Analysis of Nonlinear Dynamics in a Spur Gear Pair System

Abstract

Abstract:

A nonlinear dynamics model for a spur gear pair system was established where the backlash, the time-varying stiffness and the transmission error were considered. The nonlinear single-degree-of-freedom equations were solved by employing variable step size Runge-Kutta integration method. The nonlinear dynamics characteristics of the system were discussed for different system parameters and classified based on bifurcation diagrams, phase portraits, Poincaré maps and Fourier spectra. The chaotic motion was obtained. By means of analyzing the variation law of dynamic load, the relations between transformation process and backlash in the engaging state, which varies among the states of non-impact, single sided impact and double-sided impact, of gear system were discussed.

Key words:

nonlinear dynamics, chaos, bifurcation, dynamic load

摘要：

综合考虑齿侧间隙、时变啮合刚度、综合啮合误差等因素，建立了直齿轮副单自由度非线性动力学模型，并利用变步长Runge-Kutta法对单自由度运动微分方程进行了数值求解。结合系统的分岔图、相图、Poincaré映射图以及FFT频谱图，分析了系统在参数变化时的动力学特性，得到了系统的混沌运动规律。结合齿轮的动载荷历程，得到了齿轮啮合冲击状态在非冲击、单边冲击以及双边冲击状态之间变化时变化过程与系统参数之间的关系。

关键词:

非线性动力学, 混沌, 分岔, 动载荷

CLC Number:

null

SU Cheng, YIN Peng-Peng.

Analysis of Nonlinear Dynamics in a Spur Gear Pair System

[J]. China Mechanical Engineering, 2011, 22(16): 1922-1928.

苏程, 尹朋朋.

齿轮系统非线性动力学特性分析

[J]. 中国机械工程, 2011, 22(16): 1922-1928.

References

[1]Kahraman A, Singh R. Non--linear Dynamics of a Spur Gear Pair[J]. Journal of Sound and Vibration, 1990, 142(1):49-75.
[2]Vinayak H, Singh R, Padmanabhan C. Linear Dynamic Analysis of Multi--mesh Transmissions Containing External Rigid Gears[J]. Journal of Sound and Vibration, 1995,185 ( 1 ) : 1-32.
[3]王三民,沈允文,董海军.含摩擦和间隙直齿轮副的混沌与分叉研究[J].机械工程学报,2002,38(9):8-11. 1
[4]王立华[1],李润方[2],林腾蛟[2],杨成云[3].齿轮系统时变刚度和间隙非线性振动特性研究[J].中国机械工程,2003,14(13):1143-1146.
[5]王晓笋[1],巫世晶[1],周旭辉[2],李群力[1].含侧隙非线性齿轮传动系统的分岔与混沌分析[J].振动与冲击,2008,27(1):53-56.
[6]李明,孙涛,胡海岩.齿轮传动转子—轴承系统动力学的研究进展[J].振动工程学报,2002,15(3):249-256.
[7]Joanna M, Martin H, Eddie W R. Mathematical Models of Gear Rattle in Roots Blower Vacuum Pumps[J].Journal of Sound and Vibration, 2007, 308(3/5): 431-440.
[8]Gianluca L, Marcello M, Carlo R. Modelling of an Automated Manual Transmission System [J]. Mechatronics, 2007, 17(2/3): 73-91.
[9]Naji A R M, Hasan M. Mathematical and Physical Modelling of Bubble Growth Due to Ultrasound[J]. Applied Mathematical Modelling, 2004, 28(4): 333 -351.
[10]Albert C J L, Chen Lidi. Periodic Motions and Grazing in a Harmonically Forced, Piecewise, Linear Oscillator with Impacts[J]. Chaos, Soiltons & Fractals, 2005, 24(2): 567-578.
[11]Sun Tao, Hu Haiyan. Nonlinear Dynamics of a Planetary Gear System with Multiple Clearances [J]. Mechanism and Machine Theory, 2003, 38 (12) : 1371-1390.
[12]Giorgio B, Francesco P. Non--smooth Dynamics of Spur Gears with Manufacturing Errors [J]. Journal of Sound and Vibration, 2007, 306(1/2) :271-283.
[13]Wang Jianjun, I.i Runfang, Peng Xianghe. A Survey to Non--linear Vibration of Gear Transmission System [J]. Apple. Mech. Rev. , 2003, 56 (3) :309-329.
[14]孙智民,沈允文,李华,董海军.星型齿轮传动系统定常与奇怪吸引子的共存现象[J].振动工程学报,2003,16(2):242-246.
[15]Kahraman A, Singh R. Interactions Between Time -varying Mesh Stiffness and Clearance Non-linearities in a Geared System[J]. Journal of Sound and Vibration,1991,146(1) : 135-156.