Parametric Vibration Analysis and Control in Coupling Rotating Mechanical Drive System

Abstract

Abstract:

Taking the torsional vibration of a kind of rotating machanical
drive system as the research object,considering the influences of time-varying stiffness and nonlinear friction damping,a coupled nonlinear dynamic equation of rotating mechanical drive system was obtained on the basis of Lagrange theory.The average equation of
system was deduced with the aid of method of multiple scales.Besides,according to Hopf bifurcation theory the necessary and sufficient conditions of Hopf bifurcation and the judgment method of periodic motion's stability were given,and the bifurcation characteristics of system were analyzed under the condition of parametric resonance and internal resonance.In order to suppress instability oscillation of drive system caused by subcritical Hopf bifurcation, a nonlinear feedback control was introduced.After including the controller,the Hopf bifurcation points of system can be transferred,
and the stability and amplitude of limit cycle were controlled.Through above study,
an effective method was provided for parametric vibration ananlysis and control in nonlinear rotating machineries.

Key words: rotating machinery, torsional vibration, bifurcation control, coupling nonlinear system

摘要：

以一类旋转机械传动系统的扭振为研究对象，考虑轴系时变刚度变化和非线性摩擦阻尼力的影响，根据Lagrange原理建立了一类旋转机械传动系统的耦合非线性动力学方程，利用多尺度方法推导出了系统的平均方程，并根据Hopf分岔理论给出了系统发生Hopf分岔的充要条件及周期运动稳定性的判别方法，分析了参数共振和内共振条件下系统的分岔特性。为抑制传动系统因亚临界Hopf分岔引起的失稳振荡，引入非线性反馈控制，对系统的Hopf分岔点进行转移并控制周期运动的稳定性和幅值。研究结果为非线性旋转机械参激振动的分析及控制提供了有效方法。

关键词: 旋转机械, 扭振, 分岔控制, 耦合非线性系统

CLC Number:

O322
O415.6

LIU Shuang, LI Yan-Shu, LIU Ban, LI Hai-Bin. Parametric Vibration Analysis and Control in Coupling Rotating Mechanical Drive System[J]. China Mechanical Engineering, 2012, 23(12): 1461-1466.

刘爽, 李延树, 刘彬, 李海滨. 旋转机械耦合传动系统参激振动分析与控制[J]. 中国机械工程, 2012, 23(12): 1461-1466.

References

[1]Edwards S,Lees A W, Friswell M I. The lniluence of Torsion on Rotor/Stator Contact in Rotating Ma- chinery[J]. Journal oI Sound and Vibration, 1999, 225(4) : 767-778.
[2]Chondros T G,Labeas G N. Torsional Vibration of Acracked Rod by Variational Formulation and Nu- merical Analysis[J]. Journal of Sound and Vibra- tion, 2007,301 (3) : 994-1006.
[3]刘爽[1],刘浩然[2],闻岩[3],刘彬[1].一类耦合非线性相对转动系统的Hopf分岔控制[J].物理学报,2010(8):5223-5228.
[4]张登山[1],李华德[1].H∞扭振抑制控制器在热连轧机组上的应用[J].电工技术学报,2006,21(1):92-97.
[5]顾煜炯,杨昆.基于四端网络法的汽轮发电机扭振特性仿真[J].中国机械工程,1999,10(5):540-542.
[6]刘辉[1],项昌乐[2],郑慕侨[2].车辆动力传动系通用扭振模型的研究[J].中国机械工程,2003,14(15):1282-1284.
[7]孟令启[1],王建勋[1],吴浩亮[1],雷明杰[1].中厚板立辊轧机主传动系统的非线性扭振[J].华南理工大学学报：自然科学版,2009,37(2):25-28.
[8]刘辉[1],项昌乐[1],孙恬恬[1].车辆动力传动系统弯扭耦合振动模型的建立及复模态分析[J].机械工程学报,2010(24):67-74.
[9]Niu Xize, Qiu Jiajun. Investigation of Torsional In- stability,Bifurcation,and Chaos of a Generator Set [J]. IEEE Transaction on Energy Conversion,2002, 17(2) : 164-168.
[10]刘彬[1],刘爽[1],张业宽[1],闻岩[2].基于非线性反馈的轧机主传动机电耦联扭转系统的分岔控制[J].机械工程学报,2010(8):160-166.
[11]王立华[1],李润方[2],林腾蛟[2],杨成云[3].齿轮系统时变刚度和间隙非线性振动特性研究[J].中国机械工程,2003,14(13):1143-1146.
[12]陈思雨[1],唐进元[1].间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响[J].机械工程学报,2009,45(8):119-124.
[13]王正浩[1,2],袁惠群[2],闻邦椿[2].相对速度对转子碰摩运动特性的影响[J].机械强度,2009,31(2):175-181.
[14]钱长照[1,2],唐驾时[1].一类非自治时滞反馈系统的分岔控制[J].物理学报,2006,55(2):617-621.

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