有限长轴承非稳态油膜力自由-移动边界问题的有限条解法

讨论了不可压缩流体润滑的动载径向滑动轴承油膜压力分布的自由移动边界问题的有限条解法．将自由边界问题转化为全域(矩形域)的具有不等式约束的微分方程的边值问题，进一步化为具有不等式约束的泛函极值问题。借助有限条法在矩形域上离散这个泛函，得到了一个特殊的二次泛函的规化问题。通过变量平移变换，使其化为标准的二次规划问题。然后借助于牛顿非光滑算法，迭代求解非线性的互补方程。给出了有限长轴承真实的油膜应力分布。对于所求解方程的系数矩阵的高度稀疏性。给出了紧缩存储算法。节省了存储空间和减少了计算量。算例表明该方法是有效的。

Finite strip method of free and moving boundary problem for finite bearing with dynamical loading

The finite strip method applied for solving the oil|film pressure distribution of dynamically loaded journal bearing is presented. This is a free and moving boundary problem because the boundary of the oil-film is unknown and changed with the rotational speed of the shaft and the load subjected. The oil-film free and moving boundary problem is transformed into the constrained minimization problem subjected to the inequality constraints by means of which the domain of the solution is expanded to the fixed rectangular filed (the whole surface of the journal bearing). The quadratic programming problem is obtained when the functional is discretized by the finite strip method. Using the movement transformation of the variables, the standard constrained form for the quadratic programming is obtained. By means of the Newton-Raphson procedure with non-smooth algorithm the linear complementary equations are solved and the true oil-film pressure of the bearing (the pressures exerted on each point of the journal are positive) are obtained. Because the coefficient matrix of the equation to be solved is very sparse, the algorithm with the compact storage scheme is given and the computation cost is also reduced. The numerical examples show that the algorithm is very effective.; The finite strip method can be developed to solve the other free and moving boundary problems, for example, seepage .