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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Automotive Series
- Sprache: Englisch
- Comprehensively covers the fundamentals of vehicle dynamics with application to automotive mechatronics
- Presents a number of different design, analysis and implementation considerations related to automobiles, including power requirements, converters, performance, fuel consumption and vehicle dynamic models
- Covers the dynamics, modeling and control of not only the entire vehicle system, but also of key elements of the vehicle such as transmissions, and hybrid systems integration
- Includes exercise problems and MATLAB® codes
- Accompanied by a website hosting animations
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Seitenzahl: 459
Veröffentlichungsjahr: 2015
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Table of Contents
Cover
Automotive Series
Title Page
Copyright
Dedication
Foreword
Series Preface
Preface
List of Abbreviations and Symbols
Chapter 1: Introduction
1.1 Introductory Remarks
1.2 Motion of the Vehicle
1.3 Questions and Exercises
Chapter 2: The Wheel
2.1 Equations of Motion of the Wheel
2.2 Wheel Resistances
2.3 Tyre Longitudinal Force Coefficient, Slip
2.4 Questions and Exercises
Chapter 3: Driving Resistances, Power Requirement
3.1 Aerodynamic Drag
3.2 Gradient Resistance
3.3 Acceleration Resistance
3.4 Equation of Motion for the Entire Vehicle
3.5 Performance
3.6 Questions and Exercises
Chapter 4: Converters
4.1 Clutch, Rotational Speed Converter
4.2 Transmission, Torque Converter
4.3 Questions and Exercises
Chapter 5: Driving Performance Diagrams, Fuel Consumption
5.1 Maximum Speed without Gradient
5.2 Gradeability
5.3 Acceleration Capability
5.4 Fuel Consumption
5.5 Fuel Consumption Test Procedures
5.6 Questions and Exercises
Chapter 6: Driving Limits
6.1 Equations of Motion
6.2 Braking Process
6.3 Braking Rate
6.4 Questions and Exercises
Chapter 7: Hybrid Powertrains
7.1 Principal Functionalities
7.2 Topologies of Hybrid Powertrains
7.3 Regenerative Braking and Charging
7.4 Questions and Exercises
Chapter 8: Adaptive Cruise Control
8.1 Components and Control Algorithm
8.2 Measurement of Distances and Relative Velocities
8.3 Approach Ability
8.4 Questions and Exercises
Chapter 9: Ride Dynamics
9.1 Vibration Caused by Uneven Roads
9.2 Oscillations of Powertrains
9.3 Examples
9.4 Questions and Exercises
Chapter 10: Vehicle Substitute Models
10.1 Two-mass Substitute System
10.2 Two-axle Vehicle, Single-track Excitation
10.3 Non-linear Characteristic Curves
10.4 Questions and Exercises
Chapter 11: Single-track Model, Tyre Slip Angle, Steering
11.1 Equations of Motion of the Single-track Model
11.2 Slip Angle
11.3 Steering
11.4 Linearized Equations of Motion of the Single-track Model
11.5 Relationship between Longitudinal Forces and Lateral Forces in the Contact Patch
11.6 Effect of Differentials when Cornering
11.7 Questions and Exercises
Chapter 12: Circular Driving at a Constant Speed
12.1 Equations
12.2 Solution of the Equations
12.3 Geometric Aspects
12.4 Oversteering and Understeering
12.5 Questions and Exercises
Chapter 13: Dynamic Behaviour
13.1 Stability of Steady-state Driving Conditions
13.2 Steering Behaviour
13.3 Crosswind Behaviour
13.4 Questions and Exercises
Chapter 14: Influence of Wheel Load Transfer
14.1 Wheel Load Transfer without Considering Vehicle Roll
14.2 Wheel Load Transfer Considering Vehicle Roll
14.3 Questions and Exercises
Chapter 15: Toe-in/Toe-out, Camber and Self-steering Coefficient
15.1 Toe-in/Toe-out, Camber
15.2 Questions and Exercises
Chapter 16: Suspension Systems
16.1 Questions and Exercises
Chapter 17: Torque and Speed Converters
17.1 Speed Converters, Clutches
17.2 Transmission
17.3 Questions and Exercises
Chapter 18: Shock Absorbers, Springs and Brakes
18.1 Shock Absorbers
18.2 Ideal Active Suspension and Skyhook Damping
18.3 Suspension Springs
18.4 Brake Systems
18.5 Questions and Exercises
Chapter 19: Active Longitudinal and Lateral Systems
19.1 Main Components of ABS
19.2 ABS Operations
19.3 Build-up Delay of Yaw Moment
19.4 Traction Control System
19.5 Lateral Stability Systems
19.6 Hydraulic Units for ABS and ESP
19.7 Active Steering System
19.8 Questions and Exercises
Chapter 20: Multi-body Systems
20.1 Kinematics of Rigid Bodies
20.2 Kinetic Energy of a Rigid Body
20.3 Components of Multi-body Systems
20.4 Orientation of Rigid Bodies
20.5 Derivation and Solution of the Equations
20.6 Applications of MBS
20.7 Questions and Exercises
Glossary
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Foreword
Series Preface
Begin Reading
List of Illustrations
Preface
Figure 1 Chapters of the book
Figure 2 Bloom's taxonomy of learning
Chapter 1: Introduction
Figure 1.1 Passenger cars (and light trucks in US) per 1000 inhabitants (data from OECD 2014)
Figure 1.4 International Energy Agency (IEA) CO
2
from fuel combustion (Mt) in Road Transport (data from OECD 2014)
Figure 1.5 Importance of purchase criteria (Braess and Seiffert 2001)
Figure 1.6 MBS model of a four-wheel-drive vehicle (example of the MBS programme ADAMS)
Figure 1.7 McPherson front axle with driven wheels (from MBS programme ADAMS)
Figure 1.8 Motion of a vehicle
Chapter 2: The Wheel
Figure 2.1 Coordinates of the wheel
Figure 2.2 Normal stresses in the contact patch of the tyre
Figure 2.3 Illustration of the asymmetric normal stress distribution in the contact patch
Figure 2.4 Free-body diagram of the wheel
