Energy-based analysis and experiment for self-synchronization of two rotors installed in two-DOF translational system

An energy-based analysis for the self-synchronization of two unbalanced rotors installed in a two-DOF platform, a vibrating system with translational degrees of freedom, was performed to examine the effects of anisotropy in the vibration properties of the platform and the relative rotational directions of the rotors. Based on two conditional energy equations that were extended in the present study to apply to this system, two types of approximate analyses were formulated. One of the analyses, which was based on the solution to the set of conditional equations, revealed that the small anisotropy of the platform widens the synchronizable voltage range for co-rotating rotors, while it narrows this range for counter-rotating rotors. The other analysis, which was based on the analytical expressions for the boundaries of parameter regions satisfying each conditional equation, provided a clear understanding and theoretical predictions for the above parametric effects. The validity of the energy-based analysis as well as the analytical model was verified by comparing the analytical results not only with accurate numerical results but also with results from an experimental apparatus.