Transverse fatigue crack diagnosis in a rotordynamic system using vibration monitoring
Varney, Philip A.
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To increase efficiency, shafts are made lighter and more flexible, and are designed to rotate faster to increase the system's power-to-weight ratio. The demand for higher efficiency in rotordynamic systems has led to increased susceptibility to transverse fatigue cracking of the shaft. Shaft cracks are often detected and repaired during scheduled periods of off-line maintenance. Off-line maintenance can be expensive and time consuming; on-line condition monitoring allows maintenance to be performed as-needed. However, inadequate (or a lack of) monitoring can allow rapidly propagating cracks to result in catastrophic shaft failure. It is therefore imperative to develop on-line condition monitoring techniques to detect a crack and diagnose its severity. A particularly useful method for transverse shaft crack detection/diagnosis is vibration monitoring. Detection, and especially diagnosis, of transverse fatigue cracks in rotordynamic systems has proven difficult. Whereas detection assesses only the presence of a crack, diagnosis estimates important crack parameters, such as crack depth and location. Diagnosis can provide the operator with quantitative information to assess further machinery operation. Furthermore, diagnosis provides initial conditions and predictive parameters on which to base prognostic calculations. There is a two-fold challenge for on-line diagnosis of transverse fatigue crack parameters. First, crack characterization involves specifying two important parameters: the crack's depth and location. Second, the nature of rotating machinery permits response measurement at only specific locations. Cracks are typically categorized as breathing or gaping; breathing cracks open and close with shaft rotation, while gaping cracks remain open. This work concerns the diagnosis of gaping crack parameters; the goal is to provide metrics to diagnose a crack's depth and location. To this end, a comprehensive approach is presented for modeling an overhung cracked shaft. Two linear gaping crack models are developed: a notch and a gaping fatigue crack. The notch model best approximates experimentally manufactured cracks, whereas the gaping fatigue crack model is likely more suited for real fatigue cracks. Crack diagnosis routines are established using free and forced response characteristics. Equations of motion are derived for both crack models, including excitation due to gravity and imbalance. Transfer matrix techniques are established to expediently obtain the steady-state system response. A novel transfer matrix technique, the Complex Transfer Matrix, is developed to distinguish forward and backward whirl components. The rotor's angular response is primarily employed in this work for crack detection and diagnosis. The overhung shaft induces an increased sensitivity to variations in crack depth and location. In addition, an available overhung rotordynamic experimental test rig allows for comparison of the current analytic results to previously obtained experimental results. Under the influence of gravity, the steady-state response of the cracked system includes a prominent 2X harmonic component, appearing at a frequency equal to twice the shaft speed. The magnitude of the 2X harmonic is strongly influenced by the shaft speed. A resonant response occurs when the shaft speed reaches half of a system natural frequency. This work demonstrates that the profile of the 2X harmonic versus shaft speed is a capable diagnostic tool. Identification of the 2X resonance frequency restricts the crack parameters to certain pairs of location and depth. Following this limiting process, the magnitude of the 2X harmonic is used to identify the crack's depth and location. Orbital shapes at the rotor are discussed, as are orbital modes of the shaft deflection. Quantitative results and qualitative observations are provided concerning the difficulty of crack detection and diagnosis.