Анализа века под замором оштећеног окова везе крило труп лаке летелице

Pin-loaded attachment lugs are the most responsible for wing-to-fuselage load transfer during the flight and, therefore, their structural integrity is crucial for overall aircraft safety. The potential failure of the wing-fuselage attachment lug would almost certainly result in wing loss and, subsequently, loss of life. As a result, special attention must be devoted to the fatigue design of these parts. Since lugs are the most heavily loaded components, their load-bearing capacity must be checked in accordance with recommendations defined by aviation regulations. During the service, the highest stresses are expected to occur in the region around the attachment lug’s hole; thus, potential fatigue damage could occur and spread in this area. To prevent this, materials used in the wing-fuselage attachment manufacturing are expensive high strength fatigue-resistant alloyed steels and according to Federal Aviation Administration (FAA) regulations these attachments are not the subject of experimental verifications since they are designed as safe-life components. However, some recent events in commercial aviation indicate that damages in the wing-fuselage attachment might occur quite unexpectedly. Cracks were found on the pickle forks (parts of the wingfuselage attachment of Boeing 737NG jets) with less time in service than meets the threshold for mandatory inspections. The cracking issue has led many airlines to check their airplanes and it’s reported that approximately 50 jets have been grounded worldwide in a search of a solution for this problem. Thus, numerical investigation of this kind of attachment is absolutely justified since the evaluation of aircraft safety is of the highest importance. The research presented in this thesis was based on three main steps: i) analytical evaluation of loads acting on the wing of the light aerobatic aircraft during the flight, ii) experimental analysis of real aerobatic aircraft wing under presumed loads, and iii) numerical evaluation – based on the use of the extended finite element method (XFEM) and finite element method (FEM) – of stress intensity factors (SIFs) in the case of fatigue crack occurrence in the wing-fuselage attachment lug (SIF values are the most important for fatigue life estimation). All three steps are connected since the results of one step are used in others with the ultimate goal: to achieve the best design of lugs which will significantly increase the fatigue life of damaged lug and prevent catastrophic consequences. Experimental analysis of full-scale wing was carried out for the purpose of numerical model verification. Comparisons of deformations measured and deformations calculated in FE simulations of aircraft wing deflection under load showed very good agreement, also confirming that loads acting on the wingfuselage attachment lug were accurately evaluated in the analytical step. The detailed analysis has shown that the total maximum axial force transferred to lug by pin would be Pax,max = 208,830.7 N, whereas the maximum transverse force would be Ptr,max = 20,177.3 N. Then, to demonstrate how dangerous the crack appearance could be and to estimate the residual strength and fatigue life of the cracked component, a finite element model of the actual attachment lug was made, and analyses were carried out using the maximum forces. It was assumed that due to very high stress both the corner crack and through crack may appear in the lug, i.e. that there is a possibility of damage presence which does not spread throughout the whole thickness of the lug and a possibility of the appearance of damage through the whole thickness. The idea was to compare the growth of the corner crack with the growth of the through crack, both located at the same position, and then to assess the risk of losing the integrity of wing-fuselage attachment once the crack has occurred. The calculated number of cycles to complete failure (obtained with the help of Paris law and using XFEM in Abaqus) was – as expected – low, confirming the fact that the actual attachment lugs must be redesigned using a fail-safe approach. The assessment of obtained values of a number of cycles in XFEM analysis might be a problem since the experimental data are missing; thus, classical FEM was used to evaluate the number of cycles obtained by XFEM. The same geometry was imported into Ansys Workbench and the simulation based on the use of Unstructured Mesh Method (UMM) and Separating Morphing and Adaptive Remeshing Technology (SMART) was carried out, achieving very similar results. Differences in calculated mean values of SIFs are not significant (XFEM results are somewhat higher), while the evaluated number of cycles in Ansys is close to the number obtained using XFEM. It is important to point out that – unlike the XFEM where the same mesh is used through the whole simulation – mesh around the crack front in Ansys changes and adapts with every growth step for the purpose of better capturing the field values around the crack front nodes. Finally, after completing the above-mentioned three steps, in the final phase of work alternative designs of the wing-fuselage attachment were analyzed with the goal of achieving longer fatigue life of the damaged lug (fail-safe approach). Several geometrical parameters have been changed during the redesign process with a predefined target: increase of the number of cycles until complete failure. The new proposed design of lug brings increased mass (but not a significant increase when compared to the mass of whole attachment), but significantly improved fatigue life which reduces the possibility of lug failure before the crack is observed in regular maintenance inspections.