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兵工学报 ›› 2014, Vol. 35 ›› Issue (3): 305-311.doi: 10.3969/j.issn.1000-1093.2014.03.003

• 论文 • 上一篇    下一篇

多轴承支撑轴系的精确变形计算研究

刘越, 周广明, 张祖智, 杜万里, 马贵叶   

  1. (中国北方车辆研究所 车辆传动重点实验室, 北京 100072)
  • 收稿日期:2013-09-08 修回日期:2013-09-08 上线日期:2014-04-28
  • 作者简介:刘越(1986—),男,工程师
  • 基金资助:
    国防科技工业技术基础科研项目(2009b2542134);车辆传动重点实验室基金项目(9140C340103120C34124)

Accurate Calculation for Deformation of Multi-bearing Shafting System

LIU Yue, ZHOU Guang-ming, ZHANG Zu-zhi, DU Wan-li, MA Gui-ye   

  1. (Science and Technology on Vehicle Transmission Laboratory, China North Vehicle Research Institute, Beijing 100072, China)
  • Received:2013-09-08 Revised:2013-09-08 Online:2014-04-28

摘要: 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。

关键词: 固体力学, 矩阵位移法, Timoshenko梁, 轴承刚度, SSOR迭代法, Newton-Raphson算法

Abstract: A new modeling method of shaft-bearing stiffness coupling and an iterative method for calculating 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 distribution, 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 coupling the Timoshenko beam and bearings. The deformation of system can be solved by iterative matrix displacement 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.

Key words: solid mechanics, matrix displacement method, Timoshenko beam, bearing stiffness, SSOR iterative matrix, Newton-Raphson method

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