A Discrete Tire Model for Cornering Properties Considering Rubber Friction


In this paper, a discrete tire model of cornering properties for road vehicles relating to tire grip performance, which is important for driving stability and safety, is presented. The proposed tire model combines realistic rubber friction related to velocity and tire grip performance with deformation of the carcass. The model can describe the stress and strain of the carcass and tread, and the rubber friction coefficient at each point of the contact patch, which is affected by the distribution of the slip velocity. Meanwhile, the model incorporates the effects of the viscoelastic rubber material and power spectrum of the road, which are explicitly reflected in the rubber friction model. First, an improved rubber friction model based on the Persson theory of rubber friction is introduced in this paper. A discrete analytical tire model, which considers carcass compliance and the discretization of the tread, is then proposed. In addition, important phenomena of tire properties arising from the carcass compliance and rubber friction are analyzed and the effectiveness of the discrete analytical tire model is validated experimentally. The proposed model provides a new way to optimize the grip performance of a tire by adjusting the tire or rubber physical parameters even before the tire is made.

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  1. 1.

    Lugner, P.: Vehicle dynamics of modern passenger cars. Springer, Cham (2019)

    Google Scholar 

  2. 2.

    Pacejka, H.B.: Tire and vehicle dynamics, 3rd edn. Butterworth-Heinemann, Oxford (2012)

    Google Scholar 

  3. 3.

    Svendenius, J., Gäfvert, M.: A semi-empirical tire model for combined slips including the effects of cambering. Veh. Syst. Dyn. 43(Supp 1), 317–328 (2005)

    Article  Google Scholar 

  4. 4.

    Pauwelussen, J.P.: The local contact between tyre and road under steady state combined slip conditions. Veh. Syst. Dyn. 41(1), 1–26 (2004)

    Article  Google Scholar 

  5. 5.

    Henrichmöller, D., Benner, M.: Semi-physical tyre model for real-time capable analysis. ATZ Worldw. 116(6), 8–13 (2014)

    Article  Google Scholar 

  6. 6.

    Li, B., Yang, X., Yang, J.: Tire model application and parameter identification—a literature review. SAE Int. J. Passeng. Cars Mech. Syst. 7(1), 231–243 (2014)

    MathSciNet  Article  Google Scholar 

  7. 7.

    Sakai, H.: Theoretical and experimental studies on the dynamic properties of tyres: part 3: calculation of the six components of force and moment of a tyre. Int. J. Veh. Des. 2(3), 335–372 (1981)

    Google Scholar 

  8. 8.

    Gim, G., Nikravesh, P.E.: An analytical model of pneumatic tyres for vehicle dynamic simulations. Part 1 pure slips. Int. J. Veh. Des. 11(6), 589–618 (1990)

    Google Scholar 

  9. 9.

    Ma, B., Xu, H.G.: Vehicle unsteady dynamics characteristics based on tire and road features. Adv. Mech. Eng. 5(4), 153257 (2013)

    Article  Google Scholar 

  10. 10.

    Le Gal, A., Guy, L., Orange, G., et al.: Modelling of sliding friction for carbon black and silica filled elastomers on road tracks. Wear 264(7–8), 606–615 (2008)

    Article  Google Scholar 

  11. 11.

    Persson, B.N.: Rubber friction: role of the flash temperature. J. Phys.: Condens. Matter 18(32), 7789–7823 (2006)

    Google Scholar 

  12. 12.

    Heinrich, G., Klüppel, M., Vilgis, T.A.: Evaluation of self-affine surfaces and their implication for frictional dynamics as illustrated with a Rouse material. Comput. Theor. Polym. Sci. 10(1–2), 53–61 (2000)

    Article  Google Scholar 

  13. 13.

    Persson, B.N.: On the theory of rubber friction. Surf. Sci. 401(3), 445–454 (1998)

    Article  Google Scholar 

  14. 14.

    Selig, M., Lorenz, B., Henrichm, D., et al.: Rubber friction and tire dynamics: a comparison of theory with experimental data. Tire Sci. Technol. 42(4), 216–262 (2014)

    Google Scholar 

  15. 15.

    De Hoogh, J.: Implementing inflation pressure and velocity effects into the Magic Formula tyre model. Eindhoven University of Technology, Eindhoven (2005)

    Google Scholar 

  16. 16.

    Pottinger, M.G., Mcintyre, J.E., Kempainen, A.J., et al.: Truck tire force and moment in cornering-braking-driving on ice, snow, and dry surfaces. SAE Trans. 109(2), 629–636 (2000)

    Google Scholar 

  17. 17.

    Persson, B.N.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115(8), 3840–3861 (2001)

    Article  Google Scholar 

  18. 18.

    Westermann, S., Petry, F., Boes, R., et al.: Experimental investigation into the predictive capabilities of modern rubber friction theories. Kautsch. Gummi Kunstst. 57(12), 645–650 (2004)

    Google Scholar 

  19. 19.

    Klüppel, M., Heinrich, G.: Rubber friction on self-affine road tracks. Rubber Chem. Technol. 73(4), 578–606 (2000)

    Article  Google Scholar 

  20. 20.

    Le Gal, A., Klüppel, M.: Investigation and modelling of adhesion friction on rough surfaces. Kautsch. Gummi Kunstst. 59(6), 308 (2006)

    Google Scholar 

  21. 21.

    Grosch, K.A.: Goodyear medalist lecture. Rubber friction and its relation to tire traction. Rubber Chem. Technol. 80(3), 379–411 (2007)

    Article  Google Scholar 

  22. 22.

    Zegelaar, P.W.A.: The dynamic response of tyres to brake torque variations and road unevennesses. Delft University of Technology, Delft (1998)

    Google Scholar 

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This research is supported by National Natural Science Foundation of China (Grant Nos. 51875236 and 61790561) and China Automobile Industry Innovation and Development Joint Fund (Grant Nos. U1664257 and U1864206). We would like to gratefully acknowledge and thank the staffs in State Key Laboratory of Automotive Simulation and Control for their contribution to this study.

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Correspondence to Nan Xu.

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Xu, N., Yang, Y. & Guo, K. A Discrete Tire Model for Cornering Properties Considering Rubber Friction. Automot. Innov. 3, 133–146 (2020). https://doi.org/10.1007/s42154-020-00097-y

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  • Road vehicle
  • Tire model
  • Grip performance
  • Rubber friction
  • Running velocity