Engine Order Excitations Research Articles

Experimental Investigation of Synchronous-Flow-Induced Blade Vibrations on a Radial Turbine

In this study, a thorough experimental investigation of the synchronous blade vibrations of a radial turbine is performed for different IGV configurations. First, the blade modes are measured experimentally and calculated numerically. Subsequently, the vibrations are recorded with two redundant measurement systems during real operation. Strain gauges were applied on certain blades, while a commercial blade-tip-timing system is used for the measurement of blade deflections. The experimentally determined vibration properties are compared with numerical estimations. Initially, the vibrations recorded with the “nominal” IGV were presented. This IGV primarily generates nodal diameter (ND) 0 vibrations. Subsequently, the impact of two different IGV configurations is examined. First, a mistuned IGV, which has the same number of vanes as the “nominal” IGV is examined. By intentionally varying the distance between the vanes, additional low engine order excitations are generated. Moreover, an IGV with a higher number of vanes is employed to induce excitations at higher frequency modes and ND6 vibrations. Certain vibrations are consistently measured across all IGV configurations, which cannot be attributed to the spiral turbine casing. In addition, a turbine–compressor interaction has been observed.

An Analytical Study on the Effects of Non-Uniform Vane Spacing on Forced Response Reduction in a Mistuned Blisk Rotor in a Multistage Axial Compressor

Abstract Stators with non-uniform vane spacing (NUVS) have been sought as an effective way to reduce the rotor-forced response at certain resonance crossing of concern. A comprehensive experimental study has been conducted in Purdue three-stage axial research compressor to evaluate the effectiveness of the NUVS stator on reducing the forced response of the downstream rotor using strain gauge measurement. The experimental results showed that the classical estimation method failed to predict the reduction factor correctly, mainly due to the lack of consideration for the damping and mistuning effects. To better understand the experimental results, and to provide an efficient and more accurate analysis tool for the rotor forced response under NUVS stator excitation, a detailed analytical study was conducted in this paper. The blade-forced response was solved using an efficient, steady-state linearized approach. A single-blade analysis was done first to study the effect of damping. The case studies show that higher damping causes more overlap of the blade forced response from adjacent engine order excitations and, thus, increases the total normalized blade response under NUVS stator excitation. A mistuned blisk aeroelastic model was introduced next, with the mistuning effect modeled using the fundamental mistuning model. Both structural coupling and aerodynamic coupling effects can be included in the aeroelastic model. Similar to the experimental results, the mistuned blisk case study shows a large blade-to-blade variation in the blade-forced response under both symmetric and asymmetric NUVS stator excitation, even at a low, non-intentional mistuning level. A statistical study with 100 randomly generated mistuned blisks shows that the forced response reduction effect of a specific NUVS design could vary significantly with a small change of the mistuning pattern, which suggests that mistuning has to be carefully considered in the design, evaluation, and optimization of the NUVS stator.

Numerical Study of Low Engine Order Excitations due to Manufacturing Variability Part 1: Characterization of the Geometric Scatter and its Effect on Forced Response

Abstract The geometric scatter in the surfaces of blades and vanes due to manufacturing variability has an impact on the dynamics but also on the aerodynamics. The loss of the spatial periodicity of the flow due to the geometric variations generates an aerodynamic forcing with a wave number different from the airfoil count on the adjacent rows. In this paper, deviations from the nominal geometry are obtained from a set of scanned parts. The average manufactured geometry is computed through the point-by-point deviations between the scanned parts and the nominal geometry. Then, Principal Component Analysis is applied to the deviations from the average geometry to find a way to describe them in a simple manner. The cold geometries are reconstructed using the mean geometry and the PCA geometric modes; afterwards, a cold-to-hot process is applied to obtain the hot geometry, and finally the resulting aerodynamics are obtained using an in-house CFD solver. The described method is applied to a representative row constituted by packets of vanes. Firstly, the average packet geometry is used to analyze the aerodynamic forcing associated to the geometric variation of the airfoils inside the vane packet. After that, a conceptual study is carried out under some simplified assumptions in order to relate the geometric variability to random low engine order disturbances, using the geometric modes obtained from the PCA analysis. In both cases, the induced vibrations on the adjacent rotor row are comparable to the excitation due to the nominal blade-passing.

