Bladed Disk Assembly Research Articles

Time Periodic Control of a Bladed Disk Assembly Using Shaft Based Actuation

For a tuned or symmetrically mistuned bladed disk assembly, several vibration modes are coupled only to the axial dynamics, which forces controllers to rely on an axial actuator. A control strategy based upon deliberately mistuning in a nonsymmetric manner, which results in a time periodic dynamical system, is developed. The method presented does not require an active thrust bearing for complete controllability of a bladed disk assembly via hub based actuators.

Localization in Nonlinear Mistuned Systems with Cyclic Symmetry

In forced systems with cyclic symmetry localization can occur due toparameter uncertainties. Often, Monte-Carlo simulations are used to findregions, where the system response is sensitive to parameteruncertainties. These simulations require a large computation time.Therefore, an approximate method to calculate the envelopes of thefrequency response functions is developed in this paper. An example of anonlinear system with cyclic symmetry is a bladed disk assembly withfriction dampers. Friction dampers can be installed underneath the bladeplatforms of turbine blades. Due to dry friction and the relative motionbetween blades and dampers, energy is dissipated, which results in areduction of blade vibration amplitudes. By optimizing the mass of thefriction dampers, the best damping effects are obtained, which lead toan increase in the reliability of the turbine. In this paper, thecalculated response of a mistuned bladed disk assembly with frictiondampers is discussed. An approximate method is developed to calculatethe envelopes of the corresponding frequency response function forstatistically varying eigenfrequencies of the blades. Regions wherelocalization can occur with a high probability, are calculated by thismethod.

On some regularities in dynamic response of cyclic periodic structures

The paper deals with cyclic periodic structures modelling bladed disk assemblies of blades with friction elements for vibration damping. These elements placed between adjacent blades reduce the vibration amplitudes by means of dry friction resulting from centrifugal forces acting on the elements and relative displacements of the blades. However, the application of these friction elements results in an additional dynamical coupling which together with mistuning of some system parameters (e.g., blade eigenfrequency or contact parameters) may cause localization of vibration. In the present paper a linear approximation of such a system is investigated. The structure composed of cyclic periodic cells modelled each as a clamped-free beam interacting with each other by means of viscoelastic elements of complex stiffness is applied for dynamic system analysis. In case of free vibrations as well as in case of steady-state dynamic response to a harmonic pressure field, a perfect periodic structure and the structures with periodically mistuned parameters (blade eigenfrequencies and contact parameters) are studied. Some regularities in the dynamic response of the systems with mistuning have been noticed. Despite the fact that only a linear approximation has been used, the results and conclusions can be applied for models which describe the blade interaction in a nonlinear way.

Aeroelasticity in Turbomachines: Some Aspects of the Effect of Coupling Modeling and Blade Material Changes

Two methods are generally used for the aeroelastic analysis of bladed‐disc assemblies. The first, often referred to as the energy method, assumes that the fluid does not modify invacuum structural dynamic behavior. On the other hand, the second, based on an eigenvalue approach, considers the feedback effect of the fluid on the structure. In this paper, these methods are compared using different test cases, in order to highlight the limitations of the energy method. Within this comparison, the effect of material modifications on the coupled behavior of the assembly is examined.

Statistics of Response of a Mistuned Bladed Disk Assembly Subjected to White Noise and Narrow Band Excitation

This paper deals with the statistics of the response of a mistuned bladed disk assembly subjected to random excitation. Analytical techniques are developed to compute this statistics for two types of random excitation: white noise and narrow band. The validity of the analytical methods has been established by comparison with the results from numerical simulations. The sensitivities of the response to mistuning have been examined as a function of the width of the frequency band of the random excitation, the dominant frequency of the random excitation and the structural coupling between adjacent blades.

Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds

This paper presents important improvements and extensions to a computationally efficient reduced order modeling technique for the vibration analysis of mistuned bladed disks. In particular, this work shows how the existing modeling technique is readily extended to turbomachinery rotors with shrouded blades. The modeling technique employs a component mode synthesis approach to systematically generate a reduced order model (ROM) using component modes calculated from a finite element model (FEM) of the rotor. Based on the total number of degrees of freedom, the ROM is typically two or three orders of magnitude smaller than the FEM. This makes it feasible to predict the forced response statistics of mistuned bladed disks using Monte Carlo simulations. In this work, particular attention is devoted to the introduction of mistuning into the ROM of a shrouded assembly. Mistuning is modeled by projecting the mistuned natural frequencies of a single, cantilever blade with free shrouds onto the harmonic modes of the shrouded blade assembly. Thus, the necessary mistuning information may be measured by testing individual blades.

Friction Damper Optimization: Simulation of Rainbow Tests

Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However, optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimization via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to conduct so-called “rainbow tests” where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disk assembly. A new method of analysis—a combination of the harmonic balance method and structural modification approaches—is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called “rainbow tests” in turbomachinery applications. A simple lumped-parameter model of a bladed-disk model was used and different damper weights were modeled using friction elements with different characteristics. Resonance response levels were obtained for bladed disks with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disk assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disk is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.

Forced Response of Bladed Disk Assemblies--A Survey

This work surveys methods for modeling and analyzing bladed disk assemblies common to gas turbine aircraft. An introduction to symmetric (tuned) bladed disk dynamics is presented, followed by a literature review of studies modeling bladed disks, blade mistuning. and the effect of mistuning forced response. A summary of results is given, and suggestions for future work are made.

Whole-assembly flutter analysis of a low-pressure turbine blade

AbstractThis paper reports the findings of a flutter investigation on a low-pressure turbine blade using a 3D, non-linear, integrated aeroelasticity method. The approach has two important features: (i) the calculations are performed in a time-accurate and integrated fashion, whereby the structural and fluid domains are linked via an exchange of boundary conditions at each time step, and (ii) the analysis is performed on the entire bladed-disk assembly, thus removing the need to assume a critical vibration mode shape. Although such calculations are both CPU and in-core memory intensive, they do not require prior knowledge of the flutter mode and hence allow a better understanding of the aeroelasticity phenomena involved.The flow is modelled inviscidly but the steady-state viscous effects are accounted for using a distributed loss model. The structural model was obtained from a standard finite element (FE) representation and a large number of assembly modes were included in the calculations. The study focused on three part-speed conditions at which a number of unstable modes were known to exist from the available experimental data. The whole assembly was modelled using about 664,000 mesh points and predictions were made of aeroelastic modal time histories. From these time histories it was possible to identify the forward and backward travelling waves and to deduce the unstable modes of vibration. The theoretical predictions were found to be in very good agreement with the experimental findings.

Vibration of a Mistuned Bladed-Disk Assembly Using Structurally Damped Beams

A model of a mistuned bladed disk is created and then analyzed for both free and forced vibrations. The model consists of structurally damped, Euler ‐Bernoulli beams connected at one end using springs. The model is useful in the prediction of the response of a turbine engine bladed disk in which only some of the blades have added damping. (This situation arises in the experimental analysis of damping treatments. ) The natural frequencies and eigenfunction sets are obtained by assuming harmonic motion and imposing the boundary conditions. The eigensolution was verie ed using a small NASTRAN model. The forced response due to phased, harmonic tip loads is obtained by modalizing the equations using a technique recently developed by Turcotte (Turcotte, J. S., “ An Analytical Model for the Forced Response of Cyclic Structures,” Journal of Sound and Vibration , Vol. 209, No. 3, 1998, pp. 531 ‐536). The physical response is obtained as a function of forcing frequency by truncation and summation of the modal responses. The results are in general agreement with those of existing discrete models but have much greater detail.

