A model order reduction method based on the Component Mode Synthesis for mistunend bladed disks is introduced, with one component for the disk and one component for each blade. The interface between the components at the blade roots is reduced using the wave-based substructuring method, which employs tuned system modes. These system modes are calculated first, and used subsequently during the reduction of the individual components, which eliminates the need to build a partially reduced intermediate model with dense matrices. For the disk, a cyclic Craig-Bampton reduction is applied. The deviations of the stiffness and mass matrices of individual disk sectors are then projected into the cyclic basis of interior and interface modes of the disk substructure. Thereby it is possible to model small disk mistuning in addition to large mistuning of the blades.

Acoustic reflections and multiple blade-row effects have an impact on aeroelastic behavior, which can change the aerodynamic damping by a significant amount. However, conventional flutter analyses neglect these effects as they ignore any information about the multistage unsteady interaction. In order to capture them, the authors of this paper have developed a multistage coupling methodology for ITP’s in-house unsteady 3D frequency-domain linearized RANS solver. The current approach allows carrying out CFD simulations on a multistage environment built upon an arbitrary number of blade-rows; each one of them could also have an arbitrary number of frequencies and/or interblade phase angles. The coupling mechanism between consecutive blade-rows arises in a somewhat straightforward way after the solutions are decomposed as the sum of several spinning modes in the inter-row boundaries and the continuity of acoustic, vortical and entropic waves is enforced. This method is suitable for flutter and forced response computations, and also for tonal noise propagation. The focus of this paper is on the study of multiple blade-row effects on flutter stability margin. A brief analysis of results for a couple of simple test cases is presented to demonstrate the correctness of the method. Then, a detailed flutter analysis for a representative LPT geometry is performed and the results are compared with a single row conventional analysis. The impact of neighboring and further blade-rows, as well as spinning modes scattered from the fundamental circumferential mode, are accounted for in the unsteady aerodynamic loading of the excited blade.

The tip-timing technology has been widely developed and has become an industry standard in aircraft engine and gas turbine over past decade. The main application of the tip-timing method is to verify safe operation of blades and monitor the health of blades. But tip-timing technology gets rarely used to the last stage blade of steam turbine. Particularly the blade is designed with an integral shroud, snubber and fir-tree root. The article mainly describes the process of identifying the dynamic characterization of last stage blade with an integral shroud and snubber by contactless measurements provided by tip-timing technology. Attention is focused on the comparison of tip-timing results with the results from strain gauge data. Firstly, the frequency response of the bladed blisk is calculated by using Computer-Aided-Engineering (CAE) technologies. Secondly, according to the results of finite element modal calculation, the location of strain gauge is confirmed. The dynamic strain of blade is measured by utilizing telemetry technology. Finally, according to the design features of integral shroud, the tip-timing probe locations must be accurately confirmed in order to acquire the valid data. All probes are positioned along the radial direction of blades. The rotating vibration test of the bladed blisk has been carried out in the high-speed test rig. In order to validate the tip-timing measurement, all the results from the tip-timing, especially the resonant frequencies and damping ratios, are compared with results from the strain gauges with which only a few blades were equipped.

In this paper, a methodology is developed for analysis of modal damping in root joints of bladed discs using large finite element models and detailed description of friction contacts at contact interfaces of the joints. The methods allows the analysis of: (i) a single blade vibration and (ii) a bladed-disc assembly for any family of modes (lower and higher modes) calculating the modal damping factors for different levels of vibrations. Three-dimension solid finite element models are used in the calculations. The analysis is performed in time domain through the transient dynamics analysis. The methodology allows the use of widely available finite element packages and based on the direct calculation of the energy dissipated at root joints due to micro-slip over the multitude of contact elements modelling the surface-to-surface friction contact interactions. The numerical studies of the dependency of modal damping factors on the vibration amplitudes are performed for simplified and realistic bladed disc models for different blade mode shapes, engine-order excitation numbers and nodal diameter numbers using high-fidelity models.

