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On some approximations of the resultant contact forces and their applications in rigid body dynamics.pdf

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On some approximations of the resultant contact forces and their applications in rigid body dynamics.pdf

Mechanical Systems and Signal Processing 79 (2016) 182–191 Contents lists available at ScienceDirect Mechanical Systems and Signal Processing journal homepage: /locate/ymssp On some approximations of the resultant contact forces and their applications in rigid body dynamics Grzegorz Kudra n, Micha? Szewc, Igor Wojtunik, Jan Awrejcewicz Lodz University of Technology, Department of Automation, Biomechanics and Mechatronics, Stefanowski St. 1/15, 90-924 Lodz, Poland article info Article history: Received 15 February 2016 Accepted 23 February 2016 Available online 8 March 2016 Keywords: Friction modeling Coulomb–Contensou model Plane contact Rolling resistance abstract The work presents the possible applications and effectiveness of certain class of models of the resultant friction force and rolling resistance. The friction models are based on the integral model constructed under assumption of fully developed sliding on the plane contact area of general shape and any pressure distribution. Then the integral model of friction force and moment are approximated based on Padé approximants and their generalizations. These models are expected to be computationally effective in numerical simulations of rigid bodies with frictional contacts, such like billiard balls, Thompson top, the wobble stone and many others. In the present work two different examples of application of the developed contact models are presented and tested: a) a billiard ball rolling and sliding on the plane horizontal table; b) a full ellipsoid of revolution in contact with plane and horizontal base. 2016 Elsevier Ltd. All rights reserved. 1. Introduction There are examples of mechanical systems with frictional contacts, where one-dimensional friction model is insuf?cient to obtain correct simulation results. One can solve then the full contact problem numerically by using space discretization. It requires, however, the use of such numerical methods like ?nite element method or, at least, the integration