燃气轮机拉杆转子非线性动力学特性研究

Nonlinear Dynamic Characteristics of a Rod-Fastened Rotor System

针对燃气轮机组合式转子轮盘间存在的非线性刚度对转子动力学特性产生的特殊影响,对比研究了关于拉杆转子三次方和双线性两种非线性刚度模型的动力学特性:首先,基于双圆盘拉杆转子模型,通过三维有限元法计算得到其弯曲刚度随转角的变化规律;然后,采用三次方模型拟合非线性刚度,建立拉杆转子无量纲控制方程,并基于谐波平衡法和Broyden迭代优化算法计算稳态响应,进而分析系统参数对非线性响应的影响规律;最后,基于双线性刚度模型对比研究拉杆转子非线性响应。研究结果表明,两种模型均能模拟转子升降速过程中的幅值突变效应,但两种模型发生振幅突跳现象的原因不同,且在响应不稳定区域附近的动力学特性不同;三次方刚度模型对这种非线性现象的描述更加准确,其数值模拟结果具有更加丰富的非线性动力学行为;为避免突跳现象对转子系统造成的不良影响,通过调整非线性系统的特定参数能够改变幅频响应曲线中不稳定区域的位置,进而有效避免转子系统工作在不稳定的频率范围内。

The nonlinear bending stiffness of a rod-fastened rotor varies with the applied loads to significantly influence the dynamic characteristics. In this paper, cubic and bi-linear models are both adopted to perform a comparative analysis on the nonlinear dynamic characteristics of a rod-fastened rotor system. First, the bending stiffness of the rod-fastened rotor system with two disks is obtained using a 3 D FEM model. Then, a cubic stiffness model is applied to approximate the nonlinear stiffness, and subsequently the corresponding governing equation is derived. The harmonic balance method(HBM) and iterative optimization method based on Broyden algorithm are adopted to get the steady-state response. Besides, the influences of different parameters on rotor dynamics are further investigated. Finally, a bilinear stiffness model is utilized to conduct the comparative analysis on the dynamic response of the rod-fastened rotor system. The results show that both models can be used to demonstrate the amplitude jump behavior of the rotor system. However, these two models have different explanations on amplitude jump, so that the dynamic characteristics are different near the unstable region, and the cubic model has a more abundant nonlinear behavior than that of the bi-linear model. The results also show that, by adjusting the nonlinear system parameters, the position of the unstable region in the amplitude-frequency response curve can be changed, thereby effectively preventing the rotor system from operating in an unstable frequency region.