Application of Bispectral Analysis in Vibration Fault Detection: A Review

Mechanical system degradation always leads to the unstable and nonlinear characteristics in the dynamic responses of the system to some extent. Conventional spectral methods based on Fourier transform have limited value in showing up fault information deviating from linearity. Higher order spectral analysis (HOSA) had been reported to be effective in providing information on nonlinear response. Bispectrum as one of higher order signal analysis tools found to be a useful tool in identifying nonlinear behavior of mechanical system due to vibration faults. This paper provides an introductory treatise of to Bispectrum, and reviews its applications in machinery vibration faults detection that includes misalignment, bearing and gear faults, and cracked shafts. The effectiveness and limitation of this technique are also reported for these faults based on published literature.

The Effects of Longitudinal and Circumferential Cracks on the Torsional Dynamic Response of Shafts

Turbo generator shafts are manufactured through the extrusion process. This results in formation of weak planes along the extrusion direction. Under service loading (e.g. cyclic torsion due to electrical line faults), large longitudinal cracks often form in these shafts before the appearance of any circumferential cracks. The presence of these cracks could severely compromise the shaft resonance frequencies. Here, we investigated the dynamic response of solid turbo generator shafts with longitudinal and circumferential cracks. The longitudinal cracked section of the shaft section was modeled as a shaft with reduced effective torsional rigidity. The effective torsional rigidity was found to be a function of ratio of crack depth to the shaft radius only. The circumferential cracked section was modeled as a torsional spring, with the torsional spring constant determined using fracture mechanics principles. It was found that the resonance frequency of the shaft may be little affected by the presence of a longitudinal crack. The resonance frequencies of the shaft with the circumferential crack depend on the crack length and its location. The effects of crack surface interactions for both longitudinal and circumferential cracks were also investigated. For circumferential cracked shafts, the sever crack surface interaction results in the peak response frequency approaches to that of un-cracked shafts. However the frequency where the peak response occurs for a longitudinally-cracked shaft generally exceeds that of un-cracked shaft first resonance frequency.

An Experimental Study of Breathing Mechanism for the Transversely Cracked Shafts

Shaft fatigue crack is one of the most common defects in rotating equipment, due to its extensive operation with continuous heavy loads. Finding an efficient way to evaluate the true stiffness variation due to the crack rotation is the key step to develop both on-line and off-line crack diagnostic techniques. This study analyzed time-variant bending stiffness of elastic shafts with experimentally-induced fatigue, welding and wire cut transverse cracks. It was found that crack gap has a significant effect on the opening and closing behaviour of the transverse crack. As in the case of a cut crack, large crack gap could completely prevent the crack from closing during rotation. A fatigue crack without a clear gap shows a typical opening and closing behavior. Further, it remains fully closed within a small angular range and most of time it is partially closed. It was also observed that both switch and harmonic models cannot describe periodic stiffness variation well enough to represent the actual breathing function of the fatigue crack.