Characterization of Laws of Friction in the Context of Engine Blade Dynamics

Experience has shown that energy dissipation due to rubbing at interfaces of engine blade shrouds provides damping of bladed disk assemblies. An accurate estimate of such damping has been a subject of study for more that a decade. The most difficult parameter that influences its accurate calculation pertains to an appropriate definition of the laws of friction that relate the rubbing motion with the forces induced. This paper develops an analysis that leads to a mathematical relationship between the forces of friction damping at a vibrating interface and the corresponding relative motion. The analysis permits calculation of forces at the interface if the displacements are known or vice. The equations are cast in terms of relative motion between mating shrouds so that degenerate cases of fully locked and freely slipping can be calculated. Examples are given showing simulation results obtained using discrete structural models. Extension of the analysis to the case of a full assembly is discussed.

A Survey of Blade Tip-Timing Measurement Techniques for Turbomachinery Vibration

This paper aims at providing a comparative survey of current analysis methods for the interpretation of vibration data measured at turbomachinery rotor blade tips using optical laser probes. The methods are classified by the form of the vibration that they attempt to identify, namely, asynchronous and synchronous with respect to rotor speed. The performance of the various techniques is investigated by using both actual assembly measurements and simulated response data. In the latter case, synchronous vibration data are obtained via a multidegree-of-freedom numerical simulator that includes the structural and geometric properties of the bladed-disk assembly, the external forcing terms, and the characteristics of the optical probe. When using experimental data, the results of the tip timing analysis are compared to those obtained from standard strain-gauge tests and the relative merits of the two approaches are discussed with emphasis on the effects of blade mistuning. Existing industry standard, tip-timing analysis techniques are found to exhibit a number of inherent limitations and suggestions were made to address these deficiencies. A detailed tip-timing case study for a steam turbine rotor is presented in some detail, and other potential application areas are explored. Of particular note is the introduction of a new indirect analysis method for identifying the characteristics of synchronous vibration modes using measurements from two probes. Finally, new avenues for future analysis methods and further developments in tip-timing systems are also discussed.

FREE AND FORCED RESPONSE OF MISTUNED LINEAR CYCLIC SYSTEMS: A SINGULAR PERTURBATION APPROACH

The effect of small deterministic parameter perturbations on the forced response of nearly periodic structures with cyclic symmetry is investigated. The general methodology developed herein is applicable to anyn-degree-of-freedom, strongly coupled cyclic system with two arbitrary and independent variations in system parameters that destroy the cyclic symmetry. The specific system studied may be regarded as a simplified model of a strongly coupled bladed disk assembly. Singular perturbation methods along with modal expansion analysis are applied to gain a physical insight into the effects of parameter perturbations on the eigenvalues, the eigenvectors as well as the forced response amplitudes. The study shows that, under appropriate conditions, the splitting and veering of eigenvalues due to mistunings or small parameter variations increases the amplitude of vibration of some blades significantly compared to what would be predicted by an analysis of the perfectly tuned system. Furthermore, modal bifurcations lead to uneven vibration amplitudes irrespective of the stiffness of the coupling springs. The variations in blade amplitudes are also found to be strongly dependent on damping, and the type of engine order excitation applied to the system for the same set of mistuning parameters.

Flutter Prediction Using an Eigenvector Orientation Approach

A method for predicting the onset of coupled-mode flutter is presented. A distinguishing characteristic of this method is that it emphasizes eigenvectors rather than eigenvalues. In the popular methods based on eigenvalues, flutter is predicted as instability begins to occur, as evidenced by the movement of one or more eigenvalues from the left-hand to the right-hand side of the s-plane, or the coalescence of eigenvalues. Alternatively, the method of eigenvector orientation being presented has the potential to predict the occurence of instability. Although the eigenvectors of vibrating systems generally satisfy the orthogonality condition, there are certain cases In aeroelasticity in which they are not orthogonal. In a typical case of coupled-mode flutter, the eigenvectors Initially may be oriented orthogonally but gradually lose orthogonality as airspeed is varied. The consequence of such a progressive loss of eigenvector orthogonality on structural dynamics is a phenomenon that seems to warrant further investigation. This investigation has applications in areas such as helicopter dynamics, aeroelastic analysis of plate and shell structures, analysis of slightly mistuned bladed disk assemblies, and rotordynamics.

