Reduced-Order Models of Mistuned Cracked Bladed Disks

2010 ◽  
Author(s):  
Olguta Marinescu ◽  
Bogdan I. Epureanu ◽  
Mihaela Banu
Keyword(s):  
Finite Element ◽  
Effective Means ◽  
Structural Response ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Reduced Order ◽  
Modeling Methodology ◽  
Relative Coordinates

Predicting the influence of cracks on the dynamics of bladed disks is a very important challenge. Cracks change the structural response, which in turn changes the crack propagation characteristics. Hence, accurate and computationally effective means to model the dynamics of cracked bladed disks and blisks is particularly crucial in applications such as prognosis, guidance for repairs, characterization after repairs, design, and structural health monitoring. Most current models of bladed disks exploit cyclic symmetry to gain computational efficiency. However, the presence of cracks and mistuning destroys that symmetry and makes computational predictions much more expensive. In this work, we propose a new reduced order modeling methodology which can speed up computations by several orders of magnitude. There are two key components of the new methodology. First, the displacements and deformations of the crack surfaces are not modeled in absolute coordinates but relative coordinates. That allows for an effective model reduction based on (fixed-interface Craig-Bampton) component mode synthesis (CMS). The use of relative coordinates allows one to define one of the components in CMS as the pristine/uncracked structure (with mistuning). This approach is used in combination with a set of accurate approximations for the constraint modes used in CMS. Second, the effects of mistuning are captured by component mode mistuning (CMM) which allows the construction of extremely efficient reduced order models for the pristine/uncracked component with mistuning. The novel proposed method is applied to a finite element model of an industrial blisk. The combined presence of mistuning and cracks is shown to have important effects. Also, the proposed approach is shown to provide accurate predictions for the overall blisk while requiring computations using single-sector models only. The influence of various parameters on the accuracy of the reduced order models is investigated. Overall, the results show a very good agreement between full finite element analyses and the proposed reduced order modeling approach.

Reduced Order Models of Mistuned Cracked Bladed Disks

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Olguta Marinescu ◽  
Bogdan I. Epureanu ◽  
Mihaela Banu
Keyword(s):  
Finite Element ◽  
Effective Means ◽  
Structural Response ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Reduced Order ◽  
Modeling Methodology ◽  
Relative Coordinates

Predicting the influence of cracks on the dynamics of bladed disks is a very important challenge. Cracks change the structural response, which in turn changes the crack propagation characteristics. Hence, accurate and computationally effective means to model the dynamics of cracked bladed disks and blisks is particularly crucial in applications such as prognosis, guidance for repairs, characterization after repairs, design, and structural health monitoring. Most current models of bladed disks exploit cyclic symmetry to gain computational efficiency. However, the presence of cracks and mistuning destroys that symmetry and makes computational predictions much more expensive. In this work, we propose a new reduced order modeling methodology that can speed up computations by several orders of magnitude. There are two key components of the new methodology. First, the displacements and deformations of the crack surfaces are not modeled in absolute coordinates but relative coordinates, which allows for an effective model reduction based on (fixed-interface Craig–Bampton) component mode synthesis (CMS). The use of relative coordinates allows one to define one of the components in CMS as the pristine/uncracked structure (with mistuning). This approach is used in combination with a set of accurate approximations for the constraint modes used in CMS. Second, the effects of mistuning are captured by component mode mistuning, which allows the construction of extremely efficient reduced order models for the pristine/uncracked component with mistuning. The novel proposed method is applied to a finite element model of an industrial blisk. The combined presence of mistuning and cracks is shown to have important effects. Also, the proposed approach is shown to provide accurate predictions for the overall blisk while requiring computations using single-sector models only. The influence of various parameters on the accuracy of the reduced order models is investigated. Overall, the results show a very good agreement between full finite element analyses and the proposed reduced order modeling approach.

scholarly journals Comparative Study of Blades Reduced Order Models With Geometrical Nonlinearities and Contact Interfaces

2020 ◽  
Author(s):  
Elise Delhez ◽  
Florence Nyssen ◽  
Jean-Claude Golinval ◽  
Alain Batailly
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Performance Indicator ◽  
Element Model ◽  
Reduced Order Models ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Reduction Methods ◽  
Blade Tip ◽  
Reduced Space

Abstract This paper investigates the use of different model reduction methods accounting for geometric nonlinearities. These methods are adapted to retain physical degrees-of-freedom in the reduced space in order to ease contact treatment. These reduction methods are applied to a 3D finite element model of an industrial compressor blade (NASA rotor 37). In order to compare the different reduction methods, a scalar indicator is defined. This performance indicator allows to quantify the accuracy of the predicted displacement both locally (at the blade tip) and globally. The robustness of each method with respect to variations of the external excitation is also assessed. The performances of the reduction methods are then compared in the case of frictional contact between the blade tip and the surrounding casing. This work brings evidence that reduced order models provide a computationally efficient alternative to full order finite element models for the accurate prediction of the time response of structures with both distributed and localized nonlinearities.

