Essentials of Vehicle Dynamics

1. Auflage 2014
ISBN: 978-0-08-100058-8
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 320 Seiten

Essentials of Vehicle Dynamics explains the essential mathematical basis of vehicle dynamics in a concise and clear way, providing engineers and students with the qualitative understanding of vehicle handling performance needed to underpin chassis-related research and development.Without a sound understanding of the mathematical tools and principles underlying the complex models in vehicle dynamics, engineers can end up with errors in their analyses and assumptions, leading to costly mistakes in design and virtual prototyping activities. Author Joop P. Pauwelussen looks to rectify this by drawing on his 15 years' experience of helping students and professionals understand the vehicle as a dynamic system. He begins as simply as possible before moving on to tackle models of increasing complexity, emphasizing the critical role played by tire-road contact and the different analysis tools required to consider non-linear dynamical systems.Providing a basic mathematical background that is ideal for students or those with practical experience who are struggling with the theory, Essentials of Vehicle Dynamics is also intended to help engineers from different disciplines, such as control and electronic engineering, move into the automotive sector or undertake multi-disciplinary vehicle dynamics work. - Focuses on the underlying mathematical fundamentals of vehicle dynamics, equipping engineers and students to grasp and apply more complex concepts with ease. - Written to help engineers avoid the costly errors in design and simulation brought about by incomplete understanding of modeling tools and approaches. - Includes exercises to help readers test their qualitative understanding and explain results in physical and vehicle dynamics terms.

