轴向槽动压滑动轴承非线性油膜力解析模型

Analytical Model for Nonlinear Fluid Film Forces of Hydrodynamic Journal Bearing with Axial Grooves

本文中提出了一种求解流体润滑轴向槽径向滑动轴承非线性油膜力的解析模型.采用油膜气穴边界条件,基于Sturm-Liouville理论,求解了非线性油膜的压力分布.为了便于求解油膜动压润滑的Reynolds方程,将油膜压力函数分解为特解和通解相加的形式,润滑油膜的破裂位置通过连续性条件确定.运用分离变量法,将特解的压力分布分解为周向分离函数和轴向分离函数相加的形式,周向分离函数运用Sommerfeld变换求解.将通解的压力分布分解为周向分离函数和轴向分离函数相乘的形式.采用变量代换,将周向分离函数方程转化为Sturm-Liouville型方程,根据边界条件求得本征值和本征函数系,进而得到通解的周向压力分布;通过求解微分方程,得出轴向分离函数为含本征值的双曲正切函数.在油膜完备区域,对油膜压力分布的解析表达式进行积分,从而求得有限宽轴向槽径向滑动轴承非线性油膜力.计算结果表明:本文中提出的方法和有限差分法的结果吻合得较好,验证了本文中所提出解析模型的正确有效性.

An analytical model for nonlinear fluid film forces of hydrodynamic journal bearing with axial grooves was proposed in this study. Based on the Sturm-Liouville theory, the pressure distribution of nonlinear oil film was solved using the cavitation boundary condition. In order to solve the Reynolds equation of hydrodynamic lubrication of oil film conveniently, the oil film pressure function was decomposed into an additive form of a particular solution and a homogeneous solution, the rupture locations of lubricating oil film were determined by the continuity condition Basect on the method of separation of variables, the pressure distribution of the particular solution was divided into an additive form of the circumferential separation function and the axial separation function, and then the circumferential separation function was solved by the Sommerfeld transform. The pressure distribution of the homogeneous solution was decomposed into a multiplicative form of the circumferential separation function and the axial separation function. By using variable substitution, the circumferential separation function equation was transformed into Sturm-Liouville equation, the eigenvalues and eigenfunctions were obtained using the boundary conditions, and then the circumferential pressure distribution of the homogeneous solution was obtained. By solving the differential equation, the solution of axial separation function was expressed as a hyperbolic tangent function with eigenvalues. In complete oil film field, the analytical expression of the oil film pressure distribution was integrated to obtain the nonlinear oil film forces of finite length journal bearing with axial grooves. The results by the proposed method were in good agreement with the finite difference method, the proposed analytical model was validated.