FA .

(2:2)

The proportion of the total transmittable force FR depends on the pressure between rubber and road as well as the relative sliding velocity. The lower and more uniform the local pressure, the higher is the friction coefficient (Heißing and Ersoy 2011). The superimposition of the components causes a velocity-dependent friction coefficient (Nüssle 2002), which leads to a speed dependence of the resulting forces. These are shown in Figure 2.6 as a function of the relative sliding velocity (vslide ). The energy that must be expended to form new surfaces, due to abrasion and crackling gives rise to the cohesive portion of the frictional force. However, in most cases this proportion is negligible (Nüssle 2002). A viscous component of the friction is created due to the deformation or shearing of a liquid intermediary medium that is trapped between rubber and road, such as water or mud (Bachmann 1999). The effects described distinguish rubber friction fundamentally from classic friction. They are illustrated in Figure 2.7 in schematic diagrams. With increasing surface pressure pN between rubber and surface, the effective friction coefficient μ decreases. On the contrary, as the contact surface AR increases, the friction coefficient increases. The friction coefficient depends on the temperature as

34

Force

2 Wheels and tires

=

+

0 Relative sliding velocity

0

Figure 2.6: Qualitative relationship between force and relative sliding velocity according to Trzesniowski (2014).

Classical friction

: Normal pressure

Rubber friction

: Friction area : Relative sliding velocity

Figure 2.7: Comparison between classical friction and friction caused by rubber (schematic representation).

well as on the relative sliding velocity. The relative sliding velocity corresponds to the relative speed between the rubber of the tire and the road surface. In classic friction, a constant friction coefficient would establish itself after overcoming the static friction. In the case of rubber friction, on the other hand, the friction coefficient μ increases with increasing relative sliding velocity up to a maximum value μmax and then decreases rapidly after exceeding this maximum value. The friction coefficient then takes a constant final value, the so-called sliding friction coefficient.

2.2 Basic tire characteristics

35

Since rubber changes its properties as described in Section 2.2.1 based on temperature and load frequency, adhesive and hysteresis friction are also temperature dependent. The rubber compound of the tire can be used to set the glass transition temperature at a specific load frequency. The load frequency is adapted to the operating points of the tire in order to achieve sufficient energy reduction that causes greater adhesion (Michelin 2005). Therefore, the rubber compound of a winter tire usually has a lower glass transition temperature compared to a summer tire. Thus, given the same temperature, a winter tire is “softer” than a summer tire (Michelin 2005).

2.2.3 Rolling resistance Figure 2.8 shows a tire rolling on an even road surface. For simplification, the tire tread pattern (also referred to as tire contact patch) is assumed to be a rectangular area in this case. As the tire rolls off, rolling resistance is created, which can be expressed as a force opposing the direction of movement (Michelin 2005).

M

Contact patch exit (A) Contact patch Contact patch entry (E)

Normal pressure characteristic

Figure 2.8: Development of the tire’s rolling resistance due to normal pressure shift in the tire contact patch.

The main reasons for the rolling resistance are the viscoelastic properties of the rubber compound, which are represented in Figure 2.8 by spring-damper elements. When entering the contact area (tire contact patch relaxation area), the tire is deformed. As a result, energy is dissipated in the form of heat, which warms up the tire. This energy dissipation causes 80 to 95% of the rolling resistance; the remaining resistance is created due to the wheel’s microslip and air resistance. The values from simulations in Figure 2.9 show that the energy loss due to the warming of the tire

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2 Wheels and tires

with 65–70% for the most part takes place in the tire apex, that is, in the tread. The remaining part is distributed with 15% on the side wall and 15–20% on the bead zone (Baumgärtner 2010).

Tire apex/tread ca. 65–70%

Side walls ca. 15%

Bead zones 15–20

Figure 2.9: Distribution of energy dissipation on the tire.

The concrete deformation of the tread depends significantly on the tire pressure (Figure 2.13), the wheel load, and the stiffness of the rubber compound. Accordingly, decreasing the tire pressure or increasing the wheel load leads to a larger deformation and thus to more rolling resistance. Furthermore, there are tire vibrations that occur when driving with higher speed. Those lead to large deformations and accordingly to an increase in rolling resistance. Additionally, increasing macroroughness1 of the road surface leads to an increase of the tread’s deformation. A higher temperature of the tire, for example, caused by a higher ambient temperature or long duration of travel, leads to a lower stiffness of the tire and thus to a reduction in rolling resistance (Michelin 2005). By adjusting the rubber compound, the load frequencydependent hysteresis can be adjusted so that the rolling resistance is minimized at a certain driving speed.

2.2.4 Transmission of vertical forces In addition to longitudinal and lateral forces, the tire must also transmit vertical forces to the road that are generated by the weight of the loaded vehicle. The vertical force is determined almost solely by the effect of the filling pressure (Figure 2.10). The filling pressure exerts its effect on the carcass belt from the entire inside of the tire. However, the tire carcass can transmit thrust only to a very limited extent. Instead, the upper

1 Surface roughness of road surface between 0.5 and 50 mm.

2.2 Basic tire characteristics

37

Figure 2.10: Transmission of vertical forces (Harrer and Pfeffer 2017).

carcass threads, driven by the filling pressure, pull on the bead core and support the rim flange and thus the vertical load (Harrer and Pfeffer 2017). If the tire is loaded, it deforms in the lower area and creates a contact surface between the tire and the road, the so-called tire contact patch (Mitschke and Wallentowitz 2014). In the tire contact area filling and ground pressure must compensate. On the other hand, a higher filling pressure causes increased ground pressure caused by the reduction of the wheel–road contact patch (Harrer and Pfeffer 2017). Due to the filling air pressure-dependent size of the tire contact patch and the distribution of the bearing load, the transmission of the longitudinal and lateral forces is influenced and thus the general driving behavior of the vehicle. The performance of the tire decreases due to an incorrect filling pressure (see Section 2.2.5). As an elastic element the tire deforms depending on the magnitude of the vertically acting force. The elastic properties of the tire can be approximately explained comparing them to the way a spring acts (Heißing and Ersoy 2011). The tire spring stiffness is influenced by the structure and materials of the tire, the rolling speed, and above all by the inflation pressure of the tire. The spring’s stiffness is defined as the quotient of wheel load and tire deflection. Within the wheel load range in which a tire is stressed under usual circumstances, the deflection is therefore linearly proportional to the wheel load and the quotient represented by a constant (Reimpell and Sponagel 1988). Figure 2.11 shows the deformation as a function of the acting force (wheel load). An increasing wheel load leads to a greater deformation of the tire and, as a result, to a larger tire contact patch. A comparable behavior can be observed given a constant wheel load and decreasing filling pressure.

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2 Wheels and tires

1




3

or

1

2

3

Figure 2.11: Deformation of the tire by the wheel load (Jazar 2008).

The combination of the tire’s suspension characteristics and the unsprung masses of the vehicle creates an oscillation system. The size of the resonance frequency depends on the stiffness of the tire and thus directly on the tire’s inflation pressure. The suspension characteristic of the tire greatly influences the vehicle’s handling. Only due to that the double suspension of the vehicle by body springs and the tire is assured. The double “spring-damper system” allows comfortable and safe driving even at high speeds. Especially in racing cars, which are very hardly damped and suspended to minimize the wheel load fluctuations, the tire makes out a considerable part of the vehicle’s overall suspension (Milliken and Milliken 1995). The damping of the tire, however, compared to the damping of the chassis, is usually of minor importance.

2.2.5 Influence of tire inflation pressure on tire properties The tire inflation pressure affects different properties of the tire. Gießler (2012) investigated the influence of tire inflation pressure on the formation of the tire contact patch. This produced, among other things, the measurements shown in Figure 2.12. They show the distribution of pressure in the tire contact patch. It can be clearly seen that at lower inflation pressure, the area of the tire contact patch is larger. Accordingly, there is a lower surface pressure in the tire contact patch because a larger area is supporting the same wheel load. According to the theories of force transmission presented in Section 2.2.1, a larger tire contact patch combined with lower surface pressure leads to an increase of the maximum friction coefficient. However, Milliken and Milliken (1995) described that too low or too high tire pressure leads to an uneven loading of the tire contact patch. In the case of too low pressure, the outer areas are under significantly higher surface pressures (Figure 2.13), while the middle of the tread loaded only lightly. If the pressure is too high, this effect will be reversed qualitatively. All in all, these inhomogeneous pressure distributions in the tire contact patch lead to a decline of the maximum

2.2 Basic tire characteristics

3

4

5

6

7

8

9 bar

Distribution of normal pressure at filling pressure

39

3.69 bar

2.36 bar

1

2

2.3 bar

1.4 bar

2.2 bar

3.0 bar

Figure 2.12: Pressure distribution in the tire contact patch depending on the filling pressure (Gießler 2012).

correct

to high

to low

Figure 2.13: Influence of tire filling pressure (Trzesniowski 2014).

transmittable force. Therefore, for reasons of security, the required minimum value of the pressure in the tire should always be maintained. Furthermore, too low filling pressure holds the risk of making the tire jump off the rim during fast cornering. In 1995, the Vehicle Research Association (FAT) commissioned a study to determine μ-slip curves of car tires (Gnadler et al. 1995). Gießler (2012) and Milliken and Milliken (1995) confirmed that increasing filling pressure lowers the maximum friction coefficient (Figure 2.14). In addition, the friction coefficient maximum, as shown in Figure 2.14, is only reached at higher slip values (see Section 2.2.4). Therefore, a low pressure in the tire not only increases the maximum value, but also its longitudinal slip stiffness. The longitudinal slip stiffness corresponds to the initial slope of the μ-slip curve (see Section 2.2.4). One explanation for the increasing rigidity is that the decreasing pressure leads to a higher proportion of rubber elements in the contact area that get into contact with the road surface. This acts like a parallel connection of several spring elements, whereby the resulting stiffness increases accordingly.

40

2 Wheels and tires

1.4

Friction coefficient

1.2 1,0

pF

0.8 0.6 0.4 0.2 0

0

5

10

15

20

25

30

35

Braking slip/% Figure 2.14: Influence of filling pressure on longitudinal friction coefficient according to Gnadler et al. (1995).

The dependence of the radial and the vertical stiffness from filling pressure can, as described earlier, be regarded as linear. Figure 2.15 shows the behavior as an example for different tire variables. Increasing pressure thus increases the radial

450

245/50 ZR18

400 Radial stiffness/(N/mm)

275/40 ZR18 350 255/45 ZR18 285/40 ZR19

300

250

200

150 1.8

2.3

2.8 Tie pressure/bar

3.3

3.8

Figure 2.15: Radial stiffness of different tires according to Harrer and Pfeffer (2017).

2.2 Basic tire characteristics

41

stiffness and deteriorates the drive comfort. However, it also reduces the rolling resistance and thereby the fuel consumption of the vehicle. The tire cornering stiffness described in Section 2.3.3 is also affected by inflation pressure. The principal change due to different filling pressures is shown in Figure 2.16 (Harrer and Pfeffer 2017). At low and medium wheel loads, the cornering stiffness increases with decreasing inflation pressure. 3,500

Cornering stiffness/(N/°)

3,000

High pressure Low pressure

2,500 2,000 1,500 1,000 500 0

0

2

4 Wheel load/kN

6

8

Figure 2.16: Influence of the filling pressure on the cornering stiffness according to (Harrer and Pfeffer 2017).

However, if a certain threshold of the wheel load is exceeded, the behavior reverses. From this value, the increased inflation pressure assists the lateral tire stiffness and minimizes the tire’s transverse deformation, which may occur during cornering (Figure 2.17). Therefore, the tire with higher inflation pressure has the greater cornering stiffness (Harrer and Pfeffer 2017). However, the point of intersection depends strongly on the tire’s design. The structure, the width, the flank height, and also the processed materials of the tire have a major influence on the shape of the curve. Reliable statements about the shape of the curve and the point of intersection can therefore only be made for a specific tire.

Curve outside

Figure 2.17: Deformation of the tire when cornering.

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2 Wheels and tires

2.2.6 Influence of temperature on tire properties The tire’s temperature influences the tire’s properties such as the maximum friction value (grip) and the stiffness due to the temperature dependent change in characteristics of the rubber compound. Angrick et al. (2014) and Gutjahr et al. (2011) investigated the influence of tire temperature on various tire properties by means of test-bench measurements (Figure 2.18). In Angrick et al. (2014) a significant reduction of the cornering stiffness of three to four percent with each increase of 10 °C was reported. However, the lateral relaxation length showed no reproducible correlation to the temperature. The cause of this observation becomes clear when considering the relationship for the relaxation length (see Section 2.3.8) in lateral direction σα : cα . cy

Temperature

(2:3)

Relaxation length

Cornering stiffness

Max friction coefficient

σα =

Temperature

Temperature

Figure 2.18: Qualitative dependence of essential tire properties on temperature according to Angrick et al. (2014).

Assuming that the cornering stiffness cα and the lateral stiffness cy change equally with varying tire temperature, it can be expected that the relaxation length is approximately constant with respect to temperature. The maximum friction coefficient in lateral direction was observed to initially increase with rising temperature (Angrick et al. 2014). At a surface temperature of about 70 °C the friction coefficient reached its maximum and dropped again as the temperature continued to rise. The friction coefficient ranged from 0.6 at 20 °C to 1.5 at 70 °C in these measurements. The qualitative dependency of the maximum friction coefficient, the cornering stiffness, and the relaxation length can be summarized as shown in Figure 2.18. The qualitative course of the maximum friction coefficient and the cornering stiffness toward temperature thus are in accordance with the theory of temperature dependency of the module and the hysteresis of rubber (Figure 2.4). It should be noted that the tire’s temperature is a crucial factor concerning the tire properties which determine the driving dynamics.

2.2 Basic tire characteristics

43

How much the tire properties change in the face of temperature alterations depends strongly on the specific tire. When evaluating the results of test bench measurements, it must be regarded that these tendencies do not necessarily occur on the real vehicle, since changes in temperature and filling pressure cannot be separated while driving. An increase of the tire’s temperature always leads (with a certain temporal delay) to an increase of the air temperature within the tire. Given the correct assumption of an isochoric transformation, the thermic equation of state for ideal gases yields the relationship: p2 T2 = . p1 T1

(2:4)

The relative change in filling air temperature (in Kelvin) and the filling pressure is therefore always the same. As a rule of thumb, a pressure increase of 0.1 bar can be assumed to lead to a temperature increase of 10 Kelvin. This in turn leads to an increase in the vertical stiffness of the tire.

2.2.7 Conflicting goals of tire development In addition to the texture of the road surface and the characteristics of the vehicle itself, the tire has a considerable influence on all aspects of driving behavior. This includes comfort, handling, and driving safety as well as economic and environmental aspects. The goal of the development of tires is therefore to produce a tire that performs best considering all aspects. This results in a conflict between goals that emerge from the contradictory requirements that each individual area has on the tire. Depending on the way in which the tire is used, the priorities are weighted differently. Figure 2.19 lists some of these requirements. For example, in a sports tire, aspects such as dry braking and handling are weighted higher than comfort and rolling noise. However, in a rolling resistance-optimized tire the driving behavior is less important than the rolling resistance. Therefore, conflicting requirements arise, concerning the filling pressure, which can only be met by making compromises. For example, the vehicle’s load and maximum speed require a certain minimum pressure to ensure safe operation of the tire (EU 2014). However, the vertical stiffness increases with increasing tire pressure. This, in turn, reduces the comfort for the vehicle occupants because the road influences can be compensated less by the tire. If one aims to reduce rolling resistance, a high tire pressure is additionally important to minimize the deformation of the tire. Higher tire pressures, on the other hand, reduce the size of the tire contact patch, which results in a lower friction coefficient and thus lower maximum power transmission.

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2 Wheels and tires

Abrasion

Comfort

Rolling friction 3 2.5 2 1.5 1 0.5 0

Durability

Rolling noise

Driving Behavior

Wet braking

Aquaplaning

Dry braking

Figure 2.19: Examples of a tire’s requirements.

2.3 Mathematical description of tire forces For the mathematical description of tire force transmission different modeling approaches exist, which can be assigned to the categories of mathematical models, physical models, and mixed forms. The goal of this section is to present tire characteristics that describe the physics of the tire mathematically. Based on this a tire model is described that calculates the static tire force depending on kinematic variables. Finally, the calculation of the tire’s dynamic force is explained. For more detailed considerations of different tire modeling refer to Zomotor (1987), Burckhardt (1993), Gipser (2010), Pacejka (2006), and Mitschke and Wallentowitz (2014).

2.3.1 Classification of tire forces When modeling a vehicle, the forces’ impact between road and tire can be inferred from the contact forces and torques. These are applied forces and torques that can be determined (as opposed to reaction forces) as functions of position and velocity variables. The contact force in the tire contact patch can be broken down into three components of the wheel-fixed coordinate system KR (Figure 2.20 and Table 2.2). The forces are represented in the coordinates of the wheel-fixed coordinate system, whereby the internal rotation of the wheel is disregarded. The vertical force acts one-sided, since only compressive forces can be transmitted between tire and road. The tire forces, which arise parallel to the tire contact patch, are calculated from slip and slip angle taking into account the vertical force in appropriate force

2.3 Mathematical description of tire forces

45

OR = M Contact patch

,

Figure 2.20: Contact forces in the tire contact patch and kinematic quantities of tire and wheel-fixed coordinate system KR = {OR; xR, yR, zR}.

Table 2.2: Forces and kinematic variables of tires (see also Figure 2.20). Notation

Description

FRx

Longitudinal/circumferential force along the x-axis of KR

FRy

Lateral force along the y-axis of KR

FRz

Vertical/Ground force along the z-axis of KR

MA, B

Drive and brake torque around the y-axis of KR

vR

Velocity vector of the wheel center

vR x = vR cos α

Velocity of the wheel center in the direction of the x-axis of KR

vR y = vR sin α

Speed of the wheel center in the direction of the y-axis of KR

α

Slip angle of the tire

laws. These depend on the material combination of tire and road surface, as well as on the rubber compound and the geometrical dimensions of the tire.

2.3.2 Tires under the influence of vertical forces The stiffness of the tire in the vertical direction can be considered as largely independent from movements in the longitudinal and transverse directions. The vertical elasticity of the tire allows compression that compensates for, for example, minor road disturbances. The complex mechanical properties of the tire structure and the change in the size of the tire contact patch cause a nonlinear shape of the tire’s

46

2 Wheels and tires

spring characteristic curve. By taking solely static loads into account we yield a nonlinear force law of the form FRz = FRz ðΔzR Þ

(2:5)

(Figure 2.21). The nonlinear characteristic curve can be linearized using the static point of balance ðz0 , Fz0 Þ as a reference point, which yields the relationship FRz = FRz0 + cR ΔzR ,

(2:6)

Rz0

Normalized vertical force/( F

FR z

)

with the spring constant cR and the equilibrium force FRz0 . The tire damping is usually negligible and therefore omitted.

2

1 Linear approximation

0 0

1 z Normalized compression travel ( zR ) 0

2

Figure 2.21: Vertical force characteristic of a tire (schematic diagram).

2.3.3 Tires under the influence of longitudinal and lateral forces The transmission of circumferential and lateral forces in the tire contact patch area is subject to adhesion friction (intermolecular bonding forces between tire rubber and road surface) and hysteresis friction (tight fit due to interlocking effects between tire and road surface; see Section 2.2.2 and Gillespie (1992)). Both effects depend on small, relative movements between tire and road, which are distributed differently among the wheel contact surface. The formation of circumferential and lateral forces can be described by shear deformations of the tire contact patch, in combination with the friction between the tire contact patch and road surface. This requires a macroscopic description of the shearing mechanisms, which can be easily incorporated into a Multibody formalism. Descriptions such as longitudinal slip (circumferential slip) s and side slip angle α, which arise due to relative movements in the tire contact patch, can be used.

2.3 Mathematical description of tire forces

47

2.3.3.1 Longitudinal slip The longitudinal slip is a kinematic variable that describes the relative movement between tire and road surface in the longitudinal direction of the wheel. The wheel can take the state of motion driven, braked, and rolling without drive. For simplicity the wheel is considered to be a rigid body. The slip introduced below is therefore also referred to as rigid body slip. The contact surface of the tire degenerates from an area to a line perpendicular to the direction of travel, when modeled as a rigid body. Under the assumption of a rigid wheel, the tire moves with a combination of rolling and sliding (Schramm, et al. 2018). By considering the dynamic tire radius rdyn a substitution model is obtained, which reflects the slip well. For the radial tires, nowadays almost exclusively used, the fundamental behavior of the tire can be described sufficiently well by the substitution model (brush model) shown in Figure 2.22.

Wheel carrier r0

ρ˙R

Inextensible steel belt rdyn

ν Rx M rstat νP

MP Tread element x

E Inlet zone

L Patch length

A Outlet zone

Figure 2.22: Mechanical substitution model for the description of tire forces (Schramm, et al. 2018).

A basic assumption in this modeling is the bendable but almost not expanding steel belt. The tread is represented by corresponding tread elements whose inner ends are firmly connected to the steel belt and therefore move in line with it. In the inlet zone E of the tire contact patch, the tread elements are decelerated within an extremely short distance to a vertical speed of zero. In the outlet zone A, the tread elements lift off the roadway again. The inner ends of the tread elements move together with the belt (due to the quasistatic view) with a constant speed vP . On the other hand, they stick with their outer ends to the road. This results in a shearing of

48

2 Wheels and tires

the elements, which increases proportionally with the distance 0 < x < L from point E because of vP = const, which leads to a resulting shear stress whose integration over the tire tread pattern results in longitudinal force. Depending on the wheel being in a state of acceleration or braking sliding between tire and road occurs above a limit 0 < xstick < L. Figure 2.23 shows a free-body diagram of a flat, longitudinally rolling wheel; the variables are listed in Table 2.3. Kinematic wheel suspension variables such as camber and toe angles are neglected.

,

,

,

OR

P

Figure 2.23: Velocities, longitudinal forces, and torques of the tire in circumferential direction.

Table 2.3: Variables of the moving wheel. Symbols

Description

ρ_ R

The wheel’s angle velocity around the y-axis of the wheel-fixed system KR

ΘRyy

The wheel’s moment of inertia around the its y-axis

FRx

The wheel’s longitudinal force along the x-axis of the wheel system KR

MA, B

Drive and brake torque around the y-axis of the wheel system KR

vRx

Velocity of the wheel’s center in the longitudinal direction

vP

Velocity of the (virtual) wheel–road contact point P

rstat

Static wheel radius

rdyn =

UR 2π

Dynamic (effective) wheel radius

MP

Instantaneous center of rotation

s

Slip

sA , sB

Drive slip, brake slip

2.3 Mathematical description of tire forces

49

EULER’s equation for the wheel results to €R = MA, B − FRx rstat . ΘRyy ρ

(2:7)

€R depends on the driving and braking torque MA,B and The angular acceleration ρ the tire’s longitudinal force FRx , which acts parallel to the roadway, as well as on the rotational inertia ΘRyy . The dynamic tire radius rdyn required for the calculation of the slip is determined by the rolling circumference UR of the wheel. For this purpose, the wheel is towed without drive and braking forces at a defined vertical load at the speed of 60km=h and the rolling circumference UR is measured during the rotation of the wheel on the road. To describe the forces acting upon the wheel, the concept of rigid body slip is used (Figure 2.24). Given an ideal (slip-free) rolling movement of wheel, the velocity vP of the wheel contact point disappears and the speed of the wheel center becomes vRx = ρ_ R rdyn . Given an accelerated or braked wheel, a relative velocity within the tire contact point arises that refers to the wheel velocity (the so-called slip).

M

MP = M

MP P

P M

Driven wheel − = =

Spinning wheel = =1

P ≡ MP Free rolling wheel =0

M M

M

P MP =

Braked wheel − =

P Blocked wheel = =1

Figure 2.24: Explanation of the rigid body slip.

To be able to distinguish between driving slip sA and brake slip sB , the amount of relative speed vP in the wheel contact point P is related to the respectively larger

50

2 Wheels and tires

value of the two variables vRx and ρ_ R rdyn . The driven wheel thus results in the driving slip ðvRx < ρ_ R rdyn Þ as sA =

ρ_ rdyn − vRx vP = R . ρ_ R rdyn ρ_ R rdyn

(2:8)

The brake slip ðvRx > ρ_ R rdyn Þ of the braked wheel can be described as sB =

vR − ρ_ R rdyn vP = x . vRx v Rx

(2:9)

The combination of eqs. (2.8) and (2.9) yields for the general case sA,B =

ρ_ R rdyn − vRx

. max
ρ_ R rdyn
, jvRx j

(2:10)

The slip sA, B is thus defined for the interval ½ − 1, 1 = fsA,B 2 Rj − 1 ≤ sA,B ≤ 1g. In case of a blocked wheel ðvR ≠ 0, ρ_ R = 0Þ, the slip is described as sA, B = − 1. For a spinning wheel ðvR = 0, ρ_ R ≠ 0Þ, the slip results in sA,B = 1. The values of the longitudinal slip are therefore (Figure 2.24): spinning wheel, – sA, B = 1 driven wheel, – 0 < sA, B < 1 rolling wheel, – sA, B = 0 – − 1 < sA, B < 0 braked wheel, and blocked wheel. – sA, B = − 1 The slip is often reported as a percentage, for example, sA = 20 % equals sA = 0.2. The transmitted circumferential force FRx is generated by the tangential tensions τx in the tire contact patch (Figure 2.25). However, the tangential tensions are limited by the static friction coefficient between tire and road surface. Therefore, given a normal pressure pN and the static friction coefficient μH the tangential tension cannot exceed a value of τxmax = μH pN .

(2:11)

If τx exceeds this maximum value, the tangential tension becomes limited to the value τxmin = μG pN .

(2:12)

Therefore, the transmittable circumferential force in the tire contact patch can be described as ðA FRx =

τx dx. E

(2:13)

2.3 Mathematical description of tire forces

51

Static friction limit

Sliding friction

E

G Stiction

A Sliding

Figure 2.25: Qualitative behavior of the tangential tensions in the tire contact patch (shaded area: tire longitudinal force).

The circumferential force FRx can now be represented as a function of the circumferential slip sA, B . The qualitative behavior of the circumferential force as a function of longitudinal slip is shown in Figure 2.26. Depending on the type of tire and the road surface, the maximum transmittable longitudinal force and the shape of the curve change. The circumferential force initially increases linearly until it saturates and reaches the maximum value FRx, max . In this area static friction conditions prevail within the tire contact patch (see section EG in Figure 2.25), while in the remaining part of the tire contact patch sliding already occurs (see section GA in Figure 2.25). With increasing slip values, the point G increasingly moves toward inlet zone E, until the entire tread pattern is sliding. For small slip values, the circumferential force with the longitudinal slip stiffness cs can be described well by a linear function (Figure 2.26): FRx = cs sA, B .

(2:14)

If the slip exceeds the value sA, Bmax (Figure 2.26), the longitudinal force is reduced due to slippage in the tire contact patch surface. If the longitudinal slip continues to increase, the transmittable longitudinal force takes the value of FRx, G , which usually is smaller than the force FRx, max . In this area the complete tire contact patch is sliding. If the front wheels block, the vehicle no longer reacts to steering interventions because the blocked tires can no longer maintain lateral forces. 2.3.3.2 Lateral slip The lateral slip is determined by the slip angle α and is a kinematic variable that describes the relative movement between tire and road in the transverse or lateral direction of the wheel. If a vehicle is steered into a turn at high speed, the vehicle’s wheels develop a speed component speed component transversely to the rolling direction,

52

2 Wheels and tires

FRx

Stiction (rolling wheel) Sliding (blocked wheel)

FRx,max FRx,G = μGFz,eff

CS 0%

100%

SA,B

max

SA,B

Figure 2.26: Qualitative longitudinal force curve as a function of longitudinal slip.

which has to be considered. The slip angle α arises between the direction of movement of the wheel center and the longitudinal direction of the wheel (Figure 2.27). The slip angle α is calculated as α = arctan

vRy . vRx

(2:15)

Under normal driving circumstances, jαj < 12 (Heißing and Ersoy 2011); it is assumed that the tire contact patch has similar deformation characteristics in the longitudinal and lateral direction. Therefore, the principles used modeling lateral force transmission apply modeling simultaneously to longitudinal force transmission. Figure 2.27 shows the way in which lateral force transmission acts; important variables are listed in Table 2.4. While rolling the lateral force FRy shifts the tire contact patch transversely to the direction of travel due to its material properties. Since the wheel is rolling simultaneously, the slip angle α arises. The tread elements of the tire contact patch initially stick to the road surface. While the tire contact patch runs through, the lateral deformation of the tread pattern elements increases (Figure 2.27). At smaller slip angles, the elements adhere to the road until they leave the tire contact patch. The tangential tension in transverse direction of the tire increases linearly toward the end of the contact patch (Schramm, et al. 2018). For small slip angles, the linear law of force applies FRy = cα α.

(2:16)

2.3 Mathematical description of tire forces

53

xR vR

α

Contact patch

yR

MR z

F ′Ry

OR

nR FR y τ

Figure 2.27: Tire in response to lateral force (Matschinsky 2007).

Table 2.4: Variables of the tire concerning lateral force (see also Figure 2.27). Symbol

Description

vR

Velocity of the wheel center

α

Slip angle (lateral slip)

cα

Cornering stiffness (lateral stiffness)

FRy

Tire lateral force parallel to the y-axis of the tire system KR

F ′Ry

Reaction force

MRz

Aligning torque around the z-axis of the tire system KR

nR

Pneumatic trail due to slipping within the tire contact patch

τ

Tangential tension within the tire contact patch

Due to the increasing tangential tension τ in the direction of the patch outlet, the resulting lateral force no longer acts in the middle of the tread, but further behind, at a distance nR (tire:caster). This generates an aligning torque MRz = FRy nR

(2:17)

54

2 Wheels and tires

around the zR -axis of the wheel-fixed coordinate system KR = fOR ; xR , yR , zR g. The tire caster is calculated based on the resulting area balance point of the trapezoidal distribution of tension (Figure 2.27). With increasing transverse deformation, the tread elements in the rear region of the tire contact patch begin to slide. This limits the transmittable lateral force and reduces the tire caster and thus the aligning torque. Figure 2.28 shows the qualitative lateral force curve as a function of the slip angle. The maximum transmittable lateral force and the curve characteristics vary depending on the tire. The lateral force initially increases linearly as the tread pattern elements enter into the tire contact patch area (eq. (2.16) and Figure 2.28). Subsequently, the slip angle further increases, thus increasing the deflections of the tread elements and thereby the tangential tension. The closer to the edge of the tire contact patch the more pronounced this effect becomes. During this process, tread elements increasingly change from a state of adhering to the road to slipping. The lateral force no longer increases linearly but gradually decreases based on the slip angle. With increasing slip angle, the area in which sliding occurs extends to the front section of the tire contact patch. If the entire tire contact patch slides in transverse direction, the lateral force decreases again, similar to the longitudinal force.

FR y FR y,max

cα

≈ 14˚ α Figure 2.28: Qualitative lateral force curve as a function of the slip angle.

2.3.4 Impact of the tire’s normal forces In the normal operating range (small wheel loads), there is an approximately linear dependency of the tire forces FRx and FRy in the tire contact patch area on the current vertical force FRz . Given very high wheel loads, this dependence changes.

2.3 Mathematical description of tire forces

55

The wheel forces then increase disproportionately (degressively) in response to the vertical force, since the friction compound of the tire rubber in the tire contact patch area decreases with increasing contact pressure (see Section 2.2.2). The maximum coefficient of friction decreases with increasing wheel load. This means that an increasing vertical force of the tire does not proportionally increase the upper limit of the lateral cornering force. Thereby, the lateral dynamics of the vehicle can be influenced by changing the wheel loads (e.g., by active suspension systems; see Chapter 7). In Figure 2.29 the cornering stiffness cα of a tire is depicted as a function of the vertical force.

cα

Cornering stiffness

Nonlinear range

Linear range

Vertical wheel force FR z Figure 2.29: Qualitative dependence of the cornering stiffness on the wheel vertical force.

The transition from the linear to the nonlinear range is here defined by exceeding a defined constructional operating load FRz, B . The degressive force curve can, for instance, be accounted for by implementing an effective wheel load 0 !2 1 F Rz A, (2:18) FRz, eff = FRz @1 − eRz FRz, B which is used instead of the actual wheel load FRz to calculate the wheel horizontal forces (Ammon 2013). The degression parameter eRz typically ranges in an interval of eRz 2 ½ 0.05 . . . 0.09.

56

2 Wheels and tires

2.3.5 Influence of the camber on the lateral tire force The camber angle γ contributes additionally to the occurring lateral force of the tire. The emergence of this force can be explained using a wheel that produces a camber angle γ in relation to the road vertical (Figure 2.30). Let the lateral force caused by this camber angle be Fy ðγÞ. A wheel rolling freely given the camber angle γ would, without its bindings to the wheel suspension, move in a circular path along the imagined apex O. However, the suspension forces a movement in x direction. This can be explained by the lateral force Fy ðγÞ and the steering torque MRz ðγÞ. For small camber angles γ < 5 , the camber lateral force and the steering torque, which is caused by the camber, increase approximately linearly with the camber angle. Therefore, the linear relationships Fy ðγÞ = − cγ γ and

(2:19)

MRz ðγÞ = − cM, γ γ

(2:20)

are obtained (Schramm et al. 2018).

Suspension-enforced direction of movement Direction of movement without suspension

γ

r O

γ

MR (γ) z

O r

Fy (γ)

Fy (γ)

MR (γ) z Figure 2.30: Development of the camber-induced lateral force of the tire (Schramm et al. 2018).

2.3.6 Mathematical tire models Due to its importance for the dynamic behavior of a vehicle, the description of the tire forces requires an extraordinary degree of attention. Basically, tire models can be assigned to three basic categories: – mathematical models, – physical models, and – mixed forms. The rest of this book deals with mathematical models exclusively, since fundamental physical considerations have been covered in the previous sections.

2.3 Mathematical description of tire forces

57

A mathematical tire model frequently used in practice is the Magic Formula tire model, which was developed at the TU Delft in the Netherlands (Pacejka and Bakker 1993). It is based on a purely mathematical–empirical description of the initial and final behavior of wheel–road contact under quasistationary conditions. The model illustrates the relationship between kinematic tire variables and the tire force by employing a combination of fundamental mathematical formulas. Quasistatic measurements at test benches and with test drives using real tires are used to determine the coefficients for the force transmission formula, thereby capturing the major characteristics of the respective tire. These include, for example, cornering force, longitudinal force, and aligning torque. The advantages of this empirical tire model are among others: – modeling of the behavior of (stationary) tire characteristics with high accuracy, – the adaptation of the curve’s shape by changing only a few parameters (good adjustability and availability of data via measurements and the identification of parameters), – numerical stability and short processing times due to a steady and easy implementation and evaluation of the functions, and – the possibility to easily carry out parameter studies of tire characteristics regarding driving behavior. This empirical tire model assumes a locally flat roadway under the tire as described below. The Magic Formula models allow the linkage of relevant force variables of the tire with the rigid body slips by means of appropriately selected fundamental mathematical functions. Specifically, those links are as follows: – circumferential force Fx with circumferential slip s, – lateral force Fy with the slip angle α, and – aligning torque MRz with slip angle α. Pacejka and Bakker (1993) proposed to first determine the force–slip relationships by means of quasistatic rolling or driving tests and to approximate the acquired data with a combination of sine and arctangent functions. The formulas allow a description of the relationships with high accuracy. However, the description is limited to stationary properties. Figure 2.31 shows the basic shapes of these model functions. The requirements for the description functions are in addition to the meaningful description of all stationary tire characteristics: – a (comparably) easy access to the raw data, – the possibility of an at least partial physical interpretation of the relationships, – a high accuracy, and – an easy assessment of the resulting formulae.

58

2 Wheels and tires

Y

y Circumferential force

arctan(BCD)

D ya Sv

Lateral force

xm

x

Sh Figure 2.31: Basic tire characteristics from the Magic Formula approach and interpretation of the coefficients.

Common is, for example, the following relationship (Pacejka 2006): yðxÞ = D sinðC arctanðBx − EðBx − arctanðBxÞÞÞÞ,

(2:21)

Y ð XÞ = yðxÞ + Sv ,

(2:22)

x = X + Sh ,

(2:23)

whereby Y ð XÞ represents either the circumferential force, the lateral force, or the aligning torque, which is not treated here. The variable X represents either the longitudinal slip s or the slip angle α. The used parameters can now be interpreted as listed in Table 2.5 or shown graphically in Figure 2.31. Table 2.5: Magic Formula parameters for the tire’s longitudinal forces and torques (see also Figure 2.31). Symbol

Description

D

Maximum force or maximum torque

C

Influences the shape of the curve – stretching in the x direction

E

Additional stretching or compression of the characteristics

BCD

Slope of the characteristics at zero slip (stiffness)

Sv, Sh

Vertical or horizontal shift of the characteristics

Between parameters and typical variables of the curves the following relationships apply:

2.3 Mathematical description of tire forces

 2 ya C=1± − arcsin D π π Bxm − tan 2C E= . Bxm − arctanðBxm Þ

59



(2:24)

(2:25)

Data sets for clarification purposes of the described parameters can be found in the literature. For special applications, the parameters of the respective tires have to be approximated using data bases of measurements (Pacejka 2006). The typical appearance of the basic curve shapes in eqs. (2.21) to (2.23) can be found in Figure 2.31. However, it should be noted that this is a quasistationary description of tire forces. The actual process and the temporal properties of the construction of actual tire forces is not considered. This is instead discussed in Section 2.3.8.

2.3.7 Superposition of horizontal forces The maximum resulting force in the tire contact patch is limited and therefore consideration of the dependence on longitudinal and lateral force are necessary (e.g., when steering and braking simultaneously or accelerating in a curve). To simulate a vehicle’s behavior realistically, the effects of the tire force saturation under strong forces in the tire contact patch are to be considered. This characteristic can be described by the resulting tire force of the KAMM’s circle2 (Figure 2.32), which is based on Coulomb’s friction circle. It applies qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FR2 x + FR2 y ≤ μmax Fz, eff . (2:26) KAMM’s circle describes the relationship between longitudinal and lateral force in combination with a given type of slip. The maximum transmittable lateral force is smaller, if the longitudinal force occurs simultaneously (and vice versa). In reality, the threshold curve of the maximum transmittable horizontal force forms an ellipse, since real tires usually have a bigger adhesion limit in the longitudinal direction μmax, x Fz, eff than in the transverse direction μmax, y Fz, eff (Schramm et al. 2018). The smaller dashed circle in Figure 2.32 corresponds to the tire force given pure sliding friction μG Fz, eff . In Figure 2.33, lateral force curve, slip angle, and slip curve of the circumferential force are used to derive the KREMPEL friction ellipse (Krempel 1965). The Krempel friction ellipse corresponds roughly to KAMM’s circle (Kamm et al. 2013). For different longitudinal slips or slip angles corresponding friction ellipses can be derived.

2 Wunibald Kamm (1893–1966): German scientist in the field of motor vehicle and engine technology and one of the leading motor vehicle aerodynamicists.

60

2 Wheels and tires

,

,

Figure 2.32: Simultaneous transmission of longitudinal and lateral force (KAMM’s circle).

10° 20° when

2°

= 0N

= 1° ,

= 10°

1°2°

10°

20°

α

1°

Figure 2.33: Krempel’s friction ellipse as envelope; derivation from lateral force, slip angle, and slip curve of the circumferential force.

To be able to account for overlapping effects in different driving situations (braking or acceleration in the curve) in which both circumferential and lateral slip occur, an absolute slip term sa (the so-called combined slip) based on longitudinal slip sA, B and slip angle α is defined as

2.3 Mathematical description of tire forces

sa =

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2A, B + tan2 α

61

(2:27)

with the operating direction ψa = arctan

tan α . sA, B

The resulting tire force in direction of angle ψa is calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2A, B FR2 x ðsa Þ + tan2 αFR2 y ðsa Þ . Fψa ðsa Þ = s2a

(2:28)

(2:29)

The resulting tire longitudinal and lateral forces now read sA, B Fψ a ð s a Þ sa

(2:30)

tan α Fψa ðsa Þ. sa

(2:31)

FRa, x = Fψa ðsa Þ cos ψa = and FRa, y = Fψa ðsa Þ sin ψa =

2.3.8 Instationary tire forces In previous approaches to tire force transmission, it is assumed that lateral slip, circumferential slip, tire forces, and torques remain constant over time or change very slowly. In unsteady maneuvers such as step steering input or antiblocking system (ABS) braking, the tire forces follow the slip sizes with a delay (response time of the tire (Figure 2.34). Thus, the tire forces influence the dynamic transmission while driving. The transient construction of the tire force behaves approximately like a firstorder element and can therefore also be represented by a PT1 -element. The approximation of the temporal development of the dynamic longitudinal force is given by the differential equation of first order: Tx

dFRx + FRx = FRx , stat , dt

(2:32)

(Einsle 2010), (Heißing and Ersoy 2011). For the dynamic lateral force applies accordingly Ty

dFRy + FRy = FRy , stat . dt

(2:33)

62

2 Wheels and tires

Lateral force / N

F R = c αα 0 y

T0

Time σα Ty = | ρR rdyn |

Figure 2.34: Time course of the lateral force FRy with a slip angle jump to α0 at T0 .

The time constants Tx and Ty in eqs. (2.32) and (2.33) depend on the rolling speed of the tire and are calculated as Tx =

c c
s
and Ty =
α
. cx
ρ_ R rdyn
cy
ρ_ R rdyn


(2:34)

The parameters used in eq. (2.34) are described in Table 2.6.

Table 2.6: Formula parameters used to calculate the dynamic tire forces. Symbol

Description

cx

Static tire circumferential stiffness

cy


ρ_ rdyn
R

Static tire lateral stiffness Absolute value of the circumferential velocity

FRx , stat

Static tire longitudinal force calculated by the Magic Formula model with the slip sA, B considering Kamm’s circle

FRy , stat

Static tire lateral force calculated by the Magic Formula model with the slip angle α considering Kamm’s circle

The time course of the force construction depends on the relaxation length. This dependency is determined by the relaxation length σRx for the longitudinal force, which is derived from the quotient of the longitudinal slip stiffness cs and the tire longitudinal stiffness cx

2.3 Mathematical description of tire forces

σ Rx =

cs . cx

63

(2:35)

as well as the relaxation length σRy for the lateral force. The lateral force, in turn, is derived from the quotient of the lateral slip stiffness cα and the tire’s lateral stiffness cy σ Ry =

cα . cy

(2:36)

The relaxation length σR describes the way the tire must travel to build up about two-thirds of the dynamic tire force. Whereby, the relaxation length in the lateral direction of the tire is higher than in the circumferential direction. This is related to the lateral resilience of the tire, which is greater than the longitudinal resilience (Gipser 1999). The solution of the differential eqs. (2.32) and (2.33) yields the difference equation after discretization (Gipser 1999): FRi ðn + 1Þ = e

 − Δt T i

 FRi ðnÞ − FRi , stat ðnÞ + FRi , stat ðnÞ, i = x, y.

(2:37)

The transformation of the mathematical model from a real continuous system into a time discrete model is necessary if one would like to solve it in real time.

2.3.9 Dynamics of the braked and driven wheel The following sections cover the equations of motion in the direction of travel and force relationships on the braked and driven wheel. The equations will be summarized below. For this purpose, the designations from Figure 2.35 and Table 2.7 are used. Whereby, the dynamics of the wheel are only considered in the direction of travel. The vertical dynamics of the wheel are neglected. First, NEWTON’s equation for a wheel is mR €xR = FRx − FVAx ,

(2:38)

and the balance of forces in vertical direction is FRz = FVAz + mR g.

(2:39)

EULER’s equation regarding the wheel’s center is €R = + MA, B − FRx rstat . ΘRyy ρ

(2:40)

The relationship between rotational speed and translational speed of the wheel is obtained by means of the dynamic wheel radius introduced above

64

2 Wheels and tires

,

M ,

P Figure 2.35: Force relationships for a driven wheel.

x_ R = rdyn ρ_ R .

(2:41)

The tire’s longitudinal force can now be calculated by combining eqs. (2.40) and (2.41) FRx = ΘRyy

ΘRyy €xR MA, B €R MA, B ρ + =− + . rstat rstat rdyn rstat rstat

(2:42)

It can be derived from that relationship that the inertia of the wheel reduces acceleration and braking. In particular, when braking this has a disadvantageous effect on the performance of the ABS, since the time that the wheel takes after blocking in order to get rolling again, depends on the wheel’s moment of inertia. This is further complicated by the fact that the wheel of a driven axle has a significantly larger effective moment of inertia due to additional rotating masses of the power train (see Chapter 6). Table 2.7: Formula parameters for calculating the dynamic tire forces (see also Figure 2.35). Symbol

Description

MA, B

Drive or braking torque

FVAx , FVAz


ρ_ rdyn
R

Forces of the vehicle on the wheel in x- and z-direction Absolut value of tire peripheral speed

xR

Acceleration of the wheel center

FRz

Wheel load

mR

Mass of tire

ΘRyy

Effective moment of inertia of the wheel

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2.4 Monitoring of the tire pressure In addition to driving behavior and driving comfort, the tire inflation pressure also significantly influences fuel consumption and thus the emissions of a motor vehicle. If the pressure is too low, there is a risk of tire damage. This represents a significant risk to the driving safety. Although it is recommended to regularly check the tire inflation pressure, it is known that drivers only occasionally and partially check tire pressure. When checking, mostly only an inadequate visual inspection of the tire is performed (Hoppe et al. 2013). The tire is already at risk if the vehicle is driven on a longer trip with only 20% reduced pressure. Figure 2.36 shows that it is hardly possible to detect a lack of pressure with the naked eye. The result is more than 150,000 punctures per year in in Germany alone (Hoppe et al. 2013).

1

2 1 Correct tire pressure (2.4 bar) 2 20% lower tire pressure

3

4

3 40% lower tire pressure 4 60% lower tire pressure

Figure 2.36: Insufficient visual inspection of a lack of tire pressure (courtesy of Huf Hülsbeck & Fürst GmbH & Co. KG).

TPMS shall serve as a solution to that problem by warning the driver if the tire pressure decreases. Thereby, fuel consumption and thus CO2 emissions can be reduced by up to 4%. At the same time, a correctly adjusted tire pressure increases the tire’s service life, optimizes tire noise, and lane groove sensitivity (Hoppe et al. 2013). Since November 2014, all new vehicles within the European Union with a gross vehicle weight of up to 3.5 t have to be equipped with TPMS (EU Regulation No. 661/2009). A distinction is made between direct and indirect TPMS. These differ in the way in which the filling pressure is monitored.

2.4.1 Direct tire pressure monitoring In direct TPMS, the pressure of each tire is measured with a sensor. Figure 2.37 shows an example of a vehicle display that shows the driver both the tire

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Figure 2.37: Vehicle display with information about the tire pressure and temperature.

Figure 2.38: Example of a warning of tire pressure loss (courtesy of Nira Dynamics AB, 2016).

inflation pressure and the temperature of the air within the tire. In the event of deviations from the correct pressure, the driver is informed by a warning message, (Hoppe et al. 2013), Figure 2.37. More than 80% of the “blowouts” are the result of a gradual loss of pressure. This happens because the sidewall of the tire heats up due to excessive flexing work, which eventually results in a puncture.

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67

Direct TPMS (Figure 2.39) use a tire pressure sensor in each wheel to measure the inflation pressures and inflation air temperatures. This information is transmitted together with the individual sensor identification via radio signal (Europe 434 MHz band) to the control unit in the vehicle (Hoppe et al. 2013). This enables a tire-specific pressure display in the instrument cluster. Direct measuring systems detect both, slow diffusion losses and fast pressure losses.

Instrument cluster

Electronic control unit

Radio signal

Tire pressure sensor Figure 2.39: Scheme of a direct tire pressure monitoring system (courtesy of Huf Hülsbeck & Fürst GmbH & Co. KG).

The tire pressure sensors achieve a measuring accuracy of approx. 0.1 bar. The sensors typically provide a signal every 30 to 60 seconds. A control unit processes the information and prepares it for display in the instrument cluster. The tire pressure sensor is also referred to as wheel electronic unit. Figure 2.40 shows a sensor integrated into the rim. Figure 2.41 shows the essential components of a valve-integrated wheel electronic unit. The valve (1) is screwed to the sensor housing (2) and is attached to the valve hole on the rim. The sensor case contains a circuit board (3) with a highly integrated sensor (4) and further electronic components like a lithium button cell (5) for power supply. To ensure mechanical stability and protection against moisture, circuit board and battery are enclosed by a protective cast. A new innovative concept of tire pressure sensor attachment is the attachment of the sensor to the inside of the tread (innerliner; Figure 2.42). This type of attachment characterizes the mechanical connection of the sensor to the tire, resulting in a solid unit of sensor and tire. If the sensor moves from the rim or the valve to the tire, the centrifugal accelerations acting on the sensor and the mechanical load change accordingly. To avoid unbalance, the weight introduced should be very low ( < 10g) (Hoppe et al. 2013). Because this type of attachment allows the formation of a unit between tire and tire sensor, information about the tire can be stored by the sensor and transmitted to the vehicle. Important tire parameters are the maximum

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Figure 2.40: Tire pressure sensor integrated in the rim (courtesy of Huf Hülsbeck & Fürst GmbH & Co. KG).

Figure 2.41: Tire pressure sensor integrated in the valve (courtesy of Huf Hülsbeck & Fürst GmbH & Co. KG).

Figure 2.42: Tread-integrated tire pressure sensor (courtesy of Huf Hülsbeck & Fürst GmbH & Co. KG).

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69

permitted speed, for example, in winter tires. Exceeding this permissible speed could thus be automatically prevented or at least displayed. Another valuable information is the mounted tire type. This information could be used on the side of the vehicle to achieve a tire-specific adaptation of the chassis controller to increase driving safety and driving performance. If a sensor is mounted on the rim, it does not form a unit of tire and sensor anymore, since both are separated if the tire is changed. If the sensor is mounted on the innerliner of the tire, it is possible to estimate the tire’s footprint on the roadway using a suitable accelerometer. This is done by measuring the change of the sensor’s acceleration in the area of the wheel contact surface (Figure 2.43). If wheel contact length, tire pressure, tire temperature, and other tireand vehicle-specific information are known, it is further possible to estimate the wheel load and thus the degree to which the vehicle is loaded in general.

x-signal Running direction Acceleration ax, az

z-signal

Contact patch

x-signal

z-signal

Time Figure 2.43: Acceleration of the tire sensor while running through the contact patch (courtesy of Huf Hülsbeck & Fürst GmbH & Co. KG).

2.4.2 Indirect tire pressure monitoring In contrast to direct TPMS, indirect tire pressure monitoring systems do not measure the pressure in the tires, but primarily make use of the existing signals from the ABS wheel speed sensors (Figure 2.44). Indirect systems make use of the fact that the rolling circumference of the wheel and thus the effective rolling radius depends on the tire pressure. If the tire pressure drops, the rolling radius decreases. This, in turn, increases the wheel’s speed relative to the other wheels. Thus, by evaluating the differential speeds of all wheels, the pressure loss of individual wheels can be detected, as shown, for example, in Figure 2.45.

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Electronic control unit Wheel RPM sensor singnals

Instrument cluster

Wheel RPM sensor signals Figure 2.44: Scheme of an indirect tire pressure monitoring system according to Hoppe et al. (2013).

∆

,

ℎ

, rear

∆

Front left

∆

, front

∆

Rear left Time

∆

,left

Figure 2.45: Determination of pressure loss of the front left wheel by evaluating the differential speeds (courtesy of Nira Dynamics AB).

The change in the wheel’s speed can be very low. Therefore, very robust signalprocessing algorithms (e.g., using Kalman filters) are needed to reliably detect these differences. The algorithms are usually executed by means of the ESP control unit, because this is where the raw signals of the wheel speed sensors are received. Rolling radius differences occur, for example, when cornering or driving uphill. Those differences must be accounted for by a suitable dynamic model of the vehicle. Likewise, tire type (summer, winter, and all-season tires), tire size, temperature effects, depth change in the tire’s tread pattern, and radial tire expansion (occurring at high speeds) must be considered. This may cause a delay in the detection of pressure loss. Indirect TPMS are used since the beginning of 2000 (Hoppe et al., 2013).

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However, the method of detecting wheel speed changes does not allow to detect a simultaneous and uniform pressure loss of all four tires (as it is caused, for example, by diffusion (Figure 2.48, left). To detect simultaneous and uniform pressure losses, the spectral analysis method is used. If the tire rolls along the roadway, its eigenmode oscillations are stimulated. Some eigenmodes, such as the tire torsional mode at about 40 Hz, depend on the filling pressure (Figure 2.46, left). If the filling pressure changes, the frequency of the tire eigenmode shifts (Figure 2.46, right and Figure 2.47, right). Therefore, the system is able to detect pressure losses of a single, as well as of all four tires at the same time (Figure 2.47, right and Figure 2.48, right).

0,8 230 kPa 177 kPa

Amplitude

0,6 0,4 0,2 0 30

40

50

60

70

Frequency/Hz Figure 2.46: Left: 1. Torsional mode of the wheel–tire complex at approx. 40 Hz; right: example of a frequency shift for different filling pressures (courtesy of Nira Dynamics AG).

Wheel rpm

Amplitude

Time

Frequency

Figure 2.47: Detection of pressure loss in the front left wheel using the wheel speed change method (left) and frequency shift (right) (courtesy of Nira Dynamics AG).

All indirect TPMS can only detect relative pressure changes, either by relative wheel speed or frequency differences. If the tire is replaced or refilled, the system must be reinitialized. After refilling the tires, the driver is thus obligated to manually

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Amplitude

Wheel rpm

Time

Frequency

Figure 2.48: No detection of simultaneous and uniform pressure loss, using the wheel speed change method (left). Detection using frequency shifting technique (right) (courtesy of Nira Dynamics AG).

reinitialize the system, for example, by pressing a button. Wrong initialization can lead to incorrect driver warnings (Hoppe et al., 2013). Advantages of the indirect systems are lower costs, since no additional components have to be implemented. The disadvantage is that neither tire pressures nor the inflation air’s temperature can be measured. A correct warning depends on the correct calibration of the system. During highly dynamic driving with lateral acceleration greater than 2m=s2 , such as on racetracks, the system is inactive.

3 Vehicle dynamics and suspension system Vehicle dynamics describes the movement of a vehicle under the influence of internal and external forces and torques (Schramm, Hiller et al. 2018). These are transmitted to the vehicle via the tires and through the air. The suspension system is tasked with positioning the wheels on the road in a way that optimizes the transfer of tire forces to the road. The hereby achieved driving behavior can be tested subjectively by test drivers, or objectively using standardized parameters (DIN 2008). While these parameters have been established mostly in driving tests, over the past few years new procedures based on simulations have been gaining ground more and more (Schramm, Hiller et al. 2018). The entire driving behavior of a motor vehicle can be divided up into longitudinal, lateral, and vertical dynamics. Considering the linear part of driving dynamics, the behavior can easily be considered distinct: – Lateral dynamics describes the cornering behavior of a vehicle as well as its response to steering movements. It has a large influence on the agility and driving safety of a vehicle. – Longitudinal dynamics describes the acceleration and braking performance. Furthermore, the energy consumption of the vehicle can be essentially derived from it. – Vertical dynamics describes the reaction of the vehicle to impulses given by road unevenness and bumps and is essential to the riding comfort and (via the wheel load fluctuation), responsible for the driving safety of a motor vehicle. At the stability limit of driving dynamics and beyond however, there is a strong coupling between the directions of movement; see, for example, Lenthaparambil (2015) and Schramm, Hiller et al. (2018). In those cases, such a simplified division is no longer possible. The driving behavior is influenced substantially by the assembly groups body, wheel suspension, and especially the tires.

3.1 General definitions of vehicle motion To better understand the parameters of vehicle dynamics for lateral, vertical, and logitudinal dynamics, one first needs to describe the spatial movement of the vehicle in a suitable form. While driving, the vehicle body performs a spatial motion. To describe it, the body fixed coordinate system KV 1 (orthogonally and clockwise) is used (Figure 3.1). The 1 The index “V” stands for vehicle. https://doi.org/10.1515/9783110595703-003

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3 Vehicle dynamics and suspension system

zv Heave

Vertical axis Yaw 𝜓v

0V

Jerk xv Roll 𝜑v Longitudinal axis (vehicle longitudinal centerline)

Lateral axis Pitch yv 𝜃v Push

Figure 3.1: The six rigid body degrees of freedom of a vehicle.

origin OV of the system KV is placed in the center of mass (CoM) of the body (DIN 2008). This specific point is chosen because it makes calculations of the fundamental physical laws such as NEWTON’s and EULER’s equations much easier (Schramm, Hiller et al. 2018). The vehicle body is modeled as a rigid body for the fundamental analysis. It possesses six rigid body degrees of freedom (DoF) through which its location in space is conclusively determined. The DoF chosen here and their corresponding generalized coordinates are shown in Figure 3.1. Here, the distinction is made between translational and rotational DoF. The translational DoF are denoted by terms according to DIN (2008): – “Jerk” in longitudinal direction of the vehicle (longitudinal movement toward the xV -axis), – “Push” in lateral direction of the vehicle (lateral movement along the yV -axis), and – “Heave” (vertical movement along the zV -axis). The rotational DoF are described with the Cardan angles in the rotation sequence x ! y ! z, initiating from the inertial system, and are named as according to DIN (2008): – “Roll” (rotation around the xV -axis with angle φV ), – “Pitch” (rotation around the yV -axis with angle θV ), and – “Yaw” (rotation around the zV -axis with angle ψV ). For most driving conditions during normal operation and as a first-order approximation, the driving dynamics of the vehicle can be observed separately for the

3.2 Coordinate systems

75

longitudinal, lateral, and vertical direction, respectively. Nevertheless, the occurring forms of movement are, of course, always coupled with one another (Figure 3.2). This effect is particularly strong when driving in the (nonlinear) dynamical limits, but is also relevant when studying the dynamic interactions combined with the use of driving dynamics control systems.

Vertical dynamics carry/cushion/damp

Pi tc h

Ro ll

Longitudinal dynamics drive/brake

Yaw

Lateral dynamics steer

Figure 3.2: Relations in vehicle dynamics.

This chapter considers the lateral and vertical dynamics as well as their interaction. The longitudinal dynamics of motor vehicles is examined further in Chapter 6.

3.2 Coordinate systems The vehicle body and chassis are usually considered to consist of rigid bodies and can thus be approximated as multibody systems (MBSs) (Schramm, Hiller et al. 2018). Torsions or other deformations of the body can be neglected for many examinations. The frame can move freely in space. A body-fixed coordinate system KV = fOV ; xV , yV , zV g is introduced for the description of positions. The vehicle-fixed reference point OV lies in the body’s center of gravity (DIN 2008). The x-axis points forward toward the longitudinal direction of the vehicle, the y-axis points left in the lateral direction of the vehicle, and the z-axis is oriented perpendicular to the road surface. For the spatial description of the chassis, the three components E xV , E yV , E zV of the position vector rV in the coordinates of an inertial system KE ,2 as well as the three Cardan angles ψV (yaw), θV (pitch), and φV (roll) are introduced. Figure 3.3

2 The index “E” here means “environment.”

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3 Vehicle dynamics and suspension system



0 

 



 







O = S

O

Figure 3.3: Coordinate systems and description of the position of motor vehicles.

shows the location of the used coordinate systems. Here, rV is the vector from the origin OE of the inertial system to the origin OV of the body fixed coordinate system, V r i the vector from OV to a point Pi of the vehicle, and r i the vector from the origin of an inertial system to the rigid body point Pi . The orientation of the vehicle system KV to the inertial system KE is clearly determined by the three Cardan angles. It is assumed that at the start, the inertial system and the vehicle system have the same orientation. Then, the vehicle runs three successive rotations around predetermined axes. Every partial rotation corresponds to a Cardan angle. The sequence of rotations of the Cardan angles is as follows: – Due to the rotation around the zE -axis with the yaw angle ψV , the xE , yE , zE system transitions into the x1 , y1 , z1 -system with z1 = zE . – Due to the rotation around the y1 -axis with the pitch angle θV , the x1 , y1 , z1 system transitions into the x2 , y2 , z2 -system with y2 = y1 . – Due to the rotation around the x2 -axis with the roll angle φV , the x2 , y2 , z2 system transitions into the xV , yV , zV -system with xV = x2 . For a more detailed description of the spatial movement of motor vehicle, see Schramm, Hiller et al. (2018). The choice of this coordinate system in the area of construction often is not practical however, because the center of gravity has yet to be defined, and most coordinates, especially in the xV - direction, would become negative. For those reasons, a different coordinate system is used in CAD3 (in Figure 3.3 labeled with

3 CAD: Computer Aided Design.

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77

CAD), with its origin OCAD in the area of the forebody, for example, in the middle of the front axle. In this case, the xCAD -axis is opposite to the direction of driving.

3.3 Structure and components of the chassis The suspension system connects the wheels to the body of the vehicle. It is thus responsible for guiding the wheels and protecting the vehicle in a way that passengers, cargo, and vehicle systems do not suffer excessive loads caused by acceleration and other forces. The typical suspension system of a car is made up of the assembly groups (partially pictured in Figure 3.4):

Figure 3.4: Chassis and powertrain of the Porsche 911 Turbo S © Porsche AG.

– – – – – – – – – –

front and rear axle, including the corresponding subframe, suspension and damping (Sections 3.10.4 and 3.10.5), antiroll bars (Section 3.10.6) wheels and tires (Chapter 2), steering system (Chapter 4), brake system (Chapter 5), wheel bearings and carrier (Section 3.8), chassis control systems (Chapter 7), pedals and steering wheel (Chapters 4 and 5), and the bearing of the drive unit.

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This chapter first discusses the basics of vehicle dynamics. This includes the definition of vehicle movement as well as static and dynamic parameters of vehicle dynamics. Additionally, driving maneuvers are described to determine and evaluate the characteristics of driving dynamics. These considerations are completed by the description of the kinematics of wheel suspensions. In the course of this, the oftenused MacPherson4- and multilink wheel suspensions are discussed exemplarily. The basic structure of a suspension of an axle is shown in Figure 3.5. Elastomer-link bearing (Annular spring)

Wishbone

Spring–damper Combination Drive shaft

Brake

Antiroll bar (torsion bar)

Figure 3.5: Multilink suspension © Porsche AG.

The definitions used in this chapter refer among others to the following standards: – DIN 70000/DIN ISO 8855 Road vehicles – Vehicle dynamics and road holding ability – Vocabulary (DIN/ISO 2011); – DIN 70020 Road vehicles – Automotive engineering: part 1 (Passenger cars, definitions, dimensions, identification), part 2 (Terms and definitions for masses), and part 3 (testing conditions, maximum speed, acceleration and elasticity, mass, terms, miscellaneous) (DIN 2008); – DIN ISO 7401: Road vehicles – Lateral transient response test methods – Openloop test methods (DIN/ISO 1989); – DIN 70027: Road vehicles; specifications for wheel alignment, (DIN 1992); – SAE J670e: Vehicle dynamics technology (SAE 2008);

4 Named after its inventor, Earle S. MacPherson (1881–1960), who received a patent for the axle in 1949.

3.4 Axle kinematic properties

79

– VDI-Guideline 2057 (VDI 2002); – ISO 3888: Passenger cars – Steady-state circular driving behavior – Open-loop test methods (ISO 2012); – ISO 7401: Lateral transient response test methods (open-loop) (ISO 2011); – ISO 3888: Test track for a severe lane-change manoeuvre (closed-loop) (ISO 2002).