Dr. Pauwelussen has 20 years' experience in vehicle dynamics and currently teaches vehicle technology with a special interest in tires and driver behavior. He worked as Research Manager for vehicle dynamics at TNO for 11 years prior to his current position, where he managed a number of high profile research projects. At HAN University of Applied Sciences, he established a professional master's automotive program covering structural mechanics, vehicle dynamics and vehicle control. With a background in mathematics and mechanics, his research and teaching are focused on balancing practical engineering with a thorough, mathematical treatment.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Front Cover;1
2;Essentials of Vehicle Dynamics;4
3;Copyright Page;5
4;Dedication;6
5;Contents;8
6;Preface;10
7;1 Introduction;12
8;2 Fundamentals of Tire Behavior;18
8.1;2.1 Tire Input and Output Quantities;22
8.2;2.2 Free Rolling Tire;26
8.3;2.3 Rolling Resistance;28
8.3.1;2.3.1 Braking/Driving Conditions;29
8.3.2;2.3.2 Parasitary Forces: Toe and Camber;30
8.3.3;2.3.3 Temperature;31
8.3.4;2.3.4 Forward Speed;32
8.3.5;2.3.5 Inflation Pressure;34
8.3.6;2.3.6 Truck Tires Versus Passenger Car Tires;35
8.3.7;2.3.7 Radial Versus Bias-Ply Tires;36
8.3.8;2.3.8 Other Effects;36
8.4;2.4 The Tire Under Braking and Driving Conditions;37
8.4.1;2.4.1 Braking Behavior Explained;37
8.4.2;2.4.2 Modeling Longitudinal Tire Behavior;41
8.5;2.5 The Tire Under Cornering Conditions;44
8.5.1;2.5.1 Cornering Behavior Explained;44
8.5.2;2.5.2 Modeling Lateral Tire Behavior;50
8.6;2.6 Combined Cornering and Braking/Driving;53
8.6.1;2.6.1 Combined Slip;53
8.6.2;2.6.2 Modeling Tire Behavior for Combined Slip;58
8.6.3;2.6.3 Approximations in case of Combined Slip;59
8.7;2.7 Physical Tire Models;61
8.7.1;2.7.1 The Brush Model;63
8.7.2;2.7.2 The Brush-String Model;73
9;3 Nonsteady-State Tire Behavior;86
9.1;3.1 Tire Transient Behavior;86
9.1.1;3.1.1 The Tire Transient Model;86
9.1.2;3.1.2 Applications of the Tire Transient Model;91
9.1.2.1;Shimmy of A Trailing Wheel;91
9.1.2.2;Single Wheel Vehicle Under Repetitive Braking;94
9.2;3.2 Dynamic Tire Response to Road Disturbances;98
9.2.1;3.2.1 Introduction to the Rigid Ring Tire Model;98
9.2.2;3.2.2 Enveloping Properties of Tires to Road Disturbances;101
9.2.3;3.2.3 Dynamic Response to Road Disturbances;108
10;4 Kinematic Steering;122
10.1;4.1 Axis Systems and Notations;122
10.2;4.2 Ackermann Steering;124
10.3;4.3 The Articulated Vehicle;129
11;5 Vehicle Handling Performance;134
11.1;5.1 Criteria for Good Handling;136
11.1.1;5.1.1 ISO 4138: Steady-State Circular Test;137
11.1.2;5.1.2 ISO 7401: Lateral Transient Response Test;138
11.2;5.2 Single-Track Vehicle Modeling;142
11.2.1;5.2.1 The Single-Track Model;142
11.2.1.1;Remarks Regarding Forces Acting on the Vehicle;145
11.2.2;5.2.2 Effect of Body Roll and Lateral Load Transfer;150
11.2.2.1;Contact Forces According to Genta and Morello;152
11.2.2.2;Contact Forces According to Kiencke and Nielsen;153
11.2.3;5.2.3 Alignment and Compliance Effects;154
11.2.4;5.2.4 Effect of Combined Slip;156
11.3;5.3 Steady-State Analysis;157
11.3.1;5.3.1 Steady-State Solutions;157
11.3.1.1;Remark;158
11.3.2;5.3.2 Understeer and Oversteer;159
11.3.2.1;Definition 1;160
11.3.2.2;Definition 2;160
11.3.2.3;Definition 3;160
11.3.2.4;Definition 4;161
11.3.3;5.3.3 Neutral Steer Point;165
11.4;5.4 Nonsteady-State Analysis;167
11.4.1;5.4.1 Yaw Stability;167
11.4.1.1;Ad (i);174
11.4.1.2;Ad (ii);174
11.4.1.3;Ad (iii);174
11.4.2;5.4.2 Frequency Response;177
11.5;5.5 Graphical Assessment Methods;179
11.5.1;5.5.1 Phase Plane Analysis;179
11.5.2;5.5.2 Stability Diagram;187
11.5.3;5.5.3 The Handling Diagram;190
11.5.4;5.5.4 The MMM Diagram;197
11.5.5;5.5.5 The g-g Diagram;201
12;6 The Vehicle–Driver Interface;206
12.1;6.1 Assessment of Vehicle–Driver Performance;209
12.1.1;The Inter-Beat-Interval;215
12.1.2;The Heart Rate Variability;215
12.1.3;Pupil Diameter and Endogenous Eye Blinks;215
12.1.4;Blood Pressure Variability;215
12.1.5;Skin Conduction Response;216
12.1.6;Facial Muscle Activity;216
12.2;6.2 The Vehicle–Driver Interface, A System Approach;217
12.2.1;6.2.1 Open-Loop and Closed-Loop Vehicle Behavior;217
12.2.2;6.2.2 The McRuer Crossover Model;222
12.3;6.3 Vehicle–Driver Longitudinal Performance;223
12.3.1;6.3.1 Following a Single Vehicle;225
12.3.2;6.3.2 Driver Model and Driver State Identification;228
12.4;6.4 Vehicle–Driver Handling Performance;228
12.4.1;6.4.1 Path-Tracking Driver Model;229
12.4.2;6.4.2 Closed-Loop Handling Stability;241
12.4.3;6.4.3 Driver Model and Driver State Identification;245
13;7 Exercises;250
13.1;7.1 Exercises for Chapter 2;250
13.1.1;Question 1;250
13.1.2;Question 2;252
13.1.3;Question 3;254
13.2;7.2 Exercises for Chapter 3;255
13.2.1;Question 1;255
13.2.2;Question 2;256
13.3;7.3 Exercises for Chapter 4;257
13.3.1;Question 1;257
13.4;7.4 Exercises for Chapter 5;258
13.4.1;Question 1;258
13.4.2;Question 2;261
13.4.3;Question 3;261
13.4.4;Question 4;264
13.5;7.5 Exercises for Chapter 6;265
13.5.1;Question 1;265
13.5.2;Question 2;266
14;Appendix 1: State Space Format;268
15;Appendix 2: System Dynamics;272
15.1;A2.1 General Approach in N Dimensions;272
15.1.1;A2.1.1 Definition: Stability;273
15.1.2;A2.1.2 Definition: Asymptotic Stability;273
15.2;A2.2 System Dynamics in Two Dimensions;274
15.2.1;A2.2.1 Concluding Remark;279
15.3;A2.3 Second-Order System in Standard Form;279
16;Appendix 3: Root Locus Plot;282
17;Appendix 4: Bode Diagram;286
18;Appendix 5: Lagrange Equations;294
19;Appendix 6: Vehicle Data;296
19.1;A6.1 Passenger Car Data;296
19.2;A6.2 Empirical Model Tire Data;298
20;Appendix 7: Empirical Magic Formula Tire Model;300
21;Appendix 8: The Power Spectral Density;302
22;List of Symbols;306
23;References;310
24;Index;314

