Vibration Analyses of an Axial Turbine Wheel with Intentional Mistuning

2020 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Robby Weber ◽  
Frederik Popig
Keyword(s):  
Strong Dependence ◽  
Forced Response ◽  
Turbine Wheel ◽  
Part Load ◽  
Aerodynamic Damping ◽  
Centrifugal Stiffening ◽  
Manufacturing Procedure ◽  
Random Mistuning ◽  
Blade Frequency ◽  
Load Conditions

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 increases the risk of flutter at part load conditions. For this reason, intentional mistuning is employed 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. In this sense, two different series of blades have been made. However, 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 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. 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. Finally, mistuning patterns could be identified featuring a tremendous increase of aerodynamic damping ratios. The robustness of the solutions could be proved by superimposing additional random mistuning.

Vibration Analyses of an Axial Turbine Wheel With Intentional Mistuning

2020 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Robby Weber ◽  
Frederik Popig
Keyword(s):  
Strong Dependence ◽  
Forced Response ◽  
Turbine Wheel ◽  
Part Load ◽  
Aerodynamic Damping ◽  
Centrifugal Stiffening ◽  
Manufacturing Procedure ◽  
Random Mistuning ◽  
Blade Frequency ◽  
Load Conditions

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.

Forced Response Analysis of a Mistuned Compressor Blisk

2013 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Thomas Giersch ◽  
Jens Nipkau
Keyword(s):  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver ◽  
Displacement Based ◽  
Blade Frequency

The forced response of an E3E-type HPC-blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades namely stiffness and damping are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order and aerodynamic influences it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade alone frequencies as design variables are applied. The validity of the Whitehead-limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause 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 inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk’s stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.

Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Bernd Beirow ◽  
Thomas Giersch ◽  
Arnold Kühhorn ◽  
Jens Nipkau
Keyword(s):  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver ◽  
Displacement Based ◽  
Blade Frequency

The forced response of an E3E-type high pressure compressor (HPC) blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades, namely stiffness and damping, are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order, and aerodynamic influences, it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade-alone frequencies as design variables are applied. The validity of the Whitehead limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause 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 as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk's stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.

Analysis of the Effect of Multirow and Multipassage Aerodynamic Interaction on the Forced Response Variation in a Compressor Configuration—Part I: Aerodynamic Excitation

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Harald Schoenenborn
Keyword(s):  
Three Dimensional ◽  
Forced Response ◽  
Frame Of Reference ◽  
Aerodynamic Damping ◽  
Aerodynamic Interaction ◽  
Blade Row ◽  
Random Mistuning ◽  
Compressor Map ◽  
Response Variation ◽  
Turbomachinery Design

The aeroelastic prediction of blade forcing is still a very important topic in turbomachinery design. Usually, the wake from an upstream airfoil and the potential field from a downstream airfoil are considered as the main disturbances. In recent years, it became evident that in addition to those two mechanisms, Tyler–Sofrin modes, also called scattered or spinning modes, may have a significant impact on blade forcing. It was recently shown in literature that in multirow configurations, not only the next but also the next but one blade row is very important as it may create a large circumferential forcing variation, which is fixed in the rotating frame of reference. In the present paper, a study of these effects is performed on the basis of a quasi three-dimensional (3D) multirow and multipassage compressor configuration. For the analysis, a harmonic balancing code, which was developed by DLR Cologne, is used for various setups and the results are compared to full-annulus unsteady calculations. It is shown that the effect of the circumferentially different blade excitation is mainly contributed by the Tyler–Sofrin modes and not to blade-to-blade variation in the steady flow field. The influence of various clocking positions, coupling schemes and number of harmonics onto the forcing is investigated. It is also shown that along a speed-line in the compressor map, the blade-to-blade forcing variation may change significantly. In addition, multirow flutter calculations are performed, showing the influence of the upstream and downstream blade row onto aerodynamic damping. The effect of these forcing variations onto random mistuning effects is investigated in the second part of the paper.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Thomas Giersch ◽  
Jens Nipkau
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver

The forced response of the first rotor of an E3E-type high pressure compressor blisk is analyzed with regard to varying mistuning, varying engine order excitations and the consideration of aeroelastic effects. For that purpose, 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 technique is employed to model aeroelastic 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 aeroelastic 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 inter-blade 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.