Ушке окова са носећом осовиницом најодговорније су за пренос оптерећења са крила на труп током лета, па је њихов структурни интегритет кључан за укупну безбедност летелице. Потенцијални лом ушки окова везе крило-труп скоро сигурно би резултирао губитком крила и, последично, губитком живота путника. Због тога се посебна пажња мора посветити пројектовању ових елемената са аспекта лома услед замора. С обзиром да су ушке најоптерећенији делови окова, њихова носивост се мора проверити у складу са препорукама дефинисаним ваздухопловним прописима. Очекује се да ће током радног века доћи до појаве великих напрезања у области око отвора ушки; стога би се у овом подручју могле појавити и проширити прслине као резултат замора материјала. Да би се то спречило, материјали који се користе у производњи окова везе крило-труп јесу легирани челици високе чврстоће отпорни на замор и према прописима Федералне управе за ваздухопловство (ФАА) окови нису предмет експерименталних провера јер се пројектују као тзв. safe-life компоненте на којима током века није дозвољена појава било каквог оштећења. Међутим, неки недавни догађаји у комерцијалном ваздухопловству указују на то да би оштећења на вези крило-труп могла настати сасвим неочекивано. Откривене су прслине на тзв. носећим виљушкама (деловима везе крило-труп трупа авиона Boeing 737NG) пре времена предвиђеног за обавезни преглед овог склопа. Проблем уочених прслина навео је многе авио компаније да провере своје авионе и око 50 млазних летелица приземљено је широм света у потрази за решењем проблема. Стога је нумеричко истраживање ове врсте везе апсолутно оправдано јер је процена безбедности кључних делова авиона од највећег значаја за сигурност летелице и путника. Истраживање представљено у овој тези засновано је на три основна корака: 1) аналитичкој процени оптерећења која делују на крило лаког акробатског авиона током лета, 2) експерименталној анализи реалног крила акробатског авиона изложеног претпостављеним оптерећењима, и 3) нумеричкој процени – заснованој на употреби проширене методе коначних елемената (ПМКЕ) и методе коначних елемената (МКЕ) – фактора интензитета напона (ФИН) у случају појаве заморне прслине на ушкама окова везе крило-труп (правилно израчунате вредности ФИН-а најважније су за добру процену века елемента изложеног замору). Ова три корака су повезана јер се резултати из једног користе у другим с јасним циљем: остварити најбољи дизајн ушки који ће значајно повећати њихов век под замором кад се појави прслина и тиме спречити катастрофалне последице. У циљу верификације нумеричког модела извршена је експериментална анализа крила у пуној величини. Поређења измерених деформација и израчунатих деформација у МКЕ симулацијама угиба крила авиона под оптерећењем, показала су веома добро слагање, потврђујући да су оптерећења која делују на ушку окова везе крило-труп добро процењена у аналитичком кораку. Детаљна анализа је показала да би укупна максимална аксијална сила пренета на ушку преко осовинице била Pax,max = 208,830.7 N, док би максимална трансверзална сила била Ptr,max = 20,177.3 N. Затим, како би се проучило колико би појава прслине могла бити опасна и како би се проценила преостала чврстоћа и век трајања под замором оштећене компоненте, направљен је модел коначних елемената ушке окова и спроведене су анализе коришћењем максимални вредности сила. Претпостављено је да се због врло великог напрезања на ушки могу појавити и угаона и продорна прслина, односно да постоји могућност појаве оштећења које не иде по целој дебљини ушке и могућност појаве оштећења по целој дебљини. Идеја је била да се упореди раст угаоне прслине са растом продорне (дубинске) прслине, обе смештене на истој позицији, а затим да се процени ризик од губитка интегритета окова везе када дође до појаве оштећења. Израчунати број циклуса до потпуног лома (добијен помоћу Парисовог закона коришћењем ПМКЕ у Abaqus-у) био је очекивано низак, што потврђује чињеницу да се пројектоване ушке окова морају редизајнирати коришћењем тзв. fail-safe приступа који дозвољава појаву и раст прслине до одређене дужине. Процена добијеног броја циклуса коришћењем ПМКЕ може представљати проблем јер не постоје експериментални подаци о расту прслина на оковима; стога је класична МКЕ коришћена за процену броја циклуса добијених у Abaqus-у. Иста геометрија је увезена у Ansys Workbench и извршена је нумеричка симулација заснована на коришћењу методе неструктуриране мреже (МНМ) и SMART технологије инкорпориране у Ansys Workbench: добијени су врло слични резултати онима из Abaqus-а. Разлике у израчунатим средњим вредностима ФИН-ова нису биле значајне (вредности добијене коришћењем ПМКЕ су нешто више), док је процењени број циклуса у Ansys-у близу броја циклуса добијеног у Abaqus-у. Важно је истаћи да се – за разлику од ПМКЕ где се иста мрежа користи током целе симулације – мрежа око фронта прслине у Ansys-у мења и прилагођава са сваким кораком раста у сврху бољег „хватања“ вредности поља око чворова мреже у близини фронта прслине. Коначно, након што су завршена сва три корака, у завршној фази рада анализирани су алтернативни облици ушке окова везе крило-труп са циљем да се постигне дужи век трајања оштећене ушке коришћењем fail-safe приступа. Неколико геометријских параметара је варирано током процеса редизајна са унапред дефинисаним циљем: повећати број циклуса до потпуног лома услед замора. Нови предложени дизајн ушке доноси повећану масу (али не и значајно повећану у поређењу са масом читавог окова), али и значајно побољшан век под замором што смањује могућност потпуног лома ушки пре него што се оштећење примети у редовним прегледима као делу одржавања летелице

