Mistuning and Damping of a Radial Turbine Wheel. Part 1: Fundamental Analyses and Design of Intentional Mistuning Pattern

2021 ◽  
Author(s):  
Alex Nakos ◽  
Bernd Beirow ◽  
Arthur Zobel
Keyword(s):  
High Stress ◽  
Forced Response ◽  
Experimental Investigations ◽  
Detailed Knowledge ◽  
Turbine Wheel ◽  
Operation Conditions ◽  
Radial Turbine ◽  
Influence Coefficients ◽  
Modes Of Vibration ◽  
The Impact

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, a 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 (SNM) approach introduced by Yang and Griffin [1], which conveniently allows for accounting both differing mistuning patterns and the impact of aeroelastic interaction by means of aerodynamic influence coefficients (AIC). Further, finite element analyses are carried out in order to identify appropriate measures 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.

Mistuning and Damping of a Radial Turbine Wheel. Part 1: Fundamental Analyses and Design of Intentional Mistuning Pattern

2021 ◽  
Author(s):  
Alex Nakos ◽  
Bernd Beirow ◽  
Arthur Zobel
Keyword(s):  
High Stress ◽  
Forced Response ◽  
Experimental Investigations ◽  
Detailed Knowledge ◽  
Turbine Wheel ◽  
Operation Conditions ◽  
Radial Turbine ◽  
Influence Coefficients ◽  
Modes Of Vibration ◽  
The Impact

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, a 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 (SNM) approach introduced by Yang and Griffin [1], which conveniently allows for accounting both differing mistuning patterns and the impact of aeroelastic interaction by means of aerodynamic influence coefficients (AIC). Further, finite element analyses are carried out in order to identify appropriate measures 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.

Influence of Aerodynamic Mistuning and Aerodynamic Coupling on Vibration Behavior of Mistuned Small Radial Turbine Wheels

2017 ◽  
Author(s):  
David Hemberger ◽  
Dietmar Filsinger ◽  
Hans-Jörg Bauer
Keyword(s):  
Forced Response ◽  
Laser Vibrometer ◽  
Fe Model ◽  
Blade Vibration ◽  
Turbine Wheel ◽  
Vibration Measurements ◽  
Guide Vanes ◽  
Vibration Behavior ◽  
Operation Conditions ◽  
Radial Turbine

The study at hand analyzes the influence of aerodynamic mistuning and aerodynamic coupling on the vibration behavior of mistuned small radial turbine wheels. The aerodynamic mistuning is caused by angular non uniformity of the variable turbine guide vanes. Variable turbine guide vanes are state of the art in exhaust gas turbochargers for automotive diesel engines. Aerodynamic coupling describes the coupling of the turbine blades through the flow. It can influence the mistuned vibration behavior of the turbine wheel due to varying operation conditions, in which the turbine pressure ratio and the pressure distribution over the turbine wheel surface is changed. It was analyzed whether the aerodynamic mistuning and aerodynamic coupling must be considered for small radial turbine wheel designs. The basis for this investigation were blade vibration measurements under standstill conditions with a laser vibrometer as well as blade vibration measurements during operation with a tip timing system. The mistuned turbine eigenforms were analyzed and compared at various ambient conditions using these measurement results. By means of forced response calculations — unsteady 3D CFD and 3D FEA —, the influence of aerodynamic mistuning on the ideal tuned turbine was examined to be able to separate the aerodynamic mistuning from the mistuning of the structure. Furthermore, the superimposed effect of the aerodynamic mistuning and the mistuning of the structure on the turbine eigenforms and the amplitude amplification was analyzed using a mistuned 3D FE model and a population of samples with varying aerodynamic mistuning. It was found, that the aerodynamic coupling and aerodynamic mistuning have a negligible effect on the mistuned vibration behavior for a small radial turbine with variable turbine guide vanes. These two parameters must not be considered when designing such a turbine wheel.

Structural Dynamics with Parameter Uncertainties

1987 ◽  
Vol 40 (3) ◽  
pp. 309-328 ◽  
Author(s):  
R. A. Ibrahim
Keyword(s):  
Structural Dynamics ◽  
Structural Parameters ◽  
Normal Modes ◽  
Forced Response ◽  
Experimental Investigations ◽  
Continuous Systems ◽  
Parameter Uncertainties ◽  
Response Characteristics ◽  
Random Eigenvalues ◽  
The Impact

The treatment of structural parameters as random variables has been the subject of structural dynamicists and designers for many years. Several problems have been involved during the last few decades and resulted in new theorems and interesting phenomena. This paper reviews a number of topics pertaining to structural dynamics with parameter uncertainties. These include direct problems such as random eigenvalues and random responses of discrete and continuous systems. The impact of these problems on related areas of interest such as sensitivity of structural performance to parameter variations, design optimization, and reliability analysis is also addressed. The paper includes the results of experimental investigations, the phenomenon of normal modes localization, and the effect of mistuning of turbomachinery blades on their flutter and forced response characteristics.

