Source: http://www.proceedings.blucher.com.br/article-details/some-considerations-about-forces-and-deformations-in-tires-20147
Timestamp: 2019-04-19 10:28:36+00:00

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The existing tire models are basically of three kinds: essentially empirical (“magic formulas”), or mixed empirical/analytical, or extremely complex theoretical models almost useless in practical situations. The model here proposed does not require any empirical data, and presents a simple theoretical approach very suitable to use in project and analysis of real suspension systems. This paper suggests a physical and mathematical model for the mechanical behavior of pneumatic car tires, based on the relationship between the relative displacement of the wheel to the tire-ground contact region. This formulation, assuming small displacements, is the first step to a more comprehensive model of the tire dynamic behavior, which will be published later.
 BÖHM, F. 1966. Mechanik des Gürtelreifens. Ingenieur Archiv 35. 1966, pp. 82-10 CarBibles. 201 Car Bibles: The Wheel and Tyre Bible. [Online] 201 http://www.carbibles.com/tyre_bible.html.
 EngineeringToolbox. 2013. Elastic Properties and Young Modulus for some Materials. The Engineering Toolbox. [Online] 2013. http://www.engineeringtoolbox.com/youngmodulus-d_417.html.
 KUNG, L.E., SOEDEL, W. and YANG, T.Y. 1986. Free-vibration of a pneumatic tire-wheel unit using a ring on an elastic-foundation and a finite-element model. Journal of Sound and Vibration. June 8, 1986, pp. 181-194.
 LECOMTE, C., GRAHAM, W.R. and DALE, M. 2010. A shell model for tyre belt vibration. Journal of Sound and Vibration. May 10, 2010, pp. 1717-1742.
 MERIAN, J. L. and KRAIGE, L. G. 2008. Engineering Mechanics: Statics. USA : Wiley, 2008.
 NAKASHIMA, H. and WONG, J.Y. 1993. A 3-dimensional tire model by the finite-element method. Journal of Terramechanics. 1993, Vol. 30, 1, pp. 21-34.
 PACEJKA, H. B. and SHARP, R. S. 1991. Shear force development by pneumatic tires in steady-state conditions - a review of modeling aspects. Vehicle System Dynamics. 1991, Vol. 20, 3-4, pp. 121-175.
 PACEJKA, H. B. 2006. Tire and vehicle dynamics. 2nd. s.l. : SAE International, 2006. —. 2002. Tyre and Vehicle Dynamics (R372). s.l. : SAE International, 2002. R372. PerkinElmer Inc. 2007. Characterization of Car Tire Rubber. USA : http://www.perkinelmer.com/CMSResources/Images/44-74057APP_CharacterizationOfCarTireRubber.pdf, 2007.
 PISSARENKO, G. S., IAKOVLEV, A. P. and MATVEIEV, V. V. 1985. Prontuário de resistência de materiais. Moscow, URSS : MIR Ed., 1985. Salvagni, Ronaldo B., Alves, Marcelo A. L. and Barbosa, Roberto S. 2013. A Physical and Mathematical Model for Inflated Tires. (to be published). 2013.
 SHARP, R.S. and EL-NASHAR, M.A. 1986. A Generally Applicable Digital Computer Based Mathematical Model for the Generation of Shear Forces by Pneumatic Tyres. Vehicle System Dynamics. 1986, Vol. 15, 4, pp. 187-209.
 TIMOSHENKO, S. P. and GOODIER, J. N. 1970. Theory of Elasticity. 3rd. s.l. : McGraw Hill, 1970.
 TIMOSHENKO, S. P. and WOINOWSKY-KRIEGER, S. 1964. Theory of Plates and Shells. 2nd. s.l. : McGraw Hill, 1964.
 VIL’KE, V. G. and DVORNIKOV, M. V. 1998. The rolling of a wheel with a pneumatic tire on a plane. J. Appl. Maths Mechs. 1998, Vol. 62, 3, pp. 359-369.
 VIL’KE, V. G. and KOZHEVNIKOV, I. F. 2004. The rolling of a wheel with a reinforced tire along a plane with slipping. J. Appl. Maths Mechs. 2004, Vol. 68, pp. 909-921. —. 2001. The rolling of a wheel with a reinforced tire along a plane without slip. J. Appl. Maths Mechs. 2001, Vol. 65, 6, pp. 915-927.
 YONG, R.N., FATTAH, E.A. and BOONSINSUK, P. 1978. Analysis and prediction of tiresoil interaction and performance using finite elements. J. Terramechanics. 1978, Vol. 15, 1, pp. 43–63.
 YOUNG, W. and BUDYNAS, R. 2001. Roark''s Formulas for Stress and Strain. 7th. s.l. : McGraw-Hill, 2001.