3.4 Axle kinematic properties Together with further parameters, the terms toe-in, camber, pneumatic trail, and steering axis inclination describe the geometric and kinematic properties of the axle of a vehicle. Within the framework of development, production, and maintenance of motor vehicles, these parameters need to be measured. First, the single parameters and their relationship to each other are presented. The axle geometry of a vehicle is characterized by suitable angle and length dimensions. Additionally, the wheel center plane Π is determined for every wheel. For steered wheels, the location of the axle is added, around which the wheel pivots during steering. Hereinafter, the individual characteristics are defined. The angular position of the wheel center plane is determined by two angles. To this end, the profile of the wheel center plane Π is created with two perpendicular planes (Figure 3.6). The first plane is the road plane Σ and the other plane Ω is perpendicular to the road. The angle γ between the wheel center plane Π and the plane Ω is called camber angle and the angle δVS in plane Σ between the axis xV and the intersection of plane Π and Σ is called toe-in angle. (Figures 3.6 and 3.7; Table 3.1).

 



Π 



Ω

A

Σ

Figure 3.6: Definition of key parameters in the wheel–road plane.



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3 Vehicle dynamics and suspension system

 

 



    Figure 3.7: Definition of the toe-in angle.

Table 3.1: Important key parameters in the wheel–road plane (see also Figure 3.6). Symbol

Description

Σ

Road plane

Π

Wheel center plane

Ω

Plane in the direction of driving and perpendicular to the road plane

r

Wheel radius

A

Virtual tire contact point

M

Wheel center

γ

Camber angle

3.4.1 Toe in angle First, the toe-in angle δVS , the angle in the road plane is considered (Figure 3.7) and (Table 3.2).5 Here, either the angle of both wheels of an axle in relation to each other can be measured (total toe-in angle), or the angle of a wheel to a plane of reference (toe-in angle). A possible plane of reference is the longitudinal center plane of the vehicle. This plane is perpendicular to the road and goes through the middle of front and rear wheel. Independent of the plane of reference, the sum of toe-in angles is always equal to the total toe-in angle. The sign of the toe-in angle is positive when

5 It used to be customary to denote the toe-in as a measure of length instead of an angle. To this end, the difference of distance of the rim flanges in the front and back was measured at the level of the center of the wheels. This kind of measurement has the disadvantage that the measured value is dependent on the rim size.

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81

Table 3.2: Parameters of vehicle axles (see also Figures 3.7–3.9). Symbol

Description

r

Wheel radius

δVS

Toe-in angle

bA , bV , bB

Wheel spacing of the wheels of an axle at the front, middle, and back

γ

Camber angle

τ

Caster angle

ln

Trail

nl

Trail offset

σ

King pin angle

lσ

King pin angle offset

rr

Scrub radius

the front wheel is angled inwardly ðbA < bB Þ, see Table 3.2, meaning that the front part of the wheel is closer to the wheel on the other side than the rear part of the wheel. Consider now a vehicle whose non steered rear wheels have different toe-in angles concerning the longitudinal center plane of the vehicle. For the vehicle to go straight, the front wheels have to be turned by steering in such a way that the angle bisector of the angle in between the front wheels is parallel to the angle bisector of the angle between the rear wheels. The angle bisector of the angle in between the rear wheels thus determines the direction of the vehicle driving on a straight track. It is thus called geometric wheel axis. The angle between the geometric wheel axis and the longitudinal center plane of the vehicle is called the axle angle. According to the DIN draft “Fahrwerksvermessung,” the axle angle has a positive sign, if the geometric wheel axis in the front deviates to the left of the longitudinal center plane. If possible, the rear axle should be fine tuned so that both axles coincide in a way that the axle angle is equal to zero. This means that the toe-in angles of the rear axle should be equal. If this is not possible, for example, because the toe-in of the rear axle cannot be adjusted, the vehicle will move more or less angular to its center line when driving straight. If in this case, the front axle is adjusted to have the same toe-in angles while the steering wheel is straight (compared to the longitudinal center plane of the vehicle), the steering wheel needs to be turned when going straight according to the axle angle. The steering wheel then is not straight even though the vehicle is going straight.

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As a remedy, the toe-in angle of the front axle choses a different reference point: the geometric wheel axle. As long as the toe-in angle of the front wheels in reference to this axis is the same, the steering wheel is straight while driving straight, even though the axle angle is not zero.

3.4.2 Camber angle The second angle that describes the position of the wheel center plane is the camber angle γ (Figure 3.8). This is the angle of the wheel center toward the perpendicular of the road. The camber angle is positive when the wheel is tilted outwards at the top. When turning a steered wheel, the camber usually changes. This will be described later in combination with the measurement of the steering axle. In order to state the adjustment value for the camber of a vehicle, it thus needs to be determined at which turning angle and thus which toe-in angle, the camber is measured. Here, either every single wheel can be measured at track zero, or the camber for both wheels is measured when the wheels are directed for going straight, and therefore have the same toe-in angle. If the camber is not measured at “track zero,” the disadvantage arises that the adjustment value for the camber depends on the toe-in angle. On the other hand, camber values can be determined for both wheels at the same steering wheel position while for the measurement at “track zero,” every wheel needs to be measured individually. The vehicle manufacturer states what kinds of measurements are required for this chassis setting data. For axles that are not steered, the camber is always measured at the toe-in angle, because the single wheels can at best be brought to a toe-in angle of zero with difficulty.

Wheel center plane Π Steering axis L

Camber angle 𝛾

Figure 3.8: Definition of the camber angle and the steering axle.

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83

3.4.3 Steering axis For steered wheels, the geometry of the axle is determined by the spatial position of the steering axis6 L next to the previously described parameters. This is the axis around which a steered wheel pivots when turned (Figure 3.8). The steering axis is arranged at an angle. The puncture point of its extension with the road surface is not identical to the center of the wheel contact area. For a full description of a straight line in space, two solid angles and a point are required. The two angles for the steering axis are called caster angle and king pin angle. There are different ways to specify a point on the steering axis: Either the point of the axis in the road plane or in the plane parallel to the road at the level of the wheel center is chosen. In the first case, the point is described using the trail ln and king pin offset rr , and in the second case using the trail offset nl and king pin angle offset lσ . The angles and lines that describe the steering axis are measured in two mutually perpendicular planes that are both perpendicular to the road. The first plane is perpendicular to the road plane and parallel to the intersecting line of the wheel center plane. The second plane is perpendicular to it and thus parallel to the rotation axis. When steering, these planes move with the wheels. The parameters for describing the steering axis thus change with steering. As described in Section 3.4.2, the toe-in value at which measurement is to be done needs to be defined. In contrast to the camber, for the parameters of the steering axis, the definitions in the norms exclusively refer to toe angle zero at the single wheel. In practice, measurements are still often done when going straight, meaning with the same toe-in angle of the single wheels. There, it is assumed that the difference is relatively small and thus does not have a relevant impact. Whether this holds true, however, depends on the kinematics of the individual vehicle. Thus, the specifications of the vehicle manufacturer need to be obeyed. For measuring the axle geometry, those two planes are essential. They are one plane in longitudinal direction of the vehicle and one plane in lateral direction to the vehicle, each perpendicular to the road. The projection of the steering axis is observed for each plane. The caster angle τ denotes the angle that results between the steering axis and a perpendicular line to the road in the plane that is longitudinal to the vehicle. The caster angle is positive when the steering axis L is inclined toward the back (Figure 3.9). The king pin angle σ is measured in a plane lateral to the vehicle against a perpendicular line toward the ground. The king pin angle is positive when the steering

6 Also called spread axis.

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Steering axis L Caster angle 𝜏 Trail offset

𝜎

King pin angle

nl

l𝜎 King pin angle offset

M

D

M

A

D A ln

rr

Trail

Scrub radius

Figure 3.9: Definition of the steering axle.

axis points inward. Accordingly, the lines defining a point of the steering axis are measured within those two planes. If a point of the steering axis is defined at the height of the center of the wheels, the horizontal distance of the center of the wheel M to the steering axis is denoted, projected into the corresponding plane. The horizontal distance nl between the center of the wheel and the steering axis observed in longitudinal plane is called trail offset. If the center of the wheel lies behind the steering axis, the trail offset has a positive sign. Accordingly, the king pin angle offset lσ is the horizontal distance to the center of the wheel M to the steering axis L in the plane lateral to the vehicle. The sign is positive if the steering axis is on the inside of the vehicle compared to the center of the wheel. To determine a point on the longitudinal axle on the road plane, the tire contact point is used as a point of reference and the distance from the point where it intersects with the extended steering axis is specified. Here, the trail ln specifies the distance in the projection plane longitudinal to the vehicle. The trail is positive when the road surface intersection point of the steering axis lies before the tire contact point. In the plane lateral to the vehicle, the scrub radius rr (also called king pin offset) indicates the distance from the road surface intersection point of the steering axis to the tire contact point. If the tire contact point is outside compared to the road surface intersection point, the scrub radius is positive. A negative scrub radius gives advantages when braking on a road that is slippery on one side as the torsional torques created by the longitudinal forces of the wheels around the vertical axis induce a steering motion in the wheels. Those support the driver in compensating for the rotational motion around the vertical axis resulting from the one-sided braking forces.

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85

3.5 Fundamentals of vehicle dynamics The vehicle dynamics is one of the most essential properties and differentiation characteristics, especially for passenger cars. Thus, the fundamental parameters of vehicle dynamics are introduced below that allow the description of the vehicle dynamics of the total vehicle.

3.5.1 Description of the planar vehicle dynamics using the linear single track model The classic linear single track model created by Rieckert and Schunck in 1940 (Rieckert and Schunck 1940) allows a first, yet already meaningful assessment of the driving behavior of a motor vehicle. It uses major simplifications of fundamental driving physics, but depicts regular operating conditions physically correct. Due to its fundamental significance in understanding vehicle behavior in passenger cars, this model is discussed in detail below. The linear single track model is based on a series of essential simplifications (Schramm, Hiller et al. 2018). The velocity of the Center of Mass (CoM) S of the vehicle along its trajectory is assumed to be constant, and all lifting, rolling, and pitch movements of the vehicle are neglected. Front and rear wheels are aggregated and observed as one wheel each. The virtual tire contact points V and H, where the tire forces apply, are assumed to take effect each in the middle of the axle (Figure 3.10). With this, the linear single track model only describes the lateral dynamics of a vehicle. Using corresponding additional terms, an extension to the interaction between longitudinal and lateral dynamics is possible (see Section 3.5.6 and Schramm, Hiller et al. 2018). These assumptions already allow a first examination of the fundamental driving behavior of a motor vehicle with a dry roadway up to

S





V

H

Figure 3.10: Parameters to describe the linear single track model.

+

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3 Vehicle dynamics and suspension system

lateral accelerations of ay ≤ 0, 4g ≈ 4 sm2 .7 Above this limit, the linear approaches generally do not suffice to describe the driving dynamics correctly. Due to the assumptions made, the only possibilities of movement remaining for the mechanical replacement model are the yaw angle ψ, appearing with its derivative, the yaw rate8 ψ_ , and the side-slip angle β. The parameters ψ and β, combined with their derivatives, describe the location and movement of the vehicle body. The side-slip angle describes the deviation of the direction of velocity of the CoM from the longitudinal axis of the vehicle. The steering angle δ of the front axle is assumed to be given and is thus an input parameter for the model.

3.5.2 Equations of motion of the linear single track model Below, the equations of motion of a classical linear single track model are derived. To this end, the symbols described in Table 3.3 are used. Table 3.3: Parameters of the linear single track model (see also Figure 3.11). Symbol

Description

m, θ

Vehicle mass and moment of inertia with respect the zV -axis

lv , lh , l

Distance CoM – contact points front/rear, wheelbase

δ, δA

Steering angle at the wheel; Ackermann’s angle

ψ, ψ_

Yaw angle, yaw angle velocity

β

Side-slip angle

vv , vh

Wheel velocity, front/rear

α v , αh

Slip angle, front/rear

ρM , ρK

Distance CoM – instantaneous center of rotation, radius of curvature, trajectory

To describe its motion, the vehicle body is assumed to be a rigid body (mass m, moment of inertia θ with respect to the zV -axis). The description of movement of a vehicle in the xE , yE plane takes place in a road-fixed coordinate system KE = fOE ;xE , yE , zE g that is assumed to be an inertial system (Figure 3.11).

7 For sports cars partially even higher. 8 Also referred to as yaw angle velocity.

3.5 Fundamentals of vehicle dynamics

87

,

V K O

K ,

O ≡S ℎ

M K

ℎ

−(

−

ℎ)

ℎ

K H

,ℎ

Figure 3.11: Linear single track model – descriptions and coordinate systems.

The CoM of the vehicle moves along a trajectory that can locally be described by an osculating circle with the radius ρK , circling around the center point KA . For very small velocities v of the CoM, this point coincides with the instantaneous center of rotation M of the motion of the vehicle. Assuming small steering motions and a large curve radius relative to the dimensions of the vehicle, the steering angle δA necessary for this purely geometrical motion is results in jδA j1, lh ρM l l tan δA = qffiffiffiffiffiffiffiffiffiffiffiffiffiffi δA ≈ . ! ρ 2 2 M ρM − l h

(3:1)

The steering angle δA of the front wheels resulting from this connection is called Ackermann’s angle. In this context it can be derived that a short wheelbase requires a smaller steering angle δA for the same curve radius ρM . For any velocities, the velocity of the vehicle according to Figure 3.11 in the body-fixed coordinate system KV = fOV ;xV , yV , zV g becomes 2 3 v cos β 6 7 V (3:2) v = 4 v sin β 5. 0 The index “V” denotes the coordinate system in which the physical velocity vector is depicted.

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3 Vehicle dynamics and suspension system

For the acceleration of the CoM of the vehicle S, the following is also valid for a body-fixed system 2  3 2 3 2 3 2 3 _ + β_ sin β − v ψ _ v cos β 0 − v sin β β 6 7 6 7 6 7 6 dV v V 7 6  7 V a= + 4 0 5 × 4 v sin β 5 = 6 v ψ_ + β_ cos β 7. (3:3) + ω × Vv = 6 v cos ββ_ 7 4 5 4 5 dt 0 ψ_ 0 0 By assuming v = const and β  1, the acceleration a of the center of gravity of the   vehicle is always perpendicular to the velocity of the vehicle, aT v = 0 with the amount of  (3:4) an = jan j = a = v ψ_ + β_ . From Figure 3.11 and the definition of instantaneous center of rotation, the radius of curvature ρK = KS of the trajectory of the center of gravity results in ρK =

v . _ψ + β_

(3:5)

The radius of curvature ρK can also be calculated directly from the velocity (3.2). For the radius of curvature of a trajectory,9 its representation of parameters is given as " # xðt Þ r ðt Þ = , t ≥ 0, (3:6) yðtÞ and in the planar case 

3 x_ 2 + y_ 2 2 . ρK = x_ €y − €xy_

(3:7)

Since the scalar radius of the circle of curvature is invariant against transformations of coordinate systems, the body-fixed coordinate system can be used to calculate the velocity and acceleration vectors. With eqs. (3.2) and (3.3), this results in 3

ρK =

ðv2 cos2 β + v2 sin2 βÞ2 v3 v . =   =  _ _ _ _ _ _ _ 2 ψ + β_ v cos βv ψ + β cos β + v ψ + β sin β v sin β v ψ + β

(3:8)

For the following observations, the acceleration ay of the CoM lateral to the longitudinal axis is needed. For smaller side-slip angles β, with eq. (3.4) in a first approximation it holds:

9 Trajectory, in this case of the center of gravity.

3.5 Fundamentals of vehicle dynamics

  v2 ay = v ψ_ + β_ cos β ≈ v ψ_ + β_ = . ρK

89

(3:9)

For the calculation of horizontal tire forces, the velocities of the tire contact points are necessary (Figure 3.11). These amount to 3 2 3 2 3 2 3 2 v cos β lv 0 v cos β 7 6 7 6 7 6 7 6 V (3:10) vv = V v + V ω × VS rV = 4 v sin β 5 + 4 0 5 × 4 0 5 = 4 v sin β + lv ψ_ 5, _ ψ 0 0 0 at the front wheels and to 2 V

v cos β

3 2

0

3 2

− lh

3 2

v cos β

3

7 6 7 6 7 6 7 6 vh = V v + ω × VS rH = 4 v sin β 5 + 4 0 5 × 4 0 5 = 4 v sin β − lh ψ_ 5 ψ_ 0 0 0

(3:11)

at the rear wheels. Here, S rV and S rH are the position vectors from the CoM S of the vehicle to the tire contact point V in the front, or H in the rear, respectively. The current velocity vv of the front axle can be described with eq. (3.10), or alternatively with the slip angle αv and the steering angle δ in the body-fixed coordinate system KV : 2 3 2 3 v cos β vv cosðδ − αv Þ 6 7 6 7 V (3:12) vv = 4 v sin β + lv ψ_ 5 = 4 vv sinðδ − αv Þ 5. 0

0

The first two vector components in eq. (3.12) offer a simple relationship for the slip angle αv at the front axle for small steering angles δ tanðδ − αv Þ =

ψ_ ψ_ v sin β + lv ψ_ ≈ β + lv ! αv = δ − β − lv . v cos β v v

Accordingly, at the rear axis with 2 3 2 3 v cos β vh cos αh 6 7 6 7 V vh = 4 v sin β − lh ψ_ 5 = 4 − vh sin αh 5, 0

(3:13)

(3:14)

0

the relationship − tanðαh Þ =

ψ_ ψ_ v sin β − lh ψ_ ≈ β − lh ! αh = − β + lh v cos β v v

(3:15)

arises. The preparation of the equations of motion now requires the forces acting on the vehicle. When considering the position of the CoM S of the vehicle according to

90

3 Vehicle dynamics and suspension system

Figure 3.12, the wheel loads, meaning the normal forces between road and wheels, are

S  ,! "!

"ℎ

,ℎ

Figure 3.12: Wheel loads in the linear single track model.

Fz, v = mg

lh lv and Fz, h = mg . l l

(3:16)

The tire forces can be calculated in this simple case in accordance with Chapter 2, assuming a linear relationship with the slip angles as Fy, v = cα, v αv and Fy, h = cα, h αh .

(3:17)

Here, the cornering stiffnesses10 cα, v , and cα, h , which are typical values for the tire, occur (Figure 3.13). Fy

Lateral force

Linear range

Fz.2 > Fz.1

cα(Fz,2) Fz,1

cα(Fz,1) Slip angle

α

Figure 3.13: Relationship between slip angle and lateral tire forces for different wheel loads Fz, 1 and Fz, 2 (Schramm, Hiller et al. 2018).

10 Here, it must be noted that, in practice, elastokinematic parts of the suspensions often contribute to the cornering stiffness.

91

3.5 Fundamentals of vehicle dynamics

Outside of the marked linear area in Figure 3.13, the cornering stiffness does not have a linear relation to the wheel loads. This results in an overall nonlinear relationship between wheel loads and lateral tire forces: Fy, v = cα, v ðFz, v Þ αv and Fy, h = cα, h ðFz, h Þ αh .

(3:18)

Cornering stiffness #$

Qualitatively, a correlation emerges as shown qualitatively in Figure 3.14.

Vertical wheel force 

Figure 3.14: Correlation between cornering stiffness and wheel load (qualitative representation).

Using the accelerations in eq. (3.3), NEWTON’s equation in direction of the vehicle’s lateral direction results in  (3:19) mv ψ_ + β_ cos β = cos δ Fy, v + Fy, h . Accordingly, EULER’s equation around the body-fixed vertical axis results in the relationship € = Fy, v cos δlv − Fy, h lh . θψ

(3:20)

When now replacing the expressions for lateral tire forces by the relationships derived from eq. (3.17), as well as (3.13) and (3.15), and bearing in mind cosβ ≈ 1, cosδ ≈ 1 due to jβj, jδj  1, the two equations of motion necessary for the linear single track model emerge   ψ_ + ðcα, v + cα, h Þ β = cα, v δ and mvβ_ + mv2 + cα, v lv − cα, h lh v _   € + cα, v l2 + cα, h l2 ψ + ðcα, v lv − cα, h lh Þ β = cα, v lv δ. θψ v h v

(3:21) (3:22)

In this case, the mechanical system is not described by two differential equations of the second order, but rather by one equation of the first order and one of the second order. This is due to the assumption of a kinematic binding, resulting from the assumption of a constant longitudinal velocity.

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3 Vehicle dynamics and suspension system

With the substitution

" x=

x1

# "

x2

=

ψ_

# (3:23)

β

finally, the state normal form known from control engineering emerges 3" # " " # 2 # cα, v l2v + cα, h l2 cα, v lv − cα, h lh cα, v lv h x1 x_ 1 − v1 − θ θ θ 5 =4 + ½δ 1 cα, v |{z} x2 x_ 2 1 cα, v lv − cα, h lh 1 cα, v + cα, h − 1 − − v m m m v |fflffl{zfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl} |fflfflfflffl{zfflfflfflffl} u v2 ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflffl{zffl x _ x

(3:24)

B

A

with the ½2 × 1-state vector x, the ½2 × 2-system matrix A, the ½2 × 1-control matrix B, and the ½1 × 1 input vector u. With this, the linear single track model can be interpreted and presented as a linear dynamic system (Figure 3.15), which can be investigated with the methods of system dynamics. Especially, the transmission behavior of the vehicle can be described in simple mathematical terms. The steering angle δ here acts as the input parameter, while the state of the system is described by the yaw rate ψ_ and the side-slip angle β, which, combined with the tire forces Fy, v and Fy, h , represent the output parameters that are generally the most interesting as well.

System-

Linear

System-

input

single track model

output

x = [ xx1 ] = [ 𝛽𝜓 ] 2

Yaw rate 𝜓v

Steering angle 𝛿

Slip angle 𝛽 x = Ax + Bu Tire forces Fy,v, Fy,h

Figure 3.15: Description of the linear single track model as a dynamic system.

The depiction in eq. (3.24) is thus a suitable foundation for basic studies of driving dynamics. These are explained in the following sections, using the linear single track model. Further descriptions and explanations of the most common driving maneuvers as well as an explanation of the respective testing conditions can be found in Section 3.7.

3.5.3 Stationary steering behavior and circular drive As a simple example of the application of the equations of motion (3.24), the first examination is that of a steady-state circular drive. Here, it is assumed that the

3.5 Fundamentals of vehicle dynamics

93

steering angle δ is chosen in a way that the vehicle moves at a constant velocity on a circle with a constant radius ρ. When driving on a circle with a constant radius ρ, the steering angle δ, yaw _ and the side-slip angle β are held constant, meaning that the folangle velocity ψ, lowing simplifications apply: δ = const, δ_ = 0,

(3:25)

€ = 0, ψ_ = const, ψ

(3:26)

β = const, β_ = 0, and

(3:27)

ρK =

v v = = ρ. _ψ + β_ ψ_

(3:28)

With the additional conditions from eqs. (3.25) to (3.28), inserting those in eqs. (3.19) and (3.20), as well as considering eq. (3.17), transformation reveals the following relationship:     mv2 lh lv m lh cα, h − lv cα, v v2 = − . (3:29) αv − αh = ρl cα, v cα, h cα, v cα, h ρ l |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl} EG

The expression EG is called self-steering gradient and characterizes the typical reaction behavior of a motor vehicle to steering actions. With this, the following exemplary tasks can be processed: – Which steering wheel angle δH = iL δ with the transmission ratio iL is necessary for the vehicle to move at the constant velocity v on a circular trajectory with the radius ρ? – What typical drive behavior appears if a steering wheel angle δH is suddenly applied during a straight drive? – What happens in the transition area (transient steering behavior)? In order to answer the first question, first the slip angle and the necessary steering angle for a given circular orbit with the radius ρ are derived. From the slip angle of the rear wheel (eq. (3.15)), the side-slip angle β of the vehicle can be calculated using transformations as β = lh

ψ_ lh m lv v2 . − αh = − ρ cα, h l ρ v

(3:30)

The steering angle δ necessary for the circular trajectory results via the slip angle of the front wheel from eq. Gl. (3.13) to

94

3 Vehicle dynamics and suspension system

δ = lv

  ψ_ l l m lh cα, h − lv cα, v v2 + = δA + EG ay . + αv + β = + αv − αh = c v cα, h ρ v ρ ρ l |{z} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflα, ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |{z} δA

(3:31)

ay

EG

Steering angle 𝛿

The addend δA is Ackermann’s angle (see also eq. (3.1)), which is only dependent on the axial distance and the (constant) curvature radius ρ. With increasing velocity v, the steering angle necessary for a given circular path is amplified or reduced, depending on the sign of the self-steering gradients EG. If the steering angle δ necessary to remain on the circular orbit is larger than Ackermann’s angle δA and therefore EG > 0, the driving behavior is called under-steering; for EG < 0, on the other hand, the driving behavior is over-steering. The case EG = 0 features a neutral driving behavior (Figure 3.16).

EG = 0

𝛿 = 𝛿A + EG ×ay

2𝛿A EG > 0

Under steering

l 𝛿A = 𝜌

EG = 0

Neutral

EG < 0

Under steering 2 𝜐crit 𝜌

2 𝜐ch 𝜌

Lateral 𝜐2 acceleration ay = 𝜌

Figure 3.16: Self-steering gradient in linear observation.

From eq. (3.31), the essential relationship EG · ay = αv − αh

(3:32)

can be observed that allows for a description of the self-steering behavior using the difference between the slip angle at the front and rear wheels. Over-steering driving behavior arises, for example, in cases where the slip angle at the rear axis is larger than that at the front axis. Now, the other parameters can also be calculated. The yaw rate turns out as

3.5 Fundamentals of vehicle dynamics

v ψ_ = = const, ρ and with ay =

v2 the wheel lateral forces ρ lh lv Fy, v = m ay , Fy, h = m ay l l

95

(3:33)

(3:34)

as well as the slip angles αv =

Fy, h Fy, v m lh m lv = = ay and αh = ay . cv ch cα, v l cα, h l

(3:35)

If a steering angle δ is applied out of a straight drive, a stationary yaw angle velocity of v v ψ_ stat = = δstat ρ l + EG · v2

(3:36)

arises. That means that the yaw angle velocity has different values depending on the self-steering gradient. This expression is referred to ψ_ stat v = δstat l + EG · v2

(3:37)

as yaw gain factor at the velocity v. This factor is small for large self-steering gradients (under-steering vehicle) and large for small (negative) self-steering gradients (neutral driving behavior or over-steering vehicle, respectively). For EG = −

l 0). If otherwise the steering wheel angle requirement decreases with an increasing centripetal acceleration, the result is over-steering (EG < 0). If the steering wheel angle requirement remains constant with changing lateral acceleration, the result is neutral steering (EG = 0). Main features of the curve shape in Figure 3.26 are as follows:

Neutral steering

Under-steering дδH EG = дay

Over-steering

δA

Lateral acceleration

ay,max

ay

Figure 3.26: Self-steering gradient in steady-state circular drive.

– the intersection of the curve with the ordinate, which corresponds to Ackermann’s angle δA , – the slope in different areas of acceleration, and – the maximum possible centripetal acceleration. Ackermann’s angle δA depends on the wheelbase l and the curvature radius ρ. The gradient and the maximum centripetal acceleration depend on the mass and CoM of the vehicle, the CoM of the suspensions, and the parameters of the tires. The curve for the under-steering vehicle (Figure 3.26) can be divided up into a linear and a nonlinear part. For the linear part, the curve has a constant slope (EG is assumed constant). For the nonlinear part, the self-steering gradient rises. This is because the lateral wheel forces at the front axle reach their saturation (see Chapter 2) and the

110

3 Vehicle dynamics and suspension system

front axle moves laterally (vehicle is under-steering). For a lower self-steering gradient in the linear region, the vehicle responds more directly to steering input. 3.6.1.2 Yaw gain In order to take into account the relationships in the overall system of driver and vehicle, the reaction of the vehicle to the steering input needs to be observed. To this end, as it is usual in control engineering, the output parameter yaw angle velocity (also called yaw rate) ψ_ is correlated with the input parameter of the steering wheel angle δH . The ratio GV =

ψ_ δH

(3:85)

is called yaw gain factor (Zomotor 1987). For an instationary circular drive, the yaw gain (GV) is observed dependent on the velocity of the vehicle. It defines the stationary reaction to the steering motion, describes steering sensitivity, and indicates the intensity of the reaction at a certain velocity to the input of a steering wheel angle. With increasing yaw gain, the agility (reaction to steering angle inputs) of a vehicle increases, while the stability of the vehicle decreases. The curve of the yaw gain contains a maximum only for stable vehicles. The corresponding velocity is the characteristic velocity vch , at which the vehicle has the highest steering sensitivity (Figure 3.27). Vehicles with a rather neutral driving behavior exhibit an excessive yaw gain for large velocities and thus have a low

Instable

Y aw gain

𝜓v 𝛿H

EG < 0 EG

=

0

Stable EG > 0

vch

vcrit

Vehicle velocity v Figure 3.27: Stationary yaw gain in a circular drive.

3.6 Description of fundamental properties of dynamics in the general case

111

stability margin. For instable vehicles, the curve of the yaw reaction at a defined velocity approaches infinity. This velocity is then again called critical velocity vcrit . Further significant features of the curve are ψ_

– the magnitude of yaw gain δ V and H – the characteristic velocity vch (maximum yaw gain)

Roll angle *

3.6.1.3 Roll angle gradient The roll angle gradient (RG) describes the lateral tilt for stationary circle drives depending on lateral acceleration. To this end, the roll angle φ is described using lateral acceleration ay (Figure 3.28). The roll behavior mostly depends on the track, the CoM, the roll center axis, the spring and damping element, the stabilizer, as well as the kinematics and elasticity of the suspension. Those components also affect the self-steering behavior. The roll behavior has an influence on the comfort and driving stability. The roll angle gradient φ=ay can largely be characterized to be constant, as long as there are no active stabilizers used (Lenthaparambil 2015) and (Schramm, Hiller et al. 2018).

RG =

Centrifugal force '

Δ* Δ'8

Figure 3.28: Qualitative characteristics of the roll angle via lateral acceleration for a steady-state circular drive.

3.6.1.4 Side-slip angle gradient The side-slip angle gradient (SG) describes the characteristics of the side-slip angle β over the centripetal acceleration (Figure 3.29). The initial side-slip angle β0 is based on the curvature radius ρ and the distance from the rear axle to the center of mass lh . The increase of the curve is strongly linked with the degressive characteristic behavior of the lateral force on the rear axis (Wimmer 1997). As shown in Figure 3.29, the SG is constant for low acceleration and grows with rising lateral acceleration.

3 Vehicle dynamics and suspension system

Side slip angle β

112

0

SG = β0

Δβ Δay

Stability margin

Rear stability Lateral acceleration ay

Figure 3.29: Qualitative path of the side-slip angle over centripetal acceleration in a steady-state circular drive.

The initially only constant ratio SG describes the rear stability and for larger accelerations the stability margin of the vehicle. Additionally, the side-slip angle changes signs for larger accelerations. This is due to the growing slip angle on the wheels with increasing centripetal acceleration. The instantaneous center of the curve shifts with increasing lateral acceleration from the height of the rear axle (on which it lays during very low lateral acceleration) towards the direction of travel. If the projected center of the curve lies in front of the CoM of the vehicle, the side-slip angle changes signs (Heißing and Ersoy 2011).

3.6.2 Instationary driving behavior In order to improve the evaluation of the driving behavior, the vehicle reaction to instationary, or dynamic steering angle input needs to be analyzed. For instationary driving behavior it is especially interesting to find out how the dynamic behavior of a vehicle reacts to dynamic input of steering angles. To investigate the dynamic transmission behavior, frequency response, and step steering input are suitable parameters, (see Sections 3.7.2 and 3.7.3). 3.6.2.1 Frequency response Similar to the analysis of stationary behavior, the instationary behavior relates the output to the input.

113

3.6 Description of fundamental properties of dynamics in the general case

In order to determine the frequency response, the vehicle can be stimulated using a steering wheel motion in shape of a sinus curve with constant amplitude and linearly increasing frequency (see Section 3.7.2). By using a harmonious stimulation such as sine steering, the instationary lateral dynamics dependency on the frequency become apparent. The parameters of movement of the vehicle react with a sinusoidal behavior as well. In Figure 3.30, the chronological sequence of the system stimulation (steering _ are represented as an examwheel angle δH ) and the system response (yaw rate ψ) ple. The change in amplitude and the increasing phase shift of the yaw rate toward the steering wheel angle become apparent with increasing frequency.

20 15 10 5 0 −5 𝛿H/° 𝜓/°/s

−10 −15 −20

0

5

10

15

20

25

30

Time/s Figure 3.30: Time signal of the frequency response.

The frequency response describes the transmission of the temporal vehicle momentum into the frequency domain, by calculation the transmission function for different quantities. Mainly, to describe the instationary vehicle behavior _

– the yaw velocity frequency response (yaw frequency (GF)) δψ , H a – the lateral acceleration frequency response (lateral frequency (QF)) δ y , or H – the roll angle frequency response (roll frequency (WF)) δφ H

are used. When presenting the amplitude ratio and phase shift from output to input signal within the frequency range, amplitude and phase responses arise. Figure 3.31 represents the amplitude and phase response of the yaw velocity _ transfer ψ=δ (Bode diagram). The yaw velocity transmission shows an amplitude peak at approx. 0.9 Hz. This frequency corresponds to the yaw velocity eigenfrequency. This means that at this point, the yaw reaction of the vehicle to steering

Amplitude / o

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3 Vehicle dynamics and suspension system

0.2

Phase / o

0

-45

0

0.2

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Frequency/Hz Figure 3.31: Frequency response using the example of the yaw rate (amplitude and phase progression).

input is at its strongest. The stationary yaw gain (see Section 3.6.1) corresponds to the amplitude response from 0 Hz. For higher frequencies, the amplitude decreases monotonously, corresponding to a low-pass behavior. The phase has a lower phase shift for lower frequencies, which does however increase for higher frequencies. Information about the behavior of the vehicle under the influence of sinusoidal input can be gained using the frequency response. Furthermore it can be determined, at which frequency the reaction of the vehicle to the steering input is amplified, or dampened, and what the phase shift between both reactions is. The eigenfrequency at which the maximum elevation of the amplitude response is reached, and the extent of the elevation compared to the stationary case can be concluded as well (Meljnikov 2003) and (Zomotor 2002). According to Schindler (2007) and Zomotor (1987) only the frequency range under 2.0 Hz 13 is of interest as the frequency spectrum of the steering wheel angle created by the human driver does not have any considerable use above this frequency. When driving on a highway, the base frequencies around approx. 0.1 Hz are dominant. For a double lane change, they are between 0.6 and 1.1 Hz (Schindler 2007).

13 Sports cars up to 4 Hz.

3.6 Description of fundamental properties of dynamics in the general case

115

3.6.2.2 Step steer input For the steering wheel angle step, an abrupt excitation over time is used to examine the driving behavior. The same maneuver is described in Section 3.7.3. Here, the vehicle drives at a constant velocity on a straight line, before a steering angle of δL0 is applied at time t0 . This method examines the transition behavior of a vehicle from a straight line to a steady-state-circular drive. For a step steering input, the output parameter is correlated with the input parameter and called yaw rate transition for the yaw rate. The vehicle reacts to a steering wheel angle step by increasing the movement parameters (yaw rate, lateral acceleration) and the positional parameters (roll angle). Those parameters first increase to a higher value than the stationary values corresponding to the steering angle δLstat (overshoot). The final stationary steadystate values are reached after some oscillations (Zomotor 1987). In systems dynamics, this corresponds to the step response. The delayed build-up of the lateral axle forces results in a delayed reaction of the vehicle, the “two-phase vehicle reaction.” It is described using two points in time. The first one describes the front axle response time, at which the building of the yaw rate begins (Figure 3.33). The second point in time marks the response of the rear axle, at which the build-up of the lateral acceleration begins. Especially for under-steering vehicles, substantial time differences can occur. Using the differently timed yaw velocity and lateral acceleration development, the response times and damping of the vehicle reaction can be determined. To summarize, the vibration amplitudes and settling time depend on the damping and the eigenfrequency of the system. The speed of the driver’s steering ability is limited and thus the step steering input is closer to a ramp (Figure 3.32). In Figure 3.33, the typical yaw rate response of a vehicle to the step steering input is presented. Important values are the maximum as well as the reached yaw rate ψ_ max , and the corresponding response time Tψ_ max

40 Steering wheel angle/ o

35 30 25 20

𝛿L0

15 10 5 0

0

1

2

3

4 t0

5

6

Figure 3.32: Steering wheel angle step.

7

8

9

10

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9 8

Yaw rate/(°/s)

7 6 5

. max

4

. stat

3 2 1 0 0

1

2

3

4 0

5 6 . max

7

8

9 10 Time/s

Figure 3.33: Vehicle yaw motion after steering wheel angle step.

stationary yaw rate ψ_ stat (Zomotor 1991), (Zomotor and Roenitz 1997). The overshoot value can be defined as the ratio of maximum and stationary value Uψ_ = ψ_ max =ψ_ stat . In order to evaluate the transitional behavior, the following parameters are used primarily: ψ_ – yaw transition (GU) , δH ay – lateral transition (QU) , δH φ – roll transition (WU) . δH Those values are additionally normalized by dividing the corresponding transition behavior by the corresponding stationary end value, for example, GUnorm = GUGU . stat

3.7 Standard driving maneuvers In Section 3.6, assessment parameters were defined to qualitatively describe the stationary and instationary driving behavior. In this section, standardized driving maneuvers for an evaluation of driving dynamics are presented, which support the gain of objective, and thus comparable vehicle parameters. The standard driving maneuvers described here are still predominantly carried out with test vehicles up to today. However, in order not only to save costs but also to shorten development times, great efforts are also being made to replace them with more cost-effective procedures. Besides simulations (see Sections 3.8.4 and Section 3.9 and (Schramm, Hiller et al. 2018)) this also includes tests in driving simulators

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117

(see, e.g., Chapter 10 and (Ronellenfitsch, Degenhart et al. 2018)) or specific trials on test benches (Lefevre 2020), often in combination with real driving tests (Düsterloh, Uselmann et al. 2018). Basically, a distinction is made between open-loop and closed-loop maneuvers. In open-loop maneuver, the driver is ignored and thus does not have any influence on the measuring result. In a closed-loop maneuver, the style of driving has an important role. Thus, a comparability of results is limited, for example, for cases in which drivers with a similar driving style, or steering robots are utilized. Table 3.6 describes three open-loop driving maneuvers that are suitable for the observation of stationary conditions and instationary transmission behavior of vehicles. Table 3.6: Open-loop driving maneuver for the determination of vehicle properties. Driving maneuver

Standard Evaluation

Results

Steady-state circular drive

(ISO )

Stationary state of equilibrium

Self-steering gradient, stationary yaw gain, and roll angle gradient

Continuous sine

(ISO )

Instationary behavior in the frequency range

Frequency-dependent amplitude and phase response

Step steering input

(ISO )

Instationary behavior in the time domain

Response times, transient response

With standardized driving maneuvers it is possible to create measurements of different vehicles gained from different test areas that are consistent, reproducible, and comparable. This creates not only the so-called benchmarks for different vehicles but also the possibility to compare previous models. For a precise and reproducible measurement it is important to minimize environmental influences for all driving maneuvers, for example, by using a dry and flat road surface (Meyer-Tuve 2008). An increasingly more important application for standardized driving behaviors lies in the validation of simulation models with which – unlike in real test drives – objective data can be determined in early stages of development (Kobetz 2004). To increase comparability, the different steering transmissions of each vehicle need to be considered.

3.7.1 Maneuver steady-state circular drive The driving maneuver “Steady-State Circular Drive” according to (ISO 2012) is an important standard testing method both for the real test mode as well as the simulation technology. It is used to analyze the steering tendency, the driving behavior, and the

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stability of motor vehicles up until the threshold using the parameters EG, GV, and SG, and to make fundamental statements about the driving characteristics (see Section 3.6.1). In order to evaluate driving behavior, parameters such as steering wheel angle, vehicle velocity, side-slip angle, roll angle, lateral acceleration, and yaw angle velocity are recorded. There are four methods to record the values for the steady-state drive (ISO 2012). Here, the method of a constant radius is described as it is best suited for a limited test-driving area. On an circular radius of at least 30 m, a right and left circle are driven at a slowly and consistently increasing velocity. The steering wheel angle must be adjusted at the start of the maneuver in a way that the vehicle is within the specified radius at minimum speed. The lateral acceleration is slowly and monotonously increased up until the threshold at which it is not possible anymore to maintain the stationary condition. The driver has to adjust the steering angle in a way that the vehicle remains on the circular track. As the driver is a part of the control circuit, this is technically a closed-loop maneuver. However, due to the quasistationary testing condition, this maneuver is easily reproducible for an experienced driver, and the driver has little influence on the behavior of the system (Rau 2007). That is why this steady-state circular drive is defined as an open-loop maneuver.

3.7.2 Frequency response In order to determine the lateral transmission behavior of a vehicle in the linear range, the driving maneuver “Frequency Response” is used, which is defined in DIN/ISO (1989) or ISO/TR 8726 (1988). Here, the vehicle is considered to be a time invariant system, and the frequency response corresponds to a sine sweep with which the transmission behavior can be determined. As evaluation criteria, the zoom function (amplitude ratio) and the phase angle of the centripetal acceleration, the yaw angle velocity, and the roll angle in relation to the steering wheel angle within the frequency domain are used. In this experiment, the sinusoidal steering frequencies, starting with 0.1 Hz and slowly increased up to 3.0 Hz, are driven through using a constant steering wheel angle amplitude at a constant velocity (usually 100 km=h). The steering wheel amplitude is chosen depending on the driving velocity in such a way that a lateral acceleration of approx. 4 m=s2 (optionally 2 m=s2 or 6 m=s2 ) is reached for low frequencies (quasistationary) (Meljnikov 2003). There are two methods used for increasing the frequency. In the first method, the frequencies are varied gradually before sorting the measured data into different frequency classes and observing the resulting distribution. The measurements are repeated until every frequency class is adequately represented. In the second

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119

method (also called slide sine or sine sweep maneuver), the frequency ranges from 0.1 to 3.0 Hz are driven through at 0.1 Hz increments. To this end, it is necessary to either offer the driver a frequency clock generator, or to utilize a steering robot. The advantage compared to the first method lies in the fact that the vehicle is in a steady state and it can be implemented more quickly. In order to determine amplitudes and phase angles of the input signals (steering wheel angle) to the output signals (yaw angle velocity, centripetal acceleration, and roll angle), for example, the MATLAB-function transfer function estimate (estimation of the linear, time invariant transfer function) can be used. This determines the relationship of the cross power spectrum density of the input and output signals and the power density spectrum of the input signal. The transfer of data in the frequency domain can be achieved using the Fourier transformation. Additionally, a coherence function can be calculated, which allows for a plausibility control of the measuring signals concerning consistency. 3.7.3 Step-steer input With the driving maneuver Step-Steer Input according to DIN/ISO (1989), it is possible to analyze both the stationary and the instationary driving behavior in the linear and nonlinear range. In the experiment, the steering wheel is moved during a stationary straight drive at a constant velocity (usually 100 km=h), with a steering wheel angle velocity that is as high as possible (between 200 and 500 =s) against a stop value (δL0 ), to reach a curved path (steady-state circular drive). This results in a ramp-shaped steering excitation (Figure 3.32), as it is not possible to realize a perfect step input due to physical constraints. The amplitude of the change of steering angle is chosen depending on the velocity of the vehicle such that stationary different tire force interactions occur up to the tire limits. The evaluation criteria for the step-steer input are based on the chronological sequence of the lateral acceleration and yaw velocity reactions of the vehicle. Additionally, side-slip angles and roll angles can be observed. The reaction of the vehicle to the step-steer input corresponds to the entrance in a circular path, while the increase of driving dynamics parameters should on the one hand be sufficiently dampened, but on the other hand be as quickly as possible. The maneuver is driven for both, left and right steering angle inputs. 3.7.4 Double lane change The “Double Lane Change” is one of the standard test methods in the instationary range (ISO 1975) and (ISO 2000). The testing method aims to evaluate the driving behavior of a motor vehicle in a closed-loop situation relevant in practical driving.

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To this end, the test simulates an evasive maneuver including steering back to the right track. A slightly modified version of this test became famous in 1997 under the name “Elk Test.” Today, the test is an integral part of the testing program of automotive companies, test magazines, and organizations. The dimensions of the test track are defined with a length of the track of 110 m and a lateral offset of 3.5 m. The width is set depending on each test vehicle. Using light barriers at the beginning and end of the test section, transit time is measured. The assessment criterion is the transit time mean of at least three clean drives, in which the pylons must not be touched. In many cases, other driving dynamics parameters are used next to the measurement of time in order to investigate the instationary driving characteristics. Those include: – steering wheel angle, – steering wheel torque, – lateral acceleration, – yaw rate, – velocity, and – side-slip and roll angle. In order to evaluate the quality of the driving behavior of the tested vehicle, the required steering wheel motion and the resulting lateral acceleration are used among others (Figure 3.34).

3.8 Chassis systems and suspensions The interface between the wheels and the vehicle body is realized by the chassis, which in turn consists of the front and rear wheel suspension. There are various types of suspension systems available in vehicles. One task of the wheel suspension is to guide the wheel relative to the vehicle body in a way that the tire–road contact is optimized in every driving situation. With this, and using additionally body springs and dampers, it can be ensured that the lateral, longitudinal, and vertical forces can be redirected to the vehicle body in such a way that all requirements to driving comfort and safety can be fulfilled. Figure 3.35 shows an overview of the tasks of the chassis system.

3.8.1 Overview of the characteristics of wheel suspensions Starting from a single wheel, the first thing necessary is a wheel carrier, which contains the hub and the bearings, as well as the brake, and (for driven axles) a provision that is connected to the drive shaft. There are three ways of connecting the wheel carrier to the body that have prevailed:

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125 30

25 12.5

25 12.5 15

15 15

Pylon

7.5 7.5 7.5 7.5

7.5 7.5

2 3.5

3.5

3

1 1: 1.1 ∙ vehicle width + 0.25 m 2:1.2 ∙ vehicle width + 0.25 m 3: 1.3 ∙ vehicle width + 0.25 m Figure 3.34: Double lane change (all dimensions in m) according to ISO (2002); see also (Reński 2001).

Small vertical body accelerations

Adapted yaw dynamics

Small pitch and roll accelerations Deflection space limited by packaging

Reliable transmission of longitudinal and lateral forces

Small wheel load f luctuations

Ground clearance and vibration behavior load dependent

Figure 3.35: Requirements to the chassis system (Schramm, Hiller et al. 2018).

3.8.1.1 Rigid axles In rigid axles, the wheel carriers are joined together using a rigid axle that essentially allows translational movement along the vertical axis, as well as rotation around the longitudinal axis of the vehicle. This type of wheel suspension is rarely used in passenger cars today, and if it is, it is usually used on the rear axle.

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3.8.1.2 Twist-beam axles Twist-beam axles are derived from rigid axles. However, they furthermore allow a one-sided deflection through an elastic deformation of the axle beam. 3.8.1.3 Individual wheel suspension In an individual wheel suspension, both wheel carriers are guided in a way that they can move independently from each other primarily in vertical direction. For all types, another degree of freedom is added for steered axles, which allows the rotation of the wheel carrier around its vertical axis. An overview of most common wheel suspensions is shown in Figure 3.36.

Five link wheel suspension

Multilink wheel suspension (Section 3.8.3)

Double wishbone wheel suspension

Trapezoidal link wheel suspension

Spring-strut wheel suspension (Section 3.8.2)

Control-blade wheel suspension

Figure 3.36: Examples of common independent wheel suspensions (schematic diagram) according to Bosch, Reif et al. (2014).

Of the wheel suspensions shown in the illustration, the MacPherson axle is the predominant choice for the front axle, followed by the double wishbone axle (Heißing and Ersoy 2011) and (Kracht, Baum et al. 2016)

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123

While two axle variants play a dominant role on the front axle, the variety of different rear axle types is considerably wider. Here the twist-beam axles as well as the rigid axles and multilink axles are represented in roughly equal proportions. In 2010, they accounted for approximately three quarters of all axle types used. The rest is made up of the other axle variants (Heißing and Ersoy 2011). A MacPherson front axle suspension and a double wishbone rear axle suspension are exemplarily discussed in more detail below.

3.8.2 MacPherson spring-strut axle suspension One of the most common suspension types at the front axle is the MacPherson wheel suspension as a special implementation of the spring-strut wheel suspension (Figure 3.37). It has since then continuously been improved upon and utilized, and has become a standard design for many compact and mid-size vehicles (Unterreiner 2013). The MacPherson spring-strut axle suspension is an individual wheel suspension, at which the spring-damper element partially takes over the guidance of the wheel (Heißing and Ersoy 2011). As advantages of this design, there are low unsprung masses, a wide support base, comparably low forces on the joints, and low spatial requirements. Due to the space-saving design and the low-cost construction, this suspension type is very common in cars and light trucks (Heißing and Ersoy Body spring (4) Piston rod (5A) Rack and pinion steering (8) Damper housing (5B)

Pendulum support (2B)

Steering lever (6) Steering link (7)

Wheel carrier (1) Antiroll bar (2A) Wheel (10) Elastic bearing (9) Wishbone (3) Figure 3.37: MacPherson wheel suspension of a compact car according to Schramm, Hiller et al. (2018).

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2011). The disadvantage of the MacPherson wheel suspension lies in the inadequate spatial wheel guidance in dynamically challenging driving situation, as they occur, for example, in racing. The following model is based mainly on the elaborations concerning the MacPherson wheel suspension in (Schnelle 1990), (Unterreiner 2013), and (Schramm, Hiller et al. 2018). In Figure 3.37, a conventional spring-strut suspension is shown. The wheel (10) is pivoted on the wheel carrier (1). The wheel carrier is firmly connected to the lower half of the damper, the damper tube (5B). The piston rod (5A), the upper half of the damper, slides inside the wheel carrier fixed pipe of the damper (5B), and is mounted to the vehicle body at its upper end. The piston rod (5A), and the damper tube (5B) together form the damper and kinematically create a slider element. The components (4), (5A), and (5B) are also called spring-strut. The spring-strut thus is the connection between wheel carrier and the body of the vehicle and serves as the guide for the wheel carrier (slide guide). The spring-strut serves to spring the vehicle, to limit the compression and rebound travel (extension stop and compression stop), and to dampen vibration. The spring (4) is propped up against the body at the piston rod (5A). At the lower spring plate, the antiroll bar (2A) acts as a further force element via the pin-ended support (2B). Wishbone (3) and wheel carrier (1) are connected via a ball joint. The wishbone (3), which is mounted to the body of the vehicle via two wishbone bearings, also guides the wheel carrier. The steering motion is initiated via the tie rod (7), which has ball joints on both sides, to the steering lever (6), which is a part of the wheel carrier (1). The steering motion is introduced to the tie rod by a shift in the rack steering (8) in the direction transverse to the vehicle via a ball joint. The steering motion of the wheel is realized by turning the wheel carrier around the steering axis, which passes through the connecting line in between the ball joint on the spring-strut, and the wishbone. The wheel carrier gives in (evasion) longitudinal direction, which leads to a safer and more comfortable driving behavior. The longitudinal evasion of the front axle is reached through the comfort lateral bearing (9), which allows for a slight rotation of the wishbone around a vertical axis.

3.8.3 Multilink wheel suspension In many vehicles, the rear axle is constructed as a multilink wheel suspension with each four links (Figures 3.38 and 3.39) (Unterreiner 2013). It is called four-link wheel suspension, or control-arm wheel suspension (Heißing and Ersoy 2011). Spring (6) and damper (7) are arranged separately and supply vertical support and vibration damping. The wheel carrier (1) is connected to the body via a sword-like arm (2) and is mounted rotatable in longitudinal direction. This mobile trailing arm (2) is firmly connected to the wheel carrier (Figure 3.38). Due to its elastic properties, and depending

3.8 Chassis systems and suspensions

Damper (7)

125

Wheel carrier (1) Body spring (6) Wheel (9)

Transverse control arm (3) Spring control arm Antiroll bar (8)

Driving direction

Tie rod (4) Trailing link (2)

Figure 3.38: Multilink wheel suspension at the rear axle of a compact car (front view) (Unterreiner 2013).

Damper (7) Steering link (4) Trailing link (2)

Transverse control arm (3) Body spring (6)

Spring control arm (5) Wheel (9) Wheel carrier (1) Driving direction Figure 3.39: Multilink wheel suspension at the rear axle of a compact car (rear view) (Unterreiner 2013).

on the other laterally arranged arms (3, 4, and 5), it allows both for changes of the track and the camber. The transverse control arm (3), the tie rod (4), and the spring control arm (5) absorb the wheel lateral forces. The separation of longitudinal and lateral force support is characteristic property of the multilink wheel suspension. On the one

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hand, its construction leads to a high lateral stiffness in favor of optimized handling; on the other hand, it allows for an elasticity in longitudinal direction, which improves ride comfort (Heißing and Ersoy 2011). However, larger spatial requirements and more individual components lead to higher costs. This is why this type of suspension is usually only used in higher quality vehicles of the middle and premium class. Over time, this wheel suspension has also entered the compact class vehicles due to its good kinetic and kinematic properties (Heißing and Ersoy 2011). The MBS14 model of the suspension, as seen in Figure 3.40 using the example of the left rear wheel, consists of a wheel carrier (1), two underlying transverse control arms (tie rod (4), and spring control arm (5)), and a transverse control arm at the top (3). The kinematic substitute model of the flexible longitudinal arm consists of a rigid trailing arm (2), which is connected to the wheel carrier via a rotational joint R, and to the body via a spherical joint S. A more accurate model of the flexible arm can be reached using the initial function that is derived using a static finiteelements analysis. When limiting to an initial linear function, the joint has one degree of freedom, as shown in Figure 3.40. Wheel carrier (1)

Trailing arm (2)

Transverse control arm (3) S S

S

zc Spring displacement S Spherical joint R Rotational joint

S

R

Tie rod (4)

S

S S

Driving direction Spring control arm (5)

Figure 3.40: Rigid body model of the rear multilink wheel suspension on the left wheel (Unterreiner 2013).

3.8.4 Examination of the wheel suspension motion The position and orientation of the wheel relative to the vehicle and the road significantly influence the power transmission and thus the driving and steering behavior of the vehicle (see also Chapter 4). The wheel center trajectory as well as the camber and track angle change during wheel deflection describe the position and orientation of the wheel. These are presented as an example for the MacPherson

14 MBS: Multi-Body-System.

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127

spring-strut axle suspension and the multilink wheel suspension. The pivot points and the camber and track angle changes of the wheel suspension have been gained from measuring a typical medium-sized vehicle using a MacPherson front axle and a multilink rear wheel suspension. Using these measurements, the quality of the simulation of the wheel suspensions should be evaluated. The results of the simulation of the front and rear axle are now presented successively. 3.8.4.1 Front axle On the spatial trajectory of the wheel center in a MacPherson wheel suspension with its projections on the three planes of the axis (xR − zR , zR − yR , and xR − yR ), the wheel describes a spatial motion and simultaneous rotation during compression and rebound. During compression, the trajectory of the wheel goes slightly in the direction of the positive xR - axis (Figures 3.41 and 3.42). The track width at the front axle is slightly reduced during compression and rebound (Figure 3.42, middle diagram).

zR/m

0.04 0

–0.04 0.795 0.01 0.79 yR / m

0.785

–0.01

–0.005

0

0.005

m x R/

Figure 3.41: Simulated wheel center trajectory of the left MacPherson wheel suspension in space (Unterreiner 2013).

During compression and rebound, steering is fixed at zero position. It can be seen that the simulation qualitatively represents the measurements. The average error of the camber angle is 0.025 and that of the toe angle 0.012 (Figure 3.43). During compression, the camber angle decreases and partially becomes negative (Figure 3.43, left). This means that the wheel leans toward the vehicle. This characteristic is advantageous especially for cornering. While cornering, the vehicle body is usually leaning outward due to the centrifugal force.15 Here, the wheel on the outside of the curve is compressed, while the wheel on the inside is rebound at the same time. The front wheels lean toward the middle of the circular path, which 15 Since the roll center is generally below the center of gravity.

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0,008 0,04

0.04

0,004 0

xR/m

zR/m

zR/m

0 0

0

– 0,04

–0.04

0,005 0 –0,005 xR/m

–0,004 0,792 0,788 yR/m

0,792

0,79

0,788

yR/m

0

–0.04 Simulation Measurement 0

–0.8

–1.6 𝛾󰑅/˚

Rebound

Rebound

–0.04

toe-in

0

0.04 toe-out

0.04

zR/m

Compression

zR/m

Compression

Figure 3.42: Projection of the simulated wheel center trajectory of the left MacPherson wheel suspension on the plane (Unterreiner 2013).

Simulation Measurement

–0.2 –0.1

0

0.1 󰜓R/˚

0.2

Figure 3.43: Measured and simulated camber and toe angle progression of the left MacPherson wheel suspension (Unterreiner 2013).

is facilitated by the kinematics of the wheel in a MacPherson front axle. This leads to an improved distribution of pressure in the tire contact path and thus a larger potential to build a lateral force. During compression, the toe angle becomes negative for the front axle as well (Figure 3.43, right). Once the wheel rebounds, it turns away from the center of the vehicle (wheel goes in toe-out). This behavior is desired for powered front axles. During cornering, the steering angle is slightly influenced at the front axle (under-steering), regardless of the driver. Overall, the vehicle can be steered in a curve more calmly and stable (“forgiving”).

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129

3.8.4.2 Rear axle In Figures 3.44 and 3.45, the wheel traverses a spatial movement with a simultaneous rotation in the same time. Here, too, the trajectory of the wheel has a positive xR component during compression, which is however larger for the multilink wheel suspension compared to the MacPherson wheel suspension. In the rear axle, the average track slightly decreases during compression (Figure 3.45, middle diagram).

zR/m

0.05 0

–0.05 0.8 0.79 yR / m 0.78

0.02 0.77

0.01 x R/m

0

Figure 3.44: Simulated trajectory of the wheel center of the left multilink wheel suspension in space (Unterreiner 2013).

0.08

0.08

0.04

0.04

0

0

–0.04

–0.04

xR/m

zR/m

zR/m

0.01

0 –0.08

–0.08 –0.01 0 xR

–0.785 –0.775 yR

–0.785

–0.78 yR

–0.775

Figure 3.45: Projection of the simulated wheel center trajectory of the left multilink wheel suspension on the plane (Unterreiner 2013).

The simulation qualitatively represents the measurements (Figure 3.46). The average error of the camber angle is 0.1 and that of the toe angle 0.035 . During compression of the wheel, the toe angle increases more compared to the front axis (Figure 3.46, left), which is why the wheel on the outside with a higher

0.08 zR/m

0.04

0.04

0

0

–0.04

–0.04

–0.08

Simulation Measurement

–4 –3

–2

–1

0 1 󰛾R/°

Measurement Simulation toe-in

zR/m

0.08

toe-out

Compress

3 Vehicle dynamics and suspension system

Rebound

Rebound

Compress

130

–0.08 –0.5

0

0.5 󰜓R/°

Figure 3.46: Measured and simulated camber and toe angle progression of the left multilink wheel suspension (Unterreiner 2013).

load can realize the necessary lateral force for smaller slip angles, and additionally stabilizes the rear axis (under-steering effect). The toe angle at the rear axle behaves oppositely to the front axle. During compression of the rear wheel, the toe angle becomes positive (toe-in) (Figure 3.46, right), which is why the rear wheel turns slightly toward the vehicle during deflection. During cornering, this effect creates an additional steering angle at the rear axis (under-steering) independent from the driver, which stabilizes the vehicle at the rear axis. The deviation between simulation and measurement at the two axes can be explained on one hand by inaccuracies in measurements and on the other hand due to the neglect of elastokinematics in modeling. Schramm, Hiller et al. (2018) took into account elastokinematics using kinematic replacement mechanisms.

3.9 Three-dimensional modeling of wheel suspensions In the previous section, simulation results of wheel suspensions were presented as examples. These are extremely useful for predicting driving comfort, driving dynamics, and driving safety and are usually used at an early stage of product development. The simulations are based on mathematical models of varying complexity. The so-called black box models can be derived from measurement data, which, however, only map the input and output behavior (transmission behavior) of this wheel suspension. However, as it has already been shown, a wheel suspension consists of a large number of control arms, bearings and other metallic components with different shapes, lengths, materials, and so on. In addition, elastomer bearings are used nowadays to further increase ride comfort. A physical model of the wheel

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suspension must be created in order to ensure the parameterization of the partrelated properties. A distinction can be made between kinematic, dynamic, and elastokinematic models. Kinematic models only describe the movement of the individual components, which are compatible with the connecting joints, without taking into account the required forces and torques. Dynamic models with rigid bodies, on the other hand, execute their motion on the basis of forces and torques. Since a wheel suspension is a system consisting of many components, it is referred to as a multibody system (MBS). If elastokinematics is also considered, elastic deformations due to the forces are also observed. It should be noted that with the increasing complexity of the models, the computing time for the simulation is also increased. For example, there are different requirements for suspension models for chassis predevelopment and optimization than for models for real-time applications, such as the control of an active chassis. The models should therefore be selected and constructed depending on the applications in order to ensure a good compromise between accuracy and acceptable computing time. A number of commercial software packages for the modeling and simulation of wheel suspensions have been well established during the last decades. Among many others, the software packages Adams/Car and IPG Kinematics are named here. These include the spatial modeling of wheel suspensions. The modeling of Adams/Car is based on dynamic MBSs, whereas IPG Kinematics calculates the kinematic motion possibilities and creates a map model. Both programs offer the advantage that they already have internal vehicle-specific libraries and are therefore easier to use. In both cases, the user does not need to know the underlying equations and formalisms, which are advantageous for simulation evaluation (Adamski 2001). As this introduction already shows, the modeling of wheel suspensions is a very extensive area and is only touched on here. Further literature on modeling can be found in Schramm, Hiller et al. (2018) and Heißing and Ersoy (2011).

