The Stretching and Slipping of Belts and Fibers on Pulleys

We derive the equations of motion for an extensible belt on a pulley in which all effects of inertia, including (for the first time) acceleration due to stretching, are retained in the momentum balance. These equations are also valid for fibers and films on rollers undergoing cold draw. We apply our equations to the problem of torque transmission by a belt between two pulleys, and compare the resulting solution to solutions in which centrifugal acceleration is included but stretching acceleration is neglected (the common engineering practice), and the solution in which both centrifugal and stretching accelerations are neglected. We find that ignoring both centrifugal and stretching accelerations results in an overprediction of the maximum moment that can be transmitted, and, for a given transmitted moment, underprediction of the slip angles on the driving and driven pulleys and overprediction of belt strain rates and normal and frictional forces from the pulley on the belt in the slip zones. The common engineering practice of including the effects of centrifugal acceleration but neglecting stretching acceleration also results in errors, for example underpredicting the maximum moment that can be transmitted, overpredicting the slip angles, and underpredicting belt strain rates and normal and frictional forces on the driving pulley. The percentage error increases as the ratios of belt stiffness to centrifugal acceleration or initial belt tension decrease. [S0021-8936(00)01401-X]