Mistuned Bladed Research Articles

Forced Response of Rotating Blisks: Prediction and Correlation to Blade Tip-Timing Measurements

Abstract This paper explores two different blisk dynamic models for resonant vibration prediction of a rotating blisk test piece, i.e., the Model-BDTID and geometrically mistuned models (GMM). The former represents a mistuned blisk model with blade mistuning pattern experimentally retrieved by a recently proposed blade mistuning identification method based on blade detuning tests (BDTID). It falls into the scope of the frequency-mistuning modeling approach. The latter refers to a geometrically mistuned model constructed upon high-precision blisk geometry data by leveraging the advanced optical geometry measurement technology. A specifically developed “Sector Mode Assembling Reduction Technique” is exploited for efficient dynamic analyses of the large-sized GMM. Forced response tests are performed in a spinning rig under well-controlled laboratory condition. The blade tip-timing (BTT) technique is employed to give all-blade vibration measurements of the rotating blisk. Correlation results between the forced response predictions to BTT measurements demonstrate that both the Model-BDTID constructed upon the identified blade mistuning of the blisk at rest and the GMM, can predict the resonant vibration of the rotating blisk with satisfactory accuracy.

A Critical Analysis of Design for Reduction in Vibrations of Centrifugal Impellers

Centrifugal pumps are widely used for various applications. Numerous technical practices use centrifugal pumps, particularly when consistent and adaptable pump performance is required. Still, these can have several issues, including low efficiency when operated under off-design conditions and poor capitalization performance. These frequent transport mixtures, such as liquid and gas, and pure liquids. It is a well-known fact that several problems encountered by pumps in a pumping station are related to structural instability or impeller/blade failure. Vibrations can cause catastrophic failures in the impeller, so these must be kept to a minimum while designing the impeller. Vibration, cavitation, rough running, lower-than-expected efficiency, and shorter pump life can all be traced back to unfavorable process flow conditions. Although there are some design guidelines for pump configuration, the effects of fluctuating discharge on structural stability have yet to be investigated. An additional pressing problem is the identification of time cracks. Failure can occur due to cracks much before the design loads. In this work, we aim to investigate and analyze the centrifugal impeller design consideration. Using different methods for designing and modeling, we compared significant results and found the optimal solutions in which a centrifugal impellor can be designed. This work enables us to determine the best techniques and methods to overcome the problem of vibrations produced in the centrifugal impeller. This also helps us to understand the centrifugal pump's behavior and performance to improve its efficiency. Centrifugal impellors are compared across conditions, including free, forced, damped, and undamped systems. Three successful methods for designing and modeling a centrifugal impellor are proposed using these parameters. The methods of design and analysis provide predictions of the flow fields that are highly reliable. Regarding fluid distribution and pump efficiency, computational fluid dynamics provides various solutions that may be applied to impeller design. Using fluent software, we can better comprehend the pump's resonant operation. Blade mistuning is a severe problem that can be handled using the blade tip timing and strain gauge technique. Vibration and motor current signature analysis (MCSA) is also mentioned to investigate vibrational problems with the centrifugal impeller. Several strategies are discussed to lessen or eliminate the issue of vibrations in impellers. The limitations and disadvantages of using these techniques are discussed. The summary of results provides significant design and improvement in centrifugal pumps in the recent past.

Intentional Blade Mistuning to Emulate the Dynamic Influence of Split Ring Damper

Abstract A novel methodology to predict responses of bladed disks incorporated with a split ring damper is proposed. To account for the dynamic characteristics of a split ring damper, intentional blade stiffness mistuning is presented. It is assumed that the mistuning is proportional to the blade stiffness matrix and uniformly distributed to all blades. Therefore, responses of bladed disks integrated with a split ring damper are captured by the detuned bladed disk integrated with a continuous ring damper. The proposed method is demonstrated through a lumped parameter model and validated using a complete finite element model. A key advantage of the proposed approach is that the dynamic characteristics of a split ring damper are emulated by a continuous ring damper in the detuned bladed disk. Moreover, the approach holds the potential to facilitate reduced-order modeling (ROM) by employing sector-level calculations. This results in substantial reductions in computational efforts while maintaining accurate predictions of forced responses.