3.9.1 Kinematic models The kinematics of a wheel suspension describes the geometric movement of rigid bodies. Rotation matrices in connection with the Cardan angles for the individual joints are often used for the description. The advantage is a concise notation. The description of this procedure would lead too far in this book, so that reference is again made to Schramm, Hiller et al. (2018). However, in order to gain an understanding of the modeling method, a flat double wishbone suspension (Figure 3.47) is discussed as an example. In kinematics, for example, the motion of the lower (12) and upper wishbone (34), which are each attached to the chassis or bodywork via a rotary joint, can be described via two circular paths. Furthermore, the dependence of the two angles α1

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2

4

3 3, 2,

1 2

1,

1 Figure 3.47: Ideal kinematics of a double wishbone suspension in the y–z projection.

and α2 is defined by the length of the wheel carrier 23. This results in a system with one degree of freedom. The criteria of Kutzbach and Grübler are used to determine the number of DoF. Similarly, the speed and acceleration of the system can be determined. However, it becomes clear that implicit equations must be solved depending on the structure of a wheel suspension. This is called a kinematic loop, which results from the geometric arrangement of the system. Such equations can be solved by iterative numerical methods. This has the disadvantage that real-time simulation can no longer be guaranteed. Depending on the configuration of the wheel suspension, however, an explicit solution of the kinematics can also be found, as Schramm, Hiller et al. (2018) show. In addition, it is also possible to calculate the kinematic movement possibilities iteratively in advance and to create a characteristic map from them. Thus, a real-time capable input and output behavior model of the wheel suspension is created. However, if the parameterization is changed, a new map must be determined. 3.9.2 Dynamic models The dynamics of a wheel suspension depends on the forces and torques acting on it. The tire forces, on the one hand, and the spring/damper forces and torques of the spring/damper strut, on the other, are impressed. Within active wheel suspensions, hydraulic or electrical forces are also applied to control the chassis. The masses and inertia tensors of the individual components are also taken into account. On the one hand, this results in the static position of the wheel suspension, where all forces are balanced and the system rests. On the other hand, the kinetics in which the forces change the state of motion results from the temporal change of the impressed forces. The basis of the description of the kinetics is described by NEWTON’s16 and EULER’s17 equations, to which the d’ALEMBERT18 principle can be applied (Schramm, Hiller et al. 2018). A wheel suspension consists of several rigid bodies between which internal forces and moments act and external forces and moments attack. This results in an MBS in which

16 Sir Isaac Newton (1643–1726): English naturalist and civil servant. 17 Leonhard Euler (1707–1783): Swiss mathematician and physicist. 18 Jean-Baptiste le Rond d’Alembert (1717–1783): Mathematician and physicist.

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133

the global NEWTON–EULER equations are established on the basis of the local equations of motion of the individual rigid body. The dynamics of a general MBS are completely described by the kinematic differential equations and the equations of motion. In addition to the manual setup of these equation systems, the use of Computer Algebra Systems (CAS) such as Maple is also possible. These programs solve the equations symbolically and offer the export to other simulation software packages.

3.9.3 Elastokinematic models Elasticity is the change in the shape of solid bodies under the influence of external forces (see Figure 3.48). As can be seen from this definition, the deformation results from the solid bodies of the suspension (geometry and material) under external forces (amount and direction) that occur during the various driving maneuvers and trials on test benches. The deformations in turn result in a movement called elastokinematics (Heißing and Ersoy 2011). The extension of the MBS with deformable bodies in the elastic range results in a flexible MBS. Thus, additional DoF of elasticity are considered by modeling the individual bodies as finite-element models. The individual linear modes are determined by Craig–Bampton reduction in a modal analysis and can then be integrated into an MBS program as elastic components (Schwertassek, Wallrapp et al. 1999).

Figure 3.48: Left: Front axle of the formula student racing car; right: deformation of the elastic simulation (Kracht, Schramm et al. 2015).

The flexible MBS analysis allows an exact mapping of the elasticity and the occurring stresses. Furthermore, the individual linear system modes are mapped. By reducing the modes, the number of DoF is reduced, but there are still several hundred DoF available, so that real-time capability is not guaranteed. This modeling method is therefore suitable for the creation of a reference model with very high accuracy, which must be validated with real measurement data.

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3 Vehicle dynamics and suspension system

3.10 Vertical dynamics Vertical dynamics of a motor vehicle can both be roadway induced,19 or driver and vehicle induced20 (Lenthaparambil 2015). The vertical excitations induced by the driver include excitations caused by pitch and roll motion (see Section 3.5.5) of the vehicle caused by steering, accelerating, and braking, as well as inner excitations caused by the powertrain (running engine) and the tires (e.g., imbalances). Road-induced vertical motions are caused primarily by unevenness of the road. These unevenness causes dynamic forces in vertical direction which, in the general case, influence the vibration behavior of the vehicle in all directions. The vertical forces on the body arise primarily due to spring and damping forces, which support the vehicle body relative to the chassis and influence the motion of the body. 3.10.1 Vertical dynamic requirements of the chassis The requirements to the vehicle in vertical dynamics are varied and partially contradictory (Figure 3.35). On the one hand, the vehicle body acceleration as well as pitch and roll motions are supposed to be kept as low as possible to ensure a high level of ride comfort for passengers. On the other hand, in order to ensure a stable driving behavior and good handling, the wheel load oscillations should be limited and an even wheel load distribution has to be ensured. Adjusting for those requirements is further complicated by the limited space for the wheel suspension and the fact that both due to road conditions and increased loads in vehicles, their mass and sharp oscillations are unavoidable. A central assembly group of the chassis is the wheel suspension (Figure 3.49). This consists of the wheel bearing, a combination of elastic and damping force elements, as well as a combination of arms and further rotational and translational guide elements.

3.10.2 Roadway excitation Roadway irregularities are responsible for the majority of excitations in the area of 0 − 30 Hz on the vehicle. They stimulate lifting, pitching, and rolling motions of the vehicle. Due to their irregularity, they can usually only be described using stochastics. This means that, normally, time variables cannot be stated, but one is rather dependent on values within a frequency range, which allow statements about amplitude and

19 Excitations caused by the shape and unevenness of the road. 20 Excitations caused by driver intervention (steering, braking, accelerating).

3.10 Vertical dynamics

135

Damper Antiroll bar

Wheel

Spring Wheel carrier

Wheel bearing

Arms Wheel

Wheel bearing

Figure 3.49: Five-link rear axle of a Mercedes-Benz E-Class vehicle © Daimler AG and its associated MBS model according to Schramm, Hiller et al. (2018).

distance of unevenness in the statistical average. In order to determine the fundamental connections between the temporal and local history of unevenness of the road, first the case of a harmonious unevenness gradient is considered (Figure 3.50). In this case, the course of the irregularities as a function of distance can be described as ^ sin Ωx, up ð x Þ = u =

(3:86)

=

=

2

Figure 3.50: Path-dependent unevenness function during sine-shaped road unevenness.

with the path circular frequency Ω=

2π . L

(3:87)

The transformation x = vt into time domain results in the time-dependent unevenness function: ^ sin Ωvt = u ^ sin ωt, ut ðtÞ = u

(3:88)

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3 Vehicle dynamics and suspension system

with the time circular frequency ω = Ωv = 2π Lv and the time frequency f = sured in Hz (Figure 3.51).

=

ω 2π

mea-

2

Figure 3.51: Time-dependent unevenness function for sine-shaped road unevenness.

For a general periodic unevenness function with the period length of L, the signal can be decomposed into its frequency components using a Fourier analysis. This results in the Fourier series: ∞ X

up ðxÞ =

^k eikΩx , u

(3:89)

k=1

with the Fourier coefficients L

^k = u

ð2

Ω 2π

uðxÞe − ikΩx dx.

(3:90)

− L2

^k collectively constitute the discrete amplitude spectrum The Fourier coefficients u of the periodic excitation. In order to describe random (stochastic) road surfaces, the transition L ! ∞ needs to be executed for the period length L. This results in the Fourier integral uðxÞ =

1 2π

∞ ð

^ðΩÞeiΩx dΩ, u

(3:91)

−∞

with the continuous amplitude spectrum ^ðΩÞ = u

∞ ð

uðxÞe − iΩx dx.

(3:92)

−∞

The respective continuous amplitude spectrum for uðtÞ results in ^ ð ωÞ = u

∞ ð

−∞

1 ^ðΩÞ. uðtÞe − iωx dt = u v

The root mean square (RMS) then becomes

(3:93)

3.10 Vertical dynamics

∞ ð ðL ^ðΩÞj2 1 2 ju  ð xÞ = u ðxÞdx = limL!∞ dΩ u L L |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl} 0 0

137

2

Φu ðΩÞ

∞ ð ðT ^ðωÞj2 1 ju 2 u ðtÞdt = limT!∞ dω u ðt Þ = T T |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} 0 0

2

(3:94)

(3:95)

Φu ðωÞ

Finally, the power density spectra Φu ðΩÞ and Φu ðωÞ read as Φu ðΩÞ = limL!∞

^ðΩÞj2 ^ðωÞj2 ju ju and Φu ðωÞ = limT!∞ , L T

(3:96)

and the relationship 1 Φu ðωÞ = Φu ðΩÞ v

(3:97)

holds. The characteristics of the spectral power densities are usually represented in a diagram with double-logarithmic scales (Figure 3.52).

1,000 = 2. 2, (Ω Фu

Ω ― Фu(ω) = Фu(Ω0) Ω 0

–w

)=

0

10 w

2.

3 )= 3 m Ω0 1 c Ф u( cm 18 ) = .0, 0 2 (Ω Фu w=

=

1 0.1 0.01

1,

Spectral power density

w

Фu(Ω)/cm3 100

3 0. 3

cm

0.001

0.001 0.01 0.1 Path circular frequency Ω/cm–1 Figure 3.52: Examples of ideal patterns of spectral power densities of road unevenness.

The spectral power densities are a measure for the distribution of the power of the excitation spectrum within the entire road unevenness spectrum. The measured power densities that actually occur can be approximated by the linear function:

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3 Vehicle dynamics and suspension system

 − w Ω Φu ðωÞ = Φu ðΩ0 Þ . Ω0

(3:98)

The shape of these curves also reflects the fact that the unevenness density decreases with increasing circular path frequency or with decreasing unevenness wavelength. In Figure 3.52, Φu ðΩ0 Þ means the spectral power density in a reference circular velocity of Ω0 . This value is also called bumpiness level or general unevenness level (GUL) of the roadway. An increase of Φu ðΩ0 Þ corresponds to larger irregularities of the road. The GUL value ranges between Ω0 = 18 cm3 (very bad) and Ω0 = 0.3 cm3 (very good). The target value for German federal highways, for example, is 1 cm3 (Heißing and Ersoy 2011). The reference circular velocity Ω0 is determined as Ω0 = 1 rad=m, which corresponds to a reference wavelength of λ0 = Ω2π ≈ 6.28 m. In Figure 3.52, the exponent w 0 corresponds to the slope of the line and is also called waviness of the roadway. A magnification of w corresponds to a larger proportion of long waves in the bumpiness spectrum. The waviness varies between the values of 1.7 and 3.3. A value of w = 2 is chosen as the standard value.

3.10.3 Wheel vertical dynamics The wheel vertical dynamics arise from the nonlinear force-deflection curve described in Chapter 2, which however can be linearized around the equilibrium position. The damping of the tire can be neglected compared to that of the body suspension.

3.10.4 Body springs 3.10.4.1 Coil springs Due to the unevenness of the road, the wheels of a vehicle need to perform upward and downward motion that must be dampened and absorbed accordingly. Springs, as well as the dampers discussed in Section 3.10.5, significantly affect the driving comfort, the safety, as well as indirectly, via the wheel loads, the cornering behavior of a vehicle. Body springs are passive components of the wheel suspensions that are installed in between the wheel suspensions and the body. They react to elastic deformation with applied forces. To this end, they convert kinetic into potential energy, which is then relieved in the ensuing relaxation of the spring via the damper, mainly during compression. Suspension springs can be implemented using coil springs, leaf springs, or torsion bar springs. Passive and active pneumatic or hydraulic suspension systems are also possible (Bosch, Reif et al. 2014).

3.10 Vertical dynamics

139

Table 3.7: Important parameters of a coil spring. Symbol

Description

iF

Number of turns per unit length

d, D, L

Wire diameter, coil diameter, wire length

G, Ip

Modulus of shear of the spring material, polar moment of inertia of the wire

γ

Torsion of the coil wire

s

Deflection of the spring

cF

Resulting spring constant

τ max

Maximum shear stress

The spring effect for the mostly utilized coil springs is almost exclusively reached through the torsion of the spring coil. The curvature is negligible. Usually, the coil springs utilized as compression springs are made of steel. A coil spring can be approximated as a helicoidal, wound up torsion bar with iF coils, a length of L, with the diameter of the wire of d, the average diameter of the coil of D, and the modulus of shear G (see Table 3.7). When deflecting the spring by s, the torsion γ of the torsion bar is s D

(3:99)

G IP γ. L

(3:100)

γ=2 and thus the torque becomes Mt =

With the polar area moment of inertia IP = t force FF = 2M D , it can be concluded that FF =

1 4 32 πd ,

the length L = DπiF , and the spring

2Mt 2 G IP s 4G IP Gd4 s. = 2 = 2 s= D 8D3 iF D L D D L

(3:101)

From this, the spring constant becomes cF =

Gd4 . 8D3 iF

(3:102)

An approximation of the maximum shear stress is τmax ≈

Mt d d D2 FF 8D = 3 FF . = Ip 2 2 Ip πd

(3:103)

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3 Vehicle dynamics and suspension system

In applications of motor vehicles it is to note that the mass of a vehicle can change with every drive, which leads to different eigenfrequencies of the body in vertical direction. When observing, for example, the situation presented in Figure 3.53, the vertical eigenfrequency for the empty vehicle amounts to rffiffiffiffiffiffiffiffiffiffiffiffiffi cF (3:104) ωempty = mempty

Δ =(

−

)

Figure 3.53: Different loading situations of a motor vehicle.

and for a loaded vehicle ωloaded =

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cF . mloaded

(3:105)

That is, the following applies ωloaded = ωempty

rffiffiffiffiffiffiffiffiffiffiffiffiffiffi mempty mloaded

and

ωloaded < ωempty .

(3:106)

As this is not desirable, springs are created in a way that the spring constant c adjusts accordingly. This can be achieved using different constructive measures (Figure 3.54).

260 mm

50 mm Figure 3.54: Body spring – different versions.

3.10 Vertical dynamics

141

End stop

Spring forces F

For the case of exceeding suspension travel, corresponding stops are implemented. They are mostly stop elements made of elastomer material. Overall, the characteristics presented in Figure 3.55 emerge.

Standard working range

Spring deflection s

End stop

Figure 3.55: Vertical spring characteristics of a chassis.

3.10.4.2 Air springs Additionally to the described passive coil springs, (adaptive) air springs are used more and more in luxury cars (Figure 3.56). The advantages compared to passive body springs include the following: – The height of the vehicle above the road surface can be adjusted by adding or removing air. – The vertical eigenfrequency of the body can be adjusted virtually independent of loading conditions. – By adding or removing air spring chambers, the spring rate of the air spring can be adjusted adaptively. The air spring produces its effect by a change of volume, and thus pressure, of the encased air. By adding or removing volume (also called chambers), the volume of the air spring is changed, which leads to a corresponding change of the spring effect. This makes it possible to mitigate the spread between ride comfort and performance. Figure 3.57 shows a three-chamber air spring of the Porsche Panamera. In the front axis, the damper is integrated in the air spring and the two valves allow a dynamic charging or discharging of air chambers (Figure 3.58; Table 3.8). The spring constant cL of the air spring results from the derivative of the load force

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3 Vehicle dynamics and suspension system

pa pi

Air sleeve

FL

DL

Figure 3.56: Schematic representation of an air spring.

Air chamber 1 Damper

Air chamber 2

Switch valves

Figure 3.57: Air spring of a Porsche Panamera © Dr. h.c. Porsche AG.

Air spring

143

3.10 Vertical dynamics

3 Chambers active small stiffness

2 Chambers active medium stiffness

1 Chamber active high stiffness

Figure 3.58: Air spring of a Porsche Panamera; switching positions (Boyraz 2019).

Table 3.8: Important parameters of an air spring (see also Figure 3.56). Symbol

Description

pa , pi

Ambient and internal pressure

DT

Diameter of bearing spring

π AT = DT 4

Airfoil of the air spring

V

Air capacity

s

Deflection of the spring

cL

Resulting spring constant

FL

Spring force

FL = ðpi − pa ÞAT = ΔpAT

(3:107)

with respect to the spring travel s while taking into account the total differential to cL =

dFL dðΔpAT Þ dAT dpi dV dAT dpi = − AT − A2T . = Δp = Δp ds ds dV ds ds dV ds

(3:108)

Depending on the velocity of the deflection process, and thus the thermodynamic state change of the air, it can be distinguished between static (isothermal, κ = 1) and dynamic (adiabatic, κ = 1.4) spring operation. According to Pelz and Buttenbender (2004), an adiabatic state change can be assumed in this case, that is, κ = 1.4. This results in ΔpV κ = const )

dpi κ dpi Δp V + ΔpκV κ − 1 = 0 ) = −κ . dV dV V

(3:109)

144

3 Vehicle dynamics and suspension system

According to eqs. (3.108) and (3.109), the spring constant thus becomes cL = Δp

dAT Δp + A2T κ . ds V

(3:110)

3.10.5 Body damper While the body springs absorb shocks from the roadway, the body damper (also called shock absorber) damps the vertical oscillation of the sprung mass. It is an indispensable and safety-relevant component in vehicles, which also needs to care to reduce the normal force oscillation of the wheels, and thus the wheel-load oscillations. The body dampers transform kinetic energy of the masses involved into heat energy. Body dampers exist in various passive, active, or semiactive versions. Figure 3.59 shows two common passive versions.

Piston rod

Valves Gas cushion Piston Oil chamber

Compensating chamber

Separating piston Gas cushion Single tube gas pressure dampers

Bottom valve Twin tube gas pressure damper

Figure 3.59: Example of gas pressure absorbers.

In the twin-tube damper, the piston rod is fixed to the body and the cylinders to the wheel suspension. The cylinder contains an oil-filled working chamber and a ringshaped balance chamber, which absorbs the oil extruded from the working chamber, as well as a gas chamber of nitrogen with a pressure pretensioning of 3–8 bar. The dampening effect is caused by valves in the piston and the base plate, which restrain the oil flow depending on the direction of movement. The stronger dampening takes place in the traction phase in which the oil is pressed through the openings of the valves. When retracting (compression) the damper, the process occurs in reverse, though the restriction effect is lower due to the valves being set up differently (Figure 3.60). It follows that the force action necessary for deflection is mainly provided by springs and the mechanical energy of the decompression is relieved and transformed into heat by the damper.

145

3.10 Vertical dynamics

F

F Rebound

. ẋ

Compress

F

. ẋ Compress

Rebound

Rebound

Compress

F

. ẋ

. ẋ Compress Rebound

Figure 3.60: Damper characteristics.

In the single-tube gas pressure damper, the outer tube, and thus the compensation area, is eliminated. Instead, the compensation is achieved with a gas cushion made of nitrogen, which is under 20–30 bar of pressure and is compressed during the up and down motion by the oil of the working piston. This way, the risk of cavitation21 is avoided. 3.10.6 Stabilizers Stabilizers (antiroll bars) are used for axles with single wheel suspensions, on the one hand, to increase the ride comfort by reducing the roll movement of the vehicle during cornering. On the other hand, the improvement of driving behavior through a positive effect of the self-steering behavior of the vehicle, namely, especially the tendency of the vehicle to under- or over-steer, is just as important (Lenthaparambil 2015, Schramm, Hiller et al. 2018). 3.10.6.1 Passive stabilizers The function of a stabilizer is based on an improvement of roll stiffness of the vehicle by coupling the force effects between both wheels of an axle (Section 3.5.5, Figure 3.19). Here, the coupling is designed by constructing the stabilizer in a way that the forces can only be coupled in differing ranges of the spring. That way, the normal force differences at the front and rear axles can be influenced in such a way that a positive self-steering behavior of the vehicle can be achieved. Stabilizers are typically created using a U-shaped torsion bar spring, which is rotatably mounted in rubber sleeves directly to the vehicle body (Figure 3.61). The ends of the stabilizer are both connected via bearings to the wheel suspension with the corresponding axles. Only for differing deflections of both wheels do both levers experience different displacements, which lead to torsion of the torsion bar, and thus result in the build-up of a corresponding torsion torque. The stabilizer is mounted to the wheel suspension either via rubber sockets or hinged supports.

21 Cavitation (lat. cavitare “cave out”) is the creation and release of steam-filled cavities (steam bubbles) in liquids, when the pressure falls below the evaporating pressure of the liquid.

146

3 Vehicle dynamics and suspension system

Chassis bearing Hinged supports

Body supports

Torsion bar

Figure 3.61: Passive stabilizer according to Schramm, Hiller et al. (2018).

3.10.6.2 Active stabilizers In order to stabilize, or to mostly suppress the roll motion, and to influence the driving dynamic actively and adaptable to the situation, active stabilizers are used (Öttgen 2005) and (Sieberg, Schmid et al. 2019). To this end, passive stabilizers are divided up into two parts and the free ends are then coupled using an electric or hydraulic actuator (Figure 3.62). This actuator then allows the impression of a torsional moment, which is dependent on the torsion of the stabilizer, and which is propped up via the hinged support on the wheel carrier. A torsional moment is initiated into the body of the vehicle using the reaction forces around the longitudinal axis of the vehicle. Thus, a roll stabilization is possible and the self-steering behavior of a vehicle can directly be influenced by separating the applied torques to the front and rear axle. Usually, two active stabilizers are used. There are, however, studies about the realization of a corresponding, albeit somewhat limited function using only one active stabilizer (Lenthaparambil 2015).

Torsion bar

Actuator Hinged support

Passive stabilizer

Active stabilizer

Figure 3.62: Active and passive stabilizer function principles according to Öttgen (2005).

3.10 Vertical dynamics

147

3.10.7 Description of vertical dynamics The analysis of the vibration behavior of motor vehicles requires appropriate substitute models, whose level of detail depend on the desired findings. All of the models described in the following have in common that they are based on MBS modeling, (Schramm, Hiller et al. 2018), that is, the elements of the model are rigid bodies with mass and force elements without mass, which comply with corresponding force laws. 3.10.7.1 Quarter vehicle model One of the most basic equivalent models, which can however already deliver important findings, is the so-called quarter vehicle model (Figure 3.63). Here, the partial vehicle body is represented as a rigid body of mass mA and the wheel as another rigid body of mass mR . The elasticity of the wheel is modeled by the spring constant cR and the body spring by the spring constant cA . The body damper is represented as a viscous damper with the viscosity constant dA . The damping of the wheels can generally be neglected compared to the body damper.

Figure 3.63: Quarter vehicle model.

The road surface is described using the corresponding function ^zS ðxÞ = zS ðtÞ. From NEWTON’s equations for the masses mA and mR , using the generalized coordinates zA and zR results in the equations of motion: mA €zA + dA ðz_ A − z_ R Þ + cA ðzA − zR Þ = 0,

(3:111)

mR €zR − dA ðz_ A − z_ R Þ − cA ðzA − zR Þ + cR zR = cR zS .

(3:112)

These can be represented in matrix notation:

148 "

3 Vehicle dynamics and suspension system

mA

0

0

mR

# " .. # zA

"

..

+

€z

+

zR

M

dA − dA

− dA

# "

z_ A

#

z_ R

dA

z_

D

" +

− cA

cA

# "

zA

− cA cA + cR

zR

C

z

+

#

" =

0 cR

=

# u

h u (3:113)

From this, the equations of the quarter vehicle model result to 2

z_ A

3

2

6 7 6 z_ R 7 6 7 6 €z 7 4 A5 €zR

=

x_

=

" .. # zA Fz y

0 6 0 6 6 cA 6− m 4 A cA mR

=

=

−

0 0

1 0

cA mA

dA mA

−

cA + cR mR

dA mR

A " −

cA mA

cA mA

0

cR

−

dA mA

0

3 0 1 7 7 dA 7 mA 7 5 −

dA mR

2 −

zA

2

C

x

3

2

6 7 6 zR 7 6 7 6 z_ 7 4 A5 z_ R

+

+

3

607 6 7 6 7 607 4 5

u

B

u

+ "

+

0

cR mR

3 x

# 6 7 6 zR 7 6 7 6 z_ 7 4 A5 0 z_ R dA mA

zA

0

− cR

# u.

D

(3:114)

u

For the measurement vector y with the body acceleration €zA and the wheel load Fz , typically interesting parameters have been chosen. The eigenvalues of the system matrix A in eq. (3.114) supply information about the eigenfrequencies. These are calculated from the characteristic equation of the eigenvalue problem:   (3:115) det C − Mω2 = 0 thus 0 10 1 0 1

cA cA + cR cA + cR cR
c − m ω2
2 2 − cA − ω CB − ω C cA B − A
A
B C mA mR mR A = 0

= @|{z} A@|fflfflfflm A− @|fflfflfflfflfflfflfflffl R 2
{zfflffl ffl } ffl {zfflfflfflfflfflfflfflffl ffl }
− cA m A c A + c R − mR ω ω2

A

ω2

R

ω2

AR

(3:116) or transformed    ) ω2A − ω2 ω2R − ω2 − ω2AR ω2 = 0. For cA  cR and mR  mA is ω2AR ≈ 0. In this case, it is approximately rffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffi cA cA + cR and ω2 ≈ ωR = . ω 1 ≈ ωA = mA mR

(3:117)

(3:118)

3.10 Vertical dynamics

149

Quarter vehicle models are used, for example, to calculate the load on chassis components on different road surfaces. Here, the road-induced loads are either obtained directly from data describing the road surface or they are determined indirectly from stress or acceleration measurements (Putra, Abdullah et al. 2015, Putra, Abdullah et al. 2016, Kong, Abdullah et al. 2017). 3.10.7.2 Two-axle vehicle model In order to achieve a higher accuracy of the quarter vehicle model, the proportional body mass can be determined by separating the body mass into the three point masses mA, v (front axle), mA, h (rear axle), and mK (coupling mass) (see Figure 3.64). The following conditional equations result from the requirements for obtaining the body mass mA, ges , the CoM SA , and the moment of inertia θy = mA, total i2y (radius of gyration iy ) mA, v + mA, h + mK = mA, total ,

(3:119)

mA, v lv − mA, h lh = 0,

(3:120)

mA, v l2v + mA, h l2h = mA,

2 tota iy ,

(3:121)

and from this the equivalent masses mA, v = mA, ges

i2y lv l

, mA, h = mA,

i2y total

lh l

(3:122)

and mk = mA, ges 1 −

i2y lh lv

! .

(3:123)

In case mK = 0, the motion of front and rear axles are decoupled. For the wheel-based, proportionate body mass mA of the quarter vehicle model, mA = 21 mA, v is put in at the front axle and mA = 21 mA, h on the rear axis, respectively (Figure 3.64). Furthermore, it is necessary for a conclusive quarter vehicle model to take into account the kinematic ratio of the suspension forces, as they are represented in Figure 3.65. The kinematic ratio λ results from the compression zs at the tire contact point and the change in length zr of the body spring to λðzs Þ =

dzr z_ r = . dzs z_ s

(3:124)

The relationship between the forces Fs and Fr can be obtained most effectively by equating each performed virtual work:

150

3 Vehicle dynamics and suspension system

SA

,

,

,

,ℎ

ℎ

Figure 3.64: Two-axle vehicle model (Schramm, Hiller et al. 2018).

Figure 3.65: Kinematic ratio of the wheel suspension forces using the example of a body spring (Schramm, Hiller et al. 2018).

Fs δzs = Fr δzr = Fr

dzr dzr δzs ! Fs = Fr = λFr . dzs dzs

With this, after short calculation, the equivalent spring constant cA becomes

(3:125)

3.10 Vertical dynamics

cA =

dFs dðλFr Þ dλ dFr dλ dFr dzr = = Fr + λ = Fr + λ dzs dzs dzs dzr dzs dzs dzs |{z} |{z} cs

151

(3:126)

λ

and finally cA =

dλ Fr + λ2 cs . dzs

(3:127)

3.10.8 Objectification of vibration comfort The objectification of vibration comfort attempts to assign the subjective perception of vehicle occupants with regard to the perceived vibrations to one or more objective characteristic values, which are calculated from physically measurable quantities. The great difficulty lies in expressing the distinct comfort sensations of vibrations, which is dependent on psychophysical and psychological factors, as one value. Vibration comfort and vehicle acoustics can be seen as a part of driving comfort, which is influenced by convenience, aesthetics, ambience, and many other factors. Thereby vehicle vibrations and acoustics are based on the same physical phenomena. These lie in different frequency ranges and are therefore perceived differently by occupants. The different vibration phenomena in a vehicle can basically occur along the six DoF (translational and rotational) of the vehicle body (see Section 3.1). The root cause of the oscillations may lie in internal and external vehicle excitations. Internal excitations are caused by powertrain and wheel excitations (mainly through imbalances), which are significantly influenced by mass, stiffness, and damping. The vehicle body, which connects all parts of the car, also has a high influence on the vibration behavior through its stiffness. External excitations are mainly caused by the road conditions and the aerodynamics of the vehicle. Figure 3.66 gives an overview of important vibration phenomena and the associated frequency ranges. It should be noted that the phenomena can act in one or more dimensions and must therefore be measured differently. Vibrations in the range of the natural frequencies of organs are considered particularly unpleasant. For example, the natural frequency of the stomach is approximately 4 to 5 Hz (Dupuis and Christ 1966), which can be caused by both the body and the wheel’s natural frequencies in a vehicle. Body movements (heaving, pitching, and rolling) can have a significant effect on the perceived vibration comfort. Rolling movements may be perceived as especially unpleasant by the occupants (Enders, Burkhard et al. 2019). Vehicle body movements caused by road excitations can be analyzed by means of substitute models with different degrees of simplification. Consequently, initial

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3 Vehicle dynamics and suspension system

Wheel imbalance 12–18 Start and stop juddering 12–14 Body jittering 12–40 Steering wheel oscillations 10–15 Stuttering 8–12

Ride comfort 8–30

Jerking 3–8 Bouncing 3–6 Body vibrations 1–3 0

10

20

30

40

Frequency/Hz

Figure 3.66: Important vibration phenomena and their frequency ranges.

findings for pure heaving movements can be derived from a simplified quartervehicle model (Figure 3.63). The simplified assumption is that all four wheels are considered decoupled from each other. For the analysis of a pitch and roll motion, that is, rotations about the vehicle’s transverse and longitudinal axis, a quarter vehicle is no longer sufficient. In this case, an analysis using a two-axle vehicle model is necessary (Figure 3.64). For the creation of mathematical models for the objectification of vibration comfort, subjective evaluations and objective measurements must be brought together. The human perception of vibration is determined by empirical studies in the laboratory or by field trials. Typically the perception of vibrations must be perceived less as an aspect of the subject’s pleasure (= comfort), but rather as an aspect suffering (= discomfort). For the perception of the comfort sensation different questioning methods and evaluations are used. Known methods are the multicriteria evaluation with radar charts according to Heißing and Brandl (2002), the ATZ rating scale according to Aigner (1982), the CP50 scale according to Shen and Parsons (1997), or the Likert scale. Depending on the chosen method, the surveys can be evaluated by statistical methods as interval or ordinal scaled data. At the same time, acceleration measurements are carried out on the vehicle and test persons during the test drive. After an appropriate signal analysis, the objective

3.10 Vertical dynamics

153

measurement data are linked to the subjective surveys by a regression analysis. Numerous methods and adaptations have been developed to determine objective characteristics for the description of vibration comfort. Known methods are the procedure according to ISO 2631 (1997), (VDI 2002), (Rericha 1986), (Klingner 1996), (Cucuz 1993), (Jörißen 2012), (Festner, Eicher et al. 2017), (Burkhard, Vos et al. 2018), and (Hennecke 1995). The ISO 2631 standard, which was first described in 1974 and has since been revised several times, is increasingly used in industry. It is usually used to define target values in specification sheets and to evaluate vibrations in development. Part 1 of the standard defines methods for the measurement of periodic, random, and transient whole-body vibrations. The frequency range considered is 0.5 to 80 Hz for health, comfort, and perception as well as 0.1 to 0.5 Hz for kinetosis (motion sickness). Figure 3.67 describes the procedure for calculating an effective value for the subsequent categorization of measured accelerations.

Figure 3.67: Sequence of the effective value calculation according to the ISO 2631 standard.

Within the standard, the measured accelerations and rotation rates are differentiated by frequency-dependent rating functions depending on the respective introduction points and directions. The rating is performed by multiplying the acceleration signals with an evaluation function W in the respective frequency domain. The frequencyweighted accelerations are then calculated using the RMS value of the individual measurement points. Various methods are defined in the standard for calculating the weighted vibration intensities, whereby a weighted RMS is used as the standard procedure. The resulting effective value can then be categorized according to different discomfort levels. The influence that the suspension setup has on the vehicles body, on wheel movements, and on the occupants comfort perception is described in Figure 3.68. It shows a smoothed (filtered) fast Fourier transformation (FFT) of the accelerations at the strut mount and at the wheel center point with a soft and hard suspension setup. The results are from a mid-size car on a straight, severely damaged road and at a constant speed of 60 km/h. One recognizes the natural frequencies of the vehicle body at 1.5 Hz and the natural frequency of the wheels at 10 Hz. Between these two frequencies lies a range that is sometimes referred to as the insulation range, but which nevertheless allows unwanted vibrations to be perceived, which, for example, are caused by interactions between the body and the engine. This effect is

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3 Vehicle dynamics and suspension system

0.12 Suspension soft Suspension hard

Amplitude /-

0.1 0.8 0.6 0.4 0.2 0

0

5

10

15 Frequency/Hz

20

Amplitude /-

1.4

25

Suspension soft Suspension hard

1.2 1 0.8 0.6 0.4 0.2 0

0

5

10

15 Frequency/Hz

20

25

Figure 3.68: Frequency analysis of the measured accelerations of a compact car at the strut mount and wheel center for soft and hard suspension settings.

called spluttering and gives reason to a careful layout of the engine mounts, which are sometimes even designed as active elements. The natural frequencies of the vehicle body (strut mount) are between 1 and 3 Hz for a vehicle with soft suspension. With a hard suspension the energy is shifted into a middle-frequency area and increased in its amplitudes. The road excitations with a hard suspension are perceived more clearly and unpleasant by the occupant, but also the low-frequency excitations can lead to discomfort. However, if considering the FFT at the wheel center point, the wheel load fluctuations are simultaneously increasing with a soft suspension. This has a strongly negative impact on driving safety. This effect is also referred to as conflict of objectives in vertical dynamics. The wheel load is thereby influenced by the lifting movement of the wheels. High wheel load fluctuations lead to a deterioration in driving safety. In contrast, high vehicle body movements have a negative effect on the driving comfort. Modern adaptive or (semi-)active chassis systems try to resolve this conflict by influencing the vertical dynamics and being able to switch between different suspension setups depending on the drive.

3.10 Vertical dynamics

155

3.10.9 Oscillation frequency of wheel, seat, and body An overview of usual vertical oscillation frequencies of the wheels, the body, and the seats is shown in Figure 3.69. It is known that people react especially sensitive to excitations within a frequency range of 4 − 8 Hz. Among others, it is because the eigenfrequency of the stomach lies exactly in that area. The body and seat eigenfrequencies thus need to be set up in a way that avoids this range.

500

0 18 km /h

100 36 km /h

Upper frequency limit

Excitation frequency/Hz

30

10

Wheel

5 Seat 2 Body 1 0.5 Lower frequency limit

0.1 0.1

1

10

100 Wave length/m

Figure 3.69: Overview of the frequency ranges of vertical motion.

4 Vehicle steering The vehicle steering system allows the driver to keep the vehicle on an almost freely chosen path. Sideways or lateral motion of modern motorized vehicles is almost completely achieved by the drivers’ steering input (Harrer and Pfeffer 2017). If automated safety systems such as ESP1 are left out of consideration and average drivers are considered, the desired lateral motion of the vehicle is purely achieved through the steering system. This makes the steering system one of the most crucial parts of every motorized vehicle. Independent of the exact mechanical arrangement, the motion of a control input (usually a steering wheel) is translated to the rotational motion of one or more steered axles. This leads to an angle difference between the vehicle’s longitudinal axis and the steered wheels. Consequently, lateral forces are exerted between the tires and the road surface, causing the vehicle to follow a curved trajectory. The lateral control of a vehicle by the driver can be seen as a closed feedback loop. Here the driver influences the state of the system (vehicle) by applying input on the actuator (through the steering wheel). The change in vehicle state can then be perceived both visually and through haptic or force feedback (Figure 4.1). Besides giving the driver control over the lateral positioning of the vehicle, the steering system therefore also serves as an important source of information to the driver. The steering feel is essential to obtain a safe and precise steering of a motorized vehicle. Through the forces exerted by the steering wheel, to the driver’s hands, the driver can draw valuable information about the current state of the road–tire contact. Therefore, steering feel can be a decisive factor regarding driving comfort. In the recent decades, developments such as electric power steering (EPS) have led to an increase in possibilities for which the steering system can be used for safety or assistance purposes. This chapter provides an overview of functions and tasks for which the steering system is responsible. In order to do this, the relevance of the chassis is briefly explained before some basic engineering designs on steering systems are presented. Furthermore, this chapter contains an elaboration on the topic of power steering, both in hydraulic implementation as well as EPS, which is standard in today’s automotive industry. It will also be shown how the steering system can be evaluated with regard to safety aspects. To conclude, potential future steering systems will be discussed.

1 ESP: Electronic Stability Program, depending on the vehicle manufacturer, different names can be found. https://doi.org/10.1515/9783110595703-004

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4 Vehicle steering

Vehicle (controlled system)

Driving course (controlled variable)

Driver (controller) Road course

Steering wheel (actuator)

Vehicle response

Optical haptic kinesthetic acoustical

Haptic response

Steering wheel input torque/angle

Figure 4.1: Driver–vehicle feedback loop for lateral control (Harrer and Pfeffer 2017).

4.1 Technical requirements of vehicle steering systems The requirements for contemporary motorized vehicle steering systems can be highly diverse and sometimes even contradictory. Logically speaking it is of critical importance that the driver is able to keep the vehicle following the desired trajectory through use of the steering system. Nonetheless, other factors such as vibrations, noise levels, steering feel, fuel efficiency, and, as with all other systems in motorized vehicles, weight, installation space, and costs play key roles. While the legislative requirements regarding safety and functioning of motor vehicle steering systems are highly regulated, the steering feel can be assessed vastly different by competing vehicle manufactures and is therefore often a key differentiator between brands. Through steering (usually in conjunction with the chassis) either a comfortable and smooth ride or a sportier performance-oriented ride experience can be obtained. For the driver’s evaluation of the vehicle, steering is therefore one of the most significant attributes (see Section 4.2). The most important characteristics of a modern steering system are according to Harrer and Pfeffer (2017), Haken (2013) – precision, – reliability, – a mechanical linkage from steering wheel to the steered wheels (also as backup system for vehicles equipped with the so-called steer-by-wire), – an adequately direct translation of input to output motion to guarantee precision and accuracy in tight roads and during parking maneuvers,

4.2 Driver–vehicle interaction and steering feel

159

– an adequately low and well interpretable steering wheel torque (without power steering only achievable with indirect steering), – a consistent and predictable steering recovery when exiting corners as well as good straight-line characteristics, and – the absence of disturbances on the steering wheel (bumps, vibrations, etc.).

4.2 Driver–vehicle interaction and steering feel 4.2.1 Basic requirements for steering systems On the one hand, the steering wheel is the only input available to the average driver that allows control over lateral motion of the vehicle. On the other hand, it is an important source of information to the driver and provides real-time haptic2 feedback about the current vehicle state. Especially information on road–tire contact and road condition can be gained through the steering feel. The steering feel, as defined by Harrer and Pfeffer (2017), can be described as “The sum of visual, kinesthetic, and haptic sensation of a driver while steering a vehicle”. This describes a highly complex and subjective experience. The interaction between driver and vehicle in a feedback loop where steering is the main actuator is shown in Figure 4.1. While the so-called steering feel determines how a driver perceives a specific vehicle steering motion, the steering behavior follows the opposite route. The steering behavior describes the reaction of the vehicle due to a specific steering input. This highly personal and difficult to objectify steering feel depends in a decisive manner on the steering behavior. In order to be able to evaluate the steering feel as positive, it is necessary that the steering behavior, that is, the vehicles reaction to a steering input (steering wheel torque and angle) appears consistent and coherent (Harrer and Pfeffer 2017). For the average driver this requires a linear relationship between steering wheel angle and vehicle reaction. This behavior may only become nonlinear when the vehicle is being driven on the edge of its performance capabilities. The average driver rarely reaches this region of extreme lateral accelerations. Even though the assessment of steering (feel) can be considered a subjective task, some clear and concise requirements regarding the steering feel and behavior of a vehicle can be determined as seen below: – low steering torque during parking and maneuvering, – ease of movement, sensitivity, and accuracy, – good straight-line stability at all speeds,

2 Haptic (from Greek language); by sense of force.

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4 Vehicle steering

– good response (straight-line stability at high speeds, response to small steering wheel angles at low speeds), – sufficiently direct reaction of the steering system, – road condition feedback and feedback of the driving situation (steering feel, vibrations, information on the tire–road contact), and – comfort requirements such as suppression of uneven roads, noise suppression, and so on. In addition, other criteria such as the ones below can be added: – crash requirements (especially requirements on steering wheel and steering column), – ensuring safe steering of the vehicle, – energy efficiency (power steering), – performance (power, force, and dynamic of the actuator), – environment (corrosion, temperature, leakage, fluids, etc.), – high quality (no mechanical or electrical faults), – packaging (especially for the steering column), – weight and cost, – low friction in the steering system and steering column for a better steering feel, and – high stiffness of the steering column for a direct response. The steering torque is a decisive factor in both steering feel and steering effort. Besides statutory requirements for the maximum steering torque, significant manufacturer-specific differences are noticeable when evaluating vehicle steering. By tuning the steering assistance (around the center position), the desired steering wheel torque (steering feel) can be achieved. For this reason, there have been many different studies on the topic of objectively measuring and improving steering feel, for example, (Harrer 2007), (Harrer and Pfeffer 2017), (Lunkeit 2014, Fritzsche 2016). According to the StVO,3 for example, a safe and “low effort” steering action must always be guaranteed. This demand is specified in greater detail in the guidelines (EU 1992) (Alteration of Guideline (EU 1970)). In these documents the maximum allowed values for force exerted by the hands, and thus the maximum steering wheel torque are defined. The steering system for a passenger car must be designed in a way that, starting in a straight-line trajectory with a speed of 10 km=h, the car must be able to reach a circular trajectory with a radius of 12 m within 4 s. When loaded to the vehicles’ maximum loading capacity, the maximum allowable steering wheel force required for this maneuver is 150 N. For a vehicle equipped with power steering

3 German Road Traffic Act.

4.2 Driver–vehicle interaction and steering feel

161

the allowable force after malfunctioning of the power steering system is also defined. In this case the maneuver is done with a circular trajectory with a radius of 20 m, where the maximum allowable force is limited to 300 N. During normal driving conditions the torque on the steering wheel is in the range 2 −3 Nm. Assuming a steering wheel with a radius of 15 −20 cm, this corresponds to less than 20 N force exerted by the hands. In extreme situations (emergency evasive maneuvers for instance), much higher steering wheel forces can be reached. Since the steering system is rated as ASIL-D (automotive safety integrity level D, see Chapter 1) regarding ISO26262 (ISO 2011), a safe and reliable functionality has to be guaranteed in all driving situations. Therefore, a high effort in validation and verification is necessary.

4.2.2 Assessment criteria for steering systems Harrer (2007) lists various assessment criteria for steering systems, of which a selection will be discussed below. First, a short definition of the criterion is given. Afterwards the respective possible characteristics are listed. According to Dralle (2016) and Schäfer, Wahl et al. (2006), not only the steering system itself is relevant for assessing the steering characteristics, but also various vehicle characteristics (e.g., vehicle mass, suspension, and wheel–tire combination) like – steering wheel angle demand: necessary steering wheel angle to generate a specific wheel steering angle and consequently curve radius (too low/direct ↔ ideal ↔ too high/indirect), – steering torque: occurring torque on the steering wheel when driving the vehicle (too low ↔ ideal ↔ too high), – steering precision: vehicle reaction to steering wheel angle variations and correction needed when driving the vehicle (precise ↔ imprecise), – steering feedback: transmission of information about the contact between the tire and the track and the forces acting on the tire (too low ↔ ideal ↔ too high), – intermediate layer/directional stability: stability or correction requirement when driving straight ahead (too slow/indirect ↔ ideal ↔ too nervous / direct), – steering responsiveness: reaction of the vehicle to initial variation of the steering wheel angle (too slow ↔ ideal ↔ too nervous), – rear steering: system for applying a steering angle to the rear wheels (positive ↔ negative).

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4 Vehicle steering

4.2.3 Subject study and press analysis In principle, similar findings regarding the rating of systems or vehicles can be determined with a subject study and a press analysis. However, the methods have different advantages and disadvantages with regard to effort, costs, and the test persons or testers as well as the possibilities in the evaluation of the properties, which will be discussed in detail below. A successful subject study requires a high organizational effort. A sufficient number of subjects must be acquired and scheduled. In addition, the necessary vehicles and possibly a test site must be provided. The time required to carry out and supervise the candidates must also not be neglected. The preparation and organization effort for a press analysis, however, is low. In return, the continuous expenditure of time is significantly higher, since a sufficient number of tests and evaluations requires a press analysis over as long a period as possible. The cost of a subject study depends on the objective of the study. Driving dynamics demanding driving maneuvers cannot be carried out in traffic. In addition to the vehicles, a test area or a closed test track must be available in this case. As an alternative to subject studies with real vehicles subject studies with simulators can be performed (see Chapter 10). Under certain circumstances, a compensation of the subjects in the projected costs should be included. A press analysis can be carried out at significantly lower costs. Only costs for newspaper articles or other publications (subscriptions for online publications) incur. A subject study can document detailed information about the subjects (e.g., age, gender, driving experience, driving style, vehicle choice preferences). This documentation allows to create specific evaluations related to individual attributes. In contrast, there is almost no information about the testers in a press analysis. Consequently, only general evaluations are feasible. Conclusions on person-specific characteristics are not possible. An advantage of the press analysis, however, is that by considering foreign newspapers and publications an analysis in different markets requires only little effort. With the help of a subject study, the targeted analysis of individual properties of a system or vehicle is possible. The design of evaluation sheets or the targeted questioning of the subjects allows the specific recording of information, so that the respective question can be precisely analyzed. In addition, development vehicles (prototypes) can be inspected to obtain feedback on the new product before they are introduced to the market. As part of a press analysis, the entire product is usually evaluated. A targeted analysis of specific properties or driving maneuvers is not possible here. Only the information can be evaluated, which are addressed by the testers in the respective articles. There is no possibility to inquire specifically about certain criteria. It follows that for press tests a significantly larger database is needed than in a subject study in order to obtain a statistically sufficient number of assessments.

163

4.2 Driver–vehicle interaction and steering feel

4.2.4 Results of the press analysis on steering systems This section addresses a selection of the results of a press analysis for the evaluation of steering systems in actual vehicles of five different series (sports car, sedan, SUV) of Porsche AG derived by Düsterloh, Bittner et al. (2018). The results presented and analyzed below result from the evaluations in a total of 684 press reviews from 218 different sources, which were evaluated over a period from 02/2016 to 04/2018. The number of articles and publications from the trade press is 471 and is therefore around 68.9%. Figure 4.2 shows the ratings summed up across all series. Above the respective evaluation criterion, the numbers of the evaluations occurring in the press tests are plotted.

299

negative

too inert/indirect

too nervous

too inert

too high

too low

unprecise

too high

232

too nervous/ˊdirect

Number of ratings

250

too low

too high/in directt

300

Number of press tests evaluated: 684

too low/direct

350

200 175 150 121

114

107

100 75 50 0

1

12

Steering angle demand

15

18 4

0

Steering torque

Precision

0

3

1

Center feel/ straight-line correction effort Assessment criterion Steering feedback

4

1

Steering response

11 Rear axle steering

Figure 4.2: Press analysis on steering systems in actual vehicles of Porsche AG (Düsterloh, Bittner et al. 2018).

Figure 4.2 shows that the vehicle steering systems are generally rated positively in all criteria. Most often the criterion of the rear axle steering (310 evaluations) is evaluated, followed by the feedback (250 evaluations) and the precision (232 evaluations). Steering torque (140 ratings), steering wheel angle demand (127 ratings), and response ratings (112 reviews) are rated approximately half as often. The center feel or the straight line (22 ratings) are rated the least. With regard to the steering wheel angle demand, there is a tendency toward an high steering wheel angle demand (for indirect steering ratio). The steering torque is

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rated as low by the testers. In the evaluated press tests, there are only positive evaluations regarding the precision. The steering feedback is in most cases rated as exact. However, a clear tendency with the desire for more feedback is identifiable. The feedback is rated most critically compared to the other criteria. With regard to the center feel or the straight-line correction effort, there is only a small number of statements, which overall reflects a positive rating without a clear tendency. The response of the vehicles to steering commands is also rated as positive. With regard to the rear-axle steering systems, most of the evaluations are available, which are almost exclusively positive. For detailed analyses and results of the press analysis (market-specific evaluation according to German-language and English-language articles, series-specific evaluation), reference is made to the explanations in Düsterloh, Bittner et al. (2018). The presented results of the press analysis show some analogies to the results of a study of volunteers presented in Pfeffer and Scholz (2010). In the context of this study, the assessments of regular drivers (subjects without previous training in the assessment of steering systems) are compared to the evaluations of experts. As a result, it appears that normal drivers and experts basically give similar ratings regarding the criteria of precision, steering wheel torque, and steering wheel angle requirement. The vehicles tested in the subject study are often rated as imprecise, unlike the steering precision results presented in Figure 4.2. The steering wheel torque is judged too low by the testers of the subject study compared with to the tendency in the results of the press analysis in Figure 4.2. The steering wheel angle requirement is often too large, that is, the translation is too indirect, analogous to Figure 4.2. Regarding the feedback or the steering feel, the evaluations of the experts are more differentiated and more critical than the evaluations of the normal drivers. The critical feedback evaluations can also be seen in the press reviews in Figure 4.2.

4.3 Common designs of steering systems Since the appearance of the first motorized vehicles, the art of steering has undergone drastic changes. Besides improvements in kinematics and construction design, many different forms of power steering have been developed. In recent years, the main focus in the domain of vehicle steering systems has been with regard to EPS and the new innovative functions this feature allows. Depending on the vehicle type different forms of steering can be drawn up. Figure 4.3 shows these significantly different ways of steering. The first motorized vehicles were simply based on existing but nonmotorized vehicles. These were most commonly equipped with the so-called turntable steering systems, which were also being used for horse carriages. This type of vehicle steering, just like articulated steering, has the disadvantage that one-sided disturbances are propagated through the large torque arm (half the track width) resulting in large steering

4.3 Common designs of steering systems

Turnable steering

Articulated steering

165

Stub axle steering (Ackermann steering)

Figure 4.3: Basic construction forms of a vehicle steering system.

torques (Matschinsky 2007). Both the rotation of the steered axle (turntable-steering) and the kinking in the vehicles longitudinal axis (articulated steering) lead to a significant reduction in the vehicles’ contact area4 (Matschinsky 2007). Therefore, these types of steering can only be used at low cornering speeds. Nowadays, the articulated steering mechanism can still be found in construction and agricultural vehicles. On the contrary, stub-axle steering, which was developed in the nineteenth century, does not decrease the vehicles’ contact area. Thus, requiring less available space to fit the steering mechanism. It has therefore become the norm in vehicle steering systems and made other mechanism mostly obsolete. The stub-axle steering mechanism was patented in Munich by the inventor and carriage builder Georg Lankensperger as well as by Rudolph Ackermann in England (Matschinsky 2007). It can be found in similar forms in nearly all of today’s motorized vehicles. Steering mechanisms based on varying propulsion speeds of both wheels, as can be found in chain-driven vehicles, do not play a role in modern day passenger cars anymore. Nearly all of today’s motorized vehicles are equipped with the so-called rack and pinion steering mechanism. The rotation movement of the pinion is converted into an axial, or longitudinal, movement of the rack and results in a pivoting motion in both steered wheels. This concept is described in detail in Section 4.5. In addition to this, most commonly used rack and pinion mechanism in combination with the appropriate steering linkages and recirculating ball gears are also used (Figure 4.4). Since the vehicle moves on a circular path while cornering and both wheels move around the same point, the steering angle for the inner and outer wheel must

4 Plane on road surface which is span by all tire contact points.

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4 Vehicle steering

Steering trapezoid

Steering triangle (with rack and pinion gear)

Steering quadrilateral (with recirculating ball bearing and steering column lever)

Figure 4.4: Different types of steering linkages for a stub-axle steering system in motorized vehicles.

be different from one another. The smart arrangement of steering kinematics, for example, steering triangle in a rack-and-pinion steering mechanism is used to simultaneously optimize the steering behavior of the inner and outer wheel.

4.4 Interpreting steering kinematics When looking into the design of steering systems, a distinction must be made between a purely kinematic approach or an approach that includes the dynamics of motion of the vehicle.

4.4.1 Ackermann steering kinematics Assuming a circular trajectory at low speeds and consequently very limited centrifugal forces and negligible side-slip angles both wheels move in direction of their center plane. The movement of all wheels in the direction of their center plane (meaning zero side-slip) results in lower wear and tear on the tires. Moreover, it will decrease the total rolling resistance caused by the dynamic interaction between the road and tire surfaces. Figure 4.5 shows the top view of a vehicle with a stub-axle steering mechanism during low speed cornering. All four wheels can rotate freely in the direction of their center plane and move in a circular trajectory around point K. This modeling

4.4 Interpreting steering kinematics

δa

δ

δi

167

b

l ρ

K

δi

δ

lh

δa

y Figure 4.5: Purely kinematic, semistationary interpretation of Ackermann steering kinematics.

approach is of purely kinematic form. The resulting steering kinematic is known as Ackermann steering, explained in more detail in Chapter 3. In this geometrically based description, point K corresponds to the instantaneous center of rotation of the vehicle and is located in line with the rear-axle of the vehicle. The vehicle’s center of mass rotates around point K with a radius ρ. In the described situation it is obvious that the inner and outer wheels must have different steering angles (Figure 4.5). This simple kinematic approach of vehicle motion following a circular trajectory makes it possible to determine the necessary steering angles for both steered wheels (Table 4.1). Unlike models using a single track, also known as bicycle models, there is no uniform steering angle meaning that both left and right wheel must be considered separately (Figure 4.5), yielding the following equations: tan δa =

l y+

b 2

and

tan δi =

cot δi = cot δa −

b . l

l , y − b2

(4:1) (4:2)

In practice, especially the difference between inner and outer steering angles is of interest. To indicate this the angle δi − δa is shown above δi in Figure 4.6. A typical course for the steering angle difference corresponding to the Ackermann model is shown here. The deviation from Ackermann steering can result in an optimized load transmission, steering precision, and steering guidance as well as advantages in the packaging (see also Section 4.4.2).

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4 Vehicle steering

Table 4.1: Steering angle notations (see also Figure 4.5).

δa

Steering angle on (turn) outer wheel

δi

Steering angle on (turn) inner wheel

y

Distance from center of rear axle to the instantaneous center of rotation

b

Vehicle track width

g

rin

Deviation from Ackermann steering

Ac ke rm an n

ste er in g

Description

Steering angle difference δi − δa

Symbol

e ste al n tio en nv o C

Parallel steering Steering angle δi on the inside wheel

Figure 4.6: Comparison of Ackermann steering principle and a traditional steering principle (Mitschke and Wallentowitz 2014).

4.4.2 Dynamic approach to steering kinematics The steering kinematic model explained so far does not hold for higher speeds, as this leads to the introduction of nonzero side-slip angles for both wheels (see Chapter 2 and 3). These are dependent not only on the vehicles motion, but also on other factors such as the condition and properties of the tires (see Chapter 2). This consequently leads to a shift of the vehicle’s center of rotation towards the front axle (Figure 4.7). In a more dynamic approach to steering kinematics, it must be kept in mind that the wheels are no longer moving in the direction of their center plane. This is known as the so-called lateral slip, or side-slip (see Chapter 2). When dealing with the modeling of high-speed cornering, the vehicles motion dynamics must be taken into consideration. A centrifugal force is exerted on the

4.4 Interpreting steering kinematics

169

δa δi

αv,a

αv,i

K

l

ρ αh,i

lh

αh,a

Figure 4.7: Dynamic visualization of steering kinematics.

vehicle, located in its center of mass. This force is dependent on vehicle mass, speed as well as the cornering radius. The centrifugal force must be counteracted by force interaction between the tire and road surface. Lateral tire forces result from the side-slip angles as well as from the normal load on the wheels. When trying to determine the optimum steering angle of the wheels, it is of crucial importance which side-slip angle generates maximum lateral tire force. Due to the unevenly distributed wheel load during cornering, the potential of lateral force on the outside wheels is significantly increased compared to that on the inside. Additionally, the maximum lateral tire force for the outside wheels is reached at higher side-slip angles as for the inside wheels. In case both inner and outer wheels were to be fixed to their respective side-slip angles corresponding to their maximum lateral tire force, the outer wheels must obtain a higher steering angle than would be the case with the kinematic Ackermann approach. The angular difference between both steering angles will become negative. Because this goes against the model described by Ackermann, this is also known as anti-Ackermann steering (Haken 2013). The approaches to designing the ideal steering for high speed cornering and semistationary maneuvers, as e.g. parking, are contradictory. This conflict of interest can partially be solved by taking advantage of another effect. The centrifugal force exerted during cornering causes a rolling torque, dependent on the height of the vehicles’ center of gravity (see Chapter 3). As a result, the outer wheel compresses while the inner wheel rebounds. Through a concise connection between the inner and outer wheel, this rolling motion can be used to bring about a desired change in toe-in angle. This leads to a decrease in steering angle on the inner wheel and in an increase in steering angle on the outer wheel. A steering system designed as described

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4 Vehicle steering

will (almost) correspond to the theoretical Ackermann model at low speeds, while still allowing optimal results during high speed dynamic cornering.

4.5 Components of the steering system In most modern vehicles, the before mentioned rack and pinion steering mechanism is used. The rack and pinion, as well as the triangular linkage steering mechanism, are shown schematically in Figure 4.4. While Figure 4.4 only shows the steering kinematics of the axle and steering linkages, Figure 4.9 shows the entire steering train: from the steering wheel to the steered wheels of a typical passenger car. The torsion bar shown serves to determine the torque exerted on the steering wheel by the driver. In vehicles equipped with power steering, the torsion bar is used to regulate the amount of steering assistance aiding the driver. Further explanation regarding power steering will be omitted in this section, and the reader is instead referred to Section 4.10. The driver steers the vehicle by a control input on the steering wheel. This movement of the steering wheel is transferred through the steering column and steering shaft to the steering rack. In Figure 4.8, an example of a rack and pinion steering mechanism is shown. The motion of the steering shaft is transferred to the steering rods through the steering rack, causing the wheels to move in the desired direction. In the following sections each individual component of the steering system is elaborated upon. In the process of product development a steering test bench can be used to objectify the influence of the separate parts of the steering system (Düsterloh 2018, Düsterloh, Uselmann et al. 2019) and (Uselmann 2017).

4.5.1 Steering wheel The steering wheel is the part of the steering system that is controlled directly by the driver and is also a source of feedback to the driver regarding the dynamic driving situation. The steering wheel is thus one of the most important control interfaces between driver and vehicle (Figure 4.1). The construction, haptics, and aesthetics of the steering wheel determine the driving experience to a certain extent. In addition, various vehicle control elements as well as the clock spring and airbag system are incorporated in modern day steering wheels. Due to the development of power steering assistance (see Section 4.10), the diameter of the steering wheel is no longer a decisive factor in the controllability of the vehicle. Where older vehicles demanded a minimum steering wheel diameter to keep the required steering wheel torque exerted by the driver to an acceptable level, nowadays only the criteria regarding aesthetic, haptic, and ergonomic domain are decisive (Heißing and Ersoy 2011).

4.5 Components of the steering system

171

Steering wheel

Universal joints Steering column Wheel carrier Intermediate steering shaft Protective bellow

Rack

Steering arm Radial joint

Tie rod

Pinion shaft

Torsion bar

Axial joint (Steering) Pinion

Figure 4.8: Basic design of a rack and pinion steering system.

4.5.2 Steering column and intermediate steering shaft Nowadays, a mechanical steering column and shaft are used in nearly all passenger cars. The steering shaft provides the driver with a mechanical linkage to the steered wheels so that the wheel angle can be adjusted at any time. In reversed order, the forces and torques from the steering rack are transferred to the driver to provide continuous feedback. Therefore, not only the driving behavior of the vehicle but also the steering feel depends decisively on the steering column and shaft. The upper part of the steering path is usually coupled to the steering column. Therefore, the steering column must not only provide a stiff linkage but must also be adjustable as to provide the driver with the option of customizing the steering wheel position. The so-called fixed steering columns (lacking height adjustability of the steering wheel) are hard to find in modern-day motor vehicles. Because the steering column must possess enough stiffness to fulfil its primary objective, it can be problematic during crashes. In case of an accident, it must be avoided that the steering column penetrates through to the inside of the vehicle where it poses a significant danger to the occupants.

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In modern vehicles the steering wheel together with the steering column is moved toward the front of the vehicle during a collision, to ensure the passenger space of the vehicle is not penetrated. At the same time, the positioning of crash elements such as the airbag must be safeguarded. The connection between steering column and steering rack is guaranteed through the steering shaft. Due to limited space in the car front end, steering shafts must consist of joints to ensure they can be led around the engine. Often the steering shafts are adjustable in length, which benefits ease of assembly. The option to adjust the length of the steering shafts can also be utilized to achieve desired crash characteristics. Another advantage of the steering shafts is that they are capable of filtering out disturbances and shocks. In the simplest implementation, the steering shaft exists of a single rigid shaft with universal joints on either side. Due to the separate shafts and their connecting joints, a nonuniformity of motion occurs. This nonuniformity is known as the gimbal error. Alternatively a constant velocity joint, or CV joint, can be used (Schramm, Hiller et al. 2018). Compared to universal joints, CV joints tend to have significantly higher friction values and are known to exhibit more backlash in the vehicles steering characteristic. 4.5.2.1 Universal joints As already mentioned, universal joints are used to allow for the necessary bending points in the steering line. The rotational movement of the input shaft is transferred to a rotational movement of the output shaft through the universal joint (Figure 4.9).

φ2

φ1

α

Figure 4.9: Kinematic relationships at a universal joint.

In case the input and output shaft are not in line with each other (α≠0), the shafts will rotate at different velocities (Table 4.2). Stating for a single universal joint: φ2 = arctan

tan φ1 . cos α

(4:3)

4.5 Components of the steering system

173

Table 4.2: Variables in the universal joint (see also Figure 4.9). Symbol

Description

φ1

Input angle

φ2

Output angle

α

Deflection angle

When two separate universal joints are used in conjunction with another, it is possible to counteract the shaft fluctuation. To achieve this, both joints must have an identical deflection angle. However, in practice, this arrangement is often not possible due to space limitations in the engine compartment. In a simplified manner, it can be assumed that in case of two universal joints the following equation holds: tan φ2 =

cos α2 tan φ1. cos α1

(4:4)

When designing and constructing a steering system, it is necessary to ensure that shaft fluctuations are kept to a minimum. 4.5.2.2 Impact of nonuniformity The nonuniformity of the motion can be used specifically to achieve a variable steering ratio. For instance, this makes it possible to create a larger translation around the center point. This leads to an additional centering. Starting from the center point, the translation will then drop off slightly, but symmetrically, on either side. Consequently, a small increase in steering torque is noticeable leading to more direct steering. 4.5.3 Steering rack The steering rack transfers the rotational motion of the steering shafts to an axial movement of the steering rods. To achieve this, multiple different types of steering rack can be utilized. 4.5.3.1 Rack and pinion The Rack and Pinion mechanism is the most commonly used mechanism in modern motor vehicle steering systems. The pinion hooks into the gears of the rack, making it possible to transfer the rotational motion of the steering shaft into an axial movement of the rack. Figure 4.10 shows the setup of a rack and pinion mechanism. Besides the actual rack and pinion, hydraulic power steering elements are also

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4 Vehicle steering

Steering shaft

Tie rod Rack

Pressure piece Output Figure 4.10: Rack and pinion steering system in a passenger vehicle. In simple rack and pinion gears, it can be assumed that there is a constant ratio between pinion angle and lateral rack displacement according to Fischer, Gscheidle et al. (2013).

present. The torsion rod is located above the pinion, accompanied by the corresponding hydraulic valve. Hydraulic oil flows through this valve to the master cylinder connected to the steering rack. Depending on the rotation of the torsion bar, different hydraulic pressure tubes can be fully or partially opened. 4.5.3.2 Recirculating ball gear Besides the well-established rack and pinion gear, some vehicles are fitted with a steering system using a recirculating ball gear. The basic workings of this type of gear are illustrated in Figure 4.11. The rotational motion of the steering spindle is transferred via the balls located in the housings’ grooves to an axial movement of the ball nut. The teeth between the ball nut and sector shaft in turn translates this into the typical pivoting movement of the pitman arm. When the balls have passed the area of the ball nut, they are recirculated through guiding tubes back in the worm housing.