Figure 2.5 Rolling resistance coefficient in percentage for summer tyres (data from Reithmaier and Salzinger 2002)
Figure 2.6 Rolling resistance coefficient in percentage for winter tyres (data from Reithmaier and Salzinger 2002)
Figure 2.7 Rolling resistance coefficient in percentage for all-season tyres (data from Reithmaier and Salzinger 2002)
Figure 2.8 Aquaplaning speed for summer tyres (data from Reithmaier and Salzinger 2002)
Figure 2.9 Aquaplaning speed for winter tyres (data from Reithmaier and Salzinger 2002)
Figure 2.10 Tyre longitudinal force coefficient, , as a function of the slip
Figure 2.11 Mean deceleration divided by gravitational acceleration during braking from 80 km/h to 10 km/h for summer tyres (data from Reithmaier and Salzinger 2002)
Figure 2.12 Mean deceleration divided by gravitational acceleration during braking from 80 km/h to 10 km/h for winter tyres (data from Reithmaier and Salzinger 2002)
Chapter 3: Driving Resistances, Power Requirement
Figure 3.1 Vortex behind a car (reproduced with permissions of Daimler AG)
Figure 3.2 Vortex at A-column (reproduced with permissions of Daimler AG)
Figure 3.3 Vortex at engine compartment and at A-column (reproduced with permissions of Daimler AG)
Figure 3.4 Free-body diagram of the entire vehicle (without inertia forces at the axles)
Figure 3.5 Free-body diagram for determining the acceleration resistance (without inertia forces at the axles)
Figure 3.6 Power demand of several resistances
Figure 3.7 Tractive forces demand of several resistances
Figure 3.8 Power demand area
Figure 3.9 Forces demand map
Figure 3.10 Ideal engine delivery map for the power
Figure 3.11 Ideal engine delivery map for the tractive force
Figure 3.12 Real engine delivery map for the tractive force
Figure 3.13 Demand curve for the power
Figure 3.14 Ideal characteristic map for the power
Chapter 4: Converters
Figure 4.1 Real and ideal characteristic maps
Figure 4.5 Gear ratios for several vehicles from Mercedes
Figure 4.2 Principal mode of operation of a speed converter
Figure 4.3 Engagement of clutch when starting on a hill
Figure 4.4 Significant functional components of a friction clutch
Figure 4.7 Basic operating principle of the manual transmission
Figure 4.6 Progression ratios for several vehicles from Mercedes
Figure 4.8 Nine-speed Mercedes automatic gear unit (reproduced with permissions of Daimler AG)
Figure 4.9
Figure 4.10 Geometric (second row diagrams) and progressive (first row diagrams) transmission ratios represented for the power
Figure 4.11 Driving performance diagram (forces)
Figure 4.12 Driving performance diagram (power)
Figure 4.13 Transmission
Chapter 5: Driving Performance Diagrams, Fuel Consumption
Figure 5.1 Driving performance diagrams;
Figure 5.2 Determination of the maximum speed without gradient
Figure 5.3 Free traction, , at the intersection of traction full load characteristics for the first and second gears
Figure 5.4 Example of varying velocity
Figure 5.5 Points of best efficiency
Figure 5.6 The velocity–time dependence of the NEDC
Figure 5.7 Power and tractive forces supplied by the powertrain with an internal combustion engine and the demand for power from NEDC
Chapter 6: Driving Limits
Figure 6.1 Free-body diagram
Figure 6.2 Lift coefficients of BMW 3 Series (data from Braess 1998)
Figure 6.3 Lift coefficients of Porsche 911 (data from Harrer et al. 2013)
Figure 6.4 Components of axle loads
Figure 6.5 Foot force, acceleration, velocity and distance during the braking process
Figure 6.6 Factors influencing total braking distance
Figure 6.7 Tyre longitudinal force coefficient, , as a function of the slip
Figure 6.8 Dynamic wheel load under braking
Figure 6.9 Ideal braking force distribution
Figure 6.10 Braking force distribution on the basis of the static wheel loads
Figure 6.11 Braking force distribution on the basis of the dynamic wheel loads at
Figure 6.12 Braking force distribution on the basis of the dynamic wheel loads at
Figure 6.13 Braking force distribution on the basis of the dynamic wheel loads at and rear braking force delimiter
Chapter 7: Hybrid Powertrains
Figure 7.1 Vehicle with a parallel hybrid powertrain
Figure 7.2 The hybrid idea
Figure 7.3 Split of the power from the internal combustion engine
Figure 7.4 Electric engine integrated in the powertrain (reproduced with permissions of Schaeffler)
Figure 7.5 Regenerative braking
Figure 7.6 Boost mode
Figure 7.7 Purely electric mode
Figure 7.8 Hybrid levels
Figure 7.9 Hybrid powerpack from GM, Mercedes and BMW (reproduced with permissions of Daimler AG)
Figure 7.10 Parallel hybrid vehicle
Figure 7.11 Serial hybrid vehicle
Figure 7.12 Serial–parallel hybrid vehicle
Figure 7.13 Power–split hybrid vehicle
Figure 7.14 Components of hybrid powertrains
Figure 7.15 Driving performance diagrams
Figure 7.16 Points of energy recovery (with positive sign)
Figure 7.17 Curve of constantly recoverable power
Chapter 8: Adaptive Cruise Control
Figure 8.1 ACC control (adapted from Winner et al. 2012)
Figure 8.2 Acceleration limits for ACC: ISO 15622 and ISO 22179
Figure 8.3 Engine map: engine torque, , depending on the speed, , and the relative throttle position,
Figure 8.4 Frequency changes with different slopes to improve the relative velocity determination (adapted from Winner et al. 2012)
Figure 8.5 Frequency determination for different frequency changes, errors for the beat frequencies, each
