Analysis of belt-drive mechanics using a creep-rate-dependent friction law

An analysis of the frictional mechanics of a steadily rotating belt drive is carried out using a physically appropriate creep-rate-dependent friction law. Unlike in belt-drive mechanics analyzed using a Coulomb friction law, the current analysis predicts no adhesion zones in the belt-pulley contact region. Regardless of this finding, for the limiting case of a creep-rate law approaching a Coulomb law, all predicted response quantities (including the extent of belt creep on each pulley) approach those predicted by the Coulomb law analysis. Depending on a slope parameter governing the creep-rate profile, one or two sliding zones exist on each pulley, which together span the belt-pulley contact region. Closed-form expressions are obtained for the tension distribution, the sliding-zone arc magnitudes, and the frictional and normal forces per unit length exerted on the belt. A sample two-pulley belt drive is analyzed further to determine its pulley angular velocity ratio and belt-span tensions. Results from this analysis are compared to a dynamic finite element solution of the same belt drive. Excellent agreement in predicted results is found. Due to the presence of arbitrarily large system rotations and a numerically friendly friction law, the analytical solution presented herein is recommended as a convenient comparison test case for validating friction-enabled dynamic finite element schemes.