Imbalance vibration suppression for asymmetric rotors via an enhanced automatic dynamic balancer

Abstract

Automatic dynamic balancer (ADB) is a passive ball-bearing type of vibration control device and has been applied successfully on some rotating machineries, i.e., hand-held machine tools and optical disk drives. Recently, an enhanced automatic dynamic balancer (EADB) has been developed to extend the capability of the ADB and to achieve a perfect-balancing condition in a wider rotor speed operation range. However, the EADB cannot be applied directly to the imbalance vibration suppression for asymmetric rotors since a multi-frequency whirling limit cycle in the asymmetrically supported rotor/ADB systems prevents the assumed solution of a single-frequency whirling limit cycle for the symmetric supported rotor/ADB systems. To address the aforementioned limitation, this paper proposes an imbalance vibration suppression method for asymmetric rotors via an EADB, which can achieve rotor perfect balancing condition in a wider operation range. The non-autonomous equations of motion for an asymmetrically supported planar rotor with an EADB system is established via Lagrange's method. The perfect-balancing equilibrium of the system is solved analytically, and the multi-frequency whirling limit cycle is obtained via a multi-tone harmonic balance method whose tones are predetermined by the matrix pencil method. To destabilize the multi-frequency whirling limit cycle and to guarantee the stable perfect balancing conditions for an asymmetric rotor with an EADB, a numerical continuation method is adopted to design parameters for the EADB. The stability analysis of the perfect-balancing equilibrium and the multi-frequency whirling limit cycle are conducted by Floquet theory. The enlarged unstable whirling limit cycle solution proves the effectiveness of the proposed method.