Mistuned Bladed Research Articles

Modified Modal Domain Analysis of a Bladed Rotor Using Coordinate Measurement Machine Data on Geometric Mistuning

Modified modal domain analysis (MMDA), a reduced order modeling technique, is applied to a geometrically mistuned integrally bladed rotor to obtain its natural frequencies, mode shapes, and forced response. The geometric mistuning of blades is described in terms of proper orthogonal decomposition (POD) of the coordinate measurement machine (CMM) data. Results from MMDA are compared to those from the full (360 deg) rotor Ansys model. It is found that the MMDA can accurately predict natural frequencies, mode shapes, and forced response. The effects of the number of POD features and the number of tuned modes used as bases for model reduction are examined. Results from frequency mistuning approaches, fundamental mistuning model (FMM) and subset of nominal modes (SNM), are also generated and compared to those from full (360 deg) rotor Ansys model. It is clearly seen that FMM and SNM are unable to yield accurate results whereas MMDA yields highly accurate results.

Application of Improved Hybrid Interface Substructural Component Modal Synthesis Method in Dynamic Characteristics Analysis of Mistuned Bladed Disk Assemblies

Application of Improved Hybrid Interface Substructural Component Modal Synthesis Method in Dynamic Characteristics Analysis of Mistuned Bladed Disk Assemblies

Parallel Piezoelectric Shunt Damping of Rotationally Periodic Structures

This paper considers the RL shunt damping of rotationally periodic structures with an array of regularly spaced piezoelectric patches. The technique is targeted to the damping of a specific mode withnnodal diameters. For this particular case, one can take advantage of the shape of the targeted mode to organize the piezoelectric patches as a modal filter (in parallel loops) which reduces the demand on the inductors of the tuned inductive shunt. In the case of a perfectly rotationally periodic structure, it is possible to organize 4npiezoelectric transducers (PZT patches) in two parallel loops of 2npatches each. In this way, the demand on the inductors is reduced by4n2as compared to independent loops, which may allow a fully passive integration of the RL shunt in a turbomachinery application. The method is first illustrated experimentally on a circular plate; it is then applied to a prototype of an industrial bladed drum. The influence of blade mistuning is investigated.

Study on Parameter Identification of Mistuned Blades Based on Static Frequency Test and Finite Element Method

With elastic modulus perturbation parameter of blade as mistuned parameter, a parameter identification method of mistuned blades is presented based on static frequency test , bisection method and finite element method. Take mistuned blades of the compressor as an example,the mistuned parameter of blades are identified. The identification results show that this method is high precision and fast speed.

Vibration Reduction of Mistuned Bladed Disks by Passive Piezoelectric Shunt Damping Techniques

This paper presents a vibration control strategy based on the passive piezoelectric shunt damping technique for mistuned bladed disks. Resonant shunted piezoelectrics are attached onto the disk surface between adjacent blades to dissipate the mechanical energy. This strategy is of engineering interest because piezoelectric transducers are placed outside of the main stream in turbomachinery. This idea is developed based on a lumped-parameter bladed disk model. Both piezoelectric shunt damping and piezoelectric mistuning are introduced to minimize the blade mistuning effect. First, a tuning design is carried out to damp a specified mode for the tuned bladed disk. When blade mistuning is taken into account, a further vibration reduction is achieved by introducing an optimal piezoelectric mistuning pattern obtained by a genetic algorithm. In reality, the blade mistuning pattern is not constant in the long run. Because of various complexities, a perturbation of the blade mistuning pattern might result. In benefitting from the manageability and controllability of piezoelectric shunt circuits, an adaptive control strategy is developed to adjust the “optimal” piezoelectric mistuning pattern according to the perturbation. Numerical simulation reveals that good performance is achieved in terms of reducing the vibration of slowly time-variant, mistuned bladed disks.