4.6 Parameters of the steered wheels To the average driver, steering is the only option to influence the lateral dynamics to a desired state. By turning the steered wheels, a side-slip angle α occurs, resulting in a lateral force on the tires (Chapter 2 and 3). These lateral tire forces are the driving mechanism to ensure the vehicle follows the desired curved trajectory.

4.6 Parameters of the steered wheels

Steering worm

Ball guide tubes

175

Steering shaft

Steering nut

Tie rod

Steering lever Figure 4.11: Recirculating ball gear in vehicle steering system according to Fischer, Gscheidle et al. (2013).

4.6.1 Definition of geometric parameters of the wheel In this section the geometric parameters of the wheel and their coherence with forces and torques exerted on the steering system are briefly explained. These parameters are shown in Figure 4.12 and Table 4.3, based on the most commonly used stub-axle steering configuration. During cornering the steered wheel pivots around the steering axis L (Figure 4.12). This line crosses the vehicle’s trajectory at point D. The distance between the center contact point A and point D in the longitudinal direction (side view) is called the trail n. The trail consists of a dynamic part nD and a part nK , which is due to construction (of the suspension). It functions as the lever arm for the lateral force acting on the wheel. When looking at normal cornering situations, the combination of both the lateral force and the trail make up the steering torque (Matschinsky 2007). The distance between point D and the center contact point A in the perpendicular direction to the tire is known as the scrub radius rr . Under braking, the scrub radius provides the relevant torque arm for cornering. With different braking forces on both steered wheels, or during simultaneous braking and cornering, the scrub radius results in a steering torque that can be noticed by the driver. Driving forces that are transmitted to the driven wheel via the steering shafts, as is common in today’s vehicles, produce a torque around the steering axis through the lever arm lσ . This spread offset is also referred to as the disturbance

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Figure 4.12: Visualization of geometric parameters on the steered wheel according to Matschinsky (2007).

Table 4.3: Geometric parameters related to the steered wheel (see also Figure 4.12). Symbol

Description

L

Steering axis

σ

Spread angle between steering axis and vertical Z-axis

γ

Camber angle

τ

Caster angle

rr

Scrub radius

n

Trail

nl

Trail offset

lσ

Spread offset

δ0

Toe-in angle

r

Wheel radius

lever arm, because not only driving forces but also all disturbing forces on the freerolling wheel (e.g., road shocks, friction coefficient changes, etc.) are passed on

4.6 Parameters of the steered wheels

177

over the center of the wheel suspension to the vehicle body. Therefore, these forces result in a torque corresponding to the disturbance lever arm around the spread axis (Matschinsky 2007). The toe-in angle δ0 (not visible in Figure 4.12, but see Chapter 3) denotes the rotation of the wheel opposite to the vehicle’s longitudinal direction when the steering wheel is in the center position. The toe-in angle ensures the desired return of the wheel to a straight-line position and improves straight-line characteristics.

4.6.2 Changes in geometric parameters during cornering Due to the connection between both steered wheels, the kinematic dependencies change while cornering. Thus, it can be very useful to steer the inner and outer wheel separately (see Section 4.4.1). A change in geometric parameters will also lead to a change in all dynamic dependencies, because the lever arms of different forces have been altered. Figure 4.13 shows the change in camber angle of the wheel due to a steering input. Based on the spread angle σ, as well as the caster angle τ, the center point M describes a circular trajectory while cornering. The kinematics of the steered wheels lead to a change in camber during a steering input. This camber change can be utilized to support the vehicle dynamics.

Figure 4.13: Effect of camber changes on the steering angle according to Matschinsky (2007).

During cornering the wheel center M follows a circular trajectory inclined in space. Because the connection from DM to M is fixed, the caster angle γ changes due to the described rolling movement of the wheel around the steering axis. The suspension

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4 Vehicle steering

trail5 n changes similarly due to this rolling movement. It is subject to the trail offset nτ , in addition to the caster angle τ as a function of the steering angle δ. According to Mitschke and Wallentowitz (2014) it holds that nK = n0 + rðtan σ sin δ − ð1 − cos δÞ tan τÞ,

(4:5)

n0 = nK ðδ = 0Þ = nl + r tan τ.

(4:6)

where

The scrub radius can be calculated with rr = rs0 + n0 sin δ

(4:7)

rro = rr ðδ = 0Þ = lσ − rðtan σ + γÞ

(4:8)

where

holds. While turning the wheel as described, the wheel itself is raised slightly. This leads to a change in kinematic variables of the wheel. The resulting vertical movement causes an additional steering work since the vehicle front is moved vertically against the gravitation (see drilling torque). For this movement in vertical direction it holds that ΔzðδÞ = rr0 ½ðcos δ − 1Þ tan τ + sin δ tan σ − n0 ½sin δ tan τ − ðcos δ − 1Þ tan τ.

(4:9)

In addition, the camber angle of the steered wheel changes as follows: γðδÞ = γ0 − δ tan τ.

(4:10)

When looking at smaller steering angles, the kinematic changes of the wheel and the corresponding changes in lever arms usually have very limited effects on the working steering torques/ratios. For larger steering angles, often seen at low speeds and parking maneuvers they can have considerable effects. Figure 4.14 shows an example of the variation in kinematic parameters as a function of the steering angle.

5 A distinction must be made between suspension and pneumatic trail. The suspension trail results from the kinematics of the wheel suspension. The pneumatic trail describes the shift of center contact point relative to the point where the steering axis crosses the center’s points horizontal plane. Depending on the working forces, see Chapter 3.

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4.7 Steering transmission

Nr 1 2 3

σ 5° 12° 12°

τ rs n0 3° 50 16 3° 0 16 9° 15 5

4 12° 9° 0 R = 300, 𝛾0 = 0

3,4 2

5 1

2

40 30 20 n/mm 10 0 –10 –20 –30 –40

3,4 1

8 7 6 5 4 3 2 1 0 –1 –2 –3

𝛾/°

4 3 2 1 0 lσ/mm –1 –2 –3 –4

1

2 3 4 –40 –30 –20 –10 0

10 20 30 40

󰛿/° Figure 4.14: Effects of changes in caster angle and wheel load lever arm on the steering angle (Matschinsky 2007).

4.7 Steering transmission The angular rotation of the steering wheel is translated to a pivoting motion of the steered wheels through the steering system. This is achieved by the steering kinematics consisting of the steering column and steering shafts, as well as the steering rack and steering linkages (see Section 4.5). Of critical importance for the driver in this case is the steering ratio between the steering wheel and steering angle of the steered wheels (Table 4.4): iL, i + iL, o , 2 δH iL = . δR

iL =

(4:11) (4:12)

The steering ratio describes the dependency between the occurring steering torque and the hand torque on the steering wheel, linearly related to the steering wheel angle and the angle of the wheels. Due to the previously shown dependencies on the wheel kinematics, the steering ratio is not constant. Instead, it is dependent on the wheel angle and therefore different for the inner and outer wheel.

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4 Vehicle steering

Table 4.4: Steering angle parameters. Symbols

Description

δH

Steering wheel angle

δR

Mean angle of the steered wheels

iL

Mean steering ratio

iL, i , iL, o

Steering ratio of inner and outer wheel

sZS

Rack stroke

iLG

Ratio of the steering rack (rad/mm)

The steering ratio consists of three components: – ratio of the steering gears, – ratio of the steering linkage, and – nonuniformity of the universal joints. Because the ratios of the steering gears (rack) and the nonuniformity of the universal joints are equal for both steered wheels, the (desirable) difference in total steering ratios between the inner and outer wheel can only be explained as being due to the steering linkages (see Section 4.4). In case the desired maximum steering wheel angle is predetermined and the corresponding mechanical angle of attack of the steered wheels is known, it is possible to determine the required steering ratio. The maximum angle of attack of the steered front wheels is normally between 45 and 50 . With these angles it is typically possible to achieve a turning circle diameter of approximately 8.5 − 13 m (depending on the size of the vehicle). Commonly seen steering ratios tend to be in the range of 13 − 20, meaning that the maximum angle of the steered wheels can be achieved at 1.5 − 2.5 full rotations of the steering wheel. The steering gear can be altered to ensure that the desired ratio is realized with the given steering kinematics. In addition, a compromise needs to be made to maintain acceptable levels of comfort and hand forces during parking maneuvers. The choice of a suitable steering ratio is thus directly associated with the design of the power steering system (see Section 4.10). The introduction of power steering has made it possible to achieve relatively direct steering and comfortable hand torques at the same time. Concepts with variable steering ratios seek to solve these conflicts of interest. Different steering ratios can be realized depending on the steering wheel angle (for instance using Wandfluh steering, steering with progressive rack, or the combined use of the steering linkage and nonuniformities of the universal joints). Active systems also exist where the driver can freely select a desired ratio depending on the

4.7 Steering transmission

181

driving conditions (see Section 4.12.1). In dynamic driving situations, the ratios may also vary due to the elasticity of the steering components and bearings.

4.7.1 Ratio of the steering gear The rack and pinion steering mechanism is currently the standard in passenger motor vehicles. Therefore, in this section the focus will be completely on this type of steering gear. For the rack and pinion mechanism, the steering ratio as a function of the steering wheel angle (or pinion rotation) can be defined as iLG =

dδH , dsZS

(4:13)

As elaborated upon in Section 4.5.3, in some mechanisms of this type the ratio can be dependent on the absolute position of the rack. Usually, however, the ratio is constant over the entire range of steering wheel angles.

4.7.2 Ratio of the steering linkages Based on the selected kinematics of the steering linkages, different leverage ratios can be present depending on the actual steering angle. This results in a steering ratio of the linkages that changes with respect to the steering wheel angle. A correct choice of selected kinematics can be made in such a way as to positively influence the overall steering ratio. In addition, unequal steering angles for the inner and outer wheel can be achieved (see Section 4.4). For the rack and pinion steering mechanism, the steering linkage ratio for the inner and outer wheels can be specified as the ratio of the movement of the rack relative to the rotation of the wheel: iLZ i, o =

dsZS . dδi, o

(4:14)

The considerations in this section assume planar kinematics for the sake of simplicity. If a three-dimensional kinematic model is to be derived for the steering system, the change in leverage ratios due to vertical compression and extension of the wheels must also be considered. As touched upon earlier, the steering angle can be influenced positively by a specific adjustment of the steering kinematics during compression – as to support the dynamic driving situation. At this point, the variable dynamic ratio is not discussed in more detail and the reader is referred to other literature sources (Matschinsky 2007) and (Harrer and Pfeffer 2017).

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When considering the steering linkages and their respective leverage ratios, it must be taken into account that the components of the steering linkages (compared to the rack) possess considerable elasticity. This elasticity allows for movement in the relevant pivotal points, even without the rack itself moving. This can still result in a change of the steering angle. The steering ratio therefore also depends on the effective forces (and thus on the dynamic driving situation). Depending on the load situation of the wheel, relevant kinematic variables of the suspension (steering linkage) may change (see Chapter 3). Figure 4.15 shows a simplified visualization of this relationship for the inner steered wheel. The movement of the rack is transferred through the tie rods to the wheel carrier. This in turn ensures the desired turning of the wheel, in accordance with the relevant leverage ratios. For the tie rod a spring stiffness is assumed, which approximates the elasticity of the entire steering linkage. As an alternative to the rack and pinion mechanism, Figure 4.15 also shows a control stalk (dashed line). This translates the rotational movement (angle δKG of the ball screw) around point D in the displacement of the tie rod (Table 4.5).

Figure 4.15: Kinematics (elastokinematics) of the steering linkages for the inner steered wheel as described by Matschinsky (2007).

Due to the elastic nature of the system, the steering ratio can only be specified kinematically when looking at a statically loaded situation (constant tire forces). A special case of static load is the unloaded situation (free steering). In this case the elastic properties of the system can be fully neglected, meaning that a kinematic approach suffices. To determine the steering linkage ratio, the length of the tie rod lSt is assumed to be fixed (rigid body) – contrasting Figure 4.15. Any potential compliance in the wheel itself is also neglected further. This leads to a simplified depiction, shown in Figure 4.16. For further derivation of these concepts, only the left wheel is considered.

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183

Table 4.5: Steering rigidity parameters (see also Figure 4.15). Symbol

Description

βU , βT

Transmission angle

lSt

Tie rod length

a

Length overlap of knuckle arm and tie rod

lSH

Length of knuckle arm

e

Effective lever arm of the tie rod related to the wheel rotation

cSt

Tie rod stiffness

cδ

Torsion stiffness of the wheel around the steering axis

Figure 4.16: Planar kinematics of the steering linkages for the left front wheel, without taking into account elasticity.

The connecting points of the steering linkages form the triangle EUT in Figure 4.16. The sides EU and UT of the triangle are identified as knuckle arm length lSH and tie rod length lSt and are both constant. Thus, with the kinematic constraints, the wheel steering angle δ can be determined based on the rack displacement sZS . To describe the kinematic relationships, the origin of the coordinate system is placed in point E.

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4 Vehicle steering

Point T (connection to the rack) is only free to move along the y-axis in the coordinate system depicted in Figure 4.16. The point is thus described by the rack position and the constant value h (distance rack to steering axis). Point E is limited to planar movement. The knuckle arm and vehicle-fixed y-axis enclose the variable wheel steering angle δ. This angle is composed of the toe-in angle δ0 and an angle that results from the axial movement of the rack, symbolized as δZS . The toe-in angle is assumed negative. The wheel steer angle then becomes: δ = δ0 + δZS .

(4:15)

Since the toe-in angle is fixed, only the derivation of the above-mentioned component due related to the rack displacement will be discussed below. Applying the cosine rule for the shown steering triangle results in the following: l2St = l2SH + l2 − 2lSH l cos ζ .

(4:16)

The angle ζ can also be written in accordance with the relationships shown in Figure 4.16: ζ=

π − ðα0 + δZS Þ − θ, 2

(4:17)

where the angle α0 describes the constant angle between the knuckle arm and the x-axis in the initial state. The angle θ as seen in eq. (4.17) can similarly be expressed in the following kinematic relationship: θ = arctan

h . yZS

(4:18)

Distance h is constant and denotes the distance in x-direction between the rack and the wheel carrier (point E). The parameter yZS can vary due to movements of the steering rack. It defines the position of the rack and is composed of a constant part yZS, 0 , which describes the position of the rack in center position, and the axial displacement of the rack sZS : yZS = yZS, 0 + sZS . The length l of the steering triangle from eq. (4.15) can be determined by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l = y2ZS + h2 = ðyZS, 0 + sZS Þ2 + h2 .

(4:19)

(4:20)

Inserting the relationships from (4.18) and (4.20) into (4.16) and algebraically reordering the equation give the required relationship:

δZS = −

4.7 Steering transmission

185

π h lSt 2 − lSH 2 − ðyZS, 0 + sZS Þ2 − h2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi + arccos + α0 + arctan 2 yZS, 0 + sZS 2lSH ðyZS, 0 + sZS Þ2 + h2

(4:21)

between rack displacement and steering angle. With these relationships now specified, it is possible to obtain typical steering linkage ratios for the steered wheels. These ratios vary depending on the steering kinematics and current position of the steering rack (steering wheel position; Figure 4.17). In addition, it shows the influence of lateral forces acting on the wheel itself.

3.0 Rigid body kinematics, steering angle Rigid body kinematics, steering ratio Elasto kinematics, steering angle (1 kN) Elasto kinematics, steering ratio (1 kN)

15

2.5

Steering ratio °/mm

Steering angle/°

30

2.0 0

1.5

–15

–30 –20

–10

0

1.0 10 20 Rack and pinion displacement/ mm

Figure 4.17: Steering linkage ratios with dependency on the rack position (only the parameters applying to the left wheel are shown; forces shown act in the lateral direction).

To determine the steering angle δ during realistic dynamic loading, a finite-element model can be used. This type of modeling allows for a detailed approach concerning the kinematic parameters, including the modeling of dynamically loaded situations. Since the elasticity of the various components in the wheel suspension can potentially have a significant influence on the relevant kinematic parameters, current research activities are focused on making these elasticity-related effects predictable even without the use of a FE model. This knowledge could be utilized during vehicle operation in real time; for instance, to adjust the steering feel depending on the road and driving conditions (Kracht, Schramm et al. 2015).

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4 Vehicle steering

4.8 Steering torques for conventional steering systems In case the wheel travel (wheel vertical motion) of the vehicle during cornering is neglected, the resultant steering torque is exclusively due to the longitudinal tire forces, lateral tire forces, and self-aligning torque. As mentioned earlier, the acting lever arms usually differ depending on vehicle braking or acceleration. Therefore, this section will clarify the influence of both situations on the calculation of the steering torque. For the steering torque in case of acceleration it holds (Mitschke and Wallentowitz 2014),   (4:22) MH = ðFx, i iL, i rσi − Fx, o iL, o rσi Þ + Fy, i iL, i ni + Fy, o iL, o no + ðMz, i iL, i + Mz, o iL, o Þ, where the index i stands for inner and o for outer wheel. In the case of vehicle braking, the lever arms related to the longitudinal tire forces change, resulting in   (4:23) MH = ðFx, i iL, i rsi − Fx, o iL, o rsi Þ + Fy, i iL, i ni + Fy, o iL, o no + ðMz, i iL, i + Mz, o iL, o Þ. Ignoring the wheel travel when calculating the steering wheel torques is acceptable when considering normal driving situations. Normally, only slight steering wheel movements and, related to these, small vertical movements of the vehicle occur. Therefore, the torque around the wheels’ vertical axis can often be neglected as well. It should also be noted that the hand torques on the steering wheel calculated here are only suited for quasistatic steering situations, since the individual masses of the different components in the steering system have not been considered. 4.8.1 Steering rack forces The forces acting on the tire are transmitted to the steering system, in accordance with the steering kinematics. Decisive in many considerations regarding the steering system (for instance steering assistance) is the steering rack force, as both the steering wheel forces exerted by the driver, as well as any potential power steering forces act here. Rack forces in modern day vehicles can reach values in excess of 15kN, especially during parking maneuvers (see also Figure 4.28). During normal driving conditions, the self-aligning torques acting on the tires (see Chapter 2) are transferred through the knuckle arm and tie rod to the steering rack. Because the lever arms can vary depending on the position of the wheels, the currently acting lever arm must be known to determine the rack force. 4.8.2 Drilling torque While steering during slow driving, for instance, when parking, but especially when the vehicle is stationary, extremely high steering forces occur. These can be

4.8 Steering torques for conventional steering systems

187

explained by the so-called drilling torque. At very low speeds and simultaneous rotation of the wheels around the steering axis (in a simplified case the vertical z-axis of the wheel), the sideways forces acting on the wheel are of far less importance. This is because the tire is being rotated on its contact patch with the road surface, leading to high resistances against rotation due to the absence of a rolling motion of the wheel. The friction force between the road surface and tire’s contact patch, with corresponding lever arm from the point of engagement to the axis of rotation, create the drilling torque. For an ideal rectangular contact patch geometry and after integration over all engagements points, the drilling torque is defined by Rill (1994) as (see Table 4.6) Tdrill = 121 b2patch

d Fx, patch ωz, wheel d sx rwheel ωy, wheel

j

j

d Fx, patch d sx |fflfflfflfflffl{zfflfflfflffl ffl}

= 121 bpatch

longitudinal stiffness

bpatch ωz, wheel . rwheel jω y, wheel j

ð4:24Þ

|fflfflfflfflffl{zfflfflfflfflffl} drilling slip

Table 4.6: Physical parameters of the wheel. Symbol

Description

Tdrill

Drilling torque

bpatch

Width of contact patch

Fx, patch

Force acting on the contact patch

sx

Longitudinal slip

rwheel

Wheel radius

ωz, wheel

Angular velocity around the wheel z-axis

ωy, wheel

Angular velocity around the wheel y-axis

Related to the longitudinal stiffness, the drilling torque corresponding to the above equation is coupled to the actual tire–road contact. This points out that the drilling torque only becomes significant during low speed cornering, as the aligning slip becomes large. At very low speeds (very low angular velocities ωy, Rad Þ, the drilling torque takes on implausibly large values rather quickly. Therefore, the drilling torque is limited in accordance with the maximum possible force acting on the contact patch (Rill 1994). The maximum drilling torque is reached when the entire contact patch area slides over the road surface. Integrating over the entire tire contact patch then yields (see Table 4.7)

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TBohr, max =

1 bpatch 4

Fx, slide |fflffl{zfflffl} circumferential force in the slip aera

(4:25)

Table 4.7: Forces and torques acting on contact patch. Symbol

Description

Tdrill, max

Maximum drilling torque

Fx, slide

Friction force for slip conditions

Altogether, according to Rill (1994) the drilling torque can be defined as follows: ( Tdrill with ð4.24Þ for jTdrill j ≤ Tdrill, max . (4:26) Tdrill = Tdrill, max otherwise

4.8.3 Drilling torque during stationary steering Real measurements of steering rack forces during stationary steering show that this simplified calculation of the drilling torque does not include all significant effects. Stationary steering, however, can be of decisive importance as it relates to the effort required by the driver during parking maneuvers. During stationary steering, the tires will deform elastically before they engage in a slipping motion between the tire contact patch and road surface. This effect can be included by adjusting the drilling torque model to account for the torsion stiffness of the tire contact patch (Hesse 2011). Figure 4.18 shows the construction of a model that corresponds to the calculation of the drilling torque. When the assumption is made that no rolling motion of the wheel occurs during stationary steering (braked steered wheels), the tires will initially deform elastically until the point that slippage occurs between individual points on the tire contact patch and the road surface. This effect is shown in Figure 4.18 in a simplified manner by considering a torsion spring stiffness cpatch . The tires move inside the plane of the contact patch, until the maximum rotation without slippage is reached. The resultant drilling torque increases in accordance with the stiffness of the contact patch points. The maximum drilling torque is reached when all individual points of the contact patch are exhibiting slip (see Table 4.8): (

cpatch δpatch for
δpatch
≤ δpatch, max . (4:27) Tdrill = Tdrill, max otherwise

4.8 Steering torques for conventional steering systems

189

Σ

Figure 4.18: Drilling torque during stationary steering. Wheel rotation purely around the vertical axis (Hesse 2011).

Table 4.8: Kinematics of the contact patch (see also Figure 4.18). Symbol

Description

cpatch

Torsion stiffness of the tires

δpatch

Rotation of the contact patch with respect to the wheel

δpatch, max

Maximum rotation of the contact patch with respect to the wheel

When designing a steering system, the steering rack force is often used as a criterion. To do this, the drilling torque acting on the wheel must be converted to the effective steering rack force, which can be done using the steering kinematics. Depending on the position of the wheels, this results in an effective lever arm leff between steering rack and wheel. This parameter makes it possible to convert the steering rack force to the steering torque acting on the wheel. When describing a technical model of the vehicle steering system, methods such as those explained by Schramm (2014) could be applied. These methods continuously solve the kinematics through computation. However, it often suffices to use simpler empirical maps.

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4.8.4 Steering rack forces for large steering angles With larger steering wheel angles, it can often be observed that the front of the vehicle moves up. Due to the axle kinematics of the vehicle a vertical motion is commonly seen when cornering. This motion, from a vehicle steering perspective, is actually quite interesting. When the front of the vehicle is raised during cornering, it means that mechanical work must have been done to bring about this vertical displacement. Conversely, this means that the power steering (and thus the rack force) inevitably increases. This effect is clearly more significant in larger compared to smaller vehicles. This can logically be explained due to the fact that it requires more work to raise a heavier vehicle than is required to raise a lighter vehicle. In most vehicles this additional vertical motion results in a clear increase in rack force, especially with larger steering angles. However, if the front of the vehicle drops shortly before the final steering wheel position is reached, it can also cause the hand torque on the steering wheel to be reversed abruptly. For the calculation of the rack force, the relationship between rack displacement and the vertical motion of the vehicle is of decisive importance. This relationship can be derived, analogous to the effective lever arm, from the axle kinematics. The vertical motion of the vehicle can be expressed as a function of the rack displacement. The increase in rack force during cornering then behaves as (see Table 4.9) FZS, heave =

d zVA FVA, z . d qZS

(4:28)

Table 4.9: Parameters of the steering rack. Symbol

Description

FZS, heave

Steering rack force due to the vertical motion of the vehicle

zVA

Vertical motion on the front axle

qZS

Rack displacement

FVA, z

Vehicle normal force on the front axle

4.8.5 Steering rack force during parking The steering rack force during parking (stationary steering) is made up of both contributions due to the drilling torque and vertical motion of the vehicle: FZS = FZS, drill + FZS, heave .

(4:29)

4.9 Simplified model of rack and pinion steering

191

FZS

This model for steering rack force can be used to calculate the rack force during stationary steering. When comparing results from this model and real measured rack forces, it shows they match extremely well (Figure 4.19).

Measurement Simulation –400 –300 –200 –100

0

100

200

300

400

δL |° Figure 4.19: Steering rack force during stationary steering (Hesse 2011).

4.9 Simplified model of rack and pinion steering Figure 4.20 shows a rather simplified model of a rack and pinion steering mechanism, as can be seen in similar form in (Pfeffer and Harrer 2011) or (Bootz 2004). This mechanism consists, as described before, of the main components: – steering wheel with steering column (steering shafts), – steering gear as well as steering rack, and – steering linkages (tie rod and knuckle arm) and wheels. Ultimately, the wheel carrier and thus the wheel can be rotated via the knuckle arm, as explained in the preceding sections. When modeling the steering system, it is also advisable to include elasticity in the steering column. This serves as a model for the torsion bar that measures the driver’s hand torque, which is essential for the power steering assistance (see Section 4.10). The model proposed in this section, which is based on the rotation of the torsion bar, can be combined with the model for a power steering system. This would then act as resultant force on the steering rack or as a resultant torque on the steering column.

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4 Vehicle steering

,

Figure 4.20: Model of a rack and pinion steering mechanism as described by Bootz (2004).

As is the case in a real steering system as described in Section 4.7.2, the steering linkages show elastic properties, similar to those of the steering column. Therefore, both of these properties will be included in the model described in this section. This proposed model describes all relationship based on the front right wheel. If this model is coupled to a bicycle model, another subsystem is added, consisting of the left front wheel and steering linkage, which in turn is connected to the rack via an elastic component. The resulting force is then transferred through the rack. The rack and pinion steering mechanism consists of three main components, all connected through elastic elements. This elasticity depicts the deformation of the system under loading. In this case, especially when power steering is integrated into the model, the rotation of the steering column relative to that of the pinion gear plays a crucial role. The torsion bar measures the drivers’ hand torque, which serves as input to the power steering assistance. The kinematic descriptions of the individual subsegments of the steering system can be found in Sections 4.6 and 4.7. The aim of these sections is to derive simplified equations of motion for the steering system. To do this, the steering wheel is modeled as a separate subsystem, and the steered wheel is modeled as another separate subsystem. The kinematics of the steering linkages are limited only to inplane motion. The elasticities ensure a kinematic decoupling of the main components of the steering model. The subsystems can move independent of one another and are

4.9 Simplified model of rack and pinion steering

193

solely linked through their resulting forces. This results in a relatively easy multibody model that utilizes the steering wheel as input. Depending on the desired approach, either the steering wheel torque or steering wheel angle could be chosen as the model input. The following equations assume that the driver steers at a constant angle and, in response, receives a steering torque as feedback. To a large extent, this approach corresponds to observations from real drivers. Therefore, the steering wheel angle is selected as system input. On the side of the wheel, the self-aligning torque (which results from the tire forces; see Chapter 2) is typically assigned as system input. As described earlier, the support by the power steering assistance could be chosen as additional system input. All relevant parameters of the steering model could be chosen as system output. Especially of interest are the steering wheel torque, as it provides feedback to the driver, as well as the wheel angle, which in turn could be used as input to additional tire or vehicle models. Figure 4.21 shows a free body diagram of this simplified rack and pinion steering model. Three decoupled kinematic subsystems are visible.

Steering wheel 󰛿H MH

󰛿H

dT

cT

Wheel

󰛿R 󰛿R

MS

FRZ JS

FRZ

FZS

FSL

FR

sZS

FZS

󰛿v,l

mZS Rack Figure 4.21: Free body diagram of rack and pinion steering system.

According to the elasticities in the system, three separate kinematic regions can be identified in the proposed steering system model. The free-body diagram shows this useful division of the steering system. The equations of motion can be derived with relative ease for each separate subsystem. Without counteracting forces, rotating the steering wheel results in a

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rotation of the pinion. If the elasticity in the steering column is considered, the motion of the steering wheel and column is given by ΘLS €δH = MH − McLS − MdLS ,

(4:30)

where ΘLS is the moment of inertia of the upper steering column and the steering wheel. This segment is decoupled from the pinion through the torsion bar with stiffness cLS and damping dLS . The described relationship in this model can be used to calculate the resulting hand torque, since, as described, the steering wheel angle (and thus also its temporal derivative) is interpreted as a system input. With this approach, the pinion torque corresponds to the torsion spring torque (torsion bar, steering column elasticity), and results from the rotation of the pinion δR , the current position of the steering wheel δH , and their temporal derivatives (see Table 4.10): McLS = ðδH − δR ÞcLS ,  MdLS = δ_ H − δ_ R dLS .

(4:31) (4:32)

The rack displacement sZS is related to the angular rotation of the pinion δR directly through the pinion radius rR sZS = δR rR .

(4:33)

When using this approach, the steering rack must be modeled as a dynamic mass element. A relatively simple solution is to model the rack as a so-called one-mass oscillator. In this case the displacement of the rack can be described as mZ €sZS =

McLS MdLS + + FSL − FR − FZS. rR rR

(4:34)

The forces acting on the rack are, in addition to the already described forces on the pinion, the assisting force of the power steering system FHL (see Section 4.10), a counteracting friction force FD , and the rack force FZl, r , which is transmitted by the tie rods on both sides. The force transmitted from the tie rods to the rack depends on the self-aligning torque on the tires and the kinematic relationships of the steering linkage (see Section 4.7.2). Additionally, it depends on the inertia of the wheel (including steering linkage) relative to the steering axis. At this point, more elaborate modeling techniques are omitted and the reader is referred to literature, such as Pfeffer and Harrer (2011). It often suffices, especially when dealing with slow steering inputs, to model the steering linkages in a purely kinematic manner. In this way the self-aligning torque on the wheel can be converted directly to a force on the steering rack.

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Table 4.10: Parameters to describe the steering rack (see also Figure 4.21). Symbol

Description

δH

Steering wheel angle

δR

Pinion angle

cLS

Torsion bar stiffness

dLS

Torsion bar damping

sZS

Rack displacement

rR

Pinion radius

ΘLS

Moment of inertia of the steering column

MH

Hand torque of the driver

MdLS

Damping in torsion bar of the steering column

McLS

Torque due to rotation of the torsion bar of the steering column

FZS

Rack force due to the tire forces. Sum of forces transferred by left and right steering linkages

FR

Friction forces on the steering rack

FSL

Supporting forces from power steering assistance to the steering rack

4.10 Power steering assistance systems Steering assistance, often referred to as power steering, becomes a necessity when the hand forces required by the driver to comfortably control the vehicle become too large. An increase in weight of the vehicle often plays a crucial contribution to the steering force needed to steer the vehicle. The power steering assistance has a supportive role in controlling the vehicle by providing additional force to the steering mechanism. Because of this, even heavy vehicles can be controlled with relative ease, without sacrificing the preferable steering ratio. The first implementations of hydraulic power steering (HPS) were brought to the market halfway through the twentieth century. These systems were based on hydraulic pumps driven by the internal combustion engine of the vehicle. In the end of the 1990s these were replaced by electrohydraulic pumps for the first time. Using electrohydraulic pumps for the power steering system had a positive effect on the fuel efficiency of the vehicle, alongside considerable advantages in terms of packaging (Reimann, Brenner et al. 2012). Furthermore, since the beginning of the 1990s, electromechanical power steering (EPS) systems were occasionally used as well. Due to the relatively low steering assistance that was initially possible to generate, it took some time before EPS systems became the de facto standard in steering assistance (Pfeffer and Harrer 2011).

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4.10.1 Hydraulic power steering Hydraulic power steering utilizes a belt connected to the internal combustion engine of the vehicle to drive the hydraulic pump. A core component of this power steering system is the steering valve, located on the steering column. Depending on the driver’s hand torque, it is twisted slightly, opening or closing parts of the connected hydraulic tube. The pressurized hydraulic fluid can now flow, according to the driver’s hand torque, toward the double-acting hydraulic cylinder (servo piston) on the rack to generate the assistance force required by the driver (Figures 4.22 and 4.23).

Steering wheel

Return pipe

Valve input shaft Servo valve

Control edge

Torsion spring

Pressure pipe

Valve sleeve Pinion Load

Pump Rack

Cylinder

Figure 4.22: Basic construction of the hydraulic power steering system (Lunkeit 2014).

In this type of power steering system, the servo pump is active continuously as long as the engine is running. Usually, the classic power steering pump used is a rotary vane pump. The pump needs to guarantee a sufficient amount of hydraulic pressure in the system to ensure the steering assistance delivers satisfactory additional forces on the steering rack, even when the engine is running at low rpm (less than 1,000 U=min), for instance during slow moving traffic (Reimann, Brenner et al. 2012). Despite improvements on the hydraulic power steering system, such as the unpressurized pumping during steering wheel center position, or of modular steering valves to adjust the support force curve during operation, this technique has the disadvantage that the pump requires constant energy.

4.10 Power steering assistance systems

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120 Pressure/bar

100 80 60 40 20 0 -8

-6

-4

-2

0

2

4

6

8

Operating torque/Nm Figure 4.23: Hydraulic valve lines of hydraulic power steering (Heißing and Ersoy 2011).

4.10.2 Electrohydraulic power steering The electrohydraulic power steering (EHPS) system results from further development of the classical, purely hydraulic variant. The engine-driven pump was replaced by an electromechanical pump. The basic construction of the hydraulic system is depicted in Figure 4.24.

Control system

Sensor cable Pressure pipe Return pipe Power pack with ecu

to Current supply Pinion

Rack

Cylinder

Figure 4.24: Basic construction of the electrohydraulic power steering system.

However, the EHPS system has two main advantages over the purely hydraulic variant. The decoupling of the pump and internal combustion engine opens up more

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freedom for the “packaging” or positioning inside the engine bay compartment. The system can be designed and tested in modular fashion, adding to the ease of implementation in the vehicle. More important, however, is the fact that the pump can be regulated to fit demand. This leads to an improvement in efficiency as the pump only requires energy to pump oil if the system is in operation. Secondly, different support characteristics are possible depending on the vehicle’s speed. In the control unit, a characteristic curve can be stored that describes the magnitude of supportive steering forces as a function of the vehicle speed. This way, even in the case of low speed and exerted hand torque, the maximum amount of steering assistance can be offered to the driver, leading to a more comfortable driving experience. Conversely, during high speed dynamic driving, the steering assistance can be decreased to achieve a more precise and direct steering feel (Reimann, Brenner et al. 2012). The disadvantages of EPHS are a higher complexity due to the use of mechanical, hydraulic, and electrical parts as well as higher costs and weight.

4.10.3 Electromechanical power steering The EPS system differs from the classic hydraulic and electrohydraulic systems due to its electric actuator, directly providing supportive forces to the steering system (Figure 4.25).

Steering column

Torque sensor BLDC Motor ECU Ball screw drive

Rack

Torsion bar

Belt pulley

Pinion

Figure 4.25: Basic construction of the electromechanical power steering system (Lunkeit 2014).

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Hydraulic transmission elements are now completely obsolete. This brings significant advantages for the production of vehicles, since the sometimes complex assembly of the hydraulic system is eliminated from the manufacturing process. The EPS is characterized also in particular by the fact that the actuator only needs power when actively steering. Due to this power-on-demand system, energy can be saved in comparison to the classic hydraulic system. The electromechanical actuation of the steering assistance system has also opened up the possibility for different assistance systems, such as the active lane keeping, through the so-called four-quadrant operation (Pfeffer and Harrer 2011). In the recent years, the EPS has replaced traditional hydraulic or EHPS in most vehicles, due to the aforementioned advantages. While the EPS systems could initially only be used in small- and medium-sized cars, as the systems could not provide the supportive forces needed in heavier topof-the-range vehicles, continuous development has led to the EPS system now being capable of serving the full range of performance necessary for application in almost all vehicles. Therefore, EPS systems have become the standard for steering assistance in modern day motor vehicles (Figure 4.26 and Figure 4.27).

Steering gear Input shaft Steering torque sensor

Ball screw drive

Steering pinion Motor Hollow shaft

ECU

Rack

Figure 4.26: Electromechanical power steering © Audi AG.

Depending on the expected steering forces, different EPS variants can be fitted to different types of vehicles. The required supportive forces are clearly lower in lighter vehicles than in, for instance, an SUV (Figure 4.28). To be able to guarantee a comfortable steering feel even with heavier upper-class vehicles or SUVs, one has to resort to the relatively high-performance EPS variants. Figure 4.28 shows this relation.

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Parameters for determining the supportive force and additional steering assistance for additional functions (e.g., lane keeping)

Force flow Information flow

MEPS Electro motor

ECU

Steering gear MH

FZS

Steering mechanism

Vehicle

MH

Hand torque sensor

Figure 4.27: Block diagram of an EPS system (ZF_Lenksysteme 2014).

Performance/W

Middle class Upper class SUV Microcars Compact class Upper middle class Luxury class 1,000 °/s

360

800 EPSapa 600 EPSdp 100°/s d still at stan speed g in r e Ste

400 EPSc

200 3

4

5

6

7

8

9

10

11

12

13

14

15

16

Rack force/kN Figure 4.28: Guidelines for rack force and mechanical performance for different vehicle classes according to ZF_Lenksysteme (2014).

The following section provides a quick overview of different EPS variants and their way of functioning. 4.10.3.1 Design variants for electromechanical steering assistance systems Various designs of EPS systems are common in vehicles nowadays (Runge, Gaedke et al. 2010, Pfeffer and Harrer 2011, Reimann, Brenner et al. 2012). The design variants are categorized according to the location of the electromechanical actuator

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201

and its connection to the steering system. The most commonly used EPS variants are as follows: – EPSc on the steering column (column type), – EPS on the pinion gear (pinion type ), – EPSdp of double-pinion type (dual pinion type ), – EPSapa with axis-parallel arrangement (APA type), and – EPS directly on the steering rack (rack (concentric) type). In the following section these different variants will be briefly explained. 4.10.3.2 EPS column type Figures 4.29 and 4.30 show exemplary the EPS connected to the steering column.

Figure 4.29: Schematic assembly of EPS system. © Porsche AG.

In this type, the supportive forces of the electromechanical converter are transferred directly to the steering column. Between the motor and the steering column, a reduction gear is located, usually in the form of a worm gear. An advantage of connecting the motor directly to the steering column is that this can be done in the vehicles’ interior, where the effects of dirt and weather-related corrosion are slightly less than when located in the front compartment. The lack of acoustic damping of the system, however, leads to an increased sensitivity to noise emission. The design of the electric steering assistance connected the steering column is particularly suitable for low supportive forces, since the connection to the steering linkages do not possess high rigidity.

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Steering wheel gearing

ECU Drive pinion (Concealed) Tie rod Intermediate steering shaft

Torque sensor

Steering shaft connection Helical gears (Concealed)

Pressure piece (Concealed)

Pleated bellows Rack (Concealed) Housing

Figure 4.30: Schematic assembly of EPS column type system. Courtesy of Robert Bosch Automotive Steering GmbH.

4.10.3.3 EPS pinion type The variant of EPS where the electric motor is located close to or directly linked to the pinion gear is known as pinion type. Consequently, a much more compact construction can be achieved in comparison to the column type. In addition, the connection of the motor directly onto the pinion gear offers much more rigidity, allowing for significantly higher supportive forces. 4.10.3.4 EPS dual pinion type To further increase the allowable supportive forces an EPS system can provide, the electric motor can be connected to the steering rack with a second, independently operated pinion leading to the EPS dual pinion typevariant (Figure 4.31). Both pinions can now be optimized with regard to comfort, performance, and durability, independent of one another (Reimann, Brenner et al. 2012).

4.10 Power steering assistance systems

Rack (Concealed)

Pressure piece (Concealed)

203

Steering shaft connection Sensor cable Torque sensor Housing

Drive pinion (Concealed) Tie rod Steering pinion (Concealed)

Pleated bellows

ECU Helical gears Electromotor Overload protection device

Drive pinion Fixed bearing

Screw gear Worm gear

Spring-damper element Housing Figure 4.31: Schematic assembly of EPS double-pinion type system. Courtesy of Robert Bosch Automotive Steering GmbH.

4.10.3.5 EPS APA type The EPS in an APA converts the rotary motion of the electric motor into the desired axial displacement of the steering rack, by means of a ball screw gear. The ball screw gear has excellent properties regarding force transmission and precision (lack backlash in the gears), making it extremely suitable for use in combination with high-performance electric motors (Figures 4.32 and 4.33). The ball nut is driven by a toothed belt, where the electric motor is positioned parallel to the steering rack. When the gear ratios are properly designed, and a suitable electric motor is fitted, this type of EPS can also meet the requirements (especially for required rack force) to be used in upper class vehicles. 4.10.3.6 EPS rack concentric The EPS rack concentric type distinguishes itself from the EPS APA type, through direct transmission of the rotary motion of the electric motor to the ball screw gear

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Steering shaft connection Housing Torque sensor Steering pinion Rack Sensor cable Servo gear

Pressure piece (Concealed)

Pleated bellows ECU

Tie rod

Electromotor

Figure 4.32: Schematic assembly of EPS APA type system. Courtesy of Robert Bosch Automotive Steering GmbH.

Ball chain

Return pipe

Toothed belt

Pulley,small Pulley Ball nut

Rack

Pulley,small Figure 4.33: Schematic assembly of EPS APA type system. Construction of servo gear. Courtesy of Robert Bosch Automotive Steering GmbH.

without additional gearing mechanisms. To achieve this, the electric motor is constructed as a hollow shaft. The steering rack with ball screw gear is located inside the shaft. This direct connection to the steering rack allows for an especially precise

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205

and dynamic force transmission. However, since there are no additional gears as is the case with the EPS APA type, the motor used in the EPS concentric rack type must deliver a sufficiently high torque, even in lower rpm ranges (Reimann, Brenner et al. 2012). 4.10.3.7 Performance increase The higher supportive forces required in heavier upper-class vehicles and SUVs have led to EPS systems initially only being fitted to small- and medium-sized cars. Due to the increase in performance of the available steering systems, they are now being used in all classes of passenger vehicles. The required mechanical power for the vehicle steering can vary greatly depending on the required rack force and the steering speeds. While the rack force is significantly influenced by the vehicle weight and driving situation, the steering speed is only dependent on the respective driving maneuver (Figure 4.34).

15 Parking /steering in state

Rack force / kN

U-turns

1,400 W 1,40

10 1,200 W 1,20 1,000 W 1,00 Lane change

Handling course

600 W

5

400 W 200 W 6 60

120 Rack velocity / (mm/s)

Figure 4.34: Mechanical steering performance, depending on different driving maneuvers (SUV) (Pfeffer and Harrer 2011).

As opposed to traditional hydraulic power steering systems, the required power is extracted from the vehicles’ electrical system. The average power consumption of an EPS system is less than 10W and is thus a negligible electrical load regarding the

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4 Vehicle steering

total energy balance in the electrical system. However, depending on the situation, it can increase sharply and can reach values of up to 1 kW during parking maneuvers, even in medium-sized vehicles (Pfeffer and Harrer 2011). In case the electrical system is already under heavy load, this can lead to the EPS not being able to provide full support in extreme situations. The steering will then become sluggish. A clear sign for recognizing such a bottleneck in the systems performance is the dimming of the vehicle’s headlights during fast steering action. This is due to the steering induced lower voltage in the vehicles electrical system. Compared to the traditional hydraulic power steering systems, the use of EPS can reduce fuel consumption. This reduction depends primarily on how much steering action is performed and the consumption is therefore higher in real driving situations compared to standard operation. In standard operation, the cycle measurements (e.g., NEDC,6 see Chapter 6) are mapped as straight-line driving. Manufacturer specifications vary between 0.3 and 0.4 l=100km, with a corresponding reduction of CO2 emissions of approximately 7–8 g=km in NEDC and 0.8 l=100km in city driving conditions (TRW 2014, ZF_Lenksysteme 2014). Real vehicle measurements (Figure 4.35) show an average reduction in fuel consumption of up to 0.7 l (Pfeffer and Harrer 2011).

0.8 0.7

0.7

0.67

0.6 0.5 0.4

0.41 0.39

0.34 0.28

0.3 0.2 0.1 0 Combined

Urban NEDC Customer

Highway

Figure 4.35: Fuel saving potential of EPS when compared to HPS. Based on a BMW320i according to (Pfeffer and Harrer 2011).

4.10.3.8 Further functionalities due to electromechanical power steering The EPS can be used in the so-called four-quadrant operation. This means that even steering torques opposite that of the driver can be applied. This is a decisive advantage compared to EHPS, as it largely extends the choice of supporting actions. In addition, the magnitude of steering assistance is no longer directly linked with the

6 NEDC: New European Drive Cycle.

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207

driver’s hand torque and can be adjusted by the control unit, in accordance with current driving conditions. Both of these changes have led to the development of the following assistance systems: – lane keeping assistant, – parking assistant, – straight-line corrections, – emergency evasive maneuvers, – and so on. For more information on the topic of assistance systems in motor vehicles, the reader is referred to Chapter 9. The steering system can even act without any driver input. This is a significant step toward highly automated driving, as well as toward new steering systems such as steer-by-wire (see Section 4.12.3).

4.11 Use of test benches for the development of steering systems In the vehicle development process, the use of test benches for almost all components as well as for the entire vehicle has been established. The aim of the test bench investigations is the objective support of the development through the analysis of component and vehicle characteristics. Test bench measurements are not influenced by external weather conditions or human behavior. The precise execution of the tests by the test bench actuators as well as defined and constant environmental conditions lead to an optimal comparability of the measurement results. At this point, the test bench tests establish a link between simulations and idealized driving tests. The simulation analyzes virtual components and vehicles under optimal fully controlable conditions. At the test bench, real components and vehicles are examined under optimal conditions. In a driving test, the test of real components and vehicles takes place under real conditions. Both the simulation and the driving test can be supported by the use of test benches. In addition, test benches allow the characterization and measurement of unknown component properties, thus a realistic parameterization of the simulation models can be achieved. The analysis of individual chassis components in early phases of vehicle development can be performed with the help of the test benches, even if no prototype of the complete vehicle is available yet. Increasing product maturity even before the first use of the vehicle can reduce the risk during test drives. In particular, the carrying out of risky road tests or conceptual examinations of new components or technologies can first be carried out on the test bench, so that the products are already protected with respect to their basic functionality when first used in the vehicle. The longterm properties can be assessed by performing endurance tests with specific load spectra (Düsterloh and Schrage 2016), (Moczala and Maur 2015).

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The reduced need for prototypes allows for increased cost efficiency despite the typically high cost of purchasing and operating a test bench. Test benches can be used in contrast to prototypes for various vehicle projects, series, and vehicle generations. The above-mentioned advantages of test bench investigations therefore lead to a sustained increase in product quality (Schäuffele and Zurawka 2013), (Schimpf 2016). The test bench actuators must be able to track the loads occurring in real operation as accurately as possible in order to ensure an efficient and value-adding use of the test stands. For this purpose, the actuators must be powerful enough to reproduce the amplitudes and frequencies of the real excitations. The installation position of the test specimens must also correspond to the real case regarding load application. Precise measuring equipment is needed to generate reliable and trustworthy measurement data. If simulation models for load calculation are used in the course of the test bench examinations, these must correspond to the real vehicle with sufficient accuracy. The analysis of an active device under test also requires communication between the test bench and the test object in order to transmit all the necessary input variables to the system under test.

4.11.1 Example: test bench for electromechanical steering systems The steering system operates on a steering test bench in a virtual vehicle environment (Figure 4.36). The steering system can be excited both in terms of position

Linear actuator right Steering system

Steering actuator

Linear actuator left

Figure 4.36: Steering test rig (Düsterloh 2018).

4.11 Use of test benches for the development of steering systems

209

and force at the interface between the track rod and the wheel carrier as well as on the steering wheel (in front axle steering systems). The performance of the electrical test stand actuators is sufficient to represent all relevant test cases. The communication of the real ECU with the virtual whole vehicle model is dynamically mapped by a residual bus simulation. The test bench also provides the energy supply of the steering system. There are a large number of possible test scenarios. In addition to component properties, it is also possible to analyze the driving situation-dependent system behavior in conjunction with the overall vehicle simulation. With the aid of the steering system test bench, the quality and performance of the steering systems as well as the steering feel and driving dynamics can be cost-effectively optimized. The following list is a selection of possible test maneuvers for types of steering systems: – EPS – gear ratio between pinion angle as well as motor angle and rack travel, – stiffness of the steering column (torsion bar and steering column), – stiffness of the motor transmission (belt drive and ball screw drive), – friction of steering gear and steering column, – transmission behavior of the steering system; see also Düsterloh, Uselmann et al. (2019). – HAL – follow-up behavior (system reaction in case of failure/shutdown), – wandering behavior (behavior when the system is deactivated), – force jump (step response). – EPS and HAL – engine map (power, energy consumption, and efficiency), – reproduce and descend on real driving maneuvers. The following explanations introduce different concepts for steering system test stands. Subsequently, the properties of the test stand presented in Düsterloh and Schrage (2016) as well as in Uselmann, Preising et al. (2016) and Uselmann (2017) will be discussed in detail. Schimpf (2016) dealt with the conceptual design and implementation of a steering test bench, which is suitable for the characterization and measurement of steering systems. A full-fledged testing device with an electric steering actuator and two electric linear actuators are developed. The steering system test bench described in the following basically has a similar configuration (Figure 4.36). Similar test rigs are used in Nippold, Küçükay et al. (2017) and Stauder, Plöger et al. (2013). Nippold, Küçükay et al. (2017) used the test bench for pre-electromechanical steering systems. Stauder, Plöger et al. (2013) used the bench for subjective assessment of steering in early stages of development. The test bench concept of Shah and Gijbels (2007) converts the torques of two rotary motors into the tie rod forces via levers.

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The steering actuator is used to apply the steering wheel torque or steering wheel angle. With the help of the linear actuators, the forces and displacements of the tie rods or the rack can be traced. The implementation of real driving maneuvers can be achieved on the test bench by two different methods. First, predefined signals (e.g., from a driving test measurement) can be transferred to the test bench as test vectors and traced. In comparison to driving tests this method has the advantage that a test vector (once recorded) can be used as often as needed without variation. Secondly the steering system can be brought into a HiL simulation using suitable vehicle models and the test-bench. With the test bench software, any driving situation can be defined. Since any vehicle or environment condition as well as the driving scenario can be chosen freely for the simulation, such a HiL simulation offers a high flexibility. Figure 4.37 illustrates the relationships between the test bench actuators, the simulation model, and the steering system under test (EPS or HAL) (Düsterloh and Schrage 2016) and (Uselmann, Preising et al. 2016).

Figure 4.37: Signal correlations on the steering system test bench in HiL mode (Düsterloh and Schrage 2016).

The test rig is equipped with various sensors to record various parameters during the test (Düsterloh and Schrage 2016) and (Uselmann, Preising et al. 2016): – torque and angle of rotation of the steering actuator, – forces and positions of the linear actuators, – current consumption,

4.12 Innovative approaches to vehicle steering

– – – –

211

tension, temperature, acceleration, and steering system internal sizes.

The steering actuator and the linear actuators are specified so that all relevant test cases for the development of steering systems can be implemented. The maximum torque of the steering actuator is 50 Nm, the maximum rotational speed is 500 1=min or 3, 000 =s. Steering actuator and steering line are connected by a torque coupling. This opens on occurrence of too high torques, so that the steering actuator is protected from damage. With the help of the linear actuators, the steering system can be impressed with maximum forces of 20,000 N. The maximum stroke is 130 mm, and the maximum travel speed is 1,000 mm=s. In addition, the test bench has a variable tensioning field with various scales, stops, and alignment aids for the assembly of the individual components. The different steering systems (EPS and HAL) can be integrated on the test bench by means of specific adapters. The energy and signal transmission take place via defined interfaces between the steering and the test bench. Another possibility for increasing the test depth results from the expansion of the test bench by a climatic chamber. This makes it possible to carry out analyses of the system behavior under special outdoor conditions ( − 40  C to + 70  C). The steering test bench has a comprehensive safety concept to guarantee the safety of the test bench users. It consists of various emergency stop switches, visual and acoustic warning signalers as well as a barrier and light barriers (Düsterloh and Schrage 2016) and (Uselmann, Preising et al. 2016).

4.12 Innovative approaches to vehicle steering In addition to the traditional front wheel steering systems seen in almost all passenger vehicles, different driver supporting steering systems and innovative new steering concepts are under development, or in some cases even in use. Some of these developments will be discusses in the following section.

4.12.1 Superimposed Steering A superimposed steering system is characterized by a less rigid connection between the steering wheel and steering gear. The input angle at the steering gear is the result of superimposing the steering wheel angle, and an additionally provided angle determined by the system.

212

4 Vehicle steering

Therefore, the steered wheels can be controlled independent of the driver’s input (within limits). Superimposed steering is used primarily for two reasons: – realizing a continuously variable transmission, and – intervening steering action to maintain vehicle stability during dynamic driving, independent of the driver. Often different steering ratios can be favorable, depending on vehicle speed and the maneuver executed by the driver. While maneuvering at lower speeds, for instance, a direct steering feel is usually preferred. This means that less steering wheel rotation is required by the driver. At higher speeds (and usually also lesser road curvature), it is often preferable to have a more indirect steering feel for better controllability and stability. The superimposed steering system can, depending on vehicle speed, optimize the total steering ratio from steering wheel to steering rack by adjusting the additional steering angle in accordance with the drivers steering input. In dynamic driving situations where the vehicle is driven on the limit, the additional steering angle can be used to stabilize the vehicle (even with constant steering wheel angle). A precise steering intervention, for instance, by the ESP system, can be used to create additional vehicle yaw torque to support the maneuver. Superimposing the steering angle is achieved through a specific gear type with corresponding actuator located on the steering column. From a safety perspective, it is important for a superimposed steering system to allow for unhindered conventional steering if the available electric power is insufficient. This means that the summation gear is locked, and the driver’s steering input is coupled directly to the steering rack. BMW was the first manufacturer that brought an active superimposed steering system on the market. This type, which was launched in 2003, relied on a planetary gear to superimpose the steering angles and was known as active steering. A different construction type was launched by Audi in 2007, called dynamic steering. Instead of a planetary gear this system used a harmonic-drive gear. Disadvantages of superimposed steering systems are high complexity, costs, weight, and the need to package the extra gearing as well as high inertia in the transmission path of steering feedback from the wheels to the steering wheel. Additionally, the driver haptic feedback dosen’t always correlate to the actual driving situation.

4.12.2 All-wheel steering The assumption was made in the previous sections that only the two front wheels of the vehicle were used in the steering task. Steering concepts as described earlier are not suitable for application in rear-wheel steering, except for forklifts and other special purpose vehicles.

4.12 Innovative approaches to vehicle steering

213

The working principle of all-wheel steering is used in both the front and rear wheels of the vehicle. The idea behind all-wheel steering in passenger cars has been known since the early 1930s. Although the first series of vehicles equipped with all-wheel steering was first brought to the market by the end of the 1980s (Harrer and Pfeffer 2017). Multiple different working principles are known to achieve a steering function of the rear wheels. From a functional perspective it is important whether the frontand rear wheels can be steered separately. Distinguished are systems that use – a mechanical connection between the front and real wheels, – an (electro-) hydraulic actuator connected to the rear wheels, and – an electromechanical actuator connected to the rear wheels. The purely mechanical connection does not allow for separate steering motion of the front and rear wheels. This principle can be used to reduce the turning radius of the vehicle. In case the front and rear wheels can be steered separately, the range of possible turning radii is once again increased, as well as the ability to stabilize the vehicle. The steering behavior can be optimized, depending on the current driving situation. At low speeds, a smaller turning radius is often desired, whereas at higher speed vehicle stability is usually prioritized. Therefore, no compromises need to be made regarding this conflict of interest during the design phase. This principle is especially applicable to systems using electromechanical actuation. In addition to these more elaborate functionalities, electromechanical actuation of the rear wheels has the distinct advantage compared to mechanical or hydraulic actuation that its construction is less complex and adds less weight to the vehicle. New all-wheel steering systems also utilize electromechanical steering assistance on the rear axle through electromechanical actuators. As described, all-wheel steering systems can positively affect lateral dynamic behavior of the vehicle compared to traditional front wheel steering systems. These positive effects include increased maneuverability at low speeds as well as vehicle stabilization (for instance through dynamic driving control systems). Both can be recognized in Figure 4.38.

4.12.3 Steer-by-wire In steer-by-wire systems, the mechanical connection between the steering wheel and the wheels has been completely eliminated. The steering wheel angle is measured by a sensor and analyzed by a control unit. This control unit in turn regulates a motor so that the desired steering angle at the wheels is achieved. A second motor that actuates the steering wheel itself provides the necessary hand torque to ensure an acceptable steering feel. The basic layout of a steer-by-wire system is shown in Figure 4.39.

214

4 Vehicle steering

Low-velocity range M2 M1

Conventional steering system Conventional steering system with rear-wheel steering High velocity range

M1 M2 Figure 4.38: Change in turning radius due to all-wheel steering compared to traditional front wheel steering.

Additional functions Motor

Sensor ECU Motor Sensor

Figure 4.39: Basic layout of a steer-by-wire system.

4.12 Innovative approaches to vehicle steering

215

Compared to conventional systems, a steer-by-wire system has clear advantages in terms of functionality, as well as regarding packaging due to the elimination of mechanical components: – The elimination of mechanical components allows for new packaging concepts. In addition, the differences between left-and right-side steering vehicles are diminished. – The elimination of the steering column has considerable advantages with regard to crash behavior safety of the vehicle. – The steering angle can be controlled completely independent of driver input. Therefore, similarly to the case of superimposed steering, functions regarding the driving dynamics can be supported. – Malfunctions can be suppressed. – The steering feel (hand torque) can be adjusted independent of actual vehicle steering. – The steering behavior of the vehicle can be slightly altered in accordance with the driving situation. For instance, the steering ratio can be chosen freely. – Steer-by-wire is necessary for full autonomous driving functionality. The biggest obstacle in steer-by-wire systems is meeting the safety requirements. In case the system stops functioning, the vehicle must stay controllable at all times. While in traditional vehicle steering systems the mechanical coupling between the steering wheel and the wheels ensure that the driver always has control of the vehicle, steer-by-wire systems must be designed with redundancy in mind. This means that in case one component fails, a second must guarantee that at least basic functionality of the steering system is maintained. Especially these requirements make steer-by-wire systems extremely complex.

5 Braking systems Together with the steering system and longitudinal acceleration by the engine, the braking system is an indispensable control interface between the driver and the vehicle. The traditional purely mechanically operated braking systems have been further developed into modern day systems, which integrate sensors and actuators forming a system based more on mechatronics than mechanics. This chapter describes the basic mechanical layout and functioning of the braking system. Control systems operating on the brakes, such as antilock braking and driving stability systems, will be dealt with in Chapter 9.

5.1 Structure of the braking system A distinction can be made based upon the different tasks the respective braking system must be capable of fulfilling. In general, a braking system can be used for the tasks: – lowering the vehicle speed, – bringing the vehicle to a full stop, – preventing undesired acceleration of the vehicle during downhill driving situations, and – keeping the vehicle at a standstill. The typical functional design of a purely mechanical braking system used in passenger cars is shown in Figure 5.1. It consists of: – the brake pedal, which acts as the control interface between driver and vehicle, – the master brake cylinder, which transforms force on the pedal into hydraulic pressure, – the brake servo, which increases the hydraulic pressure, – one brake for each wheel, – a brake pressure reducing system or brake pressure limiter on the rear wheels, preventing “over-braking,” which could lead to rear wheel lock-up, and – the parking brake usually in the form of a lever or a foot pedal. In modern vehicles increasingly operated with use of electric buttons or switches.

5.2 Different implementations of braking systems Braking systems differ both in terms of their functionality as well as in terms of their construction form, which depends on the desired application area. In addition, they can offer countless support functions to aid the driver in controlling the vehicle under difficult driving conditions. https://doi.org/10.1515/9783110595703-005

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5 Braking systems

Parking brake

Brake pressure reducer / limiter reduc

Brake booster ooster Surge tank for or brake fluid Master brake cylinder

Actuation cable for parking brake Brake pedal Wheel brake with brake disc, brake caliper, and wheel brake

Figure 5.1: Basic construction form of a traditional passenger car braking system.

5.2.1 Design types In general, distinctions can be made with respect to passenger car braking systems (Reif 2011): – operating braking systems (OBS), – auxiliary braking systems (XBS), – standstill braking systems (SBS) or Parking Brakes. 5.2.1.1 Operating braking systems (OBS) OBS are used during normal operation of the vehicle, either to decelerate the vehicle or to maintain a certain speed when driving downhill. It is responsible for the deceleration of the vehicle down to a complete stop, as well as preventing a rolling motion when standing on an incline or in vehicles equipped with an automatic transmission (creep). The driver controls the OBS by using a right-foot operated pedal in nearly all motorized vehicles. 5.2.1.2 Auxiliary braking systems (XBS) XBS serve as an auxiliary braking system in case the OBS does not function properly, although performance and functionalities are often limited. It is not necessary to install a third redundancy braking system besides the OBS and SBS. Rather, it is sufficient to divide the OBS into a two or multiple circuit braking system to establish a redundant fail-safe system.

5.2 Different implementations of braking systems

219

5.2.1.3 Standstill braking systems (SBS) SBS must be able to keep vehicle in a standstill position even on inclined slopes. In doing so, no driver input force must be required, meaning that the system can keep the vehicle in a standstill even in the absence of the driver. Operating the SBS is done directly by means of a lever or pedal, either mechanically, hydraulically, electrically, or electrohydraulically operated. In the case of older passenger cars, the transmission of SBS usually consisted of a cable. Disc brakes, as well as drum brakes with shoes either on the inside or outside, can be used as parking brakes. In the case of drum brakes, parts of the OBS are often shared in its function as SBS. The system, also referred to as parking brake, usually works on the OBS of the rear axle. The input force is transmitted from the control element through the cable, onto both rear brakes, where either the brake shoes are pushed outward or the brake pads are pushed together. Alternatively, instead of using a hand brake, the operation can also be accomplished with the use of a foot pedal. In newer, and higher-class vehicles, electromechanical parking brakes are becoming more and more common. In this case, the brake shoes are pressed against the disc by actuators located on the rear calipers. These actuators can usually either be controlled with a parking brake button on the dashboard or are operated automatically without driver intervention via a control unit.

