微线段齿轮系统动力学特性分析
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摘要
利用有限元法求出了微线段齿轮的时变啮合刚度,考虑微线段齿轮齿廓的特殊性,建立了单自由度微线段齿轮传动系统的动力学模型,模型中考虑了综合误差、时变啮合刚度以及齿侧间隙。通过数值仿真分析了比对两种齿轮系统在不同转速、载荷下的动力学响应,并指出了系统的亚谐共振及其幅值跳跃特性。对比分析了两种齿轮的分叉特性,结果表明,微线段齿轮相比普通渐开线齿轮具有更好的稳定性,其系统的混沌转速区间小,在中高速重载时其系统振动幅值小,传动更加平稳。
Here,the time-varying meshing stiffness of amicro-segment gear pair was calculated by using the finite element method. Considering the particularity of a micro-segment gear's tooth profile,a 1-DOF dynamic model for a micro-segment gear transmission system was built considering comprehensive error,time-varying meshing stiffness and backlash. Through numerical simulation,dynamic responses of amicro-segment gear system and a conventional gear system were analyzed contrastively under different rotating speeds and loads. There were sub-harmonic resonances,amplitude jumping feature,and bifurcation characteristics in the two systems. The studying results indicated that the microsegment gear system has a better stability and a smaller chaotic rotating speed range than the conventional gear system does; the micro-segment gear system has a smaller vibration amplitude and its transmission is more stable under heavy load and medium-high rotating speeds.
Here,the time-varying meshing stiffness of amicro-segment gear pair was calculated by using the finite element method. Considering the particularity of a micro-segment gear's tooth profile,a 1-DOF dynamic model for a micro-segment gear transmission system was built considering comprehensive error,time-varying meshing stiffness and backlash. Through numerical simulation,dynamic responses of amicro-segment gear system and a conventional gear system were analyzed contrastively under different rotating speeds and loads. There were sub-harmonic resonances,amplitude jumping feature,and bifurcation characteristics in the two systems. The studying results indicated that the microsegment gear system has a better stability and a smaller chaotic rotating speed range than the conventional gear system does; the micro-segment gear system has a smaller vibration amplitude and its transmission is more stable under heavy load and medium-high rotating speeds.
引文
[1]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]PARKER R G,VIJAYAKAR S M,IMAJO T.Non-linear dynamic response of a spur gear pair:modelling and experimental comparisons[J].Journal of Sound and Vibration,2000,237(3):435-455.
[3]VAISHYA M,SINGH R.Strategies for modeling friction in gear dynamics[J].Journal of Mechanical Design,2003,125(2):383-393.
[4]陈思雨,唐进元,王志伟,等.修形对齿轮系统动力学特性的影响规律[J].机械工程学报,2014,50(13):59-65.CHEN Siyu,TANG Jinyuan,WANG Zhiwei,et al.Effect of modification on dynamic characteristics of gear transmissions system[J].Journal of Mechanical Engineering,2014,50(13):59-65.
[5]李发家,朱如鹏,鲍和云,等.高重合度与低重合度齿轮系统动力学分岔特性对比分析[J].中南大学学报(自然科学版),2015,46(2):465-471.LI Fajia,ZHU Rupeng,BAO Heyun,et al.Contrastive analysis of dynamic bifurcation characteristics between high contact ratio and low contact ratio gears system[J].Journal of Central South University(Science and Technology),2015,46(2):465-471.
[6]常乐浩,刘更,吴立言.齿轮综合啮合误差计算方法及对系统振动的影响[J].机械工程学报,2015,51(1):123-130.CHANG Lehao,LIU Geng,WU Liyan.Determination of composite meshing errors and its influence on the vibration of gear system[J].Journal of Mechanical Engineering,2015,51(1):123-130.
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[8]KOMORI T,ARIGA Y,NAGATA S.A new gears profile having zero relative curvature at many contact points(Logix Tooth Profile)[J].Journal of Mechanical Design,1990,112(3):430-436.
[9]FENG X Y,AIQUN W,LEE L.Study on the design principle of the Logi X gear tooth profile and the selection of its inherent basic parameters[J].The International Journal of Advanced Manufacturing Technology,2004,24(11/12):789-793.
[10]黄康,赵韩.微线段齿轮与渐开线齿轮的弯曲强度比较分析[J].农业机械学报,2001,32(1):115-117.HUANG Kang,ZHAO Han.Research on bending strength on micro-segment gear compared with involute gear[J].Transactions of the Chinese Society of Agricultural Machinery,2001,32(1):115-117.
