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.

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.

Prediction of Geometrically Induced Localization Effects Using a Subset of Nominal System Modes

2019 ◽  
Author(s):  
Thomas Maywald ◽  
Christoph R. Heinrich ◽  
Arnold Kühhorn ◽  
Sven Schrape ◽  
Thomas Backhaus
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Reduced Order Model ◽  
Vibration Measurement ◽  
Mode Shapes ◽  
Compressor Stage ◽  
Order Model ◽  
Reduced Order ◽  
Numerical Predictions

Abstract It is widely known that the vibration characteristics of blade integrated discs can dramatically change in the presence of manufacturing tolerances and wear. In this context, an increasing number of publications discuss the influence of the geometrical variability of blades on phenomena like frequency splitting and mode localization. This contribution is investigating the validity of a stiffness modified reduced order model for predicting the modal parameters of a geometrically mistuned compressor stage. In detail, the natural frequencies and mode shapes, as well as the corresponding mistuning patterns, are experimentally determined for an exemplary rotor. Furthermore, a blue light fringe projector is used to identify the geometrical differences between the actual rotor and the nominal blisk design. With the help of these digitization results, a realistic finite element model of the whole compressor stage is generated. Beyond that, a reduced order model is implemented based on the nominal design intention. Finally, the numerical predictions of the geometrically updated finite element model and the stiffness modified reduced order model are compared to the vibration measurement results. The investigation is completed by pointing out the benefits and limitations of the SNM-approach in the context of geometrically induced mistuning effects.

Inverse Determination of Moving Heat Flux Distributions Using Reduced Order Models

2014 ◽  
Author(s):  
Brian H. Dennis ◽  
Ashkan Akbariyeh ◽  
John Michopoulos ◽  
Foteini Komninelli ◽  
Athanasios Iliopoulos
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Finite Element Model ◽  
Target Surface ◽  
Element Model ◽  
Basis Functions ◽  
Reduced Order Model ◽  
Analysis Model ◽  
Order Model ◽  
Reduced Order

Optimization-based solutions to inverse problems involve the coupling of an analysis model, such as a finite element model, with a numerical optimization method. The goal is to determine a set of parameters that minimize an objective function that is determined by solving the analysis model. In this paper, we present an approach that dramatically reduces the computational cost for solving this inverse problems in this way by replacing the original full order finite element model (FOM) with a reduced order model (ROM) that is both accurate and quick to compute. The reduced order model is constructed with basis functions generated using proper orthogonal decomposition of set of solutions from the FOM. A discrete Galerkin method is used to project the differential equation on the basis functions. This approach allows us to transform the linear full order finite element model into an equivalent discrete ROM with far fewer unknowns. The method is applied to a parameter estimation problem in heat transfer. Specifically, we determine the parameters governing the magnitude and distribution of an unknown surface heat flux moving at a constant velocity across the surface of a solid bar of material. A finite element model was implemented in the commercial package COMSOL and a corresponding ROM was constructed. The ROM was coupled with an optimization algorithm to determine the parameter values that minimized the distance between the computed surface temperatures and the target surface temperature. The target surface temperature was generated using simulated measurements produced from the full order finite element model. Several optimization methods were used. The results show the approach can recover the parameters with high accuracy with twenty seven FOM runs.

A Nonlinear Finite Element Model for Leaf Springs

2003 ◽  
Author(s):  
Mohamed A. Omar ◽  
Hiroyuki Sugiyama ◽  
Ahmed A. Shabana ◽  
Wei-Yi Loh ◽  
Rena Basch
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Nonlinear Finite Element ◽  
Reduced Order Model ◽  
Body Motion ◽  
Leaf Spring ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Finite Element Model

This paper presents a nonlinear finite element model for the leaf spring that can be used in multibody applications and vehicle dynamic simulations. The floating frame of reference formulation is used in this investigation to model leaf spring nonlinear dynamics. This formulation accounts for the coupling between different modes of deformation as well as the nonlinear coupling between the rigid body motion and the elastic deformation. By employing component mode synthesis techniques, a reduced order model is obtained for the leaf spring while maintaining a good degree of accuracy. The inertia shape integrals can be calculated once in advance using a preprocessor and then stored to be used to automatically generate the nonlinear equations of motion of the leaf spring. The use of a preprocessor to evaluate the inertia shape integrals before the dynamic simulation leads to considerable saving in CPU time and allows the utilization of existing finite element computer codes to obtain the data required for the flexible body simulation. This reduced order model is implemented in a general multibody algorithm in order to examine the effectiveness and robustness of the proposed techniques. As an application, the wind-up deformation of the front suspension system of a typical sport utility vehicle under severe braking condition is investigated.

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.

A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies

1997 ◽  
Vol 119 (1) ◽  
pp. 161-167 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Bladed Disk

A reduced order approach is introduced in this paper that can be used to predict the steady-state response of mistuned bladed disks. This approach takes results directly from a finite element analysis of a tuned system and, based on the assumption of rigid blade base motion, constructs a computationally efficient mistuned model with a reduced number of degrees of freedom. Based on a comparison of results predicted by different approaches, it is concluded that: The reduced order model displays structural fidelity comparable to that of a finite element model of the entire bladed disk system with significantly improved computational efficiency; and under certain circumstances both the finite element model and the reduced order model predict quite different response from simple spring-mass models.

scholarly journals A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies

1995 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Bladed Disk

A reduced order approach is introduced in this paper that can be used to predict the steady-state response of mistuned bladed disks. This approach takes results directly from a finite element analysis of a tuned system and, based on the assumption of rigid blade base motion, constructs a computationally efficient mistuned model with a reduced number of degrees of freedom. Based on a comparison of results predicted by different approaches it is concluded that: the reduced order model displays structural fidelity comparable to that of a finite element model of the entire bladed disk system with significantly improved computational efficiency; and under certain circumstances both the finite element model and the reduced order model predict quite different response from simple spring-mass models.

Finite-Element-Based Nonlinear Modal Reduction of a Rotating Beam with Large-Amplitude Motion

2003 ◽  
Vol 9 (3-4) ◽  
pp. 235-263 ◽  
Author(s):  
Polarit Apiwattanalunggarn ◽  
Steven W. Shaw ◽  
Christophe Pierre ◽  
Dongying Jiang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Model ◽  
Rotating Beam ◽  
Order Model ◽  
Reduced Order ◽  
Modal Reduction ◽  
The Finite Element Model

A nonlinear one-dimensional finite-element model representing the axial and transverse motions of a cantilevered rotating beam is reduced to a single nonlinear normal mode using invariant manifold techniques. This system is an idealized representation for large-amplitude vibrations of a rotorcraft blade. Although this model is relatively simple, it possesses the essential nonlinear coupling effects between the axial and transverse degrees of freedom. The nature of this coupling leads to the fact that we must use many degrees of freedom, whether based on finite elements or modal expansions, in order to accurately represent the beam vibrations. In this work, the slow modal convergence problem is overcome by nonlinear modal reduction that makes use of invariant manifold based nonlinear modes. This reduction procedure generates a single-degree-of-freedom reduced-order model that systematically accounts for the dynamics of all the linear modes, or finite elements, considered in the original model. The approach is used to study the dynamic characteristics of the finite-element model over a wide range of vibration amplitudes. Using extensive simulations, it is shown that the response of the reduced-order model is nearly identical to a reference system which is based on a large-scale representation of the finite-element model, and to a reduced-order Rayleigh-Ritz model. All of the procedures presented here have been computationally automated. Hence, in this study we demonstrate that it is feasible and practical to interface nonlinear finite-element methods with nonlinear modal reduction.

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