As-manufactured rotors behave quite differently than nominal, as-designed rotors due to small geometric and material property deviations in the rotor, referred to as mistuning. The mistuning of a 20 bladed, integrally bladed rotor (IBR) will be evaluated via analytical methods, bench-top testing, and using a rotating compressor research facility. Analytical methods consist of the development of an as-manufactured model based on geometry measurements from a high fidelity optical scanning system. Benchtop testing of the IBR is done using a traveling wave excitation (TWE) system that simulates engine order excitation in stationary bladed disks for the purpose of determining potentially high responding blades due to mistuning. The compressor research facility utilizes blade tip timing (BTT) to measure the blade vibration of the IBR. The resonant response of the IBR at various modes and harmonic excitations is investigated. A comprehensive mistuning and force amplification comparison between the as-manufactured model, TWE, and the compressor rig is performed. Mistuning of each method is evaluated using three different methods. First, the tuned absorber factor (TAF), which is a metric to determine potential high responding blades, is determined for each system. Next, mistuning is analyzed by isolating individual blades both experimentally on the bench and analytically to determine the mistuning patterns. Lastly, the mistuning determined by each system will be evaluated using a reduced-order model, namely the Fundamental Mistuning Model Identification (FMM ID). It will be shown that TAF shows variability between each method providing indications TAF may not be the best approach of force amplification predictions. Basic mistuning agreements exist when isolating blades both experimentally and analytically exhibiting as-manufactured models are capable of representing full experiments. System ID methods provide a basic agreement between both the mistuning pattern and the mistuning amplification for all three methods analyzed. This ultimately shows the importance and the ability to use as-manufactured models to help increase detailed understanding of IBR’s.

One of the main challenges of the Blade Tip Timing (BTT) measurement method is to be able to determine the sensing position of the probe relative to the blade tip. It is highly important to identify the measurement point of BTT since each point of the blade tip may have a different vibration response. This means that a change in measurement position will affect the amplitude, phase and DC component of the results obtained from BTT data. This increases the uncertainty in the correlation between BTT measurements and Finite Element (FE) modelling. Also, the measurement point should ideally be located to measure as many modes as possible. This means that the probe’s position should not coincide with a node, or a position at which the sensor misses the blade tip. Changes in the sensing position usually arise from the steady state movements of the blades (change in mean displacement). Such movements are caused by changes to the static (thermal and pressure) loading conditions that result from changes in the rotational speed. Such movements usually have a constant direction at normal operating conditions, but the direction may fluctuate if the machine develops a fault. There are three main types of movements of the sensing position that are considered in this paper: (1) axial movement; (2) blade lean; (3) blade untwist. Ideally, the sensing position is known based on the geometries of both the blade and the probe, but due to different types of movements of the blade this position is lost. Very few works have researched the extraction of the sensing position. Such preliminary works have required a pre-knowledge of mode shapes and additional instrumentation. The aim of this paper is to present a novel method for the identification of the BTT sensing position of the probes relative to a blade tip, which can be used to quantify the above movements. The developed method works by extracting the steady state offset from measurements of blade tip displacements over a number of revolutions as the speed changes from zero to a certain value. Hence, that part of the offset that is due to the angular positioning error of the probes (outside the scope of this work) is cancelled out (since it is independent of speed). The change in steady state offset is then processed to identify the three possible movements. The new method is validated using a novel BTT simulator that is based on the modal model of the FE model of a bladed disk (“blisk”). The simulator generates BTT data for prescribed changes to the sensing position. The validation tests show that the novel algorithm can identify such movements within a 2% margin of error.

Intentional mistuning is a well known procedure to decrease the uncontrolled vibration amplification effects of the inherent random mistuning and to reduce the sensitivity to it. The idea is to introduce an intentional mistuning pattern that is small but much larger that the existing random mistuning. The frequency of adjacent blades is moved apart by the intentional mistuning, reducing the effect of the blade-to-blade coupling and thus the effect of the random mistuning. The situation considered in this work is more complicated because the main source for the blade damping is the effect of the aerodynamic forces (as it happens in a blisk for a family of blade dominated modes with very similar frequencies). In this case the damping is clearly defined for the tuned traveling waves but not for each blade. The problem is analyzed using the Asymptotic Mistuning Model methodology. A reduced order model is derived that allows us to understand the action mechanism of the intentional mistuning, and gives a simple expression for the estimation of its beneficial effect. The results from the reduced model are compared with those from a finite element model of a more realistic rotor under different forcing conditions.

