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Modelling of Tyre Force and Moment Generation

  • Conference paper
Rolling Contact Phenomena

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 411))

Abstract

The paper gives an overview of different types of mathematical models describing tyre force and moment generating properties that may be used in vehicle dynamics simulation studies. First a physical model based on the brush concept is treated in detail. Then. an empirical model is discussed. This model that is known by the name ‘Magic Formula’ gives a relatively good approximation of measured data. Finally, the non-steady-state behaviour is briefly discussed. The low frequency transient tyre performance is modelled by a first-order differential equation in which the relaxation length serves as parameter. The higher frequency behaviour is modelled by introducing the dynamics ofthe tyre belt.

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References

  • Bakker, E., Nyborg, L., and Pacejka, H.B. (1987). ‘Tyre modelling for use in vehicle dynamics studies’. SAE 870421.

    Google Scholar 

  • Bakker, E., Pacejka, H.B., and Lidner, L. (1989). ‘A new tyre model with application in vehicle dynamics studies’. Proceedings of the 4th Autotechnologies Conference, Monte Carlo, June 1989, SAE 890–087.

    Google Scholar 

  • Bayle, P., Forissier. J.F., and Lafon, S. (1993). ‘A new tyre model for vehicle dynamics simulations’. Automotive Technology International ‘83, pp. 193–198.

    Google Scholar 

  • Bernard, J.E., Segel, L., and Wild, R.E. (1977). ‘Tire shear force generation during combined steering and braking maneuvres’. SAE 770852.

    Google Scholar 

  • Dugoff, H., Fancher, P.S., and Segel, L. (1970). ‘An analysis oftire traction properties and their influence on vehicle dynamic performance’. Proceedings FISITA/SAE, Brussels, SAE 700–377.

    Google Scholar 

  • Fiala, E. (1954). ‘Seitenkräfte am rollenden Luftreifen’. VDI-Zeitschrift 96, p. 973.

    Google Scholar 

  • Gipser, M., Hofer, R., and Lugner, P. (1997). ‘Dynamical Tyre Response to Road Unevennesses’. Proceedings of the 2nd Tyre Colloquium, Berlin, Sept.1996, Suppl. to Vehicle System Dynamics 27.

    Google Scholar 

  • Higuchi, A., and Pacejka, H.B. (1997). ‘The relaxation length concept at large wheel slip and camber’. Proceedings of the 2nd Tyre Colloquium, Berlin, Sept.1996, Suppl. to l’ehicle System Dynamics 27.

    Google Scholar 

  • Jagt, P. van der, Pacejka, H.B., and Savkoor, A.R. (1989), A.R. (1989). ‘Influence of tyre and suspension dynamics on the braking performance of an anti-lock system on uneven roads’. Proceedings of EAEC Conf. ‘89, C382/047, IMechE 1989.

    Google Scholar 

  • Mastinu, G., Gaia77i, S., Montanaro, F., and Pirola, D. (1997). ‘A Semi-Analytical Tyre Model for Steady-and Transient State Simulations’. Proceedings of the 2nd Tyre Colloquium. Berlin, Sept.1996, Suppl. to Vehicle System Dynamics 27.

    Google Scholar 

  • Maurice, J.P., Zegelaar, P.W.A., and Pacejka, P.W.A. (1998). ‘The Influence of Belt Dynamics on Cornering and Braking Performance of Tyres’. Proceedings of the 15th IA SD Symposium. Budapest. Aug. 1997, Suppl. to Vehicle System Dynamics 29.

    Google Scholar 

  • Oosten, J. van, and Bakker, E. (1993). ‘Determination of Magic Formula tyre model parameters’. Proceedings of the 1st Tyre Colloquium, Delft, Oct. 1991, Suppl. to Vehicle System Dynamics 21.

    Google Scholar 

  • Pacejka, H.B. (1966). ’The wheel shimmy phenomenon’. Dissertation. University of Technology Delft.

