Modeling of belt-drives using a large deformation finite element formulation

In this paper, the applicability of the absolute nodal coordinate formulation for the modeling of belt-drive systems is studied. A successful and effective analyzing method for belt-drive systems requires the exact modeling of the rigid body inertia during an arbitrary rigid body motion, accounting of shear deformation, description of highly nonlinear deformations, and a simple as well as realistic description of the contact. The absolute nodal coordinate formulation meets the challenge and is a promising approach for the modeling of belt-drive systems. In this study, a recently proposed two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation has been modified to obtain a belt-like element. In the original element, a continuum mechanics approach is applied to the exact displacement field of the shear deformable beam. The belt-like element allows the user to control the axial and bending stiffness through the use of two parameters. In this study, the interaction between the belt and the pulleys is modeled using an elastic approach in which the contact is accounted for by the inclusion of a set of external forces that depend on the penetration between the belt and pulley. When using the absolute nodal coordinate formulation, the contact forces can be distributed over the length of the element due to the use of high-order polynomials. This is different from other approaches that are used in the modeling of belt-drives. Static and dynamic analysis are used in this study to show the performance of the distributed contact force model and the proposed belt-like element, which is able to model highly nonlinear deformations. Applying these two contributions to the modeling of belt-drive systems, instead of contact forces applied at nodes and low-order elements, leads to a considerable reduction in the degrees of freedom.