The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Mathias Legrand - One of the best experts on this subject based on the ideXlab platform.
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Two-dimensional modeling of unilateral contact-induced shaft precessional motions in bladed-disk/casing systems
International Journal of Non-Linear Mechanics, 2015Co-Authors: Nicolas Salvat, Alain Batailly, Mathias LegrandAbstract:The present work targets shaft whirling motions induced by direct blade/casing unilateral contact occurrences in aircraft engine bladed-disk assemblies. These contact events are favored by increasingly reduced blade-tip clearances and potentially lead to harmful interactions that may threaten the engine structural integrity. A simplified 2D in-plane finite element model representative of the engine fan stage is built, accounting for the flexibility of the shaft through two linear springs attached to the disk center node and the structural coupling provided by the fan frame and the bearings, modeled by an array of linear springs. A linear stability analysis of the reduced-order coupled system reveals two unstable zones in a selected rotational speed range, emanating from the linearly predicted modal coincidence speeds. Through a time-marching strategy, two asymmetric contact initiation mechanisms are investigated: (1) a prescribed casing distortion and (2) a mass imbalance on the bladed-disk. It is shown how the 1-Nodal Diameter mode of the first modal family of the bladed-disk is dominant when a modal interaction arises from the transient casing distortion and leads to divergent regimes. The presence of the frame/bearings coupling induces a shift in the critical speeds detected, generally characterized by a backward traveling wave in the rotating frame and a forward traveling one in the fixed frame. Further, when a mass imbalance is the excitation source, the suspension modes appear to have a major role and a stable limit cycle is reached regardless of the coupling stiffness with much lower energy levels than in divergent regimes
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Two-dimensional modeling of shaft precessional motions induced by blade/casing unilateral contact in aircraft engines
2014Co-Authors: Nicolas Salvat, Alain Batailly, Mathias LegrandAbstract:In the present work, the focus is made on the occurrence of precessional motions of the shaft---whirling motions---in bladed-disk assemblies, initiated by direct blade/casing contacts in one stage of an aircraft engine. These contact events are favored by increasingly reduced blade-tip clearances and are expected to occur during standard operating conditions. However, it has been shown that potentially harmful interactions may arise and threaten the engine structural integrity. A 2D in-plane model of an aircraft engine fan stage is built with a set of curved beams for the casing and an assembly straight beams for the bladed-disk. The flexibility of the shaft is reflected by two linear springs attached to the center node of the disk. Contact is initiated through a prescribed casing distortion and the two structures are then left free to interact. Equations of motion are solved via explicit time-marching and contact forces are computed with Lagrange multipliers method allowing to fully satisfy non-penetration conditions. Friction is accounted for through a Coulomb law and permanent sliding is assumed. Three types of regimes are identified, namely: (1) damped, (2) sustained, (3) divergent, and both forward and backward shaft precessional motions are witnessed. It is shown that the vibratory response of the bladed-disk mainly lies on the first Nodal Diameter of the first family of modes regardless of the rotational velocity or the type of regime detected. The risk of failure arising from these contact events is highlighted, in particular in the presence of forward whirl, and the need for accurate predictive tools in early design phases of the engine is emphasized.
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Structural modal interaction of a four degree-of-freedom bladed disk and casing model
Journal of Computational and Nonlinear Dynamics, 2010Co-Authors: Mathias Legrand, Christophe Pierre, Bernard PeseuxAbstract:Consideration is given to a very specific interaction phenomenon that may occur in turbomachines due to radial rub between a bladed disk and surrounding casing. These two structures, featuring rotational periodicity and axisymmetry, respectively, share the same type of eigenshapes, also termed Nodal Diameter traveling waves. Higher efficiency requirements leading to reduced clearance between blade-tips and casing together with the rotation of the bladed disk increase the possibility of interaction between these traveling waves through direct contact. By definition, large amplitudes as well as structural failure may be expected. A very simple two-dimensional model of outer casing and bladed disk is introduced in order to predict the occurrence of such phenomenon in terms of rotational velocity. In order to consider traveling wave motions, each structure is represented by its two nd-Nodal Diameter standing modes. Equations of motion are solved first using an explicit time integration scheme in conjunction with the Lagrange multiplier method, which accounts for the contact constraints, and then by the harmonic balance method (HBM). While both methods yield identical results that exhibit two distinct zones of completely different behaviors of the system, HBM is much less computationally expensive.
