Reduced-Order Models of Blisks With Small Geometric Mistuning

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Seunghun Baek ◽  
Bogdan Epureanu
Keyword(s):  
Linear Combination ◽  
Structural Properties ◽  
Dynamic Behavior ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Reduced Order ◽  
The Past ◽  
The Difference

A technique for generating reduced-order models (ROMs) of bladed disks with small geometric mistuning is proposed. Discrepancies in structural properties (mistuning) from blade to blade can cause a significant increase in the maximum vibratory stress. The effects of mistuning have been studied over the past few decades. Many researchers have studied the dynamic behavior of mistuned bladed disks by using ROMs. Many of these techniques rely on the fact that the modes of a mistuned system can be approximated by a linear combination of modes of the corresponding tuned system. In addition, the tuned system modes have been modeled in component mode mistuning by using modal participation factors of cantilevered blade modes. Such techniques assume that mistuning can be well modeled as variations in blade-alone frequencies. However, since geometric deformations contain stiffness and mass variations, mistuning can no longer be captured by cantilevered blade modes alone. To address this, several studies have focused on large and small geometric mistuning. These studies exploited the difference between tuned (with perturbed geometry) and nominal tuned mode shapes. In this work, we extend on that approach and devote particular attention to the development of ROMs of bladed disks with small geometric mistuning. The methodology requires only sector-level calculations and therefore can be applied to highly refined, realistic models of industrial size.

Reduced Order Models of Blisks With Small Geometric Mistuning

2016 ◽  
Author(s):  
Seunghun Baek ◽  
Yixin Zhao ◽  
Bogdan Epureanu
Keyword(s):  
Linear Combination ◽  
Structural Properties ◽  
Dynamic Behavior ◽  
New Technique ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Reduced Order ◽  
The Past ◽  
A New Technique

A technique for generating reduced order models (ROMs) of bladed disks with small geometric mistuning is proposed. Discrepancies in structural properties (mistuning) from blade to blade can cause a significant increase in the maximum vibratory stress. The effects of mistuning have been studied over the past few decades. Many researchers have studied the dynamic behavior of mistuned bladed disks by using ROMs. Many of these techniques rely on the fact that the modes of a mistuned system can be approximated by a linear combination of modes of the corresponding tuned system. Also, the tuned system modes have been modeled in component mode mistuning by using modal participation factors of cantilevered blade modes. Such techniques assume that mistuning can be well modeled as variations in blade alone frequencies. However, since geometric deformations contain stiffness and mass variations, mistuning can no longer be captured by cantilevered blade modes alone. To address this, a new technique is presented for generating ROMs of bladed disks with small geometric mistuning which may be a more general case of mistuning in practice.

A Comparison of Two Finite Element Reduction Techniques for Mistuned Bladed Disks

2002 ◽  
Vol 124 (4) ◽  
pp. 942-952 ◽  
Author(s):  
F. Moyroud ◽  
T. Fransson ◽  
G. Jacquet-Richardet
Keyword(s):  
Finite Element ◽  
Reduction Technique ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Mode Localization ◽  
Reduced Order ◽  
Bladed Disk ◽  
Reduction Techniques ◽  
Modal Reduction

The high performance bladed disks used in today’s turbomachines must meet strict standards in terms of aeroelastic stability and resonant response level. One structural characteristic that can significantly impact on both these areas is that of bladed disk mistuning. To predict the effects of mistuning, computational efficient methods are much needed to make free-vibration and forced-response analyses of full assembly finite element (FE) models feasible in both research and industrial environments. Due to the size and complexity of typical industrial bladed disk models, one must resort to robust and systematic reduction techniques to produce reduced-order models of sufficient accuracy. The objective of this paper is to compare two prevalent reduction methods on representative test rotors, including a modern design industrial shrouded bladed disk, in terms of accuracy (for frequencies and mode shapes), reduction order, computational efficiency, sensitivity to intersector elastic coupling, and ability to capture the phenomenon of mode localization. The first reduction technique employs a modal reduction approach with a modal basis consisting of mode shapes of the tuned bladed disk which can be obtained from a classical cyclic symmetric modal analysis. The second reduction technique uses Craig and Bampton substructure modes. The results show a perfect agreement between the two reduced-order models and the nonreduced finite element model. It is found that the phenomena of mode localization is equally well predicted by the two reduction models. In terms of computational cost, reductions from one to two orders of magnitude are obtained for the industrial bladed disk, with the modal reduction method being the most computationally efficient approach.