Forced Response of Mistuned Bladed Disks: Quantitative Validation of the Asymptotic Description

The effect of small mistuning in the forced response of a bladed disk is analyzed using a recently introduced methodology: the asymptotic mistuning model. The asymptotic mistuning model is an extremely reduced, simplified model that is derived directly from the full formulation of the mistuned bladed disk using a consistent perturbative procedure based on the relative smallness of the mistuning distortion. A detailed description of the derivation of the asymptotic mistuning model for a realistic bladed disk configuration is presented. The asymptotic mistuning model results for several different mistuning patterns and forcing conditions are compared with those from a high-resolution finite element model. The asymptotic mistuning model produces quantitatively accurate results, and, probably more relevant, it gives precise information about the factors (tuned modes and components of the mistuning pattern) that actually play a role in the vibrational forced response of mistuned bladed disks.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons

This paper draws upon the theoretical basis and applicability of the three-dimensional (3-D) reduced-order spectral-based “meshless” energy technology presented in a companion paper (McGee et al., 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis,” ASME J. Turbomach., to be published) to predict free and forced responses of bladed disks comprised of randomly mistuned blades integrally attached to a flexible disk. The 3-D reduced-order spectral-based model employed is an alternative choice in the computational modeling landscape of bladed disks, such as conventionally-used finite element methods and component mode synthesis techniques, and even emerging element-free Hamiltonian–Galerkin, Petrov–Galerkin, boundary integral, and kernel-particle methods. This is because continuum-based modeling of a full disk annulus of mistuned blades is, at present, a steep task using these latter approaches for modal-type mistuning and/or rogue blade failure analysis. Hence, a considerably simplified and idealized bladed disk of 20 randomly mistuned blades mounted to a flexible disk was created and modeled not only to analyze its free and forced 3-D responses, but also to compare the predictive capability of the present reduced-order spectral-based “meshless” technology to general-purpose finite element procedures widely-used in industry practice. To benchmark future development of reduced-order technologies of turbomachinery mechanics analysts may use the present 3-D findings of the idealized 20-bladed disk as a new standard test model. Application of the 3-D reduced-order spectral-based “meshless” technology to an industry integrally-bladed rotor, having all of its blades modally mistuned, is also offered, where reasonably sufficient upper-bounds on the exact free and forced 3-D responses are predicted. These predictions expound new solutions of 3-D vibration effects of modal mistuning strength and pattern, interblade mechanical coupling, and localized modes on the free and forced response amplitudes.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis

In this paper, a reduced order model for the vibrations of bladed disk assemblies was achieved. The system studied was a 3D annulus of shroudless, “custom-tailored,” mistuned blades attached to a flexible disk. Specifically, the annulus was modeled as a spectral-based “meshless” continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3D displacement field of mathematically complete, orthonormal “blade-disk” polynomials multiplied by generalized coefficients. The coefficients were determined by constraining the polynomial series to satisfy the extended Ritz stationary equations and essential boundary conditions of the bladed disk. From this, the governing equations of motion were generated into their usual dynamical forms to calculate upper-bounds on the actual free and forced responses of bladed disks. No conventional finite elements and element connectivity or component substructuring data were needed. This paper, Part I, outlines the theoretical foundation of the present model, and through extensive Monte Carlo simulations, establishes the analytical basis, predictive accuracy, and re-analysis efficiency of the present technology in the prediction of 3D maximum response amplitude of mistuned bladed disks having increasing numbers of nodal diameter excitations. Further applications validating the 3D approach against conventional finite element procedures of free and forced response prediction of a mistuned Integrally-Bladed Rotor used in practice is presented in a companion paper, Part II (Fang, McGee, and El-Aini, 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., to be published.

Integer Frequency Veering of Mistuned Blade Integrated Disks

As a result of more balanced blade aspect ratios of modern blade-integrated disks (blisks), interactions between disk-dominated and blade-dominated modes are becoming more and more important, especially if blade mistuning is considered. The specific vibration behavior in these transition regions is characterized by a mix of both fundamental mode types into “coupled” modes. In this paper, numerical and experimental investigations based on a front high-pressure compressor (HPC) blisk stage were carried out in order to determine the effect of blade mistuning on those regions in detail. At this, effects like mode localization and amplitude magnification are found to be weakened in an integer frequency-veering zone. Contrary to this, blisks are very sensitive to mistuning in regions of pure blade-dominated mode families with high modal density.