HCF Optimization of a High Speed Variable Geometry Turbine

2021 ◽  
Author(s):  
Alister Simpson ◽  
Sung in Kim ◽  
Jongyoon Park ◽  
Seong Kwon ◽  
Sejong Yoo
Keyword(s):  
High Speed ◽  
Forced Response ◽  
Variable Geometry ◽  
Blade Vibration ◽  
Operating Cycle ◽  
Turbine Wheel ◽  
Aerodynamic Loads ◽  
Radial Turbine ◽  
Wide Range ◽  
Variable Geometry Turbine

Abstract This paper describes the structural optimization of a high speed, 35mm tip diameter radial turbine wheel in a Variable Geometry Turbine (VGT) system, subjected to the wide range of aerodynamic loads experienced during the full operating cycle. VGTs exhibit a wide range of unsteady flow features, which vary as the nozzle vanes rotate through different positions during operation, as do the magnitudes and frequencies of the resulting pressure fluctuations experienced by the downstream turbine blades. The turbine wheel typically passes through a number of blade natural frequencies over their operating cycle, and there are a number of potential conditions where these unsteady aerodynamic loads can lead to resonant blade vibration. The focus of this work is on the development of a pragmatic design approach to improve the structural characteristics of a radial turbine blade with respect to High Cycle Fatigue (HCF), informed by detailed time-accurate Computational Fluid Dynamics (CFD) prediction of the unsteady pressure loads, coupled with FE vibration analysis to quantify the resulting blade vibration magnitudes. Unsteady CFD simulations are performed to determine the time-accurate pressure loads on the blades, and the results are used as input to forced response analysis to determine the peak alternating stress amplitudes. The detailed analysis results are then used to guide a subsequent parametric study in order to investigate the influence of key geometric parameters on the structural performance of the blade, with the optimum design identified through the use of a Goodman Diagram. The results quantify the influence of both blade thickness distribution and hub fillet details on the vibration characteristics of radial turbines.

Experimental Investigation on Natural Characteristics and Forced Response of Bladed Disks

2011 ◽  
Vol 105-107 ◽  
pp. 34-37
Author(s):  
Zhi Bin Zhao ◽  
Er Ming He ◽  
Hong Jian Wang
Keyword(s):  
Travelling Wave ◽  
Primary Objective ◽  
Forced Response ◽  
Dynamic Responses ◽  
Experimental Investigations ◽  
Wave Excitation ◽  
Bladed Disks ◽  
Bladed Disk ◽  
The Impact ◽  
Natural Characteristics

The results of an experimental investigations on the natural characteristics of tuned bladed disk and forced dynamic responses of mistuned bladed disks are reported. Three experimental bladed disks are discussed: a tuned specimen of periodic symmetry with 12-blades which are nominally identical, and two mistuned specimens, which feature small blade-to-blade variations by adding slight blocks to blade tips. All the specimens are subject to travelling wave excitation produced by piezo-electric actuators sticking on the root of blades. The primary objective of this experiment is to observe the natural characteristics of tuned bladed disk, and to research the impact of mistuning on the forced response blade amplitude magnification. Analytical predictions about the blade amplitude magnification factor are verified by the experimental results.

Mistuning and Damping Analysis of a Radial Turbine Blisk in Varying Ambient Conditions

2014 ◽  
Author(s):  
Bernd Beirow ◽  
Thomas Maywald ◽  
Arnold Kühhorn
Keyword(s):  
Frequency Response ◽  
Ambient Pressure ◽  
Forced Response ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Radial Turbine ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Technical Vacuum ◽  
The Impact

