Computational Mechanics

, Volume 47, Issue 1, pp 105–116

FASTSIM2: a second-order accurate frictional rolling contact algorithm

• E. A. H. Vollebregt
• P. Wilders
Open Access
Original Paper

Abstract

In this paper we consider the frictional (tangential) steady rolling contact problem. We confine ourselves to the simplified theory, instead of using full elastostatic theory, in order to be able to compute results fast, as needed for on-line application in vehicle system dynamics simulation packages. The FASTSIM algorithm is the leading technology in this field and is employed in all dominant railway vehicle system dynamics packages (VSD) in the world. The main contribution of this paper is a new version “FASTSIM2” of the FASTSIM algorithm, which is second-order accurate. This is relevant for VSD, because with the new algorithm 16 times less grid points are required for sufficiently accurate computations of the contact forces. The approach is based on new insights in the characteristics of the rolling contact problem when using the simplified theory, and on taking precise care of the contact conditions in the numerical integration scheme employed.

Keywords

Frictional rolling contact Fastsim algorithm Wheel-rail contact Numerical integration scheme

References

1. 1.
Shackleton P, Iwnicki SD (2007) Comparison of wheel-rail contact codes for railway vehicle simulation: an introduction to the Manchester Contact Benchmark and initial results. Veh Syst Dyn 46(1–2): 129–149Google Scholar
2. 2.
Hertz H (1882) Über die Berührung fester elastischer Körper. Journal für reine und agewandte Mathematik 92: 156–171
3. 3.
Shabana AA, Zaazaa KE, Sugiyama H (2008) Railroad Vehicle Dynamics: A Computational Approach. CRC Press, Boca Raton
4. 4.
Ayasse JB, Chollet H (2005) Determination of the wheel rail contact patch for semi-Hertzian conditions. Veh Syst Dyn 43: 159–170Google Scholar
5. 5.
Kik W, Piotrowski J (1996) A fast approximate method to calculate normal load at contact between wheel and rail and creep forces during rolling. In: Zobory I (ed) Proceedings of the second Mini Conference on Contact mechanics and Wear of Wheel/Rail systems, BudapestGoogle Scholar
6. 6.
Ayasse JB, Chollet H (2006) Wheel–rail contact. In: Iwnicki SD (eds) Handbook of railway vehicle dynamics. CRC Press, Boca Raton, pp 85–120Google Scholar
7. 7.
Kalker JJ (1990) Three-dimensional elastic bodies in rolling contact. Solid mechanics and its applications. Kluwer Academic Publishers, DordrechtGoogle Scholar
8. 8.
Kalker JJ (1979) The computation of three-dimensional rolling contact with dry friction. Int J Numer Methods Eng 14: 1293–1307
9. 9.
Vollebregt EAH (2009) User’s guide for CONTACT, J.J. Kalker’s variational contact model. Technical Report TR09-03, $${{\tt V}\mathcal{O}{\tt R}}$$tech. http://www.kalkersoftware.org
10. 10.
Kalker JJ (1982) A fast algorithm for the simplified theory of rolling contact. Veh Syst Dyn 11: 1–13
11. 11.
Kalker JJ (1973) Simplified theory of rolling contact. Delft Prog Rep Ser C1 1: 1–10Google Scholar
12. 12.
Alonso A, Giménez JG (2007) Non-steady state modelling of wheel-rail contact problem for the dynamic simulation of railway vehicles. Veh Syst Dyn 46(3): 179–196
13. 13.
Hou K, Kalousek J, Lamba H, Scott RT (2000) Thermal effect on adhesion in wheel/rail interface. In: Proceedings of the fifth international conference on contact mechanics and wear of rail/wheel systems, pp 239–244Google Scholar
14. 14.
Tomberger C, Dietmaier P, Sextro W, Six K (2009) Friction in wheel-rail contact: a model comprising interfacial fluids, surface roughness and temperature. In: Bracciali A (ed) Proceedings of the 8th international conference on contact mechanics and wear of rail/wheel systems, Firenze, pp 121–132Google Scholar
15. 15.
Dirks B, Enblom R (2009) Predition model for wheel profile wear and rolling contact fatigue. In: Bracciali A (ed) Proceedings of the 8th international conference on contact mechanics and wear of rail/wheel systems, Firenze, pp 935–943Google Scholar
16. 16.
Ziefle M, Nackenhorst U (2008) Numerical techniques for rolling rubber wheels: treatment of inelastic material properties and frictional contact. Comput Mech 42: 337–356
17. 17.
Alonso A, Giménez JG (2007) Tangential problem solution for non-elliptical contact areas with the FastSim algorithm. Veh Syst Dyn 45(4): 341–357
18. 18.
Giménez JG, Alonso A, Gómez E (2005) Introduction of a friction coefficient dependent on the slip in the Fastsim algorithm. Veh Syst Dyn 43: 233–244
19. 19.
Piotrowski J (2010) Kalker’s algorithm Fastsim solves tangential contact problems with slip-dependent friction and friction anisotropy. Veh Syst Dyn. doi:
20. 20.
Shen ZY, Li Z (1996) A fast non-steady state creep force model based on the simplified theory. Wear 191: 242–244
21. 21.
Vollebregt EAH, Iwnicki SD, Xie G, Shackleton P (2010) Assessing the accuracy of different simplified frictional rolling contact algorithms. Veh Syst Dyn (submitted). Available as Memo EV/M10.035, $${{\tt V}\mathcal {O}{\tt R}}$$tech, DelftGoogle Scholar
22. 22.
Courant R, Hilbert D (1962) Methods of Mathematical Physics, Volume II. Wiley-Interscience, LondonGoogle Scholar
23. 23.
Boussinesq J (1885) Application des Potentiels à l’Étude de l’Équilibre et du Movement des Solides Élastiques. Paris, Gauthier-VillarsGoogle Scholar
24. 24.
Cerruti V (1882) Ricerche intorno all’equilibrio dei corpi elastici isotropi. Reale Accademia dei Lincei, 13Google Scholar
25. 25.
Vollebregt EAH (1995) A Gauss-Seidel type solver for special convex programs, with application to frictional contact mechanics. J Optim Theor Appl 87(1): 47–67
26. 26.
Piotrowski J, Kik W (2007) A simplified model of wheel/rail contact mechanics for non-Hertzian problems and its application in rail vehicle dynamics simulations. Veh Syst Dyn 46: 27–48
27. 27.
Johnson KL (1985) Contact Mechanics. Cambridge University Press, Cambridge
28. 28.
Winkler E (1867) Die Lehre von der Elastizitaet und Festigkeit. Prag, Verlag von H. DominicusGoogle Scholar
29. 29.
Kalker JJ (1967) On the rolling contact of two elastic bodies in the presence of dry friction. PhD thesis, Delft University of Technology, DelftGoogle Scholar
30. 30.
Heath MT (2002) Scientific Computing: An Introductory Survey, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
31. 31.
Vollebregt EAH (2009) Refinement of Kalker’s rolling contact model. In: Bracciali A (ed) In: Proceedings of the 8th international conference on contact mechanics and wear of rail/wheel systems, Firenze, pp 149–156Google Scholar