Analytical Optimization of a Rotary Electromagnetic Shunt Damper for Freely Rotating Two Degrees-of-Freedom Torsional Vibration System

Abstract This study explores for the first time the analytical optimization of a rotary electromagnetic shunt damper. Most previous studies on electromagnetic shunt dampers focus on linear DC motors or voice coil motors, with limited exploration of freely rotating torsional vibration systems. Moreover, traditional outcomes from the established fixed-point method for mechanical dynamic vibration absorbers are not directly applicable. This is because the configuration of a spring and a dashpot in the electrical–mechanical analogy of the electromagnetic shunt damper differs from that of an ordinary mechanical dynamic vibration absorber. This article presents an optimization of the resistance and capacitance (or proportional-integral (PI) gain of current control) of the electromagnetic shunt damper for a freely rotating two degrees-of-freedom (2DoF) vibration system with an electromagnetic motor. This article analytically derives a solution that minimizes the peak of the frequency response using the fixed-point method. As a result, we found that there are cases where there are three fixed points of the transfer function or where the gains of two fixed points cannot be aligned. The analytical optimal solution obtained is not one but is divided into two or three cases, depending on the magnitude of the electromechanical coupling. Through numerical examples, this article discusses how the optimal solutions depend on the magnitude of the electromechanical coupling. In the experiment, an electromagnetic shunt damper was realized using a commercially available inverter and electromagnetic motors attached to a 2DoF torsional vibration system, and a damping effect of more than 27 dB was obtained.