关键词: 齿轮副, 非线性动力学, 分叉, 混沌

Abstract: In order to explain the complex non-linear phenomena in a spur gear pair with combined frictional excitation and clearance type non-linearity, such as sub-and supeihar-monic motions, chaotic vibration and coexisting limit cycles, a dynamic model is developed, in which non-linearities associated with frictional force on tooth faces, backlash and time-varying gear meshing stiffness are considered, A fifth-sixth order Runge-Kuttn numerical integration algorithm with variable time step was used here, The influence of the frictional forces upon the chaos and bifurcation are investigated by means of phase plots, Poincar6 maps, FFT spectra, Lyapunov exponents and bifurcation diagrams. On the basis of numerous numerical results, the following conclusions- are obtained) (1) The sub- and superharmonic motions can bo observed in the gear pair with friction and backlash. (2) With increasing frictional coefficient, the strange attractor becomes big and Lyapunov exponents get small. (3) The period-doubling route to chaos is found in the gear pair with friction and backlash, the chaos appears early and infirmly.

Key words: Nonlinear dynamics Chaos Bifurcation Gear pair