Accuracies of Reduced Order Models of a Bladed Rotor With Geometric Mistuning

2013 ◽  
Vol 136 (7) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Model Based ◽  
Bladed Rotor

The results from a reduced order model based on frequency mistuning are compared with those from recently developed modified modal domain analysis (MMDA). For the academic bladed rotor considered in this paper, the frequency mistuning analysis is unable to capture the effects of geometric mistuning, whereas MMDA provides accurate estimates of natural frequencies, mode shapes, and forced response.

A New Mistuning Identification Method Based on the Subset of Nominal System Modes Method

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Christian U. Waldherr ◽  
Patrick Buchwald ◽  
Damian M. Vogt
Keyword(s):  
Finite Element ◽  
Input Data ◽  
Measurement Data ◽  
Computational Effort ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Identification Procedure ◽  
Reduced Order ◽  
Nominal System ◽  
Identification Method

Abstract The mistuning problem of quasi-periodic structures has been the subject of numerous scientific investigations for more than 50 years. Researchers developed reduced-order models to reduce the computational costs of mistuning investigations including finite element models. One question which has also high practical relevance is the identification of mistuning based on modal properties. In this work, a new identification method based on the subset of nominal system modes method (SNM) is presented. Different to existing identification methods where usually the blade stiffness of each sector is scaled by a scalar value, N identification parameters are used to adapt the modal blade stiffness of each sector. The input data for the identification procedure consist solely of the mistuned natural frequencies of the investigated mode family as well as of the corresponding mistuned mode shapes in the form of one degree-of-freedom per sector. The reduction basis consists of the tuned mode shapes of the investigated mode family. Furthermore, the proposed identification method allows for the inclusion of centrifugal effects like stress stiffening and spin softening without additional computational effort. From this point of view, the presented method is also appropriate to handle centrifugal effects in reduced-order models using a minimum set of input data compared to existing methods. The power of the new identification method is demonstrated on the example of an axial compressor blisk. Finite element calculations including geometrical mistuning provide the database for the identification procedure. The correct functioning of the identification method including measurement noise is also validated to show the applicability to a case of application where real measurement data are available.

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 Component-Centric Reduced Order Modeling of the Dynamic Response of Linear Multibay Structures

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Yuting Wang ◽  
Marc P. Mignolet
Keyword(s):  
Natural Frequencies ◽  
Element Model ◽  
Fixed Number ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Entire Structure ◽  
Similar Mode ◽  
Fixed Interface ◽  
Proper Orthogonal

Component-centric reduced order models (ROMs) are introduced here as small-size ROMs providing an accurate prediction of the linear response of part of a structure (the β component) without focusing on the rest of it (the α component). Craig–Bampton (CB) substructuring methods are first considered. In one method, the β component response is modeled with its fixed interface modes while the other adopts singular value eigenvectors of the β component deflections of the linear modes of the entire structure. The deflections in the α component induced by harmonic motions of these β component modes are processed by a proper orthogonal decomposition (POD) to model the α component response. A third approach starts from the linear modes of the entire structure which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component, i.e., these nondominant modal contributions are “lumped” onto dominant ones. This lumping permits to increase the accuracy in the β component at a fixed number of modes. The three approaches are assessed on a structural finite element model of a nine-bay panel with the modal lumping-based method yielding the most “compact” ROMs. Finally, good robustness of the ROM to changes in the β component properties (e.g., for design optimization) is demonstrated and a similar sensitivity analysis is carried out with respect to the loading under which the ROM is constructed.

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.

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