A New Belt Friction Model that Respects a Rope’s Weight and its Position Relative to Gravitational Force

This article focuses on the issue of belt friction, which sees very frequent use in practice. It presents the derivation of a new model, which is then compared to the traditional simple Euler-Eytelwein (Capstan) model. Belt friction obeys Coulomb’s Law. Both derivations are based on the differential equilibrium of forces in a cylindrical coordinate system on an elementary segment of a fiber (rope). Compared to the Euler-Eytelwein model, the new model additionally respects the weight of the rope, the radius of the cylindrical surface, the rope’s geometry, and the rope’s position relative to gravitational force in space. First experiment using a pulley (a wheel with a semicircular groove) wrapped with a loaded rope and the measuring of the forces in the rope was used to compare the two models. The new model, which gives more precise results, is slightly more complicated than the Euler-Eytelwein model. Second experiment for measuring of lightweight rubberized polymer mesh belts is mentioned and evaluated too. The differential equation for the new model can also be solved analytically, opening up new possibilities for dealing with belt friction. Results are compared with Finite Element Method too. The article’s conclusion also presents other possible solutions for the problem of belt friction.