Shaft instantaneous angular speed for blade vibration in rotating machine

Reliable blade health monitoring (BHM) in rotating machines like steam turbines and gas turbines, is a topic of research since decades to reduce machine down time, maintenance costs and to maintain the overall safety. Transverse blade vibration is often transmitted to the shaft as torsional vibration. The shaft instantaneous angular speed (IAS) is nothing but the representing the shaft torsional vibration. Hence the shaft IAS has been extracted from the measured encoder data during machine run-up to understand the blade vibration and to explore the possibility of reliable assessment of blade health. A number of experiments on an experimental rig with a bladed disk were conducted with healthy but mistuned blades and with different faults simulation in the blades. The measured shaft torsional vibration shows a distinct difference between the healthy and the faulty blade conditions. Hence, the observations are useful for the BHM in future. The paper presents the experimental setup, simulation of blade faults, experiments conducted, observations and results.

Three-Dimensional Tailored Vibration Response and Flutter Control of High-Bypass Shroudless Aeroengine Fans

A new reduced-order design synthesis technology has been developed for vibration response and flutter control of cold-stream, high-bypass ratio, shroudless, aeroengine fans. To simplify the design synthesis (optimization) of the fan, a significant order reduction of the mechanical response and stiffness-shape design synthesis has been achieved. The assumed cyclic symmetric baseline fan is modeled as a cascade of tuned, shroudless, arbitrarily shaped, wide-chord laminated composite blades, each with a reduced order of degrees of freedom using a three-dimensional (3D) elasticity spectral-based energy model (McGee et al., 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis, ASME J. Turbomach., in press; Fang et al., 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., in press). The uniqueness of the mechanical analysis is that the composite fan was modeled as a “meshless” continuum, consisting of nodal point data to describe the arbitrary volume. A stationary value of energy within the arbitrarily shaped composite fan annulus was achieved using an extended spectral-based Ritz procedure to obtain the dynamical equations of motion for 3D free vibration response of a rotating composite high-bypass fan. No additional kinematical constraints (as in beam, plate, or shell theories) were utilized in the 3D elasticity-based energy formulation. The convergence accuracy of the spectral-based 3D free vibration response predictions was nearly one percent upper-bounds on the exact mechanical response of the baseline composite fan, particularly in the lowest five modes studied closely in this work, as typically seen with spectral-based Ritz procedures employed in the analysis. The spectral-based 3D predictions was validated against those predicted using a general purpose finite element technology widely used by industry. In off-design operation, the frequency margins of the lower flex-torsion modes of a fan may be dangerously close to integral-order resonant and empirical stall flutter boundaries. For a given baseline composite fan, it is proposed that to reduce the likelihood of resonant response and flutter on a Campbell diagram, design analysts can efficiently unite the newly developed reduced-order 3D spectral-based energy reanalysis within a novel reduced-order spectral-based Kuhn–Tucker optimality design synthesis procedure to fairly accurately restructure the Campbell diagram of a composite high-bypass ratio fan using stiffness optimization (by means of proper choices of angle-ply orientations of the blade laminates) and mass-balancing (shape) optimization (by way of blade thickness variation tuning of the lower aerodynamic loading portion of the blades between the dovetail root section and the midradial height section of the composite fan annulus). Fan design optima is summarized that (1) achieves multiple frequency margins and satisfies multiple empirical stall flutter constraints, (2) controls the twist-flex vibratory response in the lowest (fundamental) mode, and (3) ensures the mechanical strength integrity of the optimized angle-ply lay-up under steady centrifugal tension and gas bending stresses. Baseline and optimally restructured Campbell diagrams and design sensitivity calculations are presented, comparing optimum solution accuracy and validity of the proposed reduced-order spectral-based design synthesis technology against optimum solutions generated from open-source nonlinear mathematical programming software (i.e., NASA’s general-purpose sequential unconstrained minimization technique, Newsumt-A) (Miura and Schmit, Jr., 1979, ”NEWSUMT–A, Fortran Program for Inequality Constrained Function Minimization—Users Guide,“ NASA CR-159070). Design histories of fan stiffness and mass balancing (or shape) along with nondimensional constraints (i.e., frequency margins, reduced frequencies, twist-flex vibratory response, first-ply failure principal stress limits, and dovetail-to-midblade height thickness distribution) show that a proper implementation of fan stiffness tailoring (via symmetric angle-ply orientations) and mass-balancing (thickness) optimization of the fan assembly produces a feasible Campbell diagram that satisfies all design goals. An off-design analysis of the optimized fan shows little sensitivity to twist-flex coupling response and flutter with respect to small variability or errors in optimum design construction. Industry manufacturing processes may introduce these small errors known as angle-ply laminate construction misalignments (Graham and Guentert, 1965, “Compressor Stall and Blade Vibration,” Aerodynamic Design of Axial-Flow Compressors, Chap. XI, NASA SP-36; Meher-Hornji, 1995, “Blading Vibration and Failures in Gas Turbines, Part A: Blading Dynamics and the Operating Environment,” ASME Paper 95-GT-418; Petrov et al., 2002, “A New Method for Dynamic Analysis of Mistuned Bladed Disks Based on the Exact Relationship Between Tuned and Mistuned Systems,” ASME J. Eng. Gas Turbines Power, 124(3), pp. 586–597; Wei and Pierre, 1990, “Statistical Analysis of the Forced Response of Mistuned Cyclic Assemblies,” ASME J. Eng. Gas Turbines Power, 28(5), pp. 861–868; Wisler, 1988, “Advanced Compressor and Fan Systems,” GE Aircraft Engines, Cincinnati, Ohio (also 1986 Lecture to ASME Turbomachinery Institute, Ames Iowa)).

