Intentional Mistuning Research Articles

Optimization analysis of the intentional mistuning mode of the blisk with piezoelectric shunt damping patches

Optimization analysis of the intentional mistuning mode of the blisk with piezoelectric shunt damping patches

Vibration suppression of the blisk based on intentional mistuning of piezoelectric shunt damping patches

In this paper, the finite element model of the mistuned blisk with intentional mistuning of piezoelectric shunt damping patches (PSDPs) is established. In the process of modeling, the piezo-blisk substrate composite element and the substrate thickness variation element are analyzed. Then, compared with the experimental results, the feasibility and accuracy of the finite element model are verified. Finally, the impact of the circumferential position mistuning of PSDPs and piezoelectric shunt parameter mistuning on the vibration reduction of the blisk is analyzed. The results indicate that better vibration suppression effect can be obtained by reasonably designing the mistuned mode of PSDPS.

Numerical Analysis for Optimization of the Lifetime Characteristics of Radial Wheels Turbomachines by Introducing the Intentional Mistuning Parameters

Numerical Analysis for Optimization of the Lifetime Characteristics of Radial Wheels Turbomachines by Introducing the Intentional Mistuning Parameters

Characterization of the Anomalous Vibration Response of an Intentionally Mistuned LPT Rotor

The wind tunnel facility at the Centro de Tecnologías Aeronáuticas was used to perform a set of experiments to study the effect of intentional mistuning on the forced response behavior of an aerodynamically unstable low-pressure turbine rotor. The intentional mistuning patterns were implemented by adding a small extra mass to some of the blades. The forced response of the rotor was therefore expected to show two resonance peaks with similar amplitudes, corresponding, respectively, to the vibration frequencies of the blades with and without added mass. However, on the post-processing of the measurements, some anomalous behavior was observed. Near resonance, the system response was synchronous with the forcing, and the frequency sweeps exhibited two resonance peaks, but it was found that the two peaks were clearly different, with the peak at lower frequency showing a much higher vibration amplitude than the high-frequency peak, and with some blades responding at both frequencies with a similar amplitude. In order to give a correct interpretation of the experimental results, a reduced-order model is derived that takes into account only the traveling wave modes coupled by the mistuning. This model, although extremely simple, is capable of reproducing the unexpected behavior of the experiments, and gives a clean explanation of the system response. It is shown that the relative size of the mistuning with respect to the frequency difference of the involved traveling-wave modes is the key parameter for the appearance of this phenomenon.

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.

Vibration suppression by mistuning acoustic black hole dynamic vibration absorbers

This paper presents a modified add-on strategy to reduce the transverse vibration of beam structures using multiple acoustic black hole dynamic vibration absorbers (ABH-DVAs). The exact dynamic stiffness formulation of the system constituted by the host beam and arrays of ABH-DVAs is established. The intentional mistuning effect is introduced into the system by varying the taper lengths of ABH-DVAs, aiming at broadband vibration suppression. Several case studies are presented to demonstrate the effectiveness of the proposed strategy. In addition, the multi-objective optimization of the structure with minimum weight and broad attenuation band is investigated. From the numerical and experimental results, it is seen that the attenuation bandwidth of the proposed design is widened compared with that of the conventional design. The proposed strategy shows great potential for widening the attenuation band of the acoustic black hole structures.

Intentional Mistuning Effect on the Blisk Vibration with Aerodynamic Damping

Intentional mistuning is a well-known factor affecting the vibration of the blisk. This paper mainly focuses on the intentional mistuning effect on the aerodynamic damping and forced response of an axial compressor blisk with random mistuning, and the intentional mistuning types involved in this paper include alternating mistuning, single mistuning, and sector mistuning. The aerodynamic damping of the blisk and its composition are calculated based on the fundamental model of mistuning and influence coefficient method. Under the influence of intentional mistuning, the aerodynamic damping and weight coefficient of each blade in the blisk vary with the modal amplitude and phase. Then, the forced response of the blisk is calculated by the modal superposition method, and the results indicate that intentional mistuning can reduce the increase of forced response caused by random mistuning in two ways: reducing the sensitivity of the blisk to random mistuning and improving the aerodynamic damping of the blisk. Finally, it is found that sector mistuning is better in reducing the sensitivity of the blisk to random mistuning, whereas alternating mistuning is better in improving the aerodynamic damping of the blisk.

Improving Aeroelastic Stability of Bladed Disks with Topologically Optimized Piezoelectric Materials and Intentionally Mistuned Shunt Capacitance.

