International Journal of Automotive Technology

, Volume 19, Issue 1, pp 63–75 | Cite as

Tire wear estimation based on nonlinear lateral dynamic of multi-axle steering vehicle

Article

Abstract

This paper presents a novel nonlinear dynamic model of a multi-axle steering vehicle to estimate the lateral wear amount of tires. Firstly, a 3DOF nonlinear vehicle dynamic model is developed, including dynamic models of the hydropneumatic suspension, tire, steering system and toe angle. The tire lateral wear model is then built and integrated into the developed vehicle model. Based on the comparison of experimental and simulation results, the nonlinear model is proved to be better than a linear model for the tire wear calculation. In addition, the effects of different initial toe angles on tire wear are analyzed. As simulation results shown, the impact of the dynamic toe angle on the tire wear is significant. The tire wear amount will be much larger than that caused by normal wear if the initial toe angle increases to 1° - 1.5°. The results also suggest that the proposed nonlinear model is of great importance in the design and optimazation of vehicle parameters in order to reduce the tire wear.

Keywords

Tire wear Multi-axle steering vehicle Nonlinear model Lateral dynamic Toe angle 

Nomenclature

mb

vehicle body mass

mi

vehicle unsprung mass of ith axle

I11

moment of vehicle body inertia about X-axis

I33

moment of vehicle body inertia about Z-axis

I13

product of vehicle body inertia about XZ plane

Izzi

moment of inertia about Z-axis (unsprung mass of ith axle)

Xi

signed distance from i th axle to CG (the center of gravity)

hb

distance from roll center to sprung CG

hao

height of the roll center

hai

height of the roll center at ith axle

Δ

distance from mass center to steering center

Bw

vehicle wheelspan

BK

distance around two springs of the same axle

BC

distance around two dampers of the same axle

R0

free radius of the tire

RiL

load radius of the left tire of ith axle

RiR

load radius of the right tire of ith axle

kz

vertical stiffness of the tire

Ki

cornering stiffness of ith axle tire

Fs

force of the hydro-pneumatic spring

ks

stiffness of the hydro-pneumatic spring

Ceq

equivalent damping of the hydro-pneumatic spring

Kφ

vehicle body roll stiffness

Cφ

vehicle body roll damping

KiL

stiffness of the left hydro-pneumatic spring of ith axle

KiR

stiffness of the right hydro-pneumatic spring of ith axle

CiL

damping of the left hydro-pneumatic spring of ith axle

CiR

damping of the right hydro-pneumatic spring of ith axle

Ei

wheel roll steer angle per unit roll angle

u

vehicle longtitude velocity

δi

steering angle of ith axle

δiL

steering angle of left tire of ith axle

δiR

steering angle of right tire of ith axle

αi

sideslip angle of ith axle

αiL

sideslip angle of left tire of ith axle

αiR

sideslip angle of right tire of ith axle

γiL

toe angle of left tire of ith axle

γiR

toe angle of right tire of ith axle

v

vehicle lateral velocity

ψ

vehicle yaw angle

r

vehicle yaw rate

φ

vehicle roll angle

β

sideslip angle of CG

vi

lateral velocity of ith axle

ET

kinetic energy of the vehicle

EV

potential energy of the vehicle

ETi

kinetic energy of ith axle

ETbt

vehicle body kinetic energy of translational

ETbr

vehicle body kinetic energy of rotational

ETi

kinetic energy of ith axle

ED

dissipative energy of the vehicle

FQv

lateral generalized force

FQr

yaw generalized force

F

roll generalized force

FYiL

lateral force of left tire of ith axle

FYiR

lateral force of right tire of ith axle

FZiL

vertical force of left tire of ith axle

FZiR

vertical force of right tire of ith axle

Sy

lateral slip ratio

μy

lateral friction coefficient

Ky

tire cornering stiffness

Fz0

nominal vertical load of the tire

Fz

vertical load of the tire

Fzn

normalized vertical load

Fy

lateral force of the tire

\({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\phi } _y}\)

