Minimizing Maximum Modal Force in Mistuned Bladed Disk Forced Response

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Keith W. Jones
Keyword(s):  
Lower Boundary ◽  
Forced Response ◽  
Response Amplitude ◽  
Absolute Minimum ◽  
Turbine Engine ◽  
Bladed Disk ◽  
Engine Order ◽  
Modal Force ◽  
Low Amplitude ◽  
Infinite Linear

Amplitude magnification is defined as the maximum forced response amplitude of any blade on a mistuned bladed disk divided by the maximum response amplitude of any blade on a tuned bladed disk over a range of engine order excitation frequencies. This paper shows that amplitude magnification can be approximated as the maximum ratio of modal force divided by modal vector magnitude in an isolated family of turbine engine bladed disk modes. An infinite linear mistuning pattern, defined by a constant interblade stiffness increment between an infinite number of blades, is found to minimize the maximum modal force when subjected to engine order N/4 excitation. Linear mistuning, an approximation of the infinite linear mistuning pattern, approximately minimizes the maximum modal force for bladed disks with a finite number of blades when subjected to engine order N/4 excitation. From this theory, 2/N is proposed to be a lower boundary for amplitude magnification. The linear mistuning method is demonstrated to produce very low amplitude magnifications numerically and experimentally. The numerical examples suggest that linear mistuning may produce amplitude magnifications near the absolute minimum possible.

Experimental Investigation of Mode Localization and Forced Response Amplitude Magnification for a Mistuned Bladed Disk

2000 ◽  
Author(s):  
John Judge ◽  
Christophe Pierre ◽  
Oral Mehmed
Keyword(s):  
Experimental Investigation ◽  
Traveling Wave ◽  
Forced Response ◽  
Response Amplitude ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Element Analysis ◽  
Mode Localization ◽  
Bladed Disk ◽  
Out Of Plane

The results of an experimental investigation on the effects of random blade mistuning on the forced dynamic response of bladed disks are reported. The primary aim of the experiment is to gain understanding of the phenomena of mode localization and forced response blade amplitude magnification in bladed disks. A stationary, nominally periodic, twelve-bladed disk with simple geometry is subjected to a traveling-wave, out-of-plane, “engine order” excitation delivered via phase-shifted control signals sent to piezo-electric actuators mounted on the blades. The bladed disk is then mistuned by the addition of small, unequal weights to the blade tips, and it is again subjected to a traveling wave excitation. The experimental data is used to verify analytical predictions about the occurrence of localized mode shapes, increases in forced response amplitude, and changes in resonant frequency due to the presence of mistuning. Very good agreement between experimental measurements and finite element analysis is obtained. The out-of-plane response is compared and contrasted with the previously reported in-plane mode localization behavior of the same test specimen. This work also represents an important extension of previous experimental study by investigating a frequency regime in which modal density is lower but disk-blade interaction is significantly greater.

scholarly journals An Experimental Investigation of Vibration Localization in Bladed Disks: Part II — Forced Response

1997 ◽  
Author(s):  
Marlin J. Kruse ◽  
Christophe Pierre
Keyword(s):  
Experimental Investigation ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Structural Coupling ◽  
Vibration Localization ◽  
Bladed Disk ◽  
Engine Order ◽  
Localized Mode ◽  
The Impact

The results of an experimental investigation on the effects of random blade mistuning on the forced dynamic response of bladed disks are reported. Two experimental specimens are considered: a nominally periodic twelve-bladed disk with equal blade lengths, and the corresponding mistuned bladed disk, which features slightly different blades of random lengths. Both specimens are subject to traveling-wave excitations delivered by piezo-electric actuators. The primary aim of the experiment is to demonstrate the occurrence of an increase in forced response blade amplitudes due to mistuning, and to verify analytical predictions about the magnitude of these increases. In particular, the impact of localized mode shapes, engine order excitation, and disk structural coupling on the sensitivity of forced response amplitudes to blade mistuning is reported. This work reports one of the first systematic experiments carried out to demonstrate and quantify the effect of mistuning on the forced response of bladed disks.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