5.2.2 Functionality Certain distinctions can be made about the function of braking systems, with regard to the energy source used for operation. Accordingly, it is to be distinguished between braking systems that are operated by – the driver muscle force, – an assistance force, which is generated based on amplifying the driver’s force input, and – external force sources. 5.2.2.1 Muscle force braking systems In muscle force-operated systems, the force applied by the driver’s foot is transferred through a lever or pedal through either linkage, cables, or hydraulics, to the wheel brakes. 5.2.2.2 Auxiliary braking systems In auxiliary braking systems, the muscle force applied by the driver is amplified by an appropriate pneumatic (vacuum) or hydraulic device and then transmitted hydraulically through the brake lines to the wheel brakes.

220

5 Braking systems

Some vehicles are equipped with new features, such as electrical power drives using an energy recovery systems and/or driver assistance systems. In this case the servo brake, or brake booster, can also rely on electrical principles for operation. 5.2.2.3 Braking systems with external force source In this type of braking systems, the OBS is operated exclusively by external power. The intent of the driver is measured using sensors located in the brake pedal and analyzed in a control unit. Based on that previously generated hydraulic energy is forwarded to the wheel brakes through hydraulic lines. The brake fluid is stored in hydraulic accumulators in which gas (e.g., nitrogen) is compressed. Gas and liquid are separated by an elastic bubble (bladder accumulator) or a piston with rubber seal (piston accumulator). The fluid pressure is generated by a hydraulic highpressure pump and is in equilibrium with the gas pressure. A pressure regulator switches the hydraulic pump to idle as soon as the maximum pressure is reached. An example of such a power-assisted braking system is the electrohydraulic braking system (EHB), also known as sensotronic brake control (SBC). The driver’s desired course of action is measured electronically through a calibrated sensor. During normal operation no direct link is present between driver and the wheel brake. This is effectively a so-called brake-by-wire system. The sensor measures the deflection of the brake pedal and determines pedal speed and acceleration. In addition, the pressure profile in the control circuit is recorded via a pressure sensor. With this information, the control unit derives the driver’s intent and calculates the pressure required for each separate wheel brake, depending on the current driving situation. The control unit actuates the hydraulic system that can build up brake pressure for each wheel individually. Pressure sensors in each wheel’s brake line determine the actual pressure, so that the target pressure for each wheel can be readjusted accordingly. In contrast to traditional braking systems, the driver does not have a direct sensory link to the wheel brakes. A “simulator” recreates the desired brake pedal feel, which would normally be caused by counteracting forces in the hydraulic pressure lines. In case of a failure of the control unit, a direct and nonassisted connection between the master cylinder and the wheel cylinders is established through a series of valves. Admittedly, this only actuates the wheel brakes on the front axle.

5.2.3 Ideal brake force distribution At first, as a special case of the general longitudinal forces dealt with in Chapter 6, the forces acting on the vehicle’s axles during dynamic braking are investigated (Table 5.1).

221

5.2 Different implementations of braking systems

Table 5.1: Relevant parameters during braking action. Symbol

Description

Fx, v , Fx, h , Fz, v , Fz, h

Tire forces

Fx, v , Fz, v , Fx, h Fz, h

Wheel forces normalized with respect to vehicle weight

lv , lh , l

CoM to axle horizontal distances

h

CoM height

mV

Vehicle mass

b, bdes , bmax , bopt

Current, desired, maximum, and optimum deceleration (design point)

μv , μh , μ

Friction coefficients – front, rear, and total

bv , bh

Maximum deceleration in case front or rear brake circuit fails, respectively

A vehicle with a total mass of mV , distances to the horizontal center of gravity lv , lh , and the vertical height of the center of mass (CoM) h are measured from the road surface, which is assumed flat (Figure 5.2).

S mv g

h Fx,v Fz,v

Fx,h lv

lh

Fz,h

l Figure 5.2: Forces during braking action.

The forces in the tire contact points are summed up at the front and rear axle, resulting in the forces Fx, v , Fx, h acting in the direction of travel, and Fz, v , Fz, h , acting in the direction of the vertical axis. All other forces will be neglected in this approach. Yielding the torque equilibrium around the CoM S: lh Fz, h − lv Fz, v + hðFx, v + Fx, h Þ = 0.

(5:1)

Force equilibrium in the vertical direction states Fz, v + Fz, h − mV g = 0,

(5:2)

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5 Braking systems

resulting in the impulse equation for the direction of travel mV €x = − ðFx, v + Fx, h Þ.

(5:3)

Equations (5.1) and (5.3) now yield mV €x =

1 ðlh Fz, h − lv Fz, v Þ. h

(5:4)

With deceleration b = − €x and l = lv + lh , the axle loads now follow from (5.4) and (5.2)   g b Fz, v = mV lh + h (5:5) l g as well as Fz, h = mV

  g b lv − h . l g

(5:6)

As one would expect, it can be seen that the vehicle’s mass is statically divided over the front and rear axle according to the position of the CoM. In addition, there is an increase of force on the front axle and a simultaneous decrease of force on the rear axle, as a function of the deceleration b and the height h of the CoM. The maximum deceleration is achieved when the front and rear axle simultaneously reach the frictional limits, with equal friction coefficients μv = μh = μ; thus Fx, v = μFz, v

and Fx, h = μFz, h .

(5:7)

In this situation, the highest possible braking force is transferred to the front and rear axle. This yields a maximum deceleration of bmax = μg,

(5:8)

if no additional contact pressure is generated by aerodynamic measures. For a prescribed deceleration bdes , it holds that bdes = ηbmax ≤ bmax = μg,

(5:9)

where a safety factor is described by 0 < η < 1. For the front and rear axle together the following equation holds Fx, v + Fx, h = mV bdes = mV ηbmax .

(5:10)

z, v normalized with respect to the vehicle Resulting from (5.5), the vertical force F mass is   Fz, v 1 bdes  = h (5:11) Fz, v = lh + mV g l g

5.2 Different implementations of braking systems

x, v := and by (5.5), (5.7)–(5.10) as well as F

223

Fx, v mV g

  z, v = η bmax F x, v = bdes 1 lh + bdes h . x, v = ημF F g g l g

(5:12)

Corresponding to (5.6) for the rear axle   bmax  bdes 1 bdes   Fz, h = h . lv − Fx, h = ημFz, h = η g g l g

(5:13)

By elimination of the acceleration bSoll from (5.12), and after some rewriting it holds that sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 bSoll lh lh l + F =− + (5:14) x, v . g 2h 2h h Filling into (5.13) yields the relationship between the braking forces acting on both axles sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 bSoll  lh lh l   + F (5:15) − Fx, v = − + Fx, h = x, v − Fx, v . g 2h 2h h This relationship is shown in Figure 5.3. In this representation, the percentage of braking force on the rear axle is also plotted.

80%

0.4 – Fx,h

Real brake force distribution

0.35

70% 60%

0.3 Design for bopt = 0.8

0.25

50% 40%

0.2 0.15

30%

Ideal brake force distribution

20%

0.1

0.8

1.2

0.6

1.0

0.4

0.8

0.2

0.6

0

0.4

0.2

0.05 0

– – Fx,h /Fx,v

1

1.2

10% 0%

– Fx,v Figure 5.3: Example for an ideal brake force distribution with

h lh = 0.2 and = 0.54. l l

If the braking forces on both axles according to (5.15) are sufficient and with equal friction coefficients, the antiblocking assurance is equally high for both axles.

224

5 Braking systems

In reality, the ideal brake force distribution shown in Figure 5.3 can only be achieved with significant effort. It is therefore attempted to approximate the ideal distribution by means of steps that are easier to implement. A distinction is made between a rigid, a controlled, and a regulated distribution of the braking forces. 5.2.3.1 Rigid brake force distribution A rigid brake force distribution entails a distribution for which the braking forces on both axles are fixed due to the constant, purely mechanical nature of the design. This distribution is defined by the intersection between the ideal brake force curve and the straight-line, real, fixed-ratio brake force distribution. According to current EU guidelines, the real brake force distribution is defined in such a way that a deceleration of bopt = 0.8 is achieved at the intersection with the ideal brake force curve. This point is called the design point and divides the surface area of the brake force distribution in two sections. To the left of the intersection, the front axle is over-braked, and to the right of the intersection, the rear axle is over-braked. When the rear wheels lock, the vehicle becomes unstable during braking. Locking rear wheels can provide longitudinal friction forces during wheel slip, but are unable to achieve any lateral or cornering forces. Other forces, such as those induced by the road surface, can lead to a yawing movement of the vehicle. Therefore, it is of significant importance to realize maximum braking deceleration with respect to the road condition, while still preventing the rear wheels from locking. With uncertainties in all parameters in mind, the fine-tuned settings shown in Figure 5.3 are defined in such a way that the rear axle is slightly under-braked at all times. Usually the braking system of a vehicle is designed such that the front wheel will lock up first in case of an emergency braking maneuver. In the absence of ABS,1 this leads to loss of steering abilities of the vehicle, but it will remain in a straight-line trajectory due to the lateral forces still acting on the rear wheels. This will prevent the vehicle from swinging left and right uncontrollably. 5.2.3.2 Brake force control Controlling the braking force can be realized by a device that either limits or reduces the actual braking force applied. The brake pressure limiter limits the braking force on the rear axle to a fixed and constant maximum value. The limitation of the brake pressure is realized by a pressure relief valve, which prevents a further increase of the brake pressure after the specified value is reached.

1 ABS: Antilock Braking System; see Chapter 9.

5.2 Different implementations of braking systems

225

5.2.3.3 Brake force reduction With a brake pressure reducer, a closer fit to the ideal brake force distribution can be achieved for the real brake force distribution. This yields the advantage that the locking tendency of the front wheels can be reduced. The realization requires a valve that, after having reached the threshold value, only transfers part of the increased pressure to the brake cylinders on the wheels (Figure 5.4).

– Fx,h

Ideal brake force distribution

– Fx,h

Ideal brake force distribution Changeover point

Changeover point bopt

bopt

– Fx,v

– Fx,v

Figure 5.4: Controlling the brake force distribution by using a brake force limiter (left) and a brake force reducer (right).

5.2.4 Failure of a brake circuit In case of a two-way division of the braking system (see Section 5.4), it must still be possible to decelerate the vehicle in case the brakes on one axle fail. For the situation where the brakes on the front axle fail, it can be stated Fx, v = 0 and Fx, h ≤ μFz, h ,

(5:16)

mV bh = Fx, h .

(5:17)

where it holds that

So, a deceleration remains of   g bh lv bh = μ . lv − h and thus bh = μg g l + hμ l

(5:18)

For typical values corresponding to a middle-class vehicle (Bardini 2008), m l = 2.5 m, lv = 1.2 m, h = 0.5m, and μ = 1. A value of bh ≈ 3.94 2 is obtained, which is m s approximately only 40% of the maximum possible deceleration of μg = 9.81 2 . s For the front axle this results in bv = μg

lh , l − hμ

(5:19)

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5 Braking systems

which leads to bv ≈ 6.38 sm2 , when using the same parameters as before. This means that at least 65% of deceleration can still be obtained when compared to the nonfailure situation.

5.3 Assembly components of the braking system Braking systems in passenger vehicles are composed of assemblies consisting of multiple components, functioning of which usually relies on hydraulic working principles. Over time, these assemblies have been expanded to allow for the introduction of additional driver-support systems.

5.3.1 Overview and functionality The conventional construction of the braking system in a passenger car is shown in Figure 5.1. The division into two classes – operating brakes and parking brakes – and the manner how all functionalities of the braking system can be structured (Figure 5.5). The brake actuating system is composed of all components involved in initiating and controlling the braking process of the vehicle. Within the boundaries of the actuating system, the control signals are forwarded through either mechanical or electrical components. The amplitude of these signals is often magnified by an external energy source, usually obtained through a vacuum created by the combustion engine or through the vehicle’s electrical system. Input for the braking system is usually done through a calibrated control element, generally in the form of a foot pedal actuated by the driver. In special cases, this control element can also be hand-controlled instead of a foot pedal. In conventional braking systems, the brake signal is either transmitted directly to the wheel brakes or modulated by a lock-up preventing control system (see Chapter 9). For driver assistance systems, such as dynamic drive settings and adaptive cruise control, separate driver interfaces are present to provide control over the corresponding systems (see Chapter 9). The vehicle’s energy system must supply a significant amount of energy to actuate and control the wheel brakes. Passenger car braking systems exist where the actuating force is initially supplied by the driver, but then amplified by the system (auxiliary braking systems). The transmission system is composed of all components and fluids responsible for transmitting the actuating force from the actuating system to the wheel brakes. These components generally consist of hydraulic pipes and brake lines, as well as the accompanying hydraulic fluid. In most cases, there is an additional device that divides the braking pressure between the front and rear axles and redirects it accordingly. Often the braking

5.3 Assembly components of the braking system

227

Initiation of the braking operation Driver – muscle strength, switch operation Vehicle system – electronics

Parking brake

Brake Actuation device

Actuation device

Brake pedal Master cylinder Brake booster Control unit

Hand lever Pedal Switch Control unit

Power supply Muscle strength (driver) Electrical (vehicle power) Power transmission Mechanics (rods, pistons, ets.) Hydraulic Electrical Wheel brakes Disc brake Drum brake

Figure 5.5: Typical structure of the braking system in a passenger car.

pressure to the rear axle is reduced to guarantee that the rear wheels, under no circumstance, lock up before the front wheels do. This is done through the before mentioned brake pressure reducer. These requirements result from the driving dynamic requirements as dealt with in Chapter 3. The wheel brakes provide a torque that counteracts the wheels’ rotational motion. Under braking, the kinetic energy of the vehicle is converted into heat energy due to friction between the brake pads and the drums/discs. Here it is temporarily stored before the heat is released to the surrounding air. Friction brakes are used for most conventionally powered vehicles. For electric vehicles (see Chapter 6), the electric motor can additionally be used to recover energy from the brakes. This is known as energy recuperation (Table 5.2). The foot force FF applied by the driver on the brake pedal is first converted into the actuating force FB , through the transmission ratio of the foot pedal iPED (Figures 5.6 and 5.7): FB = iPED FF .

(5:20)

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5 Braking systems

Table 5.2: Relevant parameters during braking. Symbol

Description

FF , FB , FH , FA

Foot force, actuating brake cylinder force, aux. force of servo brake, amplified actuating force

FB0, FH0

Saturation point, actuating force until an auxiliary force is generated, maximum auxiliary force

iPED

Transmission ratio foot pedal

iV , V *

Constant of proportionality, magnification factor of the servo brake

FSp

Tensile force

iH

Transmission ratio of brake hydraulics

re , rstat , rdyn

Brake radius, static and dynamic tire radius

p

Brake pressure

C

*

Inner ratio

Wheel brake cylinder brake pipe Surge tank

fsp Brake fluid Foot force Brake shoe Abutment

Brake pad

Master cylinder

Wheel brake

FF Brake pedal

Figure 5.6: Layout of a drum brake.

In the servo brake (booster), which is powered either through a vacuum or hydraulically, the actuating force FB is increased by an auxiliary force FH : FA = FB + FH = iPED FF + FH .

(5:21)

The auxiliary force (FH ) characteristics are fully dependent on the servo brake booster (Breuer and Bill 2012). Since the foot force to be applied by the driver must not exceed a certain value even if the brake booster fails, the auxiliary force FH must reach a specified value.

5.3 Assembly components of the braking system

re

229

FSP

ARZ

FSP

p=

FA AHZ

ABKV

AHZ

AHZ FA = FB + FH

p=

FB

FF

FA AHZ

Figure 5.7: Force flow diagram of a braking system.

Up until the saturation point FB0 , meaning in the range of FB < FB0 , it holds with the constant of proportionality iV FH = i V FB

(5:22)

FA = ð1 + iV ÞFB = V * FB

(5:23)

and therefore

Auxiliary force FH

with the amplification factor V * = 1 + iV (Figure 5.8).

Saturation point

iV Actuation force FB

Figure 5.8: Saturation point.

230

5 Braking systems

For the region FB > FB0 and the corresponding auxiliary force FH0 , the magnification factor is limited to V* = 1 +

FH0 . FB

(5:24)

In the design phase of the braking system, the brake saturation point is defined in such a way that with a fully loaded vehicle, the actuating force FB0 will lead to the wheels just reaching the friction limits and locking occurs. Due to the hydraulic transmission, a tensile force FSp is reached acting on brake pads for each wheel. FSp is dependent on the brake booster output force FA and the hydraulic transmission of the braking cylinders iH : FSp = iH FA = iH V * FB = iH V * iPED FF .

(5:25)

With the effective surface area AHZ corresponding to the master braking cylinder and the effective surface area ARZ corresponding to the wheel braking cylinder, and when neglecting compliance and frictional effects in the system, the relationship becomes iH =

ARZ . AHZ

(5:26)

A tangential force FU is generated by the tensile force FSp in combination with an effective braking radius re . This yields a braking force of Fwheel at the tire contact point: Fwheel =

re rstat

FU

(Figure 5.9).

re Fsp rstat Fwheel

FU

Figure 5.9: Forces on the wheel.

(5:27)

5.3 Assembly components of the braking system

231

The relationship between tensile force FSp and tangential force FU is also known as the inner transmission ratio C* of the wheel brake. Among other things, the inner transmission ratio is dependent on the friction coefficient μpad between brake pad and drum/disc (see Sections 5.3.4 and 5.3.5). Using this ratio, the relationship between actuating force FF on the brake pedal and the braking force at the wheel FWheel can be formulated as FWheel ¼

re re  FU ¼ C FSp ¼ iPED V  · |fflfflffl{zfflfflffl} rstat rstat actuation mechanism

ARZ re · C FF : AHZ rstat |{z} |fflfflffl{zfflfflffl} hydraulics gear ratio

ð5:28Þ

wheel brake gear ratio

The inner transmission ratio C* is described in DIN/ISO (1997–2001) for most individual construction forms of braking systems. Examples of calculations for both drum and disc brakes can be found in Sections 5.3.4 and 5.3.5. The described relationships only consider pure mechanical braking systems. In most modern-day vehicles further functionalities have been incorporated into the braking system, especially functionalities that support the driver in situations where the vehicle is driven on its frictional limits. These interventions can either be executed by the brake booster directly or by modulating the brake pressure inside the hydraulic lines. Examples of such systems are (see Chapter 9 as well) as follows: – brake assist, which ensures the maximum possible deceleration in case the system detects an emergency braking maneuver by the driver (through high pedal force and acceleration), – antilock braking (ABS2) and traction control (TCS3), – dynamic driving control (ESP4), – adaptive cruise control (ACC5).

5.3.2 Brake pedal and master brake cylinder The brake pedal’s primary task is to transfer the foot force exerted by the driver to a piston rod, which, after being enforced by a brake booster, builds up the hydraulic pressure in the master brake cylinder. A sensitive and responsive reaction to the input force exerted by the foot is of great importance. In case of an auxiliary braking system, this mechanism must be replaced by a brake-feel simulator to recreate the conventional feel of a braking system. In general, the brake pedal, brake booster,

2 3 4 5

ABS: Antilock Braking System; see Chapter 9. TCS: Traction Control System; see Chapter 9. ESP: Electronic Stability Program; see Chapter 9. ACC: Adaptive Cruise Control; see Chapter 9.

232

5 Braking systems

and master cylinder are integrated into a single unit due to packaging and costrelated benefits. After amplification by the brake booster, the master cylinder converts the foot force applied by the driver into a hydraulic pressure that passes through the brake lines, where it is converted to force that presses the brake pads against the brake drums or brake discs, depending on the type of brake. For example, Figure 5.10 shows a tandem master brake cylinder with central valve. After actuation of the brake pedal, the push rod piston is translated to the left. As a result, the intermediate piston also displaces to the left, thereby closing the central valve, causing the pressure chamber to be sealed. That increases the pressure in both the pressure chambers. In case the foot force is reduced, both pistons move to the right. The right piston then releases the compensation bore and the central valve opens, after which the hydraulic braking fluid can once again flow back into the expansion tank.

Expansion tank

Compensating bore

Central valve Piston spring

Primary sleeve

Primary sleeve

Replenishing bore Secondary sleeve

Cylinder housing

Push rod piston Stop pin 1. Brake circuit

Piston spring 2. Brake circuit Separating sleeve Intermediate piston

Valve pin

Figure 5.10: Main or master braking cylinder (schematic visualization).

5.3.3 Brake booster In most contemporary vehicles, the foot force applied by the driver is insufficient to achieve and sustain the required brake pressure for all driving situations. Therefore, the driver’s foot force must be amplified accordingly. The primary objective of the brake booster is to keep the required foot force to a minimum, to allow for comfortable and safe braking at all times. At the same time, the brake booster must not hinder the sensitive and precise administering of the brake and ensure that it responds as expected. Brake boosters are

5.3 Assembly components of the braking system

233

very common in modern-day motorized vehicles. The required energy is extracted either from the partial vacuum at the intake manifold of the combustion engine or from a hydraulic pump, which generates the required hydraulic pressure in case the partial vacuum does not suffice. This is often the case in vehicles with DIESEL or turbocharged engines, as well as in electric vehicles. Figure 5.11 shows a vacuum pressure brake booster with a single chamber configuration. For vehicles that have a higher need of braking support, four chamber configurations also exist (Reif 2010).

Piston return spring

Vacuum port

Rolling diaphragm Working piston Vacuum valve Valve piston Piston rod

Rubber reaction disc

Brake pedal

Push rod Filter Pressure spring Outside-air valve Poppet valve Working pressure chamber Vacuum chamber Figure 5.11: Vacuum brake booster according to Fischer, Gscheidle et al. (2013).

The brake booster shown in Figure 5.11 utilizes either the intake manifold or suction pipe of the petrol engine or a hydraulic pump, to create a partial vacuum of 0.5–0.9 bar, which in turn is used to generate the auxiliary braking force. This auxiliary braking force has a positive linear relationship to the applied foot force, up until the saturation point, after which the auxiliary force does not increase further (see Section 5.3.1). The saturation point is defined in such a way that it is close to the pressure required to lock up the front wheels. The brake booster in Figure 5.11 shows an essential component in the form of a working piston with rolling diaphragm. This separates the vacuum chamber from the working chamber. The foot force transferred by the piston rod is led through the working piston onto the push rod and is simultaneously increased by the compressive force resulting from the working pressure chamber on the separation membrane. When no brakes are applied, the vacuum chamber and working pressure chamber are connected to one another, and in both chambers, and therefore also on both

234

5 Braking systems

side of the working piston, the same partial vacuum is present. In this baseline position, the working piston is kept in place by the piston return spring. When the brakes are applied, the piston rod from Figure 5.11 moves to the left, closing the poppet valve and thus the connection between the two chambers. Once again both chambers are separated from each other. When the valve piston moves further to the left, the valve that shields the working chamber against atmospheric pressure opens, leading to an inflow of atmospheric pressure via the filter and outside-air valve. The build-up of pressure is transferred through the membrane to the diaphragm plate which pushes the compressive spring and thus the push rod to the left, increasing the original foot force exerted by the driver. At the same time the rubber reaction disc is compressed. As soon as the push rod stops moving, the reaction disc expands again and exerts pressure on the valve piston. This closes the outside-air valve and a constant force amplification is provided. The resulting auxiliary force can be formulated as FH = AM Δp,

(5:29)

where AM is the effective cross-sectional area of the working piston and Δp the pressure gradient between the working chamber and vacuum chamber. In case the pedal force is reduced again, the valve piston moves back to the right, opening the connection between vacuum and working chamber and therefore equalizing the pressure. When the brakes are fully applied, the reaction disc remains compressed and the outside-air valve stays open. This results in the maximum possible pressure gradient of Δp ≈ 0.8 bar. Vehicles in which the partial vacuum supply is insufficient, such as DIESEL or electric vehicles, are typically provided with hydraulically operated brake boosters (Fischer, Gscheidle et al. 2013).

5.3.4 Drum brakes For a simplex drum brake, a torque equilibrium for the brake pad with respect to the supporting point A results in (Figure 5.12) 2aFSp − aFN + rFU = 0.

(5:30)

If the assumption of dry friction between the normal force FN and tangential force FU is made, the following relationship applies FU = μpad FN and therefore

(5:31)

5.3 Assembly components of the braking system

235

Rotating direction

Brake pressure

Piston

FSP Brake lining a FN

r FU

r

Brake drum

a

A Abutment Figure 5.12: Principal working principle of a drum brake.

 C* =

FU μpad FN = = FSp FSp

μpad

2FSp 1 − ar μpad

FSp

 =

2 1

μpad

−

r a

.

(5:32)

In this case, the inner transmission ratio C* is nonlinearly related to the friction coefficient of the brake pad. Therefore, it can vary strongly depending on the age and potential wear of the brakes, as well as on environmental conditions. One of the advantages of the drum brake is its built-in self-amplification. However, due to sensitivity to changing parameters as mentioned before, this self-amplification is not constant. This is a major disadvantage, as moisture and extreme temperature under heavy braking can lead to a significant reduction of the friction coefficient, which results in decreased braking performance. This phenomenon is known as brake fading. Due to their simple design and relatively straightforward construction, drum brakes are considerably less costly compared to disc brakes. A variety of designs have been developed over the course of history. Main forms are the simplex, duplex, and servo brakes, where the simplex design is most commonly used.

236

5 Braking systems

5.3.5 Disc brakes For a disc brake (Figure 5.13), it holds: C* =

Brake piston

FU FU, left + FU, right FSp μpad + FSp μpad = = = 2 μpad : FSp FSp FSp

Brake pads

Brake pads

(5:33)

Brake piston

Hydraulic port Hydraulic port

Hydraulic port Brake disc

Fixed caliper brake

Brake disc

Fist-caliper brake

Figure 5.13: Principal functioning of disc brakes.

Disc brakes provide the braking force by pressing two brake pads onto either side of a disc, which is attached to the wheel in a concentric manner. The brake pads are fitted inside an U-shaped brake caliper, which encompasses part of the disc. The caliper itself is attached to a nonrotating part of the vehicle (Figure 5.13). Disc brakes are almost exclusively actuated by means of a hydraulic system. The most commonly seen types of disc brakes mainly differ in the way the brake calipers are mounted. In case of a fixed-caliper disc brake, two pistons are required that press the brake pads onto either side of the disc (Figure 5.13, left ). In this case the brake calipers and pistons are firmly connected to the wheel suspension. In case of a floating-caliper disc brake, the actual brake caliper is guided (floating) by a fixed brake carrier. With this construction type, only one piston is necessary to press the inner brake pads onto the disc. The outer brake pad is pressed against the disc indirectly due to reactive forces, thus sliding the brake caliper and brake pad along. Continued development leads to the fist-caliper disc brake (Figure 5.13, right), in which the brake carrier is not necessary anymore. The brake caliper encompasses the disc like a half-opened fist. This form of disc brake has largely prevailed in passenger cars because of their simple construction, lower temperature sensitivity, and greater ease of maintenance even compared to fixed-caliper brakes. Disc brakes have

5.3 Assembly components of the braking system

237

replaced drum brakes for most passenger cars, especially when considering the front axle. Reasons behind this can largely be found in their increased braking stability and better thermal loading capacity. When exposed to higher loads, the brake force losses are considerably smaller when compared to drum brakes. In particular, the dreaded “fading” phenomenon only occurs to far lesser extent. The disadvantages of disc brakes lie in the lack of self-amplification, and in their significant higher cost compared to drum brakes. Due to the higher cost for disc brakes, even modern vehicles, albeit the smaller and less expensive models, are still often fitted with drum brakes at the rear axle. This is possible because the rear axle is usually only responsible for 25–30% of the total braking force, therefore exposing the brakes to a much lower thermal loading. An additional reason why the use of drum brakes is often preferred on the rear axle is because disc brakes provide far greater construction difficulties when implementation the parking brake.

5.3.6 Brake discs Brake discs are normally made of gray cast iron or cast steel and are composed of a flat friction ring and a brake disc hub, at which they are fixed to the wheel hub using screws, so that they rotate together with the wheel. The contact forces are considerably higher compared to drum brakes. This results in higher heat development, which is compensated for by placing the brake discs directly in the airflow around the vehicle. Difficulties arise when the vehicle is driving slowly while simultaneously requiring a high braking force, for instance, during downhill driving. Internally ventilated brake discs are constructed with, in contrast to solid brake discs, radially arranged air-flow cooling channels, which provide a ventilating effect while driving. They are usually used on the front axle due to the higher braking load.

5.3.7 Brake pads During braking, the brake pads are pressed against a friction partner that rotates synchronously with the wheel. This causes a friction force in the opposite direction that slows down the wheel’s rotational motion, thus braking the vehicle. For disc brakes the friction pairs usually consist of two separate brake pads per disc. In drum brakes, the brake pads work in conjunction with the drum itself. An important characteristic of the brake pads is that they should be made of material for which the friction coefficient varies as little as possible with fluctuations in temperature and wear. They must be temperature resistant up to approx. 800 °C without vitrification and arising mechanical loads. Commercially available brake pads consist of a support plate made of steel or cast iron, a friction lining made of a complex

238

5 Braking systems

composite of different materials and an intermediate layer, the so-called underlayer. The friction coefficient between brake pad and brake disc are usually between 0.35 and 0.4. Variations in this friction coefficient should be kept as small as possible. Nevertheless, the friction coefficient tends to fluctuate depending on speed, braking pressure, and temperature. In particular, the friction coefficient decreases disproportionately from above 700 °C, which significantly lengthens the braking distance. This is known as fading (Breuer and Bill 2012).

5.3.8 Thermal behavior of brakes The power required by the brakes of an ordinary passenger car significantly exceeds that produced by its engine. About 90% of the heat generated under braking is temporarily stored in the brake disc. The remaining 10% flows into the brake pads. The stored heat must be discharged to the surrounding air as quickly as possible, through radiation and conduction. This inevitably leads to heating of the adjacent components, such as the caliper, rim, and vehicle suspension. A critical temperature is reached when the brake pads and fluid reach over 700  C. The braking fluid heats up due to conduction from the discs to the wheel brake cylinder, which in extreme cases could lead to the build-up of vapor in the hydraulic fluid and potentially a complete failure of the brake circuit (Breuer and Bill 2012). Furthermore, the temperature has a significant influence on the friction coefficient μpad between brake pad and brake disc. Taking this into account, the following relationship for the braking torque, with a given braking pressure pB , can be formulated as follows: MB = pB AK rB μpad ðpB , TB Þ,

(5:34)

where AK is the effective contact area between the brake pad and brake disc, and rB is the distance between the axle and the center of the brake pad. The sliding friction coefficient μpad between brake pad and brake disc depends on the effective braking pressure pB and brake pad temperature TB . This relationship can be approximated (Burckhardt 1991) and (Schuster 1999). If the sliding velocity is neglected, the friction coefficient will increase with rising temperature TB , until a maximum value is reached at the optimum temperature TB, opt , after which it starts declining again. Mathematically this relationship can be approximated by the parabola "  # TB − TB, opt 2 . (5:35) μpad ðTB Þ = μpad, max 1 − cP TB, opt

5.4 Brake circuit layout

239

The parameter cP is a dimensionless material constant that maps the temperature behavior of the interaction between brake disc and pad. Similarly, the dependence of the friction coefficient on the brake pressure can be approximated by "  2 # pB , (5:36) μpad ðpB Þ = μpad, pB = 0 1 − cT * pB where cT is another dimensionless material constant, μpad, pB = 0 is the friction coefficient at zero pressure, and p*B the maximum braking pressure. As a first approximation, the equation for the friction coefficient thus results from eqs. (5.35) and (5.36) and is formulated as follows: " "  2 #  # pB TB − TB, opt 2 · μG, max 1 − cP . (5:37) μpad ðpB , TB Þ = μpad, pB = 0 1 − cT * TB, opt pB

5.4 Brake circuit layout Due to the safety aspect related to braking systems, legal regulations stipulate that the transmission between the actuator and wheel brakes must be of at least twocircuit design. There are five possible brake circuit splittings that split both brake circuits in separate segments, all specified in DIN 74000 (DIN 1992). Figure 5.14 shows the two most common mappings: – One of these brake circuit splittings used today is the II-splitting, that is, the splitting of the brake system into a brake circuit on the front axle and a further brake circuit on the rear axle (front-/rear-axle mapping). In this case, each brake circuit of the main brake cylinder acts on one axle. This type of brake

II-mapping (rear/front axle mapping) 1

2

1

2

X-mapping

Figure 5.14: Most common brake circuit mappings (Reif 2011).

240

5 Braking systems

circuit splitting is primarily used for vehicles with high rear axle loads, since if the brake circuit on the front axle fails, there must still be sufficient braking effect on the rear axle to meet the legal requirements. – The most commonly used variant of brake circuit splitting today is diagonal splitting (X-mapping). Here, one of the brake circuits acts on a front wheel and the respective diagonally opposite rear wheel. The diagonal distribution can be applied today to almost all vehicle constellations. A disadvantage is the yaw torque that acts when a brake circuit fails due to the higher proportion of front axle braking force. Today, however, this disadvantage is at least mitigated, if not compensated, by the effect of the negative steering roll radius (see Chapter 3). Furthermore, basically possible, subdivisions are the HI, LL, and HH brake circuit layouts (not shown in Figure 5.14): – In an HI brake circuit splitting, one brake circuit acts on the front axle and on the rear axle, while the other brake circuit acts only on the front axle. – With the LL brake circuit splitting, each brake circuit acts on the front axle and on one of the rear wheels. – Finally, there is the HH brake circuit splitting, where each brake circuit acts on both the front axle and the rear axle. However, these variants are less common in passenger cars and are more likely to be used in light to heavy commercial vehicles. These distributions make use of wheel brakes with double brake pistons and separate brake circuit distribution per brake piston necessary. This type of wheel brake is rarely used in passenger cars for cost reasons.

5.5 Braking process The entire braking process includes all operations that take place between initiation of the actuator, including reaction times, and the end of the braking action (DIN/ ISO 1997–2001).

5.5.1 Reaction and response times When studying brake reaction times, a distinction should be made between the driver’s individual reaction time and the technical and/or mechanical delay caused by the vehicle’s systems. The driver’s reaction time tR is dependent on the state of mind and ability to react of each individual driver. It encompasses not only the time it takes to recognize and analyze a particular situation (danger recognition), but also the time it takes to

5.5 Braking process

241

actuate the brake pedals with the appropriate foot force. This duration, which is also dependent on the circumstances, lies between 0.3 and 1.0 seconds. During this time, the vehicle keeps moving without braking action applied. A short time span passes after the brakes have been actuated by the driver. This time span can be divided into two separate parts, one being the threshold time tS , during which the deceleration of the vehicle increases, and a time span tAS − tS , during which any delays in the system are overcome but no actual braking force is active. The remaining time tBmax indicates the time span during which the vehicle is subject to the maximum braking force resulting in the deceleration amax . Therefore, the total braking process consists of the sum of the total time: tA = tR + ðtAS − tS Þ + tS + tBmax .

(5:38)

Figure 5.15 shows an example of the relevant kinematic parameters changing over time during braking action. It shows a maximum braking maneuver from a constant velocity of v0 = 25 m=s, with typical time spans of tS = 0.2 s, tAS = 0.25 s, tR = 0.5 s (see Figure 5.16). This results in a total stopping distance sA of 55.3 m over a total time span of tA = 3.78 s. In this case, the effective braking time (neglecting the drivers reaction time) equals tBmax = 3.03 s.

Figure 5.15: Relevant times during the braking process.

Figure 5.16: Stopping distance.

242

5 Braking systems

5.5.2 Braking distances Braking distances have improved dramatically over the past decades, especially in poor road and weather conditions. On the one hand, this is due to the introduction of active driver assistance systems, such as brake assist or ABS (see Chapter 9), and also due to technical improvements to the brakes (brake pads and discs) and the significant advancements in tire quality. The importance of keeping the stopping distance as short as possible is shown in Figure 5.17. It shows the stopping distances in meters at different, but quite average, vehicle decelerations under braking and an initial speed of v0=100 km/h. Assuming an average braking deceleration of 12 m=s2 and a theoretical stopping distance of 32.15 m, the remaining impact velocities corresponding to lower braking decelerations and thus longer stopping distances are also plotted. 70

70 Stopping distance

Stopping distance/m

50

50.00

Residual speed at impact on obstacle after 32.15 m

40 32.15

33.55

30

45.64 40.61 38.58

40.82 36.74 35.07 35.36

42.87

60

57.74

54.01

45.39

48.23

40 30

28.87

20

20

20.41

10

10 0 0.00

50

Residual speed/(km/h)

60

0 12

11.5

11

10.5

10

9.5

9

8.5

8

Braking deceleration/(m/s2) Figure 5.17: Stopping distances and remaining impact velocities.

The diagram shows that a vehicle with an average braking deceleration of 8 m=s2 will still be travelling at a velocity of 57.74 km=h upon hitting the obstacle located at the 32.15 m mark. Based on the assumptions made in Section 5.5.1, as well a new assumption that the braking deceleration a increases linearly over the duration of tS , and remains constant after reaching the maximum value of amax , the stopping distance can be approximated by   1 1 1 (5:39) sA = v0 ðtR + tAS Þ + amax tS2 + amax ts + v0 tBmax + amax tB2 max . 6 2 2

5.6 Servo brakes

243

Thus, the stopping distance not only depends on the maximum braking deceleration (approximately 8 m=s2 with dry road conditions) but also on the driver’s individual reaction time and the inherent response time of the braking system. Furthermore, in this case it is assumed that the driver immediately fully applies the brakes, which is usually not the case. This explains the use of so-called brake assist systems (BAS), which, based on the pedal acceleration due to the driver’s input, detects an emergency braking situation and immediately generates maximum braking pressure. In the exemplary emergency braking situation with an initial velocity of v0 = 100 km=h shown in Figure 5.15, the total stopping distance is sA = 57.72 m. Here 18.70 m accounts for the reaction and response time, and sR = 12.50 m is solely due to the driver’s reaction time.

5.6 Servo brakes Unlike in the case of trucks, the braking system of passenger cars still relies on the driver’s muscular force as input, which is usually amplified by additional modules. It is therefore quite obvious to replace the muscular force input of the driver entirely by a corresponding actuator and to capture the driver’s intent by a sensor. An advantage of this procedure is the possibility to integrate additional assistance systems with relative ease when compared to conventional braking systems.

5.6.1 Electrohydraulic brakes (EHB) The electrohydraulic braking system is a form of servo brake and is completely decoupled mechanically from the brake pedal unless in redundancy mode during system failure. The required braking pressure is generated by a high-pressure pump in a gas pressure accumulator and is available to all parts of the braking system through a series of direction specific valves. The braking system consists of three clearly separate modules: – An electronic brake pedal, which houses a movement sensor that captures the driver’s intent, and a brake feedback actuator. – Four hydraulic wheel brakes. – An electrohydraulic control unit consisting of the high-pressure pump, a valve block, and an electronic control system. From the measured pedal pressure and displacement, the desired braking force is computed. The sensor signals from the brake pedal unit are transmitted to the control unit through a cable connection. There, considering other vehicle parameters such as wheel speeds, yaw rate, lateral acceleration, and so on, wheel-specific brake pressures are determined. The electrohydraulic control unit generates the required brake pressures by the appropriate actuation of the control valves. The

244

5 Braking systems

pressurized hydraulic fluid itself is drawn from the gas pressure accumulator. Due to the separation of brake hydraulics and pedal unit during normal operation, automated assistance systems such as ABS and ESP are free from feedback. Therefore, the feedback given to the driver by the pedal unit can be freely configured. The construction and design of this type of system allows for easy integration of brake assistance systems such as ABS, ASR, and ESP without significant additional hardware modifications. Furthermore, apart from the mechanical fallback system present in an EHB, it highly resembles a brake-by-wire system that shares some of the advantages of the EMB systems (see Section 5.6.2). Advantages of the system are as follows: – excellent braking dynamics, – easy integration of driver assistance systems such as Hill Holder6, dry braking of the brake discs,7 – fundamental freedom in brake pedal feedback, – freely chosen feedback design of brake pedal, – simple implementation of auxiliary power braking system, and – independent of partial vacuum of the engine. However, the system also has certain disadvantages that have prevented widespread use: – the need to provide a mechanical or other fallback condition in the event of system failure, for example due to an electrical issue, – high costs, – because of cost-related arguments, only one brake circuit is available during emergency fallback operation, making it more difficult for weaker drivers to initiate sharp braking.

5.6.2 Electromechanical brakes (EMB) and brake-by-wire systems Electromechanical brakes operate without using a hydraulic system; therefore, no brake fluid is required. These are also referred to as dry brakes. Similar to EHB, the system consists of a brake pedal sensor with integrated control unit, regulating the four-wheel brakes. These wheel brakes are actuated purely electrically, whereas EHB uses hydraulic actuation.

6 Hillclimb Assist: Automated support system that prevents the vehicle from rolling backward during steep hill ascents. 7 Dry braking: Light application of brake pads onto brake discs to achieve optimum brake response in dry conditions.

5.6 Servo brakes

245

Therefore, the high-pressure pump and valve block are made redundant. Instead, four separate electromechanical brake actuators are used. The EMB has multiple advantages compared to EHB. The system consists of a smaller number of separate components, is more environmental friendly due to the absence of hydraulic fluid, and requires far less maintenance. Another big advantage is the fundamental independency on the existence of a mechanical transmission linkage between the brake pedal and the wheels, creating new packaging possibilities in passenger cars. A disadvantage is that to ensure two independent brake circuits, both a redundant signal as well as a redundant power grid are required. This vastly increases the demand on the vehicle’s electrical system, which makes using the conventional 12 V electrical system insufficient. These serious disadvantages, as well as the significant additional effort required to realize a mechanical fallback system usually required in safety-sensitive vehicle modules, have so far prevented large-scale usage of this braking system. However, there have been many attempts in recent years to introduce such a system, often using novel actuation principles such as the electronically controlled wedge brake (Gombert and Hartmann 2006). Further advantages and disadvantages of EMB are mostly identical to those of the EHB. Figure 5.18 shows a comparison between the aforementioned braking systems.

Master brake cylinder with brake booster and reservoir

Pedal module with pedal travel sensor and force feedback

Hydraulic unit with delivery pump and control unit

ECU

Pedal module with pedal travel sensor and force feedback

Electro hydraulic actuator with pressure accumulator and control unit Battery 1

Front axle

Rear axle

Conventional braking system

Front axle

Rear axle

Electrohydraulic braking system

Front axle

Battery 2 Actuator

Rear axle

Electromechanical braking system

Figure 5.18: Comparison of braking systems, partly according to Reif (2010).

6 Propulsion systems Establishing a suitable propulsion system was one of the main prerequisites that eventually led to the success story that is the automobile industry. While Electric Motors (EM) and Internal Combustion Engines (ICE) where equally represented as forms of propulsion since the start of the twentieth century, the internal combustion engine became the industry standard in the long period to follow. The reason behind this was the low achievable energy density in electric batteries. It was not until recent years that a paradigm shift began, triggered by a significant increase in electric drive efficiency, the looming depletion of fossil fuels, and far higher energy densities in the electric energy storage systems and last but not least the discussion about climate change. Nonetheless, the internal combustion engine will continue to play a dominant role for at least another 20 years, though expectedly more and more as part of a hybrid propulsion system (Schramm and Koppers 2013).

6.1 Basic types of powertrains A principal distinction must be made between the driven axles on the one hand, and the location of the drive unit on the other. Both factors together describe the topology of the power train. An overview of the most commonly seen powertrain structures, as well as an estimate of their respective market shares in Germany is given in Table 6.1. Nearly 99% of all vehicles have the combustion engine located in the front, with the rare exception of rear or middle placed engines as seen in some vehicle types. In 75% of all vehicles, the combustion engine is transversely mounted in the front end while the front axle is driven. This layout is a popular platform strategy due to the significant integration benefits it provides. An example of this is given by the so-called Modular Transverse Matrix1 designed by the VW-Group (Szengel, Middendorf et al. 2012). Positioning the engine directly above the driven axle results in the particular design advantage that no additional drive shafts are required. Approximately 16% of vehicles display the traditional configuration in which the engine is front mounted longitudinally and drives the rear axle. A disadvantage of this configuration is the need for additional drive shafts (cardan shafts), to transfer the engine torque from the front end of the vehicle to the rear axle; however, advantages are also present, namely the often-preferred driving dynamics and the possibility to install larger engines. Allwheel drive versions of the before mentioned configurations take up 3% and 4% respectively. The drive topologies described so far solely consider the use of internal combustion engines. The integration of electric drives into the powertrain considerably 1 German: Modularer Querbaukasten (MQB). https://doi.org/10.1515/9783110595703-006

248

6 Propulsion systems

Table 6.1: Powertrain topologies in combustion engine-driven vehicles with their respective market share (Grote and Feldhusen 2012, Ried 2014).

front

75%

front-lateral all-wheel

3%

front

1%

front-longitudinal rear

16%

All-wheel

4%

Values have been rounded off.

increases the range of possible and meaningful topologies. An up-to-date overview of the most frequently used versions in combination with a front-mounted internal combustion engine is shown in Table 6.2. An exemplary visualization of a hybrid propulsion system is shown in Figure 6.1. In the case of parallel hybrid versions, it is possible to drive either purely electric or purely using the combustion engine, see Section 6.4.4. In a power-split arrangement, the electric motor is required to operate while the vehicle is powered by the internal combustion engine. In a serial structure, only electric drives can be used. The combined arrangement allows for both serial and parallel operations.

6.2 Propulsion requirements for motorized vehicles The propulsion requirements on motorized vehicles initially result predominantly from the acting forces that hinder vehicle motion. Additionally, there are power requirements on secondary vehicle systems. These include, among others, and depending on the drive type: – the oil-and water pumps of the engine, – support systems for vehicle control, such as power steering, – heating and climate control systems, and – the alternator, where the alternator supplies the required electric energy to ensure proper functioning of all electric components and systems in the vehicle, see Chapter 8.

6.2 Propulsion requirements for motorized vehicles

249

Table 6.2: Hybrid drive topologies (Ried, Karspeck et al. 2013).

parallel P-2

Integration EM between ICE and two clutches

P-DCT

P-Axle Split

Connection EM to transmission gears of the double clutch transmission (DCT)

Drive ICE and EM on different axes

PerformanceSplit

Serial

Combined

Hybrid transmission with two EM & planetary gears. Variable transmission (eCVT4)

EM 1 (motor) connected to axle; ICE and EM 2 (generator) mechanically linked

Combination of serial and parallel topology

DCT: Double Clutch Transmission (Gearbox). eCVT: Continuous Variable Transmission realized through electronic components.

A schematic visualization of energy flows in a typical passenger car powered by an internal combustion engine is shown in Figure 6.2.

6.2.1 Driving resistance Driving resistance in its totality is the sum of all forces a vehicle must overcome in order to obtain and maintain a desired velocity and acceleration on either a flat or inclined road. The physical interpretation of driving resistances is the forces that act in the opposite direction of vehicle longitudinal motion. A division of the driving resistances is given by: – Rolling resistance, – frictional forces on the drivetrain, – air resistance, – gravitational resistance on inclines, and – inertial forces. Resistance forces caused by the air and the tire-road contact as well as friction forces in the drivetrain convert part of the vehicle’s kinetic energy into heat, most

250

6 Propulsion systems

Audi A3 Sportback e-tron

Audi

Antriebsstrang-Hybridkomponenten Drivetrain-hybrid components 06/13 E-Bremskraftverstärker Hochvolt-Batteriemodul electric brake booster high voltage battery module Leistungselektronik power electronics

Kraftstofftank fuel tank 12V-Batterie 12 volt battery

Batteriekühlung Battery cooling

1.4 TFSI Motor 1.4 TFSI engine 110 kW (150 PS) 250 Nm

Ladeanschluss charging point Hochvolt-Leitungen high voltage wiring harness

E-Maschine electric motor 75 kW/330 Nm

6-Gang e-S tronic Getriebe 6 speed e-S tronic gearbox

Figure 6.1: Hybrid-Powertrain © Audi.

Supply Internal combustion engine extraction and refinery Transport and gas station Exhaust

Drivetrain

Vehicle and wheel

Cooling water and radiation Water, oil Auxiliary aggreGear gates differenAir resistance tial Roll resistance Rotational movement

Well to tank

Tank to wheel

Translational movement Brake

Figure 6.2: Energy flows in a motorized ICE vehicle (schematic illustration) (Sankey Diagram).

6.2 Propulsion requirements for motorized vehicles

251

of which is released to the surrounding air. When driving on an inclined slope, kinetic energy is converted to potential energy, part of which is converted back into kinetic energy during downhill driving. Inertial resistance results from the acceleration of translational as well as rotational moving parts of the vehicle. In the following section the driving resistances will be represented by their respective forces; Table 6.3. Table 6.3: Driving resistance forces on the motor vehicle. Symbol

Description

FR

Wheel resistance

FS

Gravitational resistance (inclines)

FB

Inertia

FL

Air resistance

The total driving resistance becomes FW = FR + FS + FB + FL .

(6:1)

6.2.2 Wheel resistance The wheel resistance is composed of forces that result in a torque on the wheels acting in the direction opposite of vehicle motion. 6.2.2.1 Rolling resistance force The rolling resistance force results from damping properties of the tires, which causes a shift in the point of application of the tire-road normal force, placing it outside the theoretical contact point in the direction of travel; see Chapter 2. On paved roads the rolling resistance is mostly determined by the loss of work because of deformation processes of the tire. The most influential factor is the travel amplitude, which depends on the tire deflection, wheel load FN and tire pressure p, as well as on the vehicle’s velocity v dependent travel frequency. To simplify the consideration regarding rolling resistance, the so-called rolling resistance coefficient fRL is introduced. This yields the rolling resistance force FRL = fRL FN .

(6:2)

The rolling resistance coefficient is generally not a constant parameter. It depends on tire size, structure, and materials used, as well as a non-linear relation to the

252

6 Propulsion systems

normal force FN . Other dependencies are current vehicle speed v, tire pressure p and the road conditions (Table 6.4). The dependency on tire pressure can be approximated by the relationship: 1 FRL ⁓ pffiffiffi . p

(6:3)

Table 6.4: Values for rolling resistance coefficients of passenger car tires on different road surfaces. Road surface

Rolling resistance coefficient fRL

Asphalt Concrete Cobblestones Gravel

.–. .–. .–. .

6.2.2.2 Surge resistance In case of water on the road surface, the tires need to force water away to the side that has accumulated in front of the tire. This creates a surge resistance force FRS , which is dependent on the current vehicle speed and the volume of water that is displaced per unit of time. In turn, the volume to be displaced depends on the tire width b as well as the water height. The relationship can be described by FRS ⁓ b · vn ,

(6:4)

where b is the tire width and n is a coefficient which takes a value of approximately 1.6 when assuming a water height of 0.5 mm (Wallentowitz and Mitschke 2006). In case the water height and velocity exceed a limit, the surge resistance becomes independent of water height and velocity resulting in the tires’ ‘float up’, which is commonly known as aquaplaning. 6.2.2.3 Frictional resistances in bearing and wheel brakes FRR = fRR FN .

(6:5)

FRV = fRV FN .

(6:6)

6.2.2.4 Toe-in resistance

6.2 Propulsion requirements for motorized vehicles

253

6.2.2.5 Cornering resistance The cornering resistance essentially arises from the tire slip angles, which lead to a force counteracting vehicle longitudinal motion. It is approximately proportional to the 2

square of the centripetal force during cornering rv (Wallentowitz and Mitschke 2006): K

FRK = fRK

 2 2 v FN . rK

(6:7)

6.2.2.6 Spring resistance The spring resistance FRF is caused by the deflection of the wheels, as well as through conversion of kinetic energy into heat through the suspension dampers, longitudinal slip and changes in the wheels’ circumference, and dynamic axle kinematics (Haken 2013). 6.2.2.7 Total wheel resistances When all the before mentioned components that contribute to the wheels’ resistance are added up it leads to the total wheel resistance FR = FRL + FRS + FRR + FRV + FRK + FRF .

(6:8)

In real life, the rolling resistance is by far the largest contributor and is responsible for more than 80% of the total wheel resistance forces. Therefore, in further considerations the total wheel resistance is set equal to the rolling resistance (Haken 2013): FR ≈ FRL = fRL · FN = fRL · mg · cosα ≈ fRL mg.

(6:9)

6.2.3 Air resistance (Drag) The air resistance, also known as drag, is caused by motion of the vehicle resulting in a displacement of the surrounding air on the one hand, and by naturally occurring wind conditions on the other. The overall resulting force FL depends quadratically on the relative velocity between the vehicle and ambient air, the specific density of air ρL , the cross-sectional area of the vehicle A, and the drag coefficient cW : FL = cW A

ρL ðv + vW Þ2 . 2

(6:10)

The wind velocity vW is highly dependent on weather conditions and is usually far smaller than the vehicle’s speed. Therefore, it will be neglected from here onwards. The drag coefficient cW is dependent on the vehicle shape as it determines how air flows around the vehicle, resulting in frictional and compressive forces. Besides

254

6 Propulsion systems

how air flows around the vehicle, airflow through air intakes and cooling vents also plays a role (Figure 6.3).

Friction forces Pressure forces

Figure 6.3: Emergence of air resistance.

6.2.4 Gravitational resistance (inclines) When driving uphill on an inclined road with inclination angle α, the gravitational force caused by the vehicle’s weight mg is split into a normal force FN = m · g · cos α

(6:11)

perpendicular to the road surface and a downhill force FS = m · g · sin α

(6:12)

in the opposite direction of vehicle motion (Figure 6.4). The road inclination is usually not described as an angle, but as a gradient q per 100 m of horizontal distance: sin α ≈ α ≈ tan α =

Figure 6.4: Gravitational resistance.

q . 100

(6:13)

6.2 Propulsion requirements for motorized vehicles

255

In eq. (6.13) it is considered that the maximum road inclination, apart from few exceptions in mountainous terrain, is normally not larger than 10o (corresponding to a 17.6 % gradient). Therefore, sin α can be approximated by α.

6.2.5 Inertial resistance During vehicle acceleration not only translational inertia resistance FT = mV €x has to be overcome, but all rotational inertias of masses located in the drivetrain of the vehicle need to be included. These rotational masses are (Figure 6.5): – The resulting moments of inertia of the front and rear wheels together with their respective brakes JR, v und JR, h , – the resulting moment of inertia of the drive shafts and the wheel gears JA , and – the resulting moment of inertia of the engine JM together with the corresponding gears. From the calculation of kinetic energy for each individual axle  1 JR, i ’_ 2i + JA, i ’_ 2A, i + JM, i ’_ 2M, i = 2 0 1 1@ = JR, i + JA, i i2A + JM, i i2A i2G A’_ 2i , i = v, h, ffl} 2 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl

Ekin, i =

(6:14)

Ji

the total moments of inertia for the front and rear axles can be computed as Ji = JR, i + JA, i i2A + JM, i i2A i2G .

(6:15)

Combining this result and NEWTON’s second law, the effect of rotational masses on the inertial force can be stated as ! 1 X Ji FB = 1 + mV €x = λmV €x, (6:16) mV i = v, h rstat, i rdyn, i where λ is a rotational mass load factor which depends on the gear that is engaged and on the overall design of the drivetrain. Typical values for λ are in the range of 1.05 . . . 1.5.

6.2.6 The traction force equation To determine the required driving force for a motorized vehicle an equation regarding impulses on the vehicle body can be used (Figure 6.6):

256

6 Propulsion systems

1 2

1 ,

2

.

. .

.

,

,

1 2

,ℎ

1 ,

2

,ℎ

Figure 6.5: Rotating masses in the drivetrain.

S 3/4

1/2 ,1/2

,3/4

ℎ

1/2

3/4

Figure 6.6: Free body diagram of a vehicle.

  4 4 X X mV − mRi €x = − FL − mV g sin α + Xi i=1

(6:17)

i=1

where Xi are the axle forces in longitudinal direction. Accordingly, one obtains the impulse and rotational equations for a single wheel (Figure 6.7): mRi €x = − Xi + Fx, i , € i = Ji Ji ’ )

€x rdyn, i

(6:18)

= Mi − rstat, i Fx, i − ei Fz, i

Ji Mi ei €x = − Fx, i − Fz, i rstat, i rdyn, i rstat, i rstat, i

(6:19)

257

6.2 Propulsion requirements for motorized vehicles

, ̈

,

,

, ,

Figure 6.7: Free body diagram of a wheel.

where Mi are the wheel driving torques, Fx, i are the wheel forces in Xi direction, and Fz, i are the wheel normal forces. Furthermore, rstat indicates the static wheel radius and rdyn the dynamic wheel radius, see Chapter 2. By combining the eqs. (6.17)–(6.19), the set of impulses for a single wheel can be written as:   4 X Ji €x mV + r r i = 1 stat, i dyn, i (6:20) 4 4 X X Mi ei − Fz, i . = − FL − mV g sin α + r r i = 1 stat, i i = 1 stat, i From eq. (6.20) the traction force equation that summarizes the sum of all road resistance forces is obtained by solving the sum of the driving wheel forces in the longitudinal direction and the rotational load factor λ from eq. (6.16): Fdrive =

4 X MRi = FR + FL + FSt + FB = r i = 1 stat, i

1 = fr mV g + cW AρL v2 + mV gα + mV λ€x = 2   λ€x ρ mV g + cW A L v2 . = fr + α + 2 g

(6:21)

The force Fdrive describes the resulting driving force on the vehicle to maintain the current driving condition. This force can either be positive (driving) or negative (braking). Accordingly, the sum of the required driving or braking power to the driven wheels can be stated as:

258

6 Propulsion systems

PA =

4 X i=1

X  4 MRi rstat, i MR rstat rstat v= MRi ’_ Ri = v=Z v ≈ Zv r r r r rdyn stat dyn i = 1 stat, i dyn, i |{z}



 λ€x ρ mV gv + cW A L v3 . = fr + α + 2 g

Z

(6:22)

Because no significant wheel slip occurs during normal driving conditions, the static wheel radius from eq. (6.16) can be considered equal to the dynamic wheel radius rdyn . The power PA to the driven wheels is the effective mechanical power to be applied to the wheels to maintain the desired driving conditions defined by the driving velocity and current vehicle acceleration €x. At this point it should be noted that this is not necessarily the full power available from the drive unit (engine). Additionally, the power output from the drive unit has to regulate secondary vehicle systems and must also overcome internal drivetrain resistances in components subject to friction such as bearings. This can most suitably be represented with the efficiency ηA of the drivetrain de-coupled from the engine, see Section 6.6.1. From eq. (6.22), it is already possible to make simple statements about the performance and drivability of a vehicle. This includes, for example, the maximum achievable speed of a vehicle considering a flat road. This can be estimated if one assumes that for very high and constant speed, the air resistance dominates the total driving resistance of the vehicle. Equation (6.22) can then be simplified when α = €x = 0 and fr  1 to PA = cW A

ρL 3 v . 2

(6:23)

In case PA is taken as the maximum available engine power Pmax and all occurring drivetrain losses are considered using the before mentioned factor ηA , an approximation of the maximum achievable vehicle speed can be defined using the formula sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2ηA Pmax . (6:24) vmax ≈ cW AρL In a similar manner, the maximum achievable acceleration can be estimated. A somewhat standardized measure of vehicle acceleration is the duration to speed the vehicle from 0 to 100 km/h. This can be approximated when realizing that the driving energy of the vehicle is essentially converted into kinetic energy. For example, the kinetic energy required to reach a target velocity of vtarget is

6.2 Propulsion requirements for motorized vehicles

1 Ekintarget = mV v2target . 2

259

(6:25)

R The kinetic energy in eq. (6.25) is essentially derived from the average power P that the engine is able to provide during acceleration. Therefore, to achieve a veloc R ≈ Etarget is required. If one ity of vtarget in a timespan of ttarget , an average power of P ttarget 1  R ≈ η Pmax , a rough estimate can be obtained for the time renow approximates P 2 A quired to reach the target speed 1 mV . ttarget ≈ v2target · ηA Pmax 2

(6:26)

6.2.7 Ideal drive- and output mapping In case the acceleration is set to zero in eq. (6.22), the result is a progressively increasing driving curve that describes the traction force required to maintain a constant vehicle velocity. Figure 6.8 shows the relation between target speed and traction force needed, that is, the ideal drive output mapping. Either during acceleration or deceleration using the drivetrain, which is common in downhill driving situations, additional traction force components are required. For this purpose, two extra lines have been drawn in Figure 6.8 that are parallel to the stationary driving curve. The shaded area describes the desired range of the to be provided traction force.

Traction force 󰛧 Max. acceleration/inclination

Stationary force w/o inclination Velocity 󰜈

Figure 6.8: Ideal drive output mapping (Mitschke and Wallentowitz 2014).

In real life however, not all of the shaded area is realizable. It must be taken into account that the shown available tractive force can usually not be applied in full while driving off from a standstill due to the tires not having the required amount of friction. Furthermore, the total transferable driving force is of course limited by the maximum performance output of the engine. The latter leads to a hyperbolical force

260

6 Propulsion systems

PA between traction force Z and engine power PA . v Overall, this results in the area shown in Figure 6.9. A drive unit should therefore be able to cover this area as much as possible.

curve due to the relationship Z⁓

Traction force 󰛧

Traction limit Power limit Stationary force w/o inclination Velocity 󰜈

Figure 6.9: Ideal drive mapping taking into account traction-and engine performance (Mitschke and Wallentowitz 2014).

6.3 Tangential force transfer tire-road contact Using similar methods that led to the optimum brake force distribution, the drive force distribution can also be determined. The corresponding distribution can be combined with the brake force distribution from Chapter 5 to obtain a more general representation. In this section the general representation will be discussed, and a single line corresponding to both cases will be determined. Using NEWTON’s second law in the direction of travel, one obtains the relationship b=

€x  x, h , = Fx, v + F g

(6:27)

and, from Chapter 5, the normalized dynamic wheel loads z, v = lh − h · €x , F z, h = lv + h · €x , F l l l g l g

(6:28)

including the boundary condition €x = μ. g After some algebraic computations, this yields sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 l lh l h  x, h = − F − F x, v − Fx, v , 2h 2h h

(6:29)

(6:30)

6.3 Tangential force transfer tire-road contact

x, v = − lv + F 2h

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 lv l  + F x, h − Fx, h , 2h h

261

(6:31)

x, v · F x, h > 0, Figure 6.11. Interesting in this relationship are the cases for which F meaning that the longitudinal forces on both axles have the same sign. It is now possible to visualize the divisions of tire force on the rear and front axle in one x, h < 0. Additionally, x, h < 0 and eq. (6.30) for F diagram by evaluating eq. (6.31) for F Figure 6.11 shows the graph of the straight-line eq. (6.27), which represents constant acceleration.

Figure 6.10: Tangential force transmission between tire-road contact surfaces.

– Fx,v

0.5 0.8

Drive

0.3 0.6

A

0.0 0.4 –0.3

0.2

–0.5 –0.2

–0.8

–1.3 –1.5 –0.5

0.1 Brake

–1.0

–0.6 –0.8 B 0.0

0.5

Figure 6.11: Tangential force diagram.

