Frequency Sensitivity Analysis of Multi-ribbed Belt Drive Systems

Abstract

A systematic sensitivity analysis is conducted on natural frequencies of the multi-ribbed belt drive widely used for modern automotive accessories, aiming at vibration analysis and optimal design of actual belt drive systems. Linear equations of motion are established for the system, which reflect the coupling between rotational vibration of discrete elements such as pulleys and tension arms, and transverse vibration of moving elastomers such as belts. Based on coupling or not among various degrees of freedom, the whole system is divided into two sub-systems for the sake of easy solution. Equations of motion of the sub-system with aforementioned coupling are re-arranged in a matrix form. Derivations are then presented, leading to an explicit expression of sensitivity of natural frequencies with respect to any design parameter of the system. The expressions with respect to key design parameters for the tensioner and belt speed are then presented. A belt drive is taken as an example, to which sensitivity analyses are performed on the natural frequencies with respect to belt speed and other design parameters such as the length of tension arm and the rotational stiffness coefficient of coil spring at the pivot of the tensioner. The analyses are validated by results from the finite difference method.