Sommerfeld Effect Attenuation Using Switched-Stiffness Method of a Non-ideal Internally Damped Shaft–Disk System with Constant Eccentricity

TLDR: In this paper, a semi-active control scheme based on switched-stiffness method is employed to attenuate the Sommerfeld effect of a eccentric shaft-disk system driven by a brushed DC motor.

Abstract: Internally, damped shaft–disk system when driven by a non-ideal power source, i.e., limited power source often exhibits complex dynamics. Upon exceeding a critical power input near resonance, the system may contribute to increasing the transverse vibration severely rather than increasing the spin speed. This phenomenon is referred to as the Sommerfeld effect. This effect can cause instability in high speed rotor system and needs to be addressed carefully for safe and smooth operations. In the present study, a semi-active control scheme based on switched-stiffness method is employed to attenuate the Sommerfeld effect of a eccentric shaft–disk system driven by a brushed DC motor. Following, the equations of motion are solved numerically to obtain time response and amplitude frequency response with a specified supply voltage. It has been shown that as the value of switched-stiffness increases, the Sommerfeld effect is found to be attenuated. However, the rotor response is corrupted with spikes as a fallout of switching stiffness technique, which may destabilize the system and becomes critical when the switching time is very fast. The attenuation of Sommerfeld effect can be further verified through the time varying potential energy plot which is seen to be diminished after crossing the critical speed owing to the dissipative characteristics of non-potential switching stiffness force.