Aerospace ◽  
2006 ◽  
Author(s):  
Hongbao Yu ◽  
K. W. Wang
Keyword(s):  
Vibration Suppression ◽  
Periodic Structures ◽  
Electric Circuit ◽  
Forced Response ◽  
Bladed Disks ◽  
Vibration Localization ◽  
Bladed Disk ◽  
Engine Order ◽  
The Individual ◽  
Local Circuits

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 attacking the mistuning issue in the bladed disk, such as reducing the sensitivity of the structure to mistuning through mechanical tailoring, or design optimization. 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 the excessive vibration in the bladed disk caused by mistuning. 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. While 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 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 robustness of the network is investigated.

Combinatorial Optimization of Mistuned Blade Rearrangement Based on Reduced-Order FEA Model

2017 ◽  
Author(s):  
Tianyuan Liu ◽  
Ding Guo ◽  
Di Zhang ◽  
Yonghui Xie
Keyword(s):  
Combinatorial Optimization ◽  
Ant Colony Algorithm ◽  
Forced Response ◽  
Response Amplitude ◽  
Reduced Order Model ◽  
Ant Colony ◽  
Order Model ◽  
3D Fem ◽  
Reduced Order ◽  
Bladed Disk

This paper is focused on the optimization of mistuned blades assembling rearrangement under the forced response. First, in order to avoid the greatly increase of the calculation greatly by the whole circle bladed-disk finite element model, a reduced-order model is developed based on the component mode synthesis. CPU+GPU heterogeneous architecture parallel computation is used to accelerate modal analysis of the disk and blade sectors substructures. Second, a modified ant colony algorithm is applied to the combinatorial optimization to find the optimal rearrangement pattern of bladed-disk assembly. Different from classical algorithm, the individual mistuned information is used to construct heuristic function based on intentional mistuning pattern, which can avoid slow convergence of ant colony algorithm and increase the search speed efficiently. At last, a high-fidelity 3D FEM model with 43 mistuned blades is used to demonstrate the capabilities of the techniques in reducing the maximum displacement resonance response of the bladed-disk system. The numerical simulation showed that this program based on the reduced-order model proposed in this article gained 4.3 speedup compared with ANSYS full model under the scale of 500k nodes. The displacement response amplitude of the blades decreased by 32% with 60 steps (1200 times FEM calculation) by the new optimization method. The physical mechanism of reducing the bladed-disk response is explained by comparing the optimized and worst arrangement patterns. The results clearly demonstrate that the optimized rearrangement pattern of mistuned blades is able to reduce the response amplitude of the forced vibration significantly, and the algorithm proposed in this article is practical and effective.

On Force Control of an Engine Order–Type Excitation Applied to a Bladed Disk With Underplatform Dampers

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Christian M. Firrone ◽  
Teresa M. Berruti ◽  
Muzio M. Gola
Keyword(s):  
Force Control ◽  
Order Type ◽  
Forced Response ◽  
Good Precision ◽  
Force Amplitude ◽  
Excitation System ◽  
Bladed Disks ◽  
Nonlinear Dynamic Response ◽  
Bladed Disk ◽  
Engine Order

The paper presents an original multiple excitation system based on electromagnets with force control. The system is specifically designed in order to investigate the dynamics of bladed disks, since it mimics the excitation existing in a real engine. Moreover, the system is suitable for forced response tests of bladed disks with nonlinear dynamic response, like in the case of presence of friction contacts, since the amplitude of the exciting force is known with good precision. For this purpose, a device called force-measuring electromagnet (FMEM) was designed and employed during the system calibration. The excitation system is applied to the test rig Octopus, which includes underplatform dampers (UPDs). Tests were carried out under different excitation force amplitude values. The tests put in evidence the presence of mistuning and the UPDs' capability of attenuating the mistuning phenomena.

