Application of gradient-based optimization methods for a rotor system with static stress, natural frequency,and harmonic
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Application of gradient-based optimization methods for a rotor system with static stress, natural frequency, and harmonic response constraints Alexander O. Pugachev
Received: 29 June 2012 / Revised: 12 October 2012 / Accepted: 14 November 2012 / Published online: 3 January 2013 © Springer-Verlag Berlin Heidelberg 2012
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. Keywords Sizing optimization · Sequential quadratic programming · Gradient projection method · Rotordynamics · Turbine rotor
A. O. Pugachev () Institute of Energy Systems, Technische Universit¨at M¨unchen, Boltzmannstr. 15, 85747 Garching, Germany e-mail: [email protected]
1 Introduction Engineering of rotating structures is an iterative and multidisciplinary procedure with the objective of simultaneously satisfying a wide variety of requirements and constraints. Today, bringing further advances in technology is more and more associated with applying numerical optimization techniques during design phase to discover optimal structures, i.e. structures with tight constraints. Design of advanced light weight rotor structures requires special attention on stress and rotordynamic analysis. Along with stress conditions and critical speed maps, response to synchronous and nonsynchronous excitation is another essential characteristic of a rotating structure. This is especially important for modern high-speed engines and turbopumps which are likely to operate at supercritical regimes (shaft operating speed range is above several critical speeds). Therefore, taking into account shaft amplitudes becomes necessary to ensure safe designs during optimization. An excellent and still topical review of rotordynamic issues in engine design can be found in Vance and Royal (1975). The finite element method is widely used for performing stress and dynamic analysis of rotating structures. A vast number
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