| This research presents a new design methodology for rotordynamic simulations by accounting for the uncertainty of model parameters.; Eigenvalue reanalysis is coupled with Monte Carlo simulation, and is used to predict probabilities of critical speed occurrence in a specific speed range with the bearing support stiffnesses and rotor geometry, treated as random variables. Typically bearing stiffnesses are known to vary enough to create the possibility of a stiffness being substantially away from it's design stiffness so as to cause a critical speed to occur in the rotor system operating range. This research introduces a efficient method to predict the probability that a critical speed will occur in the operating range of the rotor. Speed dependent as well as constant stiffness bearings are used in these simulations. Any speed dependent system property may also be accommodated to the new procedure. A new receptance based reanalysis approach, including gyroscopic moments and speed dependent bearing stiffnesses, is employed to greatly increase computational efficiency of the approach. The reanalysis procedure is shown to be more efficient than the conventional Myklestad type transfer matrix (TMM) based probabilistic approach when applied to analysis of line type structures. Results from this new approach far outperform a QR method of eigenvalue extraction applied to the same line type structure, showing that the reanalysis approach yields greatest advantage for non-line type structure problems which are solved by QR-Jacobi methods and are unsolvable with transfer matrices. An example of this methodology is also applied to a rotor with magnetic bearings, assuming the system uncertainties can be expressed by the proportional and derivative gains of the electromechanical model. |