Optimization on Mistuning Blades Arrangement of Vibration Absorption Based on Genetic Particle Swarm Algorithm in Aero-Engine

In practical aero-engine bladed disk structure of blade mistuning is inevitable, and seriously affects the vibration characteristics of bladed disk system also on the whole aero-engine performance and life. Through the analysis, the blades arrangement order of a set of mistuned blade can greatly influence the vibration of bladed disk system, on this foundation; put forward a kind of new localization level of vibration parameters method for the characterization of mistuned system vibration localization degree. Furthermore, genetic particle swarm algorithm is used to optimize the blade arrangement sequence. The research shows that the selection of appropriate blade arrangement sequence can effectively reduce the bladed disk system forced vibration amplitude and the localization level of forced vibration.

Study on Vibration Characteristics of Mistuned Bladed Disk(Vibration Response Analysis by Reduced Model FMM)

Study on Vibration Characteristics of Mistuned Bladed Disk(Vibration Response Analysis by Reduced Model FMM)

Study on Vibration Characteristics of Mistuned Bladed Disk (Vibration Response Analysis by Reduced Model FMM)

It is well known that asymmetric vane spacing can result in decreased levels of the excitation at specific frequencies. In the previous paper, the resonant response reduction of mistuned bladed disks due to asymmetric vane spacing was studied by use of the equivalent spring-mass model. Although the mistuned bladed disk should be analyzed by FEA to accurately evaluate the resonant response reduction effect of asymmetric vane spacing, it is unrealistic due to enormous computational time. Therefore, in this study, the mistuned bladed disk is modeled by use of FMM (Fundamental Mistuning Model) to evaluate the resonant response reduction effect of asymmetric vane spacing accurately and practically. First, the frequency response analysis of a simple mistuned bladed disk consisting of flat plate blades is carried out for symmetric vane spacing, using both of FMM and the direct FE model, and the calculated results are compared to confirm the validity of FMM. Second, the frequency response analysis of a realistic bladed disk is carried out for asymmetric vane spacing, using FMM, to examine the effect of resonant response reduction effect.

