多楔带传动系统的频率灵敏度分析

为了对实际多楔带传动系统进行振动分析与设计优化，系统地研究多楔带传动系统的固有频率对关键设计参数的灵敏度。给出反映带轮、张紧臂等离散部件转动振动与各段皮带这类移动弹性体横向振动之间彼此耦合的运动方程。根据方程耦合与否以及求解的需要将该系统一分为二。对于具有运动耦合的子系统，建立矩阵形式的自由振动方程，推导出固有频率对设计参数的灵敏度表达式，由此导出固有频率对自动张紧机构设计参数和皮带传动速度的灵敏度的显式计算式。针对一多楔带传动系统，计算固有频率对张紧臂长度、扭转弹簧刚度、安装角以及带速的灵敏度，并运用有限差分法结果予以验证。

Frequency Sensitivity Analysis of Multi-ribbed Belt Drive Systems

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.