An accelerated high cycle fatigue testing approach is presented to determine the fatigue endurance limit of materials at high frequencies. Base excitation of a tapered plaque driven into a high frequency resonance mode allows the test to be completed in a significantly shorter time. This high cycle fatigue testing is performed using the tracked sine resonance search and dwell strategy. The controller monitors the structural health during the test. Any change in the dynamic response indicates crack initiation in the material. In addition, a shape optimization finite element model is conducted for the design of the tapered plaques. An integrated neural (Neural-Network) genetic (NSGA_II) optimization technique is implemented to carry out the shape optimization for this component. This process results in a significant reduction in the computational cost. A Pareto set is then produced that meets the designer’s requirements and provides the decision maker several alternatives to choose from.

A major challenge in the design of turbomachinery components for aircraft gas turbine engines is high cycle fatigue failures due to flutter. Of particular concern is the subsonic/transonic stall flutter boundary which occurs at part speed near the stall line. At these operating conditions the incidence angle is large and the relative Mach number is high subsonic or transonic. Viscous effects dominate for high incidence angles. In order to predict the flutter phenomena, accurate calculation of the steady and unsteady aerodynamic loading on the turbomachinery airfoils is necessary. The development of unsteady aerodynamic models to predict the unsteady forces and moments acting on turbomachine airfoils is an area of fundamental research interest. Unsteady Reynolds Averaged Navier-Stokes (RANS) models have been developed to accurately account for viscous effects. For these Reynolds averaged equations turbulence models are needed for the Reynolds stress terms. A transition model is also necessary. The transition onset location is determined by a transition onset model or specified at the suction peak. Usually algebraic, one or two-equation or Reynolds stress turbulence models are used. Since the Reynolds numbers in turbomachinery are large enough to guarantee the flow is turbulent, suitable transition and turbulence models are crucial for accurate prediction of steady and unsteady separated flow. The viscous flow solution of compressor airfoils at off-design conditions is challenging due to flow separation and transition to turbulent flow within separation bubbles. Additional complexity arises when the airfoils are vibrating as is encountered in stall flutter. In this investigation calculations are made of a transonic compressor airfoil in steady flow and with the airfoils oscillating in a pitching motion about the mid-chord at 0° and 10° of chordal incidence angle, and correlated with experiments conducted in the NASA GRC Transonic Flutter Cascade. To model the influence of flow transition on the steady and unsteady aerodynamic flow characteristics, the Solomon, Walker, and Gostelow (SWG) transition model is utilized. The one-equation Spalart-Allmaras model is used to model turbulence. Different transition onset models including fixed onset are implemented and compared for the two incidence angle cases. At each incidence angle, the computational model is compared to the experimental data for the steady flow case and also for pitching oscillation at a reduced frequency of 0.4. The 10° incidence angle case has flow separation over front 40% of the airfoil chord. The operating conditions considered are an inlet Mach number of 0.5 and a Reynolds number of 0.9 Million.

