scholarly journals Robust Analysis of Design in Vibration of Turbomachines

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Moustapha Mbaye ◽  
Christian Soize ◽  
Jean-Philippe Ousty ◽  
Evangeline Capiez-Lernout
Keyword(s):  
Probabilistic Approach ◽  
Robustness Analysis ◽  
Small Variation ◽  
Forced Response ◽  
Parameter Uncertainties ◽  
Modeling Errors ◽  
Manufacturing Tolerances ◽  
Response Amplification ◽  
Turbomachinery Design ◽  
Technological Methods

In the context of turbomachinery design, a small variation in the blade characteristics due to manufacturing tolerances can affect the structural symmetry creating mistuning which increases the forced response. However, it is possible to detune the mistuned system in order to reduce the forced response amplification. The main technological methods to introduce detuning are based on modifying either the blade material properties, either the interface between blades and disk, or the blade shapes. This paper presents a robustness analysis of mistuning for a given detuning in blade geometry. Detuning is performed by modifying blade shapes. The different types of blades, obtained by those modifications, are then distributed on the disk circumference. A new reduced-order model of the detuned disk is introduced. It is based on the use of the cyclic modes of the different sectors which can be obtained from a usual cyclic symmetry modal analysis. Finally, the robustness of the computational model responses with respect to uncertainties, is performed with a stochastic analysis using a nonparametric probabilistic approach of uncertainties which allows both the system-parameter uncertainties and the modeling errors to be taken into account.

scholarly journals Robust Analysis of Design in Vibration of Turbomachines

2009 ◽  
Author(s):  
Moustapha Mbaye ◽  
Christian Soize ◽  
Jean-Philippe Ousty ◽  
Evangeline Capiez-Lernout
Keyword(s):  
Probabilistic Method ◽  
Small Variation ◽  
Forced Response ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Reduced Order ◽  
Blade Shape ◽  
Manufacturing Tolerances ◽  
Response Amplification ◽  
Turbomachinery Design

In the context of turbomachinery design, a small variation in the blade characteristics due to manufacturing tolerances can affect the structural symmetry creating mistuning which increases the forced response. However, it is possible to detune the mistuned system in order to reduce the forced response amplification. The main technologic solutions to introduce detuning are based on modifying blade material properties, the interface between blade and disk, or the blade shape. This paper presents a sensitivity analysis of mistuning for a given detuning in unsteady aeroelasticity. Detuning is performed by modifying blade shapes. The different kinds of blades obtained by those modifications are then distributed on the disk circumference. A new reduced-order model of the detuned disk is constructed using the cyclic modes of the different sectors which can be obtained from a usual cyclic symmetry modal analysis. Finally a stochastic analysis using a non-parametric probabilistic method to take model and system parameters uncertainties into account in the computational model is performed.

scholarly journals Specifying Manufacturing Tolerances for a Given Amplification Factor: A Nonparametric Probabilistic Methodology

2003 ◽  
Author(s):  
Evange´line Capiez-Lernout ◽  
Christian Soize
Keyword(s):  
Inverse Problem ◽  
Probabilistic Model ◽  
Amplification Factor ◽  
Forced Response ◽  
Bladed Disks ◽  
Nonparametric Approach ◽  
Modeling Errors ◽  
Random Character ◽  
Manufacturing Tolerances ◽  
Random Uncertainties

It is known that the forced response of mistuned bladed disks can strongly be amplified in comparison with the forced response of the tuned system. The random character of mistuning thus requires the construction of probabilistics models of random uncertainties. This paper presents a nonparametric probabilistic model of random uncertainties which is adapted to the problematics of the blade mistuning. This nonparametric approach allows all the uncertainties yielding mistuning (manufacturing tolerances, dispersion of materials) to be taken into account and includes also the uncertainties due to the modeling errors. This new probabilistic model takes into account both the mistuning of the blade eigenfrequencies and the blade modal shapes. The first point concerns the construction of this nonparametric approach in order to perform a mistuning analysis. The second part is devoted to the inverse problem associated with the manufacturing tolerances. A relationship between the manufacturing tolerances and the level of mistuning is also constructed.

