复杂激励下复合行星传动系统频率耦合与耦合共振研究
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摘要
建立了考虑时变啮合刚度、啮合间隙、啮合误差等多种非线性因素的复合行星传动系统动力学模型,研究了发动机时变转矩输入、定值转矩输入等不同外界激励与多种内部非线性激励同时作用下对复合行星传动系统频率耦合的影响。在此基础上,对外部激励、内部激励以及内外部耦合激励引起的低频、高频以及低高频耦合产生的系统扭转共振问题进行了分析。结果表明:在定值转矩驱动时,齿轮啮合力与主轴剪切力的主要频率成分都为啮频及其倍频;在时变转矩驱动时,齿轮啮合力在各转速下的主要频率成分都为啮合相关频率,而主轴剪切力的主要频率成分随转速提高逐渐由啮合相关频率转变为发动机各谐次频率;系统共振转速带中,由啮合频率及其耦合频率引起的共振转速主要集中于中低速工况,而发动机激励引起的共振转速主要集中于中高速。
Dynamic model of a composite planetary transmission system was built considering multiple nonlinear factors, such as, time-varying meshing stiffness, backlash and meshing error. Influences of different external excitations, such as, time-varying torque input, and constant torque input and multiple internal non-linear excitations on frequency coupling of the composite planetary transmission system were studied. Then, the torsional resonance problems of the system caused by low frequency, high frequency and their coupling under external excitations, internal ones and their coupling were analyzed using the harmonic balance method. The results showed that when the driving torque is constant, the main frequency components of both the gear meshing force and the main shaft's shear force are meshing frequency and its multiplications; when the driving torque is time-varying, the gear meshing force's main frequency components under each rotating speed are meshing related frequencies, while the main shaft shear force's main frequency components with increase in rotating speed vary from meshing related frequencies to all order frequencies of the engine; within the system resonance rotating speed band, resonance rotating speeds excited by meshing frequencies and their coupling frequencies are mainly concentrated in the range of middle-low rotating speed, while those excited by engine excitations are mainly concentrated in the range of middle-high rotating speed.
Dynamic model of a composite planetary transmission system was built considering multiple nonlinear factors, such as, time-varying meshing stiffness, backlash and meshing error. Influences of different external excitations, such as, time-varying torque input, and constant torque input and multiple internal non-linear excitations on frequency coupling of the composite planetary transmission system were studied. Then, the torsional resonance problems of the system caused by low frequency, high frequency and their coupling under external excitations, internal ones and their coupling were analyzed using the harmonic balance method. The results showed that when the driving torque is constant, the main frequency components of both the gear meshing force and the main shaft's shear force are meshing frequency and its multiplications; when the driving torque is time-varying, the gear meshing force's main frequency components under each rotating speed are meshing related frequencies, while the main shaft shear force's main frequency components with increase in rotating speed vary from meshing related frequencies to all order frequencies of the engine; within the system resonance rotating speed band, resonance rotating speeds excited by meshing frequencies and their coupling frequencies are mainly concentrated in the range of middle-low rotating speed, while those excited by engine excitations are mainly concentrated in the range of middle-high rotating speed.
引文
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[4] 肖正明,秦大同,王建宏,等.盾构机主减速器三级行星传动系统扭转动力学[J].中国机械工程,2010,21(18):2176-2182.XIAO Zhengming,QIN Datong,WANG Jianhong,et al.Study on torsional dynamic of 3-stage planetary gears of main reducer used in driving cutterhead of shield tunnelling machine[J].China Mechincal Enigneering,2010,21(18):2176-2182.
[5] SUN W,LI X,WEI J,et al.A study on load-sharing structure of multi-stage planetary transmission system[J].Journal of Mechanical Science and Technology,2015,29(4):1501-1511.
[6] 朱伟林,巫世晶,王晓笋,等.安装误差对变刚度系数的复合行星轮系均载特性的影响分析[J].振动与冲击,2016,35(12):77-85.ZHU Weilin,WU Shijing,WANG Xiaosun,et al.Influence of position errors on the load-sharing characteristics of compound planetary gear sets considering the variable stiffness coefficient[J].Jounal of Vibration and Shock,2016,35(12):77-85.
[7] COOLEY C G,PARKER R G.A Review of planetary and epicyclic gear dynamics and vibrations research[J].Applied Mechanics Reviews,2014,66(4):040804.
[8] SUN T,HU H.Nonlinear dynamics of a planetary gear system with multiple clearances[J].Mechanism and Machine Theory,2003,38(12):1371-1390.
[9] INALPOLAT M,KAHRAMAN A.A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors[J].Journal of Sound and Vibration,2010,329(4):371-393.
[10] 王世宇.基于相位调谐的直齿行星齿轮传动动力学理论与实验研究[D].天津:天津大学,2005.
[11] 杨建明,秦大同.三环减速机的弹性动力学分析[J].机械工程学报,2000,36(10):54-58.YANG Jianming,QIN Datong.Elasto-dynamic analysis of three-ring reducers[J].Chinese Journal of Mechanical Engineering,2000,36(10):54-58.
[12] 刘辉,蔡仲昌,项昌乐.两级行星齿轮传动非线性啮合力频率耦合与动态特性研究[J].振动与冲击,2015,34(19):13-23.LIU Hui,CAI Zhongchang,XIANG Changle.Frequency coupling and dynamic characteristics of nonlinear meshing force for two-stage planetary gears[J].Jounal of Vibration and Shock,2015,34(19):13-23.
[13] MAATAR M,VELEX P.An Analytical expression for the time-varying contact length in perfect cylindrical gears:some possible applications in gear dynamics[J].Journal of Mechanical Design,1996,118(4):586-589.