Nonparametric Stochastic Modeling of Structural Uncertainty in Rotordynamics: Unbalance and Balancing Aspects

Abstract

This paper focuses on extending an earlier investigation on the systematic and rational consideration of uncertainty in reduced order models of rotordynamics systems. The current effort concentrates on the consistent introduction of uncertainty in mass properties on the modal mass and gyroscopic matrices and on the unbalance force vector. The uncertainty in mass is separated into uncertainty that maintains the rotor symmetry and the one which disrupts it. Both types of uncertainties lead to variations in the system modal matrices but only the latter induces an unbalance. Accordingly, the approach permits the selection of separate levels on the uncertainty on the system properties (e.g., natural frequencies) and on the unbalance. It was flrst found that the unbalanced response is increased by considering the uncertainty in the rotor modal mass matrices. It was next noted that the approach presented not only permits the analysis of uncertain rotors but it also provides a computational framework for the assessment of various balancing strategies. To demonstrate this unique feature, a numerical experiment was conducted in which a population of rotors were balanced at low speed and their responses were predicted at their flrst critical speed. These response predictions were carried with the uncertainty in the system modal mass matrices but with or without the balancing weights effects on these matrices. It was found that the balancing at low speed may, in fact, lead to an increase in both the mean and 95th percentile of the response at critical speed.

Dynamics analysis of a hollow-shaft rotor system with an open crack under model uncertainties

“…The influence of the PCE order on the dynamic response of an asymmetric rotor system was further investigated [38]. Other applications include the unbalance and balancing aspects [39] as well as critical speed analyses [40]. Attention to fuzzy approach was paid in Ref.…”

Effects of Bounded Uncertainties on the Dynamic Characteristics of an Overhung Rotor System with Rubbing Fault

“…In this section, the uncertainties in the rubbing rotor will be described first. We will focus on the crucial parameters related directly to the rub-impact as the effects of the regular uncertain physical parameters are intensively investigated in the stochastic domain [30,38,39]. Then, the non-intrusive uncertainty analysis procedure will be explained for the nonlinear dynamics.…”

Response analysis of an accelerating unbalanced rotating system with both random and interval variables

“…Random uncertainties are used to describe those whose precise probability density functions (PDFs) are already known. Many sophisticated applications [18][19][20][21][22] of the stochastic methods to rotordynamics can be found, including the principle of maximum entropy, the MCS, the global optimization method [23] and the perturbation method [24]. The PDF of a random quantity can be constructed from sufficient statistical information.…”