Ce travail a porté sur l’influence d’entailles micrométriques sur la tenue en fatigue à grand nombre de cycles d’un alliage de titane et la comparaison avec un cas de fretting-fatigue. Des études préliminaire sont montré que des entailles micrométriques pouvaient reproduire les champs de contraintes d’essais de fretting-fatigue. Le projet COGNAC dirigé par Safran Aircraft Engines a été créé dans l’objectif d’évaluer la faisabilité d’un modèle unique capable de simuler la tenue en fatigue de pièces subissant des sollicitations de fretting ou de fatigue en présence d’entailles. Le cadre expérimental de cette thèse est limité à la partie du projet traitant des entailles. Afin d’avoir le même état de préparation de surface, les micro-entailles et les surfaces des éprouvettes de fretting fatigue sont usinées par meulage. Afin de reproduire les gradients de contraintes observés localement pour des chargements de fretting-fatigue, des entailles en V avec des rayons compris entre 50 μm à 500 μm ont été choisies.L’étude du taux de triaxialité et du cisaillement a permis de définir une géométrie d’éprouvette de comparaison avec le fretting fatigue qui comporte 2 entailles en V inclinées en face à face. Trois campagnes expérimentales de fatigue à grand nombre de cycles ont été menées. La première sur des éprouvettes lisses meulées afin d’obtenir une limite de fatigue de référence sans concentration de contraintes. La seconde sur des éprouvettes avec une entaille non inclinée ayant une profondeur de500 μm afin d’étudier les effets du rayon de fond d’entaille sur la limite de fatigue. La dernière est une campagne sur les éprouvettes avec 2 entailles inclinées qui permettent de reproduire les champs de contrainte des essais de fretting. Les premiers stades de fissuration ont été étudiés. Les facettes de pseudo clivage, la présence d’un premier stade de fissuration et les amorçages multiples en fond d’entaille ressemblent à ce qui peut être vu sur des essais de fretting. Par contre la présence de fissures non propageantes en fond d’entaille sous la limite de fatigue n’a pas pu être démontrée, alors que ces fissures non propageantes sont observables sur les essais de fretting-fatigue. Les sites d’amorçages et les mécanismes des premiers endommagements semblent être pilotés par les zones affectées par le meulage. Enfin trois critères de fatigue ont été utilisés afin de tenter de reproduire nos résultats expérimentaux. L’approche basée sur la théorie du gradient –avec un gradient local et un impact affine du gradient- et celle basée sur la théorie de la distance critique ont fourni des résultats corrects sur les éprouvettes entaillées mais ne peuvent faire le lien avec les éprouvettes sans concentrations de contraintes. Enfin, l’approche probabiliste utilisée a produit des résultats très proches des résultats expérimentaux à la fois sur des éprouvettes lisses et des micro-entailles. La comparaison des résultats expérimentaux montrent que le champ de contrainte de Crossland proche de la surface d’amorçage du fretting-fatigue est proportionnel à celui proche d’un fond d’entaille dans le cas d’une éprouvette avec 2 entailles en face à face. Le niveau de la sollicitation des 2 essais diffère localement d’environ20%. Dans la suite des travaux, il serait particulièrement intéressant de relancer une campagne de comparaison entre fretting et entailles en utilisant un critère probabiliste pour dimensionner les essais afin de proposer une méthodologie commune de prise en compte des concentrations de contraintes dans les cas de fretting-fatigue et de concentrateurs géométriques sollicités en fatigue. / This study is about the influence of micro-notches on the high cycle fatigue behavior of a Ti64 alloy and the comparison with similar fretting fatigue tests. Preliminary studies showed that fretting-fatigue stress fields can be reproduced by micro-notched. The COGNAC project leaded by Safran Aircraft Engines was built to verify if a unique model can reproduce both fretting-fatigue and notched samples fatigue tests. The scope of this experimental study is limited to the notched samples. In this PHD thesis, the notches are grinded and the results are compared with fretting-fatigue tests on grinded surfaces. V-notched with notch root radius from 50 to 500 μm were chosen to reproduce the stress gradient of fretting-fatigue tests. A geometry with two inclined notches facing each other allows to reproduce shear stress and stress triaxiality from fretting-fatigue tests. Three different experimental studies were performed. First on un-notched specimens with a grinded surface state to produce a reference fatigue limit for grinded surface state without stress concentration. The second study the notch root radius effect on the fatigue limit with samples with one non-inclined notch of 500 μm of depth. The last one is a series of fatigue tests on samples with two inclined notches that reproduce the stress distribution of fretting-fatigue tests. Pseudo-cleavage facets, multi cracks initiations in the notch root and the presence of two propagation stages is similar to the fretting-fatigue tests mechanisms. However, non propagating cracks were not observe at the notch root while many of them were present during the fretting-fatigue test. The initiation sites and the early stages of propagation seem to be controlled by grinded affected areas. Finally, three fatigue criteria were used to try to reproduce the experimental results. The criteria based on the critical distance theory and gradient theory –with a local gradient and an affine effect of the gradient term- can reproduce the fatigue limits of notched samples but fail to predict both notched and un-notched specimen fatigue limits with a unique data set. The third one is a probabilistic criterion which success to predict the experimental fatigue limits not only of notched samples but also smooth ones. The comparisons between the experimental results of the fatigue on the specimens with two inclined notches and the fretting-fatigue shows a difference of 20%. The distribution of the Crossland stress is quite similar. In the future, it would be useful to make a new comparison between fretting-fatigue and fatigue on notches using the probabilistic criterion to design the tests. This new comparison could lead to the proposal of a unique methodology to take into account the fretting-fatigue and the fatigue on stress concentrators.

