Dynamic Modeling and Stability Analysis of Flat Belt Drives Using an Elastic/Perfectly Plastic Friction Law

Abstract

This paper presents an analysis of a nonlinear (piecewise linear) dynamical model governing steady operation of a flat belt drive using a physically motivated elastic/perfectly plastic (EPP) friction law. The EPP law models frictional contact as an elastic spring in series with an ideal Coulomb damper. As such, the friction magnitude depends on the stretch of the elastic belt and is integral to the solution approach. Application of the extended Hamilton’s principle, accounting for nonconservative work due to friction and mass transport at the boundaries, yields a set of piecewise linear equations of motion and accompanying boundary conditions. Equilibrium solutions to the gyroscopic boundary value problem are determined in closed form together with an expression for the minimum value of the EPP spring constant needed to transmit a given torque. Unlike equilibrium solutions obtained from a strict Coulomb law, these solutions omit adhesion zones. This finding may be important for interpreting belt drive test-stand results and the experimentally determined friction coefficients obtained from them. A local stability analysis demonstrates that the nonlinear equilibrium solutions found are stable to local perturbations. The steady dynamical operation of the drive is also studied using an in-house corotational finite element code. Comparisons of the finite-element solutions with those obtained analytically show excellent agreement.