ArticlePDF Available

Effect of tire camber on vehicle dynamic simulation for extreme cornering

DOI:10.1080/00423110600867309
Authors:
Xiao-Pei Lu
Xiao-Pei Lu
Xiao-Pei Lu
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Konghui Guo
Konghui Guo
Konghui Guo
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Dang Lu at Jilin University
Dang Lu
Yin-Lin Wang
Yin-Lin Wang
Yin-Lin Wang
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Download full-text PDF
Read full-text
Download citation

Abstract and Figures

Vehicle behaviors under extreme cornering are complex events that might result in rollover accidents. Simulations have been extensively used in the auto industry to protect vehicles from such accidents. Predictive capability of simulation relies on how accurate the math-based model represents the vehicle and its operating condition. Camber effects of tire are studied in this paper to promote the accuracy of simulation. First, a tire model with simplified camber effect is introduced, and the comparison between the model results and test data is shown. Then, a more precise model that includes camber effects on cornering stiffness are friction coefficient is presented. The comparison between these model results and test data is also given. In addition, the camber effects on tire overturning moment and loaded radius are studied. Finally, vehicle fishhook simulation with different tire models is conducted to further investigate the effect of tire camber on vehicle dynamics.
Figures - uploaded by Dang Lu
Author content
All figure content in this area was uploaded by Dang Lu
Content may be subject to copyright.
Content uploaded by Dang Lu
Author content
All content in this area was uploaded by Dang Lu on Jun 25, 2015
Content may be subject to copyright.
This article was downloaded by:[Lu, Dang]
[Lu, Dang]
On: 19 May 2007
Access Details: [subscription number 776525917]
Publisher: Taylor & Francis
Informa Ltd Registered in England and Wales Registered Number: 1072954
Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Vehicle System Dynamics
International Journal of Vehicle Mechanics and
Mobility
Publication details, including instructions for authors and subscription information:
http://www.informaworld.com/smpp/title~content=t713659010
Effect of tire camber on vehicle dynamic simulation for
extreme cornering
To cite this Article: Lu, Xiao-Pei, Guo, Konghui, Lu, Dang and Wang, Yin-Lin ,
'Effect of tire camber on vehicle dynamic simulation for extreme cornering', Vehicle
System Dynamics, 44:1, 39 - 49
To link to this article: DOI: 10.1080/00423110600867309
URL: http://dx.doi.org/10.1080/00423110600867309
PLEASE SCROLL DOWN FOR ARTICLE
Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf
This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction,
re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly
forbidden.
The publisher does not give any warranty express or implied or make any representation that the contents will be
complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be
independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings,
demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or
arising out of the use of this material.
© Taylor and Francis 2007
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
Vehicle System Dynamics
Vol. 44, Supplement, 2006, 39–49
Effect of tire camber on vehicle dynamic simulation for
extreme cornering
XIAO-PEI LU†, KONGHUI GUO‡, DANG LU*‡ and YIN-LIN WANG‡
†General Motors Corporation, USA
‡Jilin University, P.R. China
Vehicle behaviors under extreme cornering are complex events that might result in rollover accidents.
Simulations have been extensively used in the auto industry to protect vehicles from such accidents.
Predictive capability of simulation relies on how accurate the math-based model represents the vehicle
and its operating condition. Camber effects of tire are studied in this paper to promote the accuracy of
simulation. First, a tire model with simplified camber effect is introduced, and the comparison between
the model results and test data is shown. Then, a more precise model that includes camber effects on
cornering stiffness are friction coefficient is presented. The comparison between these model results
and test data is also given. In addition, the camber effects on tire overturning moment and loaded
radius are studied. Finally, vehicle fishhook simulation with different tire models is conducted to
further investigate the effect of tire camber on vehicle dynamics.
Keywords: Vehicle dynamics; Tire model; Camber effect; Rollover; Simulation
1. Description of tire test
Tire tests for P235/60R17 were conducted and the operating conditions and specifics include:
•pressure: 262 kPa;
•rim width: 7 in;
•test speed: 40 kph;
•slip angle (in degrees): sweep −25 to −25;
•camber angle (in degrees): 0, ±2, ±4, ±6, ±8, ±10, ±12;
•normal loads (in kN): 1.6, 4.9, 8.2, 11.5, 14.8,18.1, 21.4, 24.8.
Forces (Fx,Fy,Fz), moments (Mx,My,Mz) and loaded radius (Rl) were measured as average
values at steady state.