    Google Scholar 

  • Pacejka, H.B., and Fancher, P.S. (1972). ‘Hybrid simulation ofshear force development ofa tyre experien cing longitudinal and lateral slip’. Proceedings XI Fth FISIT.A Congress. London. p. 3/78.

    Google Scholar 

  • Pacejka, H.B. (1981 a). ‘In-plane and out-of-plane dynamics of pneumatic tyres’. l éhicle System Dynamics 10, pp. 221–251.

    Google Scholar 

  • Pacejka, H.B. (1981 b). ‘Analysis of tyre properties. Yaw and Camber Analysis’. Chapter 9 of Mechanicsof Pneumatic Tires,ed. S.K. Clark, US Gov. Printing Office 1981–0–308–639. Washington D.C.

    Google Scholar 

  • Pacejka,H.B., and Sharp. R.S. (1991). ‘Shear force development by pneumatic tyres in steady state conditions: A review of modelling aspects’. Vehicle System Dynamics 20. pp. 121–176.

    Article  Google Scholar 

  • Pacejka, H.B., and Takahashi, T. (1992). ‘Pure slip characteristics of tyres on flat and on undulated road surfaces’. Proceedings of A VEC ’92, Yokohama.

    Google Scholar 

  • Pacejka, H.B., and Bakker, E. (1993). ‘The Magic Formula tyre model’. Proceedings of the 1st Tyre Colloquium, Delft. Oct.1991, Suppl. to Vehicle System Dynamics 21.

    Google Scholar 

  • Pacejka, H.B. (1996). ‘The Tyre as a Vehicle Component’. Proceedings XXII FISIT.A Congress. Prague.

    Google Scholar 

  • Pacejka, H.B., and Besselink,1. (1997). ‘A consistent Magic Formula tyre model with dynamic extension’. Proceedings of the 2nd Tyre Colloquium, Berlin. Sept.1996. Suppl. to Vehicle System Dynamics 27

    Google Scholar 

  • Savkoor, A.R. (1970). ‘The lateral flexibility of pneumatic tires and its application to the lateral rolling contact problem’. Proceedings FIS/TA/SAE, Brussels, SAE 700378.

    Google Scholar 

  • Schlippe, B. von, and Dietrich, R. (1942). ‘Zur Mechanik des Luftreifens’. Zentral fir Wiss. Ber.. Berlin.

    Google Scholar 

  • Sharp, R.S., and El-Nashar, M.A. (1986). ‘A generally applicable digital computer based mathematical model for the generation ofshear forces by preamatic tyres’. t ’ehicle System Dynamics 15. p.187–210.

    Google Scholar 

  • Vries, E.J.H. de. and Pacejka, H.B. (1998). ‘Motorcycle Tyre Measurements and Models’. Proceedings 15th IA VSD Symposium, Budapest, Aug. 1997, Suppl. to Vehicle System Dynamics 29.

    Google Scholar 

  • W illumeit, H.P. (1969), ’Theoretische Untersuchungen an einem Modell des Luftreifens unter Seiten-and Umfangskraft’. Dissertation, Technische Universität Berlin.

    Google Scholar 

  • Zegelaar, P.W.A., and Pacejka, H.B. (1996). ‘In-plane dynamics of tyres on uneven roads’. Proceedings 14th /A V SD Symposium, Ann Arbor, Aug. 1995. Suppl. to Vehicle System Dynamics 25.

    Google Scholar 

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© 2000 Springer-Verlag Wien

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Pacejka, H.B. (2000). Modelling of Tyre Force and Moment Generation. In: Jacobson, B., Kalker, J.J. (eds) Rolling Contact Phenomena. International Centre for Mechanical Sciences, vol 411. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2782-7_5

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  • DOI: https://doi.org/10.1007/978-3-7091-2782-7_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83332-2

  • Online ISBN: 978-3-7091-2782-7

  • eBook Packages: Springer Book Archive

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