Calculation of Sidewall Lateral Stiffness of a Radial Tire Using Material Properties of Rubber Compounds

고무배합물의 물성을 이용한 레이디얼 타이어의 사이드월 횡강성 계산

  • 김용우 (순천대학교 기계자동차공학부) ;
  • 김종국 (순천대학교 대학원)
  • Published : 2003.10.01


This paper has considered the calculation of lateral stiffness of radial tire's sidewall, which consists of cord stiffness and rubber sheet stiffness, by using the material constants of rubber compounds of tire. We have suggested and illustrated how to calculate the rubber sheet lateral stiffness by considering the following aspects. First, the rubber sheet consists of various kinds of rubber compounds with different thickness along the sidewall in the radial direction. Secondly, equivalent Young's modulus of the rubber sheet can be calculated by using available experimental data of rubber compounds. The present method enables us to divide the calculation domain as many as we want, which can reduce numerical error in the calculation of geometrical and mechanical properties. We have illustrated the calculation by using the data of the radial tire for passenger car of P205/60R15.


Radial Tire;Sidewall Lateral Stiffness;Mooney-Rivlin 1st Model;Netting Theory;Rubber Compound;Equivalent Young′s Modulus


  1. Jones, Robert M., 1975, Mechanics of Composite Materials, McGraw-Hill Book Company
  2. Tonuk, E. and Unlusoy, Y. S., 2001, 'Prediction of Automobile Tire Cornering Force Characteristics by Finite Element Modeling and Analysis,' Computers & Structures, Vol. 79, pp. 1219-1232
  3. Kumar, M., 'Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites,' M.S. thesis, Mechanical Engineering, University of Oklahoma, Norman, OK, June 1981
  4. Yamazaki, S., Ogasawara, S., Akasaka, T., 1987, 'Lateral Stiffness of Radial Tires and Effect of Lowering Aspect Ratio,' JSAE Review, Vol. 8, No. 1, pp. 56-63
  5. Nicholson, D. W., 1976, 'A Note on the Classical Net Analysis of the Inflated Tire Profile,' Tire science and Technology, Vol. 4, No. 4, pp. 256-259
  6. Rotta, J., 1949, 'Zur Statik des Luftreifens,' Ingenieur Archiv, Vol. 17, pp. 129-141
  7. M. A. Crisfield, 1997, Non-linear Finite Element Analysis of Solids and Structures: Advanced Topics, John Wiley & Sons
  8. Robecchi, Edoardo and Amici, Luigi, 1973, 'Mechanics of the Inflated Tire,' Tire Science and Technology, Vol. 1, No. 3, pp. 290-345
  9. Ridha, R. A. and Clark, S. K., 1981, 'Tire Stress and Deformation' in Mechanics of Pneumatic Tires edited by S. M. Clark, pp. 482-489, U.S. Department of Transportation National Highway Traffic Safety Administration
  10. Pacejka, H., 1981, 'Tire In-plane Dynamics,' in Mechanics of Pneumatic Tires edited by Clark, S. K., pp. 726-784
  11. Takayama, M. and Yamagishi, K., 1983, 'Simulation Model for Tire Vibration,' Tire Science and Technology, Vol. 11, No. 1, pp. 38-49
  12. Huang, S. C. and Soedel, W., 1987, 'Effects of Coriolis Acceleration on the Free and Forced In-plane Vibrations of Rotatind Rings on Elastic Foundation,' Journal of Sound and Vibration, Vol. 115, No. 2, pp. 253-274
  13. Jenkins, J., 1982, 'The Circumferential Contact Problem for the Belted Radial Passenger Car Tire,' Vehicle System Dynamics, Vol. 11, pp. 325-343
  14. Stutts, D. S. and Soedel, 1992, W., 'A Simplified Dynamic Model of the Effect of Internal Damping on the Rolling Resistance in Pneumatic Tires,' Journal of Sound and Vibration, Vol. 155, No. 1, pp. 153-164
  15. Koga, H., Okamoto, K. and Tozawa Y., 1977, 'Internal Stress Analysis of the Tire under Vertical Loads using Finite Element Method,' Tire Science and Technology, Vol. 5, No. 2, pp. 102-118
  16. Tielking, J. T., 1965, 'Plane Vibration Characteristics of a Pneumatic Tire Model,' SAE 650492
  17. Clark, S. K., 1965, 'The Rolling Tire under Load,' SAE 650493
  18. Potts, G. R. and Bell, C. A., Charek, L. T. and Roy, T. K., 1977, 'Tire Vibrations,' Tire Science and Technology, Vol. 5, No. 4, pp. 202-225
  19. Akasaka, T. and Kabe, K., 1979, 'Deformation and Cord Tension of a Bias Tire in Contact with the Road,' Tire Science and Technology, Vol. 5, No. 4, pp. 171-201