Leseproben

Chapter Two

Fundamentals of Tire Behavior

Chapter 2 describes the steady-state behavior of the tire–road contact, with distinction of longitudinal slip behavior, cornering performance, and situations of combined slip. After a description of the tire input and output quantities, a discussion is given on the free rolling tire with emphasis on the effective rolling radius and the rubber deformation and local slip behavior in the tire–road contact area. This discussion is directly related to the tire rolling resistance, being discussed next. Different tire models are treated, specifically the empirical Magic Formula description (Pacejka model) for pure and combined slip conditions, and the physical brush model as well as the brush-string model.

Keywords

Effective rolling radius; rolling resistance; longitudinal slip; slip angle; friction coefficient; Magic Formula; brush model; brush-string model

In this chapter, attention is paid to the properties and resulting steady-state performance of tires as a vehicle component. With the tire as the prime contact between vehicle and road, the vehicle handling performance is directly related to the tire–road contact. The tires transfer the horizontal and vertical forces acting on the vehicle from steering, braking, and driving, under varying road conditions (slippery, road disturbances, etc.). Tire forces are not the only forces acting on the vehicle. Other forces acting on the vehicle could be from external disturbances (e.g., aerodynamic forces from crosswind). However, the contact between vehicle and road is by far the dominant factor in vehicle behavior and may be the difference between safe and unsafe conditions. Therefore, emphasis is put on the influence of tire properties in general and specifically in this chapter, which describes the tire steady-state behavior. Transient and dynamic tire performance will be discussed in Chapter 3.

The tire–road interface is schematically shown in Figure 2.1. The tire is a complex structure, consisting of different rubber compounds, combinations of rubberized fabric, or cords of various materials (steel, textile, etc.) that act as reinforcement elements (referred to as plies) that are embedded in the rubber with a certain orientation. The outer part of the tire is cut in a specific pattern (tread pattern design), referred to as the tire profile. The tire profile serves to guide the water away from the contact area under wet road conditions, and to adapt to the road surface in order to maintain a good contact (and therefore load transfer) between tire and road. Therefore, each tire has unique structural and geometrical design parameters. These parameters result in tire properties that, in combination with the vehicle, lead to vehicle performance. That means that the vehicle manufacturer will set up requirements for the tire manufacturer in terms of vehicle performance, which the tire manufacturer must fulfill. These requirements include many different things, such as:

• Good adherence between road and tire under all road conditions in longitudinal (braking/driving) and lateral (cornering) situations.

• Low energy dissipation (low rolling resistance).

• Low tire noise, which has two aspects—the effect observed inside of the vehicle and the noise emitted into the environment

• The effect observed inside the vehicle is directly related to the vibration transfer from tire, through vehicle’s suspension, toward the driver. This is a comfort issue for the driver.

• Noise emitted into the environment is undesirable from an environmental point of view.

• Good durability and therefore, good wear resistance

• Tire properties change with wear, which will in general lead to a higher tire stiffness in horizontal and vertical direction.

• Good comfort properties (filtering of road disturbances) and low interior noise transfer.

• Good subjective assessment, including predictability (consistency in response).

Figure 2.1 Tire–road interface.