1.0

̅ Fx,h

2.0

262

6 Propulsion systems

The extreme values A and B are also marked and represent the conditions for which x, v = 0), and respectively the rear ‘lifting’ of the front axle under acceleration (A,F x, h = 0) occurs. These conditions are generally not seen for axle under braking (B, F passenger cars in real-life situations, although these conditions can be of importance when considering motorcycles (Breuer and Bill 2012).

6.4 Power sources Nearly since the start of the motorized age, the internal combustion engine has dominated as a power source in motorized vehicles. In the next few years a shift toward at least partially electrically powered vehicles will take place. For this reason, both power sources as well as hybrid systems will be discussed in the following section. In order to not exceed the scope of this book, only the basic topics are dealt with in brief. For more background literature, the reader is referred to the works of van Basshuysen and Schäfer (2012) and Todsen (2012) for combustion engines as well as Keichel and Schwedes (2013) for electric drives.

6.4.1 Combustion engines Since the conception of motorized vehicles, the piston-driven internal combustion engine (ICE) has dominated as the power unit of choice. Although, due to the specifications and physical constraints related to this engine type, additional components are required to obtain a useful working engine for use in motorized vehicles. These include a speed and torque converter, as well as a clutch to enable start-up and gear changes. Both of these components are found in most manual or automatic variants. Internal combustion engines belong to the overarching class of combustion engines. The basic working principle of combustion engines is the conversion of chemical energy into mechanical energy through the combustion of an air and fuel mixture. To achieve a controlled combustion a combustion chamber is required, of which many different designs are possible depending on the desired specifications of the engine. The explosion of the air-fuel mixture that occurs during combustion inside the combustion chamber produces hot pressurized gases, which in turn move the piston which is located inside the cylinder. Figure 6.12 shows a representation of the moving parts (crankshaft, crank mechanism, pistons, camshafts, and valves) without the engine housing and other assembly parts. The engine housing (Figure 6.13) contains the cylinder, in which the piston moves up and down. Via the connecting rods, the pistons’ translational movement is converted into rotational motion of the crankshaft. The cylinder head is mounted on top of the engine housing, or case, and contains the combustion chamber as well as

6.4 Power sources

263

Camshaft

Piston Connecting rod

Crankshaft

Figure 6.12: Piston engine without housing and auxiliary aggregates.

the inlet and outlet ports and valves. The inlet port is connected to the intake system. The preparation of the air-fuel mixture takes place either in the carburetor or directly in the intake manifold/combustion chamber (fuel injection). The outlet ports lead to the exhaust pipes and the catalyst as well as additional exhaust aftertreatment systems where toxic components of the exhaust fumes are filtered out. The inlet and outlet valves open and close the connection to the combustion chamber. The valves are controlled by either a rigid or adjustable camshaft, which rotates at half the crankshaft speed. Different types of internal combustion engines (such as the WANKEL2 Engine) have not been able to compete in the open market and will therefore not be considered further in this book. One can distinguish internal combustion engines by the way the air-fuel mixture is prepared, injected, and ignited, and thus also by the underlying thermal processes that take place. The most commonly seen engine types are the OTTO3 or Petrol Engine and the DIESEL4 engines. Other engine types that rely on the principles of a heat power process have also been conceived, such as steam engines or STIRLING5 engines. However, the heat production does not necessarily need to be generated by combustion. These engine types as well as continuous combustion engines such as rockets, and gas turbines will not be dealt with in this book.

2 Felix Wankel (1902–1988): German businessman and self-taught mechanical engineer and inventor of the Wankel engine named after him. 3 Nicolaus August Otto (1832–1891): German inventor, who was engaged in the development of engine components. The OTTO cycle was named in his honor. 4 Rudolf Diesel (1858–1913): German Engineer and Inventor of the DIESEL engine. 5 Robert Stirling (1790–1878): Scottish pastor and inventor of the STIRLING engine named after him.

264

6 Propulsion systems

Intake camshaft and intake valve

Exhaust camshaft and exhaust valve

Inlet duct

Outlet duct

Piston

Connecting rod

Crankshaft

Figure 6.13: Cross-section of the cylinder head of a reciprocating engine (schematic representation).

6.4.1.1 Basic operation Typical in piston engines is the repetitive nature of the process cycle. See Figure 6.14 for an example of the Petrol Engine: 1. Aspirating the air or mixture (Stroke 1): When the intake valve is opened, and the outlet valve is closed, the piston moves downwards, sucking in the air-fuel mixture. 2. Compressing and possibly injecting the fuel (Stroke 2): Shortly after reaching the bottom dead center (BDC), the inlet valve is closed. After which the piston starts moving upwards and compresses the mixture. 3. Ignition and power stroke (Stroke 3): Shortly before reaching the top dead center (TDC), the air-fuel mixture is ignited by a sparkplug (Petrol Engine) or ignites due to the high pressure (DIESEL Engine). This exerts a force on the top of the piston, which thereby moves downwards and transmits the force to the connecting rod and generates the driving torque to the crankshaft. 4. Exhaust (Stroke 4) Opening outlet valve: Shortly before reaching bottom dead center the outlet valve is again opened. After reaching the top dead center the outlet, or exhaust valve is closed. In between is

265

6.4 Power sources

the so-called valve overlap, which allows an increase in the amount of mixture sucked in. The optimum timings are both speed-, as well as load-dependent and can be optimized by appropriately adjusting the camshaft. 󰑝 󰑝󰑧 OV

Pressure Profile

IV

󰛾

󰑝󰑢

IO

BDC: bottom dead center

Combustion

TDC: top bottom dead center IV: inlet valve OV: outlet valve Ignition IO: IV opens IC: IV closes OO: OV opens OC: OV closes 󰑝󰑧 : maximum pressure IC

Pressure curve without combustion point

Ignition delay

OO

IO

OC

󰛾 /°

OC TDC

TDC

BDC

󰑕AV

BDC

TDC

Valve lift

󰑕EV

0

Intake

180

Compress

360

Expand

540

Exhaust

󰛾 /° 720

Figure 6.14: Basic working principle of the Petrol Engine.

The detailed characteristics of each individual stroke depend on the design and construction of the engine. Much progress has been made in this field in recent years (Reiff 2016). 6.4.1.2 Combustion processes The most important combustion processes occurring in piston engines can fundamentally be described by the SEILIGER6 process. This can be understood as an idealized thermodynamic comparison process. It describes the work done by the piston engine under ideal conditions, during which the assumption is made that an ideal gas with constant specific heat is used as working medium and no flow losses occur during the gas exchange. When applied to the DIESEL engine – the SEILIGER process includes the following idealized process steps; Figure 6.15: – 1–2: Isotropic compression. The gas in the cylinder is isotropically compressed without the occurrence of heat exchanging with the environment.

6 Miron Pavlovich Seiliger (1874–1952): Russian physicist and university lecturer.

266

6 Propulsion systems

– 2–3: Isochoric7 heat supply. The mixture is ignited and combusts under constant volume (isochoric) and increasing pressure. – 3–4: Isobaric8 heat supply. Additional heat supply happens under constant pressure (isobaric), as the piston moves downwards and volume increases. – 4–5: Isotropic Expansion. The piston continues to move downwards without further heat supply, whereby the pressure decreases as the volume increases. – 5–1: Isochoric heat removal. The unused residual heat created during the gas exchange is removed. This process takes place arbitrarily fast at a constant volume, after which the next cycle begins.

Pressure / Pa 3=

3

4

2

4

2

5

5 1

1 2=

3

4

3 Specific volume / ( )

1

Figure 6.15: p − V Diagram of the SEILIGER cyclic process.

The most important occurrences that happen during this process are the constant volume processes and constant pressure processes. The isochoric process describes, in a strongly idealized manner, the combustion process in the Petrol Engine, whereas the isobaric process fundamentally depicts the processes that occur in the DIESEL engine. Both processes are shown according to their respective p − V diagram in Figure 6.16. The realistic process for a Four-stroke petrol engine is schematically shown in Figure 6.17. The area enclosed below the upper curve corresponds to the work done by the pistons. The area enclosed by the lower curve corresponds to the

7 Isochoric: State change at constant volume. 8 Isobaric: State change at constant pressure.

6.4 Power sources

Pressure / Pa 3 3

2

2

267

Pressure / Pa 2 3 3

=

2 4

2

=

3

4

=

4

4 1

4

4

1

Specific volume

=

1

Specific volume

Figure 6.16: p − V Diagram of the SEILIGER processes for OTTO (left) and DIESEL combustion (right).

3

p Combustion

Expansion

2

Ignition

Compression

4 5 1

0 Vc

VH UDC

Gas exchange

V LDC Piston travel

Figure 6.17: Real combustion process (Four-stroke petrol process).

losses due to gas movement, for example, the work required for the necessary replacement of the mixture. One of the most widespread combustion processes is the Four-stroke petrol process, which is characterized by the following process steps (Figure 6.18): – 0→1: Suction of fuel-air mixture (1st stroke) – 1→2: Compression of the mixture (2nd stroke) – 2→3: Igniting the mixture (≈ isochoric heat supply) – 3→4: Expansion (3rd stroke) – 4→5: Exhaust ≈ isochoric pressure reduction – 5→0: Removing the exhaust gases (4th stroke)

268

6 Propulsion systems

1. Cycle EV

AV

p

p

V Stroke 1: Intake

2. Cycle

p

V Stroke 2: Compress p

V Stroke 3: Ignite and work

V Stroke 4: Exhaust

Figure 6.18: Working process of a Four-Stroke Petrol Engine.

The implementation of the combustion process can be differentiated according to the time sequence of the individual strokes. There are both Two stroke and Four stroke combustion processes: – In a Four-stroke process, the before mentioned strokes are carried out in 4 cycles. A stroke can therefore be defined as either an upward or downward motion of the piston. This means that during each cycle, the crankshaft rotates twice ði = 0.5Þ. – In a Two-stroke process, all four steps are carried out in only two movements of the piston. This means a part of the process step decompression must take place outside the cylinder. The crankshaft will rotate once during each cycle. (i=1).

6.4.1.3 Comparison between Petrol- and DIESEL engines Some characteristics for the Petrol and DIESEL engines are shown in Table 6.5. Other fundamental differences between the Petrol and DIESEL engines are stated below: – DIESEL engines generally deliver higher maximum torque levels compared to petrol engines. Although in modern Petrol engines this difference is often reduced due to the addition of turbochargers. – The specific fuel consumption be (see eq. (6.53)) is usually considerably higher for petrol engines than for DIESEL engines. This is especially true during low rpms and during idling. – The rpms the engine makes are considerably higher for Petrol engines than for DIESEL engines.

6.4 Power sources

269

Table 6.5: Comparison Petrol and DIESEL engine. Properties

Petrol engine

DIESEL engine

Mixture formation

External and internal (direct injection) mixture formation

Internal mixture formation

Ignition

Spark plug

Self-ignition

Air-fuel ratio / Compression

:–: / – bar

:–: / – bar

Temperature during compression

– °C

– °C

Thermal comparison process

Constant volume

Constant pressure

6.4.1.4 Determination and assessment of engine power and efficiency Determining the performance of the engine and all the additional components is usually done according to standardized conditions, which have been defined in the industry standard (DIN 1997). Measuring of performance numbers must take place under strictly specified environmental conditions: – Environmental temperature TU = 298 K, – Environmental air pressure pU = 990 mbar. The power rating delivered to the crankshaft PM is computed by using the rotational torque MM and the angular velocity ωM of the crankshaft PM = MM ωM = 2πMM nM .

(6:32)

The total cylinder volume VH is used to describe engine size VH = nZ

π 2 D hZ . 4 Z

(6:33)

In eq. (6.33), nZ indicates the number of cylinders, DZ denotes their individual diameter, and hZ is the piston stroke. To enable accurate comparisons of different engines, the specific parameters of the engine are related to its displacement. This yields the specific engine performance PMe =

PM . VH

(6:34)

With the so-called effective mean pressure peff , which is a proportionality constant, and the total engine volume VH of the engine the total engine performance results in PM = i nM peff VH .

(6:35)

270

6 Propulsion systems

The maximum performance Pmax of the engine is referred to as rated power and the corresponding revolutions per minute nmax is known as the rated rpm.9 The performance calculated by eq. (6.32) clearly has a direct relationship to the cylinder size of the engine. Therefore, this engine characteristic is often used to compare differently sized engines. One measure of work delivered by the engine is the before mentioned mean pressure, which is defined as the (assumed) constant pressure inside the combustion chamber. It performs the same work as the actual combustion chamber pressure, which varies in time. When considering the torque applied to the clutch, the effective mean pressure is used. It can be calculated as follows: peff =

PM 2π MM = . · iVH nM i Vh

(6:36)

To determine the efficiency of the internal combustion engine the efficiency of the engine itself is used: ηM =

PM , PE

(6:37)

where PM is the mechanical net power delivered by the engine and PE is the energy per time unit extracted from the fuel. The achievable efficiency depends on the temperature at which combustion takes place and thus also on the compression ratio. The total effective engine efficiency ηM is comprised of multiple other efficiency factors: ηM = ηth ηg ηb ηm ,

(6:38)

where ηth is the thermal efficiency of the SEILIGER process, ηg is the quality grade, ηb is the loss of efficiency due to imperfect combustion and ηm describes the mechanical losses. Due to the thermal efficiency (process efficiency) ηth , the heat losses that occur in the ideal process are already considered. Therefore, it holds that ηth =

Qin − Qout Qout =1− , Qin Qin

(6:39)

during the combustion 2 ! 3 amount of heat is supplied Qin = m cV ðT3 − T2 Þ

9 Not to be confused with the maximum engine rpm.

(6:40)

6.4 Power sources

271

and during the gas extraction 4 ! 1 removed amount of heat Qout = m cV ðT1 − T4 Þ.

(6:41)

In (6.40) and (6.41) the specific heat capacity is indicated with cV . With (6.40) and (6.41) inserted into (6.39) one obtains ηth = 1 +

T1 − T4 . T3 − T2

(6:42)

Here the assumption is made that the cylinder pressures are not too large, and the ideal gas law is still in effect. Since the state changes 2 ! 3 and 4 ! 1 are isochoric, the specific volume is V2 = V3 and V4 = V1 .

(6:43)

For the isentropic state changes 1 ! 2 and 3 ! 4 it holds 

V3 V4

κ − 1  κ − 1  κ − 1 V2 T1 V4 T3 = = and = . V1 T2 V3 T4

(6:44)

With the isentropic coefficient κ from (6.44) this yields T4 T3 = T1 T2

(6:45)

and therefore, 0 1 T4 T4 − T1 T1 @ T1 − 1A T1 =1− ηth = 1 − =1− . T3 − T2 T2 T3 − 1 T2 T

(6:46)

2

With (6.44) this results in ηth = 1 −

 κ − 1 V2 1 = 1 − κ−1 , V1 ε

(6:47)

V1 VH + VC = , V2 VC

(6:48)

using the compression ratio ε=

with the stroke volume VH and the compressed volume VC in the top dead center position of the piston (Figure 6.17). It can therefore be said that the efficiency of the Petrol Engine processes increases with increasing compression ratio ε. On the one hand, the increase in ε places greater demands on the mechanics of the engine and on the other hand, it is limited by the flammability of the fuel itself. Besides its importance on fuel economy, the compression ratio has a significant impact on

272

6 Propulsion systems

– the torque delivered, – the pollution and noise emission behavior of the engine, and – other parameters that may influence use of the power source, such as cold start behavior and general drivability. During the constant pressure process which is used as the ideal comparison process for the DIESEL engine, the following relationship is given instead of the one shown in eq. (6.47), see Todsen (2012) or Labuhn and Romberg (2009): ηth = 1 −

1 εκ − 1

·

’κ − 1 , κð’ − 1Þ

(6:49)

with the strain ratio ’=

V3 . V2

(6:50)

Again, it is immediately apparent that an increase in the compression ratio increases the efficiency. However, in these considerations the strain ratio ’ is now included. The efficiency of the constant pressure process increases with increased compression and decreases with increasing injection ratio. A high compression ratio is also favorable in this case. Additionally, the smallest possible injection ratio will lead to the fastest combustion. The quality grade ηg of the process describes the power delivered in the real thermal process with respect to the theoretical power delivery determined by the SEILIGER process. Reasons behind the deviations between the two methods are the results from the workings of a real gas, its finite speed of heat supply and discharge, heat losses through the walls and flow losses during the charge cycles. The fuel conversion efficiency ηb describes the power losses due to incomplete combustion of the fuel. The mechanical efficiency ηm summarizes the mechanical losses of the engine and the additionally required components for operating the engine (oil and coolant pump, valve train, injection pump, and the friction of the bearings and piston rings). The efficiencies ηth , ηg , ηb are added and combined to form the efficiency ηi , which indicates the ratio of power delivered by the pistons Pi and the calorific value of the fuel used. Therefore, for the delivered engine power this yields PM = ηm Pi = ηm ηi PE .

(6:51)

The connecting rods convert the translational movement of the pistons into a rotational motion of the crankshaft. The torque MM delivered by the engine can be considered to be generated by a mean pressure pe in the cylinder, which is assumed to be constant during a power stroke

6.4 Power sources

peff =

2π MM MM = 4π · . · VH i VH

273

(6:52)

The mean pressures reached in DIESEL Engines are usually found between 8 and 32 bar, compared to 7 to 13 bar for naturally aspirated Petrol Engines and up to 29 bar for turbocharged engines. Since the energy content is specific to the fuel type used, they must be related to either their mass or volume. The so-called calorific value Hi is a parameter that is used in this case and describes the usable heat released during complete combustion of the respective fuel. It is shown for different types of fuel in Table 6.6.

Table 6.6: Indicative values of the calorific value Hi for different fuel types. Fuel type

Calorific value Hi





kWh kg

Calorific value Hi

kWh l

.–.

.

DIESEL

.

.

LPG

.

CNG

.

Petrol

LiOn Batterya

.–.

.–.

a

Correspond to the specific energy and energy density of the battery.

The efficiency of an internal combustion engine is not a constant. Rather, it depends heavily on the operating state of the engine, which is characterized by the current speed at the crankshaft nM and the engine’s torque delivery MM . Every load condition ðnM , MM Þ is coupled to a specific fuel consumption be =

_K m . PM

(6:53)

If this specific consumption be is plotted over the engine’s rpm range nM and the torque MM , one obtains the consumption map of the specific engine. This map is also referred to as a shell map diagram due to its characteristic shape (Figure 6.19). From this consumption map it is possible to extract the specific consumption be for each possible combination of rpm nM and torque MM , and therefore also the corresponding power delivered PM = 2π nM MM . The map is limited by the maximum achievable engine rpm range on the one hand and by the maximum torque curve on the other hand, which is also referred to as the full load curve (Figure 6.20). There exists a relationship between the specific consumption and the engine’s efficiency

274

6 Propulsion systems

Optimum (sweet spot)

Full load curve pe MM ~ bar Nm 225

be /( 230

g ) kWh

240 250

1,000

1,500

2,000

2,500

270 290 325 350 400 430 450

3,000 60 nM Min

3,500

4,000

4,500

Figure 6.19: Example of the consumption map for a combustion engine.

Max. engine torque

Full load curve Max. power

Mean effective pressure, engine torque

Optimal effective efficiency Engine torque at max. speed

Torque course on flat road Engine torque at idle speed rpm

Idle speed

Max. rpm

Figure 6.20: Characteristics of engine parameters (Schreiner 2011).

ηM =

PM PM 1 = = . _ K Hi be PE Hi m

(6:54)

6.4.2 Electric traction drives There is a large number of electric drive types available for used in motorized vehicles, each of which has its own specific advantages and disadvantages (Reif, Noreikat et al. 2012).

6.4 Power sources

275

The advantages of an electric drive are briefly summarized: – Their energy efficiency can exceed 90%, which is far superior to even the most efficient combustion engines, which struggle to reach 40% at best. – Electrically powered vehicles offer the possibility to drive emission free (at least locally). They are therefore classified as Zero-Emission Vehicles (ZEV) by the California Air Resources Board (CARB), which plays a pioneering role in the regulating emissions. – They offer the possibility of energy recuperation, meaning that they can convert kinetic energy back into electric energy during braking. Afterwards it is available again to drive the vehicle. – They have extremely low noise emissions compared to combustion engine driven vehicles. This holds mainly for low speed driving as at higher speed the other noises will start to dominate. – They allow for a simpler design of the electric drivetrain and are often easier to control. This enables the implementation of novel and advantageous vehicle designs (purpose design, see Section 6.4.5). – The large possible rpm range combined with high torque levels even at lower rpms. In general, a multistage transmission can be discarded of. – A whole range of components, such as the fuel tank, exhaust gas catalyst, oil, fuel, and water pumps as well as the starter motor are eliminated. Some other components, like the brakes, are under lower stresses. However, these advantages are partly offset by considerable disadvantages, such as the high cost of the batteries needed to store the energy required for the drive unit and the resulting short range. For automotive requirements, for example, the hybrid synchronous motor is an attractive solution. This is especially true when a small battery already suffices to achieve a high level of electrical coverage (Ried 2014). 6.4.2.1 Type, structure, and functionality Contrastingly to the internal combustion engine, in an electric traction motor the energy flow direction works both ways with equally high efficiency, making it suitable as both a drive unit and a generator that produces electrical energy. It can therefore be used to accelerate as well as decelerate the vehicle (Reif, Noreikat et al. 2012). During acceleration, the electrical machine converts most of its electrical energy into mechanical energy. In the case of deceleration, conversely, mechanical energy is converted into electrical energy which can be stored in the battery pack (Figure 6.21). This process is known as recuperation. Electric motors can be run in an overload operation for a limited period of time. The limitation of this operating state results from the respective thermal load capacity and the available cooling. This characteristic of an electric motor must be considered

276

6 Propulsion systems

Intermediate Energy storage

Circuit

Power electronics

Control pulses

Drive shaft E-motor

Current flow RPM Rotation angle

Intended signals

Regulation control

Signal ENERGY Figure 6.21: Fundamental structure of an electric motor in an electrically driven vehicle, according to Reif, Noreikat et al. 2012.

when specifying the power output during the design phase. Unlike internal combustion engines, the maximum power is only available for a limited amount of time. To allow longer overload operation, most electric motors used in electrically driven vehicles are liquid-cooled (Wallentowitz and Freialdenhoven 2011). When comparing the automotive industry to other branches of industry, a considerable amount of additional demands exist regarding reliability, robustness, dimensioning, weight, cooling and last but not least, noise emissions (El Khawly and Schramm 2010, El Khawly 2013). In electrically driven vehicles, three-phase motors are almost exclusively used, as they offer advantages in terms of efficiency and performance compared to DC motors (Leidhold 2012). Three-phase motors can be divided into the following classes based on their structure and torque generation (Figure 6.22): – Hybrid-excited synchronous machines (HSM), – permanently excited synchronous machines (PSM), – current-excited synchronous machines (SSM), – asynchronized or induction machines (ASM). Hybrid-excited synchronous machines fundamentally use the same working principles as permanent-magnet synchronous machines, but additionally utilize reluctance effect in order to generate torque. The reluctance describes the alignment of a magnetizable body within a magnetic field. Therefore, the magnets are “buried” in the rotor of the hybrid-excited synchronous machine instead of being located on the surface as is the case in permanent-magnet synchronous machines. In

6.4 Power sources

a)

b)

c)

d)

277

Figure 6.22: Essential types of E-machines and cross sections of the rotors as schematic representation: a) HSM, b) PSM, c) SSM, d) ASM (Jung and Hofer 2011, Ried 2014).

permanent-magnet synchronous machines the circulating magnetic field is generated by controlling the stator windings accordingly. On the surface of the rotors permanent magnets are placed. Due to the interaction of the magnetic fields of stator and rotor, the rotor rotates synchronously to the rotating magnetic field generated by the stator. The torque is generated by the so-called LORENTZ10 force generated by the current-carrying conductor and the magnetic field. When generating electricity on the other hand, the current is induced in the coils of the stator through the rotation of the rotor. Asynchronous or induction machines generate a circulating magnetic field due to the (ideally) sinusoidal energization of the stator windings. The rotor is designed as a cage-rotor, whose electrodes are connected via short-circuit rings. Due to the different rotational speeds of the rotating field and rotor (due to slip), a voltage is induced in the rotor. On the current-carrying conductor in the rotor’s magnetic field acts the LORENTZ force, which generates the desired torque. The working principles of current-excited synchronous machines and permanent-magnet synchronous machines are very similar, but in the former the field is generated in the rotor windings instead of using a permanent magnet. These are supplied with direct current, with which the magnetic field is created. Due to the interaction with the magnetic field inside the stator windings, the torque is generated through the LORENTZ force as well as the reluctance effect. 6.4.2.2 Characteristics The permanent-magnet synchronous machine is often used as the electric drive system in electrically driven vehicles. A general advantage of synchronous machines compared to asynchronous machines is their higher power density resulting in 10 Hendrik Antoon Lorentz (1853–1928): Dutch mathematician and physicist.

278

6 Propulsion systems

more compact design possibilities. The permanently available torque per rotor volume of synchronous machines can reach approximately 40 − 50 Nm=l, which is almost twice as high as is the case for asynchronous machines. A major disadvantage of E-machines with permanent magnets is the high material costs caused by the use of the magnets. In a hybrid-excited synchronous machine it is possible to significantly reduce the magnet mass required to deliver a certain amount of power, whereas in asynchronous- or current-excited machines magnets are completely dispensed with. In terms of efficiency, the hybrid- and current excited synchronous machines achieve highest values in the range of slightly over 90% on average. Contrastingly, the permanent-magnet excited synchronous machine reaches just short of 90% and the asynchronous working principle achieves around 85% efficiency (Jung and Hofer 2011). The manufacturing process of synchronous machines is more complex compared to that of an asynchronous machine, due to the magnets or windings that have to be installed in the rotor. What all electric motors have in common, however, is that their efficiency is significantly higher than that of internal combustion engines. This is clearly visible in the consumption curve (Figure 6.23). In addition, the specific consumption is much less dependent on the engine speed and torque desired by the driver.

Engine torque / (Nm) 250 76 %

200

80 %

150

86 % 90 %

100 50 0

70 %

–50 –100 86 %

–150 –200

76 %

90 %

80 %

–250 0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000 10,000 Rotation speed /( U ) Min

Figure 6.23: Typical consumption curve for an asynchronous machine (exemplary representation).

6.4 Power sources

279

6.4.2.3 Prospects Research is currently being conducted on transversal flux machines that deliver higher torque density and efficiencies surpassing 95% (Blissenbach 2002). Contrastingly to the above-mentioned types of electric motors, these machines have windings mounted on the rim of the rotor, thus concentrically arranged with respect to the shaft. As a result, the winding head can be removed as it does not contribute to the torque generation.

6.4.3 Power electronics Besides the HV-storage and the E-machine, the power electronics can be regarded as the third main components of the entire E-system. These performance electrics partly consist of the inverter and DC/DC converter. For use in BEVs and PHEVs, IGBTs (Insulated Gate Bipolar Transistors) are widely used as semiconductor circuits. 6.4.3.1 Type, structure, and functionality The inverter’s task is to control the current and voltages over variable amplitudes and frequencies between the HV-storage and E-machine (Cebulski 2011). During operation, the DC voltage from the HV-storage is inverted into AC voltage which can then be used to operate the electric motor. When energy is being led back to the HV-storage during energy recuperation, the inverter converts the AC voltage induced in the electric motor into DC voltage which can be contained in the HVstorage pack. The HV-battery is then being charged. The voltage inside the HV traction system can range up to 1000 V for electric and hybrid vehicles. To still operate the standard 12/14 V components in the vehicle such as lighting, entertainment systems etc. (as also used for any other automotive power net) the voltage level has to be converted to that lower level. DC/DC converters have to be used to link the HV system to the LV system (12/14 V). The DC/DC converters transfer electric energy either way but are generally used to provide electric energy for the low voltage systems (see also Chapter 8). (Reif 2010, Lindemann 2012). The core elements of the inverter are controlled semiconductor switches, linked together into a power module. In current hybrid and electric vehicles, a B6 bridge circuit is commonly used as the preferred switch topology. These consist of six circuit breakers arranged in three-bridge circuits (Figure 6.24). Due to the voltage levels and the high switching frequencies, silicon semiconductor IGBTs are typically used in PHEVs. During pulse modulation, the switches are controlled in such a way that a three-phase AC voltage is generated from DC voltage. To smoothen out the voltage a film capacitor is usually added. Due to the voltage and capacitance, the film capacitor, together with the semiconductor switches, determines the essential characteristics of the entire inverter. In addition, a sufficiently strong cooling system is required to dissipate the heat that is generated during the current-switching

280

6 Propulsion systems

S1

S3

S5

S2

S4

S6

uL12

uL23

uz

uL31 iL1

iL2

iL3 M 3~

Figure 6.24: Power electronics of the BMW ActiveE (Jung and Hofer 2011), and a diagram of a three-phase bridge circuit with six semiconductor switches (Lindemann 2012).

process. Additional components include control electronics, housings, connectors, sensor, and small miscellaneous parts (Cebulski 2011). The DC/DC converter consists of electronic performance parts that have been combined into an electrical circuit. To determine the exact design and topology of these switches, the amplitudes and quality of the input and output voltages and current are of crucial importance (Cebulski 2011). The integration of the DC/DC converter takes place in a separate housing or is located in the housing of other electronics such as the inverter (Spath, Rothfuss et al. 2011). 6.4.3.2 Characteristics In hybrid and electric vehicles, IGBTs with blocking voltages of 600 V or 1,200 V are used (Lindemann 2012). Modern converters are highly suitable with efficiencies of over 95 % and a relatively large operating range. This allows for optimal utilization of the electric motor in terms of dynamics, torque, and speed. In addition to the costs, of significant importance in performance electronics are their required installation space and their weight. Both properties are also influenced by the required component cooling. 6.4.3.3 Prospects The development goal of performance electronics used in electric drive vehicles is a more compact, lighter construction with lowered costs. A possible approach is to integrate the inverter on or into the E-machine itself. In addition, the durability of the semiconductor switches is being investigated as the high temperatures and considerable temperature swings lead to high loads, which has a negative effect on the lifespan of the components. Furthermore, new manufacturing methods and materials, such as silicon carbide (SiC) are being studied (Cebulski 2011).

6.4 Power sources

281

6.4.4 Hybrid drives Hybrid drives are usually defined as drive systems that combine a combustion engine and an electric motor. However, there have been, and still are, sporadic attempts to go beyond this confined definition. 6.4.4.1 Topology Combined internal combustion engine and electric drive hybrid vehicles can be classified according to two schemes. These are based on the drive topology on the one hand, and the degree of hybridization of the system on the other hand. Regarding the topology, three main types can be identified: – In parallel hybrid drives, both types of drive units output their power directly onto the same drive shaft. Or in case of hybrid road-mounted drives, indirectly through the road surface as connecting element. This can be done either simultaneously or individually (Figure 6.25). The advantage of a parallel hybrid is the simple integration of this principle into existing vehicle structures. – In series hybrid drives, the wheels are driven solely by the electric motor(s). The internal combustion engine is used as generator to recharge the electrical storage pack and/or to supply the electric motor with electricity (Figure 6.26). – Power split hybrid powertrains typically combine the power of the combustion engine and electric motors via a mechanical gear box that combines both inputs (Figure 6.27). In reality, combinations of the above-mentioned drive topologies are seen as well.

Power electronics Battery

Fuel tank

–

Gear transmission E-motor

Differential gear

Differential gear

+

M

M

–

Combustion engine

+ E-motor

Differential gear

Combustion engine

Power electronics Battery

Fuel tank

Figure 6.25: Parallel hybrid drives.

6.4.4.2 Degree of hybridization Another way of categorizing hybrid powertrains relates to the characteristics of their electrification (Table 6.7). A distinction is made between the following concepts.

282

6 Propulsion systems

Power electronics

Battery

Alternator

– Differential gear

Combustion engine

+ E-Motor M

Fuel tank Figure 6.26: Series hybrid drive.

Battery +

– Differential gear

E-generator

M

Combustion engine

Power electronics

M Planetary E-Motor drive Fuel tank

Figure 6.27: Power-split hybrid drive.

Table 6.7: Drive concepts sorted to increasing degree of electrification, from the ICEV to the BEV as well as exemplary functions and properties (Ried 2014). ICEV

HEV

PHEV

REX

BEV

Conv Veh.

Micro hybrid

Mild hybrid

Full hybrid

Plugin hybrid

Range Extender

E-veh

E-power

–

<  kW

<  kW

<  kW

<  kW

> kW

> kW

Emission-free driving

–

–

–

<  km

<  km

> km

> km

CO-advantage (NEDC)

Reference %

%

–%

–%

–%

%

 V socket required

–

–

–

–

Yes

Yes

Yes

Range >  km

Yes

Yes

Yes

Yes

Yes

Concept– dependent

6.4 Power sources

283

– ICEV: Internal Combustion Engine Vehicle – Internal combustion engine driven vehicle with partially electrified drive – HEV: Hybrid Electric Vehicle – PHEV: Plug-in Hybrid Electric Vehicle – REX: Electric Vehicle with Range Extender – BEV: Battery Electric Vehicle It should be noted that in the case of most powertrain structures possible today, one or more energy conversions are required. An overview of the energy chain of operation in a hybrid vehicle is shown in Figure 6.28.

Fuel tank

Combustion engine

C

Converter

Torque output

C→W→M M↔M

Traction battery EC ↔ E

M↔M Power electronics ICS

Charging unit

E-motor E↔M

Symbols

Form of energy

C EC W E M

Chemic Electro-chemic Thermic Electric Mechanic

Figure 6.28: Scheme of an internal combustion engine – electric hybrid drive with energy conversion.

6.4.4.3 Operating strategies Hybrid drive trains add additional degrees of freedom due to the availability of the electric drive unit, which leads to a variety of operating strategies: – The different drive systems can be used in a coordinated manner. Meaning that under certain circumstances, the use of the internal combustion engine is completely dispensed in order to allow for local emission-free driving. – It creates the possibility to decrease the considerable disadvantages of the internal combustion engine in certain unfavorable operating conditions, for example, in the partial load and during stop-and-go traffic situations.

284

6 Propulsion systems

– Due to the reduced requirements on the dynamics of the internal combustion engine as a part of a hybrid system, the internal combustion engine can be operated with alternative thermal processes, which have been prohibited for use in purely combustion driven vehicles for emission/efficiency reasons. The MILLER Cycle11 process (which is based on the ATKINSON12 principle), during which the inlet valve is already closed during the intake stroke, can be utilized again (van Basshuysen and Schäfer 2012). This principle is, for example, used in the Toyota Prius along with other Toyota models, as well as in the Mercedes S400 hybrid and Ford C-Max Energi. The principle is realized using a variable valve timing (Reiff 2016). The choice of the optimal operating point and the implementation in the overall operating strategy directly influence important properties of the vehicle, such as fuel consumption, response behavior, emissions, service life, and the acceptance of the vehicle by potential customers. For this purpose, a comprehensive operating strategy is required with which the energy flows in the vehicle is organized optimally. The operating strategy of a hybrid vehicle involves the timing and control of operating points of the subsystems and of each individual component. It defines the operating states of the powertrain based on the planned route which significantly influences energy consumption and emission behavior of the vehicle. Along with the thermal and electrical management, it is a considerable part of the overall vehicle management program. The operating strategies are composed of different modes, which have been illustrated in Figure 6.29, based on the example of a Mercedes Benz E-class. The operating strategies can be assigned to multiple categories, which have a significant effect on the driving behavior of the vehicle. If a method-oriented differentiation is used, optimization and rule-based strategies can be identified. 6.4.4.4 Optimization-based operating strategies In these strategies, control of the components is based on the optimization of a target function, which is a result of individual driving requirements (Figure 6.30). The target function normally includes fuel and energy consumption, as well as pollutant emission targets. However, other target variables such as acceleration capacity and drivability can also be included. In addition, boundary conditions are implemented which arise mostly from the vehicle’s performance limits, as well as from regulatory requirements.

11 Ralph Miller: American Engineer, inventor of the MILLER cycle. 12 James Atkinson (1846–1914): American Engineer, inventor of the ATKINSON cycle.

→ Maximum availability of electric motoring

Figure 6.29: Operating modes of a hybrid drive © Daimler AG.

→ Optimum use of combustion engine and electric motor

→ Preservation of the HV battery capacity for future electric motoring

→ Limited electric operation is possible

→ The current charge status is maintained

→ Pure electirc operation → Metering of electirc output via the haptic accelerator pedal (variable pressure point)

→ Electric operation or driving with the combustion engine is possible

→ Automatic selection of drive type

E-save

E-mode

Hybrid

→ Charging of the HV battery for future electric motoring

→ Electric operation is not possible

→ The HV battery is charged via the combustion engine

Charge

6.4 Power sources

285

286

6 Propulsion systems

Targets

Constraints

Actions

Power consumption – Fuel – Electrical power

Performance limits of components

Driving mode – Electrical – IC engine

Legal requirements – General – Local Emissions – Global – Local

Size energy storage

Recuperation – Brake – Sailing

General OS – Residual charge of energy storage – Travel time minimization – Efficiency

Time horizon – Currently – Long time Lack of information – Drive history – Traffic situation Driver’s request

Boost with EM Load point selection for ICV – Increase – Lowering

Computational cost

OPTIMIZATION Vehicle-based

Cross-vehicle

Cloud-based

DRIVE Figure 6.30: Optimization-based operating strategies for hybrid drives.

6.4.4.5 Rule-based operating strategies Rule-based operating strategies rely on a set of pre-defined rules, which in turn determine characteristic parameters during driving. The rules are usually realized via mapping, as is the case for the internal combustion engine. The input consists of a large variety of parameters that are constantly being measured by sensors, or that have been ordered through driver control. Another embodiment is state machines in which the response to an object in a particular state determines further action. For a more in-depth consideration of similar operating strategies the reader is referred to (Görke 2016). An example of a rule-based operating strategy for the 2016 E-Class is shown in Figure 6.31.

Preparation of charge status

Reduction of charge status

70

Electric urban motoring

Partial electric urban motoring

50

Preparation of charge status

Charge status passive

Electric motoring to destination

Limited electric motoring possible

30

Figure 6.31: Mercedes-Benz “Intelligent drive-management” route-based operating strategy © Daimler AG.

Navigation + “Hybrid” + “E+”

Route guidance

With

Route guidance

Without

100

6.4 Power sources

287

288

6 Propulsion systems

6.4.5 Implementing powertrains in the vehicle To give shape to concept designs for electrical vehicles two different developmental approaches can be utilized. In Conversion Design, a vehicle that was originally developed with an IC engine is converted to an electric drive vehicle, while the Purpose Design approach requires designing a completely new vehicle during which all new possibilities can be exploited. 6.4.5.1 Conversion design For automotive manufactures, transforming existing vehicles into an electric vehicle (Conversion Design) is a cost-effective and low-risk way to market an electric drive variant due to the significant synergy during development, design, and production. Another important factor is that current investments in existing production facilities remain useful. The vehicle’s structure and essential dimensions, as well as the body, remains unchanged even though the vehicle was originally designed to house an internal combustion engine-driven powertrain. However, during integration of additional components, design spaces are often limited as these added features had not been considered in the original design. Nonetheless, developing electric vehicles using the Conversion Design approach is still a widespread practice in the current transitional phase. 6.4.5.2 Purpose design The development based on “Purpose Design” relies on the notion of completely redesigning a vehicle to house an electric drive and thus being able to implement all new features from the start, see as an example Figure 6.32. This method, however, requires much more effort than the “Conversion Design” approach. This means that the business-risk associated with a non-optimal product market placement can be significant, although these vehicles are often trademarked by a high-quality integration of the electric components into a tailor-made vehicle construction. Especially the space required to fit the battery cells and modules can be allocated optimally.

6.5 Transmissions and shafts 6.5.1 Gears Transmissions are vehicle components which convert mechanical energy of a drive unit from one operating point ðωM , MM Þ to a different, more suitable operating point ðωA , MA Þ. For internal combustion engines, transmissions are indispensable for two reasons. First of which is because torque delivered by a combustion engine is only

6.5 Transmissions and shafts

289

Figure 6.32: Example of packaging in Electric Vehicle (Purpose Design) for a BMW i3, © BMW AG.

available from a certain minimum speed and secondly, it is not possible to cover the desired speed range of a vehicle with the speed range of an internal combustion engine, see Section 6.2.7. Rather, it is necessary to adjust the speed and torque the engine delivers depending on the driving conditions (Figures 6.33 and 6.34). This is done by a specially designed gear that provides the required mechanical translation ratio. In the following, ω refers to the rotational velocity and M refers to the corresponding torque. For the relationship between these parameters on the engine-side (before the transmission) and on the drive-side (after the transmission), the following applies with the gear ratio iG : ωA =

1 ωM , MA = iG MM . iG

(6:55)

In internal combustion engines, a device must be present that allows the temporary disengagement of the drive unit and drivetrain. In the case of vehicles with a manual gear box, a clutch is generally used and in the case of vehicles with an automatic gear box, hydraulic torque converters are used. An example of a currently used automatic gear box is shown in Figure 6.35. As the gear box is installed in a vehicle with hybrid drive, an electric motor including clutch is additionally added. In this case, the electric drive is linked to the regular transmission.

290

6 Propulsion systems

Traction force / N

Traction hyperbola 20,000 18,000 16,000 14,000 12,000 10,000

1

8,000 6,000 2 4,000

3

2,000

4 5 6

Drive resistance on flat road

0 0

50

100

150

200 250 Velocity / (km/h)

Figure 6.33: Gear ratios of a passenger car with a six-speed gear box (example).

Engine

Gear

Prop shaft

Gear shaft

Axle shaft

Drive wheels

Clutch Figure 6.34: Powertrain components for power and torque transmission.

6.5.2 Power losses in the drivetrain Besides the losses caused by the conversion of fuel or electricity into mechanical power via the engine, further losses occur in the transmission as well as in the shafts. As a result, not the power PA determined in Section 6.2.6 is responsible for the vehicles propulsion, but the power PE =

1 PA , ηA ηM

(6:56)

that must be covered by the power supply from the energy storage (Figure 6.36). In eq. (6.56) the efficiency of the drive unit ηM , which varies over the engine range, is considered as well as the total efficiency of the powertrain, excluding power required to operate auxiliary equipment.

6.6 Energy consumption

291

Figure 6.35: Automatic gear box with built-in hybrid drive © Daimler AG.

PE

Power unit

PM = ηMPE

losses (1−ηM) (1−ηM) ∙ PE = ηM

Transmission and Powertrain

PA = ηAηMPE

Drive wheels

losses ∙

PM

(1−ηA) ∙ PM

Figure 6.36: Power flow and efficiency in the powertrain of an ICEV.

An overview of the occurring power flow in the powertrain of an ICEV along with the corresponding efficiencies and other exemplary values are shown in Figure 6.37. In addition to the consumption for the propulsion of the vehicle, the real consumption must also depend on the energy required for the operation of the auxiliary equipment, which is not addressed here in any further detail. Instead, reference is made, for example, to Hesse, Hiesgen et al. (2012).

6.6 Energy consumption The fuel consumption levels of ICE vehicles have become considerably more important in recent years, particularly due to rising fuel prices and regulatory requirements. As the consumption of a motorized vehicle to a large extent depends on the driving style of the driver, it is necessary to define standardized test routes, so-called driving cycles,

Real usable energy at the piston (internal work)

Thermodynamic inevitable loss (waste heat) 3203 J Non-ideal combustion (wall heat transfer/charge change) 𝜂󰑀 2024 J

𝜂󰑖

Internal efficiency

Thermodynamically usable energy (ideal process)

5294 J 𝜂󰑡󰑕

𝜂󰑔𝜂󰑏

𝜂󰑚

Real usable energy at the crankshaft (effective work)

Mechanical Quality grade efficiency

Energy contained in the fuel

Efficiency ideal process

6 Propulsion systems

Effective efficiency

292

1606 J Friction in the engine

Figure 6.37: Efficiencies and exemplary distribution of losses in the internal combustion engine, (Schreiner 2011).

which make it possible to compare between different vehicles. This is discussed in more detail in Section 6.6.4.

6.6.1 Determining energy consumption The fuel consumption of an internal combustion engine driven vehicle required to achieve the desired longitudinal motion can be described by the following equation, in relation to distance travelled and by applying eq. (6.22) Ð tE 1 0 be · ηA · PA · dt . (6:57) Be = Ð tE 0 v · dt The energy required per unit of distance Be (unit g/m) can be calculated by integrating the product of the specific fuel consumption be (unit g/kWh) of the drive unit, the reciprocal of the transmission efficiency of the drivetrain ηA , and the driving resistance power PA , divided by the distance travelled. Equation (6.57) can now be applied in case the vehicle’s velocity profile, drive power PA , drive efficiency ηA and specific consumption be related to the trajectory consumption Be are all known. Depending on the engine speed and torque delivery, the specific fuel consumption can now be retrieved from the engine characteristic map, of which an example is shown in Figure 6.19.

6.6 Energy consumption

293

6.6.2 WILLANS curves Determining the specific consumption as a function of engine speed and torque delivery based on the engine characteristic map is a relatively ornate process. It would be better to directly specify the efficiency curve of an engine around the point of work related to the demanded power. In order to achieve this, the WILLANS curves can be used (Rizzoni, Guzzella et al. 1999). WILLANS curves describe the dependency of the power usage of an energy converter as a function of the supplied power at constant speeds. When looking at an internal combustion engine, this means the demanded power’s dependency on the energy supplied by the fuel. This results in an approximately linear profile for all speeds: PM = ePE − PV ,

(6:58)

(Figure 6.38).

PE

PV

Arctan e PM

Figure 6.38: Fundamental profile of a linear WILLANS curve.

This allows for a representation of net power based on the power delivered from the combustion engine PM to the crankshaft, with a dependency on the supplied power PE and power losses of PV . The parameter e describes the internal efficiency of the drive unit. The drive unit’s basic consumption PV is dependent on the rotational velocity and corresponds to the consumption during idling. In essence, it is the result of friction losses. Below a supplied power value of PE = e1 PV , no useful power is delivered. Using eq. (6.58), the efficiency of the drive unit can now be formulated as ηM = (Figure 6.39).

PM ePM = , PE PM + PV

(6:59)

294

6 Propulsion systems

G e

PM

Figure 6.39: Efficiency profile as calculated by eq. (6.59).

A consumption map represented by WILLANS curves is shown in Figure 6.40.

Fuel mass f low / g/s

15

𝜇𝑀= 10%

10

𝜇𝑀 = 30%

𝜇𝑀 = 20%

5,600 𝜇𝑀 = 40%

n

𝜇𝑀= 50%

4,400 5 3,200 2,000

Curves with constant rpm in 1/min

800 0

0

50

100 Engine power / kW

150

200

Figure 6.40: Consumption map in Williams-curves representation, according to Diegelmann (2008).

6.6.3 Identification of different driving states To identify different driving states, such as acceleration, braking, and coasting, eq. (6.21) can be applied to calculate the current acceleration   1 1 2 €x = v_ = (6:60) Ftraction − ðfr + αÞmV g + cW AρL v . λmV 2 Three different cases are to be distinguished: – When Ftraction > 0, the vehicle is accelerating. If the vehicle’s driving forces and resistance forces are balanced, the vehicle is moving at constant speed. – When Ftraction = 0, the vehicle is coasting (disengaged). – When Ftraction < 0, the vehicle is decelerating. Meaning that either the brakes are actuated, and/or the vehicle is decelerated using the drivetrain itself. When considering an internal combustion engine, the motion resistance is a direct

6.6 Energy consumption

295

result from the cylinder compression. In case of an electric motor, the motion resistance can be actively influenced to a near vehicle standstill. In addition, kinetic energy can be recovered (recuperation).

6.6.4 Driving cycles In vehicle technology, a driving cycle is considered vehicle motion in which the longitudinal velocityv, as well as the geographical location of the vehicle for a predefined length of time, along with other time-dependent variables are described. Two types of driving cycles can be distinguished: – Driving cycles within the framework of legally required test cycles or those determined by other organizations and the media. – Surveys of real driving trips, for example, in the context of fleet tests. 6.6.4.1 Standardized test cycles The first case involves driving cycles within the framework of statutory test cycles, which are relevant to ensure a comparable measurement of fuel consumption and pollutant emissions for different vehicles. For these test cycles the boundary conditions such as surrounding and start-up temperatures, gear change points (for manual transmissions), vehicle conditioning, loading and the start of the exhaust gas, and consumption measurements are all pre-determined. Test cycles are typically performed in controlled environments that allow for well defined, although idealized, test conditions. Often the tests are carried out on a dynamometer. Therefore, the driving resistances of each individual vehicle on the road must be determined in advance. These can then be simulated on the dynamometer test bench by corresponding actuators. There are a few test cycles that vary significantly from region to region. Table 6.8 provides an overview of some of the key test cycles used in different regions, along with certain characteristics such as average speed, phases, duration as well as other information. In Europe until 2018, the so-called New European Driving Cycle (NEDC) was used for both pure internal combustion engine driven vehicles or purely electric vehicles. For vehicles powered by combustion engines, the fuel consumption is calculated from the exhaust emissions, while the power consumption for an electric vehicle is deduced from the battery. For hybrid vehicles, fuel consumption is determined using the formula. C=

De · C1 + Dav · C2 , De + Dav

where C: Total consumption in 100lkm C1 : Consumption with fully charged battery

(6:61)

296

6 Propulsion systems

Table 6.8: Test cycles. v∅ /

km

vmax / (m/s)

amax / m/s2

Idling time / s



.



.

.

.



.

.

.

.



Europe

.

.

.

.



FTP 

USA

.

.

.

.



SFTP US

USA

.

.

.

.



SFTP SC

USA

.

.

.

.



NYCC

USA

.

.

.

.



HWFET

USA

.

.

.

.



JC

Japan

.

.



.



Driving cycle

Region

Distance / km

NEDC

Europe

.

.

WLTC

Europe

.

CADC

Europe

HYZEM

h

Vehicle-dependent modifications are possible.

C2 : Consumption with empty battery De : Pure electric range Dav : 25 km assuming an average distance between two charges However, because the electrical consumption is ignored this can lead to unrealistically low consumption making this method highly controversial. In order to improve this situation, the Worldwide harmonized Light vehicles Test Procedure (WLTP), in conjunction with the guidelines set by the UNECE-World forum‚ for harmonization of vehicle regulations was proposed as a new testing method to determine the pollutant and CO2 emissions and fuel consumption of motorized vehicles (Tutuianu, Marotta et al. 2013). This has already been introduced in the European Union, Switzerland, Iceland, Norway, Israel, Japan, and Turkey and in the near future also in China. It will apply to passenger cars and light commercial vehicles. Other countries like Russia and Australia still use the NEDC. Three different WLTC test cycles were used for vehicles of different performance classes. The method is based on the power to weight ratio – engine power/empty vehicle weight in kW / t. Most current vehicles are assigned to performance class 3, for which the velocity profile shown in Figure 6.41 has been determined. In order to make statements about vehicle behavior in actually occurring driving situations however, for instance in the context of fleet testing (see, for example, Schüller, Tewiele et al. 2015, Tewiele, Schüller et al. 2015, Schramm, Dudenhöffer et al. 2017, Koppers, Driesch et al. 2017) and by magazine editors or reviewers, normal driving tests are also performed.

6.6 Energy consumption

297

140 120

Velocity/(km/h)

100 80 60 40 20 0

0

300

600

900 Time/s

1200

1500

1800

Figure 6.41: WLTC Cycle (V. 5.3).

6.6.4.2 Real driving cycles for fleet testing More meaningful when judging actual driving scenarios are driving cycles that are obtained in fleet tests. In this case, a certain number of vehicles are equipped with special data loggers that capture driving data, or the required data is taken directly from the vehicle-bus system (Tewiele, Schüller et al. 2017), (Koppers 2018). Another possibility to investigate the behavior of electrified vehicles is the application of HiL-simulation methods (Jeschke, Hirsch et al. 2012), (Jeschke, Hirsch et al. 2014). These methods in addition allow to track the energy consumption of secondary consumers in electrified vehicles (Hesse, Hiesgen et al. 2012) (Figure 6.42). When considering electric mobility, the special features of electric vehicles must be considered, especially with regard to the possibility of regenerative braking and a different driving behavior compared to an ICEV. Driving cycles are therefore particularly important for electric vehicles but have not always been used to date (Berzi, Delogu et al. 2016), (Pfriem 2016). The basic methods for determining driving cycles, which can map the special properties of different vehicle concepts, will therefore be briefly discussed here. 6.6.4.3 Microtrip-based method One of the most commonly used methods is the microtrip-based method. A microtrip describes a journey between two stopping phases and includes the preceding idling phase. The microtrips are selected on the basis of statistical evaluation parameters. This involves comparing the parameters of a microtrip with the target parameters resulting from the entire data basis. A selection of representative microtrips is then

298

6 Propulsion systems

Energy consumption/kWh

5.0 Moers

40

4.5

Essen

Duisburg 59

4.0 288

3.5

524 8

3.0

3

F2

44

Acceleration

44

2.5

Wheel 2.0

Düsseldorf

1.5 1.0

Air

Velocity/(m/s)

0.5 0.0 50 40 30 20 10 0

0

500

Urban

1000

1500

2000

Motorway

Time/s

Urban Rural

Figure 6.42: Example of a real driving cycle including speed profile (lower) and the energy consumption regarding air, rolling- and inertial resistances (upper).

made either randomly or using the best incremental method (Galgamuwa, Perera et al. 2015). A microtrip can contain different road types, traffic situations or traffic qualities. Since there is no differentiation, this method is less suitable for traffic planning purposes. There is also the danger of a bias toward city journeys, as motorway journeys are often carried out for a long time without a stopover, (Giakoumis 2017). With this method a certain region with its characteristics can be represented. This method is also suitable for determining emissions. 6.6.4.4 Segment based method A subdivision into journey sections can also be made according to road segments or traffic quality. The initial and final speeds of a segment are not necessarily in a standstill phase. This results in the challenge to connect selected segments with the

6.6 Energy consumption

299

right speed and acceleration when combining several segments. Since the segments represent real traffic conditions and physical characteristics of a road as well as traffic quality, the method is suitable for the development of driving cycles in traffic planning and management. It is less suitable for determining consumption or emissions (Dai, Niemeier et al. 2008). One application is the driving cycle formation of pure motorway trips, in which the micro-trip method is not an option due to missing stopping phases (Galgamuwa, Perera et al. 2015). The segment-based method was used, for example, in the Australian Composite Urban Emissions Drive Cycle (CUEDC) (Galgamuwa, Perera et al. 2015). 6.6.4.5 Classification according to patterns Another method is classification according to patterns. Here, driving sequences are subdivided into heterogeneous classes using statistical methods. The driving sequences, also called kinematic segments, are defined with a homogeneous size. The driving sequences are then put together in random order, whereby the probability of a subsequent event occurring is calculated, (André 2004), (Galgamuwa, Perera et al. 2015), and (Giakoumis 2017). 6.6.4.6 Stochastic methods Furthermore, stochastic methods are also used for a driving cycle composition. The driving data are divided into driving sequences (“snippets”) according to the driving states acceleration, deceleration and constant driving (Dai, Niemeier et al. 2008), (Ashtari, Bibeau et al. 2012), and (Lin and Niemeier 2002). It is also possible to use the driving speed and acceleration (Nyberg, Frisk et al. 2014), (Gong, Midlam-Mohler et al. 2011), (Lee, Adornato et al. 2011), or additionally the gradient (Souffran, Miègeville et al. 2012) as a condition. With these methods, the probability with which a state changes into a subsequent state is mapped in a transition matrix. Using Markov chains, the sequences are then linked to form a driving cycle, see, for example, Tewiele, Driesch et al. (2018). Following the explanations in Schüller (2019), the microtrip-based method is described in more detail below. The representativeness and accuracy of a driving cycle generated by microtrips is largely determined by the evaluation parameters used to select suitable microtrips. For a targeted selection of evaluation parameters, the target parameters are therefore defined first. Subsequently, the parameters influencing the respective target parameters are identified, which flow into the driving cycle generation as evaluation parameters. The method presented, for example, in Schüller (2019) is characterized by the differentiation according to the target of the driving cycle, which enables an optimization of the driving cycle to be generated to corresponding evaluation parameters in focus. The majority of the transient driving cycles used are based exclusively on evaluation parameters, which in turn are derived from speed and acceleration data. With regard

300

6 Propulsion systems

to electric vehicles, it is interesting to consider not only the speed profile but also the current profile, which provides information on the amount of energy extracted and charged. Furthermore, driving cycles can be derived that are optimized for the representation of parameters that define battery aging effects during driving. In Schüller (2019), for example, three variants with different target parameters are examined, each of which allows different areas of investigation. These include – Speed behavior, – depiction of consumption and thus of emissions, and the – illustration of the performance. In addition to the speed, the current strength is also plotted over time in a cycle. Such a power cycle can serve as a basis for investigations of temporally changed power-based variables such as battery ageing. A typical procedure for driving cycle generation is depicted in Figure 6.43.

Recording of real driving data

Splitting into Microtrips

Removal of outliers

Clustering data

Definition of target parameters

Combination of driving sequences

Evaluation of the potential cycle

Classification into candidate cycles

Evaluation and choice

Figure 6.43: Typical procedure for cycle generation (Schüller 2019).

This approach can be used, for example, to set up driving cycles for different regions. It enables, among other things, the determination of optimized storage concepts for electric vehicles with different application areas and for different regions. In Schüller, Tewiele et al. (2017), Schüller (2019), for example, this procedure is used for a comparison between Germany and China. First, the real driving data is subdivided into driving sequences. A driving sequence describes a travel section between two points in time when the speed is zero (Figure 6.44). In order to represent a realistic driving behavior, stopping phases in a microtrip are also included. This is at the beginning of a microtrip. Figure 6.45 shows one of the driving cycles generated by Schüller (2019) using the example of a driving cycle that has been optimized for detecting battery ageing.

6.6 Energy consumption

14

Microtrip 1

Microtrip 2

Velocity/(m/s)

12

301

Microtrip 3

10 8 6 4 2 0

50

0

100

150

200 250 Time/s

300

350

400

Figure 6.44: Drive history split into microtrips (Schüller 2019).

Velocity/(m/s)

30 20 10 0 0

500

1,000 Time/s

1,500

2,000

500

1,000 Time/s

1,500

2,000

400 Current /A

300 200 100 0 –100

0

Figure 6.45: Driving cycle battery aging for Germany, based on data from Schramm, Dudenhöffer et al. (2017).

A descriptive interpretation of driving cycles can, for example, be provided by displays in which driving behavior is recorded on the basis of speed and acceleration data. Figure 6.46 illustrates this using driving data collected in the PREMIUM project (Schramm, Dudenhöffer et al. 2017) as an example. The corresponding diagrams for the NEDC and a WLTP driving cycle are also shown for comparison. One recognizes the strongly different scattering of the data point. In particular, the strong concentration of data in the NEDC can be seen.

302

6 Propulsion systems

Schüller Germany

WLTC

NEDC

Figure 6.46: Acceleration/speed distribution of the driving cycles generated in Schüller (2019) as well as of the WLTC and NEDC.

When presenting the average values of different driving cycles from Schüller (2019) and other published synthetic and transient driving cycles, the large variance of the characteristics of these cycles becomes clear only when comparing the average speed and positive acceleration (Figure 6.47). In addition to the cycle generation method, the driving data used for a particular region can lead to very different results, even if vehicles with a comparable drive concept (BEV, PHEV, ICEV) were used.

Average velocity / (m/s)

14 12 ICEVs

10 8 6 4

BEVs

2 0 0.0

0.2

0.4 0.6 0.8 Average positive acceleration / (m/s²)

1.0

Winnipeg

Amman

Lin

Dai C1

Dai C2

Shahidinejad weekday

Shahidinejad weekend

Tong

US 75

Perth 14.2

MPC

Sydney Cycle

IECa

Wuhan

Germany

Beijing

Pfriem

Figure 6.47: Comparison of different transient driving cycles in their average speed and acceleration (Schüller 2019).

6.7 Energy sources and storage

303

6.7 Energy sources and storage 6.7.1 Fossil fuels 6.7.1.1 Overview of the most important fuel types The large majority of vehicles use today the internal combustion engine as the driving unit. They operate based on fuel combustion, of which the main types can be distinguished as: – Petrol: conventional fuel based on petroleum. – Diesel: conventional fuel based on petroleum. – LPG (Liquified Petroleum Gas): in Germany also called “Autogas.” It is a byproduct of the refining process of petrol and diesel fuels. Storage takes place at room temperature and under low pressure. – NG (Natural Gas): Combustion produces significantly less hydrocarbons and the emission of particles is also considerably lower compared to the combustion of petrol. Due to its low energy density, natural gas is either stored at high pressure (up to 200 bar) as CNG (Compressed Natural Gas), or liquified at a temperature around -160 °C as LNG (Liquified Natural Gas). Petrol and diesel fuels are obtained through distillation of crude oil and consist of a complex mixture of various hydrocarbons. Together they form the majority of fuel used today. The temporal evolution of their respective overall market shares is shown in Figure 6.48. 6.7.1.2 Petrol Petrol can be obtained in different forms. Most commonly seen are the Super (octane number 95) and Super Plus (octane number 98). The octane number indicates the anti-knock properties of a petrol fuel, meaning the absence of uncontrolled selfignition. This effect is particularly noticeable in engines that operate with high compression ratios, although in modern day fuel injection vehicles it can be controlled by appropriate intervention of the engine control unit. Petrol has a boiling range between 30 and 210  C, and will ignite at an average temperature of 500  C. The Super and Super-plus fuels may contain (2016) 5% Ethanol and 10% Ethanol (Super E10) respectively. Individual suppliers also market other variants offering improved properties and additions. 6.7.1.3 Diesel Diesel has a slightly higher specific calorific value compared to petrol and is also available in various quality grades, as well as in the form of Biodiesel (up to 7%).

2017

76%

1% 1% 2% 1%

2020

79%

14%

1% 1% 3% 2%

2024

69%

10%

8%

4% 2% 7%

2025

67%

9%

8%

6% 2% 8%

2026

63%

8%

10%

9%

7% 3%

2027

61%

7%

11%

10%

8% 3%

2028

57%

6%

12%

11%

4%

10%

2029

52%

6%

13%

12%

5%

12%

2030

47%

5%

15%

13%

6%

14%

Figure 6.48: Forecast of the shares of powertrain types in the worldwide production of automobiles in the years 2017 to 2030 (BCG 2017).

0%

20%

40%

60%

80%

100%

BEV

PHEG

HEV

MHEV

Diesel

Petrol

304 6 Propulsion systems

6.7 Energy sources and storage

305

Diesel fuel has a boiling range between 180 and 360 °C and ignites at an average temperature of 250  C. In recent decades, the share of diesel-powered vehicles in Germany has steadily risen due to the higher efficiency of DIESEL engines, their comfortable torque curve, and a favorable tax advantages compared to petrol fuel. One exception could be seen in the year 2009, when a large number of smaller vehicles were registered due to the scrapping premium. These smaller vehicles are often powered by petrol engines instead of DIESEL engines. However, in response to the public debate on the pollutant emissions of vehicles with DIESEL engines and the resulting driving bans in parts of large cities in Germany, the proportion of newly registered diesel vehicles has fallen sharply in recent years (Figure 6.48). 6.7.1.4 Natural Gas (NG) Natural gas is 83–98% Methane (CH4). It is marketed either as gaseous compressed CNG (Compressed Natural Gas) or as liquified LNG (Liquified Natural Gas). LNG requires a storage volume that is a third less than that required for CNG, but the storage process itself requires more energy. Due to this reason, CNG is the most commonly seen form today. The CO2 emissions of natural gas are also significantly lower than those of petrol due to its more favorable chemical structure. The hydrocarbon ratio of natural gas is approximately 4:1, whereas that of petrol is around 2.3:1. Therefore, burning natural gas produces less CO2 and more H2 O compared to burning petrol. Consequently, a Petrol engine adapted to run on natural gas, even without further optimization, will already emit approximately 25% less CO2 emissions compared to a regular petrol-running engine at comparable power output. Natural gas-powered vehicles are usually bivalent,13 meaning that they can run on both CNG and petrol. 6.7.1.5 Liquified petroleum gas LPG is often marketed as Autogas and is obtained during the extraction process of crude oil. Its main components are propane and butane. The carbon content of LPG is also considerably lower, as burning it produces around 10% less CO2 compared to petrol.