Single Nodal Diameter Excitation of Turbine Blades: Experimental and Theoretical Study

Abstract Validating simulation results of vibrating turbine blades relies on measurements of realistic or academic cyclic structures on special test rigs. In real operation the blades are excited mainly by aerodynamic forces. For measurements of blade vibration on special test rigs, the excitation should be well known. It is desirable to use excitation spectra that consist of only a few engine order excitations. Especially for nonlinear systems, unwanted excitation orders can possibly lead to nonlinear effects which may interfere with the measurement. To separate different engine orders, an innovative electromagnetic excitation device was developed at the institution to overcome the aforementioned problems. The excitation force spectrum is controlled by a variable air gap over the circumference between device and blade. Any desired engine order excitation can be realized. Additionally, by varying the devices coil current in a harmonic fashion, frequency sweeps at constant speed can be performed. In this paper an extensive study of the excitation force spectrum of the device is conducted. Therefore, theoretical investigations of the expectable spectrum are given under simultaneous variation of air gap geometry and excitation current. These predictions are then validated by experiments featuring a small, academic bladed disk. The vibrations of the blades are measured. The device promises to create well predictable and controllable excitation force spectra which will improve the validation strategy in particular of non-linear simulation tools for the prediction of turbine blade vibrations.

Investigation of Flow Distortion Generated Forced Response of a Radial Turbine with Vaneless Volute

Abstract For a radial turbine with vaneless volute, the inflow of turbine rotor usually has a circumferential flow distortion due to the influence of the volute tongue. The rotating blades of the rotor are exposed to harmonic aerodynamic loads caused by the distortion, which may induce rotor resonance and lead to high cycle failures (HCF). To understand the forced response mechanism clearly, a numerical analysis was carried out based on a fluid structure interaction (FSI) method. The pressure functions were extracted from the results of a computational fluid dynamics (CFD) analysis by Fourier decomposition. The first three harmonic pressures were identified as the primary engine order (EO) excitations and imposed on the structural model for computational structural dynamics (CSD) simulation. The quantification and assessment of the rotor response were attained by mode superposition method. The simulation results are shown to be consistent with the predictions of Singh’s advanced frequency evaluation (SAFE) diagram.

Prediction of mistuning effect of bladed disks using eigensensitivity analysis

Vibration modes with repeated eigenvalues often occur in engineering design and analysis practices due to geometrical symmetries of structural systems such as the cyclic symmetry of bladed disk assemblies of turbomachinery. However, the degeneration of eigenvector space and the resulting discontinuities have prevented useful applications of eigensensitivities to vibration analysis of a wide class of problems with repeated modes. To overcome such difficulties, a new concept of a global design variable is developed in which all intended multivariate design modifications are grouped into a single global design variable. Eigensensitivities have then been formulated for repeated eigenvalues from which accurate predictions of vibration characteristics can be made. Further, second order eigenvalue derivatives are also employed to further improve the accuracy of predicted vibration properties. Such newly formulated eigensensitivity analysis has been effectively applied for the first time to the prediction of mistuning effect of bladed disk assemblies. Numerical results from a realistic discrete parameter model of a bladed disk have demonstrated that not only natural frequencies and mode shapes can be predicted very accurately, but also blade vibration responses under engine order excitations. In addition, the proposed eigensensitivty analysis can predict the statistical variations of blade vibrations under random mistuning. Finite element modeling and vibration testing of a practical bladed disk structure have been carried out to demonstrate the practical potential of the proposed method to be possibly integrated into finite element analysis for structural modification predictions, especially for structures with repeated eigenvalues such as bladed disks.