Each tire parameter has an effect on each of the tire properties, which makes the task of the tire designer a difficult one. Ultimately, this results in a compromise between these properties. Tire manufacturers are faced with the task of judging tire properties in terms of vehicle performance, and therefore must be able to understand this performance in detail for modeling and testing. In turn, the tire manufacturer determines the requirements for the component and material suppliers, i.e., for the rubber compounds, the cord materials, etc. This covers the tire parameters, but there are further considerations.

First, road has a certain structure, porosity, roughness, and thermal properties, all of which can vary. In general, the top layer of the road might be resurfaced every 5–7 years, depending on the traffic use. This means a cycle of 5–7 years for road properties. In addition, the road surface conditions may change due to weather conditions, day/night conditions, the traffic, and other external conditions, such as nearby housing, bridges, and viaducts.

Finally, the tire–road interface changes with the vehicle’s motion. Changes in tire load will change the tire performance, which must be accounted for in the vehicle handling analysis. When the driver is cornering, the outer tires are loaded and the inner tires are unloaded. When the driver is braking or accelerating, the tire load shifts between the front and rear wheels. An increase in vehicle speed will in general lead to more critical adverse tire–road conditions. All these effects depend on the tire inner pressure.

We will take a closer look at the structure of the radial tire (Figure 2.2). The term “radial tire” refers to the radial plies, running from bead to bead, with the bead being the reinforced (with an embedded steel wire) part of the tire, connecting the tire to the rim. However, radial plies do not give the tire sufficient rigidity to fulfill the required performance under braking and cornering conditions. For that reason, the tire is surrounded by a belt with cords (steel, polyester, Kevlar, etc.) that are oriented close to the direction of travel.

Figure 2.2 Schematic layout tire structure.

The radial plies give good vertical flexibility and therefore, good ride comfort (in case of road irregularities). Cornering leads to distortion of the tire in the contact area, which evolves into deflection of rubber and extension of the cords in that area. With an almost parallel orientation of the cords in the belt, the extension of the cords is the dominant response, which means there is a large resistance (the modulus of elasticity of the cord material by far exceeds that of rubber) against this distortion and therefore, a stiff connection between vehicle and road. One could say that the different functions of the tire (i.e., having good comfort and, at the same time, good handling performance) are well covered by this distinction between radial and belt plies. The total combination of cords and plies that contributes to the tire rigidity is called the carcass.

The radial tire was patented by A.W. Savage in 1915 [43], but was not commercially successful until Michelin improved the design in the 1950s. Before that, cars were equipped with bias-ply (or cross-ply) tires with cords that run diagonally around the tire casing. For these tires, the cords have a much larger angle in relation to direction of travel (order of magnitude 40°) compared to the belt plies of a radial tire. In addition, no distinction is made between plies alongside wall and contact area. See Figure 2.3 for a schematic layout of the cross-ply and radial tire.

Figure 2.3 Schematic layout of cross-ply and radial tire.

The cord structures (the plies) extend from contact area to sidewalls, such that deformation of the sidewalls would lead to deflections in the contact area, which would have a negative effect on wear at the shoulder of the tire. Because of the structural differences between both tires, the tread motion is reduced for the radial tire compared to the cross-ply tire, which also contributes to better fuel economy (reduced rolling resistance, see also Section 2.3). It has been shown by Moore [29] that bias-ply tires show significantly higher concentrations of shear stress, as well as normal contact pressure, at the shoulders of the tire, compared to radial tires.

The main contact between tire and road is through the tread area. Figure 2.2 indicates a tread pattern that is shaped to channel water away, with straight and s-shaped grooves that move from center of the tire to the side. We also indicated very small cuts in the pattern, referred to as sipes. These sipes are typical for winter tires and allow small motion between tread elements for rolling tires, leading to effectively larger friction on icy and snowy surfaces.

In the next section, we begin with a description of the input and output quantities of a tire. Determining what forces and moments are acting on a tire, and what input variables (such as slip, camber, and speed) these forces and moments depend on defines our language to define tire characteristics. In Section 2.2, we discuss the free rolling tire. Sections 2.3 addresses rolling resistance, with reference to all varying circumstances that can affect it. One...