Stochastic modeling of flexible rotors

Abstract

Flexible rotors are characterized by inherent uncertainties affecting the parameters that influence the dynamic responses of the system. In this context, the handling of variability in rotor dynamics is a natural and necessary extension of the modeling capability of the existing techniques of deterministic analysis. Among the various methods used to model uncertainties, the stochastic finite element method has received major attention, as it is well adapted for applications involving complex engineering systems of industrial interest. In the present contribution, the stochastic finite element method applied to a flexible rotor system, with random parameters modeled as random fields is presented. The uncertainties are modeled as homogeneous Gaussian stochastic fields and are discretized according to the spectral method by using Karhunen-Loève expansions. The modeling procedure is confined to the frequency and time domain analyses, in which the envelopes of frequency response functions, the Campbell's diagram and the orbits of the stochastic flexible rotor system are generated. Also, Monte Carlo simulation method combined with the Latin Hypercube sampling is used as stochastic solver. After the presentation of the underlying theoretical formulations, numerical applications of moderate complexity are presented and discussed aiming at demonstrating the main features of the stochastic modeling procedure of flexible rotor systems.

Uncertainty Analysis Techniques Applied to Rotating Machines

“…The rotating machine is composed of a horizontal flexible shaft discretized into 20 Euler-Bernoulli's beam elements, three asymmetric bearings (B 1 , B 2 , and B 3 ), and two rigid discs (D 1 and D 2 ). The physical and geometrical characteristics used in the FE model of the rotor system are given in [2].…”

“…Uncertain dynamic responses of flexible rotors have been analyzed by applying two main approaches, namely, stochastic and fuzzy. Thus, the uncertainty analysis has been applied in flexible rotors by using the polynomial chaos theory [1], as modeled by considering Gaussian homogeneous stochastic fields discretized by Karhunen-Loève expansion [2] or through the fuzzy approach [3,4]. These methods are well-established tools that may present limitations and drawbacks depending on the application conveyed.…”

Sensitivity Analysis of Flexible Rotor Subjected to Interval Uncertainties

“…The uncertainty modeling and quantification of flexible rotors have been analyzed by applying different numerical approaches: stochastic finite element method (Koroishi et al 2012), polynomial chaos expansion (Didier et al 2012), fuzzy finite element method (Cavalini Jr et al 2015), and fuzzy-stochastic finite element method . In those contributions, the system responses were computed in the presence of parametric uncertainties and assessed for several uncertain scenarios in order to determine the influence of each uncertain parameter on the dynamic behavior of the system.…”

Kriging Metamodeling in Rotordynamics: Application for Predicting Critical Speeds and Vibrations of a Flexible Rotor

“…For example, some parameters may vary throughout the life of a rotating machinery or some uncertainties have to be taken into account during the manufacturing monitoring. All these facts can drastically affect the vibration responses of a rotor system (see, e.g., [5][6][7][8][9][10][11][12][13]). And therefore it complicates the approach to be put in place in order to propose a robust design.…”