Probability Limits of the Critical Rotor Speeds

Rotors are manufactured with certain tolerances, implying that both outer and inner diameters of the rotor can be treated as random parameters (RP).This paper focuses on an approach for estimating the mean and variance of the critical speeds of rotors.These values allow for probabilistic determination of the upper and lower limits of critical speeds.The mean of critical speeds has to be derived iteratively due to the frequency (revolution) dependence of gyroscopic and circulation matrices.Subsequently, the critical speed is approximated using two terms of Taylor's expansion at the mean value of critical speed.It is essential to conduct sensitivity analysis of the critical speed concerning RP.This approximate approach avoids the necessity of knowing the probability function of randomly valued diameters, respecting the validity of Chebyshev's inequality.Rotor discretization in this study is achieved using the Finite Element Method.