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Volume 51 Issue 5
Sep.  2019
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Shi Jianfei, Gou Xiangfeng, Zhu Lingyun. RESEARCH ON MULTI-STABILITY CHARACTERISTICS OF GEAR TRANSMISSION SYSTEM WITH TWO-SPACE COUPLING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1489-1499. DOI: 10.6052/0459-1879-19-093
Citation: Shi Jianfei, Gou Xiangfeng, Zhu Lingyun. RESEARCH ON MULTI-STABILITY CHARACTERISTICS OF GEAR TRANSMISSION SYSTEM WITH TWO-SPACE COUPLING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1489-1499. DOI: 10.6052/0459-1879-19-093
shu

RESEARCH ON MULTI-STABILITY CHARACTERISTICS OF GEAR TRANSMISSION SYSTEM WITH TWO-SPACE COUPLING

  • School of Mechanical Engineering, Tiangong University, Tianjin 300387, China

  • Tianjin Key Laboratory of Modern Mechatronics Equipment Technology, Tiangong University, Tianjin 300387, China

  • Received Date: April 14, 2019
    Graphical Abstract
    • Abstract
  • By defining the system parameters as parameter variables and forming the parameter space, the nonlinear global dynamics of the gear transmission system under the coupling of parameter space and state space are studied in detail in this work. The correlative relationship between multiple parameters, multiple initial values and multiple stable behaviors is also obtained. Firstly, a method for calculating and identifying the multi-stable behavior of a nonlinear system under the coupling of two spaces is designed. Secondly, based on the designed method and combined with phase diagram, Poincaré map, bifurcation diagram, top Lyapunov exponent and basin of attraction, the existence and distribution of multi-stable behavior for the gear transmission system in different parameter planes are investigated numerically to better understand the motion mechanism of the system. In addition, the distribution characteristic of multi-stable behavior in the state plane is also studied on the base of the cell-to-cell mapping method. The multi-stable behavior and bifurcation that may be hidden in the parametric plane and the state plane are fully revealed. The formation mechanism of multi-stable behavior is analyzed as well. The results show that there are a large number of multiple stable behaviors which are banded distribution in the parametric planes of the gear system under the coupling of two spaces. Two different erosion phenomena, such as internal erosion and boundary erosion, are clearly observed in the state plane. The sensitivity of bifurcation points or bifurcation curves to initial values leads to the occurrence of multi-stable behavior. When the amplitude of backlash or error fluctuation changes in a small range, the global dynamic characteristics of the gear system are less affected by the backlash or error disturbance. However, the global dynamic characteristics are greatly affected by the meshing frequency. Global dynamic characteristics of the gear system become rich and complex under two-space coupling.
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  • [1] Kahraman A, Singh R . Interactions between time-varying mesh stiffness and clearance nonlinearities in a geared system. Journal of Sound and Vibration, 1991,146:135-156
    [2] Liu F, Jiang H, Liu S , et al. Dynamic behavior analysis of spur gears with constant & variable excitations considering sliding friction influence. Journal of Mechanical Science & Technology, 2016,30(12):5363-5370
    [3] Yoon JY, Kim B . Gear rattle analysis of a torsional system with multi-staged clutch damper in a manual transmission under the wide open throttle condition. Journal of Mechanical Science and Technology, 2016,30(3):1003-1019
    [4] Wei S, Han QK, Dong XJ , et al. Dynamic response of a single-mesh gear system with periodic mesh stiffness and backlash nonlinearity under uncertainty. Nonlinear Dynamics, 2017,89(1):49-60
    [5] Saghafi A, Farshidianfar A . An analytical study of controlling chaotic dynamics in a spur gear system. Mechanism and Machine Theory, 2016,96:179-191
    [6] 陈思雨, 唐进元 . 间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响. 机械工程学报, 2009,45(8):119-124
    [6] ( Chen Siyu, Tang Jinyuan . Effect of backlash on dynamics of spur gear pair system with friction and time-varying stiffness. Chinese Journal of Mechanical Engineering, 2009,45(8):119-124 (in Chinese))
    [7] Farshidianfar A, Saghafi A . Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis. Physics Letters A, 2014,378(46):3457-3463
    [8] Kaslik E, Balint St . Bifurcation analysis for a two-dimensional delayed discrete-time Hopf field neural network. Chaos, Solitons and Fractals, 2007,34:1245-1253
