Application of gradient-based optimization methods for a rotor system with static stress, natural frequency,and harmonic response constraints

Abstract

This paper demonstrates the application of gradient-based optimization methods to the minimal weight design optimization of rotor systems. A nonlinear constrained optimization problem is considered. Design variables are inner radii and wall thicknesses of shaft sections. Constraints are imposed on torsional and equivalent stresses, natural frequencies, and unbalance response amplitudes. The sizing optimization problem is solved using a gradient projection method and a sequential quadratic programming technique. A typical turbine rotor system is considered. An in-house beam-based finite element method code is used for the prediction of static and dynamic characteristics of the rotor system. Analytical sensitivity analysis is performed for the static and harmonic equations using the adjoint method. Sensitivity coefficients for the natural frequencies are obtained directly from the quadratic eigenvalue problem. Results of several optimization runs with different constraint sets show a significant shaft weight reduction in comparison with the baseline configuration with all constraints being satisfied. The two optimization methods are compared and discussed in regard to their performance.