*Corresponding author. Email: lu_dang@vip.sohu.com
Vehicle System Dynamics
ISSN 0042-3114 print/ISSN 1744-5159 online © 2006 Taylor & Francis
http://www.tandf.co.uk/journals
DOI: 10.1080/00423110600867309
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
40 X.-P. Lu et al.
2. Camber effect on tire lateral force
In this paper, UniTire model, developed by Prof. Konghui Guo of Jilin University, is used to
model the lateral force [1, 2]. The outline of the UniTire model for lateral slip combined with
camber properties includes the following equations:
Fy=sgn(Sy)·¯
F·μy·Fz(1)
¯
F=1−exp −φ−E1φ2−E2
1+1
12 φ3(2)
φ=
Ky·Sy
μy0·Fz
(3)
Sy=−
tan α+sin γ·Kyγ
Ky(4)
μy=μys+(μy0−μys)·exp −μ2
yh·log2
Vsy
Vsym
+exp −
Vsy
Vsym
 (5)
Vsy=V·cos(α) ·Sy(6)
In these equations, α,γand Fzare input quantities, αthe slip angle, γthe camber angle
and Fzthe vertical load. Fyis the tire lateral force, μythe dynamic lateral friction coefficient
determined by lateral slip velocity Vsy,μy0the tire static friction coefficient at Vsy=0 and
μys the tire slip friction coefficient at Vsy=∞.¯
Fis the non-dimensional lateral force, φthe
normalized slip ratio, Sythe slip ratio due to slip angle and camber angle, Kyγ the camber
force stiffness, Kythe cornering stiffness. E1,Ky,Kyγ,μy0,μys,μyhand Vsym are the UniTire
model parameters, which can be expressed by certain fitting functions of vertical load and/or
camber angle.
2.1 UniTire model with simplified camber effect
In most cases, camber slip is simply considered as an equivalent lateral slip input of tire
model, and the camber effect on cornering stiffness and friction coefficient is neglected. The
comparisons between simulation results of this simple model and test data are shown in
figures 1 and 2. It was observed that the simplified tire model gives obviously larger predictive
lateral forces under high vertical load.
2.2 UniTire model of camber effect
Considering camber effect on cornering stiffness and friction coefficient, the new version of
UniTire–UniTire 2.0 is presented [1,2]. The comparisons between model results and test data
are shown in figures 3–6. It can be seen that the simulation results of UniTire 2.0 have a better
agreement with the test data.
3. Camber effect on tire overturning moment and loaded radius
Tire overturning moment is also important in the investigation of vehicle rollover [3]. In
addition, the difference in the loaded radius of left and right tires yields tire roll angle, which
also affects the vehicle roll behaviors [4].
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
Effect of tire camber on vehicle dynamic simulation 41
Figure 1. Comparison of simple model with test for camber =−12◦.
Figure 2. Comparison of simple model with test for camber =−10◦.
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
42 X.-P. Lu et al.
Figure 3. Comparison of UniTire 2.0 with test for camber =−12◦.
Figure 4. Comparison of UniTire 2.0 with test for camber =−10◦.
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
Effect of tire camber on vehicle dynamic simulation 43
Figure 5. Comparison of UniTire 2.0 with test for camber =0◦.
Figure 6. Comparison of UniTire 2.0 with test for camber =8◦.
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
44 X.-P. Lu et al.
Figure 7. Block diagram of UniTire 2.0.
Figure 8. Modelling results of TOM for camber =8◦.
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
Effect of tire camber on vehicle dynamic simulation 45
Figure 9. Modelling results of loaded radius for camber =8◦.
Tire camber angle has great influence as well on overturning moment and loaded radius,
and this camber effect has been considered in UniTire 2.0 [5,6], as shown in figure 7; figures 8
and 9 show the comparisons between simulation results and test data.
4. Camber effect on vehicle fishhook simulation
In order to investigate the effect of tire camber on vehicle dynamics, vehicle fishhook simu-
lation with different tire models is conducted. A vehicle model of an SUV with independent
front suspension and the rear suspension of solid axle is built in CarSim®, shown in figures 10
and 11. The open-loop steer control is shown in figure 12, with vehicle speed maintained
constant.
Figure 10. Vehicle configuration.
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
46 X.-P. Lu et al.
Figure 11. Input screen of external tire model.
Figure 12. Input angle of steering wheel.
Figure 13. Fishhook simulation.