[11]黄康,赵韩,蒋小兵.微线段齿轮与渐开线齿轮传动效率对比试验研究[J].机械传动,2002,26(4):3-6.HUANG Kang,ZHAO Han,JIANG Xiaobing.The efficiency comparisonal test research on micro-segments gear and involute gear[J].Journal of Mechanical Transmission,2002,26(4):3-6.
[12]黄康,赵韩,田杰.微线段齿轮与渐开线齿轮温升对比实验研究[J].中国机械工程,2006,17(18):1880-1883.HUANG Kang,ZHAO Han,TIAN Jie.Experimental research on temperature rise comparison between microsegment gear and involute gear[J].China Mechanical Engineering,2006,17(18):1880-1883.
[13]刘鹏,赵韩,黄康,等.基于势能法的微线段齿轮啮合刚度模型研究[J].应用力学学报,2015,32(6):1069-1074.LIU Peng,ZHAO Han,HUANG Kang,et al.Research on meshing stiffness calculation model for micro-sgment gear based on potential energy method[J].Chinese Journal of Applied Mechanics,2015,32(6):1069-1074.
[14]SHEN Yongjun,YANG Shaopu,LIU Xiandong.Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method[J].International Journal of Mechanical Sciences,2006,48(11):1256-1263.
[15]LIN J,PARKER R G.Mesh stiffness variation instabilities in two-stage gear systems[J].Journal of Vibration and Acoustics,2002,124(1):68-76.
[16]常乐浩.平行轴齿轮传动系统动力学通用建模方法与动态激励影响规律研究[D].西安:西北工业大学,2014.
[17]孙涛.行星齿轮系统非线性动力学研究[D].西安:西北工业大学,2000.
[18]XU L,LU M W,CAO Q.Bifurcation and chaos of a harmonically excited oscillator with both stiffness and viscous damping piecewise linearities by incremental harmonic balance method[J].Journal of Sound and Vibration,2003,264(4):873-882.
[19]杨绍普,申永军,刘献栋.基于增量谐波平衡法的齿轮系统非线性动力学[J].振动与冲击,2005,24(3):40-42.YANG Shaopu,SHEN Yongjun,LIU Xiandong.Nonlinear dynamics of gear system based on incremental harmonic balance method[J].Journal of Vibration and Shock,2005,24(3):40-42.
[20]苏程,尹朋朋.齿轮系统非线性动力学特性分析[J].中国机械工程,2011,22(16):1922-1928.SU Cheng,YIN Pengpeng.Analysis of nonlinear dynamics in a spur gear pair system[J].China Mechanical Engineering,2011,22(16):1922-1928.
[21]LAU S L,ZHANG W S.Nonlinear vibrations of piecewiselinear systems by incremental harmonic balance method[J].Journal of Applied Mechanics,1992,59(1):153-160.
[22]KAHRAMAN A,SINGH R.Non-linear dynamics of a spur gear pair[J].Journal of Sound&Vibration,1990,142(1):49-75.
[2]PARKER R G,VIJAYAKAR S M,IMAJO T.Non-linear dynamic response of a spur gear pair:modelling and experimental comparisons[J].Journal of Sound and Vibration,2000,237(3):435-455.
[3]VAISHYA M,SINGH R.Strategies for modeling friction in gear dynamics[J].Journal of Mechanical Design,2003,125(2):383-393.
[4]陈思雨,唐进元,王志伟,等.修形对齿轮系统动力学特性的影响规律[J].机械工程学报,2014,50(13):59-65.CHEN Siyu,TANG Jinyuan,WANG Zhiwei,et al.Effect of modification on dynamic characteristics of gear transmissions system[J].Journal of Mechanical Engineering,2014,50(13):59-65.
[5]李发家,朱如鹏,鲍和云,等.高重合度与低重合度齿轮系统动力学分岔特性对比分析[J].中南大学学报(自然科学版),2015,46(2):465-471.LI Fajia,ZHU Rupeng,BAO Heyun,et al.Contrastive analysis of dynamic bifurcation characteristics between high contact ratio and low contact ratio gears system[J].Journal of Central South University(Science and Technology),2015,46(2):465-471.
