星轮偏心误差对浮动式星型齿轮传动动态特性的影响
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摘要
以太阳轮浮动式星型齿轮传动系统为研究对象,基于集中参数理论,建立了星型传动广义动力学模型,建模中考虑了齿轮制造偏心误差、时变啮合刚度以及间隙浮动机构等因素。采用数值解法对系统的动力学微分方程进行求解,获得了系统的受迫振动响应,利用时间历程、相平面、Poincare截面图及Fourier频谱分析了系统的动态特性。着重研究各星轮偏心误差及间隙浮动机构对星型轮系动态特性的影响规律。结果表明:星轮偏心误差增强了系统振动;不同位置、不同数量的星轮偏心误差作用,对应的系统动态响应不同;间隙浮动结构影响了系统的稳定性,不利于振动噪声的控制。
Using the lumped-parameter method,a generalized dynamic model for a star gear transmission system was established considering gear manufacturing eccentric errors and gear pair time-varying mesh stiffness and clearance floating mechanism. The system's dynamic differential equations were solved with the numerical method to get its forced vibration responses. The system's dynamic characteristics were analyzed with time histories,phase plane plots,Poincare maps and Fourier spectral analysis. The effects of star gears ' eccentric errors and clearance floating mechanism on dynamic characteristics of the system were studied. The results showed that star gears eccentric errors enhance the system's vibration; different positions and different numbers of star gears eccentric errors cause different dynamic responses of the system; the clearance floating mechanism affects the stability of the system,it is harmful to vibration and noise control.
Using the lumped-parameter method,a generalized dynamic model for a star gear transmission system was established considering gear manufacturing eccentric errors and gear pair time-varying mesh stiffness and clearance floating mechanism. The system's dynamic differential equations were solved with the numerical method to get its forced vibration responses. The system's dynamic characteristics were analyzed with time histories,phase plane plots,Poincare maps and Fourier spectral analysis. The effects of star gears ' eccentric errors and clearance floating mechanism on dynamic characteristics of the system were studied. The results showed that star gears eccentric errors enhance the system's vibration; different positions and different numbers of star gears eccentric errors cause different dynamic responses of the system; the clearance floating mechanism affects the stability of the system,it is harmful to vibration and noise control.
引文
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[8]刘振皓,巫世晶,王晓笋,等.基于增量谐波平衡法的复合行星齿轮传动系统非线性动力学[J].振动与冲击,2012,31(3):117-122.LIU Zhenhao,WU Shijing,WANG Xiaosun,et al.Nonlinear dynamic of compound planetary gear sets based on incremental harmonic balance method[J].Journal of Vibration and Shork,2012,31(3):117-122.
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[11]GU X,VELEX P.On the dynamic simulation of eccentricity errors in planetary gears[J].Mechanism and Machine Theory,2013,61(1):14-29.
[12]LIGATA H,KAHRAMAN A,SINGH A.An experimental study of the influence of manufacturing errors on the planetary gear stresses and planet load sharing[J].Journal of Mechanical Design,2008,130(4):137-139.
[13]GILL-JEONG C,PARKER R G.Influence of bearing stiffness on the static properties of a planetary gear system with manufacturing errors[J].Journal of Mechanical Science and Technology,2004,18(11):1978-1988.
[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.
[15]王峰,方宗德,李声晋.斜齿轮动力学建模中啮合刚度处理与对比验证[J].振动与冲击,2014,33(6):13-17.WANG Feng,FANG Zongde,LI Shengjin.Treatment and contrast verification of meshing stiffness in dynamic model of helical gear[J].Journal of Vibration and Shork,2014,33(6):13-17.
[16]周建星,刘更,吴立言,等.中心轮浮动式行星传动动态均载性能研究[J].机械科学与技术,2009,28(8):857-861.ZHOU Jianxing,LIU Geng,WU Liyan,et al.Load sharing characteristic of a planetary gear system with load balancing mechanism[J].Mechanical Science and Technology,2009,28(8):857-861.