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
Effect of tire camber on vehicle dynamic simulation 47
Figure 14. Comparison of roll angle.
Through external.c file, the external tire model can be embedded in CarSim’s solver. When
the vehicle roll angle reaches 87◦, the simulation is stopped. Figure 13 shows the simulation
results, and the comparisons of vehicle behaviors between UniTire 2.0, simple model and
UniTire without Mxare shown in figures 14–17.
From the simulation results, it can be observed that the tire model has great effect on
vehicle behavior and the simplified tire model gives overpredictive results for the occur-
rence of rollover; the tire overturning moment needs to be considered for an accurate vehicle
simulation.
Figure 15. Comparison of roll rate.
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
48 X.-P. Lu et al.
Figure 16. Comparison of lateral acceleration for rollover.
Figure 17. Comparison of trajectory.
5. Conclusions
1. Tire camber not only has a strong effect on the tire lateral force as an additional equivalent
lateral slip ratio but also leads to significant variation in the structural parameters of friction
coefficient and cornering stiffness.
2. If camber effects on Kyand μyare not accounted properly in tire force generation, the
resulting force from calculation will be too large in simulation of vehicle rollover. This
might explain why the existing vehicle simulation often overpredicts the occurrence of
rollover.
Downloaded By: [Lu, Dang] At: 04:23 19 May 2007
Effect of tire camber on vehicle dynamic simulation 49
3. Modeling of tire overturning moment, especially under large camber, would improve the
accuracy of the simulation.
4. The accuracy of tire model has a significant impact on the simulation result of vehicle for
extreme cornering maneuvers.
References
[1] Guo, K., Lu, D. and Ren, L., 2001, A unified non-steady non-linear tyre model under complex wheel motion
inputs including extreme operating conditions. JSAE Review,22(4), 395–402.
[2] Guo, K., Lu, D., Chen, S., Lin, W.C. and Lu, X.-P., 2004, UniTire Model–non-linear and non-steady tire model
for vehicle dynamic simulation. 3rd International Tyre Colloquium, Vienna,Austria, 29–31 August.
[3] Pacejka, H.B., 2002, Tyre and Vehicle Dynamics (Butterworth-Heinemann, an imprint of Elsevier Science).
[4] Gim, G. and Choi,Y., 2001, Role of tire modeling on the design process of a tire and vehicle system. ITECASIA
2001, Busan, Korea, 18–20 September.
[5] Lu, D., Guo, K., 2004, Experimental and theoretical study on tire overturning moment property (in Chinese).
China Mechanical Engineering,15(15), 1317–1319.
[6] Lu, D., Guo, K., Wu, H., Chen, S. and Lu, X-P., 2005, Modelling of tire overturning moment and loaded radius.
19th IAVSD Symposium, Milano, Italy, August.
... The double track model is an 8 Degrees Of Freedom model (DOF) [25], which describes the motion of the chassis with respect to the unsprung masses as the rotation about a fixed roll axis. This motion is completed by the dynamics associated to the wheel rotation, and a detailed tire model [17] that also considers the camber effect for a better prediction of the handling properties [14]. In Section V we use the double track model to test the effectiveness of the kinematic observer proposed in Section IV. ...
... Theorem 1. Consider the observer (14). Assume that the following LMI in the optimization variables 0 < P = P ∈ R 2×2 , γ ∈ R ≥0 , λ, µ ∈ R >0 is feasible: ...
... The proof is carried out in two steps. First we show that (16) implies GAS of the origin for (14) as long as r ∈ [ , ∞). Second, we show that the GAS property holds also when r ∈ (−∞, − ]. ...
View
... Thus, most suitable combination of the integral geometry of the steering system for different camber angle and toe angle is analyzed and will be optimized to get better handling and stability of vehicle during cornering conditions. Pei Lu [3] investigated the effect of tire camber angle on vehicle dynamics in terms of lateral force; for extreme cornering conditions the effect of camber angle was studied with the Uni-Tire model by Guo et al. [4]. In some case yaw dynamics was not taken under consideration [5] similar study was carried out later to find that yaw rate response is also an important function of camber variation for front and rear wheels [6]. ...
