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Abstract: The spiral bevel gears supported by rotor exhibit
emblematical phenomena of nonlinear dynamical system, such as
bifurcation, chaos and quasi-periodic response etc, and the nonlinear
frequency response characteristics of a spiral bevel gear system are
numerically examined. An eight degree freedom dynamic model is developed
which includes non-linearities associated with backlash and time-varying
meshing stiffness. The equations of coupled torsional, lateral and
longitudinal motion of the spiral bevel gear system are simplified by
defining dynamic relative transmission error, and rewritten into state
equations by introducing the state variables. With A-operator method, a
numerical algorithm is put forward, and the dynamical responses of the
geared system with harmonic internal excitation and parameter excitation
are obtained.. Numerical results show that, the system goes through the
period doubling route to chaos with change of the meshing frequency, and
through Hopf bifurcation to chaos with change of bearing stiffness.
Furthermore, the phenomena of jump always occur for different supporting
system.
Key words: Non-linear vibration Spiral bevel gear A-operator
method Chaotic vibration
CLC No: O321
V216.21
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 20020109, received in
revised form 20020720
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