Advancing Mistuning Identification and Dynamic Modeling of Blisks Through Blade Detuning Tests

Blisks extensively used in advanced aeroengines are vulnerable to vibration problems due to the high sensitivity of the blisk’s forced response to blade mistuning. This paper proposes an emerging mistuning identification technique based on blade detuning tests (BDTID) for predictive dynamic modeling of blisks. The conventional frequency-mistuning modeling approaches relying on blade mistuning identification by reduced-order model techniques and modal test data of the full blisk are also adopted to construct different mistuned models of a blisk test piece for comparison purposes. A complete assessment of these blisk models is achieved through the forced response tests in a stationary traveling wave excitation test rig. The BDTID consists of blade-detuning tests followed by a correction procedure. The detuning tests enable us to approximately evaluate the “blade-alone” frequencies through blade-by-blade impact testing in combination with a mass detuning mechanism. The correction procedure is able to evaluate the detuning test quality by the quantification of the residual interblade coupling due to mass detuning. More importantly, a robustness investigation demonstrates that this procedure is able to capture the “true” blade mistuning even in cases of poor blade detuning test quality. The resultant mistuned blisk model exhibits high accuracy in the modal correlation and forced response validation results. Compared with conventional methods, BDTID takes advantage of easy implementation with less experimental effort and has proven robust performance. It is therefore recommended for blade mistuning identification and predictive blisk dynamic modeling in a wide variety of scenarios.

Sensitivity Analysis of Transient Forced Response of Mistuned Bladed Disks Under Complex Excitation and Varying Rotation Speed

Abstract During accelerations and decelerations of gas-turbine engines, the transient vibration effects in bladed disk vibration become significant and the transient response needs to be efficiently and accurately assessed. This paper develops an effective method for efficient calculations of the sensitivity of the transient vibration response for a mistuned-bladed disk under varying rotation speeds. The sensitivities are calculated concerning two major factors: (i) the blade mistuning and (ii) the rotor acceleration/deceleration rates. The method uses the large-scale finite element modeling of the bladed disk to accurately describe the dynamic properties of the mistuned bladed disk. The method can be applied for a case when the loading is the transient load, with the amplitude and frequency spectrum changing with rotation speed. The dependency of the modal characteristics on the rotation speed is included in the formulation of the sensitivity analysis method. Efficient reduced order models are used to reduce the computational cost, which can adapt to the effects of the varying rotation speed on the natural frequencies and mode shapes of the mistuned bladed disk under transient conditions. The expressions for the sensitivities are derived analytically which provides high accuracy and speed of the calculations. The method has been implemented in a computer code and thoroughly verified using a set of test cases. The studies of transient forced response sensitivity have been performed for realistic bladed disk models.

A novel OPR-free method for blade tip timing based on adaptive variable reference blades

