汽轮发电机组轴系弯扭耦合振动的数学模型

根据汽轮发电机组轴系各轴段所处位置不同，将轴系分为3类微元轴段，在分析微元轴段力和力矩基础上，分别推导了各类轴段的弯扭耦合振动偏微分方程组。该方程组是基于分布质量模型的耦合振动数学模型，它能综合考虑机组诸多因素，比较接近实际地研究机组动力特性。该方程组是高度非线性的，轴系质量偏心是弯扭耦合的一个前提。利用本文给出的方程组，可以进行弯扭耦合振动的固有频率、振型及瞬态响应计算。

Mathematic Model of Coupling Flexural-torsioanl Vibration of Turbogenerator Set Shafts

According to the different position of shafts' segment in turbogenerator set, the shafts are divided into three types of micro segment. Based on the analysis of force and moment of the micro segment, the differential equations of coupling flexural-torsional vibration are deduced. The presented mathematic model is based on distributed mass model, so a lot of influence factors can be considered synthetically, and the obtained dynamic characteristics of turbogenerator set are more closely to the practical condition. The deduced equations are highly nonlinear, and the mass eccentricity is the precondition of coupling flexural-torsional vibration. The inherent frequency, vibration shapes and transient response of coupling flexural-torsioanl vibration can be calculated by this equations.