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 as well as 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 first found that the unbalance 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 first 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.

Stochastic finite element modeling and response analysis of rotor systems with random properties under random loads

“…Considering the random material properties in a rotor system, Sankar et al [21] presented a stochastic finite element method based on the Rayleigh beam theory to analyze the statistics of whirl speeds and modes of rotor systems. Murthy et al [22,23] presented a systematic and rational approach to modeling uncertainties in a rotor system.…”