A Two‐Disk Extended Jeffcott Rotor Model Distinguishing a Shaft Crack from Other Rotating Asymmetries

Abstract

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 theXandYvibrations 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.

Coupled bending torsional vibrations of viscoelastic rotors with fractional damper

“…The rotor rigid body rotation, rotor torsional deformation, and two orthogonal lateral deformations are considered as the degrees of freedom in their rotor dynamics model. Some researchers (Mu et al, 2007; Ramezanpour et al, 2012; Sawicki et al, 2005; Wu and Meagher, 2008; Zheng-ce et al, 2003) provide some further insight into nonlinear vibration response of rotor by taking crack into account that allows for failure analysis of rotor system considering the effect of unbalance, rubbing, and coupling of lateral and torsional vibration. Analytical/numerical predictions of rotating machinery have proven an interplay between the coupling phenomena of lateral-torsional vibrations and rotor unstable behavior especially in the case of lightly damped structure.…”

Vibration of a Misaligned Rotor System with Asymmetric Shaft Stiffness

“…Clinton Judd [2] studied the lateral-torsional vibration of a sided-loaded rotor with asymmetric shaft stiffness. Xi Wu and Jim Meagher [3] compared the vibration characteristics of a shaft crack with that of rotating asymmetry.…”