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Two-dimensional modeling of an aircraft engine structural bladed disk-casing modal interaction
Journal of Sound and Vibration, 2009Co-Authors: Mathias Legrand, Christophe Pierre, Patrice Cartraud, Jean-pierre LombardAbstract:In modern turbo machines such as aircraft jet engines, structural contacts between the casing and bladed disk may occur through a variety of mechanisms: coincidence of vibration modes, thermal deformation of the casing, rotor imbalance due to design uncertainties to name a few. These nonlinear interactions may result in severe damage to both structures and it is important to understand the physical circumstances under which they occur. In this study, we focus on a modal coincidence during which the vibrations of each structure take the form of a k-Nodal Diameter traveling wave characteristic of axi-symmetric geometries. A realistic two-dimensional model of the casing and bladed disk is introduced in order to predict the occurrence of this very specific interaction phenomenon versus the rotation speed of the engine. The equations of motion are solved using an explicit time integration scheme in conjunction with the Lagrange multiplier method where friction is accounted for. This model is validated from the comparison with an analytical solution. The numerical results show that the structures may experience different kinds of behaviors (namely damped, sustained and divergent motions) mainly depending on the rotational velocity of the bladed disk.
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Aircraft Engine Structural Rotor-Stator Modal Interaction
2005Co-Authors: Mathias Legrand, Christophe Pierre, Sébastien Roques, Bernard PeseuxAbstract:In modern turbo machines such as aircraft jet engines, contact between the casing and bladed disk may occur through a variety of mechanisms: coincidence of vibration modes, thermal deformation of the casing, rotor imbalance, etc. These nonlinear interactions may result in severe damage to both structures and it is important to understand the physical mechanisms that cause them and the circumstances under which they occur. In this study, we focus on the phenomenon of interaction caused by modal coincidence. A simple two-dimensional model of the casing and bladed disk structures is introduced in order to predict the occurrence of the interaction phenomenon versus the rotation speed of the rotor. Each structure is represented in terms of its two $k$-Nodal Diameter vibration modes, which are characteristic of axi-symmetric structures and allow for travelling wave motions that may interact through direct contact. The equations of motion are solved using an explicit time integration scheme in conjunction with the Lagrange multiplier method where friction is considered. Results of the numerical tool and theory show good agreement in the prediction of rotational speed to be avoided. To conclude, the mathematical statements of a multi-frequency domain-method are proposed. This method is to be used to circumvent numerical issues inherent to time-marching procedures.
Fabrice Thouverez - One of the best experts on this subject based on the ideXlab platform.
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Energy transfer between Nodal Diameters of cyclic symmetric structures exhibiting polynomial nonlinearities: Cyclic condition and analysis
Mechanical Systems and Signal Processing, 2020Co-Authors: Samuel Quaegebeur, Fabrice Thouverez, Benjamin Chouvion, Loic BertheAbstract:Abstract The recent trend of new design for large slender blades in turboengines facilitates structural large deformation and geometrical nonlinear vibratory effects. The cyclic symmetry properties of such structures, combined with these nonlinearities give rise to specific complex phenomena such as internal resonances or energy localization. Robust and efficient methods have been developed to recover the solutions of such problems but they currently lack proper tools to analyze the results. In this paper, a formula is provided to compute polynomial nonlinear forces directly in the cyclic (spectral) domain of a cyclic symmetric structure. This new approach enables to express the equation of motion directly in the spectral domain, and offers two main advantages. It first provides a reduction of the system by determining a priori which Nodal Diameters will be coupled and by giving a closed-form expression for a direct evaluation of the cyclic nonlinear force. The proposed approach also facilitates results interpretations. The method is applied to a simplified bladed disk with a cubic nonlinearity that models symmetric large deformation, although the analytical development is valid for any polynomial nonlinearity. A detailed analysis of the different phenomena occurring in the cyclic structure excited along a particular Nodal Diameter is provided. More precisely, a multiple scales analysis is performed and yields interesting insights of internal resonances between different Nodal Diameters. This analytical method is completed with several numerical simulations involving the harmonic balance method and bifurcation algorithms. Both of these analyses recover coherent results on the prediction of different internal resonances for traveling or standing wave excitations.