Analysis of the Effect of Multi-Row and Multi-Passage Aerodynamic Interaction on the Forced Response Variation in a Compressor Configuration: Part 1 — Aerodynamic Excitation

2017 ◽  
Author(s):  
Harald Schoenenborn
Keyword(s):  
Forced Response ◽  
Frame Of Reference ◽  
Rotating Frame ◽  
Aerodynamic Damping ◽  
Aerodynamic Interaction ◽  
Blade Row ◽  
Random Mistuning ◽  
Compressor Map ◽  
Response Variation ◽  
Turbomachinery Design

The aeroelastic prediction of blade forcing is still a very important topic in turbomachinery design. Usually, the wake from an upstream airfoil and the potential field from a downstream airfoil are considered as the main disturbances. In recent years, it became evident that in addition to those two mechanisms Tyler-Sofrin modes, also called scattered or spinning modes, may have a significant impact on blade forcing. In Schrape et al. [9] it was found that in multi-row configurations not only the next, but also the next but one blade row is very important as it may create a large circumferential forcing variation which is fixed in the rotating frame of reference. In the present paper a study of these effects is performed on the basis of a quasi 3D multi-row and multi-passage compressor configuration. For the analysis a harmonic balancing code, which was developed by DLR Cologne, is used for various setups and the results are compared to full-annulus unsteady calculations. It is shown that the effect of the circumferentially different blade excitation is mainly contributed by the Tyler-Sofrin modes and not to blade-to-blade variation in the steady flow field. The influence of various clocking positions, coupling schemes and number of harmonics onto the forcing is investigated. It is also shown that along a speed-line in the compressor map the blade-to-blade forcing variation may change significantly. In addition, multi-row flutter calculations are performed, showing the influence of the upstream and downstream blade row onto aerodynamic damping. The effect of these forcing variations onto random mistuning effects is investigated in the second part of the paper.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Bernd Beirow ◽  
Thomas Giersch ◽  
Arnold Kühhorn ◽  
Jens Nipkau
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver

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.

On the Influence of Strain Gauge Instrumentation on Blade Vibrations of Integral Blisk Compressor Rotors Applying a Discrete Model

2009 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Ku¨hhorn ◽  
Jens Nipkau
Keyword(s):  
Strain Gauge ◽  
Laser Scanning ◽  
Numerical Models ◽  
Strong Dependence ◽  
Forced Response ◽  
Frequency Resolution ◽  
Mode Shapes ◽  
Frequency Distributions ◽  
Engine Order ◽  
Blade Frequency

The effect of blade frequency mistuning on the forced response of HPC-blisks is studied by means of experimental and numerical investigations applying discrete mechanical low degree of freedom models. Besides the mistuning resulting from manufacturing and inhomogeneous material also strain gauge (S/G) induced mistuning is considered. Blade by blade measurements supported by numerical calculations are used to determine mistuning distributions within an iterative approach. Due to the stiffness contribution of high temperature S/G, a significant increase of blade alone frequencies can be proved. It is shown within laser scanning measurements that this S/G induced mistuning can cause strongly localized mode shapes. Since S/G signals are used to monitor also non-instrumented blade resonances in engine-tests, it is reasonable to consider the S/G contribution within model-updates. The numerical models introduced in this paper are adjusted to experimentally determined blade alone frequency distributions. Within simulations of the forced response it is shown in principle, that the S/G-instrumentation also affects the response of non-instrumented blades which is important with regard to the S/G calibration process. Additional investigations are addressed to the consequences of small variations in measured mistuning distributions on the maximum forced response, i. e. resulting from a changing ambient temperature while measurement or a limited frequency resolution. In this context, a strong dependence on the engine order excited, the damping level and thus the flow conditions could be proved. As an example all investigations presented in this paper are carried out for two stages of a research compressor.

Experimental and Analytical Investigations of a Low Pressure Model Turbine During Forced Response Excitation

2010 ◽  
Author(s):  
Christoph Heinz ◽  
Markus Schatz ◽  
Michael V. Casey ◽  
Heinrich Stu¨er
Keyword(s):  
Degrees Of Freedom ◽  
Timing Analysis ◽  
Dynamic Performance ◽  
Amplitude Distribution ◽  
Low Pressure ◽  
Forced Response ◽  
Operating Conditions ◽  
Linear Regression Method ◽  
Rotor Shaft ◽  
Aerodynamic Damping

To guarantee a faultless operation of a turbine it is necessary to know the dynamic performance of the machine especially during start-up and shut-down. In this paper the vibration behaviour of a low pressure model steam turbine which has been intentionally mistuned is investigated at the resonance point of an eigenfrequency crossing an engine order. Strain gauge measurements as well as tip timing analysis have been used, whereby a very good agreement is found between the methods. To enhance the interpretation of the data measured, an analytical mass-spring-model, which incorporates degrees of freedom for the blades as well as for the rotor shaft, is presented. The vibration amplitude varies strongly from blade to blade. This is caused by the mistuning parameters and the coupling through the rotor shaft. This circumferential blade amplitude distribution is investigated at different operating conditions. The results show an increasing aerodynamic coupling with increasing fluid density, which becomes visible in a changing circumferential blade amplitude distribution. Furthermore the blade amplitudes rise non-linearly with increasing flow velocity, while the amplitude distribution is almost independent. Additionally, the mechanical and aerodynamic damping parameters are calculated by means of a non-linear regression method. Based on measurements at different density conditions, it is possible to extrapolate the damping parameters down to vacuum conditions, where aerodynamic damping is absent. Hence the material damping parameter can be determined.

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