内外激励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,对降低齿轮传动系统故障有重要意义。为进一步研究风电齿轮传动系统的非线性动力学特性,采用集中参数模型建立了该系统纯扭转非线性动力学模型。该模型考虑了各齿轮副间时变啮合刚度、综合啮合误差和齿侧间隙非线性因素,以1.5 MW风机额定功率作为传递功率,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,研究了在激励频率变化下和综合啮合误差变化下系统的动力学特性。结果发现,随着激励频率的不断增大,系统会出现单周期运动、拟周期运动和混沌等动力学行为,且混沌区域会发生改变;随着综合啮合误差的增加,系统由拟周期运动演化为混沌,最终又突变为拟单周期运动,且通过改变综合啮合误差,观察激励频率变化下系统的影响,发现综合啮合误差的减小能够明显的弱化混沌运动。
Studying dynamic features of wind turbine gear systems is of great significance to reduce faults of a system. For further investigating a wind turbine's gear transmission system nonlinear dynamic characteristics,the lunped mass method was chosen,a torsional nonlinear dynamic model of the gear system was established considering nonlinear factors,such as,gear pairs' time-varying mesh stiffness,gear mesh error and backlash and taking 1. 5 MW wind turbine rated power as the transmission power. The dynamic characteristics of the system were analyzed by using time history figures,FFT frequency spectrum diagrams, phase trajectories, Poincaré sections, bifurcation diagram and largest Lyapunov exponent diagram under variations of excitation frequency and gear mesh error. Results showed that with increase in excitation frequency,there are single periodic motion,quasi periodic one and chaos to appear in the system,the chaotic region also changes; with increase in mesh error,the motion of the system changes from quasi periodic one into chaotic one,and finally it becomes a quasi-single periodic motion; reducing mesh error weakens significantly the chaotic motion.
Studying dynamic features of wind turbine gear systems is of great significance to reduce faults of a system. For further investigating a wind turbine's gear transmission system nonlinear dynamic characteristics,the lunped mass method was chosen,a torsional nonlinear dynamic model of the gear system was established considering nonlinear factors,such as,gear pairs' time-varying mesh stiffness,gear mesh error and backlash and taking 1. 5 MW wind turbine rated power as the transmission power. The dynamic characteristics of the system were analyzed by using time history figures,FFT frequency spectrum diagrams, phase trajectories, Poincaré sections, bifurcation diagram and largest Lyapunov exponent diagram under variations of excitation frequency and gear mesh error. Results showed that with increase in excitation frequency,there are single periodic motion,quasi periodic one and chaos to appear in the system,the chaotic region also changes; with increase in mesh error,the motion of the system changes from quasi periodic one into chaotic one,and finally it becomes a quasi-single periodic motion; reducing mesh error weakens significantly the chaotic motion.
引文
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[14]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]邱星辉,韩勤锴,褚福磊.风力机行星齿轮传动系统动力学研究综述[J].机械工程学报,2014,50(11):23-36.QIU Xinghui,HAN Qinkai,CHU Fulei.Review on dynamic analysis of wind turbine geared transmission system[J].Journal of Mechanical Engineering,2014,50(11):23-36.
[3]KAHRARMAN A.Free torsional vibration characteristics of compound planetary gear sets[J].Mech Mach Theory,2001,36:953-971.
[4]孙智民,季林红,沈允文.2K-H行星齿轮传动非线性动力学[J].清华大学学报(自然科学版),2003,43(5):636-639.SUN Zhimin,JI Linhong,SHEN Yunwen.Nonlinear dynamics of 2K-H planetary gear train[J].J Tsinghua Univ(Sci&Tech),2003,43(5):636-639.
[5]张慧博,王然,陈子坤,等.考虑多间隙耦合关系的齿轮系统非线性动力学分析[J].振动与冲击,2015,34(8):144-150.ZHANG Huibo,WANG Ran,CHEN Zikun,et al.Nonlinear dynamic analysis of a gear-rotor system with coupled multiclearance[J].Journal of Vibration and Shock,2015,34(8):144-150.
[6]孙涛,沈允文,孙智民,等.行星齿轮传动非线性动力学模型方程[J].机械工程学报,2002,38(3):6-10.SUN Tao,SHEN Yunwen,SUN Zhimin,et al.Study on nonlinear dynamic behavior of planetary gear train dynamic model and governing equations[J].Journal of Mechanical Engineering,2002,38(3):6-10.
[7]孙涛,胡海岩.基于离散傅里叶变换与谐波平衡法的行星齿轮非线性动力学分析[J].机械工程学报,2002,38(11):58-61.SUN Tao,HU Haiyan.Nonlinear dynamics of planetary gear transmission by harmonic balance method based on DFT[J].Journal of Mechanical Engineering,2002,38(11):58-61.
[8]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.
[9]李同杰,朱如鹏,鲍和云,等.行星齿轮系扭转非线性振动建模与运动分岔特性研究[J].机械工程学报,2011,47(21):76-83.LI Tongjie,ZHU Rupeng,BAO Heyun,et al.Nonlinear torsional vibration modeling and bifurcation characteristic study of a planetary gear train[J].Journal of Mechanical Engineering,2011,47(21):76-83.
[10]ZHAO M M,JI J C.Nonlinear torsional vibrations of a wind turbine gearbox[J].Applied Mathematical Modelling,2015,39:4928-4950.
[11]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.Yichang,China:ICECE,2011.
[12]LIN J,PARKER R G.Planetary gear parametric instability caused by mesh variation[J].Journal of Soundand Vibration,2002(1):129-145.
[13]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.
[14]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.