两齿差外啮合双联行星传动的固有特性分析
|
摘要
为揭示两齿差外啮合双联行星传动的固有特性,采用集中参数法建立了该传动系统的平移-扭转耦合动力学数学模型。通过分析各运动构件间的相对位移关系,建立系统运动的微分方程,用Matlab程序计算获得系统的固有频率和主振型。分析结果表明,该行星传动具有中心构件扭转、中心构件平移和行星轮复杂振动模式,且其主振型与一般NGW行星传动有所不同,尤其是行星轮振动模式更为复杂,具有多种不同振动模式。研究结果可为该行星传动方式应用于抛光磨头时防止共振、减振降噪及结构优化提供参考。
An analytical translational-rotational-coupling dynamic model is developed to evaluate the natural characteristics of two teeth difference external compound planet transmission by adopting centralized parameters method.The governing differential equations are established by deriving relative displacement relationships between all motional components,and Matlab is used to calculate and obtain the natural frequencies and free vibration modes of the transmission system.The analysis results show that the vibration modes are classified into rotational mode of the central members,translational mode of the central members and complicate vibration mode of the planetary gears.The vibration modes are different from the NGW planetary transmission,and especially the planetary gears vibration mode are quite complex with several different vibration modes.The research can provide useful reference for preventing resonance,vibration and noise reduction,and structure optimization of the planet transmission mode used in polishing grinding.
An analytical translational-rotational-coupling dynamic model is developed to evaluate the natural characteristics of two teeth difference external compound planet transmission by adopting centralized parameters method.The governing differential equations are established by deriving relative displacement relationships between all motional components,and Matlab is used to calculate and obtain the natural frequencies and free vibration modes of the transmission system.The analysis results show that the vibration modes are classified into rotational mode of the central members,translational mode of the central members and complicate vibration mode of the planetary gears.The vibration modes are different from the NGW planetary transmission,and especially the planetary gears vibration mode are quite complex with several different vibration modes.The research can provide useful reference for preventing resonance,vibration and noise reduction,and structure optimization of the planet transmission mode used in polishing grinding.
引文
[1]边辉.两齿差外啮合行星齿轮传动在刀架中的应用[J].制造技术与机床,2010(11):119-121.BIAN Hui.Application of the two-teeth-difference external planetary gear transmission on turret[J].Manufacturing Technology and Machine Tools,2010(11):119-121.
[2]周哲波,叶友东.新型两齿差外啮合行星传动的等磨损参数的优化模型[J].机械设计,2005,22(9):40-42.ZHOU Zhebo,YE Youdong.Optimization model of equal wearing parameters in the new typed two teeth differenced outer meshing planetary transmission[J].Journal of Machine Design,2005,22(9):40-42.
[3]叶友东,汪选要.一种新型抛光磨头的结构参数优化设计[J].机械传动,2007,31(5):40-42.YE Youdong,WANG Xuanyao.The optimal design of a new polish grinding head's structure[J].Journal of Mechanical Transmission,2007,31(5):40-42.
[4]饶振纲.行星齿轮传动设计[M].北京:化学工业出版社,2003.
[5]LIN J,PARKER R G.Planetary gear parametric instability caused by mesh stiffness vibration[J].Journal of Sound and Vibration,2002,249(1):129-145.
[6]PARKER R G,LIN J.Mesh phasing relationships in planetary and epicyclic gears[J].ASME Journal of Mechanical Design,2004,126(3):365-370.
[7]AMBARISHA V K,PARKER R G.Suppression of planet mode response in planetary gear dynamics through mesh phasing[J].Journal of Vibration and Acoustics,2006,128(2):133-142.
[8]宋轶民,许伟东,张策,等.2K-H行星传动的修正扭转模型建立与固有特性分析[J].机械工程学报,2006,42(5):16-21.SONG Yimin,XU Weidong,ZHANG Ce,et al.Modified torsional model development and natural characteristics analysis of 2K-H epicyclic gearing[J].Journal of Mechanical Engineering,2006,42(5):16-21.
[9]刘欣.基于虚拟样机技术的直齿行星传动动力学研究[D].天津:天津大学,2007.LIU Xin.Study on the Dynamics of Spur Gear Planetary Transmission Based on Virtual Prototyping Technology[D].Tianjin:Tianjin University,2007.
[10]WU X H,PARKER R G.Modal properties of planetary gears with an elastic continuum ring gear[J].ASME Journal of Applied Mechanics,2008,75(5):1-12.
[11]宋轶民,张俊,张君,等.3K-Ⅱ型直齿行星齿轮传动的固有特性[J].机械工程学报,2009,45(7):23-28.SONG Yimin,ZHANG Jun,ZHANG Jun,et al.Inherent characteristics of 3K-Ⅱspur planetary gear trains[J].Journal of Mechanical Engineering,2009,45(7):23-28.