Further reduction of vibratory stresses of blades and vanes using an appropriate damping system is required whenever the total damping of the stage is insufficient to avoid High Cycle Fatigue during the life of the blades. An alternative to standard friction based damping systems are impulse mistuning systems — a kind of vibration impact induced non-linear energy sink. Previous publications introduced impulse mistuning systems for avoidance of HCF caused by forced synchronous vibrations of blades and vanes. This included the development of the system, analytical predictions of the effectiveness as well as experimental validation. The effectiveness of the impulse mistuning systems in the case of self-excitation (e.g. flutter) has not been investigated yet to the knowledge of the authors. In this paper, a numerical study of the dynamic phenomena taking place in lumped-parameter models with negative damping and different impulse mistuning systems is presented. One of the results shown is that energy transfer takes place, whereby the vibration initiates at one mode and after some time gets transferred into higher vibration at another mode.

Circumferential grooves in the casing of an axial compressor rotor or fan are known to be beneficial by extending the operating range of the machine. The goal of this paper is to analyze, if such grooves have a significant effect on the flutter stability, too. Generally, flutter should always be avoided as these self-excited blade vibrations can lead to high-cycle fatigue and therefore may damage the blades. In the present paper, the flutter behavior of a nominal fan is analyzed by performing a unidirectional Fluid-Structure-Interaction (FSI) simulation. To model the traveling wave arising during flutter, three different possibilities are available for computational fluid dynamics (CFD): the traveling wave mode method (TWM), the Fourier transformation method (FT) and the influence coefficient method (INFC). The TWM and INFC will be used within this investigation. At first, the computed flutter stability of the commercial CFD solver ANSYS CFX is compared to the results of the academic CFD solver TBLOCK. Therefore, a MATLAB code is introduced to be able to use the very efficient INFC method in combination with ANSYS CFX. The main part of this paper deals with the examination of three different circumferential grooves. Two of them had been optimized regarding aerodynamics and aeroacoustics in a joint research project and produce a minor change in flutter behavior. The third groove is of an arbitrary chosen design and it is discussed how its axial position has an impact on the vibration characteristic of the fan. All CFD simulations are conducted for two different operating points at 100% speed and the first two eigenmodes of the fan blade.

Turbomachinery rotor-stator unilateral contact induced interactions play a growing role in lifecycle analysis and thus motivate the use of accurate numerical prediction tools. Recent literature confirmed by ongoing in-house experiments have shown the importance of thermomechanical coupling effects in such interactions. However, most available (possibly reduced-order) models are restricted to the sole mechanical aspects. This work describes a reduction technique of thermomechanical models involving unilateral contact and frictional contact occurrences between rotor and stator components. The proposed methodology is grounded on Guyan and Craig–Bampton methods for the reduction of the structural dynamics in conjunction with Krylov subspace techniques, and specifically the Craig–Hale approach, for the reduction of the thermal equations. The method has the capability to drastically reduce the size of the model while preserving accuracy. It stands as a reliable strategy to perform simulations of thermomechanical models with localized mechanical and thermal loads.

