Variability in output torque of capstan and wrap spring elements

The capstan and wrap spring devices are two contacting machine systems where output torque has an exponential dependence on the prevailing friction coefficient. Under certain assumptions, the same fundamental equation relating torque to friction coefficient can be used for both machine elements. Two complicating factors in the analysis of these units are the inherent variability of the friction coefficient and the difficulty in characterising the level of conformity between the contacting member and the hub. Thus the output torque from such devices can be unpredictable. A methodology is proposed whereby these issues can be analytically quantified. This enables theoretical formulae for the mean and standard deviation in output torque to be developed. Predictions using these formulae are compared to experimental measurements to assess the approach and to determine the magnitudes of some friction parameters. Monte Carlo numerical simulation is also employed to validate the theoretical analysis. It is shown that knowledge of the mean output torque and dispersion in output torque can then help inform the design process with such units.