[12]陈世其,赵继云,李炳文,等.超重型刮板输送机行星传动固有特性分析[J].煤炭科学技术,2011,39(11):84-87.CHEN Shiqi,ZHAO Jiyun,LI Bingwen,et al.Analysis on inherent features of planet gear driving in heavy scraper conveyor[J].Coal Science and Technology,2011,39(11):84-87.
[13]王家序,黄超,肖科,等.新型少齿差行星齿轮装置振动特性分析与实验研究[J].振动与冲击,2013,32(5):31-37.WANG Jiaxu,HUANG Chao,XIAO Ke,et al.Vibration performance analysis and experimental research on a new type planetary transmission with small number difference[J].Journal of Vibration and Shock,2013,32(5):31-37.
[14]刘明,赵永强,徐冬梅,等.空间机械臂用多级2K-H行星传动系统模块化动力学研究[J].西北工业大学学报,2014,32(4):606-611.LIU Ming,ZHAO Yongqiang,XU Dongmei,et al.Modular dynamic research on multi-stage planetary gear system[J].Journal of Northwestern Polytechnical University,2014,32(4):606-611.
[15]张俊,刘先增,焦阳,等.基于刚柔耦合模型的行星传动固有特性分析[J].机械工程学报,2014,50(15):104-112.ZHANG Jun,LIU Xianzeng,JIAO Yang,et al.Vibration analysis of planetary gear trains based on a discrete-continuum dynamic model[J].Journal of Mechanical Engineering,2014,50(15):104-112.
[16]王均刚,王勇,霍志璞.风电增速箱行星传动系统动力学方程及均载特性[J].太阳能学报,2015,36(1):26-31.WANG Jungang,WANG Yong,HUO Zhipu.Load sharing behavior and dynamic equations for planetary gear train transmission of wind turbine gearboxs[J].Acta Energiae Solaris Sinica,2015,36(1):26-31.
[17]陶庆,孙文磊,周建星.考虑齿圈柔性的行星传动系统固有特性与灵敏度研究[J].西安交通大学学报,2015,49(3):113-120.TAO Qing,SUN Wenlei,ZHOU Jianxing.Research on inherent characteristics and sensitivities of planetary gear transmission[J].Journal of Xi’an Jiaotong University,2015,49(3):113-120.
[18]叶友东,周哲波.基于SolidWorks/Simulation的两齿差外啮合双联行星传动系统模态分析[J].机械传动,2015,39(11):103-105.YE Youdong,ZHOU Zhebo.Modal analysis of two teeth difference external compound planet gear transmission system based on SolidWorks/Simulation[J].Journal of Mechanical Transmission,2015,39(11):103-105.
[19]张俊,宋轶民,张策,等.NGW型直齿行星传动自由振动分析[J].天津大学学报,2010,43(1):90-94.ZHANG Jun,SONG Yimin,ZHANG Ce,et al.Analysis of free vibration of NGW spur planetary gear set[J].Journal of Tianjin University,2010,43(1):90-94.
[20]张俊,宋轶民.NW型直齿行星传动的动力学建模与固有特性分析[J].天津大学学报,2011,44(8):677-682.ZHANG Jun,SONG Yimin.Dynamic modeling and eigenvalue evaluation of NW spur planetary gear unit[J].Journal of Tianjin University,2011,44(8):677-682.
[21]杨阳,马鹏程,秦大同,等.采煤机差动2K-H行星轮系固有特性分析[J].煤炭学报,2016,41(2):507-512.YANG Yang,MA Pengcheng,QIN Datong,et al.Analysis of natural characteristics of differential 2K-H epicyclic gear train for coal shearer[J].Journal of China Coal Society,2016,41(2):507-512.
[2]周哲波,叶友东.新型两齿差外啮合行星传动的等磨损参数的优化模型[J].机械设计,2005,22(9):40-42.ZHOU Zhebo,YE Youdong.Optimization model of equal wearing parameters in the new typed two teeth differenced outer meshing planetary transmission[J].Journal of Machine Design,2005,22(9):40-42.
[3]叶友东,汪选要.一种新型抛光磨头的结构参数优化设计[J].机械传动,2007,31(5):40-42.YE Youdong,WANG Xuanyao.The optimal design of a new polish grinding head's structure[J].Journal of Mechanical Transmission,2007,31(5):40-42.
[4]饶振纲.行星齿轮传动设计[M].北京:化学工业出版社,2003.
[5]LIN J,PARKER R G.Planetary gear parametric instability caused by mesh stiffness vibration[J].Journal of Sound and Vibration,2002,249(1):129-145.
[6]PARKER R G,LIN J.Mesh phasing relationships in planetary and epicyclic gears[J].ASME Journal of Mechanical Design,2004,126(3):365-370.
[7]AMBARISHA V K,PARKER R G.Suppression of planet mode response in planetary gear dynamics through mesh phasing[J].Journal of Vibration and Acoustics,2006,128(2):133-142.
