非零压差边界下间隙流动雷诺方程近似解析解

Approximate analytical solution of the Reynolds equation for clearance flow with pressure difference boundary conditions

为了获得间隙密封、滑动轴承等的液膜压力分布解析表达式,将间隙流动雷诺方程的解析解表示为特解和通解之和,其中特解表示为周向坐标函数和轴向坐标函数之和,通解表示为周向坐标函数和轴向坐标函数之积,结合分离变量法和非零压差边界条件,推导获得间隙流动雷诺方程的近似解析解。基于近似解析解计算间隙密封的液膜承载力和偏位角等参数,并与采用有限差分法的计算结果对比,其中液膜承载力偏差小于5%,偏位角偏差小于3°,而计算效率提高了数百倍。

In order to obtain the lubricant pressure distribution for clearance seal and fi- nite length journal bearing, the Reynolds equation with pressure difference boundary condi- tions was solved analytically. Using the method of separation of variables in an additive and a multiplieative form, a set of particular solutions of the Reynolds equation was added in the general solution of the homogenous Reynolds equation, thus a closed form approximate ana- lytical solution for Reynolds equation was presented. The load capacity and attitude angle of clearance seal were calculated according to the approximate analytical solution proposed, the load capacity error compared with the result calculated with finite difference method was less than 5 %, and the attitude angle error was less than 3 degree and the computational efficien- cy increased by hundreds of times.