Figure 8.6 Slow vehicle 1 is currently in the detection range of the ACC and leaves it again; and vehicle 2 is in the field of coverage
Figure 8.7 Vehicle circumstances as shown in Figure 8.9, the ACC may not be changed due to the faster vehicle travelling in the other lane on distance control
Figure 8.8 Vehicle 1 enters the detection range of the ACC vehicle
Figure 8.9 Vehicle 2 moves into the detection range of the ACC vehicle, vehicle 1 exits the range
Figure 8.10 Determination of the approach ability
Chapter 9: Ride Dynamics
Figure 9.1 Internal and external sources
Figure 9.2 Transfer paths of oscillations
Figure 9.3 Mount at the powerplant
Figure 9.4 Damped harmonic oscillator
Figure 9.5 Magnification function for the acceleration
Figure 9.6 Magnification functions for the wheel load fluctuation
Figure 9.7 Spring deflection
Figure 9.8 Examples of spectral irregularity densities
Figure 9.9 Evaluated vibration strengths
Figure 9.10 Evaluation functions for the seat
Figure 9.14 Evaluation function after Cucuz 1993
Figure 9.11 Quarter-vehicle model with driver mass
Figure 9.12 Spectral density of the road
Figure 9.13 Spectral density of the road with driving speed
Figure 9.15 Magnification function for seat acceleration
Figure 9.16 Spectral density of the seat vibrations
Figure 9.17 Comfort evaluation function
Figure 9.18 Spectral density of the wheel load vibrations
Figure 9.19 Magnification function of wheel load
Figure 9.20 Conflict: safety and comfort; increases starting from upper right to the end point in the left part
Figure 9.21 Conflict: comfort–safety
Figure 9.22 Pareto frontiers: comfort–safety
Figure 9.23 Torsional oscillators with one degree of freedom
Figure 9.24 Torsional oscillator with two degrees of freedom
Figure 9.25 Amplitudes of a damped absorber
Figure 9.26 Different possibilities of pendulum absorber
Figure 9.27 Centrifugal pendulum absorber
Figure 9.28 Internal crankshaft damper (reproduced with permissions of Schaeffler)
Chapter 10: Vehicle Substitute Models
Figure 10.1 Two-mass substitute systems
Figure 10.2 First and second natural frequency as a function of the body spring stiffness
Figure 10.3 Four-mass oscillator as a model of a two-axle vehicle
Figure 10.4 Two-axle vehicle with coupling mass
Figure 10.5 Relation of amplitude to frequency (undamped Duffing oscillator)
Figure 10.6 Relation of amplitude to frequency (damped Duffing oscillator)
Figure 10.7 Non-linear characteristic curves
Chapter 11: Single-track Model, Tyre Slip Angle, Steering
Figure 11.1 Single-track model
Figure 11.2 Determination of the circle of curvature using a limiting process
Figure 11.3 Free-body diagram of the single-track model
Figure 11.4 Instantaneous centre of rotation of the vehicle in motionl
Figure 11.5 Distance of the instantaneous centre of rotation from the centre of gravity
Figure 11.6 The radius of the circle of curvature
Figure 11.7 Forces on a tyre with lateral slip
Figure 11.8 Stresses in the contact area at the wheel with lateral slip
Figure 11.9 Development of lateral forces
Figure 11.10 Lateral force, self-aligning moment and tyre caster trail (from measurements with slight corrections of offsets)
Figure 11.11 Schematic diagram of a rack and pinion steering system (adapted from Mitschke and Wallentowitz 2004)
Figure 11.12 Impact of longitudinal forces in the contact area
Figure 11.13 Effect of a negative scrub radius in different driving situations
Figure 11.14 Kinematics on the single-track model
Figure 11.15 Kamm's circle and Krempel diagram (: driving; : braking)
Chapter 12: Circular Driving at a Constant Speed
Figure 12.1 Vehicle sideslip angle, , steering wheel angle, , tyre slip angles, , , and steering angle of the front wheel, , as a function of the centripetal acceleration divided by the acceleration due to gravity,
Figure 12.2 Geometric interpretation of the Ackermann angle and the vehicle sideslip angle for the disappearing tangential velocity (for a single-track model)
Figure 12.3 Geometric interpretation of the Ackermann angle for disappearing tangential velocity (for a double-track model)
Figure 12.4 Relationship between the front wheel steering angle, , and tyre slip angles, , , and the vehicle sideslip angle for steady-state cornering ()
Figure 12.5 Relationship between steering angle, , and lateral acceleration, , for several Porsche 911 models (data from Harrer et al. 2013)
Figure 12.6 Vehicle sideslip gradient for several Porsche 911 models (data from Harrer et al. 2013)
Chapter 13: Dynamic Behaviour
Figure 13.1 Stability of steady-state circular driving
Figure 13.2 Path curves (schematic) with stable and unstable driving behaviour
Figure 13.3 Countersteering: (a) Velocities in crosswinds on the single-track model; (b) split- braking (adapted from Mitschke and Wallentowitz 2004)
Chapter 14: Influence of Wheel Load Transfer
Figure 14.1 Wheel load distribution when cornering
Figure 14.2 Increase of the slip angle due to changes in wheel load distributions
Figure 14.3 Derivation of the instantaneous centre of rotation (adapted from Mitschke and Wallentowitz 2004)
Figure 14.4 Derivation of the instantaneous axis of rotation
Figure 14.5 Total system with instantaneous roll axis
Figure 14.6 Determination of wheel load changes
Figure 14.7 Anti-roll bar
Figure 14.8 Influence of the stiffness of anti-roll bars at front and rear axles
Figure 14.9 Active roll stabilization (ARS): active anti-roll bar (reproduced with permissions of ZF Friedrichshafen AG)