Theoretical Study of the Vibration Suppression on a Mistuned Bladed Disk Using a Bi-periodic Piezoelectric Network

2018 ◽  
Vol 35 (1) ◽  
pp. 17-28 ◽  
Author(s):  
Lin Li ◽  
Pengcheng Deng ◽  
Jiuzhou Liu ◽  
Chao Li
Keyword(s):  
Vibration Suppression ◽  
Robustness Analysis ◽  
Forced Response ◽  
Lumped Parameter Model ◽  
Modal Assurance Criterion ◽  
Vibration Localization ◽  
Bladed Disk ◽  
Lumped Parameter ◽  
Random Mistuning ◽  
Response Amplification

AbstractThe paper deals with the vibration suppression of a bladed disk with a piezoelectric network. The piezoelectric network has a different period (so called bi-period) from that of the bladed disk and there is no inductor in it. The system is simulated by an electromechanical lumped parameter model with two DOFs per sector. The research focuses on suppressing the amplitude magnification or reducing the vibration localization of the mistuned bladed disk. The dynamic equations of the system are derived. Both mechanical mistuning and electrical mistuning have been taken into account. The Modified Modal Assurance Criterion (MMAC) is used to evaluate the vibration suppression ability of the bi-periodic piezoelectric network. The Monte Carlo simulation is used to calculate the MMAC of the system with the random mistuning. As a reference, the forced responses of the bladed disk with and without the piezoelectric network are given. The results show that the piezoelectric network would effectively suppress amplitude magnification induced by mistuning. The vibration amplitude is even smaller than that of the tuned system. The robustness analysis shows that the bi-periodic piezoelectric network can provide a reliable assurance for avoiding the forced response amplification of the mistuned bladed disk. The amplified response induced by the mechanical mistuning with standard deviation 0.2 can be effectively suppressed through the bi-periodic piezoelectric network.

scholarly journals Vibro-Acoustical Sensitivities of Stiffened Aircraft Structures Due to Attached Mass-Spring-Dampers with Uncertain Parameters

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 174
Author(s):  
Johannes Seidel ◽  
Stephan Lippert ◽  
Otto von Estorff
Keyword(s):  
System Response ◽  
Fuzzy Arithmetic ◽  
Parameter Uncertainties ◽  
Excitation Spectra ◽  
Radiated Noise ◽  
Linking Elements ◽  
Manufacturing Tolerances ◽  
Suitable Framework ◽  
Mass Spring ◽  
The Impact

The slightest manufacturing tolerances and variances of material properties can indeed have a significant impact on structural modes. An unintentional shift of eigenfrequencies towards dominant excitation frequencies may lead to increased vibration amplitudes of the structure resulting in radiated noise, e.g., reducing passenger comfort inside an aircraft’s cabin. This paper focuses on so-called non-structural masses of an aircraft, also known as the secondary structure that are attached to the primary structure via clips, brackets, and shock mounts and constitute a significant part of the overall mass of an aircraft’s structure. Using the example of a simplified fuselage panel, the vibro-acoustical consequences of parameter uncertainties in linking elements are studied. Here, the fuzzy arithmetic provides a suitable framework to describe uncertainties, create combination matrices, and evaluate the simulation results regarding target quantities and the impact of each parameter on the overall system response. To assess the vibrations of the fuzzy structure and by taking into account the excitation spectra of engine noise, modal and frequency response analyses are conducted.

A Probabilistic Approach to Engine Balance

1999 ◽  
Vol 122 (4) ◽  
pp. 526-532 ◽  
Author(s):  
Dinu Taraza
Keyword(s):  
Internal Combustion Engines ◽  
Probabilistic Approach ◽  
Rayleigh Distribution ◽  
Statistical Characteristics ◽  
Balance Model ◽  
Combustion Engines ◽  
Normal Distributions ◽  
First Order ◽  
Rayleigh Law ◽  
Manufacturing Tolerances

