Parametric vibration stabilityof locomotivegear transmission system with tooth surface friction
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摘要: 针对机车齿轮传动系统的参数振动问题, 建立了考虑齿面摩擦时机车齿轮传动系统的动力学模型, 基于势能原理获得了齿轮时变啮合刚度, 并利用傅里叶级数展开, 利用多尺度法进行求解, 获得了系统参数振动稳定的边界条件。最后开展实例分析, 研究了齿面摩擦因数对机车齿轮传动系统参数振动稳定性的影响。分析结果表明: 不计齿面摩擦时, 当机车速度约为119.02/j km·h-1 (j是谐波项) 时, 系统会产生参数共振, 摩擦因数越大, 对应的参数共振速度越大; 在参数共振速度附近存在系统振动不稳定区域, 当系统阻尼系数和摩擦因数均为0, 谐波项分别为1、2、3、4时, 相对于参数共振速度的波动值分别为9.16、1.46、0.53、0.55 km·h-1, 系统振动不稳定; 当阻尼系数为0时, 在对应谐波项下, 与摩擦因数为0时相比, 齿面摩擦因数分别为0.1、0.2时, 系统振动不稳定区域内相对于参数共振速度的波动值分别增加了约4.88%、9.54%;当阻尼系数为0.01时, 随着摩擦因数的增大, 在系统振动不稳定区域内相对于参数共振速度的波动值不一定增加; 摩擦因数越大, 系统稳定所需的阻尼系数越小。Abstract: Aiming at solving the problem of parametric vibration of locomotive gear transmission system, the dynamic model of gear transmission system was established considering tooth surface friction.In the model, the time-varying mesh stiffness was obtained based on the potential energy method, fitted by using the technique of Fourier series, and solved by using the method of multiple scales to gain the boundary condition of parametric stable vibration.Finally, a case study was carried out for studying the influence of tooth surface friction on the parametric vibration stability.Analysis result indicates that when the resonance speed is about 119.02/j km·h-1 (j is harmonic term), the prametric vibration will happen under the condition that friction coefficint is 0.The greater the friction coefficient is, the bigger the resonance speed at corresponding harmonic term is.Meanwhile, there exist an unstable vibration region in the vicinity of resonance speed.Under the condition that the damping coefficient and the friction coefficient are 0, when the harmonic terms are 1, 2, 3, 4, respectively, the corresponding fluctuation ranges relative to resonance speeds are about 9.16, 1.46, 0.53, 0.55km·h-1, respectively, so the system is unstable.Under the condition that the damping coefficient is 0, when the friction coefficients are 0.1and 0.2, respectively, compared to the result that the friction coefficient is 0, the fluctuation ranges relative to resonance speeds increase by about4.88%, 9.54%, respectively, with the corresponding harmonic term in unstable vibration regions.But when the damping coefficient is 0.01and the system is unstable, with the increase of friction coefficient, the fluctuation range relative to resonance speeds does not necessarily increase.Furthermore, the larger the friction coefficient is, the smaller the damping coefficient required by the stability of system is.5tabs, 13figs, 30refs.
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Figure 3. Dynamic model of torsional vibration for locomotive gear transmission system
Figure 9. Curves of parametric vibration stability in plane between stiffness ratio and speed
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[1] VAISHYA M, SINGH R. Analysis of periodically varying gear mesh systems with Coulomb friction using Floquet theory[J]. Journal of Sound and Vibration, 2001, 243 (3): 525-545. doi: 10.1006/jsvi.2000.3419 [2] VAISHYA M, SINGH R. Sliding friction-induced nonlinearity and parametric effects in gear dynamics[J]. Journal of Sound and Vibration, 2001, 248 (4): 671-694. doi: 10.1006/jsvi.2001.3818 [3] VELEX P, SAINSOT P. An analytical study of tooth friction excitations in errorless spur and helical gears[J]. Mechanism and Machine Theory, 2002, 37 (7): 641-658. doi: 10.1016/S0094-114X(02)00015-0 [4] LUNDVALL O, STRMBERG N, KLARBRING A. A flexible multi-body approach for frictional contact in spur gears[J]. Journal of Sound and Vibration, 2004, 278 (3): 479-499. doi: 10.1016/j.jsv.2003.10.057 [5] HE Song, GUNDA R, SINGH R. Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness[J]. Journal of Sound and Vibration, 2007, 301 (3-5): 927-949. doi: 10.1016/j.jsv.2006.10.043 [6] HE Song, GUNDA R, SINGH R. Inclusion of sliding friction in contact dynamics model for helical gears[J]. Journal of Mechanical Design, 2007, 129 (1): 48-57. doi: 10.1115/1.2359474 [7] HE Song, CHO S, SINGH R. Prediction of dynamic friction forces in spur gears using alternate sliding friction formulations[J]. Journal of Sound and Vibration, 2008, 309 (3-5): 843-851. doi: 10.1016/j.jsv.2007.06.077 [8] KAR C, MOHANTY A R. An algorithm for determination of time-varying frictional force and torque in a helical gear system[J]. Mechanism and Machine Theory, 2007, 42 (4): 482-496. doi: 10.1016/j.mechmachtheory.2006.04.007 [9] KAR C, MOHANTY A R. Determination