Assessment of Geometric Nonlinearities Influence On NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

2021 ◽  
Author(s):  
Elise Delhez ◽  
Florence Nyssen ◽  
Jean-Claude Golinval ◽  
Alain Batailly
Keyword(s):  
Dynamical Problem ◽  
Evaluation Procedure ◽  
Large Displacements ◽  
Geometric Nonlinearities ◽  
Abradable Coating ◽  
Stiffness Evaluation ◽  
Blade Tip ◽  
Modal Derivatives ◽  
Blade Model ◽  
Selection Of

Abstract This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote reproducibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.

Assessment of Geometric Nonlinearities Influence on NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

2021 ◽  
Author(s):  
Elise Delhez ◽  
Florence Nyssen ◽  
Jean-Claude Golinval ◽  
Alain Batailly
Keyword(s):  
Dynamical Problem ◽  
Evaluation Procedure ◽  
Large Displacements ◽  
Geometric Nonlinearities ◽  
Abradable Coating ◽  
Stiffness Evaluation ◽  
Blade Tip ◽  
Modal Derivatives ◽  
Blade Model ◽  
Selection Of

Abstract This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote re-producibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.

scholarly journals Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Adrien Martin ◽  
Fabrice Thouverez
Keyword(s):  
Symmetric System ◽  
Evaluation Procedure ◽  
Geometric Nonlinearities ◽  
Modeling Process ◽  
Nonlinear Solver ◽  
Step Procedure ◽  
Stator Vane ◽  
Cyclic Symmetric ◽  
Aeronautical Industry ◽  
Modal Derivatives

The search for ever lighter weight has become a major goal in the aeronautical industry as it has a direct impact on fuel consumption. It also implies the design of increasingly thin structures made of sophisticated and flexible materials. This may result in nonlinear behaviors due to large structural displacements. Stator vanes can be affected by such phenomena, and as they are a critical part of turbojets, it is crucial to predict these behaviors during the design process in order to eliminate them. This paper presents a reduced order modeling process suited for the study of geometric nonlinearities. The method is derived from a classical component mode synthesis (CMS) with fixed interfaces, in which the reduced nonlinear terms are obtained through a stiffness evaluation procedure (STEP) procedure using an adapted basis composed of linear modes completed by modal derivatives (MD). The whole system is solved using a harmonic balance procedure and a classic iterative nonlinear solver. The application is implemented on a schematic stator vane model composed of nonlinear Euler–Bernoulli beams under von Kàrmàn assumptions.

Implementation of a Rig Test for Rotor/Stator Interaction of Low-Pressure Compressor Blades and Comparison of Experimental Results With Numerical Model

2020 ◽  
Author(s):  
Laura Pacyna ◽  
Alexandre Bertret ◽  
Alain Derclaye ◽  
Luc Papeleux ◽  
Jean-Philippe Ponthot
Keyword(s):  
Low Cost ◽  
Low Pressure ◽  
Angular Speed ◽  
Compressor Blades ◽  
Abradable Coating ◽  
Rotor Stator Interaction ◽  
Blade Tip ◽  
Numerical Tool ◽  
Short Time ◽  
Pressure Compressor

Abstract To investigate the contact phenomenon between the blade tip and the abradable coated casing, a rig test was designed and built. This rig test fills the following constraints: simplification of the low-pressure compressor environment but realistic mechanical conditions, ability to test several designs in short time, at low cost and repeatability. The rig test gives the opportunity to investigate the behavior of different blade designs regarding the sought phenomenon, to refine and mature the phenomenon comprehension and to get data for the numerical tool validation. The numerical tool considers a 3D finite elements model of low-pressure compressor blades with a surrounding rigid casing combined with a specialized model to take into account the effects of the wear of the abradable coating on the blade dynamics. Numerical results are in good agreement with tests in terms of: critical angular speed, blade dynamics and wear pattern on the abradable coated casing.

scholarly journals Reduced Order Models for Nonlinear Dynamic Analysis With Application to a Fan Blade

