齿轮轴系弯扭耦合振动理论的统一

在研究齿轮轴系的弯扭耦合振动时,有两种常用的耦合模型,即力耦合模型和几何耦合模型。本文证明,这两种耦合模型以及基于这两种耦合模型构建的齿轮轴系弯扭耦合振动方程可以被统一到一个统一的模式中;几何耦合模型是力耦合模型的特例,几何耦合模型及基于几何耦合模型的齿轮轴系弯扭耦合振动方程可分别从力耦合模型及基于力耦合模型的齿轮轴系弯扭耦合振动方程中导出,从而大大方便和简化了用几何耦合模型构建齿轮耦合轴系弯扭耦合振动方程的过程。对这两种耦合模型进行的数值计算与分析表明,在进行齿轮耦合轴系转子动力学研究时,几何耦合模型和力耦合模型具有相同的效果,而且力耦合模型中齿轮啮合刚度的取值对计算结果几乎没有影响。

Theoretical Unification of Lateral-torsional Coupling Vibration of a Geared Rotor System

In the study of lateral-torsional coupling vibration of a geared rotor system, two coupling models are available, namely force coupling model and geometry coupling model. This paper proves that the two coupling models and the lateral-torsional coupling vibration equations of a geared rotor system based on the two models can be unified into a single model. The geometry coupling model is just a special case of the force coupling model. The former and the lateral-torsional coupling vibration equations based on it can be deduced from the force coupling model and the lateral-torsional coupling vibration equations respectively, greatly simplifying the processes of establishing equations by using the geometry coupling mod- el. The numerical analysis of the two coupling models shows that they have identical effects during the study of rotor dynamics of gear-coupled rotor systems, and the value of gear mesh stiffness in the force coupling model has almost no impact on its calculation results.