轴系弯扭耦合振动的数学模型

从弯扭耦合的角度来研究旋转轴系的振动，将能更准确地把握轴系的动力学特性，从而为轴系的安全运行提供更有效的保障。本文建立了一个基于分段连续质量模型的轴系弯扭耦合振动数学模型，该模型考虑了不平衡、陀螺力矩、转动惯量、剪切变形及阻尼的影响，因而是一个比较精确的模型。从所得到的微分方程可以得出：当轴系存在不平衡时，扭转振动与弯曲振动之间存在着很明显的相互耦合关系，而且是高度非线性的。而当轴系没有不平衡时，扭转振动会对弯曲振动产生微弱的影响，而弯曲振动对扭转振动没有影响。

Mathematic model of coupled bending and torsional vibration of shaft systems

If the coupled bending and torsional vibration of the rotating shaft system is studied, its dynamic charcteristics can be grasped more exactly, and more efficiently insurance for the safely run of the shaft system can be provided. A mathematic model of the coupled bending and torsional vibration of shaft systems based on a continuous mass model is built. Unbalance, gyroscopic, rotary inertia, shear deformation and damping are considered in this model, so it is a comparatively accurate model. According to the differential equation of the mathematic model, the following conclusion can be drawn, if unbalance exists, the bending vibration and torsional vibration are coupled distinctly, and their relation is highly nonlinear. If unbalance does not exist, the torsional vibration will affect the bending vibration slightly, but the bending vibration will not affect the torsional vibration.