Application of the Proper Orthogonal Decomposition Method for Damage Detection in Rotor-Bearing Systems

Abstract

Unusual vibration levels in rotating equipment usually caused by unbalance, misalignment, mechanical looseness, propagating cracks and other sources of malfunctions. Appearance of these damages often excites destructive vibration amplitudes in rotor systems. In this thesis, we focus on the induced vibration by propagating cracks in a rotating shaft. Detecting crack in its early phase of propagation might help in preventing further damage in the equipment as well as avoiding economic and human loss. The proper orthogonal decomposition (POD) is employed here as a crack detection technique for early damage detection by identifying the vibration signature of the cracked rotor response. The applicability of the POD to cracked rotors is explored with a cracked Jeffcott rotor model. The covariance matrix of horizontal and vertical whirl amplitudes is formed based on the numerical integration of the considered cracked rotor equations of motion. For the numerical solution, the POD is directly applied to the obtained covariance matrix. The proper orthogonal values (POVs) and the proper orthogonal modes (POMs) are acquired for various crack depths and rotational speeds. It is observed that both POMs and their corresponding POVs are highly sensitive to the crack in the neighborhood of critical and subcritical rotational speeds. In addition, the sensitivity zones of the POVs and POMs to the crack propagations coincide with the unstable zones of the cracked system obtained by Floquet's theory. Moreover, the POVs are found to be sensitive to the change in the unbalance angle direction under the effect of the crack, especially, at the critical and subcritical rotational speeds. The POM slope of the largest POV II is also found to be affected by the unbalance force angle direction of the cracked Jeffcott rotor system. Accordingly, it can be concluded that the appearance of the crack highly alters the POVs and POMs of the system. In addition, the change in the unbalance force angle significantly change the peaks values and their locations under the effect of the crack. These phenomena's can be used as unique vibration signatures to detect the appearance of the crack in an early phase of propagation. Therefore, we conclude that the POD method accompanied with an intentionally induced unbalance mass could be an efficient tool for crack detection since it can be directly applied to the experimental data of vibration amplitudes.

Date of Award	Apr 2017
Original language	American English
Supervisor	Mohammad Alshudeifat (Supervisor)