Sensitivity Analysis and Optimization of Undamped Rotor Critical Speeds to Supports Stiffness

Abstract

This paper introduced a new approach that employed the assumed-modes method and the receptance method, to the sensitivity analysis and the optimization of rotor-bearing systems. First, the frequency equation in terms of receptances was derived. The natural frequencies and the critical speeds for a typical rotor system were then illustrated. Beginning with the receptance equation, the authors, for the first time, derived a sensitivity matrix and employed it into an optimization process. The topographical method in conjunction with the variable metric method followed for the optimal solution. In the solution process, the sensitivity matrix provided important information for search direction. Examples of critical speeds adjustment via supports change in an optimal sense were illustrated. Numerical results showed that the approach was very efficient and the solutions were very accurate. This approach, in addition, provided such valuable information as which supports dominated specific critical speeds. The developed approach proved to be very helpful to rotor engineers in both rotor modification and rotor design.