考虑轴承刚度耦合性和非线性的多支撑轴系有限元分析方法

Method of Finite Element Analysis for Multi-support Shaft System Based on the Coupling and Nonlinearity of Bearing Stiffness

针对多支撑轴系分析的难点,提出一种考虑轴承刚度耦合性和非线性的有限元计算方法。建立一种轴承单元,考虑了轴承刚度的耦合性和非线性及轴承预紧、滚子锥角等细节因素,推导得到了轴承单元刚度矩阵的解析表达式。采用考虑了剪切变形的欧拉梁单元建立轴模型,将轴与轴承模型进行组合得到系统计算模型,并采用NR法进行求解。通过算例验证,所提出的方法能够准确地计算出给定外载荷下多支撑轴系中各轴承各方向的载荷和系统的变形,且具有较高的计算效率,适用于多支撑轴系问题的分析计算。

A non-linear finite element calculation method based on the coupling and nonlinearity of bearing stiffness is presented to solve the difficulties for the analysis of multi-support shaft system. A bearing element is built in the present method. The coupling and nonlinearity of bearing stiffness, the preload of bearing, the roller taper angle, and the other details are considered, and the analytical expression of bearing stiffness matrix is deduced. The shaft is modeled by Euler beam element with shear deformation, and system computational model is assembled by the model of shaft and bearings. The NR method is used to solve the model. An example shows that this method can calculate the load of each bearing in every direction and the shaft deformation for multi-support shaft system by given external load correctly. This method has high computational efficiency, and is suitable for the analysis of multi-support shaft system.