转子-叶片系统非线性振动和动态稳定性分析

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摘要以转子-叶片耦合系统作为研究对象，在主共振条件下，分析其振动响应和动态稳定性。基于广义 Hamilton原理建立系统的运动微分方程，采用Coleman变换和复平面变换用于系统自由度缩减并利用多尺度方法展开求解。研究了法向碰摩力、摩擦系数、阻尼、支承刚度、圆盘偏心量等因素对转子系统稳态响应的影响，并采用龙格-库塔数值积分方法验证多尺度摄动解的准确性。研究结果表明，较大的法向碰摩力会诱发系统产生失稳现象，此外，随着圆盘偏心量和支承刚度的增加，系统的跳跃频率和共振峰值增大，而阻尼的增加将提高系统的稳定性。

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	李炳强1
	马辉1
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	曾劲1
	郭旭民1
	崔璨1

关键词 ：主共振, 转子-叶片系统, 稳定性, 非线性振动

Abstract：The vibration response and dynamic stability of a coupled rotor-blade system were investigated under main resonances. The equations of motion were derived by using the Hamilton principle, and then the Coleman and complex transformations were adopted to obtain the reduced-order system. The nonlinear vibration and stability of the system were studied by the multiple scales method. The influences of normal rubbing force, friction coefficient, damping, support stiffness, mass eccentricity of the rotor on the steady state response of rotor-blade system were investigated. The accuracy of the multiple scales perturbation solution was verified by the Runge-Kutta numerical integration method. The results show that greater rubbing force will increase the response amplitude and make the system instable. In addition, increasing the damping will enhance the stability of the system. Along with the increasing of mass eccentricity and support stiffness, the jump-down frequency, the resonant peak, as well as the frequency range in which the system has unstable response will increase. It needs larger damping to guarantee the stability of the system.

Key words： main resonances rotor-blade system stability nonlinear vibration

收稿日期: 2017-12-04 出版日期: 2019-03-15

引用本文:

李炳强1，马辉1,2，曾劲1，郭旭民1，崔璨1. 转子-叶片系统非线性振动和动态稳定性分析[J]. 振动与冲击, 2019, 38(6): 15-22.
LI Bingqiang1，MA Hui1,2，ZENG Jin1，GUO Xumin1，CUI Can1. Nonlinear vibration and dynamic stability analysis of a rotor-blade system. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(6): 15-22.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I6/15

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