To Study the Influence of Variation in Camber and Toe on Handling of Passenger Vehicle during Cornering
Conference Paper
  • Jan 2019
Study of Vehicle dynamics has always been the essential area for automotive industries. The vehicle perfor-mance, handling and ride comfort are realized because of at most care and the effort that has gone into design and assembly of components and subsystems. Steering and suspen-sion system takes its due importance as it provides the driver not only to give the necessary input for the vehicle motion but also for its directional control and stability. Hence, this subsystem needs to be optimized in order to obtain good handling and ride control of the vehicle. The wheel alignment is the key requirement for the vehicle that depends on steering axis inclination, scrub radius, camber, castor and toe angles, out of which toe and camber are easily adjustable time to time. For frequent cornering events these parameters can’t remain same. Camber plays important role in deciding cornering force during maneuver, on straight roads it doesn’t affect much but on frequent cornering event it must be adjusted such that it should give good handling characteristics. Multi-body dynamic model of a sedan car is built in ADAMS Car software with different subsystems. This assembly of car is simulated for different recognized handling tests like, constant speed cornering, acceleration during cornering and braking during cornering. Thus, it is understood that the dynamic behavior of a passenger car is influenced by these design parameters of steering and suspension geometry. The present work predicts, the most suitable combination of the integral geometry of the steering system for different camber angle and toe angle and their optimized values to give the better handling and stability for the vehicle during different cornering conditions.
View
... On the contrary, two wheeled vehicles (i.e. bikes and motorcycles) take benefit from the tilting angle to compensate for the fictitious inertial force effects when cornering, improving the stability and performance. The lateral force is not only generated by the side slip angle, but is also induced by the camber effect (Lu et. al, 2006). The latter outcome is generated by the dynamic change of the camber angle to ensure maximum contact of the tyre with the road surface during cornering. ...
Modelling and Simulations of a Narrow Track Tilting Vehicle
Article
Full-text available
  • Oct 2016
Narrow track tilting vehicle is a new category of vehicle that combines the dynamical abilities of a passenger car with a motorcycle. In the presence of overturning moments during cornering, an accurate assessment of the lateral dynamics plays an important role to improve their stability and handling. In order to stabilise or control the narrow tilting vehicle, the demand tilt angle can be calculated from the vehicle’s lateral acceleration and controlled by either steering input of the vehicle or using additional titling actuator to reach this desired angle. The aim of this article is to present a new approach for developing the lateral dynamics model of a narrow track tilting vehicle. First, this approach utilises the well-known geometry ‘bicycle model’ and parameter estimation methods. Second, by using a tuning method, the unknown and uncertainties are taken into account and regulated through an optimisation procedure to minimise the model biases in order to improve the modelling accuracy. Therefore, the optimised model can be used as a platform to develop the vehicle control strategy. Numerical simulations have been performed in a comparison with the experimental data to validate the model accuracy.
View
... By varying these parameters in an adaptive manner, the dynamic characteristics of the vehicle can be varied on a real-time basis. Among all these parameters, camber angle is one of the several attributes for a suspended wheel which maximizes lateral grip (Lu et al., 2006). Camber is the angle between the top and bottom of the tire and true vertical as viewed from the front side. ...
Active Camber and Toe Control Strategy for the Double Wishbone Suspension System
Article
  • Jan 2018
The present research work proposes a method for improving handling characteristics of the vehicle by controlling camber and toe angle using double wishbone suspension arms in an adaptive manner. This is accomplished by two telescopic arms with actuators which changes camber and toe angle of the wheel dynamically to deliver best possible traction and manoeuvrability. Active suspension controllers are employed to trigger the actuators based on the camber and toe angle from sensors for reducing the existing error. Hence the arms are driven by the actuators in a closed loop feedback manner with help of a separate PID controller. A quarter car physical models with double wishbone suspension is modelled in SolidWorks and simulated using MATLAB for analysis. The simulation result shows an improvement of 58% in camber and 96% improvement of toe characteristics. A prototype of the proposed system is developed and subjected to the same test as the simulation system. The prototype achieved an improvement of 46.34% in camber and a 93.35% in the toe variation of the active system over the passive system. Further, the prototype was able to achieve 89% of camber reduction and 45% of toe reduction with respect to the simulation.
View
... In conventional cars, the side slip is the main source of the cornering force and the camber is usually set as a fixed value. In recent years, however, the topic of camber control with a focus on directly varying camber has been well-researched to take advantage of the camber contribution in generating the cornering force (Horiguchi et al., 2013;Kuwayama et al., 2007;Laws, 2010;Lu et al., 2006;Nemeth and Gaspar, 2013;Park and Sohn, 2012;Koensgen et al., 2013). The researches show that camber control can improve vehicle stability, safety, and manoeuvrability. ...
