Vibration analysis of a cracked rotor with an unbalance influenced breathing mechanism

The breathing mechanism of a shaft crack is an advantageous tool for describing the stiffness changes that occur in the shaft. Unbalance can affect the breathing mechanism of the crack and may produce behaviors that are significantly different to weight-dominant breathing patterns. As such, cracked rotors with large permissible residual unbalance will require new models to accurately describe the vibration of the rotor. In this study, the breathing mechanism of a crack is modeled to include the effects of unbalance loading and then the time-varying stiffness of the cracked rotor is determined. Consequently, MATLAB ode15s function (an adaptive step solver) is used to numerically integrate the equations of motion of a finite element cracked rotor that incorporates the proposed crack breathing model. The predicted 1X, 2X and 3X harmonic components of a rotor with deep crack (80% of radius) were seen to significantly differ between the proposed model and an existing weight-dominant model. Due to the significant differences in the breathing mechanisms and vibration results of the two models, the weight-dominant breathing model was deemed unsuitable for modeling the vibration of cracked rotors with large permissible residual unbalance.