A simple non-dimensional model to describe the flutter onset of labyrinth seals is presented. The linearized equations for a control volume which represents the inter-fin seal cavity, retaining the circumferential unsteady flow perturbations created by the seal vibration, are used. Firstly, the downstream fin is assumed to be choked, whereas in a second step the model is generalized for unchocked exit conditions. An analytical expression for the non-dimensional work-per-cycle is derived. It is concluded that the stability of a two-fin seal, depends on three non-dimensional parameters, which allow explaining seal flutter behaviour in a comprehensive fashion. These parameters account for the effect of the pressure ratio, the cavity geometry, the fin clearance, the nodal diameter, the fluid swirl velocity, the vibration frequency and the torsion center location in a compact and interrelated form. A number of conclusions have been drawn by means of a thorough examination of the work-per-cycle expression, also known as the stability parameter by other authors. It was found that the physics of the problem strongly depends on the non-dimensional acoustic frequency. When the discharge time of the seal cavity is much greater than the acoustic propagation time, the damping of the system is very small and the amplitude of the response at the resonance conditions is very high. The model not only provides a unified framework for the stability criteria derived by Ehrich [1] and Abbot [2], but delivers an explicit expression for the work-per-cycle of a two-fin rotating seal. All the existing and well established engineering trends are contained in the model, despite its simplicity. Finally, the effect of swirl in the fluid is included. It is found that the swirl of the fluid in the inter-fin cavity gives rise to a correction of the resonance frequency and shifts the stability region. The non-dimensionalization of the governing equations is an essential part of the method and it groups physical effects in a very compact form. Part I of the paper[3] detailed the derivation of the theoretical model and drew some preliminary conclusions. Part II analyzes in depth the implications of the model and outlines the extension to multiple cavity seals.

The optimization of the mechanical design process of turbomachinery has been a subject of research for decades. In this context, many researchers developed efficient numerical methods to calculate the vibration response of bladed disks. In most cases, the studies are restricted to one single operating point of the system, which is sufficient for many applications. For turbomachinery with variable operating points, the conventional computation methods must be extended. Changing the turbine’s rotational speed Ω leads to entirely new load conditions. On the one hand, structural mechanical properties (e.g. stiffening effects) depend on the rotational speed. On the other hand, in case of coupled blades, the pressure distributions in the joints are sensitive to the rotational speed. In this paper, a model of a steam turbine blade is investigated numerically and experimentally. Beside the tip shroud contact, multiple contacts at the root of the blade are considered. The steady-state vibration response is calculated by the well-known harmonic balance method (HBM) and an alternating frequency-time scheme (AFT). In case of variable operating conditions, the stiffness matrix can be described as a matrix polynomial of second order in Ω 2 . The preload at the joints is based on nonlinear quasistatic finite element analysis and also depends on the rotational speed. For the first time, a computational methodology is presented for the calculation of the forced response of a fully bladed disk with multiple contacts considering rotational speed dependent structural mechanical properties and, in particular, contact pressures. The experimental study is conducted in two steps. Firstly, a single blade model is investigated at non-rotating test conditions. Here, the blade is clamped with two dummies at the shroud. The vibration response is measured for various pressure distributions at the shroud contact. The comparison with simulation results shows a very good agreement. The second step of the experimental study will be the future investigation of a bladed disk assembly on a rotating test rig. An overview of the test rig including operation conditions, excitation methods and measurement techniques is given at the end of the paper.

In modern compressors the assessment of blade vibration levels as well as health monitoring of the components are fundamental tasks. Traditionally, this assessment is done by the application of strain gauges to some blades of the assembly. In contrast to strain gauges, blade tip timing (BTT) offers a contactless monitoring of all blades of a rotor and there is no need of a telemetry system. A major issue in the interpretation of BTT data is the heavily undersampled nature of the signal. Usually, newly developed BTT algorithms are tested with sample data created by simplified structural models neglecting many of the uncertainties and disturbing influences of real applications. This work focuses on the creation of simulated BTT datasets as close as possible to real case measurements. For this purpose a subset of nominal system modes (SNM) representation of a compressor rotor is utilized. This model is able to include a large number of features present in real measurements, such as mistuning, static blade deflections due to centrifugal loads, aerodynamic damping and multiple mode resonances. Additionally, manufacturing deviations of the blade geometry, probe positioning errors in the BTT system and noise in the time of arrivals (TOAs) are captured by the BTT simulation environment. The main advantage of the created data is the possibility to steadily increase the signal complexity. Starting with a “perfect” signal the simulation environment is able to add different uncertainties one after the other. This allows the assessment of the influence of different features occurring in real measurements on the performance and accuracy of the analysis algorithms. Finally, a comparison of simulated BTT data and real data acquired from a rig test is shown to validate the presented approach of BTT data generation.

