Fast algorithm estimating the Jeffcott cracked rotor dynamics and stiffness variation including chaotic behavior

A nonlinear algorithm which includes Cheng et al.[1] crack breathing function for a Jeffcott rotor is used to dramatically reduce the processing time to compute nonlinear stiffness and vibration responses, regardless if the behavior is unstable chaotic. Crack breathing is normally driven by weight dominance, but here the vibration displacement vector and state of stress at crack location is obtained based on a SERR and LEFM. Nevertheless, among other things, our algorithm saves computational effort post-processing Chengs crack breathing function to establish the COB. To validate our method, estimation of the system stiffness evolution due to vibration vs. that of O. S. Jun et al.[2] are compared; both yield qualitatively and quantitatively similar results. Moreover, for the first time to the authors acknowledge, for certain damped vertical rotor configuration cases dissipative chaotic behavior occur; this is verified by the stiffness variation, the vibration orbit response and corresponding spectrum; which are efficiently computed and shown. To evaluate the cracked rotor stability, the procedure given in[4] is followed, the largest Lyapunov exponent LLE is extracted to the numerically obtained vibration signals. Finally the computational efficiency between the proposed method and the accurate time consuming procedure as proposed by O. S. Jun et al., is compared in terms of the predicted stiffness evolution. Under similar conditions the former is nearly three orders of magnitude faster than the latter one; and even under chaotic behavior our approach is attractive and applicable to fatigue analysis, computation of stress intensity factor SIF, remaining useful life estimation RUL, and other time consuming studies.