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.

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

2000 ◽  
Author(s):  
François Moyroud ◽  
Torsten Fransson ◽  
Georges Jacquet-Richardet
Keyword(s):  
Finite Element ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Computationally Efficient ◽  
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 area is that of bladed-disk mistuning. To predict the effects of mistuning, computationally efficient methods are necessary to make it feasible, especially in an industrial environment, to perform free vibration and forced response analyses of full assembly finite element models. Due to the size of typical finite element models of industrial bladed-disks, efficient reduction techniques must be used to systematically produce reduced order models. 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 inter-sector 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 is based on a Craig and Bampton substructuring and reduction approach. The results show a perfect agreement between the two reduced order models and the non-reduced 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 1 to 2 orders of magnitude are obtained for the industrial bladed-disk, with the modal reduction method being the most computationally efficient approach.

Reduced Order Model for a Two Stage Gas Turbine Including Mistuned Bladed Disks and Shaft Interaction

2009 ◽  
Author(s):  
Luis A. Boulton ◽  
Euro Casanova
Keyword(s):  
Finite Element ◽  
Gas Turbine ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Order Model ◽  
Two Stage ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk ◽  
The Impact

A number of previous works have suggested that in some cases the interaction between shaft and bladed disk modes could significantly modify the dynamics of the whole assembly i.e. the bladed disks mounted on a flexible shaft. This paper presents the application of a previously published reduced-order modeling technique to the dynamical modeling of a real two stage gas turbine, including the bladed disks and the shaft. In the resulting reduce order model, mistuning is included in the bladed disk models and the shaft is modeled using beam finite elements according to the classical rotordynamic approach. Generation of finite element parent model for the real turbine is presented and discussed as well as simplifications used in order to generate the reduced order model. Comparisons are made between the reduced model and the full finite element solution for free response frequencies and mode shapes in order to assess the methodology and to evaluate the impact of simplifying hypothesis considered in model generation. Finally, this work also shows interaction between shaft modes and bladed disk modes, therefore confirming that stage independent analysis might not be adequate for predicting the global dynamic response of some turbomachinery rotors.

The Effect of Lashing Wire Location on Mode Localization of Mistuned Bladed Disks

2012 ◽  
Vol 510 ◽  
pp. 160-164
Author(s):  
Ai Lun Wang ◽  
Qiang Huang
Keyword(s):  
Finite Element ◽  
Significant Influence ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Bladed Disks ◽  
Mode Localization ◽  
Bladed Disk ◽  
Natural Characteristics

The finite element models of bladed disks with different lashing wire locations were established. The natural characteristics and mode shapes of bladed disks with different lashing wire locations were compared, and the effect of lashing wire location on the natural characteristics and mode localization of bladed disks were analyzed. These results show that different lashing wire locations could carry different natural frequencies to bladed disk, and there must be one lashing wire location with the highest frequencies. Lashing wire location has a significant influence on the mode localization of the mistuned bladed disks, and the mode localization of the bladed disks is less sensitive to mistuning when the lashing wire is in the middle of blades.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Experimental Investigation of Mode Localization and Forced Response Amplitude Magnification for a Mistuned Bladed Disk

2000 ◽  
Author(s):  
John Judge ◽  
Christophe Pierre ◽  
Oral Mehmed
Keyword(s):  
Experimental Investigation ◽  
Traveling Wave ◽  
Forced Response ◽  
Response Amplitude ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Element Analysis ◽  
Mode Localization ◽  
Bladed Disk ◽  
Out Of Plane

The results of an experimental investigation on the effects of random blade mistuning on the forced dynamic response of bladed disks are reported. The primary aim of the experiment is to gain understanding of the phenomena of mode localization and forced response blade amplitude magnification in bladed disks. A stationary, nominally periodic, twelve-bladed disk with simple geometry is subjected to a traveling-wave, out-of-plane, “engine order” excitation delivered via phase-shifted control signals sent to piezo-electric actuators mounted on the blades. The bladed disk is then mistuned by the addition of small, unequal weights to the blade tips, and it is again subjected to a traveling wave excitation. The experimental data is used to verify analytical predictions about the occurrence of localized mode shapes, increases in forced response amplitude, and changes in resonant frequency due to the presence of mistuning. Very good agreement between experimental measurements and finite element analysis is obtained. The out-of-plane response is compared and contrasted with the previously reported in-plane mode localization behavior of the same test specimen. This work also represents an important extension of previous experimental study by investigating a frequency regime in which modal density is lower but disk-blade interaction is significantly greater.

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.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
C. Fang ◽  
O. G. McGee ◽  
Y. El Aini
Keyword(s):  
Finite Element ◽  
Theoretical Basis ◽  
Energy Model ◽  
Forced Response ◽  
Particle Methods ◽  
Test Model ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk ◽  
Flexible Disk

This paper draws upon the theoretical basis and applicability of the three-dimensional (3-D) reduced-order spectral-based “meshless” energy technology presented in a companion paper (McGee et al., 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis,” ASME J. Turbomach., to be published) to predict free and forced responses of bladed disks comprised of randomly mistuned blades integrally attached to a flexible disk. The 3-D reduced-order spectral-based model employed is an alternative choice in the computational modeling landscape of bladed disks, such as conventionally-used finite element methods and component mode synthesis techniques, and even emerging element-free Hamiltonian–Galerkin, Petrov–Galerkin, boundary integral, and kernel-particle methods. This is because continuum-based modeling of a full disk annulus of mistuned blades is, at present, a steep task using these latter approaches for modal-type mistuning and/or rogue blade failure analysis. Hence, a considerably simplified and idealized bladed disk of 20 randomly mistuned blades mounted to a flexible disk was created and modeled not only to analyze its free and forced 3-D responses, but also to compare the predictive capability of the present reduced-order spectral-based “meshless” technology to general-purpose finite element procedures widely-used in industry practice. To benchmark future development of reduced-order technologies of turbomachinery mechanics analysts may use the present 3-D findings of the idealized 20-bladed disk as a new standard test model. Application of the 3-D reduced-order spectral-based “meshless” technology to an industry integrally-bladed rotor, having all of its blades modally mistuned, is also offered, where reasonably sufficient upper-bounds on the exact free and forced 3-D responses are predicted. These predictions expound new solutions of 3-D vibration effects of modal mistuning strength and pattern, interblade mechanical coupling, and localized modes on the free and forced response amplitudes.

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.

scholarly journals Effects of Bearings and Housing on Mode Localization of a Nearly Cyclic Symmetric System

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Y. F. Chen ◽  
I. Y. Shen
Keyword(s):  
Finite Element ◽  
Reference System ◽  
Deductive Reasoning ◽  
Mode Shapes ◽  
Symmetric System ◽  
Finite Element Analyses ◽  
Localized Modes ◽  
Mode Localization ◽  
Bladed Disk ◽  
Cyclic Symmetric

This technical brief is to study how flexible bearings and housing affect mode localization of a nearly cyclic symmetric system with mistuning. This study is conducted via finite-element analyses and deductive reasoning. A reference system studied is a bladed disk with two groups of 24 localized modes. When bearings and housing are introduced into the reference system, their presence changes natural frequencies, mode shapes, and the number of the localized modes. Moreover, the mistuning causes bearing forces to surge for all the localized modes. A deductive reasoning based on the existing literature supports the observation from the finite-element analyses.

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