Vibration and crack detection of a rotor with speed-dependent bearings

The vibration of a shaft-disk rotor containing a transverse crack and supported by speed-dependent bearings is investigated. With crack released energy, the flexibility due to crack is first evaluated. An energy principle in conjunction with the assumed-mode method follow to yield the discrete equations of motion of periodic, time-varying coefficients From the FFT analysis of the displacement responses, the two-times shaft speed component (2Ω) is extracted and serves as a good index to detect the crack location and depth. Response amplitudes to the variations of crack depth and crack location are then discussed and a technique of crack identification is introduced with the aid of response contour maps of two sensing probes.