Monitoring rotor blade vibrations is imperative in aero-engine testing and service. Blade tip timing (BTT), a promising technique for such monitoring, assesses the operational status of rotor blades through non-intrusive measurement of blade tip displacement. Traditional BTT technology relies on the Once-Per-Revolution (OPR) probe, which poses installation challenges and introduces measurement uncertainties in practical applications. This paper introduces a novel OPR-free approach, employing Adaptive Variable Reference Blades (AVRB) for non-intrusive measurement of rotor blade vibrations. The method assumes a stochastic mistuning of blades within the same stage, resulting in non-simultaneous resonance of blades at a given speed. In each revolution, the vibration level of individual blades is determined by assessing the deviation between the average speed of a blade, as measured by two adjacent BTT probes, and the average speed across the entire circumference. Consequently, a non-vibrating blade is adaptively identified and selected as the reference blade. The relative vibration levels among blades vary dynamically during different revolutions, influenced by mistuning features, leading to variability in the reference blades. These adaptive variable reference blades can then replace the OPR probe, aiding in the computation of vibration displacement and further parameter identification of blades. To validate the effectiveness of the proposed method, a five-degree-of-freedom numerical model is utilized for simulation. Additionally, experiments involving both a five-bladed disk and an eight-bladed disk are conducted to validate the proposed approach. Numerical simulations and two sets of test results demonstrate a fundamental agreement between the blade vibration displacement calculated using the proposed method and the outcomes obtained through the traditional BTT method with OPR. The relative error in the identified blade vibration frequency derived from the blade vibration displacement, as determined by both methods, does not exceed 1 %. Additionally, the relative error in the amplitude of the blade vibration displacement is within the range of 10 %.

Dynamic characteristics of vibration localization of mistuned bladed disk due to shroud and blade damages

Dynamic behaviors of turbine blades are important for the dynamic design of whole-bladed disk systems. The bladed disk systems with shrouds are used to achieve advanced functions in operation. The shrouds are used to connect several blades as a bladed packet, and several bladed packets are assembled as a bladed disk. Previous researches mainly focus on the mistuning of the bladed disk. However, in operation, the shrouds often suffer damage and wear, and it will lead to shrouds mistuning. The shroud is a critical component for adjusting the coupling strength of the blade to the blade. The innovation of this paper is to study the coupling dynamics problem caused by blade mistuning and shroud damage. The localized vibration of the bladed disk is caused by the blade mistuning, and the shroud damage can also cause the localized vibration of the bladed disk. The coupling dynamic behaviors of bladed disk caused by blade mistuning and shroud damage are important. Therefore, the dynamic behaviors of a mistuned bladed disk with the shroud are important for the bladed disk. A numerical method is conducted to investigate the dynamic characteristics of the whole bladed disk with shroud. The coupling effect between shroud and blade mistuning on the dynamic behaviors of the bladed disk is researched. The numerical model is validated by assuming the shroud and blade mistuning is zero. The coupling effect of shroud and blade mistuning leads to the characteristics being more complicated. Bladed packet is the basic part of the bladed disk with shroud. In order to study the modal characteristics of bladed packets due to shroud, an experiment is conducted. It is worth noting that the first sub remains invariable with the increasing of stiffness ratio.

Transient Resonance Passage of a Mistuned Bladed Disk with and without Underplatform Dampers

In this work, the vibration response of an academic free-standing turbine blisk is analyzed in regard to transient resonance passages. Measurement data are recorded using strain gauges and tip timing to evaluate the blades first bending mode both linearly and with two different types of underplatform dampers. These results are validated against steady-state responses and show good agreement with each other. To examine the effects of a transient resonance passage, response functions of each blade are evaluated both with and without the underplatform dampers. It is shown that friction damping is able to inhibit any appearance of a transient ring-down. Additionally, a multi-mass oscillator model with frictional contacts is analyzed, which qualitatively exhibits the same dynamics as the measurements. Due to geometric mistuning, all blades exhibit different vibration responses. This can lead to a transient amplitude amplification, which is observed on several blades. Analogously, this phenomenon can be mitigated by friction damping.

A novel mathematical model for the design of the resonance mechanism of an intentional mistuning bladed disk system

Abstract. Bladed disk systems with advanced functions are widely used in turbo-machineries. However, there are always deviations in physical dynamic properties between blades and blades due to the tolerance and wear in operation. The deviations will lead to vibration localization, which will result in high cycle fatigue and accelerate the damage of the bladed disk system. Therefore, many intentional mistuning patterns are proposed to overcome this larger local vibration. Previous studies show that intentional mistuning patterns can be used to reduce the vibration localization of the bladed disk. However, the determination of the resonance mechanism of the intentional mistuning bladed disk system is still an unsolved issue. In this paper, a novel mathematical model of resonance of an intentional mistuning bladed disk system is established. Mistuning of blades and energy resonance are included in this theoretical model. The method of the mechanical power of the rotating blade for one cycle is applied to obtain the resonance condition. By using this theoretical model, the resonance mechanism of an intentional mistuning bladed disk is demonstrated. The results suggest that the ideal results can be obtained by adjusting the intentional mistuning parameter. This paper will guide the design of the dynamic characteristics of the intentional mistuning bladed disk.

