Two-dimensional domain structure of dynamical parameters of combining spiral gear transmission
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摘要: 构建了并车螺旋锥齿轮传动含间隙非线性动力学模型,采用变步长Gill数值法对振动方程进行了求解。将胞映射法引入齿轮动力学全局性态域界分析中,获得了动力学参数二维域界解结构。分别考虑了系统在齿侧间隙、综合误差、时变刚度以及阻尼比等参数域界结构中的稳态特性,借助相图、Lyapunov指数(LE)、Poincaré截面、快速傅里叶频谱分析(FFT)等手段研究了齿轮系统在多参数域共同激励下的动态分岔行为,验证了胞映射法在齿轮动力学参数域设计中的准确性。结果表明:当阻尼比ξ∈[0.025,0.225]时,在间隙和综合误差激励下系统均通过倍周期分岔进入混沌;较大阻尼比有助于系统处于稳态周期域中;时变啮合刚度激励下,系统在周期域和混沌域之间发生跃迁,域界附近参数的微小波动将导致吸引子进入另一吸引域中。
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关键词:
- 域界结构 /
- 胞映射法 /
- Lyapunov指数 /
- 分岔 /
- 混沌
Abstract: The nonlinear dynamical model including piecewise backlash was created for combining spiral gear train, the governing equations of motion was solved by employing variant-step Gills numerical algorithm. The cell-mapping technique was put forward to investigate the two dimensional basins of dynamic parameters. Parametric excitations covering the backlash, transmission error, time-varying mesh stiffness and damping ratio, were considered in basin planes in terms of steady solutions. The dynamical bifurcation behavior under the excitation of various parameters was performed by means of the phase portrait, Lyapunov exponent (LE), Poincaré section and fast Fourier transform (FFT). It is validated that Cell-mapping approach is effective in gear dynamic parameter design. The result shows that the system leads to chaos via period-doubling cascades under the backlash and transmission error while large damping ratio within the range ξ∈[0.025,0.225] is beneficial to periodic states of the system. Under the excitation of time-varying mesh stiffness, significant transition between periodic response and chaotic motion was exhibited, small changes nearby parametric domain boundary guided the attracter into another basin of attraction.-
Key words:
- dynamical domain structure /
- cell-mapping technique /
- Lyapunov exponent (LE) /
- bifurcation /
- chaos
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[1] KWON H S,KAHRAMAN A,LEE H K,et al.An automated design search for single and double-planet planetary gear sets[J].Journal of Mechanical Design,2014,136(7):1-13. [2] ERITENEL T,PARKER R G.An investigation of tooth mesh nonlinearity and partial contact loss in gear pairs using a lumped-parameter model[J].Mechanism and Machine Theory,2012,56(1):28-51. [3] FARSHIDIANFAR A,SAGHAFI A.Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems[J].Nonlinear Dynamics,2013,75(4):783-806. [4] 孙智明,沈允文,李素有.封闭行星齿轮传动系统的扭振特性研究[J].航空动力学报,2001,16(2):163-166.SUN Zhimin,SHEN Yunwen,LI Suyou.A study on torsional vibration in an encased differential gear train[J].Journal of Aerospace Power,2001,16(2):163-166.(in Chinese) [5] SUN J Q,HSU C S.Global analysis of nonlinear dynamical systems with fuzzy uncertainties by the cell mapping method[J].Computer Methods in Applied Mechanics and Engineering,1990,83(2):109-120. [6] 唐进元,熊兴波,陈思雨.基于图胞映射方法的单自由度非线性齿轮系统全局特性分析[J].机械工程学报,2011,47(5):59-65.TANG Jinyuan,XIONG Xingbo,CHEN Siyu.Analysis of global character of single degree of freedom nonlinear gear system based on digraph cell mapping method[J].Journal of Mechanical Engineering,2011,47(5):59-65.(in Chinese) [7] 刘宏,王三民,刘海霞.弹性支承下弧齿锥齿轮系统参数平面中的域界结构研究[J].振动与冲击,2010,29(12):173-176.LIU Hong,WANG Sanmin,LIU Haixia.Domain boundary structure in param eter plane of a spiral bevel gear system with elastic supports[J].Journal of Vibration and Shock,2010,29(12):173-176.(in Chinese) [8] 刘梦军,沈允文,董海军.齿轮系统参数对全局特性影响的研究[J].机械工程学报,2004,40(11):58-63.LIU Mengjun,SHEN Yunwen,DONG Haijun.Research on the affection of the gear system parameters on the global character[J].Journal of Mechanical Engineering,2004,40(11):58-63.(in Chinese) [9] FARSHIDIANFAR A,SAGHAFI A.Bifurcation and chaos prediction in nonlinear gear systems[J].Shock and Vibration,2014,79(3):1-8. [10] GOU Xiangfeng,ZHU Lingyun,CHEN Dailin.Bifurcation and chaos analysis of spur gear pair in two-parameter plane[J].Nonlinear Dynamics,2015,79(3):2225-2235. [11] 贺群,徐伟,方同,等.Duffing系统随机分岔的全局分析[J].力学学报,2003,35(4):452-460.HE Qun,XU Wei,FANG Tong,et al.Global analysis of stochastic bifurcation for doffing systems[J].Acta Mechanica Sinica,2003,35(4):452-460.(in Chinese) [12] LING Hong,SUN Jianqiao.Bifurcations of fuzzy nonlinear dynamical systems[J].Communications in Nonlinear Science and Numerical Simulation,2006,11(1):1-12. [13] GUO Y,PARKER R G.Dynamic analysis of planetary gears with bearing clearance[J].Journal of Computational and Nonlinear Dynamics,2012,7(4):614-620. [14] PARKER R G,WU X H.Vibration modes of planetary gears with unequally spaced planets and an elastic ring gear[J].Journal of Sound and Vibration,2010,329(11):2265-2275. [15] Celso G,Edward O,James A.et al.Sudden changes in chaotic attractors,and transient chaos[J].Physica D:Nonlinear Phenomena,1983,7(1):181-200. [16] GE Z M,LEE S C.A modified interpolated cell mapping method[J].Journal of Sound and Vibration,1997,199(2):189-206. [17] WOLF A,SWIFT J B,SWINNEY H L,et al.Determining Lyapunov exponents from a time series[J].Physica D:Nonlinear Phenomena,1985,16(3):285-317. [18] CHANG-JIAN C W.Bifurcation and chaos of gear-rotor-bearing system lubricated with couple-stress fluid[J].Nonlinear Dynamics,2015,79(1):749-763.
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