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Model reduction of nonlinear cyclic structures based on their cyclic symmetric properties
Mechanical Systems and Signal Processing, 2020Co-Authors: Samuel Quaegebeur, Benjamin Chouvion, Fabrice ThouverezAbstract:Abstract Displacement control of bladed-disks is of primary stake for turbo-engineers. Such structures present cyclic symmetric properties that allow some specific reduction techniques. For linear problems, the equation of motion projected on spectral components, also called Nodal Diameters, gives a system of equations in which the unknowns are uncoupled. Each Nodal Diameter can therefore be considered independently. However in real applications, the presence of nonlinear terms couples the different Nodal Diameters and makes the spectral equation of motion more complex to handle. This paper deals with this difficulty and presents two main results. It first gives an analytical derivation to determine which Nodal Diameters get coupled by friction nonlinearities. Such procedure reduces the size of the model but also the number of unknowns in the system by considering only the interacting Nodal Diameters. This method is general and allows to tackle a wide range of industrial problems. However this may not be sufficient for an efficient resolution of the nonlinear system since the nonlinear forces must first be evaluated in the physical domain, and, a priori, for all the sectors of the cyclic system before being computed in the spectral domain. The second main originality of the paper is the development of different strategies on this matter. One is analytical, valid for any excitation and is straightforward to implement, while the others are based on specific assumptions on the deformed shape but offer further reduction. The new methodologies are validated on a simplified bladed-disk with different excitation forces and different friction’s laws. They show very good accuracy and a substantial computation time reduction.
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Modal Testing of a Full-Scale Rotating Woven Composite Fan Using Piezoelectric Excitation
Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM, 2019Co-Authors: Antoine Mabilia, Edouard Jaeghere, Lionel Sanchez, Claude Gibert, Fabrice Thouverez, Laura GiovannoniAbstract:An experimental facility for testing full-scale bladed disks in vacuum conditions and under centrifugal load is described in this paper. The special feature of the PHARE#1 test rig is its multichannel excitation system which allows to excite woven composite fan blades with any spatial and phase distribution as well as synchronous or non-synchronous vibration forcing with respect to rotation speed. The configuration of the excitation system allows each blade to be excited independently and therefore Nodal Diameter excitations can be performed with traveling (forward, backward or mixed) or standing waves. First rotations of the PHARE#1 test rig produced results at different rotation speeds, for several modes, Nodal Diameters and excitation levels. Typical results analysis and findings are presented in this paper.
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Dynamics of Multistage Bladed Disks Systems
Journal of Engineering for Gas Turbines and Power, 2007Co-Authors: Denis Laxalde, Jean-pierre Lombard, Fabrice ThouverezAbstract:This paper presents a new and original method for dynamical analysis of multistage cyclic structures such as turbomachinery compressors or turbines. Each stage is modeled cyclically by its elementary sector and the interstage coupling is achieved through a cyclic recombination of the interface degrees of freedom. This method is quite simple to set up; it allows us to handle the finite element models of each stage's sector directly and, as in classical cyclic symmetry analysis, to study the Nodal Diameter problems separately. The method is first validated on a simple case study which shows good agreements with a complete 360 deg reference calculation. An industrial example involving two HP compressor stages is then presented. Then the forced response application is presented in which synchronous engine order type excitations are considered.