The paper presents an original probabilistic model of the balance of internal combustion engines. The model considers the manufacturing tolerances and predicts the most probable value of the first-order residual unbalance for engines that—theoretically—have the first order forces and moments balanced. It has been found that, assuming normal distributions of the geometric and mass parameters of the reciprocating mechanisms of a multicylinder engine, the unbalancing forces and moments are statistically distributed according to a Rayleigh law. The mode of the Rayleigh distribution, which represents the most probable value of the residual unbalance, is expressed in terms of the statistical characteristics of the parameters subjected to manufacturing tolerances. In this way, the tolerances and, especially the ones admitted for the reciprocating masses, are directly correlated to the expected value of the residual unbalance making it possible to establish reasonable limits for these tolerances. Validation of the probabilistic balance model is demonstrated by computer simulation. [S0742-4795(00)01704-X]

Analysis of the Effect of Multi-Row and Multi-Passage Aerodynamic Interaction on the Forced Response Variation in a Compressor Configuration: Part 2 — Effects of Additional Structural Mistuning

2017 ◽  
Author(s):  
Johann Gross ◽  
Malte Krack ◽  
Harald Schoenenborn
Keyword(s):  
Epistemic Uncertainty ◽  
Element Model ◽  
Forced Response ◽  
Aerodynamic Loading ◽  
Multi Stage ◽  
Blade Row ◽  
Random Mistuning ◽  
Response Variation ◽  
Stage Analysis ◽  
Turbomachinery Design

The prediction of aerodynamic blade forcing is a very important topic in turbomachinery design. Usually, the wake from the upstream blade row and the potential field from the downstream blade row are considered as the main causes for excitation, which in conjunction with relative rotation of neighboring blade rows, give rise to dynamic forcing of the blades. In addition to those two mechanisms so-called Tyler-Sofrin (or scattered or spinning) modes, which refer to the acoustic interaction with blade rows further up- or downstream, may have a significant impact on blade forcing. In particular, they lead to considerable blade-to-blade variations of the aerodynamic loading. In part 1 of the paper a study of these effects is performed on the basis of a quasi 3D multi-row and multi-passage compressor configuration. Part 2 of the paper proposes a method to analyze the interaction of the aerodynamic forcing asymmetries with the already well-studied effects of random mistuning stemming from blade-to-blade variations of structural properties. Based on a finite element model of a sector, the equations governing the dynamic behavior of the entire bladed disk can be efficiently derived using substructuring techniques. The disk substructure is assumed as cyclically symmetric, while the blades exhibit structural mistuning and linear aeroelastic coupling. In order to avoid the costly multi-stage analysis, the variation of the aerodynamic loading is treated as an epistemic uncertainty, leading to a stochastic description of the annular force pattern. The effects of structural mistuning and stochastic aerodynamic forcing are first studied separately and then in a combined manner for a blisk of a research compressor without and with aeroelastic coupling.

Analysis of the Effect of Multirow and Multipassage Aerodynamic Interaction on the Forced Response Variation in a Compressor Configuration—Part I: Aerodynamic Excitation

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Harald Schoenenborn
Keyword(s):  
Three Dimensional ◽  
Forced Response ◽  
Frame Of Reference ◽  
Aerodynamic Damping ◽  
Aerodynamic Interaction ◽  
Blade Row ◽  
Random Mistuning ◽  
Compressor Map ◽  
Response Variation ◽  
Turbomachinery Design

The aeroelastic prediction of blade forcing is still a very important topic in turbomachinery design. Usually, the wake from an upstream airfoil and the potential field from a downstream airfoil are considered as the main disturbances. In recent years, it became evident that in addition to those two mechanisms, Tyler–Sofrin modes, also called scattered or spinning modes, may have a significant impact on blade forcing. It was recently shown in literature that in multirow configurations, not only the next but also the next but one blade row is very important as it may create a large circumferential forcing variation, which is fixed in the rotating frame of reference. In the present paper, a study of these effects is performed on the basis of a quasi three-dimensional (3D) multirow and multipassage compressor configuration. For the analysis, a harmonic balancing code, which was developed by DLR Cologne, is used for various setups and the results are compared to full-annulus unsteady calculations. It is shown that the effect of the circumferentially different blade excitation is mainly contributed by the Tyler–Sofrin modes and not to blade-to-blade variation in the steady flow field. The influence of various clocking positions, coupling schemes and number of harmonics onto the forcing is investigated. It is also shown that along a speed-line in the compressor map, the blade-to-blade forcing variation may change significantly. In addition, multirow flutter calculations are performed, showing the influence of the upstream and downstream blade row onto aerodynamic damping. The effect of these forcing variations onto random mistuning effects is investigated in the second part of the paper.

