The driver coupled to a driven system through mechanical couplings is very common in rotating machinery. These couplings can present angular and parallel misalignments with more or less degree due to manufacturing tolerances or maintenance proceedings. Theoretical and experimental analyses have been published demonstrating the effects of rotor misalignment and the vibration stability of rotor systems. In this work the nonlinear formulation of a magnetorheological fluid journal bearing is included in the finite element model that evaluates the nonlinear responses of a complete rotor system subject to rigid coupling misalignment. The modified Reynolds equations for Bingham viscoplastic materials are implemented in the finite element procedures to evaluate the nonlinear hydrodynamic reaction forces acting on the bearing positions. The finite element formulation for the shaft-line and mechanical couplings is based on the Timoshenko beam theory. Misalignment forces are calculated and included in the equations of motion. The nonlinear dynamic responses are calculated by the modified Newmark method incorporating the Newton–Raphson iteration method to find the equilibrium position at each time step. Bifurcation analysis demonstrates the influence of misalignment to obtain periodic and period-doubling orbit for the center position of the rotor. Results are demonstrated through displacements versus time and frequency responses.

中文翻译：

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磁流变挤压薄膜滑动轴承支撑转子的非线性建模与分析

通过机械联轴器耦合到被驱动系统的驱动器在旋转机械中非常常见。由于制造公差或维护程序，这些联轴器可能会出现或多或少的角度和平行错位。已发表的理论和实验分析证明了转子不对中的影响和转子系统的振动稳定性。在这项工作中，磁流变流体轴颈轴承的非线性公式包含在有限元模型中，该模型评估受刚性联轴器不对中影响的完整转子系统的非线性响应。宾汉粘塑性材料的修正雷诺方程在有限元程序中实施，以评估作用在轴承位置上的非线性流体动力反作用力。轴系和机械联轴器的有限元公式基于 Timoshenko 梁理论。计算错位力并将其包含在运动方程中。非线性动力响应是通过改进的 Newmark 方法计算的，该方法结合了 Newton-Raphson 迭代方法，以找到每个时间步的平衡位置。分岔分析证明了未对准对获得转子中心位置的周期和倍周期轨道的影响。结果通过位移与时间和频率响应的关系来证明。非线性动态响应是通过改进的 Newmark 方法计算的，该方法结合了 Newton-Raphson 迭代方法以找到每个时间步的平衡位置。分岔分析证明了未对准对获得转子中心位置的周期和倍周期轨道的影响。结果通过位移与时间和频率响应的关系来证明。非线性动态响应是通过改进的 Newmark 方法计算的，该方法结合了 Newton-Raphson 迭代方法以找到每个时间步的平衡位置。分岔分析证明了未对准对获得转子中心位置的周期和倍周期轨道的影响。结果通过位移与时间和频率响应的关系来证明。