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.

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.

Lattice Boltzmann Flow Simulations With Applications of Reduced Order Modeling Techniques.

2014 ◽  
Author(s):  
Donald L. Brown ◽  
Jun Li ◽  
Victor M. Calo ◽  
Mehdi Ghommem ◽  
Yalchin Efendiev
Keyword(s):  
Lattice Boltzmann ◽  
Reduced Order Modeling ◽  
Reduced Order ◽  
Flow Simulations ◽  
Modeling Techniques

Modeling Constrained Layer Frictional Interfaces With Discontinuous Basis Functions

2011 ◽  
Author(s):  
M. R. Brake ◽  
M. J. Starr ◽  
D. J. Segalman
Keyword(s):  
Continuous System ◽  
Reduced Order Modeling ◽  
Basis Functions ◽  
Mode Shapes ◽  
Symmetric Model ◽  
Reduced Order ◽  
Linear Mode ◽  
System A ◽  
Modeling Techniques ◽  
A New Technique

Constrained layer frictional interfaces, such as joints, are prevalent in engineering applications. Because these interfaces are often used in built-up structures, reduced order modeling techniques are utilized for developing simulations of them. One limitation of the existing reduced order modeling techniques, though, is the loss of the local kinematics due to regularization of the frictional interfaces. This paper aims to avoid the use of regularization in the modeling of constrained layer frictional interfaces by utilizing a new technique, the discontinuous basis function method. This method supplements the linear mode shapes of the system with a series of discontinuous basis functions that are used to account for nonlinear forces acting on the system. A symmetric, constrained layer frictional interface is modeled as a continuous system connected to two rigid planes by a series of Iwan elements. This symmetric model is used to test the hypothesis that symmetric problems are not subjected to the range of variability seen in physical structures, which have non-uniform pressure and friction distributions. Insights from solving the symmetric problem are used to consider the case where a non-uniform distribution of friction and pressure exists.

Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part I: Theoretical Models

2000 ◽  
Vol 123 (1) ◽  
pp. 89-99 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Modal Analysis ◽  
Theoretical Models ◽  
Complex Structures ◽  
Bladed Disks ◽  
Component Structure ◽  
Reduced Order ◽  
Practical Applications ◽  
Dynamic Analyses ◽  
Modeling Techniques ◽  
Model Size

Component mode synthesis (CMS) techniques are widely used for dynamic analyses of complex structures. Significant computational savings can be achieved by using CMS, since a modal analysis is performed on each component structure (substructure). Mistuned bladed disks are a class of structures for which CMS is well suited. In the context of blade mistuning, it is convenient to view the blades as individual components, while the entire disk may be treated as a single component. Individual blade mistuning may then be incorporated into the CMS model in a straightforward manner. In this paper, the Craig–Bampton (CB) method of CMS is formulated specifically for mistuned bladed disks, using a cyclic disk description. Then a novel secondary modal analysis reduction technique (SMART) is presented: a secondary modal analysis is performed on a CB model, yielding significant further reduction in model size. In addition, a straightforward non-CMS method is developed in which the blade mistuning is projected onto the tuned system modes. Though similar approaches have been reported previously, here it is generalized to a form that is more useful in practical applications. The theoretical models are discussed and compared from both computational and practical perspectives. It is concluded that using SMART, based on a CB model, has tremendous potential for highly efficient, accurate modeling of the vibration of mistuned bladed disks.

scholarly journals A Reduced-Order Model of Detuned Cyclic Dynamical Systems With Geometric Modifications Using a Basis of Cyclic Modes

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Moustapha Mbaye ◽  
Christian Soize ◽  
Jean-Philippe Ousty
Keyword(s):  
Reduction Method ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Element Analysis ◽  
Disk Model ◽  
Reduced Order ◽  
Bladed Disk ◽  
Forced Responses ◽  
Sector Matrix

A new reduction method for vibration analysis of intentionally mistuned bladed disks is presented. The method is built for solving the dynamic problem of cyclic structures with geometric modifications. It is based on the use of the cyclic modes of the different sectors, which can be obtained from a usual cyclic symmetry modal analysis. Hence the projection basis is constituted; as well as, on the whole bladed disk, each sector matrix is reduced by its own modes. The method is validated numerically on a real bladed disk model, by comparing free and forced responses of a full model finite element analysis to those of a reduced-order model using the new reduction method.

scholarly journals Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part II: Application

2000 ◽  
Vol 123 (1) ◽  
pp. 100-108 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Theoretical Models ◽  
Companion Paper ◽  
Reduced Order Modeling ◽  
Bladed Disks ◽  
Reduced Order ◽  
Component Interface ◽  
Forced Responses

In this paper, the component-mode-based methods formulated in the companion paper (Part I: Theoretical Models) are applied to the dynamic analysis of two example finite element models of bladed disks. Free and forced responses for both tuned and mistuned rotors are considered. Comprehensive comparisons are made among the techniques using full system finite element solutions as a benchmark. The accurate capture of eigenfrequency veering regions is of critical importance for obtaining high-fidelity predictions of the rotor’s sensitivity to mistuning. Therefore, particular attention is devoted to this subject. It is shown that the Craig–Bampton component mode synthesis (CMS) technique is robust and yields highly reliable results. However, this is achieved at considerable computational cost due to the retained component interface degrees of freedom. It is demonstrated that this problem is alleviated by a secondary modal analysis reduction technique (SMART). In addition, a non-CMS mistuning projection method is considered. Although this method is elegant and accurate, it is seen that it lacks the versatility and efficiency of the CMS-based SMART. Overall, this work shows that significant improvements on the accuracy and efficiency of current reduced order modeling methods are possible.

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