中文摘要：

针对润滑液膜中空化问题,引入Fischer-Burmeister函数,提出一种求解满足质量守恒雷诺方程的半光滑牛顿迭代算法.该算法将空化问题的非线性互补关系转化为等式约束方程,避免了迭代计算中的不等式约束识别问题.算法可将空化约束方程与雷诺方程、力平衡方程、变形方程等同时纳入牛顿迭代方程组,有效解决了传统松弛迭代算法需要多重嵌套循环带来的效率低下问题及压力与膜厚的强耦合性带来的收敛困难问题.计算实例表明,该算法计算效率高、收敛性好,且易应用于弹流润滑分析中,在滑动轴承和机械端面密封等多种物理模型下均有良好的适用性.

英文摘要：

A semi-smooth newton iterative algorithm was presented to solve the Reynolds equation, where a massconserving cavitation model was considered. In this study, the cavitation problem was treated as a constraint equation,where film pressure and void fraction were complemented nonlinerly. Cavitation equation coupled with Reynolds equation, equilibrium equation and deformation equation were formulated as a system of equations. The algorithm had a high efficiency instead of using multi-iteration which is widely used in relaxed iterative algorithm. It also had a strong convergence property benefited from substituting the linearity between film thickness and pressure into the Reynolds eqaution. Case studies show that this model can be easily applied into EHD analysis, and can be widely used in journal bearing, mechanical face seal and other lubricant issues.