Rotor balancing via an enhanced automatic dynamic balancer with inductively coupled shunt circuit

Despite the elegant nature of the automatic balancing principle for passive imbalance vibration control, the co-existence of undesired whirling limit-cycles is a major impediment to the more widespread application of automatic dynamic balancing devices also called automatic dynamic balancer (ADB) in industry. To enlarge the region of stable perfect balancing and to eliminate whirling limit-cycles, we develop an innovative enhanced ADB system. This new idea harnesses the automatic balancing principle via moving permanent magnet balancer masses which are inductively coupled to a parallel resistor-inductor-capacitor (RLC) circuit. It is found that the circuit parameters can be adjusted properly to suppress the whirling limit-cycle to enlarge the perfect balancing region. We start from a Lagrangian description of the system and get nonlinear autonomous equations-of-motion. We then solve two dominant steady-state solutions for the enhanced ADB system. One solution is for the perfect balancing equilibrium points (EPs), which can be solved analytically. While the other solution is for the whirling limit-cycle which is solved via a harmonic balance method. The stability of these solutions is then evaluated through eigenvalue analysis and Floquet theory. The newly involved electrical parameters, such as coupling coefficient, equivalent capacitance, and equivalent resistance, are designed via an arc-length continuation method to destabilize the limit-cycle solutions to then guarantee stable rotor balancing.