Steady Mechanics of Belt-Pulley Systems

Abstract

Steady state analysis of a two-pulley belt drive is conducted where the belt is modeled as a moving Euler-Bernoulli beam with bending stiffness. Other factors in the classical creep theory, such as elastic extension and Coulomb friction with the pulley, are retained, and belt inertia is included. Inclusion of the bending stiffness leads to nonuniform distribution of the tension and speed in the belt spans and alters the belt departure points from the pulley. Solutions for these quantities are obtained by a numerical iteration method that generalizes to n-pulley systems. The governing boundary value problem (BVP), which has undetermined boundaries due to the unknown belt-pulley contact points, is first converted to a standard fixed boundary form. This form is readily solvable by general purpose BVP solvers. Bending stiffness reduces the wrap angles, improves the power efficiency, increases the span tensions, and reduces the maximum transmissible moment.