Nonparametric Stochastic Modeling of Uncertainty in Rotordynamics—Part I: Formulation

Abstract

A systematic and rational approach is presented for the consideration of uncertainty in rotordynamics systems, i.e., in rotor mass and gyroscopic matrices, stiffness matrix, and bearing coefficients. The approach is based on the nonparametric stochastic modeling technique, which permits the consideration of both data and modeling uncertainty. The former is induced by a lack of exact knowledge of properties such as density, Young’s modulus, etc. The latter occurs in the generation of the computational model from the physical structure as some of its features are invariably ignored, e.g., small anisotropies, or approximately represented, e.g., detailed meshing of gears. The nonparametric stochastic modeling approach, which is briefly reviewed first, introduces uncertainty in reduced order models through the randomization of their system matrices (e.g., stiffness, mass, and damping matrices of nonrotating structural dynamic systems). Here, this methodology is extended to permit the consideration of uncertainty in symmetric and asymmetric rotor dynamic systems. More specifically, uncertainties on the rotor stiffness (stiffness matrix) and/or mass properties (mass and gyroscopic matrices) are first introduced that maintain the symmetry of the rotor. The generalization of these concepts to uncertainty in the bearing coefficients is achieved next. Finally, the consideration of uncertainty in asymmetric rotors is described in detail.

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.…”

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

“…In practice, however, this is not the case and uncertainty/ variability in those properties does exist, as is well exemplified by the occurrence of unbalance, and a few, mostly recent, investigations [1][2][3][4][5][6] have focused on the introduction of such uncertainty in rotordynamic analyses. In practice, however, this is not the case and uncertainty/ variability in those properties does exist, as is well exemplified by the occurrence of unbalance, and a few, mostly recent, investigations [1][2][3][4][5][6] have focused on the introduction of such uncertainty in rotordynamic analyses.…”

“…Of particular interest here is the work of Murthy et al [2,3], which has provided an extension of the nonparametric methodology used extensively in other structural dynamics applications in which uncertainty must be modeled. This methodology is based on first developing a reduced order (modal) model of the "mean" system, i.e., the one without uncertainty.…”

“…[2,3] is quite extensive, including the formulation and application of uncertainty on either the rotor stiffness or mass properties as well as bearing properties. [2,3] is quite extensive, including the formulation and application of uncertainty on either the rotor stiffness or mass properties as well as bearing properties.…”

Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system

“…Section 2 exposes the method in detail. Finally, Soize [27,28] developed a non-parametric approach which does not require identification of the uncertain local parameters. A deeper overview of these several methods is available in successive review papers by Ibrahim et al [29,30] and Schüeller et al [19,31,32].…”