卷吸速度方向与椭圆短轴成一夹角的弹流润滑渐近网格加密算法

Progressive Mesh Densification(PMD)Method in Elastohydrodynamic Lubrication of Elliptical Contacts with Arbitrary Entrainment

针对数值求解卷吸速度方向与椭圆短轴成一夹角的重载薄膜弹流润滑问题,提出将渐进网格加密(progressive mesh densification,PMD)算法的思想应用于此类问题的求解,建立了此类问题雷诺方程的离散差分格式,运用快速傅里叶变换算法计算点接触弹性变形,采用PMD网格跳转方法加速迭代收敛,最后得到此类问题的完全数值解和油膜形状分布图,并与前人的实验数据进行了对比分析。结果表明:在重载薄膜润滑条件下,数值求解结果与前人的实验结果相一致;与直接在最终网格上进行迭代相比,文中提出的方法可以在粗糙网格上迅速消除误差,为高密度网格提供更好的初值,从而使计算收敛速度提高1倍以上,证明了PMD算法在求解此类问题时具有良好的收敛性和有效性。

To numerically solve the elastohydrodynamic lubrication problem that entraining velocity vector has an oblique angle with the minor axis of Hertzian contact ellipse under heavy loading and thin film lubrication conditions,the progressive mesh densification （PMD） method is used,and a discrete differential scheme for Reynolds equation is set up.The fast Fourier transform is adopted to calculate the elastic deformation for point contact,and the PMD method is used to accelerate the iterative convergence.Moreover,a complete numerical solution and the film thickness distribution are obtained and compared with the experimental results from literatures to validate the model.The results show that,under heavy loading and thin film lubrication conditions,this numerical solution is in accordance with the experimental results,proving that the PMD method is effective and has fine convergent behavior for solving this kind of problem.