多轴承支撑轴系的精确变形计算研究

Accurate Calculation for Deformation of Multi-bearing Shafting System

针对传动系统中典型的多轴承支撑轴系结构,提出了轴和轴承刚度耦合建模方法以及轴系结构精确变形迭代求解方法。基于轴承几何学、接触力学理论,采用Newton-Raphson算法实现轴承接触应力和变形计算、轴承内部载荷分配计算、轴承滚动体力学平衡方程组的求解,建立轴承刚度矩阵。实现轴承与Timoshenko梁的刚度耦合,形成轴系刚度矩阵,并通过松弛迭代法求解稀疏刚度矩阵。改变轴承刚度矩阵完成迭代过程,获得系统的精确变形。通过算例,验证了该计算方法收敛快、对初值要求低,计算精度较高。

A new modeling method of shaft-bearing stiffness coupling and an iterative method for calculat- ing the deformation of multi-bearing shafting system are presented for the typical complex multi-bearing shafting system used in driving system. The bearing stiffness matrix is created by Newton-Raphson method through the following steps ： calculation of contact stress and deformation, calculation of internal load dis- tribution, and solution of rolling elements mechanics equilibrium equations, which is based on the theory of bearing geometry and contact mechanics. The shafting system stiffness matrix is constructed by cou- pling the Timoshenko beam and bearings. The deformation of system can be solved by iterative matrix dis- placement method of variable bearing stiffness, which is applied to SSOR iterative matrix. It is proven that the method has better convergence, lower demand to initial data, and higher accuracy, which is more convenient to use for engineering design.