Investigations on Maximum Amplitude Amplification Factor of Real Mistuned Bladed Structures

2012 ◽  
Author(s):  
David Hemberger ◽  
Dietmar Filsinger ◽  
Hans-Jörg Bauer
Keyword(s):  
Amplification Factor ◽  
Maximum Amplitude ◽  
Experimental Results ◽  
Blade Vibration ◽  
Turbine Wheel ◽  
Local Variance ◽  
Measurement Results ◽  
Theoretical Investigations ◽  
Maximum Amplification ◽  
Amplitude Amplification

The production of bladed structures, e.g. turbine and compressor wheels, is a subject of statistical scatter. The blades are designed to be identical but differ due to small manufacturing tolerances. This can be local variance of material properties and geometrical deviations, which is indicated as mistuning of the structure. This article deals with the amplitude amplification factor of bladed structures caused by mistuning of real geometries. Theoretical investigations and also experimental results show, that mistuning of the structure leads to an amplification of blade vibration amplitudes and hence to increased stresses in blades. The existing theoretical considerations by Whitehead from 1966 and Kenyon & Griffin from 2001 are compared with results of blade vibration measurements. For that purpose, measurement results of turbine and compressor wheels from publication in recent years were analyzed. These experimental results stem from measurements with strain gauges as well as tip timing measurements to determine blade vibration amplitudes. In addition to this extended literature survey, the authors also examined results from in-house tip timing measurements of a radial turbine wheel from a vehicular turbocharger. The maximum amplification factor (MAF) and the degree of localization were evaluated. The comparison with the theory by Kenyon & Griffith revealed that the estimated maximum amplification factor was always higher than the values from the analyzed data. The measured MAF were besides one exception of a highly localized vibration form, which does not meet the theory’s assumptions, between 54% and 99.5% of the expected value. In this sense the theory has been proven.

Experimental Investigation of the Grouped Blade Vibration for Steam Turbine by Non-Contact Sensors

2017 ◽  
Author(s):  
Tomomi Nakajima ◽  
Kiyoshi Segawa ◽  
Hiromichi Kitahara ◽  
Akimitsu Seo ◽  
Yutaka Yamashita ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Steam Turbine ◽  
Maximum Amplitude ◽  
Amplitude Distribution ◽  
Maximum Response ◽  
Blade Vibration ◽  
Air Jet ◽  
Measurement Results ◽  
Calculation Results ◽  
Contact Sensors

All turbine blades have mistuned structures caused by manufacturing variations within the manufacturing tolerance, such as the geometrical deviations and variance of material properties. The mistuning effect has a known tendency to increase the dynamic stress, but it is also known to be difficult to predict the maximum vibration response before the operation. This paper studies the blade vibration of grouped blades in a low-pressure steam turbine. The study objectives are to characterize the vibration behavior of the grouped blade structure and to evaluate the maximum response of all blades in a stage by experiments. An experimental investigation is carried out in a vacuum chamber, and blades are excited by an air jet during start-up and shut-down. The circumferential blade amplitude distribution is measured by non-contact sensors and strain gauges. The circumferential blade amplitude distribution is found to differ depending on vibration modes and nodal diameters, but the relative tendency is almost the same for all types of operation at each mode and all nodal diameters. Therefore, the median of all experimental results obtained with the non-contact sensors are used in a comparison with calculation results and two theoretical curves obtained using equations from the literature. In comparing the measurement results and the calculation results, the circumferential blade amplitude distribution is not the same with all modes and nodal diameters. However, the maximum amplitude magnification is about 1.5–1.8, and all measurement results are lower than the results for the two theoretical equations. This means the maximum response compared to the tuned blade can be evaluated on the safe side by the two theoretical equations.

Experimental Investigation of the Grouped Blade Vibration for Steam Turbine by Noncontact Sensors

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Tomomi Nakajima ◽  
Kiyoshi Segawa ◽  
Hiromichi Kitahara ◽  
Akimitsu Seo ◽  
Yutaka Yamashita ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Steam Turbine ◽  
Maximum Amplitude ◽  
Amplitude Distribution ◽  
Maximum Response ◽  
Blade Vibration ◽  
Air Jet ◽  
Measurement Results ◽  
Calculation Results ◽  
Noncontact Sensors

All turbine blades have mistuned structures caused by manufacturing variations within the manufacturing tolerance, such as the geometrical deviations and variance of material properties. The mistuning effect has a known tendency to increase the dynamic stress, but it is also known to be difficult to predict the maximum vibration response before the operation. This paper studies the blade vibration of grouped blades in a low-pressure steam turbine. The study objectives are to characterize the vibration behavior of the grouped blade structure and to evaluate the maximum response of all blades in a stage experimentally. An experimental investigation is carried out in a vacuum chamber, and blades are excited by an air jet during start-up and shut-down. The circumferential blade amplitude distribution is measured by noncontact sensors (NCSs) and strain gauges (SGs). The circumferential blade amplitude distribution is found to differ depending on vibration modes and nodal diameters (NDs), but the relative tendency is almost the same for all types of operation at each mode and all NDs. Therefore, the median of all experimental results obtained with the NCSs is used in a comparison with calculation results and results of two theoretical curves obtained using equations from the literature. In comparing the measurement results and the calculation results, the circumferential blade amplitude distribution is not the same with all modes and NDs. However, the maximum amplitude magnification is about 1.5–1.8, and all measurement results are lower than the results for the two theoretical equations. This means the maximum response comparison to the tuned blade gives an evaluation on the safe side by the two theoretical equations.