It is well known that bladed disks with certain patterns of mistuning can have higher aeroelastic stability than their tuned counterparts. This requires small but accurate deviation of the mechanical properties on each blade sector, and currently it is difficult to realize by mechanical manufacturing. In this paper, we propose an adaptive strategy to realize the intentional mistuning for the improvement of aeroelastic stability. The basic idea is to bond or embed piezoelectric materials to each blade and use different shunt capacitance on each blade as the source of mistuning. When the shunt capacitance varies from zero (open-circuit, OC) to infinity (short-circuit, SC), the stiffness of each blade changes within a relatively small interval. In this way, the required small difference of stiffness among blades is altered into a relatively larger difference of the shunt capacitance. This provides a more feasible and robust way to implement the intentional mistuning, provided that the variation interval of blade stiffness between OC and SC contains the limits of required mistuning. Thus, it is critical to maximize the ability of changing the blade stiffness by shunt capacitance with limited amount of piezoelectric materials. To do so, a straightforward approach is proposed to get the best distribution of piezoelectric materials on the blade for the targeting mode. This approach is based on the FE model of the bladed disc, and the piezoelectric materials are introduced by replacing elements (if they are embedded) or adding an extra layer of elements (if they are bonded). An empirical balded disc with NASA-ROTOR37 profile is used as the example. With a proper design of the mistuning pattern and replace use piezoelectric materials of only 10% the blade mass, the proposed method can significantly improve the aeroelastic stability of bladed disks.

Prediction and optimization of fatigue life of an axial bladed disk with intentional mistuning

Prediction and optimization of fatigue life of an axial bladed disk with intentional mistuning

Fatigue life of radial turbomachines at changing thickness blades taking into account intentional mistuning

Fatigue life of radial turbomachines at changing thickness blades taking into account intentional mistuning

Mathematical modeling and its application in intentional mistuning of parameters and optimization of life characteristics of turbomachines

Mathematical modeling and its application in intentional mistuning of parameters and optimization of life characteristics of turbomachines

Probabilistic analysis-based vibration characteristics of intentionally mistuned blisk

The machining error, wear and material dispersion lead to serious vibration and large local instability in aeroengine’s blisk. To restrain the vibration and reduce the fluctuation, the intentional mistuning is adopted, and a methodology named multi-stage multi-objective coordinated extremum response surface method-based reduced-order model (MSMO-CERSM-ROM) is proposed to investigate the probabilistic distribution of intentionally mistuned blisk. The basic idea of this approach is that the large complex structure involving multiple disciplines is divided into substructures only including single discipline. This method not only can dramatically improve the computational efficiency and accuracy of the multi-objective and multi-stage response surface model but also effectively solve the nonlinear and implicit function. The probabilistic analysis of intentionally mistuned blisk via MSMO-CERSM is investigated based on the deterministic analysis via the ROM. Finally the intentionally mistuned blisk is solved compared with the tuned and passive mistuned blisk to verify the validity and rationality of the present methodology. These results manifest that the stability is strengthened, and the output response are reduced, which plays an important role in probabilistic design for complex mechanical structures

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.

Effect of Intentional Mistuning on Dynamic Characteristics of a Energy Turbomachine Bladed Disk

In this article the effect intentional mistuning of an axial turbomachine bladed disk has been analyzed in order to reduce forced response due to low-order engine excitation. The maximum value of forced response of turbomachine rotor’s blades with mistuning parameters is usually much more than the value of the tuned rotors. An increase level mistuning of this critical value actually leads to a decrease magnifications of the forced response. Thus, the actual work has been introducing some degree of intentional mistuning in the design to achieve these purposes. The effectiveness of intentional mistuning has been researched at the design stage of the bladed disk in the energy turbomachines, which is introduced into the rotor’s design by changing the nominal mass of the blades in harmonic models.

Impact of Mistuned Underplatform Dampers on the Nonlinear Vibration of Bladed Disks

Abstract Before the final experimental validation and certification of a turbo-engine, designers perform a numerical simulation of its vibratory properties, among other things, in order to estimate its lifespan and adjust the design in an optimization process. One possible practical solution to decrease the vibratory response is to add underplatform dampers to the system. These components dissipate energy by friction and are widely employed in turbomachinery. However, a specific underplatform damper is usually efficient only for a specific mode. The purpose of this work is to investigate the possibility of adding different kinds of underplatform dampers to the cyclic structure in order to decrease the vibratory energy over a larger panel of modes. Different methods exist to determine the vibrations of nonlinear cyclic symmetric systems, but creating a robust methodology to account for the additional effect of mistuning remains a big challenge in the community. In this paper, the structure is mistuned through the friction coefficient of the dampers and not by altering its geometry, as is usually done in the literature. First, assuming a cyclic symmetric structure, the performance of the dampers is assessed for specific modes. Then, employing a method recently developed, the efficiency of an intentional mistuning pattern of underplatform dampers is studied and an optimal pattern proposed.

