轴承非线性油膜力的一种变分近似解

基于自由边值理论和凸集上的变分方法，提出一种求解当轴颈大扰动时实际轴承瞬态油膜力的近似公式。公式中引入一个参数来模拟油膜破裂自由边界（雷诺边界条件），则凸集上的泛函极值问题就转换为求此参数的代数极值问题。对椭圆轴承在轴颈作大范围扰动情况下的计算结果表明，这一方法达到了很高的精度，可用于转子－轴承系统的非线性动力分析，能大量降低数值计算瞬态油膜力所需的计算量。

A Variational Approximate Solution For Nonlinear Oil-Film Forces of Sliding Bearing

Based on the free boundary theory and variational method on convex set, an approximate formula to compute the instantaneous oil film forces for real bearings with large perturbed motions of the journal is presented in this paper. By simply introducing a parameter, the given method manipulates the free boundary of the cavitation (Reynolds boundary condition) and, as a result, the functional minimization problem on convex set is transformed to an algebraic minimization problem. The method is performed on an elliptical bearing with large perturbed motions of the journal. The numerical results show high accuracy of the proposed formula. This semi analytical model might be used in the nonlinear dynamics of the rotor bearing system, so that the computing times used in numerical process for obtaining instantaneous oil film forces could be reduced greatly.