scholarly journals A Study on the Influence of Different Constraint Modes and Number of Disc Springs on the Dynamics of Disc Spring System

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jiacheng Zhou ◽  
Chuzhe Zhang ◽  
Ziqiu Wang ◽  
Kuanmin Mao ◽  
Xiaoyu Wang
Keyword(s):  
Amplification Factor ◽  
Maximum Amplitude ◽  
Assembly Process ◽  
Good Consistency ◽  
Before And After ◽  
Simulation And Experiment ◽  
Spring System ◽  
The Relationship ◽  
Maximum Amplification ◽  
Disc Spring

In this work, the influences of constraint modes and the number of disc springs on the dynamic characteristics of the disc spring system are studied by simulation and experiment. The amplitudes and amplification factors of the disc spring system under different constraint modes and different numbers of disc springs are obtained. The results show that the maximum amplitude and amplification factor both appear at the constraint modes of locking and no preloading, which indicates that the locking and no preloading is the best constraint mode among the four different constraint modes. Moreover, the amplitude of the disc spring system first increases and then decreases with the number of disc springs increasing, while the amplification factor increases with the number of disc springs increasing. The maximum amplification factor (10.21 in experiment) of the disc spring system appears at 10 disc springs. By studying the relationship between the number of disc springs and amplification factor and damping, we find that the damping of the disc spring system can be reduced by increasing the disc spring numbers, and thus, the corresponding amplification factor can be improved. Furthermore, as the number of disc spring increases, the height differences of disc springs before and after locking are all close to 3 mm, which indicates that the amount of locking compression in the assembly process has a good consistency when the number of disc springs changes. The aforementioned works can provide guidance for the industrial production in screen vibration.

scholarly journals Quantitative Experimental and Theoretical Investigations on the Interaction of Shock Waves with Magnetic Fields

1969 ◽  
Vol 24 (10) ◽  
pp. 1449-1457
Author(s):  
H. Klingenberg ◽  
F. Sardei ◽  
W. Zimmermann
Keyword(s):  
Magnetic Fields ◽  
Shock Waves ◽  
Physical Model ◽  
Spectroscopic Method ◽  
Experimental Results ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Theoretical Predictions ◽  
Interaction Of Shock Waves

Abstract In continuation of the work on interaction between shock waves and magnetic fields 1,2 the experiments reported here measured the atomic and electron densities in the interaction region by means of an interferometric and a spectroscopic method. The transient atomic density was also calculated using a one-dimensional theory based on the work of Johnson3 , but modified to give an improved physical model. The experimental results were compared with the theoretical predictions.

scholarly journals Investigations on the Blade Vibration of a Radial Inflow Micro Gas Turbine Wheel

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Shijie Guo
Keyword(s):  
Gas Turbine ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Turbine Blades ◽  
Pressure Fluctuations ◽  
Leading Edge ◽  
Coupled Modes ◽  
Blade Vibration ◽  
Turbine Wheel ◽  
Micro Gas Turbine

This paper demonstrates the investigations on the blade vibration of a radial inflow micro gas turbine wheel. Firstly, the dependence of Young's modulus on temperature was measured since it is a major concern in structure analysis. It is demonstrated that Young's modulus depends on temperature greatly and the dependence should be considered in vibration analysis, but the temperature gradient from the leading edge to the trailing edge of a blade can be ignored by applying the mean temperature. Secondly, turbine blades suffer many excitations during operation, such as pressure fluctuations (unsteady aerodynamic forces), torque fluctuations, and so forth. Meanwhile, they have many kinds of vibration modes, typical ones being blade-hub (disk) coupled modes and blade-shaft (torsional, longitudinal) coupled modes. Model experiments and FEM analysis were conducted to study the coupled vibrations and to identify the modes which are more likely to be excited. The results show that torque fluctuations and uniform pressure fluctuations are more likely to excite resonance of blade-shaft (torsional, longitudinal) coupled modes. Impact excitations and propagating pressure fluctuations are more likely to excite blade-hub (disk) coupled modes.

An Assessment of the Value of Theory in Predicting Gas-Bearing Performance

1961 ◽  
Vol 83 (2) ◽  
pp. 195-200 ◽  
Author(s):  
S. Cooper
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Experimental Methods ◽  
Experimental Results ◽  
Theoretical Investigations ◽  
Gas Bearing ◽  
Theoretical Results

The object of the paper is to indicate the value of theoretical investigations of hydrodynamic finite bearings under steady-state conditions. Methods of solution of Reynolds equation by both desk and digital computing, and methods of stabilizing the processes of solution, are described. The nondimensional data available from the solutions are stated. The outcome of an attempted solution of the energy equation is discussed. A comparison between some theoretical and experimental results is shown. Experimental methods employed and some difficulties encountered are discussed. Some theoretical results are given to indicate the effects of the inclusion of slip velocity, stabilizing slots, and a simple case of whirl.

