Forced response of mistuned bladed disks using reduced-order modeling

Kruse, Marlin; Pierre, Christophe

doi:10.2514/6.1996-1545

Cited by 32 publications

(16 citation statements)

References 8 publications

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“…Figure 2 shows the occurrence of numerous natural frequency veering regions. Earlier studies [18,31] have shown that large increases in the mistuned forced response, relative to the tuned response, are likely to occur in veering regions. Therefore, the ability of CMM models to capture the mistuned response in veering regions was tested, and two such regions were investigated: veering region 1 is located at three nodal diameters, around 28 kHz; and veering region 2 is located at five nodal diameters, around 34 kHz.…”

Section: Small Mistuning Case Studymentioning

confidence: 97%

“…As mentioned earlier, there are two blade-dominated mode groups in this range. In all four cases, 136 tuned-system normal modes (26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43) were used as a basis, but mistuning projections were performed differently. In Fig.…”

Section: Nonproportional Mistuningmentioning

confidence: 99%

“…In region 1, a single eigenvalue mistuning pattern corresponding to the seventh cantilevered-blade mode has a dominant effect, as in the proportional mistuning case. For the CMM reduced-order model, 106 tuned-system normal modes (22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34) were retained. Figure 17 shows the forced response in veering region 1 by the FEM and the CMM model.…”

Section: Nonproportional Mistuningmentioning

confidence: 99%

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Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration

et al. 2007

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New techniques are presented for generating reduced-order models of the vibration of mistuned bladed disks from parent finite element models. A novel component-based modeling framework is developed by partitioning the system into a tuned bladed disk component and virtual blade mistuning components. The mistuning components are defined by the differences between the mistuned and tuned blade mass and stiffness matrices. The mistuned-system model is assembled with a component mode synthesis technique, using a basis of tuned-system normal modes and attachment modes. The formulation developed is general and can be applied to any mistuned bladed disk, including those with large geometric mistuning (e.g., severe blade damage). In the case of small (i.e., blade frequency) mistuning, a compact reduced-order model is derived by neglecting the attachment modes. For this component mode mistuning model, the blade mistuning is projected first onto the component modes of a tuned, cantilevered blade, and then projected again onto the tuned-system normal modes via modal participation factors. In this manner, several natural frequencies of each mistuned blade can be used to capture systematically the effects of the complex physical sources of mistuning. A numerical validation of the developed methods is performed for both large and small mistuning cases using a finite element model of an industrial rotor. Nomenclature c = aerodynamic coupling damping matrix projected onto tuned-system normal modes E = Young's modulus F = real Fourier matrix f = excitation force vector j = 1 p K = stiffness matrix in physical coordinates M = mass matrix in physical coordinates N = no. of blades N h = no. of the retained tuned-system normal modes corresponding to harmonic h p = modal coordinates q,q h = set of tuned-cantilevered-blade mode participation factors for the blade motion in the retained tunedsystem modes in physical coordinates and in cyclic coordinates U = set of the retained tuned-cantilevered-blade normal and boundary modes v, v = mistuned-cantilevered-blade normal mode participation factor for a tuned-cantilevered-blade normal mode and set of the factors x = physical coordinates = structural damping coefficient = nondimensional mistuning parameter = reduced stiffness matrix or stiffness projection to the retained component modes , = eigenvalue and diagonal matrix of eigenvalues of the retained component normal modes = reduced mass matrix or mass projection to the retained component modes , = set of the retained component normal modes in physical coordinates and in cyclic coordinates = component interface modes ! = frequency Subscripts b, i = finite element degrees of freedom (DOF) of the cantilevered-blade boundary and interior H = maximum harmonic number h = harmonic number n = blade number o = tuned blade R = set of the retained cantilevered-blade normal mode numbers r = rth cantilevered-blade normal mode = finite element DOF of the blades = finite element DOF of the disk = generalized coordinates for the retained component normal m...

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Section: Small Mistuning Case Studymentioning

confidence: 97%

Section: Nonproportional Mistuningmentioning

confidence: 99%

Section: Nonproportional Mistuningmentioning

confidence: 99%

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Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration

et al. 2007

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“…This technology has intensively been studied in the framework of the linear dynamic analysis (see for instance, [4,5,6,7,8,9,10,11,12,13,14]), for which the mistuning effects have been modeled using either parametric probabilistic approaches (see for instance, [15,16,17,18,19]), or using the nonparametric probabilistic approach ( [20,21,22]), and for which the optimization of alternating patterns has been studied (see for instance, [23,24,25,26]).…”

Section: Introductionmentioning

confidence: 99%

Robust dynamic analysis of detuned-mistuned rotating bladed disks with geometric nonlinearities

et al. 2019

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This work is devoted to the robust analysis of the effects of geometric nonlinearities on the nonlinear dynamic behavior of rotating detuned (intentionally mistuned) bladed disks in presence of unintentional mistuning (simply called mistuning). Mistuning induces uncertainties in the computational model, which are taken into account by a probabilistic approach. This paper presents a series of novel results of the dynamic behavior of such rotating bladed disks exhibiting nonlinear geometric effects. The structural responses in the time domain are analyzed in the frequency domain. The frequency analysis exhibits responses outside the frequency band of excitation. The confidence region of the stochastic responses allows the robustness to be analyzed with respect to uncertainties and also allows physical insights to be given concerning the structural sensitivity. The bladed disk structure is made up of 24 blades for which several different detuned patterns are investigated with and without mistuning.

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“…Different reduced-order modeling techniques have been developed to compute the dynamic behavior of mistuned bladed disks with reduced computational time [2,3,4,5,6,7,8,9,10,11,12,13,14]. These finite element model of the structures.…”

Section: Introductionmentioning

confidence: 99%

Identification of mistuning and model updating of an academic blisk based on geometry and vibration measurements

Nyssen

Golinval

2016

Mechanical Systems and Signal Processing

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In this work, an experimental modal analysis is performed on an academic bladed disk using a base excitation to identify the mistuning of each blade. Optical measurement is used to obtain the exact geometry of the structure and to be able to associate geometrical mistuning to each blade. Differences are observed between the experimentally identified mistuning and the geometrical mistuning. Since the bladed disk is a onepiece structure, there is no welded connections between the blades and the disk and the material properties can be assumed to be uniform. It can be shown that these differences come from non uniform clamping conditions, and that this mistuning is of the same order of magnitude than the variations in the geometry of the structure. It follows that the precise characterisation of mistuning for industrial structures is in practice illusory because of the numerous factors introducing mistuning, such as the clamping conditions, aerodynamic damping, wear in service, etc.

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Forced response of mistuned bladed disks using reduced-order modeling

Cited by 32 publications

References 8 publications

Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration

Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration

Robust dynamic analysis of detuned-mistuned rotating bladed disks with geometric nonlinearities

Identification of mistuning and model updating of an academic blisk based on geometry and vibration measurements

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