Kinematics of a steering tyre with adjustable caster
Article
  • Jan 2017
This paper presents the kinematics of a steerable tyre with a variable caster. It serves as a first step towards developing the theory of variable caster steering in which wheel camber is controlled by the variable caster. The homogeneous transformation was utilised as a tool to develop the kinematics. The wheel camber, extracted from the kinematics, was expressed as a function of steering angle and suspension parameters in general case. The movement of the ground-contact point along the tyre perimeter was also taken into account. The kinematics was developed without small-angle-approximation. Therefore, the kinematic model is applicable to the case of the variable caster. A practical mechanism for the variable caster was also suggested to introduce the idea of the task. The required kinematics of such suspensions is derived from the general case to provide a visual understanding. The kinematics was then validated by a multi-body model built in ADAMS software.
View
Feasibility and performance analyses for an active geometry control suspension system for over-actuated vehicles
Article
To build an over-actuated vehicle, the chosen equipment is composed of an active four-wheel drive and steering systems, a torque vectoring system, and an active braking system. In general, the goal of the over-actuated vehicle is to improve stability and handling performance for both conventional and autonomous vehicles. This paper presents an active geometry control suspension system (AGVS), based on a 3-DOF parallel mechanism, which is capable of acting simultaneously on the camber, the rear-wheel steering and the body roll angles. The aim of this study is to analyse the performance and feasibility of this active suspension mechanism when assembled in a C-class vehicle. These analyses were developed through a co-simulation scheme implemented in CarSim and Simulink software for three different manoeuvres: steady-state cornering, fishhook and double lane change. The performance analysis provides a comparison of the same C-class vehicle equipped with different systems, from the original to the fully actuated one. The conducted simulations reveal how superior a multi-purpose control system is when compared to the other single-actuated systems, and how it can manage the necessary trade-off among the selected metrics, namely, the roll gradient, the understeer gradient, the yaw rate, the body roll angle, and the lateral acceleration. In the feasibility analysis of AVGS the demanded actuator power and force in typical manoeuvres was assessed. In addition, the required ranges for the camber and rear-wheel steering actuations, as well as for the mechanism joints, were determined. The vehicle equipped with AGVS demonstrates improvements of dynamic behaviour in both steady-state and transient manoeuvres.
View
View
View
Tire Carcass Camber and its Application for Overturning Moment Modeling
Article
  • Apr 2013
The properties of contact patch are key factors for tire modeling. Researchers have paid more attention to the contact patch shape and vertical pressure distribution. Some innovative concepts, such as Local Carcass Camber, have been presented to explain special tire modeling phenomena. For a pragmatic tire model, a concise model structure and fewer parameters are considered as the primary tasks for the modeling. Many empirical tire models, such as the well-known Magic Formula model, would become more complex to achieve satisfactory modeling accuracy, due to increasing number of input variables, so the semi-empirical or semi-physical modeling method becomes more attractive. In this paper, the concept of Tire Carcass Camber is introduced first. Different from Local Carcass Camber, Tire Carcass Camber is an imaginary camber angle caused only by lateral force on the unloaded tire. Similar to tire camber, Tire Carcass Camber is assumed to have the same effect on the properties of contact patch and also on tire mechanics. Thus in tire modeling, the camber effect can be expressed as the function of the total camber, which is the sum of tire camber and Tire Carcass Camber. In order to demonstrate the rationality of Tire Carcass Camber concept, the improved semi-physical model of tire overturning moment is presented, and the modeling accuracy is compared with the original model. The comparison shows that the concept of Tire Carcass Camber improves modeling accuracy. Finally, through the comparisons of tire overturning moment between an empirical model and the improved semi-physical model, it can be seen that semi-physical modeling method gets higher modeling accuracy with the same number of model parameters.
View
Simulation Analysis of the Effect of Tire and Suspension Non-Linearities on the Handling Response of Rigid and Articulated Vehicles
Article
  • Jun 2011
This paper presents a simulation based analysis of the effect of various non-linearities on vehicle handling of rigid and articulated vehicles. First a description of a non-linear vehicle model is presented and non-linearities, including tires, suspension elasto-kinematics, springing and damping are discussed. Later sections present the simulations results for the effects of each non-linearity. Simulation analyses are carried out for the case of step steering maneuvers, which permit to deduce the overall vehicle model response variation in steady-state and dynamic conditions.