Chapter 15: Toe-in/Toe-out, Camber and Self-steering Coefficient
Figure 15.1 Toe and camber
Figure 15.2 Influence of toe-in on the slip angle
Figure 15.3 Influence of camber on the slip angle
Chapter 16: Suspension Systems
Figure 16.1 Principles of wheel suspension systems
Figure 16.2 Double wishbone (or A-arm) suspension
Figure 16.3 Changes of toe and camber during compression and rebound of the suspension (adapted from Mitschke and Wallentowitz 2004)
Figure 16.4 Solid axle
Figure 16.5 McPherson front axle of a Mercedes B-Class (reproduced with permissions of Daimler AG)
Figure 16.6 Principal components of a McPherson front axle suspension
Figure 16.7 Rear axle of a Mercedes B-Class (reproduced with permissions of Daimler AG)
Figure 16.8 McPherson front axle of a Mercedes M-Class (reproduced with permissions of Daimler AG)
Figure 16.9 Rear axle of a Mercedes M-Class (reproduced with permissions of Daimler AG)
Figure 16.10 Multi-link rear axle of a Mercedes C-Class (reproduced with permissions of Daimler AG)
Figure 16.11 Design principle of a five-link suspension
Figure 16.12 Explanation of an elastokinematic point
Figure 16.13 A five-link suspension similar to the LSA rear suspension of the Porsche 911 Carrera
Chapter 17: Torque and Speed Converters
Figure 17.1 Dual dry clutch (reproduced with permissions of Schaeffler)
Figure 17.2 Operating principle of a dual-clutch transmission
Figure 17.3 Dual-clutch transmission
Figure 17.4 Dual clutch transmission with two axial countershafts; first gear engaged (reproduced with permissions of Dr. Ing. h. c. F. Porsche AG)
Figure 17.5 Dual clutch transmission with two axial countershafts; second gear engaged (reproduced with permissions of Dr. Ing. h. c. F. Porsche AG)
Figure 17.6 Clutch disc with torsional damper and centrifugal pendulum absorber (reproduced with permissions of Schaeffler)
Figure 17.7 Operating principle of a clutch disc with multi-stage torsional damper
Figure 17.8 Dual-mass flywheel with centrifugal pendulum absorber (reproduced with permissions of Schaeffler)
Figure 17.9 Overview of passenger car transmissions
Figure 17.10 Two-stage countershaft transmission with five gears (the fifth gear with direct transmission)
Figure 17.11 Automatic transmission, 8 gears, first gear engaged
Figure 17.12 Trilok converter with centrifugal absorber and clutch (reproduced with permissions of Schaeffler)
Figure 17.13 Characteristic curve of a Trilok converter
Figure 17.14 One pulley and a part of chain of a CVT (reproduced with permissions of Schaeffler)
Figure 17.15 Operating principle of a CVT
Chapter 18: Shock Absorbers, Springs and Brakes
Figure 18.1 Monotube shock absorber
Figure 18.2 Monotube shock absorber: details of flow for compression (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.3 Monotube shock absorber: details of flow for rebound (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.4 Twin-tube shock absorber
Figure 18.5 Twin-tube shock absorber: details of flow for compression (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.6 Twin-tube shock absorber: details of flow for rebound (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.7 Proportional valve in a CDC (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.8 Ideal active body control (the actuator is repositioned by its forces)
Figure 18.9 Active vertical system of Mercedes S-Class (reproduced with permissions of Daimler AG)
Figure 18.10 Skyhook damper (adapted from Mitschke and Wallentowitz 2004)
Figure 18.11 CDC: Continous damping control (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.12 CDC shock absorber (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.13 Suspension springs
Figure 18.14 Functioning principle of an air spring
Figure 18.15 Functioning principle of an air spring with constant volume
Figure 18.16 Functioning principle of an air spring with constant mass of gas (hydropneumatic spring)
Figure 18.17 Air spring with an additional volume (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.18 Air spring without an additional volume (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.19 Air spring in a truck wheel suspension (reproduced with permissions of ZF Friedrichshafen AG)
Figure 18.20 Disc brake with a fixed caliper
Figure 18.21 Disc brake with a floating caliper
Figure 18.22 Brake circuit configurations
Figure 18.23 Brake circuit configurations
Chapter 19: Active Longitudinal and Lateral Systems
Figure 19.1 Components of an ABS
Figure 19.2 Topological principle of the first ABS from Bosch (1978) with one velocity sensor for the Cardan velocity
Figure 19.3 Hydraulic connections for the ABS (cf. Robert Bosch 2007)
Figure 19.4 Operating areas of ABS (adapted from Robert Bosch 2007)
Figure 19.5 Operating areas of ABS with slip angle (adapted from Robert Bosch 2007)
Figure 19.6 Control cycle of an ABS (adapted from Robert Bosch 2007; discontinuities are added in the time derivative of at the switching points of the valves, since a discontinuity in the time derivative of the braking pressure results in a discontinuity of : . At the point with the slip rate is smaller than zero, , the slip is greater than ; at the points with the braking moment and the moment from the tangential force are equal: )
Figure 19.7 Pressure build-up for split- without delayed pressure build-up
Figure 19.8 Delayed pressure build-up for a small vehicle
Figure 19.9 Delayed pressure build-up for a large vehicle
