车辆行星齿轮啮合刚度的建模及分析研究
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摘要
齿轮副啮合刚度的周期性变化是行星齿轮传动系统产生振动的主要内部激励,深入研究齿轮的啮合刚度对解明齿轮系统的振动特征具有重要意义。采用能量法、有限元法和矩形波法分别建立了行星齿轮啮合刚度激励模型,并采用这3种模型分别求解了太阳轮、行星轮以及行星轮齿圈综合啮合刚度,对比了这3种模型求解啮合刚度的优劣。结果表明,3种刚度激励下的复合行星排各个构件的振动加速度幅值相差很小,且有限元法计算得到的振动加速度幅值稍大于解析法计算得到的振动加速度幅值,矩形波法计算得到的加速度幅值最小。
The periodical variation of meshing stiffness of the gear pair is the main internal excitation of the vibration generated by the planetary gear transmission system. It is of great significance to deeply study the meshing stiffness of the gear system for the vibration characteristics of the gear system. The energetic method,the finite element method and the rectangular wave method are used to establish the meshing stiffness model of planetary gears respectively. These three models are used to solve the integrated meshing stiffness of the solar wheel,planetary gear and internal ring gear respectively. Then,the advantages and disadvantages of these three models for calculating mesh stiffness are compared. The results show that the vibration acceleration amplitudes of compound planet gear members under these three kinds of stiffness excitations have a small difference. The amplitude of vibration acceleration calculated by the finite element method is slightly larger than that calculated by the analytical method,and the amplitude of the acceleration calculated by the rectangular wave method is the smallest.
The periodical variation of meshing stiffness of the gear pair is the main internal excitation of the vibration generated by the planetary gear transmission system. It is of great significance to deeply study the meshing stiffness of the gear system for the vibration characteristics of the gear system. The energetic method,the finite element method and the rectangular wave method are used to establish the meshing stiffness model of planetary gears respectively. These three models are used to solve the integrated meshing stiffness of the solar wheel,planetary gear and internal ring gear respectively. Then,the advantages and disadvantages of these three models for calculating mesh stiffness are compared. The results show that the vibration acceleration amplitudes of compound planet gear members under these three kinds of stiffness excitations have a small difference. The amplitude of vibration acceleration calculated by the finite element method is slightly larger than that calculated by the analytical method,and the amplitude of the acceleration calculated by the rectangular wave method is the smallest.
引文
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[9]石照耀,康焱,林家春.基于齿轮副整体误差的齿轮动力学模型及其动态特性[J].机械工程学报,2010,46(17):55-61.
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[11]杨长辉,徐涛金,许洪斌,等.基于Weber能量法的直齿轮时变啮合刚度数值计算[J].机械传动,2015,39(2):59-62.
[12]刘国华,李亮玉.含间隙和时变啮合刚度的渐开线齿轮副齿廓修形研究[J].中国机械工程,2007,18(12):1409-1413.
[2]邓晓龙,朱大林,方子帆.三自由度串联行星变速箱传动方案设计的图论法[J].机械传动,2002,26(2):11-13.
[3]李亚熙,马彪,李和言,等.应用齿形制动器的行星变速箱换挡特性研究[J].机械传动,2017,41(12):49-53.
[4]崔玲丽,张飞斌,康晨晖,等,等.故障齿轮啮合刚度综合计算方法[J].北京工业大学学报:2013,39(3):353-358.
[5] YANG D C H,LIN J Y. Hertzian damping,tooth friction and bendingelasticity in gear impact dynamics[J]. Journal of Mechanisms,Transmissions and Automation in Design,1987,109(2):189-196.
[6] CHEN Z G,SHAO Y M. Dynamic simulation of spur gear withtooth root crack propagating along tooth width and crack depth[J]. Engineering Failure Analysis,2011,18(8):2149-2164.
[7] CHAARI F,FAKHFAKH T,HADDAR M. Analytical modelling of spurgear tooth crack and influence on gearmesh stiffness[J]. European Journal of Mechanics-A/Solids,2009,28(3):461-468.
[8]唐进元,蒲太平.基于有限元法的螺旋锥齿轮啮合刚度计算[J].机械工程学报,2011,47(11):23-29.
[9]石照耀,康焱,林家春.基于齿轮副整体误差的齿轮动力学模型及其动态特性[J].机械工程学报,2010,46(17):55-61.
[10]韩勤锴,王建军,李其汉.考虑延长啮合时齿轮副啮合刚度模型[J].机械科学与技术,2009,28(1):52-55.
[11]杨长辉,徐涛金,许洪斌,等.基于Weber能量法的直齿轮时变啮合刚度数值计算[J].机械传动,2015,39(2):59-62.
[12]刘国华,李亮玉.含间隙和时变啮合刚度的渐开线齿轮副齿廓修形研究[J].中国机械工程,2007,18(12):1409-1413.