Study on Transient Vibration of Bladed Disk Passing through Resonance (Transient Response Analysis of Mistuned Bladed Disk)

In a variable speed engine, it is impossible to avoid the resonance during operation. In a constant speed engine, the resonance during start-up or shut-down also cannot be avoided. Therefore, the increase of the acceleration rate passing through the resonance is considered as one of the effective methods for reducing the vibratory stress of the blade and increasing the reliability of the turbo-machinery. In this study, the transient vibration analysis of the mistuned bladed disk passing through the resonance is carried out, using the conventional modal analysis method and the numerical integration. First, the mistuned bladed disk is modeled by the equivalent spring-mass model, and the steady frequency response analysis is carried out by the Monte Carlo simulation, in order to obtain the worst mistuning. Second, for the mistuned bladed disk of the worst mistuning, the transient vibration analysis in passing through the resonance is carried out, and the effect of the acceleration rate and the blade damping on the transient vibration response is examined in detail. From these results, it is concluded that the larger the acceleration rate is, the smaller the mistuning effect is.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Aeroelastic Stability Assessment of an Industrial Compressor Blade Including Mistuning Effects

This paper presents a comprehensive investigation into the aeroelastic stability behavior of a transonic front blade in an industrial compressor when operating outside its normal range of service parameters. The evolution of the airfoil’s aeroelastic stability in the first flexural mode is studied as the front blade operation progresses towards choked flow conditions. First, linearized 3D flutter computations representing today’s industry standard are performed. The linearized calculations indicate a significant, shock-driven flutter risk at these off-design flow conditions. To further explore the aeroelastic behavior of the rotor and to find a viable solution toward flutter risk elimination, two parallel investigations are undertaken: (i) flow perturbation nonlinearity effects and potential presence of limit-cycle oscillation, and (ii) effects of blade mistuning and flutter mitigation potential of intentional mistuning, including its impact on forced response behavior. The nonlinear harmonic analyses show that the minimum aerodynamic damping increases rapidly and essentially linearly with blade oscillation amplitude beyond the linear regime. Thus, a state of safe limit-cycle oscillation is predicted for the fully tuned blade. Additionally, it is found that intentional, realizable blade frequency offsets in an alternating pattern efficiently stabilize the blade. Finally, it is verified that alternating mistuning has a beneficial effect versus the inevitable random mistuning also in the forced response.

An adaptive control strategy based on passive piezoelectric shunt techniques applied to mistuned bladed disks

This paper mainly presents an adaptive control strategy based on passive piezoelectric shunt techniques for mistuned bladed disks. Resonant shunted piezoelectric patches are attached onto the disk between adjacent blades to reduce the blade vibration through blade–disk coupling. This piezoelectric network is of engineering interest since piezoelectric transducers are placed out of the main stream in turbomachinery. Piezoelectric damping and piezoelectric mistuning are exploited to minimize blade mistuning effects in this study. Initially an optimal piezoelectric mistuning obtained by genetic algorithm optimization is introduced into a given blade-mistuned disk to achieve a further blade vibration mitigation. In reality the blade mistuning pattern is not constant in the long run. Benefiting from the manageability and controllability of piezoelectric shunt circuits, this adaptive control strategy is to adjust the “optimal” piezoelectric mistuning pattern according to the slowly varying blade mistuning pattern. Numerical simulation reveals that a good performance is achieved with respect to reducing the vibration of time-variant mistuned bladed disks.

The Effect of Lashing Wire Location on Mode Localization of Mistuned Bladed Disks

The finite element models of bladed disks with different lashing wire locations were established. The natural characteristics and mode shapes of bladed disks with different lashing wire locations were compared, and the effect of lashing wire location on the natural characteristics and mode localization of bladed disks were analyzed. These results show that different lashing wire locations could carry different natural frequencies to bladed disk, and there must be one lashing wire location with the highest frequencies. Lashing wire location has a significant influence on the mode localization of the mistuned bladed disks, and the mode localization of the bladed disks is less sensitive to mistuning when the lashing wire is in the middle of blades.

Structural Damping Identification for Mistuned Bladed Disks and Blisks

To accurately predict the dynamics of most structures, a representation of damping must be used. This paper focuses on structural damping and the identification of structural damping for complex systems with cyclic symmetry such as bladed disks and integrated (one-piece) bladed disks (blisks) with mistuning. The damping identification methodology is demonstrated together with two measurement filters for a complex structure, namely an integrated bladed disk with stiffness mistuning.