Characterization of Sommerfeld Effect for an overhung Crack Rotor Dynamic System Using Active Magnetic Bearing

The amount of power required to operate the system in the post-resonance period is indicated by the Sommerfeld effect, a nonlinear jump phenomenon that occurs in an unbalanced rotor-motor system. This study examines the behavior of a rotor–bearing system with a breathing crack, emphasizing the role of active magnetic bearings (AMB) in reducing vibrations induced by both the crack and rotor unbalance.

This article describes the full transient (ODE45) and steady state descriptions of the Sommerfeld effect in a crack unbalanced rotor-motor-AMB system. Harmonic balance method (HBM) is used to solve the nonlinear second order differential equations through finite element method (FEM) for steady state analysis. A linearized 4-pole active magnetic bearing is considered for the current analysis. To study the system’s steady-state Sommerfeld effect, the power balance method is employed.

The analysis demonstrate that (i) frequency response plot for various cracked depth by changing the crack position. Our analysis is focused on the first critical speed, and how the cracked depth affect its first critical speed. (ii) Input voltage vs rotor speed (Sommerfeld effect) is plotted to know the jump voltage (escape voltage). (iii) How the change in bias current (AMB) affect the system vibration amplitude as well as the jump voltage is studied.

A detail comparison between steady state and transient analysis is mention in this paper. The system overall system vibration amplitude decreases as the bias current is increased from 0 A to 1 A. The system response becomes more periodic with higher bias current effectively reducing the influence of the crack.