2019 ◽  
Author(s):  
Mikel Balmaseda ◽  
G. Jacquet-Richardet ◽  
A. Placzek ◽  
D.-M. Tran
Keyword(s):  
Normal Modes ◽  
Nonlinear Dynamic Analysis ◽  
Evaluation Procedure ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Stiffness Evaluation ◽  
Fan Blade ◽  
Proper Orthogonal ◽  
Good Agreement

Abstract In the present work reduced order models (ROM) that are independent from the full order finite element models (FOM) considering geometrical non linearities are developed and applied to the dynamic study of a fan. The structure is considered to present nonlinear vibrations around the pre-stressed equilibrium induced by rotation enhancing the classical linearised approach. The reduced nonlinear forces are represented by a polynomial expansion obtained by the Stiffness Evaluation Procedure (STEP) and then corrected by means of a Proper Orthogonal Decomposition (POD) that filters the full order nonlinear forces (StepC ROM). The Linear Normal Modes (LNM) and Craig-Bampton (C-B) type reduced basis are considered here. The latter are parametrised with respect to the rotating velocity. The periodic solutions obtained with the StepC ROM are in good agreement with the solutions of the FOM and are more accurate than the linearised ROM solutions and the STEP ROM. The proposed StepC ROM provides the best compromise between accuracy and time consumption of the ROM.

Dynamic characteristics analysis of blade-casing rubbing faults with abradable coatings

2020 ◽  
pp. 095440622094155
Author(s):  
Junhong Zhang ◽  
Xin Lu ◽  
Jiewei Lin ◽  
Liang Ma ◽  
Huwei Dai
Keyword(s):  
Rotor System ◽  
Rotating Speed ◽  
Fundamental Frequencies ◽  
Abradable Coating ◽  
Characteristics Analysis ◽  
Blade Tip ◽  
System Vibration ◽  
Initial Clearance ◽  
Abradable Coatings ◽  
Dynamic Characteristics Analysis

In this paper, a dynamic model of a “0-2-1” rotor system with rubbing fault between blade and abradable coated casings is developed. The sub-model of rubbing force considers scraping work energy of coating, casing stiffness, and initial clearance between blade tip and casing. A rotor rig is established and samples of abradable coatings are introduced into the rubbing experiment. Vibration characteristics of the rotor system under blade-casing rubbing fault are analyzed. Effects of rotating speed and initial clearance on the rub force and the system vibration are studied. Results show that the vibration of rotor focuses on the fundamental and multiple fundamental frequencies due to the blade-casing rubbing with the abradable coating. The multiple fundamental frequencies, the 2 × and 3 × in particular, are greatly affected by the rotating speed. The fractional harmonic frequencies are strongly influenced by the initial clearance between the blade tip and casing. Besides, the rotating speed and the initial clearance between the blade tip and abradable coating on the casing also affect the amplitude and distribution of the rub force.

Effective Modal Derivatives Based Reduction Method for Geometrically Nonlinear Structures

2011 ◽  
Author(s):  
Paolo Tiso
Keyword(s):  
Reduction Method ◽  
Order Reduction ◽  
Second Order ◽  
Geometrically Nonlinear ◽  
Vibration Modes ◽  
Model Order ◽  
Modal Derivatives ◽  
Dynamics Problems ◽  
Modal Truncation ◽  
Selection Of

Effective Model Order Reduction (MOR) for geometrically nonlinear structural dynamics problems can be achieved by projecting the Finite Element (FE) equations on a basis constituted by a set of vibration modes and associated second order modal derivatives. However, the number of modal derivatives generated by such approach is quadratic with respect to the number of chosen vibration modes, thus quickly making the dimension of the reduction basis large. We show that the selection of the most important second order modes can be based on the convergence of the underlying linear modal truncation approximation. Given a certain time dependency of the load, this method allows to select the most significant modal derivatives set before computing it.

