用整体传递矩阵法计算旋转机械整机固有频率特性

Calculating Natural Frequency Characteristics by Integrated Transfer Matrix of Complete Set of Rotary Machines

工程中分析多转子系统固有特性常采用子结构传递矩阵法,由于具体结构的复杂性和多样性,用子结构法计算时处理繁琐,编制通用程序困难.为克服子结构传递矩阵法的缺点,给出了整体传递矩阵法计算过程.取各转子状态向量的集合作为系统的状态向量,将各转子通过耦合单元联接起来,该方法不会引入未知内力和位移,也不必建立分割处的平衡方程或变形协调条件.推导了各向同性耦合单元的传递矩阵,并进行了算例验证.由计算结果可见,整体传递矩阵法计算精度较高,它保持了传递矩阵法编程简单、计算工作量小和运算速度快的特点,为开发通用软件提供了有效的方法.

Sub-structure transfer matrix is often used to analyze the natural characteristics of multi-rotor systems. But, it is not easy to develop a versatile program for the transfer matrix because of its complexity in calculation and diversity of structures. A calculation procedure is thus given to integrate all the state vectors of individual rotors together so as to form a systematical state vector to link all rotors together through coupling elements. In this way no unknown internal force and displacement will be introduced in and no balance equations or conditions to coordinate different deformations are required at division points. Derives the transfer matrix of isotropic coupling element with some examples given to verify it, and results showed that the integrated transfer matrix is higher in computational accuracy and available to keep such advantages of conventional transfer matrix as easy to program, small workload and high operating speed. Thus, it provides an effective way to develop a versatile program.