Axial motion of flat belt induced by angular misalignment of rollers

Flat belt widely used in many industrial applications suffers from axial motion when the centrelines of the rollers are not perfectly parallel. To reveal the relation between the belt axial motion and the angular misalignment of rollers, an analytic model for researching the belt axial motion in a 2-rollers flat belt system was first proposed, considered the internal mechanical feedback in endless belt. The belt axial motion was described by using a set of delay differential equations. The responses of the belt under varied angular misalignments of two rollers were solved by using fourth-order Runge-Kutta method. The results showed that when the angular misalignment of rollers was suddenly changed, the belt might exhibit a steady motion after an evanescent transitional state stage. Further, the close-form axial velocity of the belt in the steady state stage was deduced. In the steady state stage, the belt could move to the side in which the center distance of two rollers was smaller. The magnitude of the belt axial velocity was approximately in direct proportion to the absolute value of angular misalignment of rollers. It seemed that the direction of the driving roller rotation did not affect the direction of the belt axial motion.