Two state of the art finite element reduction techniquespreviously validated against the direct finite element method,one based on classical modal analysis and another based oncomponent mode synthesis, are applied for efficient mistunedfree vibration and forced response analysis of several bladeddisk geometries. The methods are first applied to two testcases in order to demonstrate the differences in computationalefficiency as well as to validate the methods againstexperimental data. As previous studies have indicated, nonoticeable differences in accuracy are detected for the currentapplications, while the method based on classical modalanalysis is significantly more efficient. Experimental data(mistuned frequencies and mode shapes) available for one of thetwo test cases are compared with numerical predictions, and agood match is obtained, which adds to the previous validationof the methods (against the direct finite element method). The influence of blade-to-blade coupling and rotation speedon the sensitivity of bladed disks to mistuning is thenstudied. A transonic fan is considered with part span shroudsand without shrouds, respectively, constituting a high and alow blade-to-blade coupling case. For both cases, computationsare performed at rest as well as at various rotation speeds.Mistuning sensitivity is modelled as the dependence ofamplitude magnification on the standard deviation of bladestiffnesses. The finite element reduction technique based onclassical modal analysis is employed for the structuralanalysis. This reduced order model is solved for sets of randomblade stiffnesses with various standard deviations, i.e. MonteCarlo simulations. In order to reduce the sample size, thestatistical data is fitted to a Weibull (type III) parametermodel. Three different parameter estimation techniques areapplied and compared. The key role of blade-to-blade coupling,as well as the ratio of mistuning to coupling, is demonstratedfor the two cases. It is observed that mistuning sensitivityvaries significantly with rotation speed for both fans due toan associated variation in blade-to-blade coupling strength.Focusing on the effect of one specific engine order on themistuned response of the first bending modes, it is observedthat the mistuning sensitivity behaviour of the fan withoutshrouds is unaffected by rotation at its resonant condition,due to insignificant changes in coupling strength at thisspeed. The fan with shrouds, on the other hand, shows asignificantly different behaviour at rest and resonant speed,due to increased coupling under rotation. Comparing the twocases at resonant rotor speeds, the fan without shrouds is lessor equally sensitive to mistuning than the fan with shrouds inthe entire range of mistuning strengths considered. This thesis’scientific contribution centres on themistuning sensitivity study, where the effects of shrouds androtation speed are quantified for realistic bladed diskgeometries. However, also the validation of two finite elementreduction techniques against experimental measurementsconstitutes an important contribution. / NR 20140805

This dissertation presents an approach to use blade tip timing measurements with finite element analysis to predict the fatigue life of a low pressure steam turbine last stage blade under high backpressure and low flow conditions. Material fatigue properties were determined through the extended universal material law for FV566 material, along with different temper scenarios. A finite element model of a blade with damping pins was developed, using the principle of cyclic symmetry for a perfectly tuned model. Pre-stress modal analysis was conducted, incorporating damping via friction and plasticity for initial 20% overspeed test. The finite element model was verified by two experimental tests: the first being a blade impact test and the second a telemetry strain gauge test in a balance pit. Fatigue life analysis was conducted under the assumption that non-synchronous vibration is experienced by the blade and that only one mode is dominant in the vibration. The results from the fatigue analysis corresponded to the location of the cracks experienced on the blades. The results show twelve orders of magnitude lower life at low load, high backpressure conditions, compared to high load high pressure conditions. The research was further extended to check the same vibratory response on the first three modes, up to their tenth nodal diameters. This was done to analyse fatigue life in a case that a different mode was excited. / Dissertation (MEng)--University of Pretoria, 2020. / Eskom Rotek Industries / Mechanical and Aeronautical Engineering / MEng / Unrestricted

