变参数对少齿差行星减速器振动特性影响及实验
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摘要
建立了一种综合考虑时变啮合刚度、啮合阻尼、啮合误差、齿侧间隙和输入转速等多参数的少齿差行星减速器弯扭耦合非线性动力学模型。分析计算了该减速器的啮合误差激励,根据啮合特性推导出时变啮合刚度,并建立系统多参数、多处非线性和多自由度的动力学微分方程。利用Matlab求解各参数对系统非线性振动特性的影响,最后进行实验进行分析验证不同转速、负载对系统振动特性的影响。结果表明:时变啮合刚度、啮合阻尼、齿轮误差、齿侧间隙及转速对减速器振动影响较大,振动实验结果与仿真分析趋势基本一致,验证仿真分析的正确性。
A transverse-torsional coupled nonlinear dynamic model for a small tooth number difference planetary gear reducer with consideration of the time-varying meshing stiffness, meshing error, meshing damping, gear backlashes and the speed of input was established. Meshing error of the reducer was calculated,according to the meshing characteristics the time-varying mesh stiffness was deduced,and the system dynamic differential equation was established with multiple parameters,multiple nonlinear and multiple degrees of freedom. Matlab was used to solve the effect of variation of parameters to the vibration characteristics of the system; finally,the experiment was conduct to verify the influence of different speed and load on the system vibration characteristics. The results show that the timevarying meshing stiffness,meshing damping,meshing error,gear backlashes and the speed of input have a great influences on reducer,and the trend of experimental results obtained are in good agreement with the calculated,verify the correctness of the simulation analysis.
A transverse-torsional coupled nonlinear dynamic model for a small tooth number difference planetary gear reducer with consideration of the time-varying meshing stiffness, meshing error, meshing damping, gear backlashes and the speed of input was established. Meshing error of the reducer was calculated,according to the meshing characteristics the time-varying mesh stiffness was deduced,and the system dynamic differential equation was established with multiple parameters,multiple nonlinear and multiple degrees of freedom. Matlab was used to solve the effect of variation of parameters to the vibration characteristics of the system; finally,the experiment was conduct to verify the influence of different speed and load on the system vibration characteristics. The results show that the timevarying meshing stiffness,meshing damping,meshing error,gear backlashes and the speed of input have a great influences on reducer,and the trend of experimental results obtained are in good agreement with the calculated,verify the correctness of the simulation analysis.
引文
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[2]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):141-147.
[3]刘斌彬.少齿差传动多齿弹性啮合效应的研究[D].天津:天津大学,2007.
[4]孙智民,沈允文,王三民,等.星型齿轮传动系统的非线性动力学分析[J].西北工业大学学报,2002,20(2):222-226.
[5]Theodossiades S,Natsiavas S.Non-linear dynamics of gear-pair systems with periodic stiffness and backlash[J].J.Sound Vib.,2000,229(2):287-310.
[6]李润方,王建军.齿轮系统动力学-振动、冲击、噪声[M].北京:科学出版社出版社,1997.
[7]Kuang J H,Yang Y T.An estimate of mesh stiffness and load sharing ratio of a spur gear pair[C]//Proceedings of the 6th International Power Transmission and Gearing Conference-Volume 1,ASME DE-Vol.43-1,1992.
[8]Kiekbusch T,Sappok D,Sauer B,et al.Calculation of the combined torsional mesh stiffness of spur gears with two-and three-dimensional parametrical FE models[J].Stroj Vestn-J Mech Eng.,2011,57(13):1246–1251.
[9]唐增宝,钟毅芳.齿轮传动的振动分析与动态优化设计[M].武汉:华中理工大学出版社,1994.
[10]邓四二,贾群义.滚动轴承设计原理[M].北京:中国标准出版社,2008.
[11]http://www.skf.com/cn/zh/products/index.html[OL].2012:12.
[12]Harris Tedric A,Kotzalas Michael N.Rolling bearing analysis(fifth ed.)[M].New York:Taylor&Francis Group,LLC.CRC Press Inc,2006.