Damping mistuning effects on the amplification factor and statistical investigation of vane packet

Abstract Turbine engine compressors consist of many stages. Each stage consists of rotating blades and stationary vanes. Interactions between the rotating blades and the stationary vanes create traveling periodic excitations. The structure is also periodic because its construction has the form of spatially repeated units. Tuned bladed disks are spatially repetitive structures, and their geometry is fully described by that of a sector. The dynamic characteristics of a sector determine the dynamic behavior of the entire tuned structure. Hence, modern structural analysis of bladed disks takes advantage of the assumption of cyclic symmetry. In general, however, vanes consist of several packets; each packet having multiple sectors interconnected with a platform and a casting. The vane system is partially periodic but not cyclic symmetric since the packets are not strongly connected with each other. Due to this fact, the methodologies to understand the dynamic responses of cyclically symmetric structures are not applicable to a vane system. Therefore, a new approach to investigate vane responses under traveling wave excitations and the effect of mistuning between the blades of vanes is presented. A mode-based methodology is used to identify the most responding mode under a traveling wave excitation. Also, a reduced order model (ROM) for calculating the effect of a damping mistuning combined with a stiffness mistuning on a vane packet is presented. A novel methodology for statistical analyses to investigate the effect of damping mistuning in a vane is presented also. The developed ROMs are validated by comparing ROM-predicted steady state harmonic responses to full-order analyses in ANSYS. It is observed that the maximum error of the ROM-predicted amplitude is under 1%. Based on the developed ROMs, a simple algebraic equation is derived for predicting amplification factors by introducing the concept of unit damping mistuning. Amplification factors for all engine order excitations are examined to verify the performance of the proposed methodology. The effects of damping mistuning are studied statistically through Monte Carlo simulations.

A Modified Nonlinear Modal Synthesis Scheme for Mistuned Blisks with Synchronized Switch Damping

In the authors’ previous work (MSSP 2017), we show that the synchronized switch damping based on negative capacitor (SSDNC) is a good candidate for vibration suppression of tuned blisks. In this paper, we consider the mistuned case and propose an efficient numerical approach to accelerate the required statistical analysis. Although SSDNC is a type of nonlinear piezoelectric damping, through an in-depth nonlinear modal analysis, we show that the modal information of the system remains unchanged with respect to the nonlinear modal amplitude. Based on this, an accelerated nonlinear component modal synthesis (NCMS) method is proposed to predict and further analyse the dynamic characteristics of the nonlinear system. The precision and efficiency of the proposed method is compared with that of the multiharmonic balance method. The stochastic characteristics of the blisk are studied with two sources of mistuning. The first one is random stiffness mistuning and the second one is capacitance mistuning. The investigation is carried out with different mistuning levels and under different engine-order excitations. The results show that the NCMS method can accurately predict the forced response of the mistuned blisk with SSDNC, and the calculation cost can be considerably reduced. Two advantages of the SSDNC technique applied to the mistuned blisk have been revealed in the statistical view. The first one is that the SSDNC can suppress the amplified vibration induced by the mistuning of the blisk significantly. The second one is that the vibration-suppression performance of SSDNC is insensitive to the mistuning of the blisk and that of the electrical circuits.

A comparison between the friction and piezoelectric synchronized switch dampers for blisks

In this work, we explore the feasibility of applying the synchronized switch damping on negative capacitor damper to integrally bladed disks (blisks) by comparing its damping performance with that of the friction ring with the same added mass. Both dampers are coupled to the disk of the blisk. Namely, the friction ring is in contact with the underside of the wheel and the piezoelectric materials for synchronized switch damping on negative capacitor are bonded on the disk as well. The lumped parameter models are used for the blisk and dampers, and the multi-harmonic balance method is employed to obtain the steady-state response under engine-order excitations. The vibration-reduction performance of the dampers are compared with respect to the excitation level, the engine order, and multi-mode. This leads to a discussion concerning the parameter design for the synchronized switch damping on negative capacitor damper to achieve a comparable single-mode damping as the friction ring. We show that the synchronized switch damping on negative capacitor damper has a better performance for multiple modes and at a wider range of excitation level. These results indicate that the synchronized switch damping on negative capacitor damping can be a promising solution for the vibration reduction of blisks where the spatial and spectral distributions of the excitation are rich.