The Flutter Stability of Mistuned Bladed Disks Subjected to the Coriolis Effect

Abstract Intentional frequency mistuning referred to as detuning is known to be an effective mean to prevent aeroelastic flutter in gas turbines. The Coriolis effect, which is usually discarded, can reduce the mistuning effects and therefore compromise the stabilizing effect of detuning with respect to flutter. This paper presents an original study of the influence of the Coriolis effect on the aeroelastic stability of a single-piece bladed disk (blisk), which made it possible to highlight for the first time the complex interactions between flutter, mistuning, and the Coriolis effect. The blisk is modeled with a lumped parameter model and the aeroelastic self-excitations using Whitehead's theory. A genetic algorithm is used to determine the best detuning pattern to stabilize the flutter-prone blisk. The results show that if the detuning pattern is identified without taking the Coriolis effect into account, the detuned blisk can still be prone to flutter. The key driver of this loss of stability is the frequency separation of the modes resulting from the Coriolis effect, which decreases the mode interactions that are required to stabilize the system. This article demonstrates the need to consider the Coriolis effect when studying the aeroelastic stability of cyclic structures with flexible disk and blade-disk coupling. By doing so, it is shown that a higher level of detuning is needed to compensate the adverse effects of Coriolis and ensure stability to flutter.

Novel Neural Network for Predicting the Vibration Response of Mistuned Bladed Disks

Inevitable mistuning in cyclic bladed disk structures would cause vibration amplification phenomena that seriously reduce the reliability of the bladed disk. The ability to accurately and quickly predict the dynamic responses is critical to investigating the dynamic behavior of the mistuned system. However, it is still challenging because the mistuned responses are extremely sensitive to the random mistuning parameters. In this work, a novel mistuned system deep neural network model (MS-DNN) is presented to predict the dynamic responses of mistuned bladed disks through the mistuning parameters for both the lumped parameter model and the large-scale finite element (FE) model, which decouples the vibration equations of the mistuned system and uses a neural network to replace the coupling process. MS-DNN is divided into two levels, namely, the blade and the disk. The blade-level neural networks are used for forward and backward propagation of mistuning parameters in the different blades, and the disk-level neural network is used to replace the physical coupling process in the disk of multiple mistuning parameters from individual blades, with data transmission between the neural networks via blade–disk boundary nodes. The expected physical response of the blade tip is predicted through MS-DNN. All neural networks in MS-DNN show high prediction accuracy on both training sets and unknown test sets. For the FE model of the industrial bladed disk, the effect of the number of boundary nodes selected as the data interface between neural networks on the prediction accuracy is also investigated. The results show that, for unknown test data, the predicted response has an value of 0.998 versus the actual response with an amplification factor error of less than 0.388%.

Sector Mode Assembling Reduction Technique for High-Fidelity Blisk Models with Geometry Mistuning

