Development and Validation of a Model for Flat Belt Tracking in Pulley Drive Systems

Abstract

This investigation examines the problem of lateral belt motion (“tracking”) in belt drive systems using a mechanics-based approach. It is shown that the motion of a belt over a pulley of arbitrary shape with angular misalignment between the belt and pulley axes can be decomposed into two simpler problems: belt transport over a locally conforming cone and that over a cylindrical pulley at the specified angle of misalignment. The physical models are based on the assumptions that lateral deformations of the belt may be treated as those of a slender beam and that no slip occurs between the belt and the pulley surface. In the case of the conical pulley, a similarity parameter that incorporates the nominal pulley radius, mean normal stress in the belt and its stiffness and width is identified as the primary controlling influence on the tracking behavior. For the problem of tracking on a cylindrical pulley at a steering angle, a kinematic model is found to correctly predict the scaling of the tracking speed. In both models, it is necessary to introduce empirical constants to account for physical effects that have not been included. The tracking speed predicted by these models is nevertheless found to compare well with numerical simulations and experiments. The models are then used to determine the equilibrium position of a belt on a circular-arc crowned pulley. The predicted position was found to be in good agreement with experimental data, indicating that the present approach can be used as the basis for a systematic design procedure.