多楔带传动系统频率灵敏度分析.docVIP

多楔带传动系统的频率灵敏度分析( 侯之超 王象武 劳耀新 (清华大学汽车安全与节能国家重点实验室 北京 100084) 摘要：为了对多楔带传动系统进行振动分析与设计优化，系统地研究了多楔带传动系统的固有频率对关键设计参数的灵敏度。给出了反映带轮、张紧臂等离散部件转动振动与各段皮带这类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，建立了矩阵形式的自由振动方程，推导了固有频率对设计参数的通用的灵敏度表达式，由此导出了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，计算了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，并运用有限差分法予以验证。 关键词：多楔带传动系统 耦合振动 固有频率 灵敏度分析 中图分类号：TK414.4 Sensitivity Analysis on the Frequencies of Multi-ribbed Belt Drive Systems HOU Zhichao WANG Xiangwu LAO Yaoxin (State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084) Abstract: In order to study the vibration and optimal design of multi-ribbed belt drive systems, a systematic sensitivity analysis is conducted on natural frequencies of multi-ribbed belt drive widely used for modern automotive accessories. Linear equations of motion are established for the system, which reflect the coupling between rotational vibration of discrete elements such as the pulleys and tensioner arms, and transverse oscillation of belt spans that are axially moving continua. 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 about the sub-system with aforementioned coupling are re-arranged in a matrix form. Derivations are then presented, leading to an explicit expression about sensitivity of the 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 and initial oriental angle of the tensioner 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 and a previous app