Non-Linear Modeling of Centrifugal Stiffening Effects for Accurate Bladed Component Reduced-Order Models

The modeling of centrifugal stiffening effects on bladed components is of primary importance in order to accurately capture their dynamics depending on the rotor angular speed. Centrifugal effects impact both the stiffness of the component and its geometry. In the context of the small perturbation framework, when considering a linear finite element model of the component, an assumption typically made in the scientific literature involves a fourth-order polynomial development of the stiffness matrix in terms of the angular speed. This polynomial development may fail to provide an accurate representation of the geometry evolution of a blade. Indeed, the error on the blade-tip displacement associated to the use of a linear finite element model quickly reaches the same order of magnitude as the blade-tip/casing clearance itself thus yielding a 100 % error on the blade-tip/casing clearance configuration. This article focuses on the presentation of a methodology that allows for creating accurate reduced order models of a 3D finite element model accounting for centrifugal stiffening with a very precise description of the blade-tip/casing clearance configuration throughout a given angular speed range. The quality of the obtained reduced order model is underlined before its numerical behaviour in the context of non-linear dynamic simulations be investigated. It is evidenced that the new reduced order model features specific interactions that could not be predicted with a linear model. In addition, results highlight the limitations of numerical predictions made for high angular speeds with a linear model. Finally, a particular attention is paid to the numerical sensitivity of the proposed model. As a downside of its increased accuracy, it is underlined that its computation must be done carefully in order to avoid numerical instabilities.