Blade mistuning in blisks arises primarily from the scatters of blade geometry profiles caused by manufacturing tolerance, in-service wear, blade repairs, etc. There is a recent trend to capture the blade-to-blade geometry variances through precise geometry measurements by a 3D optical scanning system in order to obtain an improved blade geometric mistuning evaluation capability. However, this usually leads to prohibitive computational costs due to the large-scale, high-fidelity industrial blisk finite element models. This paper develops an original model reduction approach, Sector Mode Assembling Reduction Technique (SMART), specifically for the high-fidelity blisk model fully mistuned by blade geometric variances, with either topologically compatible or incompatible blade meshes. The basic idea of SMART is to construct the sector-level reduction mode basis by strategically assembling the truncated cyclic modes independently computed for each “isolated” sector with assumed cyclic symmetry at the sector interfaces. Benefiting from the block structure of the SMART mode basis, the reduced-order models are derived by a series of sector-level projections with a relatively low memory requirement and computational cost. Another hidden benefit is that the SMART approach enables efficient structural modification predictions of the global blisk modes because only the modes of the sectors undergoing blade modification need to be re-evaluated and replaced in the SMART mode basis. The SMART approach is applied into a high-fidelity “as-measured model” of a blended blisk, constructed upon the geometry measurement by the state-of-the-art 3D optical scanning technology. It is fully demonstrated that the reduced-order model derived by SMART, featured by a minimal size, is able to reproduce the dynamics of the full-order as-measured blisk model with high accuracy.

A Modal Interpretation for Aeroelastic Stability Enhancement of Mistuned Bladed Disks

Understanding the mechanism of the aeroelastic stability improvement induced by mistuning is essential for the design of bladed disks in aero-engines. In this paper, a quantitative interpretation is given. It starts by projecting the mistuned aeroelastic modes into the space spanned by the tuned modes. In this way, the mistuned aeroelastic damping can be expressed by the superposition of the tuned damping. Closed-form expressions are found, providing clear interpretations of several frequently reported trends in the literature. Further, a prediction approach is proposed, where the analysis of aeroelastic coupling only needs to be performed once, and it is decoupled from the analysis of the mistuning effect. The advantages are two-fold. First, the design of the mistuning pattern is accelerated. Second, this allows one to introduce more accurate data or models of aeroelastic damping. An empirical bladed disk with NASA-ROTOR37 profile is used as an example, and the alternate, wave, and random patterns are considered.

Exploration of blade detuning tests for mistuning identification of blisks

This paper presents a novel blade mistuning identification method based on blade detuning tests. Blade detuning tests consist of blade-by-blade impact testing in a blisk with detuning masses purposefully attached on all the blades except the one currently under test. Due to the quite simple test setup and implementation, the detuning tests enable to estimate the blade frequency mistuning pattern of the blisk with low experimental effort. However, it was proved that non-negligible residual inter-blade coupling is responsible for an inaccurate identification of the truly ‘blade-alone’ mistuning pattern from the blade detuning test results. Therefore, a novel mistuning identification method is herein proposed in order to improve the accuracy of the estimated mistuning pattern. This method fully exploits the blade detuning test results and includes the residual inter-blade coupling due to the mass detuning mechanism. The quantification and the introduction of the residual inter-blade coupling into the identification procedure leads to the determination of a more accurate ‘blade-alone’ frequency mistuning pattern. This novel mistuning identification method is firstly validated in a numerical test case and then applied to a real blisk test piece.

Modelling and analysis of a bladed drum subject to the Coriolis and mistuning effects

The interaction between the Coriolis and mistuning effects on a finite-element model (FEM) of a simplified bladed drum compressor has been investigated in this paper. The Subset of Nominal Modes (SNM), the Component Mode Mistuning (CMM) and the Integral Mode Mistuning (IMM) techniques have been chosen and adapted to consider the reduction of the Coriolis matrix. Both free and forced responses of the ROMs have been validated using the FEM solutions as the benchmark. A new analysis using Monte Carlo simulations has been performed to consider disc and blade mistuning independently, and to study the domination of one over the other. The impact of the Coriolis effect has been highlighted through observation of the model with and without the Coriolis matrix. The evolution of the global dynamic behaviour with rotational speed has been investigated for the first time for different excitation frequencies and engine orders (EO). This in-depth investigation of a blisk allowed a better understanding of the interaction between the Coriolis and mistuning effects. The blade-dominated responses and the modes which remain close to the veering regions have strong mistuning effects, with significant localisation and amplitude magnification. The results mainly highlight that the disc-dominated and the blade–disc responses tend towards a tuned behaviour with the appearance of travelling waves.