Albert C. J. Luo - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Vibration of Heated Co-rotating Disks
Journal of Vibration and Control, 2007Co-Authors: Nader Saniei, Albert C. J. LuoAbstract:Nonlinear vibrations of co-rotating disks with thermal effects are investigated under non-uniform temperature distributions relative to airflow induced by disk rotation. For analytical investigation of thermal effects, the temperature distribution patterns are obtained through the heat transfer coefficients measurements. The natural frequencies for symmetric and asymmetric responses of an 86 mm Diameter computer memory disk are computed. When the disk is heated, its stiffness becomes larger for the two lowest Nodal Diameter numbers and smaller for the other Nodal Diameter numbers. This implies that the vibration of heated, rotating disks for the higher Nodal Diameter numbers may be induced more easily than the cooled one.
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Thermal Effects on the Natural Frequency of Nonlinear, Co-Rotating Disks
Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise Parts A B and C, 2005Co-Authors: Albert C. J. Luo, Nader Saniei, William Ray HarpAbstract:Thermal effects on the natural frequency for the nonlinear free vibration of co-rotating disks are investigated for non-uniform temperature distributions relative to airflow induced by disk rotation. The natural frequencies for symmetric and asymmetric responses of a 3.5 inch Diameter computer memory disk are calculated. When the disk is heated, its stiffness becomes larger for the two lowest Nodal Diameter numbers and smaller for the other Nodal Diameter numbers. It implies that the vibration of heated, rotating disks for the higher Nodal Diameter numbers may be induced more easily than the cooled one.
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Asymmetric responses of rotating, thin disks experiencing large deflections
Computers & Mathematics with Applications, 2003Co-Authors: Albert C. J. Luo, C. D. MoteAbstract:AbstractAn analytical nonlinear solution for the asymmetric mode vibration of rotating disks is given in this paper through a recently developed, accurate plate theory instead of the von Karman model. The nonlinear solution can reduce to the linear one when nonlinear effects vanish. The symmetrical response is also recovered when the Nodal Diameter vanishes. The natural frequency varying with rotation speed and deflection amplitude is investigated through a 3.5-inch Diameter computer memory disk. From this investigation, it is found that the softening of rotating disks may occur for larger Nodal-Diameter numbers. The methodology given in this paper can be applied to nonlinear responses in structures such as rotating shafts and traveling plates
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Thermally Induced, Nonlinear Vibrations of Rotating Disks
Nonlinear Dynamics, 2001Co-Authors: Nader Saniei, Albert C. J. LuoAbstract:The natural frequency and responses for the nonlinear free vibration ofheated rotating disks are presented analytically when nonuniformtemperature distributions pertaining to the laminar and turbulentairflow induced by disk rotation are considered. The nonuniformtemperature distributions on the disk are highly dependent on itsrotation speed. The natural frequencies for symmetric and asymmetricresponses of a 3.5 inch Diameter computer memory disk are calculated.When the disk is heated, its stiffness becomes larger for the two lowestNodal Diameter numbers and smaller for the other Nodal Diameter numbers.It implies that the vibration of heated, rotating disks for the higherNodal Diameter numbers may be induced more easily than the cooled one.The results for the nonlinear vibration can reduce to those for thelinear vibration when the nonlinear effects vanish. To furtherinvestigate of the interaction of thermal and nonlinearity of rotatingdisks, the temperature distribution for such a rotating disk needs to bedeveloped.
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An Analytical Solution for the Nonlinear Vibration of Rotating, Thin Disks
Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise, 1999Co-Authors: Albert C. J. Luo, C. D. MoteAbstract:Abstract The response, natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the Luo and Mote’s plate theory of 1998. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish, and they are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch Diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when Nodal-Diameter numbers are small and the softening of rotating disks occurs when Nodal-Diameter numbers becomes larger. The critical speeds of softening disks decrease with increasing deflection amplitudes.
