Dynamic contact/impact problems, energy conservation, and planetary gear trains Original Research Article

The paper is a continuation of the work presented in [Comp. Meth. Appl. Mech. Eng. 190 (2001) 1903], aimed at modeling of a general class of dynamic contact/impact problems for systems of rigid bodies. The contact is assumed to be frictionless, and the main challenge is to model the exchange between the kinetic and elastic energies in the system. This calls for a discretization scheme that conserves linear and angular momentum and, first of all, the total energy at the discrete level. Such a scheme has been presented in [Comp. Meth. Appl. Mech. Eng. 190 (2001) 1903], and in this work we complement it with a very general treatment of the no-penetration condition for two elastic bodies. The approach is based on the concept of the sign (Rvachev) function, and it provides a natural generalization of the classical point-to-line condition [Arch. Computat. Meth. Eng. 2 (1995) 1]. The work has been motivated with the modeling of planetary gear trains and has resulted in the first (to our best knowledge) two dimensional parallel finite element simulator for gear sets [Parallel finite element simulator of planetary gear trains, Ph.D. Dissertation, The University of Texas, 2001].