Modal Analyses of an Axial Turbine Blisk With Intentional Mistuning

The potential of intentional mistuning to reduce the maximum forced response is analyzed within the development of an axial turbine blisk for ship diesel engine turbocharger applications. The basic idea of the approach is to provide an increased aerodynamic damping level for particular engine order (EO) excitations and mode shapes without any significant distortions of the aerodynamic performance. The mistuning pattern intended to yield a mitigation of the forced response is derived from an optimization study applying genetic algorithms. Two blisk prototypes have been manufactured a first one with and another one without employing intentional mistuning. Hence, the differences regarding the real mistuning and other modal properties can be experimentally determined and evaluated as well. In addition, the experimental data basis allows for updating structural models which are well suited to compute the forced response under operational conditions. In this way, the real benefit achieved with the application of intentional mistuning is demonstrated.

Investigation of Forced Response Sensitivity of Low Pressure Compressor With Respect to Variation in Tip Clearance Size

This study aims to numerically investigate the sensitivity of the forced response with respect to the variation of the tip clearance setting of a low pressure compressor BluM™(monoblock bladed drum) when it is subjected to low engine order excitations. Two different types of blades are employed in the upstream row in order to generate the low engine order excitations. The forced response as well as the aerodynamic damping is numerically estimated using the TWIN approach. The experiments are conducted to measure the forced response for the nominal tip gap to validate the numerical results. Further, simulations are performed for a range of tip clearances. The variation of the steady load distributions due to the changes of the tip clearance are analyzed and presented. The aerodynamic damping and the forced response are calculated and compared for different tip clearances. It is observed that aerodynamic damping increases significantly with tip gap, whereas the excitation forces are reduced. As consequence of these two evolutions, the forced response decreases drastically for larger tip clearance.

Next Generation Traveling-Wave Excitation System for Integrally Bladed Rotors

AbstractAn n-harmonic traveling-wave excitation (nTWE) system that was developed for the U.S. air force research laboratory turbine engine fatigue facility (TEFF) is described. This traveling-wave system is designed to simulate engine order excitations on stationary integrally bladed rotors (IBRs) and dual flow-path IBRs (DFIBRs) for the purpose of measuring forced response amplification due to mistuning. This new system extends beyond traditional traveling-wave systems by its capability to generate a combination of n engine order (EO) harmonics for IBRs as well as different EO harmonics simultaneously to both inner- and outer-blade sets of DFIBRs. This system can excite both IBRs and DFIBRs of differing sizes and number of blades with electromagnetic excitation. Scanning vibrometry mounted above the test specimen is used to measure any localization due to mistuning. Sources of error in the nTWE system are discussed and experimental forced response levels are shown for a 22-blade IBR.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

The forced response of the first rotor of an engine 3E (technology program) (E3E)-type high pressure compressor (HPC) blisk is analyzed with regard to varying mistuning, varying engine order (EO) excitations and the consideration of aero-elastic effects. For that purpose, subset of nominal system modes (SNM)-based reduced order models are used in which the disk remains unchanged while the Young's modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient (AIC) technique is employed to model aero-elastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades' Young's modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aero-elastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

Probabilistic Mistuning Assessment Using Nominal and Geometry Based Mistuning Methods

Two deterministic mistuning models utilizing component mode synthesis methods are used in a Monte Carlo simulation to generate mistuned response distributions for a geometrically perturbed integrally bladed rotor. The first method, a frequency-perturbation approach with a nominal mode approximation used widely in academia and industry, assumes airfoil geometric perturbations alter only the corresponding modal stiffnesses while its mode shapes remain unaffected. The mistuned response is then predicted by a summation of the nominal modes. The second method, a geometric method utilizing non-nominal modes, makes no simplifying assumptions of the dynamic response due to airfoil geometric perturbations, but requires recalculation of each airfoil eigen-problem. A comparison of the statistical moments of the mistuned response distributions and prediction error is given for three different frequency ranges and engine order excitations. Further, the response distributions are used for a variety of design and testing scenarios to highlight impacts of the frequency-based approach inaccuracy. Results indicate the frequency-based method typically provides conservative response levels.

