A mathematical model of a cracked rotor and an asymmetric rotor with two disks representing a turbine and a generator is utilized to study the vibrations due to imbalance and side load. Nonlinearities typically related with a “breathing” crack are included using a Mayes steering function. Numerical simulations demonstrate how the variations of rotor parameters affect the vibration response and the effect of coupling between torsional and lateral modes. Bode, spectrum, and orbit plots are used to show the differences between the vibration signatures associated with cracked shafts versus asymmetric shafts. Results show how nonlinear lateral-torsional coupling shifts the resonance peaks in the torsional vibration response for cracked shafts and asymmetric rotors. The resonance peaks shift depending on the ratio of the lateral-to-torsional natural frequencies with the peak responses occurring at noninteger values of the lateral natural frequency. When the general nonlinear models used in this study are constrained to reduce to linear torsional vibration, the peak responses occur at commonly reported integer ratios. Full spectrum analyses of the X and Y vibrations reveal distinct vibration characteristics of both cracked and asymmetric rotors including reverse vibration components. Critical speeds and vibration orders predicted using the models presented herein include and extend diagnostic indicators commonly reported.


Mechanical Engineering

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