The stretching and slipping of belts and fibers on pulleys

We derive the equations of motion for an extensible belt on a pulley in whi ch all effects of inertia, including (for the first time) acceleration due to stretching, are retained in the momentum balance. These equations are al so 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 pull eys, and compare the resulting solution to solutions in which centrifugal a cceleration is included but stretching acceleration is neglected (the commo n engineering practice), and the solution in which both centrifugal and str etching accelerations are neglected. We find that ignoring both centrifugal and stretching accelerations results in an overprediction of the maximum m oment that can be transmitted, and, for a given transmitted moment, underpr ediction of the slip angles on the driving and driven pulleys and overpredi ction of belt strain rates and normal and frictional forces form the pulley on the belt in the slip zones. The common engineering practice of includin g the effects of centrifugal acceleration but neglecting stretching acceler ation also results in errors, for example underpredicting the maximum momen t that can be transmitted, overpredicting the slip angles, and underpredict ing belt strain rates and normal and frictional forces on the driving pulle y. The percentage error increases as the ratios of belt stiffness to centri fugal acceleration or initial belt tension decrease. [S0021-8936(00)01401-X ].