Mistuning Modeling and its Validation for Small Turbine Wheels

2013 ◽  
Author(s):  
David Hemberger ◽  
Dietmar Filsinger ◽  
Hans-Jörg Bauer
Keyword(s):  
Amplification Factor ◽  
Numerical Models ◽  
Lower Sensitivity ◽  
Fe Model ◽  
Mode Localization ◽  
Geometric Deviations ◽  
Probabilistic Study ◽  
Calculated Amplitude ◽  
Amplitude Amplification ◽  
The Ideal

The production of bladed structures, e.g. turbine and compressor wheels, is a subject of statistical scatter. The blades are designed to be identical but differ due to small manufacturing tolerances. This so called mistuning can lead to increased vibration amplitudes compared to the ideal tuned case. The object of this study is to create and validate numerical models to evaluate such mistuning effects of turbine wheels for automotive turbocharger applications. As a basis for the numerical analysis vibration measurements under stand-still conditions were carried out by using a laser surface velocimeter (LSV). The scope of this investigation was to identify the mistuning properties of the turbine wheels namely the frequency deviation from the ideal, cyclic symmetrical tuned system. Experimental modal analyses as well as blade by blade measurements were performed. Moreover 3D scanning techniques were employed to determine geometric deviations. Numerical FE models and a simplified multi degree of freedom model (EBM) were created to reproduce the measured mistuning effects. The prediction of mode localization and the calculated amplitude amplification were evaluated. The best results were obtained with a FE model that employs individual sectorial stiffnesses. The results also indicate that the major contribution to mistuning is made by material inhomogeneities and not by geometric deviations from ideal dimensions. With the adjusted FE model a probabilistic study has been performed to investigate the influence of the mistuning on the amplitude amplification factor. It has been found that at a certain level of mistuning the amplification factor remains constant or slightly decreases. By introducing intentional mistuning a lower sensitivity as well as a decrease of the amplitude amplification could be achieved.

Buckling and Post Buckling Behavior of a Transversely Stiffened Ship Hull Model

1964 ◽  
Vol 8 (04) ◽  
pp. 7-21
Author(s):  
H.G. Schultz
Keyword(s):  
Reasonable Agreement ◽  
Ship Hull ◽  
Buckling Load ◽  
Experimental Results ◽  
Postbuckling Behavior ◽  
Pure Bending ◽  
Box Girder ◽  
Buckling Behavior ◽  
Theoretical Investigations ◽  
Post Buckling

In the paper presented the behavior of a transversely formed box-girder model subjected to pure bending is discussed, where the deck plating of the model is loaded above the buckling load. The experimental results obtained are in reasonable agreement with theoretical investigations and show the influence of fabrication initiated plate deflections on the buckling and postbuckling behavior of the deck plating clearly. A method is suggested for determining the buckling load of plates having large initial deformations.

Magnetization and Curie Temperature of Ferromagnetic Ultrathin Films: The Influence of Magnetic Anisotropy and Dipolar Interactions (invited)

1991 ◽  
Vol 231 ◽  
Author(s):  
P. Bruno
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Curie Temperature ◽  
Magnetic Anisotropy ◽  
Long Range ◽  
Ultrathin Films ◽  
Experimental Results ◽  
Dipolar Interactions ◽  
Surface Gradient ◽  
Theoretical Investigations

AbstractTheoretical investigations of the magnetization and Curie temperature of ferromagnetic ultrathin films in the presence of magnetic anisotropy and long-range dipolar interactions are presented. The Curie temperature of fcc (001) cobalt ultrathin films is calculated and compared with experimental results on Co/Cu (001) films. The influence of an external magnetic field, and the surface gradient of the magnetization are also discussed.

The Submicron Fabrication Process for T Gate With a Flat Head

2018 ◽  
Author(s):  
Xiaoyu Su ◽  
Zhongjing Ren ◽  
Hao Sun ◽  
Yong Shi ◽  
Quan Pan
Keyword(s):  
Optical Microscope ◽  
Fabrication Process ◽  
Experimental Results ◽  
General Process ◽  
Gate Structure ◽  
Measurement Results

T gate structure is traditionally manufactured with a valley in its head, which requires the thickness of the head layer to thicker than the height of foot layer. As is presented in this paper, an innovative submicron fabrication process is investigated for T gate structures to construct a flat head in order to get rid of that constraint. In detail, the reason why conventional T gate fabrication cannot manufacture a flat head is analyzed, and then a general process for flat head T gate structure is proposed considering various resist and structure materials. After that, a typical submicron sample has been manufactured using aluminum and NiTi. Furthermore, the particular photo resists and recipes adopted in that sample are considered. To clearly illustrate the proposed technique as well as verify its feasibility, top views of the structure under optical microscope along with the measurement results of thickness after every step are recorded. According to those experimental results, the valley in T gate’s head is proved to be avoided during fabrication.

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