平行不对中约束下大范围转动弹性梁非线性动力学建模与振动机制

Nonlinear Dynamic Modeling and Vibration Mechanism of a Large Range Rotating Elastic Beam under Parallel Misalignment Constraints

为了有效抑制或消除不对中约束响应,研究其非线性动力学特性和振动机制。针对柔性大范围转动弹性梁机构,综合应用Galerkin法和Hamilton原理建立转动梁的动力学模型。借助转子动力学理论和拉格朗日法推导联轴器平行不对中运动学约束方程。基于运动学约束关系,利用行波叠加原理构建弹性梁在平行不对中约束下的非线性动力学模型。应用高阶Runge-Kutta法分析弹性梁非线性动力学行为。研究结果表明:转速为10 rad/s时,联轴器不对中量对弹性梁的动力学特性影响较小。当转速为150 rad/s、不对中量从0增加到0.50 mm时,梁的横向振幅则由0.18 mm激增到10.06 mm,提高了2个数量级,而纵向振幅也由0.13 mm增至7.30 mm,表明高速下不对中量与系统稳定性存在强耦合,其微小变化会引起显著的突发性、非线性激振。转速和不对中量的增加会增大联轴器离心力且呈倍频、径向交替变化,引起转动梁的外激励突变导致系统快速失稳,这也是大型旋转机械运行速度不高的重要原因。

To effectively suppress or eliminate the misalignment constraint response,the nonlinear dynamic characteristics and vibration mechanism were investigated.For the flexible large range rotating elastic beam mechanism,the Galerkin and Hamilton were applied to establish the dynamics model of the rotating beam.The kinematic constraint equations coupling with parallel misalignment were derived with the help of rotor dynamics theory and the Lagrangian method.Based on the kinematic constraint relationship,the nonlinear dynamics model of the elastic beam under the parallel misalignment constraint was constructed by using the traveling wave superposition principle.The higher-order Runge-Kutta method was applied to analyze the nonlinear dynamic behavior of the elastic beam.The results show that when the speed is 10 rad/s,the misalignment of the coupling has little effect on the dynamic characteristics of the elastic beam.When the speed reaches 150 rad/s,the misalignment increases from 0 to 0.50 mm,the transverse amplitude of the beam increases from 0.18 mm to 10.06 mm,which increases the two orders of magnitude,and the longitudinal amplitude increases from 0.13 mm to 7.30 mm,indicating that there is a strong coupling between the misalignment and system stability at high speed,and its small changes can cause significant sudden and nonlinear excitation.The increase in speed and misalignment can increase the centrifugal force of the coupling with multi-frequency and radial alternation change,causing sudden changes in the external excitation of the rotating beam and leading to rapid destabilization of the system,which is also an important reason that the operation speed of large rotating machinery is not high.