Mobile Interface CMS Method for Vibration Characteristics Prediction of Mistuned Bladed Disk with Different Coupling Degrees

The prediction of vibration characteristics was studied in the mistuned bladed disk by the mobile interface prestressed component mode synthesis (CMS) superelement method. When the strongly, generally, and weakly coupling in the mistuned bladed disk, according to the results of the direct FEM method, the prediction accuracy of this method was verified and compared with the fixed-interface CMS method by using the relative error of dynamic frequency, vibration mode matching function, and dimensionless root mean square error of vibration amplitudes. It is pointed that for mistuned bladed disk in the strong coupling, the prediction accuracy of dynamic frequency and vibration amplitudes are higher by the mobile interface CMS method and the vibration modes are matched with the direct method. In weak coupling, the results of dynamic frequency and vibration modes predicted by the mobile interface CMS method and the fixed-interface CMS method are consistent with the direct method, but the vibration amplitudes’ prediction error of the mobile interface CMS method is lower than that of the fixed-interface CMS method. In general coupling, the mobile interface CMS method has higher dynamic frequency prediction accuracy at low order, and the two methods have comparable dynamic frequency prediction accuracy at high order. The vibration modes predicted by the two methods are matched with the direct FEM method, and the prediction accuracy of vibration amplitude by the mobile interface CMS method is better than that of the fixed-interface CMS method. The results indicate that the mobile interface CMS method could more accurately predict vibration characteristics of the mistuned bladed disk with different coupling degrees and could be an effective measurement for studying the vibration characteristics of the mistuned bladed disk system.

Investigation of Structurally and Aerodynamically Mistuned Oscillating Cascade Using Fully Coupled Method

Abstract There seems to be a lack of clear and systematic understanding of physical behavior and mechanisms of mistuned blade rows, particularly in the context of the aerodynamic mistuning versus the structural (frequency) mistuning. A high-fidelity fully coupled method is desirable to investigate the vibration characteristics of aeroelasticity problems with strong fluid–structure interaction effects, as well as blade mistuning effects. In this work, the direct nonlinear time-domain fully coupled method is adopted to investigate the dynamics mechanism of a mistuned oscillating cascade. The main objectives are two-folds, first to elucidate the basic vibration characteristics of a mistuned blade row, and second to examine the aeroelastic effects of mistuning. Three conditions of interest are considered: (a) the structural mistuning only, (b) the aerodynamic mistuning only, and (c) a combination of the two. The present results show that first a mistuned configuration tends to vibrate with the same frequency and a predominantly constant interblade phase angle. Vibration amplitudes of the blades vary significantly with a strong mode localization effect for the structural mistuning. For the concurrent structural-aerodynamic mistuning, the localization is stronger than in the standalone structural mistuning case. Second, a monotonic increase of the aeroelastic stability with the structural mistuning magnitude is observed. On the other hand, the aerodynamically mistuned cascade shows a stabilizing effect with a small amount of mistuning but exhibits a destabilizing effect with a large mistuning. Furthermore, these results indicate a quite remarkable interplay between the structural and the aerodynamic mistuning. At a condition where the tuned cascade is still stable, an aero-mistuning induced unstable behavior is observed. An introduction of a large magnitude of frequency mistuning which would be stabilizing for a tuned cascade, is instead shown to have a destabilizing effect for the present combined aero-structural mistuning case.