Investigation on the Robustness of Rotor/Stator Contact Interactions With Respect to Small Mistuning

Abstract In this work, the impact of small mistuning on rotor/stator contact interactions is investigated. First, a detailed study of a rotor/stator interaction between the first bending modes and the second engine order is presented in the tuned case. Then, a numerical investigation on the effect of mistuning on the studied rotor/stator contact interaction is carried out. In particular, a stochastic analysis is performed to evaluate the robustness of the interaction with respect to the mistuning level. Simulations are conducted using a reducedo rder model (ROM) of an industrial-bladed disk that combines both physical degrees-of-freedom (along blades tip for contact treatment) and modal coordinates. Mistuning is introduced in the tuned ROM by means of a modified version of the component mode mistuning method that allows to keep physical degrees-of-freedom within the reduced basis. Nonlinear amplification factors, i.e., the amplification factors in the context of contact nonlinearities, are compared with their linear counterparts, and the latter are computed using a linear forcing on each blade using a two nodal diameters traveling wave excitation on the mistuned and the tuned bladed disk. The comparison between the linear and nonlinear amplification factor for each sample highlights that no correlation exists between a mistuning pattern leading to high amplifications in a linear context or when contact nonlinearities are taken into account. Therefore, dedicated analyses on the effect of mistuning should be undertaken with contact nonlinearities considerations at the design stage especially if intentional mistuning is considered.

Key Action Mechanisms of Intentional Mistuning

Intentional mistuning is a common procedure to decrease the uncontrolled vibration amplification effects of the (unavoidable) random mistuning, and to reduce the sensitivity to it. The idea is to introduce an intentional mistuning pattern that is small, but much larger than the existing random mistuning. The frequency of adjacent blades is moved apart by the intentional mistuning, reducing the blade-to-blade coupling and, thus, the effect of the random mistuning. In order to clearly show the action mechanisms of intentional mistuning, we focus in this work in a quite simple configuration: forced response of a blade dominated modal family in a mistuned rotor with linear material damping. The problem is analysed using the asymptotic mistuning model methodology. A more reduced order model is derived that allows us to understand the relevant parameters behind the effect of intentional mistuning, and gives a simple expression for the estimation of its beneficial effect. The results from the reduced model are checked against detailed FEM simulations of two mistuned rotors.

Analysis of experimental results of turbomachinery flutter using an asymptotic reduced order model

Flutter of bladed disks is an instability mechanism where the aerodynamic flow pumps energy into the blade vibration. This energy is dissipated through dry friction, normally at the blade-disk attachment, and this balance defines the blade vibration amplitude that sets in. The magnitude of this final vibration amplitude is crucial to correctly estimate the blade fatigue life. In the context of the European project FUTURE, a series of flutter experiments were carried out for a realistic low-pressure turbine with different intentional mistuning patterns. To analyze the results, a simple 3 degrees of freedom per sector mass-spring model is set up with the experimental configuration parameters. This mass-spring system still requires very long integration times due to: (i) the large difference between the fast elastic oscillation time and the slow time associated with the aerodynamic instability, friction, and mistuning, and (ii) the presence of many aerodynamically unstable modes with very similar growth rates. A multiple-scale method is applied to further simplify the mass-spring system. The blade elastic oscillation is filtered out, and the resulting asymptotic reduced order model reduces considerably the integration time required to reach a converged solution. It is found that the final vibration state of the mistuned problem depends on the selected initial conditions, so the model is run for a large number of random initial conditions to explore the possible final states. The asymptotic model gives results that show a good agreement with the experimental measurements, and it also allows to explain the origin of the peaks in the travelling wave content of the final solution found in the experiment for the intentionally mistuned configurations.

Multiwave Vibrations in Mistuned Cascades With Tip-Shroud Friction

Abstract Measurements taken during aero engine tests and in the field showed that flutter vibrations of shrouded blades can feature rich wave content (multiwave flutter vibrations). In a previous work, we demonstrated that this behavior can be explained by the nonlinear interaction of aeroelastically unstable traveling wave modes. The resulting vibrations are quasi-periodic. In this work, we show that the nonlinear modal interaction is not strictly needed, but actually mistuning alone can explain the multiwave form of flutter vibrations. The resulting vibrations are periodic and dominated by only a single mode shape of the mistuned system. However, unrealistically high mistuning intensities are needed to obtain significant contributions of multiple wave forms under the considered strong inter-blade coupling. Thus, we conclude that mistuning cannot explain the rich wave content observed in the measurements. Moreover, mistuning tends to hamper the nonlinear modal interactions and, thus, the occurrence of quasi-periodic multiwave flutter vibrations. This implies that intentional mistuning is not only useful to stabilize flutter but might also play an important role in developing flutter-tolerant blade designs.

Vibration Analyses of an Axial Turbine Wheel With Intentional Mistuning

Abstract The last-stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes, unfavorable flow conditions may occur, which can lead to flow separation in some circumstances. Consequently, there is the risk of flutter in principle, particularly at nominal speed under part load conditions. For this reason, intentional mistuning is employed by the manufacturer with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits since only two different blade designs are allowed. In this sense, two different series of blades have been made. However, it is well known that small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional but unwanted deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since centrifugal stiffening effects significantly attenuate the blade-to-blade frequency difference in this particular case. Focusing on the first flap mode, it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed evokes an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Again, only two different blade designs are admitted. Finally, mistuning patterns could be identified causing a tremendous increase of aerodynamic damping ratios. The robustness of the solutions found could be proved by superimposing additional random mistuning.