Figure 19.10 Components of an ESP system (adapted from Robert Bosch 2007)
Figure 19.11 Complete ESP hydraulics (cf. Robert Bosch 2007 or Bauser and Gawlik 2013)
Figure 19.12 Schematic diagram of active steering with planetary gear; variable steering ratio
Chapter 20: Multi-body Systems
Figure 20.13 McPherson front axle in an MBS model
Figure 20.1 Frames and coordinate systems
Figure 20.2 Two rigid bodies
Figure 20.3 Revolute joint
Figure 20.8 Cardanic joint
Figure 20.9 Definition of rotational matrices by axis systems
Figure 20.10 Explicit Euler method
Figure 20.11 Rocker arm valve drive (example from the MBS software ADAMS)
Figure 20.12 Rear-driven powertrain (example from the MBS software ADAMS)
Figure 20.14 Step steer result
Figure 20.15 Quasi-steady-state cornering (for small lateral acceleration with some initial oscillations)
Figure 20.16 Modes for the free interface method
List of Tables
Chapter 5: Driving Performance Diagrams, Fuel Consumption
Table 5.1 WLTP vehicle classes
Chapter 9: Ride Dynamics
Table 9.1 Typical values for uneven road parameters
Automotive Series
Series Editor: Thomas Kurfess
Vehicle Dynamics
Meywerk
May 2015
Vehicle Gearbox Noise and Vibration: Measurement, Signal Analysis, Signal Processing and Noise Reduction Measures
Tůma
April 2014
Modeling and Control of Engines and Drivelines
Eriksson and Nielsen
April 2014
Modelling, Simulation and Control of Two-Wheeled Vehicles
Tanelli, Corno and Savaresi
March 2014
Advanced Composite Materials for Automotive Applications: Structural Integrity and Crashworthiness
Elmarakbi
December 2013
Guide to Load Analysis for Durability in Vehicle Engineering and Speckert
Johannesson
November 2013
Vehicle Dynamics
Martin Meywerk
Helmut-Schmidt-University (University of the Federal Armed Forces Hamburg), Germany
This edition first published 2015
© 2015 John Wiley & Sons Ltd
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A catalogue record for this book is available from the British Library.
For my wife Annette and my children Sophia, Aljoscha, Indira and Felicia
Foreword
This book is an extract of lectures on vehicle dynamics and mechatronic systems in vehicles held at the Helmut-Schmidt-University, University of the Federal Armed Forces, Hamburg, Germany. The lectures have been held since 2002 (Vehicle Dynamics) and 2009 (Vehicle Mechatronics). The book is an introduction to the field of vehicle dynamics and most parts of the book should be comprehensible to undergraduate students with a knowledge of basic mathematics and engineering mechanics at the end of their Bachelor studies in mechanical engineering. However, some parts require advanced methods which are taught in graduate studies (Master programme in mechanical engineering).
I wish to thank Mrs Martina Gerds for converting the pictures to Corel Draw with LaTeX labels and for typing Chapter 9. My thanks go to Mr Darrel Fernandes, B.Sc., for the pre-translation of my German scripts. I especially wish to thank Mr Colin Hawkins for checking and correcting the final version of the book with respect to the English language. My scientific assistants, especially Dr Winfried Tomaske and Dipl.-Ing. Tobias Hellberg, I thank for proofreading, especially with regard to the technical aspects. Special thanks for assistance in preparing a number of Solid Works constructions for pictures of suspensions and transmissions as well for help in preparing some MATLAB diagrams go to Mr Hellberg. Last but not the least, my thanks go to my family, my wife, Dr Annette Nicolay, and my children, Sophia, Aljoscha, Indira and Felicia, for their patience and for giving me a lot of time to prepare this book.
Series Preface
The automobile is a critical element of any society, and the dynamic performance of the vehicle is a key aspect regarding its value proposition. Furthermore, vehicle dynamics have been studied for many years, and provide a plethora of opportunities for the instructor to teach her students a wide variety of concepts. Not only are these dynamics fundamental to the transportation sector, they are quite elegant in nature linking various aspects of kinematics, dynamics and physics, and form the basis of some of the most impressive machines that have ever been engineered.
Vehicle Dynamics is a comprehensive text of the dynamics, modeling and control of not only the entire vehicle system, but also key elements of the vehicle such as transmissions, and hybrid systems integration. The text provides a comprehensive overview of key classical elements of the vehicle, as well as modern twenty-first century concepts that have only recently been implemented on the most modern commercial vehicles. The topics covered in this text range from basic vehicle rigid body kinematics and wheel dynamic analysis, to advanced concepts in cruise control, hybrid powertrain design and analysis and multi-body systems. This text is part of the Automotive Series whose primary goal is to publish practical and topical books for researchers and practitioners in industry, and post-graduate/advanced undergraduates in automotive engineering. The series addresses new and emerging technologies in automotive engineering supporting the development of next generation transportation systems. The series covers a wide range of topics, including design, modelling and manufacturing, and it provides a source of relevant information that will be of interest and benefit to people working in the field of automotive engineering.
