【摘要】 研究了非解析径向椭圆轴承支承的转子系统的稳定性和分岔。考虑了转动惯量的影响,利用非线性油膜力以增加数值计算的精度。在不需要额外再解Reynolds方程的情况下,采用等参有限元法,求解了具有Reynolds边值条件的流体润滑椭圆型变分约束方程,使得动力积分过程中所需非线性油膜力及其Jacobian矩阵能够同时计算完成并且具有足够且协调一致的精度。在稳定性分析中,运用打靶法和轨迹预测追踪算法研究了系统非线性不平衡响应,结合Floquet理论研究了随着轴承设计参数改变时非线性轴承—转子系统T周期运动的局部稳定性和分岔行为。更多还原

【Abstract】 The stability and bifurcation of a rotor system with non-analytical elliptical bearing supports are analyzed. The effects of inertia can be taken into consideration in the model of rotor system. Nonlinear oil film force is adopted to increase the numerical accuracy. Based on the isoparametric finite element with eight nodal points method, variational inequalities with Reynolds boundary arising in fluid lubrication are solved. Nonlinear oil film forces and their Jacobian matrices that are needed at dynamic integration are calculated simultaneously, and compatiable accuracy is obtained with little increase of computing efforts. In the stability analysis, the periodic unbalance responses of the system are obtained by shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions with the change of bearing design parameter value are obtained by the Floquet theory. The numerical examples show that the schemes of this study have good precision.更多还原