A complementarity-based rolling friction model for rigid contacts
In this work (also, preprint ANL/MCS-P3020-0812, Argonne National Laboratory) we introduce a complementarity-based rolling friction model to characterize dissipative phenomena at the interface between moving parts. Since the formulation is based on differential inclusions, the model fits well in the context of nonsmooth dynamics, and it does not require short integration timesteps. The method encompasses a rolling resistance limit for static cases, similar to what happens for sliding friction; this is a simple yet efficient approach to problems involving transitions from rolling to resting, and vice-versa. We propose a convex relaxation of the formulation in order to achieve algorithmic robustness and stability; moreover, we show the side effects of the convexification. A natural application of the model is the dynamics of granular materials, because of the high computational efficiency and the need for only a small set of parameters. In particular, when used as a micromechanical model for rolling resistance between granular particles, the model can provide an alternative way to capture the effect of irregular shapes. Other applications can be related to real-time simulations of rolling parts in bearing and guideways, as shown in examples.
KeywordsVariational inequalities Contacts Rolling friction Multibody Complementarity
A. Tasora thanks Ferrari Automotive and TP Engineering for financial support. Mihai Anitescu was supported by the U.S. Department of Energy, under Contract No. DE-AC02-06CH11357.
- 6.Calvetti F, Nova R (2004) Micromechanical approach to slope stability analysis. Degradations and instabilities in geomaterials. Springer, Berlin Google Scholar
- 8.de Coulomb CA (1821) Théorie des machines simples en ayant égard au frottement de leurs parties et à la roideur des cordages. Bachelier, Paris Google Scholar
- 10.Facchinei F, Pang J (2003) Finite-dimensional variational inequalities and complementarity problems, vol 1. Springer, Berlin Google Scholar
- 12.Hairer E, Nørsett SP, Wanner G (2010) Solving ordinary differential equations. Springer, Berlin Google Scholar
- 13.Haug EJ (1989) Computer-aided kinematics and dynamics of mechanical systems. Prentice-Hall, Englewood Cliffs Google Scholar
- 18.Kinderleher D, Stampacchia G (1980) An introduction to variational inequalities and their application. Academic Press, New York Google Scholar
- 24.Pacejka HB (2005) Tire and vehicle dynamics, 2nd edn. SAE International, Warrendale Google Scholar
- 26.Rankine WJM (1868) Manual of applied mechanics. Charless Griffin, London Google Scholar
- 31.Studer C, Glocker C (2007) Solving normal cone inclusion problems in contact mechanics by iterative methods. J Syst Des Dyn 1(3):458–467 Google Scholar
- 34.Tasora A, Negrut D, Anitescu M (2008) Large-scale parallel multi-body dynamics with frictional contact on the graphical processing unit. J Multi-Body Dyn 222(4):315–326 Google Scholar
- 35.Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice. Wiley-Interscience, New York Google Scholar
- 37.Weisbach JL (1870) A manual of the mechanics of engineering and of the construction of machines, vol 3. Van Nostrand, New York Google Scholar