    [9] Peng MS, Jiang ZH , Jiang, XX. Multi-stability and complex dynamics in a simple discrete economic model. Chaos Solitons and Fractals, 2009,41:671-687
    [10] Algaba A, Gamero E, Rodrguez AJ . A bifurcation analysis of a simple electronic circuit. Communications in Nonlinear Science and Numerical Simulation, 2005,10:169-178
    [11] Yi N, Zhang QL, Liu P , et al. Codimension-two bifurcations analysis and tracking control on a discrete epidemic model. Journal of Systems Science and Complexity, 2011,24:1033-1056
    [12] Luo GW, Shi YQ, Zhu XF , et al. Hunting patterns and bifurcation characteristics of a three-axle locomotive bogie system in the presence of the flange contact nonlinearity. International Journal of Mechanical Sciences, 2018,136:321-338
    [13] Luo GW, Lv XH, Zhu XF , et al. Diversity and transition characteristics of sticking and non-sticking periodic impact motions of periodically forced impact systems with large dissipation. Nonlinear Dynamics, 2018,1:1-33
    [14] 吕小红, 罗冠炜 . 冲击渐进振动系统相邻基本振动的转迁规律. 力学学报, 2017,49(5):1091-1102
    [14] ( Lü Xiaohong, Luo Guanwei . Transition law of adjacent fundamental motions in vibro-impact system eith progression. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(5):1091-1102 (in Chinese))
    [15] 乐源 . 一类碰撞振动系统在内伊马克沙克--音叉分岔点附近的局部两参数动力学. 力学学报, 2016,48(1):163-172
    [15] ( Yue Yuan . Local dynamical behavior of two-parameter family near the neimark-sacker-pitchfork bifurcation point in a vibro-impact system. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(1):163-172 (in Chinese))
    [16] Shi JF, Zhang YL, Gou XF . Bifurcation and evolution of a forced and damped Duffing system in two-parameter plane. Nonlinear Dynamics, 2018,93:749-766
    [17] Mason JF, Piiroinen PT . Saddle-point solution and grazing bifurcation in an impacting system. Chaos, 2012,22(1):1-6
    [18] Mason JF, Piiroinen PT . The effect of codimension-two bifurcation on the global dynamics of a gear model. Journal on Applied Dynamical Systems, 2009,8(4):1694-1711
    [19] Xiang L, Gao N, Hu A . Dynamic analysis of a planetary gear system with multiple nonlinear parameters. Journal of Computational and Applied Mathematics, 2018,327:325-340
    [20] Gou X, Zhu L, Chen D . Bifurcation and chaos analysis of spur gear pair in two-parameter plane. Nonlinear Dynamics, 2015,79:2225-2235
    [21] 郜志英, 沈允文, 董海军 等. 齿轮系统参数平面内的分岔结构. 机械工程学报, 2006,42(4):68-72
    [21] ( Gao Zhiying, Shen Yunwen, Dong Haijun , et al. Bifurcation structure in parameter plane of gear system. Chinese Journal of Mechanical Engineering, 2006,42(4):68-72 (in Chinese))
    [22] 林何, 王三民, 董金城 . 并车螺旋锥齿轮传动动力学参数二维域界结构分析. 航空动力学报, 2017,32(8):2017-2024
    [22] ( Lin He, Wang Sanmin, Dong Jincheng . Two-dimensional domain structure of dynamical parameters of combining spiral gear transmission. Journal of Aerospace Power, 2017,32(8):2017-2024 (in Chinese))
    [23] 苟向锋, 陈代林 . 双参变量下齿轮--转子系统扭转振动特性分析. 工程力学. 2014,31(11):211-216
    [23] ( Gou Xiangfeng, Chen Dailin . Dynamic analysis on torsional vibration of gear-rotor system in two parameters plane. Engineering Mechanics, 2014,31(11):211-216 (in Chinese))
    [24] Guo Y, Parker RG . Dynamic Analysis of Planetary Gears With Bearing Clearance. Journal of Computational and Nonlinear Dynamics, 2012,7(4):04100201-04100215
    [25] Mason JF, Piiroinen PT, Wilson RE , et al. Basins of attraction in non-smooth models of gear rattle. International Journal of Bifurcation and Chaos, 2009,19:203-224
    [26] Li QH, Lu QS . Coexisting periodic orbits in vibro-impacting dynamical systems. Appl. Math. Mech., 2003,24:261-273
    [27] 夏雨, 毕勤胜, 罗超 等. 双频1: 2激励下修正蔡氏振子两尺度耦合行为. 力学学报, 2018,50(2):362-372
    [27] ( Xia Yu, Bi Qinsheng, Luo Chao , et al. Behaviors of modified Chua's oscillator two time scales under two excitatoins with frequency ratio at 1: 2. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):362-372 (in Chinese))
    [28] 陈振阳, 韩修静, 毕勤胜 . 离散达芬映射中由边界激变所诱发的复杂的张弛振荡. 力学学报, 2017,49(6):1380-1389
    [28] ( Chen Zhenyang, Han Xiujing, Bi Qinsheng . Complex relaxation oscillation triggered by boundary crisis in the discrete Duffing map. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(6):1380-1389 (in Chinese))
    [29] Jafari S, Pham VT, Golpayegani SMRH , et al. The relationship between chaotic maps and some chaotic systems with hidden attractors. International Journal of Bifurcation and Chaos, 2016,26:650211
    [30] Zhao HT, Lin YP, Dai YX . Hopf bifurcation and hidden attractors of a delay-coupled Duffing oscillator. International Journal of Bifurcation and Chaos, 2015,25:1550162
    [31] Shi JF, Gou XF, Zhu LY . Bifurcation and erosion of safe basin for a spur gear system. International Journal of Bifurcation and Chaos, 2018,28(14):1830048301
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