Attenuation of Sommerfeld effect in a four DOF vibration system driven by a non-ideal induction motor

Abstract

The Sommerfeld effect is a phenomenon in which a non-ideal prime mover fails to provide enough energy around the resonance speed in a vibration system, resulting in resonance capture and a nonlinear jump. This study discusses the successful techniques for attenuating the Sommerfeld effect in a vibration system with four degrees of freedom (DOFs) driven by a non-ideal induction motor. The kinetic equations of the system are derived using the Lagrange function. Additionally, the mean rotational speed and stability of a non-ideal motor are studied by energy balance and perturbation analysis method. Then, the relationship between electromagnetic torque and motor speed in the Sommerfeld effect is analyzed. The Sommerfeld effect exists near the natural frequencies (NFs) with electrical frequency increased or decreased. The main reason is that the gradually increasing mechanical load power of the vibrating system near the NFs contradicts the finite electromagnetic output power of the non-ideal induction motor. Moreover, the validity of the proposed methods is demonstrated through numerical analysis and simulation. The Sommerfeld effect can be effectively mitigated by appropriately increasing the damping coefficient, reducing the installation distance, and minimizing both the eccentric mass and eccentricity radius of the rotor.