[8]宋轶民,许伟东,张策,等.2K-H行星传动的修正扭转模型建立与固有特性分析[J].机械工程学报,2006,42(5):16-21.SONG Yimin,XU Weidong,ZHANG Ce,et al.Modified torsional model development and natural characteristics analysis of 2K-H epicyclic gearing[J].Journal of Mechanical Engineering,2006,42(5):16-21.
[9]刘欣.基于虚拟样机技术的直齿行星传动动力学研究[D].天津:天津大学,2007.LIU Xin.Study on the Dynamics of Spur Gear Planetary Transmission Based on Virtual Prototyping Technology[D].Tianjin:Tianjin University,2007.
[10]WU X H,PARKER R G.Modal properties of planetary gears with an elastic continuum ring gear[J].ASME Journal of Applied Mechanics,2008,75(5):1-12.
[11]宋轶民,张俊,张君,等.3K-Ⅱ型直齿行星齿轮传动的固有特性[J].机械工程学报,2009,45(7):23-28.SONG Yimin,ZHANG Jun,ZHANG Jun,et al.Inherent characteristics of 3K-Ⅱspur planetary gear trains[J].Journal of Mechanical Engineering,2009,45(7):23-28.
[12]陈世其,赵继云,李炳文,等.超重型刮板输送机行星传动固有特性分析[J].煤炭科学技术,2011,39(11):84-87.CHEN Shiqi,ZHAO Jiyun,LI Bingwen,et al.Analysis on inherent features of planet gear driving in heavy scraper conveyor[J].Coal Science and Technology,2011,39(11):84-87.
[13]王家序,黄超,肖科,等.新型少齿差行星齿轮装置振动特性分析与实验研究[J].振动与冲击,2013,32(5):31-37.WANG Jiaxu,HUANG Chao,XIAO Ke,et al.Vibration performance analysis and experimental research on a new type planetary transmission with small number difference[J].Journal of Vibration and Shock,2013,32(5):31-37.
[14]刘明,赵永强,徐冬梅,等.空间机械臂用多级2K-H行星传动系统模块化动力学研究[J].西北工业大学学报,2014,32(4):606-611.LIU Ming,ZHAO Yongqiang,XU Dongmei,et al.Modular dynamic research on multi-stage planetary gear system[J].Journal of Northwestern Polytechnical University,2014,32(4):606-611.
[15]张俊,刘先增,焦阳,等.基于刚柔耦合模型的行星传动固有特性分析[J].机械工程学报,2014,50(15):104-112.ZHANG Jun,LIU Xianzeng,JIAO Yang,et al.Vibration analysis of planetary gear trains based on a discrete-continuum dynamic model[J].Journal of Mechanical Engineering,2014,50(15):104-112.
[16]王均刚,王勇,霍志璞.风电增速箱行星传动系统动力学方程及均载特性[J].太阳能学报,2015,36(1):26-31.WANG Jungang,WANG Yong,HUO Zhipu.Load sharing behavior and dynamic equations for planetary gear train transmission of wind turbine gearboxs[J].Acta Energiae Solaris Sinica,2015,36(1):26-31.
[17]陶庆,孙文磊,周建星.考虑齿圈柔性的行星传动系统固有特性与灵敏度研究[J].西安交通大学学报,2015,49(3):113-120.TAO Qing,SUN Wenlei,ZHOU Jianxing.Research on inherent characteristics and sensitivities of planetary gear transmission[J].Journal of Xi’an Jiaotong University,2015,49(3):113-120.
[18]叶友东,周哲波.基于SolidWorks/Simulation的两齿差外啮合双联行星传动系统模态分析[J].机械传动,2015,39(11):103-105.YE Youdong,ZHOU Zhebo.Modal analysis of two teeth difference external compound planet gear transmission system based on SolidWorks/Simulation[J].Journal of Mechanical Transmission,2015,39(11):103-105.
[19]张俊,宋轶民,张策,等.NGW型直齿行星传动自由振动分析[J].天津大学学报,2010,43(1):90-94.ZHANG Jun,SONG Yimin,ZHANG Ce,et al.Analysis of free vibration of NGW spur planetary gear set[J].Journal of Tianjin University,2010,43(1):90-94.
[20]张俊,宋轶民.NW型直齿行星传动的动力学建模与固有特性分析[J].天津大学学报,2011,44(8):677-682.ZHANG Jun,SONG Yimin.Dynamic modeling and eigenvalue evaluation of NW spur planetary gear unit[J].Journal of Tianjin University,2011,44(8):677-682.
[21]杨阳,马鹏程,秦大同,等.采煤机差动2K-H行星轮系固有特性分析[J].煤炭学报,2016,41(2):507-512.YANG Yang,MA Pengcheng,QIN Datong,et al.Analysis of natural characteristics of differential 2K-H epicyclic gear train for coal shearer[J].Journal of China Coal Society,2016,41(2):507-512.