Investigation of Alternate Mistuned Turbine Blades Non-Linear Coupled by Underplatform Dampers

2013 ◽  
Author(s):  
S. Tatzko ◽  
L. Panning-von Scheidt ◽  
J. Wallaschek ◽  
A. Kayser ◽  
G. Walz
Keyword(s):  
Turbine Blades ◽  
Forced Response ◽  
Mode Shapes ◽  
Nodal Diameter ◽  
Frictional Contacts ◽  
Bladed Disk ◽  
Engine Order ◽  
Bladed Disk Assembly ◽  
Last Stage ◽  
Software Code

Freestanding turbine blades have typically low structural damping and thus require additional friction damping devices, such as underplatform dampers. The friction coupling between neighboring blades reduces response amplitude and increases resonance frequency. Along with forced response excitation large blades, especially of last stage, could be excited by fluid structural interaction (flutter). To prevent such excitation alternate mistuned blade patterns are beneficial disturbing traveling waves in the stage. In this paper the influence of alternate mistuning is investigated with a simplified oscillator chain as well as a bladed disk assembly coupled by frictional contacts. It is pointed out that the performance of friction coupling can be improved by alternate mistuning as long as the engine order of the excitation is below quarter of the number of blades. Alternate mistuning causes a mode coupling between two nodal diameter vibration mode shapes allowing for energy transfer. The in-house developed software code DATAR is enhanced and alternate mistuning can be applied to the blades as well as to the damping elements. For validation the DATAR code was applied to an alternate mistuned last stage blade of a Siemens gas turbine and compared with available field engine measurement.

Optimal Design of Intentional Mistuning for a Bladed Disk With Interval Uncertainty

2015 ◽  
Author(s):  
David Yoo ◽  
Jiong Tang
Keyword(s):  
Optimal Design ◽  
Design Optimization ◽  
Probability Of Failure ◽  
Forced Response ◽  
Response Amplitude ◽  
Interval Uncertainty ◽  
Probabilistic Constraints ◽  
Worst Case ◽  
Bladed Disk ◽  
Gradient Based

This paper presents a methodology for the optimal design of intentional mistuning for a mistuned bladed disk with interval uncertainty. For a bladed disk where blades are weakly coupled, presence of random mistuning can easily induce vibration localization. This phenomenon will lead to great amplification in response amplitude of certain blades. To achieve desired reliability of a bladed disk, amplified response must be reduced to certain level, which requires probabilistic or reliability analysis. In this study, it is considered that blades have random distribution and coupling between blades has interval uncertainty. To treat the interval uncertainty appropriately, the worst-case combination of interval couplings is searched first, then probability of failure is evaluated under the worst-case condition. To increase reliability of a bladed disk, intentional mistuning is used in this study. While applying the intentional mistuning, it is also wanted to minimize the degree of intentional mistuning to minimize the cost of implementation. To find optimal combination of intentional mistuning parameters to achieve dual goals, gradient-based design optimization approach is utilized, which is expected to guarantee efficient convergence. To carry out gradient-based design optimization, sensitivities of objective function and probabilistic constraints with respect to intentional mistuning parameters are derived. During the sensitivity analysis, distribution of forced response amplitude is identified through Gaussian fit and eigenvalue perturbation theory is referred to. Monte Carlo simulation is utilized to accurately calculate probability of failure and its sensitivity. The proposed method is demonstrated with numerical examples of two distinct bladed disks.

A Comparative Study on the Dynamic Characteristics of Bladed Disks With Piezoelectric Network and Piezoelectric Shunt Circuit

2016 ◽  
Author(s):  
Jiuzhou Liu ◽  
Lin Li ◽  
Pengcheng Deng ◽  
Chao Li
Keyword(s):  
Modal Analysis ◽  
Dynamic Characteristics ◽  
Energy Analysis ◽  
Vibration Suppression ◽  
Forced Response ◽  
Bladed Disks ◽  
Electromechanical Systems ◽  
Bladed Disk ◽  
Engine Order ◽  
Shunt Circuit

