摘要
根据油膜的物理特性,在动力积分、迭代过程中实时修正具有下游Reynolds边界条件的轴承流体润滑椭圆型变分方程,使其等价为变分不等式.运用八节点等参有限元方法,同时完成非线性油膜力及其Jacobian矩阵的计算.运用Newton-Raphson方法求得转子平衡点时,同时求得了作为副产品的轴承的刚度和阻尼系数.将预估-校正机理和Newton-Raphson方法相结合,提出了计算轴承-转子系统Hopf分岔点(对应于线性失稳转速)的方法.将预估-校正机理与Poincaré-Newton-Floquet方法相结合,分析了T周期运动的局部稳定性和分岔现象.结果表明,采用八节点等参有限元方法同时完成非线性油膜力及其Jacobian矩阵的计算时,同传统方法相比计算量减少,且精度协调一致;将预估-校正机理和Newton-Raphson方法相结合,可以方便地计算轴承-转子系统Hopf分岔点;将预估-校正机理与Poincaré-Newton-Floquet方法相结合,可以避免初值选取困难,快速求得系统周期解及其分岔点.所建立的计算方法具有省时、精度高等优点,可用于指导滑动轴承-转子系统设计.
The stability and nonlinear dynamic behavior of an elastic rotor system with hydrodynamic bearing supports were analyzed. The elliptical variational equations applied for the fluid lubrication of the bearing with free boundary conditions were continuously revised to satisfy the variational inequalities at every step of the dynamic integration and iteration by taking into account the physical characteristics of the oil film. The nonlinear oil film forces and their Jacobian matrices of compatible accuracy were calculated simultaneously using the isoparametric finite element method with eight nodal points. The equilibrium positions of the hydrodynamic bearing-rotor system were determined making use of Newton-Raphson method and the damping and stiffness coefficients of the supporting bearing were simultaneously obtained as the byproducts. A new method combining predictor-corrector mechanism and Newton-Raphson method was presented to calculate the Hopf bifurcation point corresponding to the critical speed of the system. Besides, the local stability and bifurcation behaviors of the T periodic motions were analyzed based on numerical examples and making use of Floquet theory. As the results, it was feasible to calculate the nonlinear oil film forces and their Jacobian matrices of compatible accuracy more efficiently using the isoparametric finite element method with eight nodal points than the conventional calculation method. The difficulty in selecting initial values was avoided by combining the predictor-corrector mechanism and Poincare-Newton-Floquet method, which made it possible to compute the periodic responses and their bifurcation points for the system with less calculation and higher precision. The established methods were characterized by computing time saving and good precision, and could be used to guide the design of the journal bearing-rotor systems in engineering.
出处
《摩擦学学报》
EI
CAS
CSCD
北大核心
2005年第1期61-66,共6页
Tribology
基金
国家自然科学基金资助项目(50275116)
科技部"863"计划资助项目(2002AA414060
2002AA503020).
关键词
流体润滑
径向滑动轴承
轴承—转子动力学
有限元方法
分岔
非线性
Bifurcation (mathematics)
Dynamic mechanical analysis
Finite element method
Lubricating oils
Lubrication
Matrix algebra
Nonlinear systems
Numerical methods