6.7.2 Alternative fuels Due to the inherent scarcity of fossil fuels, attempts have long been made to replace fossil fuels with alternative fuels source derived from renewable processes.

13 Double-valued.

306

6 Propulsion systems

6.7.2.1 Hydrogen Hydrogen can be based on both fossil fuels such as natural gas or be obtained through electrolysis of water. Similar to natural gas, hydrogen can be stored either at very low temperature ð− 253  CÞ or under very high pressure ð700 barÞ (Reif, Noreikat et al. 2012). Other storage procedures are currently still in the research and development phase. Hydrogen can be combusted in traditional internal combustion engines or be used in fuel cells to generate electrical energy. 6.7.2.2 Biodiesel Biodiesel is obtained by splitting oils and fats followed by a subsequent conversion with methanol or ethanol. However, since methanol is derived from coal, the resulting fuel is not fully renewable in this case (Reif, Noreikat et al. 2012). 6.7.2.3 Biogas Biogas is obtained through a fermentation process of biomass, and can be used as natural gas after separate cleaning and CO2 removal processes (Reif, Noreikat et al. 2012). 6.7.2.4 Synthetic fuels During the production of gas (GTL – Gas to liquid), coal (CTL – Coal to Liquid), or based on biomass (BTL – Biomass to Liquid), individual molecular chains are newly formed using the Fischer-Tropsch synthesis. As a result, combustion gases of the resulting fuel are almost completely free of nitrogen oxides, hydrocarbons, and carbon monoxide (Reif, Noreikat et al. 2012).

6.7.3 Electrical energy storage 6.7.3.1 Requirements on electrical energy storage In EV, HEV, and PHEV, the electrical energy storage device is by far the bulkiest, heaviest, and most expensive component in the scope of electrification. The main purpose of the battery pack is firstly to store electrical energy and secondly to supply the required energy to the electric motors to enable pure electric driving. Additionally, other functions also benefit from the higher voltage. For PHEVs, the battery pack can be charged directly using the main power grid. The battery pack must fulfill several requirements in order to be used in a motorized vehicle. To provide the electric drive unit with the required power input of 60–180 kW, a voltage of between 300–400 V is generally required. To ensure a sufficient range, a battery pack capacity of 15–30 kWh or more for fully electric vehicles is required. For hybrid vehicles this capacity is usually in the range of 2–15 kWh, depending on their design. The number of charging cycles before battery

6.7 Energy sources and storage

307

degradation has made recharging useless must be more than 1,000 cycles.14 Battery Packs are made up of cells that store energy chemically before converting it back into electricity when required, for instance in Lithium-Ion batteries by intercalation15 of Lithium. The battery cells are placed in a housing together with the necessary contacts and wiring. Additionally, the operating electronics and if possible an air conditioning system are added. With current battery pack technology for PHEVs, the battery pack itself consists of multiple Lithium-Ion cells. The actual number depends on the required capacity and voltage. Different cell designs are possible, along with various material options. Although all are rechargeable, their properties depend heavily on the materials used. LithiumIon Batteries offer an unrivaled level of performance and energy density when compared to other battery types. Additionally, they do not show memory effects, have a low self-discharge rate, and their internal resistance is relatively low resulting in a high level of efficiency. A disadvantage is the comparatively high cost of construction. Furthermore, Lithium-Ion Cells are subject to both cyclic and calendar degradation processes. These lead to decreased nominal capacity after a certain number of charging cycles and after the cells have reached a certain lifespan in general. Damaging processes are responsible for these phenomena that depend heavily on the application range of the cells themselves. Currently, the limit to which the cells can be used without issue is assumed to be around 80% of the remaining capacity. Further problems arise when the temperature limits are reached to which the Lithium-Ion cells can be used. For this reason, the cells are usually cooled when used in motorized vehicle applications. Lead-based batteries and nickel-metal hybrid (NiMH) batteries are far less expensive in production and have long been used as a power source in special vehicles. However, their energy density is too low for application as power source in electrically driven motorized vehicles. For current and most likely also future vehicle concepts, nearly all manufacturers rely solely on Lithium-Ion Technology as the energy storage solution (Vezzini 2009). 6.7.3.2 Layout of the Lithium-Ion battery The typical layout of the Lithium-Ion Battery is shown schematically in Figure 6.49. In particular, one recognizes the essential modules found in nearly all electrical energy storage systems:

14 This is based on the option that the energy storage can still be used as stationary storage, for example, as part of a home solar system. 15 Storing

Communication interface

DC/DC converter

– SOC management –cell monitoring –thermal management –operating algorithm –fault management

Battery Management-System BMS

Figure 6.49: Modular layout of the Lithium-Ion battery pack.

Vehicle bussystem

Vehicle power net 12 V

housing

Temperature

SOC

Current level

Voltage

HV-interface

Module n

Module 2

Module 1

Cooling temperature

cell

Cooling system

cooling water port

308 6 Propulsion systems

6.7 Energy sources and storage

– – – –

309

The Lithium-Ion Cells, which are all connected to form a module, the Battery management system (BMS), the cooling system, the electrical wiring and communications interface to the vehicle.

A fully functioning battery system is shown in Figure 6.50. Powertrain harness

Cell modules Cell current rail

Current sensor Master switch module

Electronics slave module Cell

Fuse Vehicle interface

Housing Electronics main module

Internal harness

Figure 6.50: Battery system, © Johnson Matthey Battery Systems.

The total voltage delivered by a battery pack results from the series connection of each individual cell into modules.16 These exact voltages supplied by each module are the sum of voltages of all of the connected cells. Thus, for a total voltage of, for example, 360 V, the module could consist of a hundred cells of 3.6 V each. The required amount of charge is achieved through parallel connections between the modules or cells (Figure 6.51). 6.7.3.3 Cell functioning Multiple different design types and materials can be used to form Lithium-Ion Cells, all of which rely on the same principle of operation. Each cell consists of two electrodes, a separator, and an electrolyte (Figure 6.52). During the charging and discharging processes, lithium ions are discharged onto an electrode, migrate through the electrolyte, and are consequently stored in the crystal

16 Also known as pack.

310

6 Propulsion systems

Cell Cell Module

Figure 6.51: Series and parallel connection of cells and modules.

Separator

Electrolyte solution

Metal oxide O2

Al

Co

Charge

Graphite C

Li+

Cu Li+

Li+ Discharge

Cathode foil

SEI - layer

Anode foil

Figure 6.52: Basic structure of a lithium-ion cell.

lattice of the other electrode. Referring to the positive and negative electrodes is done analogous to the discharge process as the cathode and anode. The cathode is usually constructed of a metal oxide, whereas the anode is made of a carbon structure such as graphite. The highly porous electrode materials are applied onto thin metal foils by means of binding and conductive materials. The metal foils also function as a conductor. Aluminum foil is often used for the cathode, whereas the anode is usually made of copper. The electrodes are separated by the separator, through which the lithium ions can move, but not the electrons. This prevents short-circuiting the system. The ability

6.7 Energy sources and storage

311

of the electrons to move between the two electrodes is warranted using an electrolyte. This is usually made up of a non-aqueous solution, or, as is the case in novel lithium polymer cells, a gel-like polymer. At the interface between the anode and the electrolyte, a passive boundary layer (SEI – Solid Electrolyte Interface) is formed, which results from the decomposition of the electrolyte. The SEI increases the internal resistance of the cell. Two coated electrodes combined with one separator form one layer, of which multiple are joined together into one cell. The designs of lithium-ion cells range from cells with high energy densities and moderate amperages to cells with smaller energy densities and higher amperages, thus higher power density. The coating thickness also varies. Generally, a thinner coating increases the achievable power density while at the same time decreasing energy density (Ecker and Sauer 2013). Today’s cells reach voltages of 2.2 to 4.2 V each, depending on the materials used as the active components. A typical voltage seen often in commercially available cells is 3.6 V. Currently, three different formats are used for lithium-ion cells (Figure 6.53): – Prismatic and cylindrical cells have a solid shell. The layers of electrodes and separators are wound into either cylindrical or prismatic cells. – Pouch cells, also referred to as foil cells or “coffee bags,” have the electrodes and separators stacked on top of each other.

Terminals And Pressure Relief Value

Terminals

Terminals

Anode

Pressure Relief Value Separator Metal Housing Cathode

Metal Housing

Cylindrical Cell

Anode Separator

Prismatic Cell

Cathode

Pouch Cell

Figure 6.53: Construction forms of battery cells © Johnson Matthey Battery Systems.

The dimensions of the prismatic and pouch cells are standardized in accordance with (DIN 2011), whereas the dimensions of the cylindrical cells are standardized by the American National Standards Institute, also known as ANSI, (www.vartamicrobattery.com 2013). Table 6.9 contains the names and dimensions of these standardized cells. Additionally, each cell can be designed with or adapted to

312

6 Propulsion systems

Table 6.9: Types of cells and their standardized dimensions. Source: © Johnson Matthey Battery Systems.

DIN: Prismatic L x B x D /mm DIN: Pouch L x B / mm

ANSI: Cylindric D x H / mm

PHEV1

PHEV2

BEV1

BEV2

85 x 173 x 21

91 x 148 x 26,5

115 x 173 x 32

115 x 173 x 45

PHEV

BEV

165 x 227

162 x 330

18650 18 x 65

different dimensions to fit the installation space inside a certain vehicle. However, these cells do not achieve the indicated values of the standardized components. Another disadvantage is the effort it takes to adapt the manufacturing equipment to meet the specific dimensional requirements. – Cylindrical cells are commonly found in electronics used in entertainment, household, or industrial appliances (Ecker and Sauer 2013). However, their relatively large cooling requirements and the often poor vehicle-placement possibilities have made them rare in electrical vehicles. – Prismatic cells tend to be very stable as well as protected from any mechanical damage due to their solid housing. A clear downside of this housing is the fact that it adds more weight and thus limits the energy density of the cell. – The Pouch cell displays similar but opposite advantages and disadvantages compared to the prismatic cell due to its lack of a solid housing.

6.7.3.4 Cathode materials The various lithium-ion cells distinguish themselves by the active material used at the cathode side. Each material will result in a cell with specific advantages and disadvantages. Each material combination can lead to significant differences in terms of energy density, power density, safety, stability, lifespan, and costs (Dinger, Martin et al. 2010). A single material that exhibits advantages in all disciplines does not exist. The material choice is therefore highly dependent on each individual application and the corresponding requirements, most of which can only be partially met. Table 6.10

6.7 Energy sources and storage

313

shows an overview of properties of the most used cathode materials. These properties are also influenced by the respective mixing ratio and the cell design. Because of this, value ranges are given for some parameters, such as for energy density. Table 6.10: Essential cathode materials for lithium-ion cells, according to Vezzini (2009) and Ecker and Sauer (2013). Lithium cobalt oxide

Lithium Lithium manganese- nickel oxide oxide

Lithium nickel mangnese cobalt

Lithium iron phosphate

Abbreviation

LCO

LMO

LNO

NMC

LFP

Chemical Structure

LiCoO

LiMnO

LiNiO

LiNiMnCoO

LiFePO

Advantage

High energy density

High thermal stability

High energy density

Depends on the mixing ratio of LCO, LMO, and LNO

Safe

Disadvantage

High costs

Dissolves partially in electrolyte

Low thermal stability

Voltage / V

.

.

n. A.

.

.

Energy density / Wh/kg

–

–

n. A.

–

–

Low energy density

Lithium cobalt oxide (LCO) is often used in consumer and household electronics, where the safety and durability requirements are usually lower compared to those for vehicle applications. This material combination allows a high energy density but is also quite costly due to the high cobalt content. Other commonly used cathode material combinations are Lithium nickel oxide (LNO) and Lithium Mmanganese oxide (LMO), of which the respective advantages and disadvantages are listed in Table 6.10. In Lithium nickel manganese cobalt cells (NMC), the three added materials are mixed in such a way as to optimize the resulting properties of the cell. These cells can thus be tailor-made for each application. Depending on the mix, the energy density of LCO, the safety of LMO, and the performance of LNO can be combined. Another cathode material combination is Lithium iron phosphate (LFP), which provides a low energy density but is considerably safer in operation (Ecker and Sauer 2013). In the battery pack of the BMW ActiveE, NMC cells are used providing an energy density of about110 Wh=kg (Jung and Hofer 2011). The volumetric energy density of these cells generally lies between 190 and 250 kWh=l (Howell 2012). Due to the properties mentioned in this section, NMC cells are frequently applied in current day applications (Zschech 2010).

314

6 Propulsion systems

Data found in literature gives values for power densities between 500 W=kg for electric vehicles and 3, 000 W=kg for hybrid vehicles. In between are values for PHEVs. The reason for this broad variation can be attributed to different cell designs in terms of power and energy on the one hand, and a dependence on other operating conditions on the other. These include, for example, the amount of charge, as a full battery pack allows a higher power output than an empty pack. In addition, the output may drop significantly after expiration of the battery’s service life as well as outside the advised temperature range of 20 to 40  C (Ecker and Sauer 2013). The cells are connected either in parallel or in series and are joined together with the required mechanical and electrical components, such as contact points and the housing, to form a complete module. These modules are then connected in series or in parallel to form a battery pack, as shown in Figure 6.54. The interconnection between the cells and modules defines the battery pack’s characteristics, such as its capacitance and maximum current and voltage outputs. 6.7.3.5 Battery management system (BMS) Controlling and protecting electrical energy storage systems requires additional components. A cell monitoring system, often abbreviated as CSC (Cell supervision circuit), monitors the cell’s voltage and temperature. It also compensates for different charge states of the cells. The cell monitoring system is connected via a bus to the Battery Management System (BMS). The BMS controls all processes inside the energy storage system, for example, the circuit of relays, but also provides security and diagnostic functions. Additionally, it controls the cooling system and estimates the current state of the cells in terms of performance, charge state, and degree of age-induced degradation. In the case of safety-related malfunctions, during service, or when the battery is not being used, the electric energy storage is disconnected from the vehicle’s electrical system via fuses and relays in the switchbox (Auto/ Manual-Disconnect). Various concepts exist to cool down these types of electric energy storage systems. The BMW ActiveE is fitted with a water-glycol cooling system, which is connected to the vehicle’s cooling circuit via a heat exchanger (Jung and Hofer 2011). 6.7.3.6 Structure of the sub-assemblies Besides the components required to control and protect the system, the cells contribute most to the electric energy storage systems in terms of weight and volume. Empirical analysis on existing PHEVs has provided volume and mass fractions of the storage cells with respect to the entire storage system, as shown in Figure 6.55 (Ried 2014). The mass fraction is around 60 % and the volume fraction ranges between 30 and 40 %, corresponding to a minimal and maximum use of space respectively.

6.7 Energy sources and storage

a)

315

c)

b)

Figure 6.54: Lay-out of an electrical energy storage system: a) Cell, b) Module, c) Pack or electrical energy storage system. Source: (Ried 2014).

70

Mass share Mass and volume share cells/%

60

Volume share

50 40 30 20 10 0

Vehicle A

Vehicle B

Vehicle C

Vehicle D

Vehicle E

Figure 6.55: Mass and volume fractions of cells with respect to the total electric storage in existing PHEVs in liquid-cooled conversion design, but with different topologies and cell types (Ried, Wittchen et al. 2013).

6.7.3.7 Prospects Battery cells now account for a very large proportion of the total cost of an electrically powered vehicle. For the coming years and decades, however, technical progress in both the materials used and the production methods is expected to lead to a significant reduction in costs per kWh of stored charge (Figure 6.56). In theory, further cost reductions could also be achieved in the longer term if batteries could be made smaller again in the future, if extended fast-charging options were available on a widespread basis. In fact, however, the trend tends to be toward larger battery packs today.

316

6 Propulsion systems

500

Price/€/kWh)

400

400 € 360 € 275 €

300

225 € 171 €

200

135 €

107 €

100 0

2013

2014

2015

2016

2017

2018

2019

84 €

2020

Figure 6.56: Worldwide price evolution for Lithium-Ion Batteries from 2013 to 2020 (in Euro/kWh). Years 2018 to 2020 projected target values (Horváth&Partners 2018).

In addition to lithium-ion cells, researchers are looking into lithium air (Li-O2 ) and lithium-sulfur (Li-S) cells. These combinations achieve specific energy densities with a factor seven to nine higher than conventional cells, although they still pose problems in terms of safety and lifespan. In fact, Li-O2 cells currently only reach a few hundred cycles. Research on Anode materials is also being conducted, where silicon fractions could achieve higher energy densities compared to graphite. Theoretically, energy densities could be increased by a factor eleven, were it not for the biggest issue being the volume change of almost 400% during a single cycle. It is still unclear whether one of the above mentioned technologies will eventually meet the standards required for automotive application (Ecker and Sauer 2013). Further development of the well-established Lithium-Ion Technology will allow for energy density increases of about 50% by 2020 and an additional 40% by 2025 (Howell 2012). The reader is referred to Ried (2014) and Ried, Karspeck et al. (2013) for a more in-depth analysis and prognosis on electric drive systems, in particular with regard to the costs and achievable range related to hybrid vehicle.

7 Vehicle safety In complex systems like road traffic, risks cannot be fully avoided. Therefore, the global increase of traffic density and the constantly growing complexity of traffic create ever greater challenges for all traffic participants. While the number of vehicles in 1950 was at 2.4 million vehicles, six decades later, there were 52.3 million vehicles on the roads in Germany alone (Destatis 2011). With approximately 79% passenger vehicles hold the largest share of this rapid increase. The quick development of motorization has also massively driven the expansion of the road network. However, the infrastructure did not expand to the same extent as the amount of traffic. While the share of motor vehicles between 1950 and 2010 increased by more than 1,000 %, the federal road network (including federal highways and roadways) only increased by 200 % (Bundesanstalt für Straßenwesen) (Heide 2014). Similar trends can be observed globally. The result was a continuous increase of traffic density and thus a steadily growing general risk of collision in traffic. The accident statistics of the German Institute for Transport Research thus shows a nearly parallel increase of traffic accidents and the respective amount of motor vehicles (Figure 7.1).

7.1 Areas of vehicle safety 7.1.1 Definitions First, it is useful to clarify what safety is in the context of traffic. (Absolute) safety is commonly understood to be the absence of danger. According to Kramer (2013), “the accident (as a synonym for the not-normal case, and thus the incident)” can be defined as follows: “An accident is an event in which the difference between given driving task and its fulfilment exceeds a permissible value (unmastered control task), which immediately results in damage that is determined both in kind and severity”.

According to DIN/VDE (1987), damage is a disadvantage due to the violation of legally protected interest of a particular technical operation or condition. The damage is to be differentiated according to its extent. Here, both property damage to the motor vehicles involved and other affected goods and personal injuries can occur. Risk is the expected frequency of an event creating damage, and the extent of losses occurred in case of that event. With this, a definition can also be formulated according to DIN/VDE (1987) for the term “danger”: Danger is a situation in which the risk is greater than the largest acceptable risk of a certain technical operation or state. Using this, the term safety can now be described according to DIN/VDE (1987) as a situation in which the risk is smaller than the largest acceptable risk of a certain technical operation or state. https://doi.org/10.1515/9783110595703-007

7 Vehicle safety

30

70 60

Number of motor vehicles

50

Number of accidents registered by police

25 20

40 15 30 10

20

5

10 0 1900

1920

1940

1960 Year

1980

Number of accidents × 100,000

Number of motor vehicles × 1,000,000

318

0 2020

2000

Figure 7.1: Development of the amount of motor vehicles and the number of police recorded traffic accidents in Germany between 1906 and 2010.

When designing a new vehicle, measurements ensuring maximum safety of all traffic participants are of utmost importance. With this, the development of safety components is one of the most important stages in the development process of new vehicles both for people involved in development and the quality control accompanying production. A distinction is made between active and passive safety systems. The measures of active and passive safety can, for example, be classified using the temporal sequence (Figure 7.2). In normal driving conditions, the driver is supported in his driving by supplying information. This is followed by the phase of accident prevention while the driver assistance systems support the driver (see Chapter 9). Once an accident becomes inevitable, measures are taken in the pre-rash phase that are aimed at reducing the severity of accident and injury. This is followed by measures of passive

Information

Accident prevention

Warning and support

Precrash

In-crash

Postcrash

Accident

Normal driving condition

Intervention and conditioning

Active safety

Figure 7.2: Classification of active and passive safety.

Retention

Rescue

Passive safety

Rescue

7.1 Areas of vehicle safety

319

safety. These include not only constructive measures of the vehicle structure but also furthermore passive and active restraint systems such as belts with tensioners and a multitude of airbags. In the developments of the recent years, both passive and active systems have grown together more and more, so that, today, safety concepts are usually called integral safety concepts. Active safety systems help the driver in critical situations to avoid an accident. They are thus also called accident avoidance measures. They can furthermore be implemented to decrease the severity of accident consequences by intervention right before the accident (see, e.g., (Maurer 2013)), or a preconditioning of the vehicle and its passengers. Among others, these include the driver assistance systems described in Chapter 9, for example, ABS, ESP, adaptive light control, LDW, as well as the socalled precrash systems (Kurutas 2011), (Kurutas, Claas et al. 2006). The passive systems contain all systems and components that reduce the consequences of an occurring accident. They have an especially protective effect in collisions. Here, more and more not only the self-protection (protection of the own vehicle and its passengers) but also the protection of other road users (partner and counterparty protection) are crucial. The measures implemented do not include only the vehicle structure, which is supposed to protect passengers during an accident, but also the so-called restraint systems, which are supposed to decelerate the forward motion of a passenger in such a way that the severity of injuries is as low as possible. This includes the earliest possible participation of passengers in the deceleration of the vehicle. The construction measures of today’s vehicles include, for example, the separation of the vehicle structure into a deformation-rigid passenger compartment, as well as selectively chosen deformation zones in the front and back of the vehicle, which are supposed to reduce the impact energy during a collision in a controlled manner. Today, the restraint systems mainly consist of belts with pretensioners and a multitude of airbags in the interior of the vehicle.

7.1.2 Systems of active safety Systems of active safety actively intervene in the driving to alleviate critical situations or avoid them altogether. They thus mainly serve in accident prevention. Systems of active safety are furthermore, for example, the driver assistance systems such as vehicle dynamics control, brake assist, and lane monitoring systems. The most important aspects of active safety are as follows: – Driving stability that includes the driving behavior and the controllability of the vehicle, for example, in curves, as well as its reaction to steering, braking, and acceleration maneuvers of the driver. – Driver-fitness safety describes the protection of passengers, as well as the driver, against vibrations, noise, and other interference.

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7 Vehicle safety

– Perceptual safety describes safeguarding and improving the perception of the surrounding traffic, environment, and the behavior of the vehicle. – Operating safety describes the possibility of a simple and error-free operation of the vehicle before and during driving, without distracting the attention of the driver. It is primarily ensured using a clear and intuitive design of the control elements of the vehicle.

7.1.3 Systems of passive safety As a reaction to the increase in the number of serious traffic accidents, especially resulting in death in the 1950s and 1960s, massive efforts were made in the development of passive safety systems. The primary goal was the reduction of the risk of injury of passengers in the event of a collision. Significant milestones in these efforts were the development of the security passenger compartment by Mercedes in 1951 and the first standard installation of the three-point safety belt by Volvo in 1956. Due to the slow and hesitant use of seat belts by passengers, only the intervention of legislators in 1976, who implemented the requirement to wear a seat belt, resulted in a sustained decline in the number of severe traffic accidents with fatalities (Figure 7.3). As a result of the technical and legislative measures taken, the number

Killed/1,000 inhabitants in Germany 1973 0.8 ‰ BAC 1973/74 Oil crisis

25 20

1957 50 km/h in towns

1972 100 km/h in country roads

15 10

Cruise control system

1974 rocommended speed on motorways 1980 obligation to wear crash helmets ABS 1980 obligation to Seat belts wear seatbels Airbag

1998 0.5 ‰ BAC

ESP BAS

ASR

ACC Emergency brake assistant Tire pressure monitoring system

5 3,307 0 53 55

60

65

75

80

85

90

95

2,000

Lane keeping Adaptive assist high beam

05

10

14

Figure 7.3: Fatal traffic accidents in Germany 1953–2014; data source: German Federal Office for Statistics. Filled circles refer to the introduction of new technical systems to prevent accidents; empty circles mark introduction of new legal requirements. BAC: Blood alcohol content.

7.1 Areas of vehicle safety

321

Number of accidents and personal injuries × 1,000

of deaths in Germany fell to 3,177 in 2014 (Destatis 2018) and to approximately 25,300 in the EU in 2017 (European_Parliament 2019). The peak of accidents involving serious personal injuries had already been passed in the 1970s (Figure 7.4). What followed was a stabilization of accidents with personal injuries and a rapid, steady decrease of traffic accidents with serious personal injuries and deaths. 2,500 Number of personal injuries 2,000

Number of accidents registered by police

1,500 1,000 500 0 1940

1950

1960

1970

1980 Year

1990

2000

2010

2020

Figure 7.4: Personal injuries in traffic accidents in Germany 1950–2010.

Interesting is the constant distribution of fatal accidents across the individual road types over the years. Here, at least regarding Germany, a uniform decrease in the numbers can be observed, as Figure 7.5 shows. The introduction of airbags in 1980 further improved this favorable development. A further and indispensable part in this development was the continuous advancement of vehicle structures, which allowed for a dissipation of the kinetic energy that occurs during a collision. To reach this, an optimal distribution of the deformation energy to the vehicle structure is necessary. At the same time the deformation of the passenger compartment is to be prevented, or at least reduced. With this, the body structure of the vehicle plays an important role in passenger protection for the first time (Kramer 2013). In the years following 1980, there were no decisive improvements in passive safety at first. The Euro NCAP crash test 1997 (European New Car Assessment Program) (NCAP 2013, NCAP 2016) triggered strong efforts of manufacturers to increase the levels of safety in new vehicles. The result was a targeted design of the vehicle structures according to the new and challenging crash disciplines. Today, these interpretations determine the body, and following this, the function of the frame during a crash.

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7 Vehicle safety

8,000 7,503

Highways 6,977

7,000 6,000

6,842

Federal roads

6,613

Country roads 5,842 5,361

5,091

5,000

District roads Urban roads

4,949 4,477

4,152

Total

4,009 3,648 3,600 3,339 3,377 3,4593,206 3,180

4,000 3,000 2,000 1,000 0

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Figure 7.5: Killed traffic participants by road type 2000–2017; data source: (Radke 2018).

7.1.4 Legal rules and regulations Vehicles are, of course, not only subjected to the worldwide NCAP crash tests relevant for consumer protection. Rather, each vehicle series needs to achieve a variety of regulatory approvals to achieve road legality. The approval processes as well as the assessment criteria used are based on the country-specific safety regulations. In Europe, these test procedures are determined by the so-called ECE1 regulations (EWG). This is a catalogue of regulations that summarizes the uniform technical regulations for wheeled vehicles in the EU. In passive safety, there are predefined objectives for frontal, lateral, or rear crashes as well as pedestrian protection, which must be demonstrated using predetermined test procedures. This either results in the fulfillment of requirements, or the exposure of deficits. These results are not required to be published. The NCAP consumer protection tests typically significantly go beyond the regulatory requirements. The NCAP awards the well-known safety stars for passing the tests, which are often well covered by the media, and thus promotes competition between manufacturers. As a result, new vehicles are built not only to meet the criteria relevant for approval but also to pass the crash tests relevant to consumer protection. Internationally, there is a multitude of other rules and requirements; for example, the American “Federal Motor Vehicle Safety Standard (FMVSS),” which defines

1 ECE: Economic Commission for Europe; ECE regulations are internationally agreed upon, uniform technological requirements for motor vehicles, as well as parts and equipment for them.

7.1 Areas of vehicle safety

323

the minimum requirements of vehicle components, or the crash tests according to the “US NCAP” or “J NCAP” requirements (Companion 2016). Figure 7.6 shows an excerpt from the crash disciplines specific to organization and regulation.

Consumer protection Europe USA

OBD

FF

Euro-NCAP

64 km/h

–

US-NCAP

–

56 km/h

IIHS

64 km/h

Japan

JNCAP

–

– 55 km/h

China

C-NCAP

–

50 km/h

Legal regulations

OBD

FF

Europe

ECE-R94;96/79/EC

56 km/h

–

USA

FMVSS 208

40 km/h

56 km/h

Japan

TRIAS GB 11551–2003

56 km/h 56 km/h

50 km/h

China

50 km/h

Figure 7.6: Examples for laws about passenger protection and tests by consumer protection organizations. OBD: Offset deformable barrier test; see Section 7.24 FF: full frontal test; see Section 7.2.3

For a vehicle to be registerd in different countries it needs to be able to pass each of the country specific crash tests (Figure 7.7). This is linked to a significant overhead due to the multitude of different regulations. The influence of crash disciplines on the design of the vehicle structure can be shown, for example, using the small-overlap test, which has been performed by the American organization IIHS since 2012 (IIHS 2014). In this not-yet determined by law test procedure, the vehicle collides with a rigid barrier going 64 km=h with a 25% overlap. The new testing procedure hit the German vehicle manufacturers among others unprepared and at first resulted in unexpectedly bad performance of the German premium vehicles, which are otherwise deemed especially safe (IIHS 2012). Following this, the crash discipline was promptly included in the test portfolio of the manufacturers and the measures derived from it were swiftly implemented. Due to the aforementioned reasons, the development of the car body in terms of its structural stiffness depends largely on the requirements resulting from the actual accident. For example, this can be recognized by a kind of accident that often occurs in the United States and was thus responsible for the establishment of a special testing procedure. In parts of the United States, there have been many accidents recorded with roll-overs at roads without planks in embankments close to the

324

7 Vehicle safety

US NCAP

Euro NCAP 0°

0°

50 km/h

Hybrid III 5%

Hybrid III 5% Hybrid III 5%

IIHS

56 km/h

Hybrid III 50%

Hybrid III 5%

ODB 40%

ODB 40% 0°

0°

64 km/h

Hybrid III 50% Q3 Q6

Hybrid III 50% Q1.5 Q10

WS 50%

R=150 mm

64 km/h

Hybrid III 50%

SID IIs

ES=2 re /h/ 27 °

km

50 km/h 90°

55 km/h

AE-MDB, 1300 kg Q1.5 Q10 Q3 Q6

0°

64 km/h

Hybrid III 50%

62

50 km/h 90° ØR+150 mm

Flat 150 SOB 25%

MDB IIHS, 1500 kg

MDB, 1358 kg SID IIs

SID IIs

Far side occupant protection

WS 50%

Rigid 254 mm Pole

32 km/h 75°

SID IIS

32 km/h 75°

Rigid 254 mm Pole

Figure 7.7: Schematic illustration of a few international crash disciplines (Companion 2016).

road. Thus, the test procedures relevant to registration were supplemented by roof impression tests and roll-over tests. In Europe, those tests are not used as these kinds of accidents are statistically rarer. The respective requirement catalogues thus are primarily focused on present and actual accident statistics. The necessary categorization is done by first roughly separating the accident scenarios in frontal, lateral, and rear impacts. In Germany, the frontal crash is by far the most common type of collision (Figure 7.8). The seemingly obvious assumption that this kind of accident also causes the most fatalities can however not be confirmed by statistics, as shown in Figure 7.9.

7.2 The role of the vehicle structure

325

Roll-over 2%

Side crash 23 %

Frontal crash 51% Rear crash 24%

Figure 7.8: Distribution of types of accidents in Germany (Destatis 2012).

Rear crash 4% Roll-over 11 % Under tunneling 12 %

Side crash 45 % Frontal crash 28 %

Figure 7.9: Distribution of fatalities per type of accident (Destatis 2012).

The actually biggest risk results from lateral collisions. Here, the passengers are exposed to especially high loads because the missing deformation path (crumple zone) makes it hard to protect them (see Section 7.2).

7.2 The role of the vehicle structure The design of a vehicle structure with regard to the reduction of the ramifications of accidents is extremely difficult. As in different areas of the vehicle body, the difficulty results from the fact that the requirements are often in conflict with other requirements. In this case, these are, for example, packaging, design, or other criteria. Even in the area of passive and active safety, such as the partner protection (especially the protection of pedestrians), conflicting demands arise. This leads to different development goals that need to be consolidated: – At least parts of the structure need to be so rigid that passengers have sufficient survival space available.

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– On the other hand, the structure needs to be able to absorb a great amount of energy in a given period of time such that the deceleration load can be kept sufficiently small for passengers. – The requirements of insurance companies, which have an interest to minimize repair cost resulting from smaller collisions, need to be taken into consideration as well (RCAR 2011). The latter requirement, for example, leads to designs in which frontal structural elements are cascaded with increasing stiffness. This increasing longitudinal stiffness ensures that deformations only occur in the outer area, which can be repaired cost effectively. In large collision velocities, this design however wastes deformation path, as the front elements with the necessary low stiffness succumb to smaller forces than would otherwise be possible. Furthermore, this design also makes the recognition of the severity of a collision more difficult for the airbag control unit (Heide 2014). Additionally, starting in the early 1970s with the first oil crisis, the demand for a reduction of vehicle mass to reduce fuel consumption arose. Since the 1990s, this demand has further been strengthened by legislators with limits for CO2 emissions (see Chapter 6). The emission of CO2 is directly related to fuel consumption, which is decisively impacted by vehicle mass. Comfort and safety systems, on the other hand, increase the fuel consumption due to their weight and energy consumption. Therefore, all vehicle manufacturers are eager to reduce vehicle mass if possible. Depending on vehicle mass and features, a weight saving of 100 kg, the consumption can be decreased by up to 0.5l per 100 km (Schramm and Koppers 2014). What follows is a trend towards the so-called lightweight design. The implementation of further reducing vehicle mass can, on the one hand, be achieved by modern construction, and, on the other hand, by using alternative materials such as aluminum, high-strength lightweight steel, or carbon fiber-reinforced plastics. The material lightweight design offers the bigger potential of the two measures. Today, significant weight reductions of the body can be achieved using the measures mentioned. Materials such as carbon are comparatively expensive and are thus only deployed hesitantly. Next to the expensive primary materials, the primary cost driver is the high cost of production. The use of aluminum, plastics, and magnesium is also possible, though it also comes with the disadvantage of a much costlier production. There is thus a different constructive way, which opts for a reduction of materials by optimizing the structural topology. Here, massive castings are replaced by loadoriented rib structures and hollow core profiles where possible. Furthermore, wall thickness is reduced in low-stress areas and stress-free sectors are omitted entirely if possible. These measures are based on structural or constructive lightweight design (Friedrich 2013). The measures realized in this regard however must under no circumstances reduce the passive safety and thus each require a careful mechanical structure analysis to rule out structural failure. The passenger compartment therefore must

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327

– provide a survival space for passengers and thus exhibit a high stiffness in severe accidents, and – have crumple zones, which break down the kinetic energy uniformly and passenger-friendly by deformation. Even with the mentioned tensions between different design requirements, modern vehicle bodies today have reached a level of development, which allows for a direction of the forces of a crash in a way that the protection for passengers is as good as possible. Figure 7.10 shows this for a frontal and a lateral crash using the example of the E-Class introduced in 2016 (W213).

Figure 7.10: The flow of forces (light arrows) in the body during a frontal collision (left) and a lateral collision (right) © Daimler AG.

Next to the optimal deformation of the body to deflect the energy in collisions, the use and the correct deployment of the restraint systems such as airbag and belt pretensions are important. Here, on the one hand the optimal placement of crash sensors and, on the other hand, the signal transmission characteristics of the structural elements play a significant role. The structure of the body thus should provide acceleration signals that are easy to interpret to definitely distinguish a park bump from a critical accident. Next to a statement about the deformation behavior of the vehicle structure, the deformation behavior and the crash signal transmission must be analyzed. In the prototype phase, cost- and time-intensive crash tests are carried out, and during the construction phase, simulations with finite elements are run. On the other hand, during the concept phase or the predevelopment, neither hardware nor CAD data (Computer Aided Design) are regularly available to design simulations or component tests that are adequately detailed. That is why other approaches have been suggested. During the concept phase, it is often necessary to quickly gain insights about the signal curve and to derive from it design criteria for new structures. To this end,

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Acceleration

a multibody model was developed in Heide (2014), which describes the essential elements of the vehicle front sufficiently accurate to credibly simulate signal curves depending on the type of crash. The choice of abstraction level here depends on the physical requirements based on the findings of a data analysis. To this end, at first, a typical (filtered) acceleration progression is considered over time (Figure 7.11). In the figure, there are points of time marked during with the deformation of single body parts begins (change of event).

ss

Cro

m ea

x

b

sh

Cra

bo

ud

git

Lon

l ina

am

1

be

am

2

be

Event change Crash signal

ud

git

Lon

l ina

Time

Figure 7.11: Typical course of acceleration during a frontal crash (Heide 2014).

During collisions, different kinds of typical impact are distinguished: – frontal crash, – lateral impact, – rear impact, and – roll-over.

7.2.1 Example frontal crash In the following example of a frontal crash, some typical kinds of crash are described that are to be represented by the crash tests (Figure 7.12).

7.2.2 AZT/RCAR test The AZT/RCAR test is an “insurance” test established by the “Allianz-Zentrum für Technik,” in order to estimate the repair required for light rear-end collisions and to thus better classify them. This type of damage test, also called repair crash, is executed with a collision velocity of approximately 15 km=h against a hard barrier with a degree of coverage of 40% (Figure 7.12). In such light collisions, there must not be

7.2 The role of the vehicle structure

AZT

ODB

329

FF

10o

Figure 7.12: Typical accident scenarios for the frontal structure.

any costly damage to the carriage or the restraint systems. One consequence of this requirement is that restraint systems must not be activated. Thus, the minimum trigger level must be above the deceleration curve of this repair test. Despite the unilateral load, there must not be any damage to the longitudinal structure to the body and the parts in the forebody. In 2006, the repair test requirements have been tightened further by adding an additional 10 barrier.

7.2.3 FF (full frontal) In a full-frontal crash, a vehicle hits a rigid obstacle with the entire front. Depending on the respective regulations, this high-speed crash is operated at collision velocities between 50 and 56km=h. In the United States, Japan, and China, this crash scenario is part of the standard portfolio, while it is not tested in Europe.

7.2.4 ODB (offset deformable barrier) The offset deformable barrier (ODB) test with a deformable barrier is both part of the European frontal collision regulations and an integral part of international test procedures. The frontal part of the barrier used consists of a soft aluminum honeycomb structure. The rear part consists of a massive block of concrete. This crash structure imitates the deformation behavior of a second vehicle as a collision partner. The coverage ratio of 40% initiates an offset crash as the offset frontal crash is the most often recorded traffic accident with personal injury according to accident statistics. This and further standardized procedures make it possible to gain insights during early stages of development of a vehicle into the deformation behavior and the

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signal transmission of the vehicle structure in different load situations. That way, potential vulnerabilities can be recognized early on and corrected if necessary.

7.3 Basic course of a frontal collision Fundamentally, three distinct and consecutive phases can be distinguished in a collision crash: – the initiation of impact (precrash), – the collision, and – the crash consequences (postcrash).

7.3.1 Physical considerations concerning the frontal crash In the following, only the frontal crash is subject of a fundamental physical analysis. The lateral crash is subject of different rules due to the completely different conditions of the deformation behavior. First, it is assumed that the kinetic energy existing before the collision is completely dissipated during the collision. In this case, the existing kinetic energy at the start of the crash is completely converted into deformation energy during the crash. In the following, the collision is viewed as a classic shock operation according to NEWTON’s law of impact and the state at the start of the collision in t = 0 is compared to the state after the collision in t = tend . In this case, the state can each be described by the impulse I = mv. One has ð  a FDef ðτÞ + F a ðτÞ dτ ΔI = I ðtend Þ − I ð0Þ = tend

(7:1)

t=0 a and all other external forces F a , which are tempowith the deformation force FDef rally variable during and which therefore need to be integrated over

the
crash,

a
time. Assuming
FDef

F a
and a crash duration Δt approaching zero, as well as neglecting the temporal development of the deformation force, eq. (7.1) can thus be formulated to

ΔI = I ðtend Þ − I ð0Þ = m1 ðvend − v0 Þ,

(7:2)

with m1 being the mass of the first crash partner. When now considering two crash partners that move with the velocities 0 v1 and 0 v2 before the crash and e v1 and e v2 after (Figure 7.13), the conservation of momentum ensures ΔI1 = ΔI2 ) m1 e v1 + m2 e v2 = m1 0 v1 + m2 0 v2

(7:3)

7.3 Basic course of a frontal collision

!1

331

!2

2

1 Figure 7.13: Frontal collision of two vehicles.

as well as from NEWTON’s law of impact for the partially elastic crash with the coefficient of impact2 ε:   e v1 − e v2 = − ε 0 v1 − 0 v2 . (7:4) Equations (7.3) and (7.4) are two linear equations with the two unknown factors of v1 and e v2 . After several transformations to solve for the first crash partner, the equation e

e

v1 = 0 v1 −

 m2 0 v1 − 0 v2 ð1 + εÞ m1 + m2

(7:5)

arises and correspondingly for the second crash partner e

v2 = 0 v2 −

 m 1 0 v2 − 0 v1 ð1 + εÞ. m1 + m2

(7:6)

From this relationship, each velocity changes can be derived during the collision. One has Δv1 = e v1 − 0 v1 = −

 m 2 0 v1 − 0 v2 ð1 + εÞ m1 + m2

(7:7)

Δv2 = e v2 − 0 v2 = −

 m 1 0 v2 − 0 v1 ð1 + εÞ. m1 + m2

(7:8)

and

For the loss of kinetic energy during the impact arises   1 1 1 0 2 1 ΔE = e E − 0 E = m1 e v12 + m2 e v22 − m1 v1 + m2 0 v22 2 2 2 2

(7:9)

and with eqs. (7.5) and (7.6) the relationship ΔE =

2   1 m1 m2 0 v1 − 0 v2 1 − ε 2 . 2 m1 + m2

2 Also called the coefficient of restitution.

(7:10)

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In a collision with a rigid barrier, for example, in eq. (7.5) m1 = m, m2 ! ∞, e v1 = v, and e v2 = 0. This results in e

  1 v1 = − vε and ΔE = mv 2 1 − ε 2 . 2

(7:11)

The calculated loss ΔE of kinetic energy in both vehicles is transformed during the collision in form of conversion work at the vehicles and heat. The latter can be neglected below, that is, it is ð

tend

ΔE ≈ − Wdef = −

a Fdef ðτÞdτ.

(7:12)

t=0 a ðtÞ, only qualitative statements can be For the temporal force development Fdef made at this time (see also Figure 7.11).

7.3.2 Parameters for accident severity In order to assess the accident severity, a series of benchmarks can be utilized that can be determined using the parameters calculated in Section 7.3.1. Here, it is hypothesized that for each of the chosen indicators, the damage presented is similar. 7.3.2.1 EBS (equivalent barrier speed) In the criterion of the equivalent barrier speed (EBS), the impact velocity to a flat, rigid barrier is used for comparison, in which the same change of form work Wdef is done as in the real accident. 7.3.2.2 ETS (equivalent test speed) The measure equivalent test speed (ETS) corresponds to the impact velocity to a suitable, fixed or movable, barrier, in which the same change of form work is done as in the real accident. Here, it is assumed that the damages arising can represent those created in the real accident. 7.3.2.3 EES (energy equivalent speed) The criterion energy equivalent speed (EES) is based on the impact velocity to an arbitrary fixed obstacle in which the same change of form work is done as in the real accident. The velocity vEES is then calculated as rffiffiffiffiffiffiffiffiffiffiffiffiffi Wdef . (7:13) vEES = 2 m

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7.4 Restraint systems

7.3.2.4 Change of velocity Δv The change of velocity criterion is based on the difference between collision and discharge velocity. 7.3.2.5 Ride-down effect The ride-down effect allows a statement about the extent in which the passenger protection systems are effective during an accident (see Section 7.4.1). Using the maximum deformation path smax of the vehicle, the deformation path of the vehicle sRD at time tRD from when the restraint of the passengers comes into effect it is calculated to RDE =

smax − sRD 100%. smax

(7:14)

A value of 100% means that the deceleration of the passengers begins at the same time as the deceleration of the vehicle at t = 0. Correspondingly, a value of 0% means that the passenger has not experienced any deceleration due to the restraint systems until the time of maximum vehicle deformation.

7.4 Restraint systems Restraint systems are used with the objective to keep the forces acting on the passengers during an accident as low as possible. This is achieved by controlling the depletion of the passengers’ kinetic energy. In modern vehicles several different passenger protection systems are used (Figure 7.14): Data leads

Roof airbag

Side airbag

Out-of-position sensor Front passenger’s airbag Belt Pretensioner

Precrash sensor Driver’s airbag Side airbag sensors Up-frontsensors

Control unit

Figure 7.14: Typical equipment of restraint systems in a motor vehicle.

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– seat belts with pretensioners and force limiters, – front, side, and roof airbags, and – roll-over protection systems. The greatest protection is offered by the seat belts as they alone take on approximately 50 − 60 % of the passenger’s kinetic energy (Bosch, Reif et al. 2014) and furthermore prevent the ejection of passengers during a roll-over. Optimal results can be reached using a suitable combination of the effect of belt and airbag systems. This requires a network of the individual protection systems (Figure 7.15), as well as a careful coordination of the trigger times for each protection system (Figure 7.16).

Airbag system

Crash sensors

Igniter

Airbag

Micro controller Vehicle occupants

Belt system

Belt tensioner Seat belts Limiter

Figure 7.15: Fundamental function and network scheme of a restraint system.

7.4.1 Seat belts and pretensioners Seat belts protect passengers by letting them take part in the deceleration of a vehicle during an accident as soon as possible. By doing this, the forward motion of the passengers is supposed to be limited as much as possible to avoid a collision with parts of the interior or the windshield. The basic sequence of passengers’ forward velocity and displacement during a frontal collision is shown in Figure 7.16. Without interference of the seat belts, the passengers would move forward unabated and subsequently hit parts of the interior of the vehicle (dotted line). With seat belt and airbag, the movement of the passenger is decelerated early, and the forward movement is thus inhibited (solid line).

335

7.4 Restraint systems

A

B

C

D A impact

50

100

Occupant velocity 󰜈 /(

km ) h

C belt tightened 80

D airbag filled

40

s 60

30 󰜈 Without restraint system

20

s With restraint system

10

0

20

40

60

40

20

Occupant forward displacement s/cm

B actuation of belt tensioner and airbag

80 Time t / ms

Figure 7.16: Delay and forward movement of a passenger during a frontal crash.

Today’s vehicles are usually supplied with three-point belts with automatic retractor. The buckle is attached to the seat in adjustable seats; the retractor is connected to the B- or C-pillar (Figure 7.14). Belt pretensioners support the protective effect of belts by largely eliminating the usually existing belt slack. Some of the belt slack is caused by the passenger. Especially winter clothing but also other circumstances that prevent the belt from lying flat on the passenger’s body are typical reasons. Additional belt slack arises due to the so-called film reel effect and stretch of the belts (Kurutas 2011). During the impact, the pretensioners pull the belts closer around the body of the passenger and thus keep the upper body as close to the seat back as possible. The maximum forward movement with tightened belts is at approximately 2 cm; the procedure of tightening takes between 5 and 10 ms (Bosch, Reif et al. 2014). Belt pretensioners are used not only for frontal impact but also increasingly for side impacts. Shoulder pretensioners and/or belt buckle pretensioners are used. The combined and coordinated use of both systems offers the best protection. Shoulder pretensioners are activated pyrotechnically. Here, a propelling charge is electronically ignited whose released gas load turns the belt roller via a piston and a steel cable (Figure 7.17). Today’s belt pretensioners allow a pull-back of the belt of 12 cm in 10 ms. The ignition of the belt pretensioners is irreversible due to the pyrotechnical release and thus must be safeguarded using an appropriate algorithm in order to distinguish between, for example, running over a curb and crashing

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into a rigid obstacle. Before an accident (precrash), reversible, electronically powered belt tensioners have been used for a few years, which can be triggered, for example, by a recognized skidding of the vehicle (Kurutas, Elsäßer et al. 2006, Kurutas 2011).

Belt

Piston Squib

Cylinder

Ignition lead Propellant charge Steel cable Belt reel

Figure 7.17: Shoulder belt tensioners according to Bosch, Reif et al. (2014).

To avoid injuries of passengers caused by belts and tensioners, excessive acceleration peaks must be avoided. To this end, a belt force limiter is used that increases the length of the belt once a predetermined force of the belt is reached. This is reached by either implementing appropriate deformation elements into the reels or by implementing tear seems into the belts.

7.4.2 Airbag systems 7.4.2.1 Front airbag Above a certain speed, even a seat belt in combination with a tensioner cannot prevent the passenger from hitting, for example, his/her head on the dashboard or the steering wheel. Therefore, the effect of seat belts is complemented by front airbags. These are usually combined and coordinated with the belt systems and ensure an absorption of passenger movement, so that even at higher velocities, the probability of fatal injuries can be reduced. The airbags are generally controlled by a central control unit. The ignition signal is triggered based on the acceleration signals measured by crash sensors. Then, pyrotechnically operated gas generators blow up the driver and passenger airbag within few milliseconds. The airbag is controlled so that it is fully inflated before the passenger gets in contact with it. In the ongoing course of the crash, the airbag partially deflates, thus absorbing the kinetic energy of the passenger with noncritical acceleration and force figures. The airbag has to be fully inflated before the driver’s displacement reaches approximately 12.5 cm. Given an impact at 50 km/h onto a rigid obstacle, this leads to

7.4 Restraint systems

337

a total time of about 40 ms after impact. The decision whether the ignition of an airbag is necessary or not needs to be taken within 10 − 15 ms after the impact. Until then, the crash needs to be recognized and analyzed by the algorithm. This leaves another approximately 30 − 35 ms for the airbag to fully unfold. After another 80 − 100 ms, the airbag has emptied through the outlet openings. The entire process from impact to standstill of the vehicle thus only takes approximately 120  150 ms. The mentioned values are an example for the driver’s airbag. For the passenger side, the values concerning the ignition decision are comparable, while the filling time for the (larger) airbag on the passenger side is slightly higher with approximately 50 ms. To prevent injuries of passengers that are “out of position” (e.g., are leaning too far forward or infants in rear-facing child seats), the ignition of the frontal airbag and its inflation take place in situation-dependent manner. To this end, measures of interior observation and seat occupancy detection are used (see Section 7.5). 7.4.2.2 Side airbag Side airbags protect against the consequences of a side crash. They inflate, for example, for head protection along the roof section (e.g., inflatable tubular systems, window bags, inflatable curtains), the front door, or the backrest (thorax bags, upper body protection). The timely release of the side airbags is even more difficult than in the front part due to the missing crumple zone and the small distance between the passenger and the side parts of the vehicle structure. In lateral crashes there is thus only a time of approximately 5 − 10 ms for the activation of the protective measures. The inflation time of the approximately 12 l thorax bags may not exceed 10 ms. 7.4.2.3 Airbag control unit In addition to sensors (acceleration, pressure, and sound sensors) and actuators (gas generators), the airbag control unit is an indispensable component of a restraint system. Typical functions may include: – collision or roll-over detection by analyzing the sensor signals, – control of the restraint systems, – separation of the battery, and – turning off the fuel supply and triggering of an emergency call. Besides to the typical design using a central control unit, networked systems are used that are distributed onto multiple devices with different functions. The main components of a central control unit are as follows (Figure 7.18): – microcontroller with operating system, trigger algorithm, diagnosis, and so on, – a redundant backup path (e.g., implemented as a logic circuit or microcontroller), – internal sensors, – energy supply,

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7 Vehicle safety

Energy supply

Energy reserve

Redundant safety path

Power net

Microcontroller External crash sensors

Input stages

Other sensors

Operating system Trigger algorithm ETC

Mechanic switches

Amplifiers for ignition circuits and actuators

Internal sensors

Ignition circuits and actuators

Communication interface Bus system

Crash

Roll-over

Figure 7.18: Basic construction of a central airbag control unit according to Reif (2014).

– – – –

energy reserve, bus coupling unit, redundant power amplifiers for ignition circuits and actuators, and inputs for external sensors and switches.

Furthermore, a communication interface allows the propagation of the event of an accident to other vehicle systems. With this, further measures can be initiated, such as the control of displays in the electronic instrument cluster, the transmission of diagnostic information, warning lights, and so on. Modern vehicles also use automatic crash notification signals to initiate an automatic emergency call. 7.4.2.4 Gas generators The gas generator is responsible for producing of gas and for filling the airbag within only a few milliseconds (Schlott 1996). The gas generators are usually constructed cylindrically and contain pyrotechnical propellants to create the blowing agent for the airbags, which are activated by an electrical ignition element (firing pellet (Figure 7.19). The driver’s airbag, for example, which is built into the wheel, has a volume of approximately 60 l and the passenger airbag built into the glove box has a volume of 120 l. Both are fully filled within approximately 30 ms after the ignition by the gas generator. However, there are also other sizes of airbags that vary depending on different criteria; see Section 7.4.2.5. The gas generator consists of a combustion chamber made of aluminum or steel that absorbs the pyrotechnical propellant. The propellant is inserted in the shape of pressed pellets in order to offer a surface area that is as large as possible. The gas generated during the burn is led into the cushion through corresponding

7.4 Restraint systems

339

Airbag Metal housing

Discharge openings

Ignition mixture Propellant in pill form

Igniter with squib

Figure 7.19: Cylindrical gas generator (schematic diagram).

holes. The propellant is ignited by means of resistance wire that is coated with a pyrotechnical primary charge. The ignition of the propellants in the seat belt pretensioners works similarly. The gas generators fill each respective gas cylinder. Next to the classic gas generators, there are also concepts for hybrid gas generators. These consist of a combination of propellant and pressure cylinder. For this, a pressure cylinder filled with a gas mixture, which is under 250 bar of pressure, is opened with a propellant. The escaping gas that is cooled due to the loss of pressure is then heated by the ignited propellant during the transition into the airbag (Schlott 1996). 7.4.2.5 Airbags The airbag or air sack is the actual namesake of the airbag system. Airbags are available in various shapes and sizes. Next to circular shapes on the driver and rectangular shapes on the passenger side (Figure 7.21), there is a variety of different shapes used in the side and head area (Figure 7.20). Besides various geometric designs, there are also very different sizes of airbags. In the front area, the size classes “Euro-size,” “Mid-size,” and “Full-size” have emerged. These terms describe the size of the airbags that are dependent on the constructive conditions of the vehicle body, the power, and design of the gas generator and especially the protection objective. Historically, the differences in the volume of the airbags used are based on different regulations and protection philosophies of the manufacturers, especially in the United States and Europe. In the United States, airbags have been used as standalone restraint systems (“Fullsize” airbag), while the airbag (“Euro-size” airbag) in Europe has been implemented as a supplement to the safety belt. Thus, airbag volumes from 25 to 35 l on the driver’s and approximately 60 l on the passenger’s side were common. This

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Front passenger's airbag Head airbags

Driver's airbag

Side airbags

Figure 7.20: Airbag system with front, side, and head airbags © BMW AG.

Ignition leads

Cover passenger airbag Airbag control unit

Figure 7.21: Driver’s and front passenger’s airbag.

development seems to be moving toward a state in which airbag volumes (mid-size airbags) from 45 to 60 l on the driver and 80 to 120 l on the passenger side are used (Kramer 2013). 7.4.2.6 Airbag cover The interface between the airbag module with gas generator and airbag, and the passenger compartment is the airbag cover panel. The challenges in creating this interface lay in the requirement for a light and defined ripping during the ignition of the airbag, on the one hand, and the fit of the cover to the individual design of the interior of the vehicle (Schlott 1996).

7.4 Restraint systems

341

7.4.3 Trigger sensors and algorithms The accelerations during an accident are measured using one or more longitudinal and lateral measuring sensors, called trigger sensors. The total change in velocity is then calculated from the acceleration values. The evaluation of lateral acceleration is also helpful in a frontal crash to recognize, for example, angular and offset crashes. Today, micromechanical acceleration sensors are generally used that are either built directly into the airbag control unit or a sensor module. These sensors, however, detect a collision at a certain delay because an acceleration of the passenger compartment is delayed due to the deformation of the front of the vehicle. Therefore, satellite sensors are furthermore partially implemented in the front of the car (the so-called up-front sensors) and thus enable a trigger decision at a very early point in time (Figure 7.14). Satellite sensors are also implemented in the side, which can be based on different physical principles. In addition to acceleration sensors, there are sensors that recognize, for example, pressure changes in the cavity of the doors, or recently also measure body sound changes.

Figure 7.22: Airbag control unit with crash sensors © BMW AG.

The detection of the time of a collision must be supplemented by an evaluation of the type and severity of an accident. This means that, for example, edge climbs, curb crossings, or potholes must not trigger the restraint systems. To this end, the signals collected by the sensors are first prepared and processed by interpreting

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algorithms (Figure 7.23) that are parameterized using the data from corresponding crash tests and simulations. Filtered crash signal t

Threshold t

a

Crash signal

Lookup table dv

t

dv

Signal balance

t

t a dv

a

Integrated crash signal t dv

Figure 7.23: General sequence of crash detection (Heide, Schramm et al. 2009, Heide 2014).

The algorithms for front and lateral impacts generally differ. For vehicles with rollover recognition, an additional roll-over algorithm is run. The inputs for the front crash algorithm mainly consist of the signals of the central acceleration sensors in longitudinal direction, which are generally integrated into the control unit (see Figure 7.22), and the satellite sensors, which are possibly mounted to the front of the vehicle. The signals placed in the interior capture the delays that the passenger compartment and thus the passengers are exposed to. The signal of the satellite sensors3 detects the acceleration of the front of the vehicle. The severity of the accident and possibly the direction of the impact as well as the coverage of the impact area can be calculated using the difference of intensity and time of the different sensor signals. Algorithms for the recognition of a lateral impact use the signals of the internal sensors that measure lateral acceleration and the signals of the pressure sensors in the doors and the acceleration sensors placed in the area of the crumple zones. Due to the much smaller crumple zones at the side of the vehicle, the requirements for shorter trigger times are much higher here than in the front. Generally, the preparation and evaluation of the signals correspond to the approach of the front. Depending on the kind of crash, typical trigger times for a lateral crash are within 4−15 ms (Reif 2014). The fact that the trigger decision needs to be made as early as possible during the accident is valid for all kinds of accidents. One challenge in this is that during the early phase of an accident, the acceleration shows only low numbers of g forces.

3 Also known as up-front sensors.

7.4 Restraint systems

343

100 80

Panel and foam

Deformation force/kN

Over the course of the accident however, accelerations between 100 g (in the central control unit) or 500 g in satellite sensors are possible. In so-called no-fire situations such as driving over high curbs at higher velocities, there are however larger acceleration peaks during which the systems must not be triggered (Reif 2014). For this reason, further criteria are included in the trigger decision. The triggering of the components of the restraint systems are described here using the example of a frontal crash. The decision of whether the restraint systems are triggered generally has to be made within approximately 10 − 20 ms. The decision needs to be made using the signals available from the built-in sensors. One example of such a signal is shown in Figure 7.23. The acceleration course mirrors the main load paths and the collaboration of the individual structural components as shown in Figure 7.24.

60 40

Front part longitudinal beam

Passenger compartment

Rear part longitudinal beam

Crashabsorber

20 0 0

100

200

300 400 Deformation/mm

500

600

Figure 7.24: Deformation sequence of the main load paths (Heide 2014).

The acceleration signal first needs to be filtered to remove nonrelated vibration frequencies. The crash signal is integrated to calculate the reduction in velocity. In a side crash, the conditions are fundamentally different from those in a frontal crash due to the missing crumple zone. Therefore, other measures are required here. To this end, the lateral structures are designed to be especially robust. Additionally, for example, pressure sensors are built into the doors that send a signal to the airbag control unit once a certain threshold is exceeded. This direct crash recognition in the outer side structure allows for an activation of all required restraint and safety systems, such as side and head airbags as well as belt pretensioners as quickly as possible. Doing this, the time between the start of the collision and any contact to passengers is used optimally.

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7.5 Passenger detection In order to avoid the dangers resulting from bad positioning of passengers, on the one hand, and unnecessary damages to the vehicle due to the ignition of an airbag, on the other hand, modern vehicles are equipped with sensors that, for example, recognize the occupancy status of a seat. To this end, the ignition of an airbag depends on whether a seat is occupied by a passenger. Modern vehicles measure the weight of each passenger to determine whether each seat is occupied. Beyond the recognition of occupancy, settings of the airbag ignition are changed depending on the weight classification. Figure 7.25 shows an example of a sensor mat that is directly integrated into the seat and that allows a corresponding recognition. Furthermore, there are other transponder-based techniques for the recognition of child seats, which also recognize the direction of installation of the seat. For further information, refer to corresponding specialized literature; see, for example, Kramer (2013).

Sensor pad

Figure 7.25: Seat occupancy recognition (source: BMW).

7.6 Vehicle roll-over Besides the protective measures taken for front and lateral impacts, the protection for roll-over accidents is very important. On the one hand, the protective and supportive roof structure during roll-overs is missing, for example, in convertibles, which must be compensated by safety bars or similar mechanisms in this vehicle type. On the other hand, for example, SUVs show a greater tendency for roll-overs than conventional vehicles due to the higher center of gravity. For this kind of accident, recognition concepts are used that measure the rotation around the longitudinal axis using a

7.6 Vehicle roll-over

345

yaw rate sensor, and additionally measure the acceleration in lateral and vertical direction in order to check the plausibility of the ignition decision as well as help recognize the kind of roll-over (embankment, slope, curb impact, or soil trip roll-over) (Bardini, Hiller et al. 1996, Bardini, Hiller et al. 1997, Bardini 2008, Schramm, Hiller et al. 2018). Depending on the roll-over situation, rotation rate, and lateral acceleration, the protective measures need to be adapted to the situation. The ignition is triggered after 30–3,000 ms. The roll-over plays a special role compared to other kinds of accidents in some respects. This is especially valid concerning the safe and timely detection of the vehicle roll-over event. For frontal or lateral collisions, the recognition of the accident can be based on the measured high acceleration of the vehicle. The recognition of a crash is then almost exclusively based on the significant decelerations of the vehicle resulting from the abrupt slow-down. The situation is different however in the timely recognition of an impending roll-over. During the time in which the ignition decision for restraint systems needs to be made, except in the case of a combined accident, there is generally no plastic vehicle deformation information available. During this time, only dynamic sequences for the recognition of a vehicle rollover are available. To this end, an equipment with corresponding sensors is necessary, which has only been available in large-scale production since the late 1980s. Simulations can be used efficiently and extensively (Bardini 2008). The first more detailed description of an active roll-over protection system has been created by Daimler AG (Baumann, Matthias et al. 1989, Bossenmaier and Brambilla 1989). Shortly afterward, the vehicle manufacturers BMW and Audi have introduced comparable reversible protection systems in their vehicles. One of the reasons for the reluctant distribution was the already mentioned fact that sensors first needed to be made available that were able to reliably and timely detect rollover accidents. In 1996, the Robert Bosch GmbH was the first automotive supplier of a novel sensor concept, that was based on the rotation rate measurement, which had already been used by ESP systems (Groesch, Mattes et al. 1996). To analyze the emergence of roll-over accidents, detailed accident data are necessary. The NHTSA4 offers a multitude of different roll-over scenarios, which can be utilized to identify the circumstances and types of roll-over accidents, which are consulted in the gathering of field data in the CDS database (Crashworthiness5 Data System) (Bardini 2008): – Trip-over occurs when the lateral movement of a vehicle is abruptly slowed or stopped. This can be caused, for example, by a curb, a pothole, or soft soil that a wheel is dug in.

