滑动轴承油膜力Jacobi矩阵的一种快速算法

Rapid Algorithm to Jacobi Matrices of Nonlinear Oil-film Forces in Journal Bearings

基于变分不等方程理论,把滑动轴承油膜力及其Jacobi矩阵的求解转换为求解一组三对角矩阵代数方程,采用一种修正的追赶法同步快速求解。同时将系数矩阵分解为轴颈运动相关量和常矩阵乘积叠加的形式,常矩阵一次求得反复调用,大大减少冗余运算。算例表明,采用本文算法,结果精度得到保证,运算时间大幅减少,能很好地揭示滑动轴承-转子系统的非线性动力特性。

Based on the theory of variational inequality, the solution of the oil-film force and the corresponding Jacobian matrices in the journal bearing is transformed to solve a set of linear algebraic equations with tri-diagonal coefficient matrices, which are rapidly solved with an amendatory direct-method synchronously. The coefficient matrix is decomposed to an assembling of the part relative with journal motion and the part of invariable matrix, the latter can be prepared in advance and can be repeatedly used, many redundant operations are eliminated. The numerical illustrations show that the method can diminish the computing time remarkably under the accuracy guaranteed. The dynamic analysis of a journal bearing-rotor system with this algorithm reveals the nonlinear dynamic behaviors obviously.