Published in IMAC XXV Conference and Exposition on Structural Dynamics: Orlando, Florida, February 19, 2007.
A practical cracked rotor model with two disks representing a turbine and generator is studied using a four degree of freedom model; two transverse displacements and two torsional angular displacements. The differential equations of a rotor with a crack, unbalance, and constant radial force are first derived in detail using energy principles. The nonlinearities related with a “breathing” crack are incorporated, which distinguishes this paper from others studying stiffness anisotropy of a rotor with a similar rotor configuration. Through numerical simulations, this paper demonstrates the lateral-torsional coupling that occurs with a shaft crack and predicts torsional critical speed frequencies at fixed non-integer ratios of lateral to torsional natural frequency. The spectrum of the torsional vibration is shown to contain super-synchronous critical speeds related to the lateral natural frequency. The unique frequency response of the torsional motion predicted by this model could be employed for early detection of a cracked rotor.