4 NHTSA: National Highway Traffic Safety Administration. 5 Crash consistency: Ability of a vehicle structure to protect passengers during an accident.

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7 Vehicle safety

– Turn-over occurs when a vehicle rolls over without any outside impact due to centrifugal forces and without changes in the surface friction of the road. This type of roll-over is more likely in vehicles with a higher center of gravity than in common passenger vehicles. It can occur on surfaces such as asphalt, gravel, or grass. – Fall-over occurs when a vehicle drives on a sloping surface and the center of gravity moves outside of the wheel contact points. The main difference to the turn-over is the existence of a sloping road surface, for example, an embankment or a ditch. – Flip-over occurs when a vehicle experiences angular momentum along its longitudinal axis due to contact with a ramp-like object such as a barrier or a boundary wall. – Climb-over occurs when a vehicle rises due to a collision with a rigid object such as a concrete barrier and comes to rest behind it. In contrast to the tripover on a curb, the collision object in this kind of accident has a greater height, which is at least as high as the diameter of the wheel. – Bounce-over occurs when a vehicle bounces off a rigid object after a collision and rolls over due to this impact immediately. In contrast to the climb-over, the vehicle does not surpass the collision object and comes to rest in front of it. – A collision occurs when a vehicle rolls over directly due to a collision with another vehicle (e.g., in a crossing accident in which a vehicle is rammed laterally by another). – End-over-end always occurs when a vehicle primarily rolls over its lateral axis (pitching movement prevails).

7.6.1 Physical considerations concerning the tipping of vehicles The roll-over process involves complex interactions of forces both in and to the vehicle. Within the scope of this book, these processes can only be explained using simple analytical models. To this end, the fundamental mechanical processes are observed for the quasistatic state of tilting. For a more detailed analysis of the rollover process, see Bardini (2008) and Schramm, Hiller et al. (2018). The simplest approach to analyzing tilting processes is modeling the vehicle as a rigid body neglecting deformations of the wheels or suspension. At the moment of the beginning of the side roll-over, the resulting forces are shown in Figure 7.26, assuming φ = 0. When creating the equilibrium of moments around the supporting tire contact point A, it follows mg

bV − hS may = 0. 2

(7:15)

7.6 Vehicle roll-over

S ℎ

347

W

ℎ A /2

Figure 7.26: Forces during the tipping process of a vehicle.

Assuming that there is no lateral slipping between tire and road surface, the start of a roll-over can occur when the torque of the lateral force Fy is surpassed by the aligning torque of the weight force. When assuming a maximum value of g for the lateral acceleration ay , it is found SSF =

bV = 1. 2hS

(7:16)

The quantity SSF is also called state stability factor. The stability concerning lateral roll-overs increases with SSF. An SSF < 1 can already lead to a roll-over at a lateral acceleration of g once a correspondingly large lateral force Fy can be established. This can occur either due to friction of the tires or due to an obstacle, such as the edge of a sidewalk. The SSF underestimates the roll-over potential. Especially rolling of the vehicle and tire suspension are not considered in this case. This leads to the situation shown in Figure 7.26. Here, the equilibrium of moments around the outside and, thus supporting, tire contact point reveals  bV (7:17) − sinφ ðhS − hr Þ − may ½hr + cosφðhS − hr Þ = 0. mg 2 For a small roll angle φ at the start of the roll-over, the following relationship can be approximated  bV (7:18) g − φ ðhS − hr Þ − ay hS = 0. 2

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When replacing the roll angle φ by the quotient of the torque of the lateral force around the tire contact point and the roll elasticity cφ (see Chapter 3), the following condition arises: cφ cφ ay bV = SSF · . = g 2hS mgðhS − hR Þ + cφ mgðhS − hR Þ + cφ

(7:19)

The SSF is decreased by the second factor. Another reduction results from the lateral deformation of the tires due to the corresponding reduction of the track width (Bardini 2008). By balancing the kinetic energy that is available for a roll-over, a further approximation of the roll-over potential of vehicles can be made. When the observed vehicle has the lateral velocity vy , the following relationship results from the conservation of angular motion concerning the tire contact point at the beginning of the roll-over: mvy hS = ΘxA ωx .

(7:20)

Here, ΘxA describes the moment of inertia around the tire contact point and ωx the roll angle velocity. For a roll-over to be possible at all, the rotational energy must at least suffice to move the center of gravity of the vehicle beyond the tire contact point. Therefore, the condition 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 b 1 (7:21) mg@ h2S + V − hS A = ΘxA ω2x . 4 2 must be met. Inserting eq. (7.20) in (7.21) results in 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 b 1 m2 V − hS A = vy2 h2S mg@ h2S + 4 ΘxA 2 and finally solving for the lateral velocity, the following condition arises: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1ffi u  2 2 u2gΘ bV u xA @ t 1+ − 1A . vy = CSV = mhS 2hS

(7:22)

(7:23)

The acronym CSV stands for critical sliding velocity. If the lateral velocity of the vehicle exceeds this value, a rollover can occur, for example, when hitting a curb. Typical values for passenger cars are between 17 and 25 km/h (Bardini 2008).

8 Automotive electrical system The electrical system of a motor vehicle consists of a variety of electrical and electronic components. The first electrical powernets in automobile history only consisted of the generator (alternator), battery, electrical starter, lighting, as well as the necessary wiring harness. Even today the most common assumption of the definition “electrical powernet” is only connected to the pure power supply of a vehicle. Since modern vehicles are built of a variety of electronic components in addition to the electrical ones, the classic terminology is no longer sufficient. On the contrary, it is generally necessary to differentiate between the electrical powernet (for the power supply of the electrical components) and the information wiring system (for the communication between different components). For communication between individual components and electronic control units (ECUs), a variety of different bus systems are now used for motor vehicles. As early as 2003, the share of electrical and electronic components in relation to the total manufacturing costs of a vehicle was around 30% (Otterbach and Schütte 2004). In addition to that the allocated development costs for the software required in the vehicle have to be included as well. All in all, these figures add up to more than one-third of the total cost of a vehicle. Especially in recent years, not least due to the discussion about electric mobility and the significant enhancements of driver assistance systems, the area of the vehicle’s electrical powernet has become even more in focus of automotive development. Electrical and electronic components are the main carriers of the innovations made by the automotive sector today. Frequently, electrification forms the foundation to be able to realize the scope of operation we see today. The requirements of a modern motor vehicle are much more diverse than they were just a few decades ago. In particular, the demands in terms of comfort and infotainment but also the economy and safety are strong drivers for the further development of electrical and electronic vehicle systems. The increase in electrical components in the vehicle has led to the fact that the entire electrical system of a motor vehicle now has a very high complexity. For example, in 1949, the electrical wiring of the Mercedes model 170 V had 40 circuits with 60 contacts. Due to the many electrical components today’s vehicles have between 1,000 and 4,000 wires (circuits) with a total length of 2–4 km and a weight of up to 60 kg (Heuermann and Ernst 2014). Depending on the vehicle condition, repeated situations of energy shortage take place. In addition to providing energy for individual components, the vehicle-wide provision of information (e.g., sensor data) also comes into focus. Overall, the high complexity and importance of electrical systems for modern motor vehicles can also be deduced from the fact that more than one-third of all vehicle breakdowns are caused directly or indirectly by the electrical system. In addition, if start-up problems are taken into consideration of this statistic

https://doi.org/10.1515/9783110595703-008

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8 Automotive electrical system

as well (Figure 8.1), which are often caused by a discharged battery, 50% of all vehicle breakdowns at least involve electrical or electronic components (ADAC 2009). Exhaust system 2% Clutch/ transmission 5%

Others 14%

Other electrics 38%

Cooling and heating 6% Fuel injection system 7% Wheels and tires 7%

Engine 8%

Ignition system 13%

Figure 8.1: Statistics on the causes of vehicle failures from the ADAC breakdown statistics 2009 (ADAC 2009).

8.1 Energy powernet The energy powernet includes all components for the provision, storage, and distribution of electrical power as well as the electrical consumers in the vehicle. With the advancing electrification of vehicle systems and their components as well as the introduction of new electrical systems into the motor vehicle, the supply of individual components with electrical power in today’s vehicles has become a highly complex task.

8.1.1 History Until the middle of the last century, the provision of electrical power in motor vehicles was a rather minor function. The average power consumption was only a few watts and the primary task of the powernet was to supply the starter. During a journey, only a few consumers, such as headlights, signal lights, or spark plugs, had to be operated. It was possible to provide the electric power for the starting process with a 6 V battery. This battery then was recharged while driving by relatively lowpower (DC) generators. However, 6 V battery used until the 1960s soon proved to be too weak to also supply any additional consumers in the vehicle. Since then, the 12 V battery (24 V for trucks) is the dominant powernet source in the car sector. Today’s batteries and the corresponding alternators can supply a large number of different, sometimes very powerful, consumers with electrical energy.

8.1 Energy powernet

351

By the end of the twentieth century, however, the demand for electrical power supply had changed dramatically. The introduction of a wide variety of electrical consumers, some of which have very high-power requirements, into the powernet has meanwhile led to an average power consumption of up to 3 kW for the operation of the electrical vehicle components (Figure 8.2).

Average power requirement / kW

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1950

1960

1970

1980

1990

2000

2010

2020

Year Figure 8.2: Average electrical power requirement in the motor vehicle according to values of Wallentowitz and Reif (2008).

If the power peaks are taken into consideration, the very high requirement in terms of power supply can be recognized more clearly. For some systems, a short-term power requirement of up to 14 kW may occur (Figure 8.3). When taking those short-term power peaks into consideration and comparing them with the power provided by the alternator to the electrical system, it becomes very clear that the still in use 12 V powernet reaches its limits. The battery must increasingly serve as a power source even while driving, as the alternator cannot provide all the power. Consistently there are power shortages that can even not be supplied by the battery and the alternator together. In addition, unfavorable driving profiles can lead to a negative charge balance, which would mean that the starting capability of the vehicle cannot be guaranteed in the long term. It has therefore been observed for quite some time that the electrical consumers in the motor vehicle are regulated by an energy management system in such a way that the functionality of the essential components is assured. Therefore, in the 1990s, an increase in the electrical powernet voltage from 12 to 42 V was discussed (Schöttle, Schramm et al. 1996). The purpose of this new voltage level was to solve the issue of power shortages of consumers with a very high-power level. Due to various problems, however, the defined standard of 42 V has never become a standard in worldwide series production.

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8 Automotive electrical system

16 14

Short-term peak power battery

Electrical power / kw

12 Short-term peak power generator 10 8 6 4 2 0 Low Medium High

Low Medium High

2000

2005

Low Medium High Equipment rate 2010

Year

Figure 8.3: Accumulating peak power in motor vehicles according to the values of Schöttle and Threin (2000) and Fabis (2006).

Meanwhile, a standard of 48 V for electrical systems of motor vehicles was introduced. The 48 V powernets are also based on the experience with the (failed) introduction of the 42 V powernets and will probably find themselves in mass production in the medium term. In addition to the installed power performance increase, there are also thoughts about keeping the electrical consumption of electrics/electronics as low as possible in order to cover the required performance. This is also based on the demand for more energy-efficient vehicles. An additional consumer with the continuous power consumption of 100 W causes an additional consumption of approximately 0.1 l=100 km and thus has roughly the same influence as an additional weight of the vehicle of 50 kg (Schramm 2012, Schramm and Koppers 2014). The powernet is now one of the most expensive parts purchased by the manufacturer of a modern motor vehicle. In particular, the many different components that supply the vehicle’s powernet with electrical power and connect information technology drive the complexity of the vehicle’s electrical system in modern vehicles. For reasons of efficiency, it has not been useful for some time to use a single powernet variant per vehicle that supplies all possible components. For a vehicle, there are often varieties of different powernet variants, which vary widely depending on how the vehicle is equipped. For example, a vehicle without electric seat heating does not need the wiring for such a heater. If the corresponding wiring is not installed, both costs and weight are saved. With the extremely high number of

8.1 Energy powernet

353

possible combinations of electrical consumers defined by the customer who has ordered the vehicle, it is no longer possible to design a small number of predefined powernets that ideally cover all possibilities. The latest developments are that a socalled custom cable harness (CCH) is used. The supplier of the powernet thus supplies the exactly fitting wiring harness for an ordered vehicle configuration. This configuration could be unique (even for very large vehicle programs). The production and logistics of such CCH places very high demands on both the vehicle manufacturer and the supplier.

8.1.2 Structure and mode of operation of today’s powernets The basic structure of the energy powernet has changed little with the introduction of different voltage levels. Basic components are the energy source (alternator), energy storage (battery(s)), and a variety of consumers. The basic steps of the energy flow in the electrical system are shown in Figure 8.4.

Combustion engine Alternartor ηCE ͌ 10 – 30% ηAl ͌ 40 – 65% Fuel

Wme Wch

Losses Usable energy

Cable harness Consumer ηCH ͌ 90 – 98% ηCH ͌ 10 – 100%

Wel

Wel

Wme

Wel

Wel

Wef Wel

Effective energy

Wel Wth

Battery ηBatt ͌ 60 – 85%

Figure 8.4: Energy conversion and flow in the electrical system according to Büchner and Bäker (2005).

The energy of the motor vehicle1 is still carried predominantly in form of liquid fuel and is converted inside the internal combustion engine mainly for the purpose of

1 For the purposes of this chapter, vehicles powered by internal combustion engines are regarded as standard. In the case of electrically powered vehicles, the structure of the vehicle electrical powernet and thus the energy supply changes in such a way that the conversion of the energy bound in the fuel into electrical energy by the generator is eliminated.

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8 Automotive electrical system

driving into mechanical energy. The alternator is used to convert this energy for electrical power requirements into electrical energy. This is then used to supply the components of the electrical system and to charge the battery sufficiently. Since the conversion of mechanical energy into electrical energy is directly dependent on engine speed, different supply states occur in the vehicle electrical powernet system depending on the driving condition (Figure 8.5).

Current Idle rpm speed Load current (current on-board network load) Supply only from battery-battery is discharging

Supply only by alternator battery is charging Supply by alternator and battery-battery is discharging

Alternator rpm Figure 8.5: Electrical supply conditions in the motor vehicle according to Büchner and Bäker (2005) and Bosch (2007).

The alternator speed and the required power demand are decisive for the state of supply in the electrical system. Depending on its speed, the alternator can supply a maximum current (at a constant voltage of approx. 14 V). If this power is sufficient to operate at least all consumers, the power surplus that may be present will ensure that the battery is charged. If the demand for power exceeds the supply of the alternator, the powernet voltage drops to the battery voltage and the battery serves the difference between the required power demand and the maximum alternator power. When the engine is at standstill or below a minimum speed (depending on the alternator control), the battery is the sole source of energy in the electrical system (especially the case during starting). This results in the basic conditions of the powernet, as summarized in Table 8.1. With the 12 V vehicle electrical system used today, there are sometimes significant fluctuations in the vehicle powernet voltage depending on these conditions. An overview of the different voltage levels is shown in Figure 8.6 Regarding the function of various powernet components, the starting process (especially when using start–stop systems) often represents an extreme situation, as the battery terminal voltage is significantly reduced. The starter, which is powered

8.1 Energy powernet

355

Table 8.1: Powernet supply states in response to the driving operation. Vehicle state

Alternator

Battery mode

Charge balance

Standby current (alarm system, access systems, . . .)

Off

Discharge capacity crucial

PL > 0

Standstill consumers (fan, radio, . . . )

Off

Discharge capacity crucial

PL > 0

Start

Off

Discharge internal resistance PL > 0 decisive (maximum battery power)

Idling (small consumers only)

Active

Load

PL < PG

Idling

Active

Discharge (depending on active electrical consumers)

PL > PG

Driving mode

Active

Charging

PL < PG

Driving with high power (e.g., EPS)

Active

Discharge

PL > PG

Typical charging voltage range Typical discharge voltage range 11 Minimum voltage 9 while driving

12

14

15 16

6 Maximum voltage in normal operation Minimum voltage at engine start

0

34 Maximum dynamic voltage peak (load dump) No polarity reversal

Figure 8.6: Powernet voltage in the 12 V electrical powernet according to the values from Henneberger (2013).

exclusively by the battery, has such high powers that the first voltage drop in the starting process leads to values of approximately 6 V in the powernet supply. Normally, this first voltage drop during the starting process only takes a few hundredths of

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8 Automotive electrical system

a second, but in unfavorable vehicle conditions, the battery terminal voltage can drop to a level that in extreme cases leads to individual components coming out of their functional voltage range. The flickering of display devices or lighting is just an example of the effects perceivable by the customer. To prevent such a scenario, voltage supporting measures are used in some cases. However, these are avoided as often as possible for cost reasons. Depending on the scenario, very different powernet supply voltages (battery terminal voltage) may occur. Figure 8.6 shows areas of the terminal voltage with the corresponding operating states. During normal vehicle operation, voltages of 11–12 V usually occur when the engine (alternator) is not running. Usual voltages during charging (running alternator) are approximately 14 V. However, conditions of other voltage levels can also occur again and again, usually very briefly. This is especially the case when high-performance consumers are active. 8.1.2.1 The classic 12 V electrical powernet As with all common vehicle electrical powernet variants, the alternator (G) is the only energy source that supplies the electrical current for the consumers (R) (Figure 8.7). In addition to the required load current, a sufficient charging current must also be provided for the battery to enable a positive charging balance via a drive cycle. This ensures sufficient battery charge regardless of driving operation. A suitable voltage regulation of the alternator reacts to fluctuations in the consumption of electrical power. This keeps the powernet system voltage almost constant. This ideally constant voltage of approximately 14 V ensures both battery charging and maximum functional availability of all electrical components.

Line resistance

Line resistance

Consumers (R)

Alternator (G)

…

Battery (B)

Figure 8.7: Structure of a classic single-battery electrical powernet, as it occurs in the current standard 12 V battery form.

8.1 Energy powernet

357

If all consumers are considered together, this results in a very simple structure. According to the node rule, the following applies in a simple single-battery vehicle powernet (Table 8.2):

Table 8.2: Designations of the currents in the simple single-battery powernet. Formula symbol

Description

IG

Alternator current

IB

Battery current (charging current)

IV

Sum of all consumer currents

IG = IB + IV

(8:1)

If the maximum alternator power is not sufficient to supply all consumers with the required power, the powernet voltage automatically drops to the level of the battery voltage. In this case, the battery now acts as an additional energy supplier in the vehicle electrical system. The battery current (charging current) is then negative and the battery is getting discharged. 8.1.2.2 Positioning of the battery in the vehicle Since the battery only needs to be connected to the alternator through the wiring harness, the position in the vehicle can be freely selected. In passenger vehicles, the battery can usually be installed in the engine compartment or in the boot. The choice of suitable positioning is based on various criteria. Some of the criteria are explained in Table 8.3. 8.1.2.3 A 42 V electrical powernet In the 1990s, the 42 V powernet power supply system seemed to be a possible successor to the still used 12 V system seen as standard (Schöttle, Schramm et al. 1996). As early as the end of the last century, the focus was increasingly shifted to electrified consumers to be used in motor vehicles and with newly developed electrical systems a large number of new electrical consumers were integrated into the vehicle’s electrical system. This meant that the limits of the 12 V powernet power supply seemed to have been reached. The introduction of the significantly higher voltage level should improve the power supply and thus ensure the functionality of the electrical systems. In addition, various systems were discussed, which would inevitably have required an increased voltage level.

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8 Automotive electrical system

Table 8.3: Positioning the battery according to Fabis (2006).

Advantages

Engine compartment

Trunk

Small cable lengths (alternator to battery) ensure good battery charging. The arrangement ensures a stabilization of the powernet system voltage, since all consumers are arranged “behind” the battery. The battery thus smooths voltage peaks. Optimum starter voltage due to the short cable lengths from battery to starter (optimized starting capability). In winter operation, the engine waste heat heats the battery. This has a positive effect on charging efficiency at cold temperatures.

More constant ambient temperatures lead to a reduction in battery aging Additional options for packaging in the engine compartment (space saving) Improved protection against environmental influences such as contamination and moisture Potential for optimized weight distribution. Axle load optimization particularly useful for heavy engines

Disadvantages High temperatures possible in summer operation. This may lead to outgassing. Reduction in service life due to changing and unfavorable environmental conditions. Contamination with operating media, e.g., oil and moisture.

Significantly increased cable lengths lead to an increase in cable weight (approx.  kg) and cable losses (both when charging the battery and especially when starting)

The increased powernet system voltage allows a current that is four times lower while providing the same power (Figure 8.9). This results in significantly reduced cable cross sections and higher efficiency. Significantly higher outputs can be achieved with the same currents. This enables new functionalities. The continuous further development of the 12 V powernet with the increase of the available energy (more powerful alternators) and improved energy storage systems (batteries) as well as the implementation of targeted measures to limit power consumption have meant that the 12 V power supply systems are still in use today. With the optimization of the 12 V system additional costs, which would have been caused by a switch to 42 V systems were not justified, especially since an application that could not have been operated without a higher voltage level was not present.2 With a few exceptions, the 42 V system, therefore, has not been applied to this day.

2 This would have been the case, for example, with the introduction of electromagnetic valve control. Other applications that require a higher voltage level, such as Xenon headlamps, are supplied by locally higher voltages.

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359

8.1.2.4 A 48 V electrical powernet In recent years, discussion about increasing the powernet system voltage came up again. With the 48 V powernet system, another standard for the vehicle electrical system has been defined. As with the discussion about the 42 V powernet supply system, ensuring the functions of innovative and powerful electrical consumers in the vehicle plays a decisive role here. However, unlike 15 years ago, the reduction of CO2 emissions is another important aspect and a decisive driver for the development of the powernet power supply (Figure 8.8).

Percent of the answers given

40

30

20

10

0

Stricter legislation on Stricter legislation on carbon dioxide carbon dioxide emissions worldwide emissions in EU

Meeting new OEM standards

Increased demands on the E / E functionality in vehicles

Figure 8.8: Drivers for the development of a 48 V powernet (Hornick 2013).

The possibilities of CO2 savings through a more efficient electrical powernet system and the needs-oriented use of electrical loads are manifold in conjunction with an increased powernet voltage. On the one hand, the new powernet supply voltage allows the power supply system to be weight-optimized, as the required cable cross sections can be adapted. On the other hand, systems such as the automatic start–stop system can be improved even further, thereby the introduction of the 48 V standards play an important role in complying with the CO2 regulations (ZVEI 2015). The discussion on electric mobility in particular has also raised public awareness (customer awareness) of issues such as energy-efficient driving and electrical systems in vehicles. The definition of a further voltage standard for electrical systems in motor vehicles below 60 V (still permissible contact voltage) has the purpose of achieving the greatest possible electrical system performance without additional protective measures. Today’s hybrid vehicles (mild hybrid, see Chapter 6) often use voltages above the 60 V limit, which makes the entire electrical system expensive. At the same time, it must be assumed that at approximately 200–300 A via one conductor the maximum possible current is reached. Figure 8.9 shows the simplified relationship between available system performance for 12 and 48 V system.

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8 Automotive electrical system

Current / A

1,600 1,400

12 V

1,200

48 V

1,000 800 600 400 200 0 1

2

3

4

5

6

7

8

9

10

11 12 13 14 15 Power net performance / kW

Figure 8.9: Reduction of the load current with constant powernet power supply.

The significant increase in available system power can be used both for increasing the recuperation power and for boosting (support during acceleration with the electric motor). The 48 V technology will therefore be used in hybrid systems and make a considerable contribution to the required CO2 reduction (ZVEI 2015). The conversion from the current 12 V electrical system to a 48 V electrical system will only be possible successively. For this reason, powernet systems with different voltage levels will be available in the medium term. Such systems (as they also occur in every electrically or partially electrically driven vehicle) already allow the integration of new components and the associated functionality without demanding the completely new development of all (very established and mature) components. The core of a powernet power system with two voltage levels is a DC/ DC converter that allows energy to be transmitted from one voltage level to the other and vice versa (Figure 8.10). The consumers at 48 V level can, as already described, have a significantly higher power than those at the classic 12 V level. This is particularly interesting for heating systems but also for systems in the field of driving dynamics (electric steering, roll stabilization, etc.). Due to the higher performance, these can offer an extended functional range. However, central components in the 48 V system are the 48 V battery and the so-called starter generator. The electrical machine in the 48 V system can be used both to start the vehicle and as an alternator (Table 8.4). The increased power enables very good starting capability, significant power braking (recuperation) via the alternator and “boosting“ (support during acceleration) (ZVEI 2015).

361

8.1 Energy powernet

DC/DC

12 V Consumers

SG Starteralternator

48 V

…

12 V

…

48 V Consumers E.G. EPS, heating Figure 8.10: Structure of a powernet power supply system with two voltage levels.

Table 8.4: Opportunities and risks of a 48 V powernet power supply compared to the usual 12 V powernet power supply (ZVEI 2015). Chances

Risks

Possibility of CO2 and consumption reduction

Initially higher costs due to new components and a more complex structure

Higher recuperation and powernet power output Increased risk of arcing due to higher voltage of up to  kW level Implementation of new functionalities, e.g., in the area of driver assistance or for energy saving (integration of high-performance consumers)

Work with two voltage levels. Risk of short circuits need for wiring and coordination of both voltage levels

Potential for weight reduction (even with inertial Additional DC/DC converter with medium to high extra weight due to the second battery and a power necessary for dual voltage powernet DC/DC converter) power supply Integration of established architectures can be used with regard to cost efficiency

Electromagnetic compatibility

No contact protection necessary

8.1.2.5 Electrical powernets in electromobility The structure of the powernets of electrically powered vehicles is very similar to those in the previous section. A general distinction is made between the high-voltage and low-voltage ranges. Both areas are connected by a DC/DC converter. Compared to the 48 V powernet supply system, the electric drives are operated at significantly higher voltages. The voltage level therefore is also much higher. The used traction batteries have voltages of around 400 V. More detailed information to this can be

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8 Automotive electrical system

found in Chapter 6. This high voltage level is required for the high power required to propel the vehicle.

8.2 Energy storage Energy storage is one of the central functions of the vehicle’s energy powernet. The energy storage has the task to supplying all electrical consumers with electrical power during vehicle standstill (combustion engine off). Furthermore, it has to supply the starter during the starting process. Very high currents occur for that short time. Especially in modern motor vehicles, however, the energy storage (battery) must also serve as a buffer in order to counteract bottlenecks in the supply of consumers with electrical power. The demands on the energy storage system due to the starting process are fundamentally different from those that come with the supply of electrical components at standstill. Two parameters are of decisive importance for the selection of a suitable energy storage system: – The power density indicates the maximum power that the storage medium can deliver. – The energy density of the storage is a measure for the duration of the power output, which means how much energy can be stored. In principle, various systems can be used to store the electrical energy (Figure 8.11). The selection of the energy storage (or a combination of different storages) is therefore always based on the function and the system costs. Systems that require very high short-term power in the powernet require a very high-power density. This is the case with today’s hybrid vehicles, for example, when the braking energy is fed back into the battery and is needed again for starting. If a constant power is applied for a longer period, the energy density is decisive. For traction batteries (see Chapter 6), both criteria are equally in focus. Therefore, lithium-based batteries have established themselves here. A comparison of different storage media is shown in Figure 8.12. Despite the comparatively low performance of lead-acid batteries, they can be found in all standard vehicle electrical systems. Their still widespread use can be explained by the very mature and mastered technology, the established recycling system and the comparatively low system costs. The lead-acid batteries used are very inexpensive and at the same time very robust. With the recent development of electrically powered vehicles the desire for power-intensive consumers in the powernet and the adjustment of the voltage level, various types of storage are now being discussed for the supply of the classic powernet. In the case of electric storage devices in motor vehicles, a distinction is often made between so-called starter batteries and traction batteries (storage devices for driving electric or hybrid vehicles) (Reif 2011). Particularly in the area of traction

8.2 Energy storage

363

Electrochemical storage

System Cost / (€/kW)

600

Mechanical storage Electrical storage

500

Doublelayer capacitors

400 Fast flywheels 300

200

Li, NiMh, NiCd batteries

Superconducting magnetic energy storage devices

Lead batteries

100 Slow flywheels Water and compressed air 0.001

0.01

0.1

1

10

100

1,000

10,000

Buffering time / h Figure 8.11: Comparison of the system costs of different selected storage systems (Benger 2007).

batteries, rapid further development is currently taking place, driven by the development of new drive technologies. In some areas, energy storage technologies, so-called ultracapacitors, can also be found. These offer interesting possibilities especially in combination with other systems for energy storage. It can be assumed that the costs for Li-ion systems, which are often used in electric vehicles, and their performance will be significantly optimized in the coming years. Figure 8.13 shows the expected development of various industrial nations; see also Chapter 6. Even if these forecasts for both the energy density of the storage media and the expected costs differ considerably in some cases, it can be assumed that both will develop positively. The different characteristics of individual storage materials are listed in Table 8.5.

8.2.1 Starter batteries The term starter battery is based on the original function of the battery in the vehicle’s electrical system. In the early powernet power supplies, a battery was required

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8 Automotive electrical system

100,000

Gravimetric power density/(W/kg)

10,000

DSK

Li-Ion LiM-polymer

1,000 Lead

100

10 Ni-Cd

0

20

40

Ni-MH

NaNiCl

60 80 100 120 140 160 Gravimetric energy density/(Wh/kg)

180

200

Figure 8.12: Comparison of the performance of current energy storage systems in motor vehicles according to Wallentowitz and Freialdenhoven (2011).

1000 Japan USA (DOE) Germany (BMBF/ISI) China (MOST/MIIT) South Korea (MKE)

Cost in €/kWh

700 600 500 400 300 200 100 0

350 Energy density in Wh/kg

900 800

300 250 200 150 100 50 0

2010

2015

2020

2010

2015

2020

Figure 8.13: Forecast development of the system costs of Li-ion batteries and their performance (Thielmann 2012).

 Wh/kg  Wh/l  W/kg  W/l . V . V . V − to  °C –% –%/month /

–%/month

%

− to  °C

. V

. V

. V

 W/kg  W/l

 Wh/kg  Wh/l

NiMH

>/

− to  °C

. V

. V

. V

 W/kg  W/l

 Wh/kg  Wh/l

Li-ion

>/

,

%/month

–%

 to  °C

. V

. V

. V

 W/kg  W/l

 Wh/kg  Wh/l

Na/NiCl

>/>

k/k

%/month

− to  °C

. V

. V

. V

, W/kg , W/l

. Wh/kg . Wh/l

UCap

8.2 Energy storage

365

366

8 Automotive electrical system

to operate the electric starter. After the starting process, the alternator was then able to supply the few available electrical consumers. The starter battery chemically stores the electrical energy supplied by the alternator during the journey. If necessary, the energy can be released again. As already explained in Section 8.1.2 this is necessary both when the vehicle is stationary and in some driving conditions. The battery in the vehicle’s electrical system always has to be designed according to certain criteria. The installed consumer power (in particular the power of the starter) and the alternator power during operation are decisive for this. The components battery, starter, and alternator must be harmonized regarding – consumer output, – alternator current output at engine speed in driving mode, – charging voltage and starting temperature (Reif 2011). Problem-free starting of the vehicle represents a great challenge for the battery especially at low temperatures. It is therefore important that the battery maintains the high performance even during the starting process at temperatures as low as − 25  C (Reif 2011). Since the battery is the sole energy supplier for the powernet during vehicle standstill and a discharged battery directly impairs vehicle availability (starting capability), it is particularly considered in the design of the powernet power supply. In particular, various standardized tests are carried out to ensure the appropriate dimensioning of the battery. The following criteria must be observed when designing the battery (Reif 2011): – rush hour traffic in winter with day and night rides for 1 week at 0  C and a week at 20  C (remaining battery capacity of at least 50% after these driving cycles), – start at −20  C, – the running time of the parking lights (12 h), – the flashing of the hazard warning light (3 h), – it must be possible to operate loads that operate with the ignition key removed (standby current loads) and to then start the engine. More information on the prescribed battery tests and the battery design procedures can be found in the relevant standards of the individual manufacturers. So-called lead-acid batteries are still the predominant technology for energy storage in the electrical powernet of motor vehicles. Although there are now some further developments such as the so-called AGM battery or gel batteries, the basic mode of operation has remained the same. A lead-acid battery consists of two electrodes, which are made of lead (Pb), lead sulfate (PbSO4 ), or lead dioxide (PbO2 ) depending on the charge state. The two lead electrodes are immersed into the electrolyte. The electrolyte used in the classic leadacid battery is sulfuric acid (Figure 8.14).

8.2 Energy storage

–

Pb

367

+

PbSO4 PbO2

PbSO4 Crystallization Pb2+

Crystallization

2− 4

−

Pb2+

2− 4

Diffusion

−

Diffusion 2

−

+

2+

Pb2+

Transfer reaction Pb

4+

+2

−

Transfer reaction 2H2O

4H+ + 2O2−

PbO2

Figure 8.14: Schematic discharge process of a lead accumulator according to Heinemann (2007).

When fully charged, the negative electrode of the battery consists of a porous spongy lead and the positive electrode of lead dioxide. The electrochemical processes in a battery cell during discharge can be described using the following reaction equations: Positive pole: PbO2 + SO24 − + 4H3 O + + 2e − ! PbSO4 + 6H2 O,

(8:2)

Pb + SO24 − ! PbSO4 + 2e −

(8:3)

Negative pole:

This results in an overall reaction of Pb + PbO2 + 2H2 SO4 ! 2PbSO4 + 2H2 O + electric energy:

(8:4)

For the charging process, the equations are shown reverse under the supply of electrical energy. In eq. (8.4) it is easy to see that when the battery cell is discharged, part of the sulfuric acid is converted to water. This changes the concentration of the acid (electrolyte) with the state of charge (SoC) of the battery. When discharged, the electrolyte consists of a 17% sulphuric acid solution with a density of 1.12 kg=l. In the fully charged state, the proportion of sulfuric acid in the electrolyte is approximately 37%, which increases the density of the electrolyte to 1.28 kg=l. By measuring the

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8 Automotive electrical system

acid density, the SoC of a battery can be determined on the basis of this relationship (Reif 2011). The arrangement of two lead electrodes and electrolyte shown above results in a nominal voltage of 2.12 V per battery cell. To receive the batteries used in vehicles with a nominal voltage of 12 V (previously 6 and 24 V in commercial vehicles), several cells (e.g., 6 in a 12 V battery) must be connected in series.

8.2.2 Characteristics and guidelines for lead-acid batteries

Discharge voltage / V

The concept for accumulators (batteries in motor vehicles) is defined according to DIN (1985). In addition, the parameters for lead-acid batteries in motor vehicles are defined in IEC (2000). New starter batteries can be described in defined load cases based on the variables described in the regulations. However, the values can only be transferred to batteries in operation to a limited extent. As already mentioned, the capacity of a battery depends on both temperature and battery current and consequently cannot be described by a fixed value. Comparable measurements must therefore be based on fixed load cases. Especially regarding the (cold) starting capability of a motor vehicle, the influence of temperature on battery performance plays a decisive role. Figure 8.15 shows the dependence of the terminal voltage and the degree of battery discharge depending on the ambient temperature.

12

9 –18 °C

27 °C

6 End-of-discharge voltage 3

0 Discharging time Figure 8.15: Discharging of a 12 V battery with the cold test current ICC at −18 and 27  C according to Reif (2011).

8.2 Energy storage

369

It can clearly be seen that low temperatures have a negative influence on the performance of a vehicle battery. On the one hand, the terminal voltage decreases while applying the same discharge current with the temperature. This is because the electrochemical processes in the battery are slowed down. Second, the final discharge voltage is also reached much sooner. This means that the battery has a significantly reduced capacity at low temperatures. It can be clearly seen that characteristic quantities describe a battery change depending on the ambient conditions (Reif 2011). The detailed (standardized) descriptions for – cell voltage, – nominal voltage, – idle and open-circuit voltage, – internal resistance, – terminal voltage, – gassing voltage, – (nominal) capacity, and the – (cold) test current can be taken from technical literature (Reif 2011), or directly from standardization literature. The capacity and charging of a battery are described in more detail below. 8.2.2.1 Capacity definitions The capacity K of a battery refers to the amount of charge that can be taken from a charged battery. However, the capacity of a battery is by no means constant. It depends on the ambient conditions (especially the temperature, see above) and the aging state (SoH).3 Battery capacity is also significantly dependent on battery current (PEUKERT effect). The actual removable capacity of a battery can only be determined exactly by completely discharging the battery. Battery manufacturers therefore work with a nominal capacity of KN , which represents a minimum capacity. This value is guaranteed under standardized conditions (25  C and a new battery) and is used to design the vehicle electrical powernet. In practice, nominal capacities are specified for different discharge durations (different discharge current). The nominal current IN represents the discharge current, which completely discharges the battery of the nominal capacity in a certain time (N-hours). The most common values for nominal capacities can be found in Table 8.6. The respective nominal current for the individual capacitances can very easily be determined by the relationship of

3 SoH: State of Health.

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8 Automotive electrical system

Table 8.6: Designations for the nominal capacity at different discharge durations (Heinemann 2007). Designation

Application

Discharge time/h

K2

Electric road vehicles



K5

Industrial traction operation



K10

Stationary applications



K20

Automotive applications



IN =

KN with t0 = 1 h. N t0

(8:5)

Since the respective capacitances are only defined for the special discharge current and in a normalized environment, normalized capacitances K are also used in some applications. These indicate the ratio of the current capacity of a battery, considering the discharge current, the temperature, and the State of Health (SoH) to the nominal capacity K=

Kact , KN

(8:6)

(Heinemann 2007). The capacity describes, as defined before, the “size” of the battery. In contrast to the capacity, the charge of a battery describes the energy that can still be drawn from that same battery. The degree of discharge qðtÞ describes the ratio of the amount of charge withdrawn since the last full charge QðtÞ to nominal charge Qnom of the battery at a certain discharge current I . The degree of discharge is defined as qðtÞ =

Qð t Þ . Qnom

(8:7)

This means that the battery is fully charged when the degree of discharge qðtÞ = 0. When the degree of discharge equals 1, this means that the battery is completely discharged. It should be noted that in practice values for q could also match numbers above 1. This is always the case when either low discharge currents or higher temperatures are used. As explained in the previous chapter, this increases capacity. This means that more charge can be withdrawn than nominally available. The dependence of the capacity/degree of discharge of a battery on the discharge current was discovered by PEUKERT4 in 1897 and has been known as the PEUKERT effect ever since.

4 Wilhelm Peukert (1855–1932).

8.2 Energy storage

371

8.2.2.2 Definition and determination of the state of charge While the degree of discharge is a measure of the amount of charge already removed from a battery, in practice it is rather decisive to know how large the remaining amount of charge in a battery is. This allows a statement about the further operation (e.g., how long different consumers can still be operated) by the battery (Figure 8.16). The State of Charge (SoC) is used as a measure for how much charge still remains in the battery. The SoC thereby describes the ratio of currently removable electrical charge to maximum charge with a full battery

State of function sof battery status

SoC

SoH

Reversible changes

Irreversible changes

Battery conditions available capacity internal resistance (Quiescent) voltage gas development acid density temperature …

Figure 8.16: Schematic representation of the influence of the battery parameters according to Heinemann (2007).

SoC =

QRest ðT Þ . KN ðT Þ

(8:8)

Since both the capacity of the battery (maximum charge) and the amount of charge that can be removed depend on the temperature, the SoC of an otherwise unchanged battery varies with the temperature. If all values are set to the nominal temperature Tnom , the nominal charge status can be determined. According to DIN (1985) the SoC is defined as follows: – The SoC is the ratio of a current stored amount of electricity compared to an allocated capacity KN of a battery. – The definition is based on the quantity of charge stored and not on the quantity that can be removed.

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8 Automotive electrical system

– Specifying the removable charge would require knowledge of both the discharge conditions and the battery history. – As a first approximation, the SoC can be determined relatively reliably via the time integral of the current and a normalization to the nominal capacity (with estimation of the secondary reaction current). Knowledge of the actual SoC of the battery is of great importance for many modern systems in motor vehicles. It must be ensured that all relevant systems can be operated continuously. If the battery charge is insufficient, start–stop systems, for example, are deactivated to prevent further discharge of the battery. Depending on the SoC, an energy management system can be operated in the vehicle. For this purpose, either loads can be switched off (load shedding) or the alternator voltage (only possible during operation) can be increased, which leads to improved battery charging. To determine the battery charge, the energy management (battery management) is of decisive importance in the vehicle. Load balancing procedures have become established in practical applications but require constant recalibration of the parameters. The reason for this is the change in battery behavior due to self-discharge and aging. During a charge and discharge cycle, there are always losses within the battery. Depending on the operating state, part of the charge or discharge current is converted into heat. Therefore, the battery charge absorbed and the charge available after charging differ. The ratio of both quantities is called the charging factor. It can be interpreted as the electrical efficiency of the battery. 8.2.2.3 Aging state of a battery SoH The SoC of the battery describes the current SoC of the battery in relation to the battery capacity. However, the nominal capacity of a battery is not constant over its lifetime. The capacity KNcurrent then differs significantly from the nominal capacity KNnom due to battery aging. The quotient of both variables is defined as the SoH SoHN =

KNcurrent ðTnom Þ . KNnom ðTnom Þ

(8:9)

The determination of the SoC requires a recalibration of the nominal capacity at regular intervals due to the unavoidable battery aging, since the maximum removable charge also changes with it. Determining the current nominal capacity is a difficult task in practice. The determination of the current charge state (e.g., for an energy management system) can therefore only be displayed with limited accuracy. Main causes for typical aging of lead-acid batteries are (Hönes 1994): – Cycling of the battery with the consequence of grid corrosion, – frequent overcharging of the battery, – deep discharge, and – long-lasting partial cycling.

8.3 Modeling of the battery behavior

373

Both during cycling and deep discharge, lead sulfate crystals are formed, which are significantly larger than the usual ones. These very large crystals are inactive in the electrochemical reaction. They are therefore not converted back into lead during the usual battery charging process. The “large” crystals attach themselves to the electrodes, which leads to a reduction of the active electrode surface and thus to a deterioration of the reactivity. This process is known as sulfation. Under certain circumstances, the “large” crystals formed by sulfation may become detached from the electrodes. These then sink to the bottom of the battery and form a conductive connection between the electrodes. In extreme cases, this can destroy the battery. In modern gel or Absorbent Glass Mat (AGM) batteries the detachment and sinking of sulfates is prevented. In principle, however, aging and the associated reduction in capacity must also be considered here.

8.3 Modeling of the battery behavior Depending on the intended use of a battery modeling, there are very different versions of numerical models. These range from models that provide information about the electrochemical processes to very simple models that alone reflect the course of the terminal voltage. In vehicles usually, battery models are used that describe the electrical (terminal) behavior of batteries. In particular, such models can be used to map the different energy flows in the vehicle electrical system. Therefore, it must be possible to make a reliable statement about the terminal voltage depending on the time, load profile, the SoC, and the aging state of the battery. The SoC is, as explained in Section 8.2.2, a measure of the reversible changes in the battery during charging and discharging. An SoC of 1 (100 %) corresponds to a fully charged battery. On the other hand, the aging state SoH of the battery describes irreversible changes (damages) of the battery. Both variables together make it possible to determine the current battery condition and should be considered in a suitable way within a battery model. If a battery model is to be used to simulate the electrical energy flows in the vehicle electrical powernet, there are several variables that such a model must include. The following values must be reliably determined for different operating conditions (such as varying temperature and different power requirements) both for charging and discharging the battery (Heinemann 2007): – Current SoC, – time of full discharge, – time of full charging (charging process), – available charge QðtÞ and energy EðtÞ, – terminal voltage curve uðtÞ, and – temperature profile (of the electrolyte).

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8 Automotive electrical system

In addition, for the use of a battery model in practice, it is often decisive that the aging state of the battery is included in the simulated behavior. This means there is the possibility of adapting the battery behavior specifically to the behavior of a no longer new battery. Implementing battery aging as part of the dynamic battery model is often an unjustifiable effort in practice. In most cases, relatively short time spans are considered in vehicle system simulations. By contrast, battery aging is a very slow process and it is therefore usually sufficient to adapt the battery model to the current SoH by means of suitable parameterization. Numerous different battery models can be found in the literature. Some of these differ considerably in their requirements and can be used for a wide variety of applications. In the following, a simplified battery model is derived, which aims to determine the terminal voltage depending on the battery charge and the battery current. In addition, temperature effects during loading and unloading are included. Such a model should always be used when power supply and, if necessary, energy management in the vehicle electrical system are to be simulated. Neither internal battery effects nor very fast transient processes can be simulated. The equivalent circuit diagram shown in Figure 8.17 is suitable for modeling the terminal voltage curve of a lead-acid battery in operation. While the main branch defines the voltage during battery discharge, further charge losses occur during charging, which can be mapped via the parasitic branch. This allows different behavior in case of charging and discharging.

1 0

2

1

Main branch

Parasitic branch

Figure 8.17: Equivalent circuit diagram for modeling of a lead-acid battery (Jackey 2007).

The core of the model is the cell voltage UH (Jackey 2007). The cell voltage depends on both the temperature and the current charge state (Table 8.7): 100  UH, 0 = UH, 0 − KE ð273 C − ΘE Þð1 − SoCÞ.

(8:10)

8.3 Modeling of the battery behavior

375

Table 8.7: Formula symbols for modeling the battery behavior. Formula symbols

Description

UH, 0

Open circuit voltage of the battery cell

100 UH, 0

Open circuit voltage of the battery cell in fully charged state

KE

Temperature constant for voltage adjustment

ΘE

Electrolyte temperature

SoC

State of charge of the battery

R0

Terminal resistance

R0100

Terminal resistance in fully charged state (SoC = )

A0

Absolute term

R1

Main branch resistor RC element

C1

Branch capacity

τ1

Time constant RC element

R2

Main branch resistance

A21 , A22

Absolute terms

Im

Principal branch current

Inom

Nominal current of the battery

IP

Loss current through the parasitic branch

UPN

Voltage across the parasitic branch

GP0

Absolute term

τP

Time constant of the parasitic branch

UP0

Constant voltage for calculation of parasitic currents

AP

Absolute term

ΘE

Electrolyte temperature

ΘEF

Freezing temperature of the electrolyte

CB

Battery capacity during operation (current maximum charge that can be stored)

KC0, 1 , 2

Absolute term

C0*

Idle capacity at 0 °C in As. Depends, among other things, on the aging state of the battery

ΘU

Ambient temperature

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8 Automotive electrical system

Table 8.7 (continued ) Formula symbols

Description

Θ t0

Initial temperature

PS

Power loss over R0 and RP

CΘ

Thermal capacity

RΘ

Thermal resistance

In the load case, the terminal voltage of the battery is reduced depending on the load current. This is caused by the so-called internal resistance of the battery. In the simplest case, the internal resistance R0 can be assumed to be constant. For a more exact description of the real terminal voltage of a battery, a resistance depending on the SoC is used here: R0 = R100 0 ½1 + A0 ð1 − SoCÞ

(8:11)

In addition to the terminal resistance, other components are located in the electrical circuit diagram of the battery as well. If a battery current flows, an RC element and another resistor act in series in the main branch of the battery. That RC-element consisting of R1 and C1 is used to determine the transient behavior of the battery (at very fast changes in battery current). The behavior thereby is allowed by approximately equaling the value of a PT1 element. The resistance R1 is proportional to the logarithm of the discharge depth DoC ; see eq. (8.12). By determining the absolute term of time of a real battery (e.g., by measurements), the value of the capacity C1 can be determined: R1 = − R1, 0 lnðDoCÞ,

(8:12)

τ1 = R1 C1 .

(8:13)

The second main branch resistor R2 serves to further reduce the terminal voltage depending on the battery current (especially when the battery is low charged). This effect is also important for the battery charging process: R2 = R2, 0

efA21 ð1 − SoCÞg . 1 + eA22 Im =Inom

(8:14)

It is clear to see that the resistance R2 increases disproportionately with large battery currents and discharged batteries. The terminal voltage then drops significantly. Besides the main branch of the battery model, the battery model presented here contains a so-called parasitic branch according to Jackey (2007). This branch is only active when the battery is charging and makes it possible to map the charge

8.3 Modeling of the battery behavior

377

losses of the battery in a suitable manner. These losses depend on the current electrolyte temperature and also cause further heating of the battery (see thermal model of the battery):  UPN

IP = UPN GP0 e½ðτP + 1ÞUP0 

Θ

+ AP 1 − Θ E EF

.

(8:15)

The loss current described here is very low in normal battery operation. As it can also be seen from the equation, only with high SoC (almost fully charged battery) and high charging voltages (high voltage across the branch) there are significant leakage currents. The previous descriptions are suitable for determining the corresponding values; for example, the terminal voltage for a known battery charge depending on an applied load or charging current. But in order to assure that the battery model can also be used for simulations over longer periods of time, it is necessary to change the charge state accordingly over time. The charging and capacity model described below serves this purpose. The battery charge can be determined relatively easily from the initial battery charge and the integral of the main branch current over time: ðt QB ðtÞ = QB, t0 −

Im ðτÞdτ.

(8:16)

t0

The maximum charge of the battery is called battery capacity. It is also not a constant value, but depends on the battery current and the temperature:

CB ðI, ΘE Þ =

 KC0 C0* 1 +

ΘE − ΘEF

1 + ðKC0 − 1Þ

KC1

 KC2 .

(8:17)

I I*

From the present battery capacity (maximum battery charge) and the battery charge determined via the integral QB , the present value of the battery SoC can be determined very easily: SoC =

QB . CB ð0, ΘE Þ

(8:18)

Compared to the SoC, which determines the capacity of a battery at idle (without load), the battery charging depth DoC (Depth of Charge) indicates this value for a medium load: DoC =

QB . CB Iavg , ΘE 

(8:19)

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8 Automotive electrical system

Finally, the interactions of the power losses in the battery during charging and discharging with the battery temperature are considered. The electrolyte temperature of the battery depends not only on the losses in the battery but also on the ambient temperature. For the temperature ΘE the following context can be written: ΘE ðtÞ = Θt0 +

ðt P − S t0

ΘE − ΘU RΘ

CΘ

dτ.

(8:20)

The model presented can be used to simulate the terminal voltage curve of a vehicle battery using suitable parameters. Electrochemical effects cannot be considered. It can be used to simulate batteries of different parameterization (states). However, it does not cover aging in a long-term simulation.

8.4 Alternators in motor vehicles The alternator supplies the electrical powernet of a vehicle with the required electrical power. Together with the battery, which supplies the loads during the starting process and in vehicle standstill, the alternator must guarantee a reliable power supply. The alternator output and battery capacity must therefore be well matched to each other and to the power requirements in the energy powernet. In typical vehicle usage cycles, the alternator must be able to maintain a positive charge balance. This is the only way to guarantee the function/startability of the vehicle. The alternator discussed in this section represents the claw pole alternator typical for the usual 12 V system. This is a synchronous machine with excitation winding. If the powernet system voltage is increased (see Section 8.1.2, 48 V powernet supply), other electrical machines are also used. Here, however, the considerations should be limited to the classic vehicle alternator. The continuing trend toward electrification of components has led to a significant increase in number and individual power demand of the consumers. Alternators used today already have a maximum output of over 3 kW (more than 200A at 14 V). In addition to the maximum power output of an alternator, it is also important for the optimum supply of all electrical components in the powernet power supply system that the required electrical power is available in the broadest possible speed range. Even at idling speed, current alternators therefore deliver a third of their rated power. An important parameter of alternators in motor vehicles is the electrical energy generated per weight. This size shows the importance of powerful components while striving to make optimum use of resources. As Figure 8.18 shows, the maximum alternator current or maximum alternator power depends on the respective speed. To ensure that the alternator can provide enough power even at low engine speeds, such as idling, transmission ratios between crankshaft and alternator in the range of 1:2 to 1:3 are used.

8.4 Alternators in motor vehicles

379

Alternator current/ alternator power

Increasing temperature

0 0

rpm

Figure 8.18: Qualitative representation of the current characteristic of a three-phase alternator. Inscribed in the illustration nL names the idle speed and nmax the maximum speed of the motor/ alternator. The dependence of the maximum alternator current on engine speed and temperature can be seen.

In addition to the speed, the temperature also limits the maximum alternator output. At high temperatures, there are greater losses, so that the maximum output of the alternators decreases as the temperature rises (Figure 8.18). To keep the output voltage of the alternator constant (so that an optimal function of the electrical components can be guaranteed), a suitable control is used. Depending on speed, load, and temperature, the excitation current is controlled in such a way that the output voltage remains constant. However, in the event of large load jumps in the vehicle electrical system, the voltage may briefly deviate from the set point. This is the case either when suddenly connecting or disconnecting (especially powerful) components. In this case, the control must first react to the new powernet status and readjust the alternator accordingly. This can lead to a voltage hole or a voltage peak. The alternator control is also used to set different powernet supply voltages depending on weather conditions. At low temperatures, for example, it may be necessary to slightly increase the voltage so that the battery is optimally charged. At high temperatures, the voltage may be lowered to prevent overcharging of the battery.

8.4.1 Design of vehicle alternators Due to the high complexity of the electrical powernet system, the role of the alternator in the vehicle has also changed. As already mentioned, the first alternators (dynamos) were only necessary to operate the electric lights (and signals) and to recharge the battery after a start. In particular, the requirements for maximum power and constant

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voltage in different (transient) states have increased significantly. According to Reif (2011), today’s vehicle alternators must meet the following requirements: – Ensuring a positive track record over different driving cycles, – realization of a positive charge balance of the battery to ensure start ability, – power supply for all consumers in driving operation (only possible for highperformance consumers and highly transient consumers in cooperation with the battery), – supply fluctuation-free, load-condition-independent voltage over the entire speed range, – robust design regarding temperature, humidity, dirt, vibrations, and so on, – minimized component weight (high power density), – small installation space and inexpensive packaging, – low operating noise, and – low losses (optimized efficiency). The design or selection of an alternator for a special vehicle must therefore be carried out against the background of the power requirements. Battery, alternator, and installed consumers must be well matched to each other.

8.4.2 Efficiencies of vehicle alternators The efficiency of the alternator plays a decisive role, in particular due to the demand for resource-saving mobility and the simultaneous increased demands on the powernet power supply. The degree of efficiency is generally a very good measure of the efficiency of an alternator as an energy converter. It indicates the ratio of power output to power consumed. The vehicle alternator converts mechanical power into the electrical power required in the vehicle powernet. The alternator efficiency is thus defined as η=

Pelec . Pmech

(8:21)

Of course, the efficiency of an alternator is not constant over the entire operating range. Depending on the speed and load, the various sources of loss occur to varying degrees. Figure 8.19 breaks down the sources of loss of an alternator as a function of the speed. The losses are divided into two groups. Some of the losses depend on the speed of the alternator. These increase with increasing speed due to mechanical friction and hysteresis during magnetization. On the other hand, there are losses that are dependent on the alternator current. These do not increase further at high speeds. Iron and copper losses and mechanical losses caused by friction account for the largest share of losses. Copper losses are the power dissipation due to the

Alternator power P Losses V

8.5 Simplified model of a vehicle alternator

381

: consumed mechanical power : mechanical losses +

: copper losses in the stator +

: iron and additional losses : rectifier losses : excitation losses : delivered electrical power

rpm Figure 8.19: Overview of power losses in the alternator according to Reif (2011).

ohmic resistance in the conductor loops. The iron losses are caused by hysteresis due to the constantly changing magnetic field in the stator and rotor. Mechanical losses are caused by friction in bearings as well as by flow resistances (air friction), for example, in fans. The maximum efficiencies of vehicle alternators are in the range of approximately 65%. Under normal operating conditions, the efficiency of 55 − 60% on average in driving operation is not exceeded (Büchner and Bäker 2005).

8.5 Simplified model of a vehicle alternator In this section, the alternator is modeled to obtain a simplified mathematical representation that makes it possible to represent the coupling with the powernet and with the mechanics of the internal combustion engine. In the simplest case, the alternator can be described as a regulated voltage source. In normal driving operation, the voltage regulation of the alternator has the task of keeping the alternator voltage almost constant at 14 V independent of the respective vehicle electrical system loads. If the applied load exceeds the maximum power available from the alternator, the alternator voltage drops. Depending on the maximum alternator current (in the current state), a voltage results in the vehicle powernet. In this case, the alternator can be described as a constant current source. This very simplified view

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of the alternator as a constant voltage or current source (depending on the load) already provides a first, albeit very simplified alternator model. However, this can only describe the electrical side of the alternator and also this is only in strongly reduced form. According to Reif (2012), a vehicle alternator consists of four parts: – The magnetic circuit of the excitation field, – voltage generation in the three-phase winding (stator coils), – rectification of the rotary phase alternating voltage, and – voltage regulation (see also Figure 8.20).

ALTERNATOR

Stator coil

,

Voltage regulator

Excitation coil

Rectifier

Electrical machine

Figure 8.20: Block diagram of the function of a alternator model according to Hesse (2011).

The rotor of the alternator is coupled with the rotational movement of the combustion engine. The rotary movement of the rotor (with the exciter coil) induces a voltage in the three stator coils. This produces a three-phase alternating voltage. A simple diode circuit (rectifier) is then used to generate the DC voltage required in the vehicle from this alternating voltage. Since the magnitude of the induced voltage in the stator coils depends on the change in the effective magnetic flux over time, they are defined by the rotational speed of the rotor and the magnetic flux density of the excitation field. The exciter field is influenced by the voltage regulator in such a way that the alternator voltage corresponds to the current set point (normally approx. 14 V). The following describes a simple model of an alternator according to the block diagram shown in Figure 8.20.

8.5.1 Electrical machine The electrical machine consists of the exciter and stator coils. The excitation coils are used to generate a magnetic field of the desired size. For this purpose, the regulated

8.5 Simplified model of a vehicle alternator

383

excitation voltage UF is applied, which is then converted to the excitation current IF . This flows through the coils and a magnetic field is formed. For the current through the coil as a function of the applied voltage applies (Büchner and Bäker 2005): dIF , UF = URF + ULF = RF IF + LF dt ð 1 ðUF − RF IF Þdt. IF = LF

(8:22) (8:23)

The symbols used here and in the continuous part of the section are defined in Table 8.8 . The current IF that flows through the exciter coil determines the desired magnetic field strength HF . According to Böge (2007) for HF approximately, the expression

Table 8.8: Formula symbols of the models for the electrical machine of a vehicle alternator set. Formula symbol

Description

IF

Exciter coil current

LF

Inductance of the excitation coil

URF

Voltage drop across the ohmic resistance of the excitation coil

UF

Voltage applied to excitation coil

HF

Magnetic field strength

lF

Mean magnetic path length

N

Winding number

nG

Alternator speed

ωint

Theoretical internal angular velocity of the alternator

p

Number of pool pairs (typically  or )

Φeff

Effective magnetic flux

ΦF

Magnetic flux due to the excitation field

Φk

Partial compensation of the excitation field by current in the stator coils

u, v, w

Coil windings of the considered pool pair

A

Cross-sectional area of a coil

θj

Angle of rotation of the coil j

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Table 8.8 (continued ) Formula symbol

Description

Lj

Inductance of the stator coil j

N

Winding number of the coil

ij

Alternating current in the stator coil j

uind

Induced alternating voltage

kind

Coefficient of induction

HF =

N IF lF

(8:24)

can be used. The magnetic flux density BF required for further calculations results as a function of the field strength BF = f ðHF Þ via the magnetizing characteristic. A relative movement occurs between the exciter coil and the stator coil. This changes the effective field of excitation through the stator coils. The relative movement is proportional to the rotation frequency of the alternator. The following applies: ωG = 2πnG .

(8:25)

By using several arrangements of coils, each of them consisting of three coils rotated by 120 (pole pairs) in the alternator, a theoretical internal rotation frequency is used for the calculation in this alternator model. This is greater by the factor of the number of pole pairs than the actual physical quantity. Thus, it is possible to calculate with only one coil arrangement leading to: ωint = pωG .

(8:26)

As a further simplification of the notation, the following indices u, v, w are used for the three coils of a pole pair. The induction of a voltage into the coils of the pole pairs results in a (desired) current flow. However, this weakens the effective magnetic field (and thus the effect). This results in the effective magnetic flux (Fuest and Döring 2015): Φeff , j = ΦF, j − Φk, j , j = u, v, w.

(8:27)

During operation, a relative movement (rotation) occurs between the exciter coils and the stator coils, as already described. Also under the assumption that the magnetic flux density in the exciter coils is not adjustable by the exciter coil BF , the variable magnetic flux acts on the three coils of the stator winding depending on the current angle of rotation (Böge 2007):

8.5 Simplified model of a vehicle alternator

ΦF, j = BF A sin Φj , j = u, v, w.

385

(8:28)

Since the three coils (u, v, w) have a fixed arrangement (rotation of 120 ) to each other, the following relationship can be established: R Θu = ΘG = ωG dt, Θv = Θu − 32 π

and

(8:29)

Θw = Θu + 32 π. The partial compensation of the excitation field by the currents flowing in the stator coils (self-induction) described above results in (Böge 2007): Φk, j =

Lj ij . N

(8:30)

This allows the AC voltage at the respective stator coils to be determined at idle speed, (Fuest and Döring 2015): uj, ind = ωint pkind Φeff , j .

(8:31)

Under load, that is, while an alternator current flows, the voltage at the individual coils is further reduced by the ohmic resistance and the inductance of the coil.

8.5.2 Rectifier To obtain the DC voltage required in the vehicle electrical powernet (alternator terminal voltage), the AC voltage quantities derived in the previous section must be interconnected and rectified in a suitable manner. Both are done with the help of a simple rectifier circuit (Figure 8.21). The rectifier is constructed with six diodes. The diodes limit the current flow so that the desired DC voltage is applied to the alternator terminal. The alternator terminal voltage results from (Table 8.9): UG = UPos − UNeg .

(8:32)

The voltages UPos and UNeg result from the shown rectifier circuit as follows: UPos = max uPos, j , UNeg = min uNeg, j , j = u, v, w.

(8:33)

The quantities uPos, j and uNeg, j represent only the positive or negative half-waves of the associated coil voltage. The half-waves are separated by the diode circuit. In addition, the diodes cause a voltage drop:

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8 Automotive electrical system

UJQ/

Y

UX

! Z

UTU

Figure 8.21: Rectifier circuit according to Henneberger (2013). The three coil voltages of the coils u, v, w are connected in a star configuration. The six diodes shown here align the sizes equally.

Table 8.9: Symbols for modeling the rectifier circuit. Formula symbol

Description

UPos

Potential between coils and positive alternator terminal

UNeg

Potential between coils and negative alternator terminal

8  dij