Specifying Manufacturing Tolerances for a Given Amplification Factor: A Nonparametric Probabilistic Methodology

Abstract

To cite this version:Evangéline Capiez-Lernout, Christian Soize. Specifying manufacturing tolerances for a given amplification factor: a nonparametric probabilistic methodology. ASME. ASME Turbo Expo: Land, Sea and Air 2003, Jun 2003, Atlanta, Georgia, United States. ASME, GT-2003GT- -38050, pp. 1-12, 2003 ABSTRACTIt is known that the forced response of mistuned bladed disks can strongly be amplified in comparison with the forced response of the tuned system. The random character of mistuning thus requires the construction of probabilistics models of random uncertainties. This paper presents a nonparametric probabilistic model of random uncertainties which is adapted to the problematics of the blade mistuning. This nonparametric approach allows all the uncertainties yielding mistuning (manufacturing tolerances, dispersion of materials) to be taken into account and includes also the uncertainties due to the modeling errors. This new probabilistic model takes into account both the mistuning of the blade eigenfrequencies and the blade modal shapes. The first point concerns the construction of this nonparametric approach in order to perform a mistuning analysis. The second part is devoted to the inverse problem associated with the manufacturing tolerances. A relationship between the manufacturing tolerances and the level of mistuning is also constructed.

Blade Manufacturing Tolerances Definition for a Mistuned Industrial Bladed Disk

“…½ (black dashed-dotted line), ½ ½ (gray dashed-dotted line), ½ ½ (black dotted line) and ½ ½ (gray dotted line). As it was seen on a simple numerical example [18], this kind of graph has a maximum which allows two types of specifications to be considered. One of this specification consists in defining tolerances of the blade with high precision, whereas the other one consists in intentionally mistuning the blade.…”

“…The random geometry model allows the random mass matrix M para ℄ and the random stiffness matrix K para ℄ to be constructed for blade . It can be shown [18] that dispersion parameters AE Å and AE Ã can be identified by the equation…”

“…For each blade, it is assumed that random uncertainties mainly affect the dynamics of the blade with fixed coupling interface [18]. Consequently, the nonparametric probabilistic approach is implemented with respect to the matrix…”

“…The theory concerning this inverse problem related to the definition of the blade manufacturing tolerances has been previously developed and validated for a simple numerical case [18]. Let us recall that the main steps of such an approach are based on´½µ the construction of a mean reduced matrix model for each blade because the probability model related to the nonparametric approach is implemented from reduced matrices;´¾µ the construction of the probability model by using the maximum entropy principle under constraints defined by the available information; three scalar parameters allowing the dispersion of the random mass, damping and stiffness matrices to be controlled constitute the data input of the nonparametric approach;´¿µ the identification procedure of these dispersion parameters with respect to the physical parameters which describe the random geometry of the blades.…”

Stochastic Behaviour of Mistuned Stator Vane Sectors: An Industrial Application

“…However, the geometric and material dispersion due to the manufacturing tolerances, sources of mistuning, makes the assumption of cyclic symmetry far from reality. Indeed, the mistuning has a non-negligible effect on the vibratory behaviour of the bladed disks by localizing an important part of the energy on a reduced number of blades which can lead to a premature vibratory fatigue of the component [2,5,11,14]. This phenomenon of modal localization is conditioned, on the one hand, by the coupling stiffness between the blades and the disk and, on the other hand, by the rate of mistuning.…”