Mistuning parameter identification and vibration localization analysis of the integration rotor

This paper deals with the coupling vibration characteristic of the disk-blade-shaft integration rotor. First, a reduced-order model (ROM) based on an improved hybrid interface component mode synthesis method (IHISCMSM) is carried out, which takes the prestress effect into account. The frequency of the disk-blade-shaft integration rotor at different rotating speeds are calculated and the influence of selecting different mode truncation numbers is investigated. In order to quantitatively evaluate the coupling degree of blade and disk, the coupling factor is defined from the perspective of strain energy, and the influence of prestress on system’s dynamic is discussed. Then, an experimental modal analysis is performed on blades to identify the mistuning parameters, and the mode localization of the disk-blade-shaft integration rotor is analyzed with and without blade mistuning. The results indicate that there are several types of coupling modes among blade, disk and shaft of the integration rotor. After considering the prestress, the frequency increases, and the axial coupling vibration degree and radial coupling vibration degree of the integration rotor change. The mode localization of mistuned rotor is more likely to occur in the modes dominated by mistuning stage blades. There also exists a subtle mode localization phenomenon for tuned integration rotor.

Mistuning and Damping of a Radial Turbine Wheel. Part 1: Fundamental Analyses and Design of Intentional Mistuning Pattern

Abstract The radial turbine impeller of an exhaust turbocharger is analyzed in view of both free vibration and forced response. Due to random blade mistuning resulting from unavoidable inaccuracies in manufacture or material inhomogeneities, localized modes of vibration may arise, which involve the risk of severely magnified blade displacements and inadmissibly high-stress levels compared to the tuned counterpart. Contrary, the use of intentional mistuning (IM) has proved to be an efficient measure to mitigate the forced response. Independently, the presence of aerodynamic damping is significant with respect to limit the forced response since structural damping ratios of integrally bladed rotors typically take extremely low values. Hence, detailed knowledge of respective damping ratios would be desirable while developing a robust rotor design. For this, far-reaching experimental investigations are carried out to determine the damping of a comparative wheel within a wide pressure range by simulating operation conditions in a pressure tank. Reduced-order models are built up for designing suitable intentional mistuning patterns by using the subset of nominal system modes approach introduced by Yang and Griffin (2001, “A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes,” J. Eng. Gas Turbines Power, 123(4), pp. 893–900), which conveniently allows for accounting both differing mistuning patterns and the impact of aeroelastic interaction by means of aerodynamic influence coefficients. Further, finite element analyses are carried out in order to identify appropriate measures of how to implement intentional mistuning patterns, which are featuring only two different blade designs. In detail, the impact of specific geometric modifications on blade natural frequencies is investigated. The first part of this three-part paper is focused on designing the IM pattern. The second and third part following, later on, will address the topics (i) experimental validation after implementation of the IM pattern at rest and under rotation, and (ii) the development of an approach for fast estimating damping ratios in the design phase.

Stereo-DIC Measurements of a Vibrating Bladed Disk: In-Depth Analysis of Full-Field Deformed Shapes

Vibration measurements of turbomachinery components are of utmost importance to characterize the dynamic behavior of rotating machines, thus preventing undesired operating conditions. Local techniques such as strain gauges or laser Doppler vibrometers are usually adopted to collect vibration data. However, these approaches provide single-point and generally 1D measurements. The present work proposes an optical technique, which uses two low-speed cameras, a multimedia projector, and three-dimensional digital image correlation (3D-DIC) to provide full-field measurements of a bladed disk undergoing harmonic response analysis (i.e., pure sinusoidal excitation) in the kHz range. The proposed approach exploits a downsampling strategy to overcome the limitations introduced by low-speed cameras. The developed experimental setup was used to measure the response of a bladed disk subjected to an excitation frequency above 6 kHz, providing a deep insight in the deformed shapes, in terms of amplitude and phase distributions, which could not be feasible with single-point sensors. Results demonstrated the system’s effectiveness in measuring amplitudes of few microns, also evidencing blade mistuning effects. A deeper insight into the deformed shape analysis was provided by considering the phase maps on the entire blisk geometry, and phase variation lines were observed on the blades for high excitation frequency.