Dynamics of a Jeffcott rotor with slant crack

A simple Jeffcott rotor model of a rotor with a slant crack is presented. Flexibility matrix of the rotor with slant crack is developed and the stiffness coefficients based on the flexibility values are used in the equations of motion. Response-dependent nonlinear breathing crack model is used to evaluate unbalance response of the cracked rotor. Comparison between rotor with slant and transverse crack is made with regard to the flexibility/stiffness coefficients and the unbalance response characteristics. The flexibility matrix for slant crack case is more populated with additional cross-coupled coefficients compared to the transverse crack case. The rotor with slant crack is found to be stiffer in lateral and longitudinal directions, but more flexible in torsion, compared to the one with transverse crack. The response of the rotor with the two types of cracks (transverse and slant) is analysed at subharmonic resonances to explore possibilities of distinctive features in their response. Spectrum cascade plot for lateral and longitudinal vibrations exhibit distinctive response features for slant and transverse crack rotors.