Vehicle Dynamics presents a number of different designs, analysis and implementation considerations related to automobiles including power requirements, converters, performance, fuel consumption and vehicle dynamic models. The text is written from a very pragmatic perspective, based on the author's extensive experience. The book is written such that it is useful for both undergraduate and post-graduate courses, and is also an excellent reference text for those practicing automotive systems design and engineering, in the field. The text spans a wide spectrum of concepts that are critical to the understanding of vehicle performance, making this book welcome addition to the Automotive Series.
Thomas Kurfess
October 2014
Preface
This books covers the main parts of vehicle dynamics, which is divided into three topics: longitudinal, vertical and lateral dynamics. It also explains some applications, especially those with a mechatronic background, and outlines some components.
Figure 1 provides an overview of the chapters of the book. The main parts (longitudinal, vertical and lateral) as well as applications and component chapters are grouped together. Many principal aspects of dynamics are explained by using simple mechanical models (e.g. quarter-vehicle model and single-track model). As the virtual development process with very complex multi-body systems (MBS) is used in the design of modern cars, this simulation technique is described very briefly in the last chapter. Although these MBS models are able to predict many details, the user of such models should understand the principles of how vehicles behave, and the main theory behind dynamic behaviour. It is therefore important to learn the basic dynamic behaviour using the simple models described in this book.
Figure 1 Chapters of the book
Chapter 1 contains some general data for vehicles. These remarks are followed by an introduction to some of the basics of frames and axis systems. This introduction should be read by everyone. Following this are the three groups of longitudinal, vertical and lateral dynamics, which are largely independent. The longitudinal and the vertical parts are completely independent of the other parts and may be read and understood without any knowledge of the other parts. The third group, containing the lateral dynamics part, includes a number of aspects that may be difficult to understand without first reading the longitudinal or the vertical part.
The application chapters can only partly be understood without reading the corresponding theory chapter. Readers are therefore recommended to start with the basic parts: the basics for Chapters 7 (Hybrid Powertrains), 8 (Adaptive Cruise Control) and 17 (Torque and Speed Converters) can be found in the longitudinal dynamics chapters, while lateral dynamics is important for Chapter 16 (Suspension Systems), in the case of Chapter 18 (Shock Absorbers, Springs and Brakes) a knowledge is required of vertical dynamics as well as some aspects of longitudinal and lateral dynamics. Chapter 19 (Active Longitudinal and Lateral Systems), as the name reveals, involves longitudinal and lateral aspects. Chapter 20 is nearly independent of the theoretical considerations.
Figure 1 includes the letters B and M, which stand for Bachelor and Master, behind every chapter. Chapters of level B should be comprehensible for undergraduate students with a knowledge of engineering mechanics and mathematics at the end of their Bachelor studies in mechanical engineering. Topics covered are: algebra; trigonometric functions; differential calculus; linear algebra; vectors; coordinate systems; force, torque, equilibrium; mass, centre of mass, moment of inertia; method of sections, friction, Newton's laws, Lagrange's equation. In chapters followed by level M, an advanced knowledge is useful, as is usually taught to graduate students: ordinary differential equations (ODE), stability of ODEs, Laplace transformation, Fourier transformation, stochastic description of uneven roads and spectral densities.
At the end of nearly each chapter, you will find some questions and exercises. These are for monitoring learning progress or for applying the material learned to some small problems. For this reason, the questions and tasks are arranged in classesaccording to Bloom's taxonomy of learning (cf. Figure 2).
Figure 2 Bloom's taxonomy of learning
The simplest class is Remembering, which means that you only have to remember the correct content (e.g. a definition or a formula). You should be able to answer the questions of the second class Understanding if you have understood the content. The tasks of the third class Application involve applying the content to some unknown problem. The remaining three classes Analysing, Evaluating and Creating are more suited to extended student works, such as Bachelor or Master theses, and are therefore rarely included in this book.
List of Abbreviations and Symbols
The tables on the following pages summarize the mathematical symbols and abbreviations used in this book. In most cases (but not in all), the indices used with the symbols indicate the following:
vehicle
body
wheel
tyre
:
,
,
Sometimes a symbol, which is needed only in a very local part of the book, could be used in another meaning than it is described in the following tabular, as well as sometimes the units can differ from those given in the tabular. Symbols that occur only in a small part of the book are not listed in the tabular.