The thesis deals with the fatigue resistance of material MAR-M 247 at temperatures of 650 °C, 800 °C and 900 °C. Based on the results obtained, curves of durability ("S/N curves") were drawn and the effect of temperature on the fatigue behaviour of nickel-based superalloys MAR-M 247 and IN713 LC was evaluated. Fractographic analysis was used to examine the failure mechanism and the effect of casting defects on the fatigue crack initiation.

For many materials and components like in high speed trains and airplanes fatigue failures occur in the range of over 107 load cycles which is called the high cycle fatigue range. A modern version of the springs was invented which are applied in a certain application. Ultrasonic fatigue testing (20 kHz machine) was conducted for evaluating the steel of the springs. This research explores the fundamental understanding of high cycle fatigue testing of strip steel and assesses a stainless martensitic chromium steel at the high cycle fatigue range. Finite element modeling was conducted to gain knowledge about the effect of various parameters. Significant attention was devoted to the fatigue failure initiations by SEM/EDS. The work demonstrated that the method of investigation for high cycle fatigue test is reliable. Fatigue failure at this range was initiated by internal defects which all included non-metallic inclusion. A critical distance was defined Within the strip fatigue specimen where all the fatigue failure initiated. The 3D stress field in the specimen was determined by FEM modeling and the local applied stress at the whole of the flat part of specimen and critical distance was estimated. FEM was also employed to give additional information about the effect of parameters. It was established that damping had the largest influence. The local applied stress of the fatigue test was calculated by means of FEM and SEM analysis. It was used to adjust the S-N curve which resulted in 15% lower values than the nominal applied stress.

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Total pressure non-uniformities in an axial flow compressor can contribute to losses in aerodynamic operability through a reduction in stall margin, pressure rise and mass flow, and to loss of structural integrity through means of high cycle fatigue (HCF). HCF is a primary mechanism of blade failure caused by vibrations at levels exceeding material endurance limits. Previous research has shown total pressure distortions to be the dominant HCF driver in aero engines, and has demonstrated the damaging results of total pressure distortion induced HCF on first stage fan and compressor blade rows [Manwaring et al., 1997]. It is, however, also of interest to know how these distortion patterns propagate through a rotor stage and impact subsequent downstream stages and engine components. With current modeling techniques, total pressure distortion magnitudes can be directly correlated to induced blade vibratory levels and modes. The ability to predict downstream distortion patterns then allows for the inference of blade vibratory response of downstream blades to inlet distortion patterns. Given a total pressure distortion excitation entering a blade row, the nonlinear Volterra series can serve as a predictor of the downstream total pressure profile and therefore provide insight into the potential for HCF in downstream blade rows. This report presents the adaption of nonlinear Volterra theory to the prediction of the transport of non-uniform total pressure distortions through an axial flow compressor. The use of Volterra theory in nonlinear system modeling relies on the knowledge of Volterra kernels, which capture the behavior of a system's response characteristics. Here an empirical method is illustrated for identifying these kernels based on total pressure distortion patterns measured both upstream and downstream of a transonic rotor of modern design. A Volterra model based on these kernels has been applied to the prediction of distortion transfer at new operating points of the same rotor with promising results. Methods for improving Volterra predictions by training Volterra kernels along individual streamlines and normalizing total pressure data sets by physics-based parameters are also investigated. / Master of Science

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