normalized slip ratio

Fy

normalized lateral force

Ey

curvature of the lateral force

Vsym

friction characteristic parameters

Vsy

slip speed between the road and tire

Rwear

wear mass per unit time and unit area

Pf

wear power per unit area

Ff

friction force

Vs

sliding speed of friction

η

proportion of the tire tread pattern

Dpatch

width of the tire grounding mark

Apatch

contact area of friction

Apatch_iL

area of the left tire grounding of ith axle

Apatch_iR

area of the right tire grounding of ith axle

ΔhiL

wear height of left tire of ith axle

ΔhiR

wear height of right tire of ith axle

Δhi

average wear height of ith axle

ρ

rubber density of the tire tread

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cho, J. C. and Jung, B. C. (2007). Prediction of tread pattern wear by an explicit finite element model. Tire Science and Technology 35, 4, 276–299.MathSciNetCrossRefGoogle Scholar
  2. Cho, J. R., Choi, J. H. and Kim, Y. S. (2011). Abrasive wear amount estimate for 3D patterned tire utilizing frictional dynamic rolling analysis. Tribology International 44, 7-8, 850–858.CrossRefGoogle Scholar
  3. Cho, J. R., Shin, S. W. and Yoo, W. S. (2005). Crown shape optimization for enhancing tire wear performance by ANN. Computers & Structures 83, 12-13, 920–933.CrossRefGoogle Scholar
  4. Da Silva, M. M., Cunha, R. H. and Neto, A. C. (2012). A simplified model for evaluating tire wear during conceptual design. Int. J. Automotive Technology 13, 6, 915–922.CrossRefGoogle Scholar
  5. Grosch, K. A. (2008). Rubber abrasion and tire wear. Rubber Chemistry and Technology 81, 3, 470–505.MathSciNetCrossRefGoogle Scholar
  6. Guo, K. H. (2011). Theory of Vehicle Handling Dynamics. Phoenix Science Press. Jiangsu, China.Google Scholar
  7. Huang, H. B., Chiu, Y. J. and Jin, X. X. (2013). Numerical calculation of irregular tire wear caused by tread selfexcited vibration and sensitivity analysis. J. Mechanical Science and Technology 27, 7, 1923–1931.CrossRefGoogle Scholar
  8. Klüppel, M. (2015). Wear and abrasion of tires. Encyclopedia of Polymeric Nanomaterials, 2015, 2600–2604.CrossRefGoogle Scholar
  9. Knisley, S. (2002). A correlation between rolling tire contact friction energy and indoor tread wear. Tire Science and Technology 30, 2, 83–99.MathSciNetCrossRefGoogle Scholar
  10. Li, H. P., Shi, B. Q. and Zhang, W. M. (2006). Optimal design of heavy modular multi-axle trailer's steering mechanism. Lifting the Transport Machinery 2006, 8, 38–41.Google Scholar
  11. Li, Y., Zuo, S., Lei, L., Yang, X. and Wu, X. (2012). Analysis of impact factors of tire wear. J. Vibration and Control 18, 6, 833–840.CrossRefGoogle Scholar
  12. Lupker, H., Cheli, F., Braghin, F., Gelosa, E. and Keckman, A. (2004). Numerical Prediction of car tire wear. Tire Science and Technology 32, 3, 164–186.CrossRefGoogle Scholar
  13. Ma, L. F., Wang, J., Xu, L. F. and Ouyang, M. G. (2015). Optimized torque distribution strategy for in-wheeldrive electric vehicles to reduce tire wear. Vehicle Power and Propulsion Conf. (VPPC), 1–5.Google Scholar
  14. Miller, G., Reed, R. and Wheeler, F. (1991). Optimum Ackerman for improved steering axle tire wear on trucks. SAE Paper No. 912693.CrossRefGoogle Scholar
  15. Qin, G. (2011). Research on Complex Mechanical System Modeling and Its Application in Multi-axle Chassis Development. Ph. D. Dissertation. Huazhong University of Science & Technology. Wuhan, China.Google Scholar
  16. Rodríguez-Tembleque, L., Abascal, R. and Aliabadi, M. H. (2010). A boundary element formulation for wear modeling on 3D contact and rolling-contact problems. Int. J. Solids and Structures 47, 18-19, 2600–2612.CrossRefMATHGoogle Scholar
  17. Rodríguez-Tembleque, L., Abascal, R. and Aliabadi, M. H. (2011). A boundary elements formulation for 3D frettingwear problems. Engineering Analysis with Boundary Elements 35, 7, 935–943.MathSciNetCrossRefMATHGoogle Scholar
  18. Sakai, H. (1996). Friction and wear of tire tread rubber. Tire Science and Technology 24, 3, 252–275.CrossRefGoogle Scholar
  19. Shen, Y. H., Gao, Y. and Xu, T. (2016). Multi-axle vehicle dynamics stability control algorithm with all independent drive wheel. Int. J. Automotive Technology 17, 5, 795–805.CrossRefGoogle Scholar
  20. Stalnaker, D. O. and Turner, J. L. (2002). Vehicle and course characterization process for indoor tire wear simulation. Tire Science and Technology 30, 2, 100–121.CrossRefGoogle Scholar
  21. Stalnaker, D., Turner, J., Parekh, D., Whittle, B. and Norton, R. (1996). Indoor simulation of tire wear: Some case studies. Tire Science and Technology 24, 2, 94–118.CrossRefGoogle Scholar
  22. Xu, N. (2012). Study on the Steady State Tire Model under Combined Conditions. Ph. D. Dissertation. Jilin University. Changchun, China.Google Scholar
  23. Yang, J., Wang, G. L., Wan, Z. J., Liang, C. and Zhou, H. C. (2016). Non-natural equilibrium contour design for radial tire and its influence on tire performance. Int. J. Automotive Technology 17, 4, 639–649.CrossRefGoogle Scholar
  24. Yu, F. and Lin, Y. (2005). Vehicle System Dynamics. China Machine Press. Beijing, China.Google Scholar
  25. Zhu, Y. F., Ding, H. G., Zhang, X. J. and Li, X. (2015). Tire cornering wear control of multi-axle vehicle. Machinery Design and Manufacture 09, 295, 85–88.Google Scholar
  26. Zhuang, J. D. (2002). Advanced Technology of Tire. Beijing Science and Technology Press. Beijing, China.Google Scholar
  27. Zuo, S. G., Ni, T. X., Wu, X. D., Wu, K. and Yang, X. W. (2014). Prediction rocedure for wear distribution of transient rolling tire. Int. J. Automotive Technology 15, 3, 505–515.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Automotive Engineers and Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Automotive Simulation and ControlJilin UniversityChangchun, JilinChina

Personalised recommendations