Parametric Reduced Order Models for Bladed Disks With Mistuning and Varying Operational Speed

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Eric Kurstak ◽  
Ryan Wilber ◽  
Kiran D'Souza
Keyword(s):  
Finite Element ◽  
Forced Response ◽  
Reduced Order Models ◽  
Small Frequency ◽  
Bladed Disks ◽  
Modal Expansion ◽  
Reduced Order ◽  
Finite Element Calculations ◽  
Different Types ◽  
Reduced Space

A considerable amount of research has been conducted to develop reduced order models (ROMs) of bladed disks that can be constructed using single sector calculations when there is mistuning present. A variety of methods have been developed to efficiently handle different types of mistuning ranging from small frequency mistuning, which can be modeled using a variety of methods including component mode mistuning (CMM), to large geometric mistuning, which can be modeled using multiple techniques including pristine rogue interface modal expansion (PRIME). Research has also been conducted on developing ROMs that can accommodate the variation of specific parameters in the reduced space; these models are referred to as parametric reduced order models (PROMs). This work introduces a PROM for bladed disks that allows for the variation of rotational speed in the reduced space. These PROMs are created by extracting information from sector models at three rotational speeds, and then the appropriate ROM is efficiently constructed in the reduced space at any other desired speed. This work integrates these new PROMs for bladed disks with two existing mistuning methods, CMM and PRIME, to illustrate how the method can be readily applied for a variety of mistuning methods. Frequencies and forced response calculations using these new PROMs are compared to the full order finite element calculations to demonstrate the effectiveness of the method.

Parametric Reduced Order Models for Bladed Disks With Mistuning and Varying Operational Speed

2018 ◽  
Author(s):  
Eric Kurstak ◽  
Ryan Wilber ◽  
Kiran D’Souza
Keyword(s):  
Forced Response ◽  
Reduced Order Models ◽  
Order Model ◽  
Small Frequency ◽  
Bladed Disks ◽  
Modal Expansion ◽  
Reduced Order ◽  
Finite Element Calculations ◽  
Different Types ◽  
Reduced Space

A considerable amount of research has been conducted to develop reduced order models of bladed disks that can be constructed using single sector calculations when there is mistuning present. A variety of methods have been developed to efficiently handle different types of mistuning ranging from small frequency mistuning, which can be modeled using a variety of methods including component mode mistuning (CMM), to large geometric mistuning, which can be modeled using multiple techniques including pristine rogue interface modal expansion (PRIME). Research has also been conducted on developing reduced order models that can accommodate the variation of specific parameters in the reduced space; these models are referred to as parametric reduced order models (PROMs). This work introduces a PROM for bladed disks that allows for the variation of rotational speed in the reduced space. These PROMs are created by extracting information from sector models at three rotational speeds, and then the appropriate reduced order model is efficiently constructed in the reduced space at any other desired speed. This work integrates these new PROMs for bladed disks with two existing mistuning methods, CMM and PRIME, to illustrate how the method can be readily applied for a variety of mistuning methods. Frequencies and forced response calculations using these new PROMs are compared to the full order finite element calculations to demonstrate the effectiveness of the method.

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.

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.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
O. G. McGee ◽  
C. Fang ◽  
Y. El-Aini
Keyword(s):  
Finite Element ◽  
Predictive Accuracy ◽  
Equations Of Motion ◽  
Response Prediction ◽  
Companion Paper ◽  
Energy Model ◽  
Forced Response ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk

In this paper, a reduced order model for the vibrations of bladed disk assemblies was achieved. The system studied was a 3D annulus of shroudless, “custom-tailored,” mistuned blades attached to a flexible disk. Specifically, the annulus was modeled as a spectral-based “meshless” continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3D displacement field of mathematically complete, orthonormal “blade-disk” polynomials multiplied by generalized coefficients. The coefficients were determined by constraining the polynomial series to satisfy the extended Ritz stationary equations and essential boundary conditions of the bladed disk. From this, the governing equations of motion were generated into their usual dynamical forms to calculate upper-bounds on the actual free and forced responses of bladed disks. No conventional finite elements and element connectivity or component substructuring data were needed. This paper, Part I, outlines the theoretical foundation of the present model, and through extensive Monte Carlo simulations, establishes the analytical basis, predictive accuracy, and re-analysis efficiency of the present technology in the prediction of 3D maximum response amplitude of mistuned bladed disks having increasing numbers of nodal diameter excitations. Further applications validating the 3D approach against conventional finite element procedures of free and forced response prediction of a mistuned Integrally-Bladed Rotor used in practice is presented in a companion paper, Part II (Fang, McGee, and El-Aini, 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., to be published.

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.

Predicting Blade Stress Levels Directly From Reduced-Order Vibration Models of Mistuned Bladed Disks

2005 ◽  
Vol 128 (1) ◽  
pp. 206-210 ◽  
Author(s):  
Sang-Ho Lim ◽  
Christophe Pierre ◽  
Matthew P. Castanier
Keyword(s):  
Finite Element ◽  
Good Accuracy ◽  
Forced Response ◽  
Turbine Engines ◽  
Order Model ◽  
Bladed Disks ◽  
Element Analysis ◽  
Reduced Order ◽  
Modeling Techniques ◽  
Stress Levels

The forced vibration response of bladed disks can increase dramatically due to blade mistuning, which can cause major durability and reliability problems in turbine engines. To predict the mistuned forced response efficiently, several reduced-order modeling techniques have been developed. However, for mistuned bladed disks, increases in blade amplitude levels do not always correlate well with increases in blade stress levels. The stress levels may be computed by postprocessing the reduced-order model results with finite element analysis, but this is cumbersome and expensive. In this work, three indicators that can be calculated directly from reduced-order models are proposed as a way to estimate blade stress levels in a straightforward, systematic, and inexpensive manner. It is shown that these indicators can be used to predict stress values with good accuracy relative to finite element results, even for a case in which the displacement and stress levels show different frequency response trends.

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