Critical Speed Analysis of a Single Stage Impulse Type High-Speed Steam Turbine Rotor Disc

Resonance is a common thread that runs through almost every branch of engineering. Yet, this phenomenon often goes unnoticed, silently resulting in inconveniences, such as causing a bridge to collapse or a helicopter to fl y apart, to name a few. It is, therefore, of utmost importance to avert resonance, for which determining the frequency of the system becomes indispensible. In complex rotating structures, as one considered in this paper, theoretical determination of frequency is as diffi cult and laborious as a task can be. Finite element analysis has proven to be an effective tool to handle such a task. Resonant vibrations incited by the running speed harmonic excitations, steam impinging frequency, engine order excitations are fundamental causes for failure of turbine components. The mainstream discipline that is encompassed by this paper is the modal analysis. Modal analysis is performed to estimate the critical speeds and study the mode shapes of the bladed rotor disc under prestressed condition.

Vibration Suppression of Mistuned Coupled-Blade-Disk Systems Using Piezoelectric Circuitry Network

For bladed-disk assemblies in turbomachinery, the elements are often exposed to aerodynamic loadings, the so-called engine order excitations. It has been reported that such excitations could cause significant structural vibration. The vibration level could become even more excessive when the bladed disk is mistuned, and may cause fatigue damage to the engine components. To effectively suppress vibration in bladed disks, a piezoelectric transducer networking concept has been explored previously by the authors. While promising, the idea was developed based on a simplified bladed-disk model without considering the disk dynamics. To advance the state of the art, this research further extends the investigation with focus on new circuitry designs for a more sophisticated and realistic system model with the consideration of coupled-blade-disk dynamics. A novel multicircuit piezoelectric transducer network is synthesized and analyzed for multiple-harmonic vibration suppression of bladed disks. An optimal network is derived analytically. The performance of the network for bladed disks with random mistuning is examined through Monte Carlo simulation. The effects of variations (mistuning and detuning) in circuit parameters are also studied. A method to improve the system performance and robustness utilizing negative capacitance is discussed. Finally, experiments are carried out to demonstrate the vibration suppression capability of the proposed piezoelectric circuitry network.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

Extensive investigations have been conducted to study the vibration localization phenomenon and the excessive forced response that can be caused by mistuning in bladed disks. Most previous researches have focused on analyzing∕predicting localization or attacking the mistuning issue via mechanical tailoring. Few have focused on developing effective vibration control methods for such systems. This study extends the piezoelectric network concept, which has been utilized for mode delocalization in periodic structures, to the control of mistuned bladed disks under engine order excitation. A piezoelectric network is synthesized and optimized to effectively suppress vibration in bladed disks. One of the merits of such an approach is that the optimum design is independent of the number of spatial harmonics, or engine orders. Local circuits are first formulated by connecting inductors and resistors with piezoelectric patches on the individual blades. Although these local circuits can function as conventional damped absorber when properly tuned, they do not perform well for bladed disks under all engine order excitations. To address this issue, capacitors are introduced to couple the individual local circuitries. Through such networking, an absorber system that is independent of the engine order can be achieved. Monte Carlo simulation is performed to investigate the effectiveness of the network for a bladed disk with a range of mistuning level of its mechanical properties. The robustness issue of the network in terms of detuning of the electric circuit parameters is also studied. Finally, negative capacitance is introduced and its effect on the performance and robustness of the network is investigated.

Turbine forced response prediction using an integrated non-linear analysis

The forced response due to flow defects caused by the upstream blade rows is predicted for two turbines: intermediate pressure (IP) and low pressure (LP). The prediction method is based on an advanced numerical tool where the compressible viscous flow field is modelled by solving Favre-averaged Navier-Stokes equations with the Baldwin and Barth turbulence model. The flow solution is coupled to a modal model of the structure and information is exchanged every time step between the fluid and the structural domains. The hybrid unstructured mesh is moved at each time step to follow the structural motion using a spring analogy. For the IP turbine, the method was used to rank two different designs of nozzle guide vanes. For the LP turbine, special emphasis was placed on predicting vibration amplitudes due to high and low engine order excitations. Predictions and measurements were found to be in good agreement for both turbines. Due to insufficient experimental data, it was difficult to assess the accuracy of the low engine order computations, although it was shown that the model was capable of undertaking such a task.

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.