 ZACHOW, D. 1997. 3D membrane shell model in application of a tractor and PKW tyre. VEHICLE SYSTEM DYNAMICS. 1997, Vol. 27, Suppl. S, pp. 163-172.
Salvagni, Ronaldo de Breyne; "SOME CONSIDERATIONS ABOUT FORCES AND DEFORMATIONS IN TIRES", p. 169-180 . In: In Anais do XXIII Simpósio Internacional de Engenharia Automotica - SIMEA 2014 [=Blucher Engineering Proceedings]. São Paulo: Blucher, 2015. . São Paulo: Blucher, 2015.
BÖHM, F. 1966. Mechanik des Gürtelreifens. Ingenieur Archiv 35. 1966, pp. 82-101. CarBibles. 2011. Car Bibles: The Wheel and Tyre Bible. [Online] 2011. http://www.carbibles.com/tyre_bible.html. EngineeringToolbox. 2013. Elastic Properties and Young Modulus for some Materials. The Engineering Toolbox. [Online] 2013. http://www.engineeringtoolbox.com/youngmodulus-d_417.html. KUNG, L.E., SOEDEL, W. and YANG, T.Y. 1986. Free-vibration of a pneumatic tire-wheel unit using a ring on an elastic-foundation and a finite-element model. Journal of Sound and Vibration. June 8, 1986, pp. 181-194. LECOMTE, C., GRAHAM, W.R. and DALE, M. 2010. A shell model for tyre belt vibration. Journal of Sound and Vibration. May 10, 2010, pp. 1717-1742. MERIAN, J. L. and KRAIGE, L. G. 2008. Engineering Mechanics: Statics. USA : Wiley, 2008. NAKASHIMA, H. and WONG, J.Y. 1993. A 3-dimensional tire model by the finite-element method. Journal of Terramechanics. 1993, Vol. 30, 1, pp. 21-34. PACEJKA, H. B. and SHARP, R. S. 1991. Shear force development by pneumatic tires in steady-state conditions - a review of modeling aspects. Vehicle System Dynamics. 1991, Vol. 20, 3-4, pp. 121-175. PACEJKA, H. B. 2006. Tire and vehicle dynamics. 2nd. s.l. : SAE International, 2006. —. 2002. Tyre and Vehicle Dynamics (R372). s.l. : SAE International, 2002. R372. PerkinElmer Inc. 2007. Characterization of Car Tire Rubber. USA : http://www.perkinelmer.com/CMSResources/Images/44-74057APP_CharacterizationOfCarTireRubber.pdf, 2007. PISSARENKO, G. S., IAKOVLEV, A. P. and MATVEIEV, V. V. 1985. Prontuário de resistência de materiais. Moscow, URSS : MIR Ed., 1985. Salvagni, Ronaldo B., Alves, Marcelo A. L. and Barbosa, Roberto S. 2013. A Physical and Mathematical Model for Inflated Tires. (to be published). 2013. SHARP, R.S. and EL-NASHAR, M.A. 1986. A Generally Applicable Digital Computer Based Mathematical Model for the Generation of Shear Forces by Pneumatic Tyres. Vehicle System Dynamics. 1986, Vol. 15, 4, pp. 187-209. TIMOSHENKO, S. P. and GOODIER, J. N. 1970. Theory of Elasticity. 3rd. s.l. : McGraw Hill, 1970. TIMOSHENKO, S. P. and WOINOWSKY-KRIEGER, S. 1964. Theory of Plates and Shells. 2nd. s.l. : McGraw Hill, 1964. VIL’KE, V. G. and DVORNIKOV, M. V. 1998. The rolling of a wheel with a pneumatic tire on a plane. J. Appl. Maths Mechs. 1998, Vol. 62, 3, pp. 359-369. VIL’KE, V. G. and KOZHEVNIKOV, I. F. 2004. The rolling of a wheel with a reinforced tire along a plane with slipping. J. Appl. Maths Mechs. 2004, Vol. 68, pp. 909-921. —. 2001. The rolling of a wheel with a reinforced tire along a plane without slip. J. Appl. Maths Mechs. 2001, Vol. 65, 6, pp. 915-927. YONG, R.N., FATTAH, E.A. and BOONSINSUK, P. 1978. Analysis and prediction of tiresoil interaction and performance using finite elements. J. Terramechanics. 1978, Vol. 15, 1, pp. 43–63. YOUNG, W. and BUDYNAS, R. 2001. Roark''s Formulas for Stress and Strain. 7th. s.l. : McGraw-Hill, 2001. ZACHOW, D. 1997. 3D membrane shell model in application of a tractor and PKW tyre. VEHICLE SYSTEM DYNAMICS. 1997, Vol. 27, Suppl. S, pp. 163-172.

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