多楔带传动系统固有频率计算的约化行列式法

Method Based on a Reduced Characteristic Determinant for Frequencies of Multi-Ribbed Belt Drive Systems

研究发动机附件多楔带传动系统固有振动特性的计算问题。在简要介绍系统振动特点与运动方程的基础上,对于具有运动耦合的子系统,给出了矩阵形式的自由振动方程。基于数学推导,分析了因自动张紧臂运动导致的特征函数奇异性,通过分离奇异项将原特征值问题转化为常规特征值问题,提出了一种计算固有频率的特征行列式约化算法,有效避免了因函数奇异而产生的伪根和丢根问题。以一个三带轮模型带传动系统为例,通过频率计算与分析比较,验证了所提出方法的正确性与效率。

This paper reports a numerical method for the inherent characteristics of a multi-ribbed belt drive system in the modem vehicle engines. Following introduction to vibrations in the system and corre- sponding equations, motion equations of the key sub-system are presented in a matrix form. Mathematical analysis reveals the extra singularity of the characteristic determinant due to motion of the automatic tensio- ner arm. By extracting singular terms from the characteristic equations of the system, the eigenvalue prob- lem is converted to an ordinary one. A new approach based on reduced characteristic determinant is ob- tained for the natural frequency. The new approach eliminates extra singularity of the original characteristic determinant and avoids the cases of obtaining pseudo eigenvalues or missing the real ones. The natural fre- quencies of a model belt drive system with three pulleys are calculated and compared with those obtained from previous methods, which validates the efficiency and applicability of the new method.