摘要
基于流体润滑的变分不等方程理论,提出加权有限元方法求滑动轴承非线性油膜力。选择了适当的权函数后,可用一维单元来逼近二维问题,且极少的单元划分即可达到相当高精度。采用一维线性元离散化的系数矩阵为对称三对角阵,可通过修正的追赶法,无需迭代直接求得满足离散变分不等方程的解。计算结果表明,与二维有限元方法相比,算法可达到千分位精度,而计算时间大为缩短。
Based on the variational inequality theory of hydrodynamic lubrication, this paper presents a fast method to calculate the oil-film forces of journal bearings with the Reynolds boundary condition. Chosen a felicitous weighting function, two-dimensional questions could be interpolated by one-dimensional elements with high accuracy. The method gives the coefficient matrix in tri-diagonal form and then discrete variational inequalities are solved by a direct method. Numerical examples show that the results of this method agree well with those of the oil-film force model computed by the two-dimensional finite element method, and that significant computing time is saved. This low time-consuming method can be used to analyze the nonlinear dynamics of the rotor-bearing system.
出处
《工程力学》
EI
CSCD
北大核心
2006年第5期163-167,156,共6页
Engineering Mechanics
关键词
滑动轴承
油膜力
加权函数
有限元
变分不等方程
journal bearing
nonlinear oil-film force
weighting function
finite element method
variational inequality
