Three-dimensional Large Deformation Finite Element Analysis of Belt Drives

Abstract

In this paper, methods for the large deformation finite element analysis of belt drives are presented. The new nonlinear dynamic formulations for belt drives are based on the three-dimensional large deformation absolute nodal coordinate formulation. Two different belt drive models that have different numbers of degrees of freedom and different modes of deformation are presented. Both three-dimensional finite elements are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations. In the first model, a thin plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects is used. In the second model, a cable element obtained from a more general threedimensional beam element by eliminating degrees of freedom which are not significant in some cable and belt applications is used. Both finite elements used in this investigation allow for systematic inclusion or exclusion of the bending stiffness, thereby enabling one to systematically examine the effect of bending on the nonlinear dynamics of belt drives. The finite element formulations developed in this paper are implemented in a general purpose three-dimensional flexible multi-body algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The plate formulation also allows using a surface distribution of the contact forces; such a distribution can not be obtained using beam elements since this element is represented by its centerline. Contact forces on the surface are compared to analytical results of similar but twodimensional model. The friction and normal force distributions are in agreement with analytical models. Some differences in results between the plate, cable and analytical formulations are obtained and discussed.