Belt Drive Mechanics With Absolute Nodal Coordinate Finite Element Verification

Abstract

This paper presents preliminary analytical and numerical procedures for the analysis of the motion of extensible belt/pulley systems. These procedures can be used to accurately predict the change in the belt velocity, tension force, normal force, friction force and the cross section deformations along the belt length at the steady state condition. The methods used in this paper relax the assumption of constant shear and internal moment along the belt length, leading to more accurate results as compared to the results obtained using previous models. The analytical solution obtained in this paper is validated by comparing it with the solution obtained using absolute nodal coordinate formulation (ANCF) finite elements. It is shown that considering the effect of the internal moment and assuming that the contact between the belt and the pulley has three stages lead to more realistic prediction of the belt system variables and more accurate values for the angles in the belt/pulley sliding zones. The change in the angular velocity of the driven pulley with respect to the driving pulley, the change in the cross section dimensions, and the belt stretch are predicted. The results obtained in this study also demonstrate that formulations presented in this paper lead to more accurate prediction for the belt tension, friction and normal forces. ANCF structural finite elements provide more general kinematic description that can be used to predict the cross section deformation and its coupling with the extension and bending of the belts and rubber chains.