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Effect of tire camber on vehicle dynamic simulation for extreme cornering

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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.
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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
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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
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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=1exp φE1φ2E2
1+1
12 φ3(2)
φ=
Ky·Sy
μy0·Fz
(3)
Sy=−
tan α+sin γ·K
Ky(4)
μy=μys+y0μys)·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, Kthe camber
force stiffness, Kythe cornering stiffness. E1,Ky,K,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].
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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.
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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.
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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.
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44 X.-P. Lu et al.
Figure 7. Block diagram of UniTire 2.0.
Figure 8. Modelling results of TOM for camber =8.
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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.
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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.
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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.
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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.
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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.
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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.
Tyre and Vehicle Dynamics (Butterworth-Heinemann, an imprint of
  • H B Pacejka
Pacejka, H.B., 2002, Tyre and Vehicle Dynamics (Butterworth-Heinemann, an imprint of Elsevier Science).