Single crystal blades used in high pressure turbine bladed disks of modern gas-turbine engines exhibit material anisotropy. In this paper the sensitivity analysis is performed to quantify the effects of blade material anisotropy orientation on deformation of a mistuned bladed disk under static centrifugal load. For a realistic, high fidelity model of a bladed disk both: (i) linear, and (ii) non-linear friction contact conditions at blade roots and shrouds are considered. The following two kinds of analysis are performed: (i) local sensitivity analysis, based on first order derivatives of system response w.r.t design parameters, and (ii) statistical analysis using polynomial chaos expansion. The polynomial chaos expansion is used to transfer the uncertainty in random input parameters to uncertainty in static deformation of the bladed disk. An effective strategy, using gradient information, is proposed to address the “curse of dimensionality” problem associated with statistical analysis of realistic bladed disk.

Prevention of high cycle fatigue failures of blades caused by increased level of vibrational stresses is important problem in engine design and development. Different types of dampers are usually installed under the blade platforms in the region between the shanks of adjacent blades are usually used to reduce the vibrational stresses in the turbine blades. The action of these dampers is based on the vibrational energy dissipation by the dry friction forces arising due to the relative displacement of the contacting surfaces of the damper and the blade. Adoption of a reliable choice of damper design mass and stiffness at the design stage of the aircraft engines requires an experimentally validated estimation of its damping efficiency and its influence on the blade frequency characteristics. The dampers need to be tested under conditions that are maximally close to the operational conditions. This paper presents an analysis of the stress gauging results of a turbine wheel with box-type dampers of various mass. The tests were carried out on a dynamic bench where resonance oscillations of a stage for a given mode were excited by one of the harmonics to a given rotational speed under the corresponding forces pressing the dampers onto the blade platform. An estimation of the damper efficiency in a wider range of pressing forces was also obtained by conducting the laboratory tests using on a specially designed vibration unit that simulates the dampers effect on a set of three blades. Numerical analysis of the damper mass and stiffness influence on the frequency and damping characteristics of a real turbine wheel was performed. Obtained experimental data and the GAP model of contact interaction of the insert with blades were used in the MSC. Nastran software package. Analysis showed a satisfactory correlation between the calculated and experimental estimates of the decrease in resonant stresses and resonance frequency changes when the dampers are inserted. The results presented here confirm the possibility of increasing the reliability of the choice of mass and stiffness of turbine blade dampers at the design stage.

Due to the changing demands in the energy production sector which leads to higher numbers of run ups and run downs, the importance of transient processes increase. Further information on the occurring blade vibration amplitudes during these processes could be used to explore new potential for longer lifetime and efficiency. Recent publications have shown that the amplitude of a mistuned blisk during a resonance passage can exceed the stationary response of the same system [1]. This underlines the importance of a better understanding of what happens during resonance passage. The effect is described as transient amplitude amplification of mistuned structures (TAMS). In this paper the effect will be investigated theoretically as well as in experiments. The main cause of the described effect seems to be the splitting of double eigenfrequencies due to mistuning. Therefore, the focus lies on methods to deliberately influence and seperate eigenfrequencies. First, simulations are done to predict parameter values which tend to show the TAMS effect. It is then shown how a significant transient amplitude amplification can be created on a test rig depending on the intentional mistuning. For realization an experimental setup with contactless measurement and acoustic excitation is deployed on a simplified blisk.

Forced response is the main reason for high cycle fatigue in turbomachinery. Not all resonance points in the operating range can be avoided especially for low order excitation. For highly flexible CFRP fans an accurate calculation of vibration amplitudes is required. Forced response analyses were performed for blade row interaction and boundary layer ingestion. The resonance points considered were identified in the Campbell diagram. Forced response amplitudes were calculated using a modal approach and results are compared to the widely used energy method. For the unsteady simulations a time-linearised URANS method was applied. If only the resonant mode was considered the forced response amplitude from the modal approach was confirmed with the energy method. Thereby forced response due to BLI showed higher vibration amplitudes than for blade row interaction. The impact of modes which are not in resonant to the total deformation were investigated by using the modal approach, which so far, only considers one excitation order. A doubling of vibrational amplitude was shown in the case of blade row interaction for higher rotational speeds. The first and third mode-shape as well as modes with similar natural frequencies were identified as critical cases. The behaviour in the vicinity of resonance shows high vibration amplitudes over a larger frequency range. This is also valid for high modes with many nodal diameters, which have a greater risk of critical strain.