Nader Saniei - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Vibration of Heated Co-rotating Disks
Journal of Vibration and Control, 2007Co-Authors: Nader Saniei, Albert C. J. LuoAbstract:Nonlinear vibrations of co-rotating disks with thermal effects are investigated under non-uniform temperature distributions relative to airflow induced by disk rotation. For analytical investigation of thermal effects, the temperature distribution patterns are obtained through the heat transfer coefficients measurements. The natural frequencies for symmetric and asymmetric responses of an 86 mm Diameter computer memory disk are computed. When the disk is heated, its stiffness becomes larger for the two lowest Nodal Diameter numbers and smaller for the other Nodal Diameter numbers. This implies that the vibration of heated, rotating disks for the higher Nodal Diameter numbers may be induced more easily than the cooled one.
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Thermal Effects on the Natural Frequency of Nonlinear, Co-Rotating Disks
Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise Parts A B and C, 2005Co-Authors: Albert C. J. Luo, Nader Saniei, William Ray HarpAbstract:Thermal effects on the natural frequency for the nonlinear free vibration of co-rotating disks are investigated for non-uniform temperature distributions relative to airflow induced by disk rotation. The natural frequencies for symmetric and asymmetric responses of a 3.5 inch Diameter computer memory disk are calculated. When the disk is heated, its stiffness becomes larger for the two lowest Nodal Diameter numbers and smaller for the other Nodal Diameter numbers. It implies that the vibration of heated, rotating disks for the higher Nodal Diameter numbers may be induced more easily than the cooled one.
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Thermally Induced, Nonlinear Vibrations of Rotating Disks
Nonlinear Dynamics, 2001Co-Authors: Nader Saniei, Albert C. J. LuoAbstract:The natural frequency and responses for the nonlinear free vibration ofheated rotating disks are presented analytically when nonuniformtemperature distributions pertaining to the laminar and turbulentairflow induced by disk rotation are considered. The nonuniformtemperature distributions on the disk are highly dependent on itsrotation speed. The natural frequencies for symmetric and asymmetricresponses of a 3.5 inch Diameter computer memory disk are calculated.When the disk is heated, its stiffness becomes larger for the two lowestNodal Diameter numbers and smaller for the other Nodal Diameter numbers.It implies that the vibration of heated, rotating disks for the higherNodal Diameter numbers may be induced more easily than the cooled one.The results for the nonlinear vibration can reduce to those for thelinear vibration when the nonlinear effects vanish. To furtherinvestigate of the interaction of thermal and nonlinearity of rotatingdisks, the temperature distribution for such a rotating disk needs to bedeveloped.
Almudena Vega - One of the best experts on this subject based on the ideXlab platform.
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Tip-Shroud Labyrinth Seal Effect on The Flutter Stability of Turbine Rotor Blades
Journal of Turbomachinery, 2019Co-Authors: Roque Corral, Michele Greco, Almudena VegaAbstract:Abstract The effect of the tip-shroud seal on the flutter onset of a shrouded turbine rotor blade, representative of a modern gas turbine, is numerically tested, and the contributions to the work per cycle of the aerofoil and the tip shroud are clearly identified. The numerical simulations are conducted using a linearized frequency-domain solver. The flutter stability of the shrouded rotor blade is evaluated for an edgewise mode and compared with the standard industrial approach of not including the tip-shroud cavity. It turns out that including the tip shroud significantly changes the stability prediction of the rotor blade. This is due to two facts. First, the amplitude of the unsteady pressure created in the inter-fin cavity due to the motion of the airfoil is much greater than that of the airfoil. The impact of this contribution increases with the frequency. Second, the effect of the outer shroud of the rotor blade, which usually is not included either in the simulations, has an opposite trend with the Nodal Diameter than the airfoil reducing the maximum and minimum damping. It is concluded that the combined effect of the seal and its platform tends to stabilize the edgewise mode of the rotor blade for all the examined Nodal Diameters and reduced frequencies. Finally, the numerical results are shown to be consistent with those obtained using an analytical simplified model to account for the effect of the labyrinth seals.