[6]常乐浩,刘更,吴立言.齿轮综合啮合误差计算方法及对系统振动的影响[J].机械工程学报,2015,51(1):123-130.CHANG Lehao,LIU Geng,WU Liyan.Determination of composite meshing errors and its influence on the vibration of gear system[J].Journal of Mechanical Engineering,2015,51(1):123-130.
[7]赵韩,梁锦华.微线段齿廓的形成原理及特性[J].机械工程学报,1997,33(5):7-11.ZHAO Han,LIANG Jinhua.Constructing principle and features of tooth profiles with micro-segments[J].Chinese Journal of Mechanical Engineering,1997,33(5):7-11.
[8]KOMORI T,ARIGA Y,NAGATA S.A new gears profile having zero relative curvature at many contact points(Logix Tooth Profile)[J].Journal of Mechanical Design,1990,112(3):430-436.
[9]FENG X Y,AIQUN W,LEE L.Study on the design principle of the Logi X gear tooth profile and the selection of its inherent basic parameters[J].The International Journal of Advanced Manufacturing Technology,2004,24(11/12):789-793.
[10]黄康,赵韩.微线段齿轮与渐开线齿轮的弯曲强度比较分析[J].农业机械学报,2001,32(1):115-117.HUANG Kang,ZHAO Han.Research on bending strength on micro-segment gear compared with involute gear[J].Transactions of the Chinese Society of Agricultural Machinery,2001,32(1):115-117.
[11]黄康,赵韩,蒋小兵.微线段齿轮与渐开线齿轮传动效率对比试验研究[J].机械传动,2002,26(4):3-6.HUANG Kang,ZHAO Han,JIANG Xiaobing.The efficiency comparisonal test research on micro-segments gear and involute gear[J].Journal of Mechanical Transmission,2002,26(4):3-6.
[12]黄康,赵韩,田杰.微线段齿轮与渐开线齿轮温升对比实验研究[J].中国机械工程,2006,17(18):1880-1883.HUANG Kang,ZHAO Han,TIAN Jie.Experimental research on temperature rise comparison between microsegment gear and involute gear[J].China Mechanical Engineering,2006,17(18):1880-1883.
[13]刘鹏,赵韩,黄康,等.基于势能法的微线段齿轮啮合刚度模型研究[J].应用力学学报,2015,32(6):1069-1074.LIU Peng,ZHAO Han,HUANG Kang,et al.Research on meshing stiffness calculation model for micro-sgment gear based on potential energy method[J].Chinese Journal of Applied Mechanics,2015,32(6):1069-1074.
[14]SHEN Yongjun,YANG Shaopu,LIU Xiandong.Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method[J].International Journal of Mechanical Sciences,2006,48(11):1256-1263.
[15]LIN J,PARKER R G.Mesh stiffness variation instabilities in two-stage gear systems[J].Journal of Vibration and Acoustics,2002,124(1):68-76.
[16]常乐浩.平行轴齿轮传动系统动力学通用建模方法与动态激励影响规律研究[D].西安:西北工业大学,2014.
[17]孙涛.行星齿轮系统非线性动力学研究[D].西安:西北工业大学,2000.
[18]XU L,LU M W,CAO Q.Bifurcation and chaos of a harmonically excited oscillator with both stiffness and viscous damping piecewise linearities by incremental harmonic balance method[J].Journal of Sound and Vibration,2003,264(4):873-882.
[19]杨绍普,申永军,刘献栋.基于增量谐波平衡法的齿轮系统非线性动力学[J].振动与冲击,2005,24(3):40-42.YANG Shaopu,SHEN Yongjun,LIU Xiandong.Nonlinear dynamics of gear system based on incremental harmonic balance method[J].Journal of Vibration and Shock,2005,24(3):40-42.
[20]苏程,尹朋朋.齿轮系统非线性动力学特性分析[J].中国机械工程,2011,22(16):1922-1928.SU Cheng,YIN Pengpeng.Analysis of nonlinear dynamics in a spur gear pair system[J].China Mechanical Engineering,2011,22(16):1922-1928.
[21]LAU S L,ZHANG W S.Nonlinear vibrations of piecewiselinear systems by incremental harmonic balance method[J].Journal of Applied Mechanics,1992,59(1):153-160.
[22]KAHRAMAN A,SINGH R.Non-linear dynamics of a spur gear pair[J].Journal of Sound&Vibration,1990,142(1):49-75.