of time-varying contact length, friction force, torque and forces at the bearings in a helical gear system[J]. Journal of Sound and Vibration, 2008, 309 (1/2): 307-319. [10] LIU Gang, PARKER R G. Impact of tooth friction and its bending effect on gear dynamics[J]. Journal of Sound and Vibration, 2009, 320 (4/5): 1039-1063. [11] BRETHEE K F, GU Feng-shou, BALL A D. Frictional effects on the dynamic responses of gear systems and the diagnostics of tooth breakages[J]. Systems Science and Control Engineering, 2016, 4: 270-284. doi: 10.1080/21642583.2016.1241728 [12] WANG San-min, SHEN Yun-wen, DONG Hai-jun. Chaos and bifurcation analysis of a spur gear pair with combined friction and clearance[J]. Chinese Journal of Mechanical Engineering, 2002, 38 (9): 8-11. doi: 10.3901/JME.2002.09.008 [13] ZHU En-yong, WU Shi-jing, WANG Xiao-sun, et al. Study on nonlinear dynamic model of planetary gear train sets with friction force[J]. Journal of Vibration and Shock, 2010, 29 (8): 217-220, 236. [14] CHEN Si-yu, TANG Jin-yuan, LUO Cai-wang, et al. Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction[J]. Mechanism and Machine Theory, 2011, 46 (4): 466-478. doi: 10.1016/j.mechmachtheory.2010.11.016 [15] YANG Zheng, SHANG Jian-zhong, LUO Zi-rong. Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness[J]. Journal of Central South University, 2013, 20 (12): 3461-3470. doi: 10.1007/s11771-013-1870-7 [16] JIANG Han-jun, SHAO Yi-min, MECHEFSKE C K. Dynamic characteristics of helical gears under sliding friction with spalling defect[J]. Engineering Failure Analysis, 2014, 39 (4): 92-107. [17] FENG Zhi-heng, WANG Shi-long, LEI Song, et al. Effects of time-varying friction coefficient on hypoidgear dynamics[J]. Journal of Chongqing University, 2011, 34 (12): 9-15. [18] ZHANG Jing, CHEN Bing-kui, KANG Chuan-zhang, et al. Dynamic analysis for spur gears considering friction effect[J]. Journal of Vibration and Shock, 2012, 31 (21): 126-132. [19] LI Wen-liang, WANG Li-qin. CHANG Shan, et al. Impact of tooth surface friction on harmonic resonance of gear system[J]. Journal of Jilin University: Engineering and Technology Edition, 2013, 43 (5): 1290-1294. [20] LI Wen-liang, WANG Li-qin. CHANG Shan, et al. Tooth friction bending effect of helical gear on gear dynamics[J]. Journal of Ship Mechanics, 2013, 17 (8): 937-943. [21] LI Xiao-zhen, ZHU Ru-peng, LI Zheng-min-qing, et al. Influences of frictional coefficient on vibration characteristic of face-gear transmission system[J]. Journal of Vibration Engineering, 2014, 27 (4): 583-588. [22] FENG Hai-sheng, WANG Li-qin, ZHENG De-zhi, et al. Analysis on high power density gear transmission efficiency considering tooth friction[J]. Journal of South China University of Technology: Natural Science Edition, 2014, 42 (9): 24-29. [23] SHENG Dong-ping, ZHU Ru-peng, JIN Guang-hu, et al. Bifurcation characteristic and modeling of transversetorsional spur gear vibration considering friction and multiple clearances[J]. Journal of Aerospace Power, 2015, 30 (2): 498-506. [24] LU Feng-xia, WANG Hao-fei, ZHU Ru-peng, et al. Dynamic characteristics analysis of double helical gear pairs considering teeth surface sliding friction[J]. Journal of Vibration and Shock, 2016, 35 (9): 204-212. [25] YAO Yuan, ZHAO Shi-Yin, XIAO Fei-xiong, et al. The effects of wheelset driving system suspension parameters on the readhesion performance of locomotives[J]. Vehicle System Dynamics, 2015, 53 (12): 1935-1951. doi: 10.1080/00423114.2015.1108446 [26] THEODOSSIADES S, NATSIAVAS S. Non-linear dynamics of gear-pair systems with periodic stiffness and backlash[J]. Journal of Sound and Vibration, 2000, 229 (2): 287-310. doi: 10.1006/jsvi.1999.2490 [27] LI Gui-xian, YU Guang-bin, WEN Jian-min, et al. Method of multiple scales in solving nonlinear dynamic differential equations of gear systems[J]. Journal of Jilin University: Engineering and Technology Edition, 2008, 38 (1): 75-79. [28] CHEN Zai-gang, SHAO Yi-min. Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth[J]. Engineering Failure Analysis, 2011, 18 (8): 2149-2164. [29] CHEN Zai-gang, SHAO Yi-min. Dynamic features of a planetary gear system with tooth crack under different sizes and inclination angles[J]. Journal of Vibration and Acoustics, 2013, 135 (3): 1-12. [30] SAINSOT P, VELEX P, DUVERGER O. Contribution of gear body to tooth deflections-a new bidimensional analytical formula[J]. Journal of Mechanical Design, 2004, 126 (4): 748-752. -
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