Application of Optimization Methods in Rotor Dynamics

Abstract

The purpose of this study is to investigate the optimal design of rotors with respect to different objective functions. The dynamic behavior of a rotating system is strongly influenced by various parameters such as mass and stiffness distribution, rigid disk inertial properties, bearing locations and coefficients. To a greater or lesser extent, all bearings are flexible and all bearings absorb energy. Moreover, load deflection relationships are often a function of shaft speed. An optimal design can be achieved by minimizing a selected target function subjected to specific constraints within a set of reasonable bounds for inner and outer diameters of the different stations, stiffness and damping coefficients of the support bearings and their positions. Optimal design of rotors has been reported by many authors in the literature. However, all of these optimization analyses considered beam elements instead of solid elements to the best knowledge of the authors. Nowadays three-dimensional models of rotors are common practice in the industry. Therefore solid models of rotating systems are considered in the current work. Stability criteria, critical speeds, weight, real and complex eigenfrequencies, and unbalance responses may be defined as a set of objective functions and constraints. In order to judge the stability, the equivalent damping ratio is evaluated. The determination of the damped critical speeds is accomplished using a Campbell diagram, a plot of damped natural whirl frequencies versus spin speeds, which is generated by determining the natural frequencies over a range of rotational speeds. A mode-tracking procedure is implemented in order to sort the complex eigenvalues. The complete finite element analysis including the complex design optimization problem of the rotor system at hand is conducted in PERMAS. For this purpose several optimization algorithms are available. Furthermore gradient-based and derivative free methods can be used. A combined shape and sizing optimization is used to illustrate the procedure by means of an example taken from the literature.