Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions |
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| Authors: | Zhao Chun-Yu Zhang Yi-Min and Wen Bang-Chun |
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| Affiliation: | School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China |
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| Abstract: | We derive the non-dimensional coupling equation of two
exciters, including inertia coupling, stiffness coupling and load
coupling. The concept of general dynamic symmetry is proposed to
physically explain the synchronisation of the two exciters, which
stems from the load coupling that produces the torque of general
dynamic symmetry to force the phase difference between the two
exciters close to the angle of general dynamic symmetry. The
condition of implementing synchronisation is that the torque of
general dynamic symmetry is greater than the asymmetric torque of
the two motors. A general Lyapunov function is constructed to derive
the stability condition of synchronisation that the non-dimensional
inertia coupling matrix is positive definite and all its elements are
positive. Numeric results show that the structure of the vibrating
system can guarantee the stability of synchronisation of the two
exciters, and that the greater the distances between the
installation positions of the two exciters and the mass centre of
the vibrating system are, the stronger the ability of general
dynamic symmetry is. |
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| Keywords: | synchronisation vibrating system symmetry stability |
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