A mistuned radial turbine impeller is analyzed with respect to the impact of varying ambient pressures and temperatures as well on frequency response functions and modal damping ratios. Beginning at room conditions, a finite element model of an impeller wheel at rest is updated based on experimentally determined mistuning in terms of blade dominated frequencies. The following numerical forced response analyses yield a maximum blade displacement amplification of 67% compared to the tuned reference. In addition, modal damping ratios are determined in dependence on the ambient pressure ranging from technical vacuum at 1 mbar up to 6000 mbar in a pressure chamber. Shaker excitation and laser Doppler vibrometry response measurement is employed in this context. A linear dependence of modal damping ratios on ambient pressure and a dominating damping contribution of the surrounding air even for higher modes could be proved. Moreover, the experimental determination of frequency response functions (FRF) at technical vacuum yields a better separation of resonance peaks compared to room conditions at 1013 mbar and hence, this data allows for more accurate model-updates in principle. It is proved that numerical models updated regarding mistuning at room conditions are well suited to predict the forced response at arbitrary pressures if measured modal damping ratios at these pressures are considered. Finally, within analyzing the effect of increasing structural temperatures with the surrounding air at 1013 mbar included slightly decreasing resonance frequencies but strongly increasing FRF-amplitudes are determined.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

scholarly journals On Kaufmann's theory of the impact of the pianoforte hammer

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
Keyword(s):  
Initial Conditions ◽  
Practical Importance ◽  
Prima Facie ◽  
Point Of View ◽  
Infinite Length ◽  
Modes Of Vibration ◽  
Rigorous Treatment ◽  
The Subject ◽  
Set Up ◽  
The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

scholarly journals Experimental investigations on diesel engine using alumina nanoparticle fuel additive

2021 ◽  
Vol 13 (2) ◽  
pp. 168781402098840
Author(s):  
Mohammed S Gad ◽  
Sayed M Abdel Razek ◽  
PV Manu ◽  
Simon Jayaraj
Keyword(s):  
Diesel Engine ◽  
Diesel Fuel ◽  
Alumina Nanoparticles ◽  
Experimental Investigations ◽  
Fuel Additive ◽  
Alumina Nanoparticle ◽  
Fuel Injectors ◽  
Performance And Emission ◽  
And Performance ◽  
The Impact

Experimental work was done to examine the impact of diesel fuel with alumina nanoparticles on combustion characteristics, emissions and performance of diesel engine. Alumina nanoparticles were mixed with crude diesel in various weight fractions of 20, 30, and 40 mg/L. The engine tests showed that nano alumina addition of 40 ppm to pure diesel led to thermal efficiency enhancement up to 5.5% related to the pure diesel fuel. The average specific fuel consumption decrease about neat diesel fuel was found to be 3.5%, 4.5%, and 5.5% at dosing levels of 20, 30, and 40 ppm, respectively at full load. Emissions of smoke, HC, CO, and NOX were found to get diminished by about 17%, 25%, 30%, and 33%, respectively with 40 ppm nano-additive about diesel operation. The smaller size of nanoparticles produce fuel stability enhancement and prevents the fuel atomization problems and the clogging in fuel injectors. The increase of alumina nanoparticle percentage in diesel fuel produced the increases in cylinder pressure, cylinder temperature, heat release rate but the decreases in ignition delay and combustion duration were shown. The concentration of 40 ppm alumina nanoparticle is recommended for achieving the optimum improvements in the engine’s combustion, performance and emission characteristics.

scholarly journals A FEM-Based 2D Model for Simulation and Qualitative Assessment of Shot-Peening Processes

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2784
Author(s):  
Georgios Maliaris ◽  
Christos Gakias ◽  
Michail Malikoutsakis ◽  
Georgios Savaidis
Keyword(s):  
Process Parameters ◽  
Material Properties ◽  
Shot Peening ◽  
Qualitative Assessment ◽  
Experimental Investigations ◽  
Elastoplastic Material ◽  
Size Distributions ◽  
User Friendly ◽  
The Impact ◽  
2D Model

Shot peening is one of the most favored surface treatment processes mostly applied on large-scale engineering components to enhance their fatigue performance. Due to the stochastic nature and the mutual interactions of process parameters and the partially contradictory effects caused on the component’s surface (increase in residual stress, work-hardening, and increase in roughness), there is demand for capable and user-friendly simulation models to support the responsible engineers in developing optimal shot-peening processes. The present paper contains a user-friendly Finite Element Method-based 2D model covering all major process parameters. Its novelty and scientific breakthrough lie in its capability to consider various size distributions and elastoplastic material properties of the shots. Therewith, the model is capable to provide insight into the influence of every individual process parameter and their interactions. Despite certain restrictions arising from its 2D nature, the model can be accurately applied for qualitative or comparative studies and processes’ assessments to select the most promising one(s) for the further experimental investigations. The model is applied to a high-strength steel grade used for automotive leaf springs considering real shot size distributions. The results reveal that the increase in shot velocity and the impact angle increase the extent of the residual stresses but also the surface roughness. The usage of elastoplastic material properties for the shots has been proved crucial to obtain physically reasonable results regarding the component’s behavior.

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