Table 1 List of symbols
Symbol
Description
Units
Acceleration of the vehicle
m/s
Aerodynamic area
m
Tyre slip angle (or locally used angle)
rad
ABS
Anti-lock braking system
–
Clothoid parameter
m
ACC
Adaptive cruise control
–
Angle of inclination of the road
rad
Progression ratio of a transmission
1
,
Tyre slip angle (
front;
rear)
rad
Average tyre slip angle (
front;
rear)
rad
Inner tyre slip angle (
front;
rear)
rad
Outer tyre slip angle (
front;
rear)
rad
ASF
Active front steering
–
ASR
Anti-slip regulation
–
Vehicle sideslip angle
rad
Camber angle
rad
Cornering stiffness
N/rad
Mean cornering stiffness
N/rad
Aerodynamic drag coefficient
1
Aerodynamic lift coefficient (
front;
rear)
1
CPVA
Centrifugal pendulum vibration absorber
–
Aerodynamic crosswind coefficient
1
DAE
Differential algebraic equations
–
Toe-in
, toe-out
rad
Wheel load change at the inner wheel
;
(
front;
rear)
N
Wheel load change at the outer wheel
;
(
front;
rear)
N
Inertial reference frame
–
Efficiency of the differential
1
Efficiency of the engine
1
Mean efficiency of the engine
1
Efficiency of the
drivetrain (transmission and differential)
1
Mean efficiency of the drivetrain
(speed and torque converter, differential)
1
Efficiency of the
th gear of
the transmission
1
ESP
Electronic stability programme
–
Table 2 List of symbols
Symbol
Description
Units
Tyre reference frame
–
Vehicle reference frame
–
Eccentricity at the wheel
m
Eccentricity at the wheels of axle
(
front;
rear)
m
Wheel reference frame,
perpendicular to the road plane
–
Aerodynamic drag in the longitudinal
N
direction for simplified models in longitudinal dynamics
Aerodynamic drag force in the
-direction
N
for single track model and wheel load transfer
Aerodynamic drag force in the
-direction
N
Aerodynamic lift force in the
-direction
N
Basic demand of tractive force:
N
Frequency of the received signal
Hz
Gradient resistance
N
Combined gradient and inertial resistance
for
N
Ideal (demand) characteristic map of tractive force
N
Acceleration or inertial resistance
N
FMCW
Frequency modulated continuous wave
–
Rolling resistance coefficient
1
Frequency of the transmitted signal
Hz
Coefficients for
approximation (
)
1
Rolling resistance
N
Total tractive force demand:
N
Force supplied at the wheel from the powertrain for gear
N
Section force for tyre-road
N
Section force for tyre-road
N
(
front;
rear)
Section force (wheel load) (
front;
rear)
N
Wheel load aerodynamic portion (
front;
rear)
N
Wheel load static portion (
front;
rear)
N
Table 3 List of symbols
Symbol
Description
Units
Wheel load dynamic portion (
front;
rear)
N
Wheel or axle load in the
-direction
N
Gravitational acceleration
m/s
Weight of the axle
(
front;
rear)
N
Weight of body (sprung mass)
N
Distance: centre of mass
– road
m
Distance: centre of mass of the body – road
m
Distance: centre of mass
– road
m
HP
Pump
–
Distance: Centre of pressure
– road
m
for air flow in the
-direction
HSV
High-pressure selector valve
–
Transmission ratio of the differential (final drive)
1
Transmission ratio of the gearbox;
1
for a stepped transmission:
Total transmission ratio
1
Transmission ratio of gear
of the transmission,
1
Moment of inertia of the axle
kg m
Moment of inertia of gear, differential, Cardan shaft
kg m
Moment of inertia of engine, clutch
kg m
Moment of inertia of the vehicle with respect to the
-axis
kg m
Angle of rotation of the body of the vehicle
rad
Instantaneous curvature (
) of the vehicle path
1/m
Wavenumber of an uneven road
rad/m
Wheelbase; distance between front and rear axle
m
Distance in the
direction between front axle
centre of mass and centre of mass
of the vehicle
m
Distance in the
direction between rear axle
centre of mass and centre of mass
of the vehicle
m
Rotational mass factor
1
Eigenvalue with respect to time
1/s
Distance: centre of gravity
–
m
centre of pressure
in the
direction
Table 4 List of symbols
Symbol
Description
Units
Tyre longitudinal force coefficient
1
Aerodynamic moment
Nm
Coefficient of adhesion
1
Mass of the axle (
front;
rear)
kg
Section moment at the axle
Nm
(
front;
rear)
Mass of the body or sprung mass of the vehicle
kg
MBS
Multi-body systems
–
Centre of curvature
–
Instantaneous centre of rotation
–
Torque supplied from the engine
N
Full load moment of the engine
Nm
Input moment (e.g. at input of transmission or clutch)
Nm
Moment where the power of the engines
Nm
reaches a maximum
Torque loss from the engine
N
Maximum torque of the engine
Nm
Full load moment of the engine at
Nm
Full load moment of the engine at
Nm
Output moment (e.g. at input of transmission or clutch)
Nm
Coefficient of pure sliding
1
Total mass (sprung and unsprung mass)
kg
Torque supplied at the wheel from the powertrain
N
Total caster trail
m
Engine speed (revolutions)
rad/s
Input speed or revolutions (e.g. at input of transmission or clutch)
rev/s
Input speed (revolutions) of transmission at gear
rad/s
Kinematic caster trail
m
Maximum speed of the engine
rpm
Minimum speed of the engine
rpm
Output speed or revolutions (e.g. at input of transmission or clutch)
rev/s
Engine speed where the power of the engines
rpm
reaches a maximum
Maximum revolutions per minute of the wheel
rpm
Output speed (revolutions) of transmission at gear
rad/s
Table 5 List of symbols
Symbol
Description
Units
Tyre caster trail
m
Wheel speed (revolutions)
rad/s
Number of gears in a transmission
1
ODE
Ordinary differential equation
–
OEM
Original equipment manufacturer
–
Input angular velocities (e.g. at input of transmission or clutch)
rad/s
Output angular velocities (e.g. at input of transmission or clutch)
rad/s
Gradient (inclination) of a road
1
Yaw angle
rad
Roll angle
rad
Full load power of the engine
W = Nm/s
Power of aerodynamic drag force (
:
)
W = Nm/s
Angle of rotation of the axle
(
front;
rear)
rad
Pitch angle of the body
rad
Basic demand of power:
N
Angular velocity gear, differential, Cardan shaft
rad/s
Power supplied from the engine
W = Nm/s
Angular velocity engine, clutch
rad/s
Power of combined gradient and inertial resistance
W = Nm/s
Power of gradient resistance
W = Nm/s
Spectral density of the stochastic road surface irregularity
m
Coefficient of roughness
m
Total power demand:
N
Ideal (demand) characteristic map of power at the wheel
N
Input power (e.g. at input of transmission) in Chapter 4
W = Nm/s
Power of inertia forces in Chapter 3
W = Nm/s
Maximum power of the engine reaches a maximum
W = Nm/s
Output power (e.g. at input of transmission)
W = Nm/s
Power of rolling resistance (
:
)
W = Nm/s
Total power demand:
N
Rotational angle of the wheel w.r.t the
-axis
rad
Table 6 List of symbols
Symbol
Description
Units
Power supplied at the wheel from the powertrain for gear
W = Nm/s
Power at the wheel
W = Nm/s
Mass density of air
kg/m
Instantaneous radius of curvature of the vehicle path
Scrub radius: distance between the intersection
m
of the steering axis with road and the centre of the contact patch
Kingpin offset between the wheel centre and the steering axis
m
Dynamic rolling radius
m
Dynamic rolling radius (
front;
rear)
m
Static radius of a wheel
m
Static radius of the wheels of the axle
(
front;
rear)
m
Inclination angle of the steering axis; angle from the
direction to the projection of the steering axis on to the
-
-plane
rad
Slip at wheels of the axle
(
front;
rear)
1
Track of the axle
(
front;
rear)
m
Centre of mass of the vehicle (sprung and unsprung mass)
–
Centre of mass of a wheel
–
SOV
Switch over valve
–
Centre of pressure
–
Chapter 1Introduction
Automobiles have been used for over 100 years for the transportation of people and goods. Despite this long period, essential elements of an automobile have in principle remained the same, i.e. four wheels and an internal combustion engine with a torque converter drive. However, the technical details of an automobile have changed a great deal, and the complexity has increased substantially. This has partly gone hand in hand with general technical progress, on the one hand, and increasing customer demands, on the other. Legal requirements have also led to distinct changes in automobiles.
