Equilibrium and Belt-Pulley Vibration Coupling in Serpentine Belt Drives

Abstract

Serpentine belt drives with spring-loaded tensioners are now widely used in the automotive industry. Experimental measurements show that linear system vibration coupling exists between the pulley rotations and the transverse span deflections. Former models that treat the belt as a string and neglect the belt bending stiffness cannot explain this coupling phenomenon. In this paper, a new serpentine belt system model incorporating the belt bending stiffness is established. The finite belt bending stiffness causes nontrivial transverse span equilibria, in contrast to string models with straight span equilibria. Nontrivial span equilibria cause linear span-pulley coupling, and the degree of coupling is determined by the equilibrium curvatures. A computational method based on boundary value problem solvers is developed to obtain the numerically exact solution of the nonlinear equilibrium equations. An approximate analytical solution of closed-form is also obtained for the case of small bending stiffness. Based on these solutions, the effects of design variables on the equilibrium deflections and span-pulley coupling are investigated.