气体箔片轴承静态工作点求解

Solution of Quiescent Point in Gas Foil Bearings

气体箔片轴承静态工作点的计算属于典型的弹流耦合问题,需要进行可压缩流体雷诺方程和板壳弹性变形方程的耦合迭代求解。为确定任意给定载荷下气体箔片轴承的静态工作点,提出了一种“二分法搜索+不动点迭代”的求解策略,二分法用于搜索偏心率,不动点迭代用于寻找偏位角。弹流耦合求解中雷诺方程采用基于质量流量守恒的差分法离散进行超松弛迭代求解,顶层箔片采用Kirchhoff薄板模型进行有限元求解,以整周式及三瓦插入式气体箔片轴承为算例进行了求解及分析,结果表明:偏心率、偏位角与文献[2]最大误差分别为6.60%和3.76%,且偏心率的误差随着外载荷的增大会显著减小;相对于刚性表面轴承,柔性表面轴承中的偏位角对偏心率的变化更加敏感。

The calculation of quiescent point of gas foil bearings(GFB)is a typical elastohydrodynamic coupling problem,requiring the coupling iterative solution of the Reynolds equation of compressible fluid and the elastic deformation equation of plate-shell.In order to determine the quiescent point of GFB under any given load,a solution strategy of“dichotomy search+fixed point iteration”is proposed,where the dichotomy is used to search eccentricity,and the fixed point iteration is used to find attitude angle.During the elastohydrodynamic coupling solution,the Reynolds equation is discretized by the difference method based on the conservation of mass and flow,and the over relaxation iterative solution is carried out.The top foil is established by the Kirchhoff thin plate model,and solved by finite element method.Taking the single-pad GFB and three-pad insertion GFB as examples,the solution and analysis are carried out.The results show that:compared with eccentricity and attitude angle obtained in literature[2],the maximum errors are 6.60%and 3.76%respectively,and the error of eccentricity decreases significantly with the increase of external load;compared with rigid surface bearings,the attitude angle of flexible surface bearings is more sensitive to the change of eccentricity.