A new reduced order modeling technique for nonlinear vibration analysis of mistuned bladed disks with shrouds is presented. It has been shown in the literature that the loss of cyclic symmetry properties which is known as mistuning could considerably increase the response level, localize the vibration around few number of blades and finally bring high cyclic fatigue. The developed reduction technique employs two component mode synthesis methods, namely, the Craig-Bampton (CB) method followed by a modal synthesis based on loaded interface modeshapes (Benfield and Hruda). In the new formulation the fundamental sector is divided into blade and disk components. The CB method is applied to the blade, where nodes lying on shroud contact surfaces and blade-disk interfaces are retained as master nodes, while modal reductions is performed on the disk sector with loaded interfaces. The use of loaded interface component modes allows removing the blade-disk interface nodes from the set of master nodes retained in the reduced model. The result is a much more reduced order model with no need to apply any secondary reduction. In the paper it is shown that the reduced order model of the mistuned bladed disk can be obtained with only single-sector calculation, so that the full finite element model of the entire bladed disk is not necessary. Furthermore, with the described approach it is possible to introduce the blade frequency mistuning directly into the reduced model. In this way, reduction is performed only once in case of multiple analyses, necessary for statistical characterization of the nonlinear response of the system. The nonlinear forced response is computed using the harmonic balance method (HBM) and alternating frequency/time domain (AFT) approach. Friction contacts are introduced into the FE model using a 3D contact element. Numerical simulations revealed the accuracy, efficiency and reliability of the new developed technique for nonlinear vibration analysis of mistuned bladed disks with shroud friction contacts.

The present numerical study aims at examining the influence of intrarow interaction effects in aerodynamic damping predictions of an axial turbine rotor. The investigated operating point corresponds to a resonance crossing associated with the fundamental engine order of the stator blade row. Accordingly, the pressure perturbations induced by the vibration of the rotor at its modal frequency are found to be coincident in frequency and thus superimpose with the pressure perturbations resulting from intrarow interaction phenomena. A methodology for extracting vibration induced pressure perturbations for the subsequent calculation of the vibration induced modal aerodynamic damping is established and applied within the scope of the present study. Applying this methodology, both the influence of the underlying mean and transient flow field as well as the influence of acoustic wave reflections at the adjacent stator blade row is investigated on the predicted aerodynamic damping. In this context, the underlying mean flow field, which is found to be slightly altered in the presence of intrarow interaction phenomena, was proven to have a significant influence on vibration induced pressure perturbations. Moreover, acoustic wave reflections at the adjacent stator blade row are found to have the capability of influencing the aerodynamic damping depending on their actual phasing when impinging onto the turbine rotor.

This paper introduces an improvement of the stress calibration methodology of stator blades to consider a nodal diameter of interest of the structure. The proposed calibration procedure and the search for optimal excitation set-up are detailed. To this purpose, the following points are addressed. Experimental modal analyses are performed using both accelerometers and strain gages. Post-processing techniques are developed to determine the nodal diameters of the identified modes. SAFE (Singh’s Advanced Frequency Evaluation) diagrams are computed from the experimental data and compared with the diagrams obtained numerically by finite elements computations. Multiple excitations are used to appropriate the targeted modes. A comparative study of different shaker types, of the number of excitation points and of their location is performed. Calibration is achieved by comparing strain measurements taken on one gage installed on the engine and velocities measured using laser vibrometers. It allows reducing the impact of the instrumentation on the modal content. The calibration factors obtained by the novel proposed procedure are compared to the ones given by the currently used methodology.