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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 supeiharmonic 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 be 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
CLC No: TH113
国家自然科学基金(50075070)和西北工业大学博士创新基金资助项目. Received 20011008, received in
revised form 20020420 |