SUMMARY

The demand for higher efficiency in rotordynamic systems has led to increased susceptibility to transverse fatigue cracking of the shaft. Inadequate condition monitoring can allow propagating cracks to result in catastrophic shaft failure. A useful method for transverse shaft crack detection/diagnosis is vibration monitoring. Diagnosis estimates important crack parameters, such as crack depth and location, and provides quantitative information to assess further machinery operation. There is a two-fold challenge for on-line diagnosis of crack parameters. First, crack characterization involves specifying both the crack's depth and location. Second, rotating machinery permits response measurement at only specific locations.

A comprehensive approach is presented for modeling an overhung cracked shaft. Two gaping crack models are developed: a notch and a gaping fatigue crack. The notch best approximates experimentally manufactured cracks, whereas the gaping fatigue crack is likely more suited for real fatigue cracks. 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 response.

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. 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.