Vibration of a mistuned bladed-disk assembly using structurally damped beams

Vibration of a mistuned bladed-disk assembly using structurally damped beams

A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies

A reduced order approach is introduced in this paper that can be used to predict the steady-state response of mistuned bladed disks. This approach takes results directly from a finite element analysis of a tuned system and, based on the assumption of rigid blade base motion, constructs a computationally efficient mistuned model with a reduced number of degrees of freedom. Based on a comparison of results predicted by different approaches, it is concluded that: The reduced order model displays structural fidelity comparable to that of a finite element model of the entire bladed disk system with significantly improved computational efficiency; and under certain circumstances both the finite element model and the reduced order model predict quite different response from simple spring-mass models.

An improved single-parameter tip-timing method for turbomachinery blade vibration measurements using optical laser probes

This paper presents an improved analysis method for the interpretation of the vibration data measured at turbomachinery blade tips using optical laser probes. A multi-degree-of-freedom numerical simulator, which includes the structural and geometric properties of the bladed-disk assembly, the external forcing terms and the characteristics of the optical probe, has been developed to assess the reliability of the various data processing techniques to identify the natural frequencies and mode shapes of bladed-disk assemblies. It has been demonstrated that the Zablotsky—Korostelev single parameter technique, which is a de-facto standard in the aerospace industries, has inherent limitations associated with it. An improved and more rigorous method is presented for deriving the blade arrival times and a non-linear solution technique is suggested for their numerical determination. Finally, the effect of blade mistuning on the accuracy of the proposed method is also investigated.

VIBRATION ANALYSIS OF SHAFT-BLADED DISK SYSTEM BY USING SUBSTRUCTURE SYNTHESIS AND ASSUMED MODES METHOD

An analytical substructure synthesis and assumed modes method is developed to investigate the effect of the flexibility of a bladed disk assembly on the vibrational mode of a flexible rotor system. In modeling the system, Coriolis forces, gyroscopic moments and centrifugal stiffening effects are taken into account. Then the coupled vibrations between the shaft and bladed disk are extensively investigated, by using simplistic models, as the shaft rotational speed and the pretwist and stagger angles of blade are varied.

Comparison of two finite element approaches for analysis of rotating bladed-disk assemblies

Abstract Two finite element approaches are implemented to account for the rotational non-linearities involved in dynamic analysis of rotating bladed-disk assemblies: the distributed mass (DM) and lumped mass (LM) approaches. The DM approach treats the structure as a continuum with mass points uniformly distributed in the structure, while the LM approach treats the structure as a collection of discrete concentrated mass points. These two approaches are used here exclusively for considering rotational effects in the dynamic analysis and should not be confused with the consistent and lumped mass approaches for representing the mass matrix. It has been found that the analysis results obtained using the DM and LM approaches are in close agreement for test problems studied. In addition, for transient analysis using explicit time integration, the LM approach has been found to be significantly more efficient than the DM approach.

Analysis of mistuned cyclic systems using mistune modes

The bladed disk assembly, a prime example of a cyclic system, forms an important component of modern turbomachinery. Vibrations of the blades leads to fatigue damage and limits their service life. Analysis of these systems is complicated by the combination of coupling of blade dynamics with mistuning of the blade properties. The present study of mistuned cyclic systems encompasses a complete model of a bladed disk assembly which includes multiple degrees-of-freedom per blade, aerodynamic coupling, and structural coupling. A systematic analysis of this model allows the determination of the effect of mistune pattern, along with excitation mode, on the forced response amplitudes of the blades. The main motivation of this study is to gain a better understanding of the dynamics of cyclic systems. Through this understanding, better designs of these components will be possible. The concept of mistuning modes is introduced to provide a generalized method of describing the mistuning of bladed disk assemblies. Perturbation analyses reveal which constant interblade phase angle modes will contribute to the response as a result of given mistune modes and excitation modes. Results generated through a computational study demonstrate the range of validity of the perturbation approaches.