Vibration Analysis of a Shaft-Disc System for On-line Crack Detection

This dissertation research concerns detection of cracks in rotating shaft-disc systems using the vibration-based methods. Turbines, pumps and jet engines are some examples of the shaft-disc systems, where crack failures may cause catastrophic effects. Detection of cracks at the early stages of growth is thus vital for prevention of failures, and has been the subject of many studies. Various crack detection methods such as ultrasonic, x-ray and vibration-based methods have been widely developed. Among these, the vibration-based methods are better suited for on-line crack detection. The reliability of such methods, however, relies upon the acquisition of an adequate vibration signature and its correlation with the crack, particularly for small size cracks. The reported studies have employed varying signal processing and crack modeling methods, although the models generally lack of consideration of effects of crack location and other possible faults. An analytical model of a flexible shaft with two transverse fatigue cracks and two discs mounted on rigid/ resilient supports is formulated, and the corresponding boundary and continuity conditions are developed. A modified harmonic balance method is subsequently proposed for solutions of the governing equations of the analytical model to investigate changes in the selected vibrational properties such as shaft critical speeds, shaft center orbits and super-harmonic components of the steady-state lateral response to an unbalance excitation. The effects of single crack properties such as depth and location on the responses are investigated considering short/long and rigid/flexible bearing supports. The crack is considered as a breathing crack, and is characterized by an exponential function, which facilitated its integration in the modified harmonic balance method. Furthermore, the effects of two cracks’ characteristics such as depth, location and relative angular position on selected vibrational properties are studied. Each crack is initially described by a breathing function proposed by Mayes and Davies, which is subsequently modified as a softly-clipped cosine function to accurately describe saturation in breathing phenomenon. The response characteristics of the cracked shaft are also compared with those of the system with an intact shaft in order to identify potential measures for detecting cracks. The validity of the proposed analytical model and the solution strategy is illustrated through comparisons of the model results with those obtained from a finite element model and limited experiments. The crack-induced changes in transient lateral responses of the shaft-disc system are also considered for transverse crack detection. The shaft-disc system is simply modeled as a Jeffcott rotor to compute its start-up responses in the lateral direction. The breathing behavior of the crack is characterized with respect to stress intensity factor at different points on the crack edge at each shaft angle. A positive stress intensity factor corresponds to the open part of the crack, while the closed part shows a negative stress intensity factor. The breathing crack excites super-harmonic components of the transient as well as the steady-state lateral responses. Time-frequency representation of the transient lateral response obtained from Hilbert-Huang transform based on an improved empirical mode decomposition is used for crack detection. The results show that observed changes in the transient and steady-state lateral vibration responses could lead to effective detection of relatively small size cracks.