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.

Application of a Reduced Order Modeling Technique for Mistuned Bladed Disk-Shaft Assemblies

2007 ◽  
Author(s):  
Bartolome´ Segui´ ◽  
Euro Casanova
Keyword(s):  
Finite Element ◽  
Synthesis Method ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Modeling Technique ◽  
Disk Model ◽  
Reduced Order ◽  
Bladed Disk ◽  
Global Dynamic

This paper presents a reduced-order modeling technique, based on a component mode synthesis method specifically tailored for bladed disks, that allows the resulting low-order model to be attached to a shaft. Mistuning is included in the bladed disk model and the shaft is modeled using uniaxial finite elements according to the rotordynamic approach. The proposed formulation is applied to an example finite element model of a bladed disk, for both tuned and mistuned blades. Comparisons are made between the reduced model and the full finite element solution for free and forced responses in order to assess the methodology. The forced response amplitudes of the blades are found to vary significantly with the inclusion of a flexible shaft. This work suggest that stage independent analyses might not be adequate for predicting the global dynamic response of rotating assemblies of turbomachines.

Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds

1999 ◽  
Vol 121 (3) ◽  
pp. 515-522 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Modeling Technique ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Reduced Order ◽  
Synthesis Approach

This paper presents important improvements and extensions to a computationally efficient reduced order modeling technique for the vibration analysis of mistuned bladed disks. In particular, this work shows how the existing modeling technique is readily extended to turbomachinery rotors with shrouded blades. The modeling technique employs a component mode synthesis approach to systematically generate a reduced order model (ROM) using component modes calculated from a finite element model (FEM) of the rotor. Based on the total number of degrees of freedom, the ROM is typically two or three orders of magnitude smaller than the FEM. This makes it feasible to predict the forced response statistics of mistuned bladed disks using Monte Carlo simulations. In this work, particular attention is devoted to the introduction of mistuning into the ROM of a shrouded assembly. Mistuning is modeled by projecting the mistuned natural frequencies of a single, cantilever blade with free shrouds onto the harmonic modes of the shrouded blade assembly. Thus, the necessary mistuning information may be measured by testing individual blades.

scholarly journals Approaches for Reduced-Order Modeling of Electrically Actuated von-Karman Microplates

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Shahid Saghir ◽  
M.I. Younis
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Electrostatic Force ◽  
Element Model ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Linear Eigenvalue Problem ◽  
Von Karman ◽  
Wide Range ◽  
Von Kármán

This article presents and compares different approaches to develop reduced-order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First, we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. Results among the various reduced-order modes are compared and are also validated by comparing to results of the finite-element model. Further, the reduced-order models are employed to capture the forced dynamic response of the microplate under small and large vibration amplitudes. Comparison of the different approaches is made for this case.

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

2000 ◽  
Author(s):  
Ronnie Bladh ◽  
Matthew P. Castanier ◽  
Christophe 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 (DOF). 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.

How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

2016 ◽  
Vol 23 (05) ◽  
pp. 1650019 ◽  
Author(s):  
Christian Gogu ◽  
Anirban Chaudhuri ◽  
Christian Bes
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Computational Cost ◽  
Reduced Order Modeling ◽  
Finite Element Models ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Separable Monte Carlo

Many sampling-based approaches are currently available for calculating the reliability of a design. The most efficient methods can achieve reductions in the computational cost by one to several orders of magnitude compared to the basic Monte Carlo method. This paper is specifically targeted at sampling-based approaches for reliability analysis, in which the samples represent calls to expensive finite element models. The aim of this paper is to illustrate how these methods can further benefit from reduced order modeling to achieve drastic additional computational cost reductions, in cases where the reliability analysis is carried out on finite element models. Standard Monte Carlo, importance sampling, separable Monte Carlo and a combined importance separable Monte Carlo approach are presented and coupled with reduced order modeling. An adaptive construction of the reduced basis models is proposed. The various approaches are compared on a thermal reliability design problem, where the coupling with the adaptively constructed reduced order models is shown to further increase the computational efficiency by up to a factor of six.

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

2017 ◽  
Author(s):  
Elias Khalifeh ◽  
Elsa Piollet ◽  
Antoine Millecamps ◽  
Alain Batailly
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Angular Speed ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Linear Finite Element ◽  
Centrifugal Stiffening ◽  
Blade Tip

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.

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