Random Field Modeling and Analysis of Rotor Bladed Disc Sector Using a Data Driven PCE Based Approach

Abstract

Abstract Bladed disc systems, are designed to be rotationally periodic i.e. each sector repeats itself in an angular manner. This ensures that the response characteristics preserve this rotational periodicity and is defined as a tuned system. However, due to manufacturing limitations, there are invariably random spatial variations in the sectors which constitute the rotor. This in turn destroys the periodicity (angular symmetry) of the rotor. Such a system is defined as a mistuned system, leads to energy localization and makes the rotor susceptible to damage leading to a loss of its service life. This study focusses on developing a methodology for modeling the random spatial inhomogeneities and integrating with finite element analysis for estimating the behavior of a sector of a rotor blade assembly. Approximations for the non-Gaussian random fields for the spatial inhomogeneities are directly developed from the data set of measurements available from coordinate measuring machine (CMM). Subsequently, Rosenblatt’s transformations are applied to each component of the discrete measurement data set for polynomial chaos (PC) representation of the parameter to get the estimated probability density function (pdf). Spearman’s rank correlation coefficient (SRCC) is calculated to obtain the correlation parameter. Kullback–Liebler entropy (KLE) is used as a metric to compare the estimated pdf obtained through the PC representation of the measured data. The in-house PC based developed codes are subsequently integrated with commercially available finite element software which enable quantifying the propagation of the spatial random uncertainties into the response characteristics. Statistical processing of the response quantities is carried out to estimate probabilistic measures of the corresponding response quantities.