Blade Root Joint Modelling and Analysis of Effects of Their Geometry Variability on the Nonlinear Forced Response of Tuned and Mistuned Bladed Disks

2020 ◽  
Author(s):  
Adam Koscso ◽  
E. P. Petrov
Keyword(s):  
Harmonic Balance Method ◽  
Forced Response ◽  
High Fidelity ◽  
Contact Interactions ◽  
Bladed Disks ◽  
Element Mesh ◽  
Disk Model ◽  
Bladed Disk ◽  
Nonlinear Contact ◽  
Manufacturing Tolerances

Abstract One of the major sources of the damping of the forced vibration for bladed disk structures is the micro-slip motion at the contact interfaces of blade-disk joints. In this paper, the modeling strategies of nonlinear contact interactions at blade roots are examined using high-fidelity modelling of bladed disk assemblies and the nonlinear contact interactions at blade-disk contact patches. The analysis is performed in the frequency domain using multiharmonic harmonic balance method and analytically formulated node-to-node contact elements modelling frictional and gap nonlinear interactions. The effect of the number, location and distribution of nonlinear contact elements are analyzed using cyclically symmetric bladed disks. The possibility of using the number of the contact elements noticeably smaller than the total number of nodes in the finite element mesh created at the contact interface for the high-fidelity bladed disk model is demonstrated. The parameters for the modeling of the root damping are analysed for tuned and mistuned bladed disks. The geometric shapes of blade roots and corresponding slots in disks cannot be manufactured perfectly and there is inevitable root joint geometry variability within the manufacturing tolerances. Based on these tolerances, the extreme cases of the geometry variation are defined and the assessment of the possible effects of the root geometry variation on the nonlinear forced response are performed based on a set of these extreme cases.

A Probabilistic Analysis of Single-Degree-of-Freedom Blade Vibration

1993 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
Mehmet Imregun ◽  
David J. Ewins
Keyword(s):  
Natural Frequencies ◽  
Probabilistic Approach ◽  
Substantial Reduction ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Cumulative Probability ◽  
Blade Vibration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stiffness And Damping

The effects of random stiffness and damping variations on damped natural frequencies and response levels of turbomachinery blades are investigated by employing probabilistic approach using a single-degree-of-freedom (SDOF) model. An important feature of this study is the determination of the cumulative probability distributions for damped natural frequencies and receptance frequency response functions without having to compute their probability density distributions since it is shown that those of stiffness and damping can be used directly. The advantage of this approach is not only in the simplicity of problem formulation but also in the substantial reduction of computational requirements. Furthermore, results suggest that both stiffness and damping properties should be considered as random parameters in statistical analyses of forced response.

Forced Response Analysis of a Mistuned Compressor Blisk Comparing Three Different Reduced Order Model Approaches

2016 ◽  
Author(s):  
Mauricio Gutierrez Salas ◽  
Ronnie Bladh ◽  
Hans Mårtensson ◽  
Paul Petrie-Repar ◽  
Torsten Fransson ◽  
...  
Keyword(s):  
Structural Modeling ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Energy Localization ◽  
Order Model ◽  
Foreign Object Damage ◽  
Reduced Order ◽  
Manufacturing Tolerances ◽  
Blade Failure

Accurate structural modeling of blisk mistuning is critical for the analysis of forced response in turbomachinery. Apart from intentional mistuning, mistuning can be due to the manufacturing tolerances, corrosion, foreign object damage and in-service wear in general. It has been shown in past studies that mistuning can increase the risk of blade failure due to energy localization. For weak blade to blade coupling, this localization has been shown to be critical and higher amplitudes of vibration are expected in few blades. This paper presents a comparison of three reduced order models for the structural modeling of blisks. Two of the models assume cyclic symmetry while the third model is free of this assumption. The performance of the reduced order models for cases with small and large amount of mistuning will be examined. The benefits and drawbacks of each reduction method will be discussed.

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