[2]孙智民,季林红,沈允文,等.齿侧间隙对星型齿轮传动扭振特性的影响研究[J].机械设计,2003,20(2):3-6.SUN Zhimin,JI Linhong,SHEN Yunwen,et al.Influence of backlashes on tosional vibration of star gear train[J].Journal of Machine Design,2003,20(2):3-6.
[3]孙智民,季林红,沈允文.负载对星型齿轮传动动态特性的影响分析[J].机械科学与技术,2003,22(1):94-97.SUN Zhimin,JI Linhong,SHEN Yunwen.Influence of exteral load on dynamic behavior of star gear system[J].Mechanical Science and Technology,2003,22(1):94-97.
[4]鲍和云.两级星型齿轮传动系统分流特性及动力学研究[D].南京:南京航空航天大学,2006.
[5]朱自冰,朱如鹏,鲍和云.两级星型齿轮传动系统非线性动力学研究[J].航空动力学报,2007,22(11):1963-1970.ZHU Zibing,ZHU Rupeng,BAO Heyun.Non-linear dynamic study of 2-stage star gear train[J].Journal of Aerospace Power,2007,22(11):1963-1970.
[6]周璐,巫世晶,李景,等.2K-H行星轮系的平移扭转模型建立与非线性动态特性分析[J].振动与冲击,2016,35(12):71-76.ZHOU Lu,WU Shijing,LI Jing,et al.Establishment of translation and torsional model and nonlinear dynamic characteristic analysis for 2K-H planetary gear trains[J].Journal of Vibration and Shork,2016,35(12):71-76.
[7]石珍,王家序,肖科,等.少齿差行星减速器振动特性仿真与实验研究[J].振动与冲击,2014,33(20):133-139.SHI Zhen,WANG Jiaxu,XIAO Ke,et al.Vibration characteristics simulation and experimental research on a planetary reducer with small tooth number difference[J].Journal of Vibration and Shork,2014,33(20):133-139.
[8]刘振皓,巫世晶,王晓笋,等.基于增量谐波平衡法的复合行星齿轮传动系统非线性动力学[J].振动与冲击,2012,31(3):117-122.LIU Zhenhao,WU Shijing,WANG Xiaosun,et al.Nonlinear dynamic of compound planetary gear sets based on incremental harmonic balance method[J].Journal of Vibration and Shork,2012,31(3):117-122.
[9]CHAARI F,FAKHFAKH T,HBAIEB R,et al.Influence of manufacturing errors on the dynamic behavior of planetary gears[J].The International Journal of Advanced Manufacturing Technology,2006,27(7/8):738-746.
[10]DONG Huimin,ZHANG Kai,WANG Delun,et al.Dynamic modeling of planetary gear train for vibration characteristic analysis[J].Mechanisms,Transmissions and Applications,2015,31:187-195.
[11]GU X,VELEX P.On the dynamic simulation of eccentricity errors in planetary gears[J].Mechanism and Machine Theory,2013,61(1):14-29.
[12]LIGATA H,KAHRAMAN A,SINGH A.An experimental study of the influence of manufacturing errors on the planetary gear stresses and planet load sharing[J].Journal of Mechanical Design,2008,130(4):137-139.
[13]GILL-JEONG C,PARKER R G.Influence of bearing stiffness on the static properties of a planetary gear system with manufacturing errors[J].Journal of Mechanical Science and Technology,2004,18(11):1978-1988.
[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.
[15]王峰,方宗德,李声晋.斜齿轮动力学建模中啮合刚度处理与对比验证[J].振动与冲击,2014,33(6):13-17.WANG Feng,FANG Zongde,LI Shengjin.Treatment and contrast verification of meshing stiffness in dynamic model of helical gear[J].Journal of Vibration and Shork,2014,33(6):13-17.
[16]周建星,刘更,吴立言,等.中心轮浮动式行星传动动态均载性能研究[J].机械科学与技术,2009,28(8):857-861.ZHOU Jianxing,LIU Geng,WU Liyan,et al.Load sharing characteristic of a planetary gear system with load balancing mechanism[J].Mechanical Science and Technology,2009,28(8):857-861.