scholarly journals Elément de poutre multicouche avec glissement d’interface

2007 ◽  
pp. 559-581
Author(s):  
Blaise Rebora ◽  
François Frey
Keyword(s):  
Arbitrary Number ◽  
Beam Element ◽  
Large Displacements ◽  
Corotational Formulation ◽  
Geometric Nonlinearities ◽  
Small Strains ◽  
Number Of Layers ◽  
Von Karman ◽  
Interlayer Slip ◽  
Von Kármán

This paper presents a multilayered two node planar beam element, straight or shallow, of Bernoulli type, with an arbitrary number of layers with interlayer slip. Material and geometric nonlinearities are included. Small strains and slips are assumed. Large displacements are dealt with von Karman strain coupled with corotational formulation. No locking appears. Various tests show the capabilities of this element.

scholarly journals Reduced Order Models for Nonlinear Dynamic Analysis With Application to a Fan Blade

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Mikel Balmaseda ◽  
G. Jacquet-Richardet ◽  
A. Placzek ◽  
D.-M. Tran
Keyword(s):  
Normal Modes ◽  
Nonlinear Dynamic Analysis ◽  
Evaluation Procedure ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Stiffness Evaluation ◽  
Fan Blade ◽  
Proper Orthogonal ◽  
Good Agreement

Abstract In this work, reduced order models (ROM) that are independent from the full order finite element models (FOM) considering geometrical nonlinearities are developed and applied to the dynamic study of a fan. The structure is considered to present nonlinear vibrations around the prestressed equilibrium induced by rotation enhancing the classical linearized approach. The reduced nonlinear forces are represented by a polynomial expansion obtained by the stiffness evaluation procedure (STEP) and then corrected by means of a proper orthogonal decomposition (POD) that filters the full order nonlinear forces (StepC ROM). The linear normal modes (LNM) and Craig-Bampton (C-B) type reduced basis are considered here. The latter are parameterized with respect to the rotating velocity. The periodic solutions obtained with the StepC ROM are in good agreement with the solutions of the FOM and are more accurate than the linearized ROM solutions and the STEP ROM. The proposed StepC ROM provides the best compromise between accuracy and time consumption of the ROM.

scholarly journals Predicting Tomato Seedling Morphology by X-ray Analysis of Seeds

1994 ◽  
Vol 119 (2) ◽  
pp. 258-263 ◽  
Author(s):  
W.J. van der Burg ◽  
J.W. Aartse ◽  
R.A van Zwol ◽  
H. Jalink ◽  
R.J. Bino
Keyword(s):  
Free Space ◽  
Evaluation Procedure ◽  
Germination Test ◽  
High Quality ◽  
Seedling Morphology ◽  
Tomato Seedling ◽  
X Ray ◽  
Size And Morphology ◽  
Selection Of

Studies based on X-ray photographs were conducted to predict the morphology of tomato (Lycopersicon esculentum Mill.) seedlings at transplanting stage. Currently, seed-lot quality of tomato seeds for growing commercial transplants is determined with grow-out tests in the greenhouse because the standard germination test fails to predict the percentage of normal or usable transplants (UTs). These grow-out tests, however, are difficult to standardize. An X-ray evaluation procedure is presented as an alternative. X-ray images nondestructively provide information on embryo size and morphology and the amount of endosperm and the area of free space. These parameters correlate well with the morphology of 14-day old seedlings. Cotyledon morphology has the highest correlation with the percentage of UTs. A test based on the evaluation of X-ray images, classifying the cotyledon morphology and seed free space, predicts the percentage of UTs more accurately than the currently used germination test. A second method based on an equation that uses the probabilities of all X-ray categories proportionally predicts the percentage of UTs of primed seeds more accurately than the first method. Selecting individual seeds based on X-ray images has the potential to raise the percentage of UTs of seed lots. On the average, the percentage of UTs of control seeds was 22% higher after hand selection based on X-ray evaluation. Primed seeds gave 12% higher results. Hence, X-ray analysis can predict seedling performance and enable the selection of high-quality seeds.

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