Parallel finite element simulator of planetary gear trains

This dissertation describes a new approach for numerical simulations of the dynamic response of planetary gear systems. Linear elasticity model superimposed on rigid body motion is employed to describe the motion of interacting gears. Frictionless contact is assumed which calls for a time integration algorithm which conserves the total energy. The model must also allow for simulating a multiple deformable body contact. The discrete model is constructed using the discretization in time approach. The initial boundary-value problem is first discretized in time, resulting in a series of one time step boundary-value problems. A weak form of the single time step problem is then stated as a system of variational inequalities. After a finite element discretization, that leads to the problem of a minimization of a quadratic form with linear inequality constraints. The numerical implementation is done within 2D hp90, a two-dimensional finite element code, which allows for both h and p adaptation. Next, a parallel, portable code has been developed on a distributed memory machine using MPI. Simulations of the planetary gear trains obtained using the developed software are presented.