支承刚度变化下风电齿轮传动系统的非线性动力学特性
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摘要
风电齿轮传动系统的动力学研究对降低其振动和噪声、提高系统稳定性和进一步探究其故障机理具有重要意义。为进一步研究其非线性动力学特性,采用集中参数模型建立风电齿轮传动系统平移-扭转动力学模型,该模型考虑了非线性因素如各齿轮副的时变啮合刚度、综合啮合误差和齿侧间隙,结合时间历程图、FFT频谱图、相图、Poincaré截面图、分岔图及最大Lyapunov指数图分析了系统在随激励频率变化和随支承刚度变化下的动力学特性。结果发现,系统随着激励频率的不断增大会表现出单周期运动、拟周期运动和混沌等多种非线性动力学行为。随着支承刚度的增加,系统由2周期运动经激变进入混沌运动,最终又回归至周期运动,且通过改变支承刚度观察激励频率变化下系统的影响,发现支承刚度的增加能够弱化混沌,增加周期窗口,并出现混沌运动延后的现象。
Nonlinear dynamic analysis of wind turbine gear transmission system is very important to reduce its noise and vibration,improve the stability of the system and further explore its fault mechanism. The translational-torsional dynamic model of a wind turbine gear transmission system with time-varying meshing stiffness,meshing errors and tooth backlash was established. The system's dynamic characteristics were analyzed with variation of excitation frequency and support stiffness using time history diagram,FFT frequency spectrum one,phase one,Poincaré section one,bifurcation one and the maximum Lyapunov exponent graph. The results showed that the system reveals single periodic motion,quasiperiodic motion and chaos,etc. nonlinear dynamic behaviors with increase in excitation frequency; the system behavior changes from a 2-period motion into chaotic one,and comes back to periodic motion with increase in support stiffness;increase in support stiffness can weaken chaotic motion,increase the periodic motion window and delay chaotic motion.
Nonlinear dynamic analysis of wind turbine gear transmission system is very important to reduce its noise and vibration,improve the stability of the system and further explore its fault mechanism. The translational-torsional dynamic model of a wind turbine gear transmission system with time-varying meshing stiffness,meshing errors and tooth backlash was established. The system's dynamic characteristics were analyzed with variation of excitation frequency and support stiffness using time history diagram,FFT frequency spectrum one,phase one,Poincaré section one,bifurcation one and the maximum Lyapunov exponent graph. The results showed that the system reveals single periodic motion,quasiperiodic motion and chaos,etc. nonlinear dynamic behaviors with increase in excitation frequency; the system behavior changes from a 2-period motion into chaotic one,and comes back to periodic motion with increase in support stiffness;increase in support stiffness can weaken chaotic motion,increase the periodic motion window and delay chaotic motion.
引文
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[13]LIN J,PARKER R G.Planetary gear parametric instability caused by mesh variation[J].Journal of Sound and Vibration,2002(1):129-145.
[14]PARKER R G.A physical explanation for the effectiveness of planet phasing to suppress planetary gear vibration[J].Journal of Sound and Vibration,2000,236(4):561-573.
[15]李润方,王建军.齿轮系统动力学---振动、冲击、噪声[M].北京:科学出版社,1997.
[2]KAHRARMAN A.Planetary gear train dynamics[J].Journal of Mechanical Design,1994,116(3):713-720.
[3]LIN J,PARKER R G.Analytical characterization of the unique properties of planetary gear free vibration[J].Journal of Vibration and Acoustics-Transactions of the ASME,1999,121(3):316-321.
[4]SHENG Dongping,ZHU Rupeng,JIN Guanghu,et al.Bifurcation and chaos study on transverse-torsional coupled2K-H planetary gear train with multiple clearances[J].Journal of Central South University,2016,23(1):86-101.
[5]李晟,吴庆鸣,张志强,等.两级行星齿轮系分岔与混沌特性研究[J].中国机械工程,2014,25(7):931-937.LI Sheng,WU Qingming,ZHANG Zhiqiang,et al.Bifurcation and chaos characteristics of two-stage planetary gear train sets[J].China Mechanical Engineering,2014,25(7):931-937.
[6]林腾蛟,王丹华,冉雄涛,等.多级齿轮传动系统耦合非线性振动特性分析[J].振动与冲击,2013,32(17):1-7.LIN Tengjiao,WANG Danhua,RAN Xiongtao,et al.Coupled nonlinear vibration analysis of a multi-stage gear transmission system[J].Journal of Vibration and Shock,2013,32(17):1-7.
[7]WANG Xiaosun,WU Shijing.Nonlinear dynamic modeling and numerical simulation of the wind turbine’s gear train[C]∥International Conference on Electrical and Control Engineering(ICECE),2011.
[8]田亚平,褚衍东,饶晓波.混合轮系扭转非线性振动建模与分岔特性研究[J].兰州交通大学学报,2016,35(3):125-131.TIAN Yaping,CHU Yandong,RAO Xiaobo.Nonlinear torsional vibration modeling and bifurcation characteristic study of a mixed gear train[J].Journal of Lanzhou Jiaotong University,2016,35(3):125-131.
[9]杨军.风力发电机行星齿轮传动系统变载荷激励动力学特性研究[D].重庆:重庆大学,2012.
[10]佘凯,程广贵,丁建宁,等.支承轴承作用下齿轮系统动力学分析[J].机械设计与制造,2016(4):198-202.SHE Kai,CHENG Guanggui,DING Jianning,et al.Dynamic analysis of spur gear system considering back-up bearings[J].Machinery Design and Manufacture,2016(4):198-202.
[11]李贵彦.支承刚度和啮合间隙变化时弧齿锥齿轮传动系统的分岔与混沌行为[C]∥第十二届全国非线性振动暨第九届全国非线性动力学和运动稳定性学术会议论文集.镇江,2009.
[12]XIANG Ling,JIA Yi,HU Aijun.Bifurcation and chaos analysis for multi-freedom gear-bearing system with timevarying stiffness[J].Applied Mathematical Modelling,2016,40(23/24):10506-10520.
[13]LIN J,PARKER R G.Planetary gear parametric instability caused by mesh variation[J].Journal of Sound and Vibration,2002(1):129-145.
[14]PARKER R G.A physical explanation for the effectiveness of planet phasing to suppress planetary gear vibration[J].Journal of Sound and Vibration,2000,236(4):561-573.
[15]李润方,王建军.齿轮系统动力学---振动、冲击、噪声[M].北京:科学出版社,1997.