This paper is meant to contribute a further investigation of the dynamic characteristics of the bladed disks with piezo-network and piezo-shunt circuit. The non-engine-order (NEO) excitation is taken into account from a practical point of view, and the mechanisms of vibration suppression of the two electromechanical systems are explained by means of the modal analysis and the energy analysis. First of all, the dynamic equations are derived based on a lumped parameter electromechanical model, and a normalizing process is used to make the analysis results more general. After the modal analysis of the electromechanical systems, the vibration suppression effect is analyzed when the bladed disk is excited by the engine-order (EO) excitation and the NEO excitation respectively. Then, an energy analysis of the electromechanical systems is performed to understand the dynamic behaviors of the systems better. Finally, the effect of reducing the amplitude magnification of the mistuned bladed disk is investigated. The research results turn out that the electrical natural frequencies (induced by electrical elements) of the system with piezo-shunt circuit are dense, while those of the system with piezo-network are not. When the system is excited by an EO excitation, the energy dissipated by resistors in the shunt circuit is slightly more than that in the network. However, the former is much less than the latter when the system is excited by an NEO excitation. A statistical analysis has been performed and proved that both the piezo-shunt circuit and the piezo-network can compensate the amplitude magnification of the forced response induced by mistuning, and the piezo-network has a better performance when the bladed disk is excited by an NEO excitation.

Separation of Up and Downstream Forced Response Excitations of an Embedded Compressor Rotor

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Shreyas Hegde ◽  
Zhiping Mao ◽  
Tianyu Pan ◽  
Laith Zori ◽  
Rubens Campregher ◽  
...  
Keyword(s):  
Forced Response ◽  
Response Analysis ◽  
Wave Reflections ◽  
Compressor Rotor ◽  
Forcing Function ◽  
Engine Order ◽  
Aerodynamic Interaction ◽  
Stator Vane ◽  
Modal Force ◽  
The Individual

The aerodynamic interaction of upstream and downstream blade rows can have a significant impact on the forced response of the compressor. Previously, the authors carried out the forced response analysis of a three-row stator-rotor-stator (S1-R2-S2) configuration from a 3.5-stage compressor. However, since the stator vane counts in both the stators (S1 and S2) were the same, it was not possible to separate the excitations from both the rows as they excited the rotor at the same frequency. Hence, a new configuration was developed and tested in which the stator 1 blade count was changed to 38 and stator 2 blade count was maintained at 44 in order to study the individual influences of the stator on the embedded rotor. By using this method, the excitations from both rows can be determined, and the excitations can be quantified to determine the row having the maximum influence on the overall forcing. To achieve this, two sets of simulations were carried out. The three-row stator-rotor (S1-R2-S2) simulation was carried out at both the 38EO (engine order) and 44EO crossings at the peak efficiency (PE) operating condition. The two-row stator-rotor analysis (S1-R2) was carried out at the 38EO crossing, and the other two-Row (R2-S2) analyses were carried out at the 44EO crossing. The steady aerodynamics was preserved in both the cases. A study was done to determine the contribution of wave reflections from the stator inlet and exit planes to the forcing function. Two conclusions drawn from this study are as follows: (1) the modal force value decreased after the upstream stator was removed, which proved that wave reflections from this stator were significant and (2) the increase in modal force was in-line with experimental observations.

Experimental Demonstration of Maximum Mistuned Bladed Disk Forced Response

2003 ◽  
Vol 125 (4) ◽  
pp. 673-681 ◽  
Author(s):  
J. A. Kenyon ◽  
J. H. Griffin
Keyword(s):  
Traveling Wave ◽  
Close Agreement ◽  
Maximum Amplitude ◽  
Forced Response ◽  
Maximum Response ◽  
Experimental Demonstration ◽  
Wave Excitation ◽  
Bladed Disk ◽  
Engine Order ◽  
Structural Mode

A theory was previously developed for predicting robust maximum forced response in mistuned bladed disks from distortion of a structural mode. This paper describes an experiment to demonstrate the theory. A bladed disk is designed to be sufficiently sensitive to mistuning to obtain maximum response. The maximum amplitude magnification from mistuning is predicted using the theory, 1.918. The bladed disk is intentionally mistuned to obtain the maximum response, and the response to an engine order traveling wave excitation is measured. The measured amplitude magnification is in close agreement with the theory. The robustness of the maximum response is demonstrated.

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