摘要
为了研究时变齿面啮合摩擦、侧隙和啮合刚度对齿轮副非线性振动的影响,以齿轮副啮合线上的相对扭转位移为广义坐标,建立了考虑摩擦、齿侧间隙的直齿圆柱齿轮副非线性动力学模型,采用变步长Runge-Kutta数值积分法求得了系统的周期响应和混沌响应。通过分岔图比较,时变齿侧间隙幅值对系统分岔特性的影响较小,时变摩擦对系统分岔影响较大,摩擦导致系统提前进入和退出混沌。采用FFT对位移频谱分析,发现含有摩擦时系统的超谐和次谐响应成分增多;比较Poincare映射图得出,摩擦使系统混沌吸引子有所变大,但混沌程度有所下降。研究结果为齿轮系统的结构设计和参数选择提供理论依据。
The main factors which caused complex nonlinear vibration in a spur gear pair were tooth surface time-varying friction, time-varying backlash and time-varying mesh stiffness. With the relative displacement of gear meshing line as the generalized coordinates, the dynamic modeling of a spur gear pair was established and the cycle response and chaos response were obtained by 4 ～ 5 order variable step Runge-Kutta numerical method. The analysis of the bifurcation diagram shows that the time-varying backlash amplitude has less effect on the system bifurcation characteristic while the time-varying friction has large effect on the system bifurcation as the friction result in system entering and exiting chaos. And an analysis of displacement response spectrum by FFT shows that the sup-harmonic and sub-harmonic components responses of the system increase with friction. The comparison between two systems under the Poincare map shows that friction makes the chaos attractor bigger, but the chaotic degree decrease.
作者
康军凤
田亚平
KANG Junfeng;TIAN Yaping(Basic Teaching Department, Finance ＆ Trade Vocational College ,Lanzhou 730000, China;School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China)
出处
《钦州学院学报》
2018年第3期8-11,16,共5页
Journal of Qinzhou University
关键词
时变摩擦
时变齿侧间隙
非线性动力学
齿轮副
time-varying frication
time-varying backlash
nonlinear dynamics
gear pair
