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Abstract: A three-degree freedom nonlinear dynamics model of a gear
pair system is established. Since the system’s Jacobi matrix does not
always exist in traditional understanding, then a numerical method for
calculating the greatest Lyapunov exponent is presented directly based
on the definition of Lyapunov exponent. As the system’s chaotic
attractors often have fractal dimension, then the method of how to
calculate the system’s correlation dimension is illuminated and the
system’s correlation dimension is calculated. By comparing the results
with the system phase plot and the Poincaré map, the validities of the
methods to calculate the greatest Lyapunov exponent and the correlation
dimension are proved. On this basis, the system’s dynamic characters are
analyzed by changing the damping ratio, composite error and the backlash
in the system. The system’s bifurcation plots, the greatest Lyapunov
exponent plots and the correlation dimension are given when the
parameter is changing respectively. Then the changing laws of the
system’s numerical characters can be obtained.
Key words: Gear Nonlinear dynamics Lyapunov exponent Correlation
dimension
CLC No: TH113
国家自然科学基金资助项目(50075070).
Received 20020715, received in revised form 20030410
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