View
Role of Tire Modeling on the Design Process of a Tire and Vehicle System
Conference Paper
Full-text available
  • Sep 2001
In order to make the final judgement on the design of a vehicle system regarding on the evaluation of handling performance, subjective assessment is currently the only criteria. For the purpose of virtual subjective tests through computer simulation, the adequate models of a vehicle, a tire, a driver, and a proving ground are necessary. A tire model represented only with its forces and moments generated between a tire and road surface is not good enough to express a driver's subjective perception on tire motion during cornering maneuver. In order to improve human perception, in this study, pneumatic trail, lateral deformation and loaded radius are introduced in addition to lateral force and moments. Formulations presented here are for transient cornering maneuver as well as steady-state condition.
View
The UniTire model: A nonlinear and non-steady-state tyre model for vehicle dynamics simulation
Article
Full-text available
  • Jan 2005
The UniTire model is a nonlinear and non-steady-state tyre model for vehicle dynamics simulation and control under complex wheel motion inputs involving large lateral slip, longitudinal slip, turn slip and camber. The model is now installed in the driving simulator in the Automobile Dynamic Simulation Laboratory at Jilin University for studying vehicle dynamics and their control systems. Firstly, the nonlinear semiphysical steady-state tyre model, which complies with analytical boundary conditions up to the third order of the simplified physical model, is presented. Special attention has been paid to the expression for the dynamic friction coefficient between the tyre and the road surface and to the modification of the direction of the resultant force under combined-slip conditions. Based on the analytical non-steady-state tyre model, the effective slip ratios and quasi-steady-state concept are introduced to represent the non-steady-state nonlinear dynamic tyre properties in transient and large-slip-ratio cases. Non-steady-state tyre models of first-order approximation and of high-order approximation are developed on the basis of contact stress propagation processes. The UniTire model has been verified by different pure and combined test data and its simulation covered various complex wheel motion inputs, such as large lateral slip, longitudinal slip, turn slip and camber.
View
Modelling of tire overturning moment and loaded radius
Article
Full-text available
For evaluation of vehicle handling, subjective assessment is currently almost the only criterion. For the purpose of reducing cycle time and avoiding error of subjective assessment, the close-loop objective evaluation system through computer simulations has become an inevitable choice [Gwanghun, G.I.M. and Yongchul, C.H.O.I., 2001, Role of tire modeling on the design process of a tire and vehicle system. ITEC ASIA 2001, Busan, Korea, September 18–20; Guo, K., Ding, H., Zhang, J., Lu, J. and Wang, R., 2003, Development of longitudinal and lateral driver model for autonomous vehicle control. International Journal of Vehicle Design, 36(1), 50–65]. For this reason, the more accurate models of vehicle, tire and driver are necessary. Since structure and operating conditions of tires are very complicated, many researchers have paid more attention to the modeling of tire properties and varieties of tire model have been done to describe the tire behaviour of longitudinal, lateral forces and aligning moment [Pacejka, H.B., 2002, Tyre and Vehicle Dynamics. Butterworth-Heinemann, an imprint of Elsevier Science, ISBN 0-7506-5141-5]. However, there are few studies for the tire overturning moment (TOM), especially under large slip angle and camber angle. For the simulation of vehicle rollover, the expression accuracy of TOM is rather important. In addition, the difference of the loaded radius of left and right tires yields tire roll angle and that also affects vehicle roll behavior. In this paper, the modeling of TOM and loaded radius are presented first, and then the modeling results are compared with tire test data.
View
View
A unified non-steady non-linear tyre model under complex wheel motion inputs including extreme operating conditions
Article
  • Oct 2001
This study is to describe the transient force and moment characteristics of tyres involving large lateral slip, longitudinal slip, turn-slip and camber, and to develop a dynamic tyre model applicable to vehicle dynamic simulation and control for extreme operating conditions. Based on the steady state USES tire model [4,6], the effective slip ratios and quasi-steady concept are introduced to represent the non-linear dynamic tire properties in large slip cases. A high-order non-steady tyre model is presented. Special attention has been paid on the relationship between turn-slip and camber. Various kinds of experiments are performed to verify the tire model.
View
Tyre and Vehicle Dynamics (Butterworth-Heinemann, an imprint of
  • Jan 2002
  • H B Pacejka
Pacejka, H.B., 2002, Tyre and Vehicle Dynamics (Butterworth-Heinemann, an imprint of Elsevier Science).