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 Chin. Phys. B, 2010, Vol. 19(3): 030301    DOI: 10.1088/1674-1056/19/3/030301
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# Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions

Zhao Chun-Yu(赵春雨), Zhang Yi-Min(张义民), and Wen Bang-Chun(闻邦椿)
School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China
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.
Keywords:  synchronisation      vibrating system      symmetry      stability
Received:  20 November 2008      Revised:  15 October 2009      Accepted manuscript online:
 PACS: 45.20.da (Forces and torques) 45.80.+r (Control of mechanical systems) 45.20.dc (Rotational dynamics) 02.30.Yy (Control theory)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.~50535010 and 10702014), the Project of Liaoning Province Science (Grant No. 2008S095) and the National High Technology Research and Development Program of China (Grant No.~2007AA04Z442).