A Statistical Characterization of the Effects of Mistuning in Multi-Stage Bladed Disks

2011 ◽  
Author(s):  
Kiran X. D’Souza ◽  
Bogdan I. Epureanu
Keyword(s):  
Reduced Order Modeling ◽  
Single Stage ◽  
Bladed Disks ◽  
Statistical Characterization ◽  
Reduced Order ◽  
Design Component ◽  
Bladed Disk ◽  
Modeling Approach ◽  
Multi Stage

A great deal of research has been conducted on the effects of small random variations in structural properties, known as mistuning, in single stage bladed disks. Due to the inherent randomness of mistuning and the large dimensionality of the models of industrial bladed disks, a reduced order modeling approach is required to understand the effects of mistuning on a particular bladed disk design. Component mode mistuning (CMM) is an efficient compact reduced order modeling method that was developed to handle this challenge in single stage bladed disks. In general, there are multiple stages in bladed disk assemblies, and it has been demonstrated that for certain frequency ranges accurate modeling of the entire bladed disk assembly is required because multi-stage modes exist. In this work, a statistical characterization of structural mistuning in multi-stage bladed disks is carried out. The results were obtained using CMM combined with a multi-stage modeling approach previously developed. In addition to the statistical characterization, a new efficient classification method is detailed for characterizing the properties of a mode. Also, the effects of structural mistuning on the characterization of the mode is explored.

A Statistical Characterization of the Effects of Mistuning in Multistage Bladed Disks

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Kiran X. D’Souza ◽  
Bogdan I. Epureanu
Keyword(s):  
Reduced Order Modeling ◽  
Single Stage ◽  
Bladed Disks ◽  
Statistical Characterization ◽  
Reduced Order ◽  
Design Component ◽  
Bladed Disk ◽  
Modeling Approach ◽  
Bladed Disk Assembly

A great deal of research has been conducted on the effects of small random variations in structural properties, known as mistuning, in single stage bladed disks. Due to the inherent randomness of mistuning and the large dimensionality of the models of industrial bladed disks, a reduced order modeling approach is required to understand the effects of mistuning on a particular bladed disk design. Component mode mistuning (CMM) is an efficient compact reduced order modeling method that was developed to handle this challenge in single stage bladed disks. In general, there are multiple stages in bladed disk assemblies, and it has been demonstrated that for certain frequency ranges accurate modeling of the entire bladed disk assembly is required because multistage modes exist. In this work, a statistical characterization of structural mistuning in multistage bladed disks is carried out. The results were obtained using CMM combined with a multistage modeling approach previously developed. In addition to the statistical characterization, a new efficient classification method is detailed for characterizing the properties of a mode. Also, the effects of structural mistuning on the characterization of the mode is explored.

Reduced Order Modeling for Multi-Stage Bladed Disks With Friction Contacts at the Flange Joint

2017 ◽  
Author(s):  
Giuseppe Battiato ◽  
Christian M. Firrone ◽  
Teresa M. Berruti ◽  
Bogdan I. Epureanu
Keyword(s):  
Displacement Field ◽  
Fourier Coefficients ◽  
Normal Modes ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Single Stage ◽  
Bladed Disks ◽  
Reduced Order ◽  
Multi Stage

Most aircraft turbojet engines consist of multiple stages coupled by means of bolted flange joints which potentially represent source of nonlinearities due to friction phenomena. Methods aimed at predicting the forced response of multi-stage bladed disks have to take into account such nonlinear behavior and its effect in damping blades vibration. In this paper a novel reduced order model is proposed for studying nonlinear vibration due to contacts in multi-stage bladed disks. The methodology exploits the shape of the single-stage normal modes at the inter-stage boundary being mathematically described by spatial Fourier coefficients. Most of the Fourier coefficients represent the dominant kinematics in terms of the well-known nodal diameters (standard harmonics), while the others, which are detectable at the inter-stage boundary, correspond to new spatial small wavelength phenomena named as extra harmonics. The number of Fourier coefficients describing the displacement field at the inter-stage boundary only depends on the specific engine order excitation acting on the multi-stage system. This reduced set of coefficients allows the reconstruction of the physical relative displacement field at the interface between stages and, under the hypothesis of the Single Harmonic Balance Method, the evaluation of the contact forces by employing the classic Jenkins contact element. The methodology is here applied to a simple multi-stage bladed disk and its performance is tested using as a benchmark the Craig-Bampton reduced order models of each single-stage.