The importance of automobiles becomes evident when we look at the graphs in Figures 1.1–1.4. You should bear in mind that the abscissas of most graphs are partitioned logarithmically. The quantity, the distances travelled and the distances travelled per capita are at a very high level, or these values are increasing at a high rate. If we look at some European countries or the United States of America, we can recognize stagnation at a high level, whereas emerging economies exhibit high rates of growth. The need to develop new, economic and ecological vehicles is evident. In order to do this, engineers should be familiar with the basic properties of automobiles. As the automobile is something which moves and which not only moves forward at a constant velocity, but also dynamic behaviour depends on these basic properties. Consequently, the basic dynamic properties form the main topic of this book.
Figure 1.1 Passenger cars (and light trucks in US) per 1000 inhabitants (data from OECD 2014)
Figure 1.2 Road passenger km (million pkm) (data from OECD 2014)
Figure 1.3 Passenger km/capita (data from OECD 2014)
Figure 1.4 International Energy Agency (IEA) CO2 from fuel combustion (Mt) in Road Transport (data from OECD 2014)
The ecological aspect could be a dramatic limiting factor in the development of vehicles throughout the world. If the number of cars per 1000 inhabitants in China and Hong Kong grows from 22 in the year 2007 to 816, which is the number in the USA, then this represents a factor of 40. If we now multiply the CO2 emissions of the USA from the year 2007 by 40, we obtain around 57 000 Mt, which is 12 times the world CO emissions from fuel combustion in road transport for the year 2007. This seems to be very high (or perhaps too high), and vehicles with lower fuel consumption or hybrid or electric powertrains will have to be developed and improved in the coming decades.
The presentation of the most important buying criteria in Figure 1.5 highlights the ecological and economic aspects as well as safety, handling behaviour and comfort. The last three points, namely safety, handling behaviour and comfort, are strongly linked with the driving dynamics and suspension, making these aspects of particular importance in the automotive industry. Safety is generally subdivided into active safety (active safety systems help to avoid accidents) and passive safety (passive safety systems protect the occupants during an accident).
Figure 1.5 Importance of purchase criteria (Braess and Seiffert 2001)
It is evident that the dynamics of the vehicle is of crucial importance because of the impact on active safety; handling behaviour and comfort are also closely associated with the properties of vehicle dynamics. For this reason, particular emphasis is placed on the aspect of dynamics in this course.
The aim of this course is to define and identify the basic concepts and relationships that are necessary for understanding the dynamics of a motor vehicle.
The content of this textbook is limited to the essentials, and the course closely follows the monograph of Mitschke and Wallentowitz 2004 (German). Further recommended reading can be found in the bibliography at the end of this book, e.g. Heissing and Ersoy 2011, Dukkipati et al. 2008, Gillespie 1992, Jazar 2014, or Reimpell et al. 2001.
1.1 Introductory Remarks
The content of this book is divided into four parts: longitudinal dynamics, vertical dynamics, lateral dynamics and structural design of vehicle components and automotive mechatronic systems. Longitudinal dynamics is included in Chapters 2–7, which discuss the process of acceleration and braking. Key importance here is given to the total running resistance, the demand and supply of power and the driving state diagrams. In Chapters 7 and 8, additional systems of longitudinal dynamics are described: alternative powertrains and adaptive cruise control systems. In Chapters 9 and 10, the behaviour of the vehicle when driving on an uneven surface is explained in the context of vertical dynamics. These chapters study the basics of the theory of oscillations and the influence of vibrations on humans. Lateral dynamics, the contents of Chapters 11–15, describes the handling behaviour of a vehicle during cornering. Important concepts such as slip, oversteer and understeer, toe and camber angle are explained. It deals with the influence of wheel load on the handling behaviour.
Chapters 16–19 highlight the engineering design (structural) aspects of an automobile. In addition to speed and torque converters, they also discuss brakes and chassis elements of active safety systems, such as anti-lock braking system (ABS), anti-slip regulation (ASR) and electronic stability programme (ESP). In Chapter 20, multi-body systems (MBS) are explained. MBS are computational models which allow more precise calculations of the dynamic behaviour of vehicles.