A Reduced Order Model for Nonlinear Dynamics of Mistuned Bladed Disks With Shroud Friction Contacts

2018 ◽  
Author(s):  
S. Mehrdad Pourkiaee ◽  
Stefano Zucca
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Reduced Model ◽  
Order Model ◽  
Bladed Disks ◽  
Statistical Characterization ◽  
Reduced Order ◽  
Bladed Disk

A new reduced order modeling technique for nonlinear vibration analysis of mistuned bladed disks with shrouds is presented. It has been shown in the literature that the loss of cyclic symmetry properties which is known as mistuning could considerably increase the response level, localize the vibration around few number of blades and finally bring high cyclic fatigue. The developed reduction technique employs two component mode synthesis methods, namely, the Craig-Bampton (CB) method followed by a modal synthesis based on loaded interface modeshapes (Benfield and Hruda). In the new formulation the fundamental sector is divided into blade and disk components. The CB method is applied to the blade, where nodes lying on shroud contact surfaces and blade-disk interfaces are retained as master nodes, while modal reductions is performed on the disk sector with loaded interfaces. The use of loaded interface component modes allows removing the blade-disk interface nodes from the set of master nodes retained in the reduced model. The result is a much more reduced order model with no need to apply any secondary reduction. In the paper it is shown that the reduced order model of the mistuned bladed disk can be obtained with only single-sector calculation, so that the full finite element model of the entire bladed disk is not necessary. Furthermore, with the described approach it is possible to introduce the blade frequency mistuning directly into the reduced model. In this way, reduction is performed only once in case of multiple analyses, necessary for statistical characterization of the nonlinear response of the system. The nonlinear forced response is computed using the harmonic balance method (HBM) and alternating frequency/time domain (AFT) approach. Friction contacts are introduced into the FE model using a 3D contact element. Numerical simulations revealed the accuracy, efficiency and reliability of the new developed technique for nonlinear vibration analysis of mistuned bladed disks with shroud friction contacts.

Reduced Order Modeling Techniques for Dynamic Analysis of Mistuned Multi-Stage Turbomachinery Rotors

2001 ◽  
Author(s):  
Ronnie Bladh ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Modal Analysis ◽  
Reduced Order Modeling ◽  
Stage Model ◽  
Reduced Order ◽  
Modal Data ◽  
Bladed Disk ◽  
Multi Stage ◽  
Modeling Techniques ◽  
Forced Responses ◽  
Stage Modeling

Recent findings indicate that structural interstage (stage-to-stage) coupling in multi-stage rotors can have a critical impact on bladed disk dynamics by altering significantly the flexibility of the disk. This affects local eigenfrequency veering characteristics, and thus a design’s sensitivity to mistuning. In response to these findings, two reduced order modeling techniques are presented that accurately capture structural interstage coupling effects, while keeping model sizes at practical levels. Both free and forced responses of an example two-stage rotor are examined using novel component-mode-based reduced order modeling techniques for mistuned multi-stage assemblies. Both techniques employ an intermediate multi-stage model constructed by component mode synthesis (CMS), which is further reduced by either: (a) partial secondary modal analyses on constraint-mode partitions; or (b) a full-scale secondary modal analysis on the entire multi-stage CMS model. The introduced techniques are evaluated using finite element results as a benchmark. The proposed reduced order modeling techniques are shown to facilitate accurate multi-stage modeling and analyses with or without blade mistuning, using only computationally inexpensive modal data from a cyclic disk sector and a single blade per stage. It is concluded that the most promising and practically feasible approach may be a combination of approaches (a) and (b), in which secondary modal analyses and truncations are first carried out on disk-blade constraint-mode partitions, followed by a tertiary modal analysis on the resulting multi-stage model. In conclusion, by alleviating the restriction to single-stage analyses, the presented multi-stage modeling techniques will enable engineers to analyze the dynamics of mistuned turbomachinery rotor assemblies with greater confidence.

scholarly journals A nonintrusive adaptive reduced order modeling approach for a molten salt reactor system

2020 ◽  
Vol 141 ◽  
pp. 107321 ◽  
Author(s):  
Fahad Alsayyari ◽  
Marco Tiberga ◽  
Zoltán Perkó ◽  
Danny Lathouwers ◽  
Jan Leen Kloosterman
Keyword(s):  
Molten Salt ◽  
Reduced Order Modeling ◽  
Reactor System ◽  
Molten Salt Reactor ◽  
Reduced Order ◽  
Modeling Approach
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