SHAPE DESIGN SENSITIVITY ANALYSIS AND OPTIMIZATION FOR 2-D STRUCTURAL COMPONENTS UNDER MIXED MODE FRACTURE USING EXTENDED FINITE ELEMENT METHOD AND LEVEL SET METHOD

Weight and service life are often the two most important considerations in the design of structural components. This research incorporates a novel crack propagation analysis technique into shape optimization framework to support design of 2-D structural components under mixed-mode fracture for: (i) maximum service life subject to an upper limit on weight, and (ii) minimum weight subject to specified minimum service life. In both cases, structural performance measures are selected as constraints and CAD dimensions are employed as shape design variables. Fracture parameters, such as crack growth rate and crack growth direction are computed using extended finite element method (XFEM) and level set method (LSM).XFEM is a computational technique in which special enrichment functions are used to incorporate the discontinuity of structural responses caused by crack surfaces and crack tip fields into finite element approximation. The LSM employs level set functions to track the crack during the crack propagation analysis. As a result, this method does not require highly refined mesh around the crack tip nor re-mesh to conform to the geometric shape of the crack when it propagates, which makes the method extremely attractive for crack propagation analysis.However, shape sensitivity analysis for crack propagation involves calculating derivatives of enrichment functions employed in XFEM that are discontinuous or unsmooth. The proposed sensitivity analysis method in this study overcomes these issues and calculates accurate derivatives of both crack growth rate and direction with respect to design variables. The proposed method employs (i) semi-analytical method for the derivatives of stresses and displacements, and (ii) material derivatives for the SIFs obtained from the domain form of the interaction integral, and therefore, the crack growth rate and direction. The method enables computation of sensitivity coefficients of fracture parameters for a growing crack and is up to 40% faster than the commonly used finite-difference method.Two different optimization approaches--a batch-mode, gradient-based, nonlinear optimization and an interactive what-if analysis--are used for optimization. An engine connecting rod example is used to demonstrate the feasibility and accuracy of the proposed method. The design optimization process can successfully handle arbitrary 2-D geometries and can solve general design problems that are most commonly encountered, such as design for maximum life and design for minimum weight

Numerical analysis of fatigue crack growth in welded joints with multiple defects

In the case of welded steel structures (such as pressure equipment), welded joints are often critical location for stress concentrations, due to different mechanical properties and chemical composition compared to the parent material, and due to changes in geometry. In addition, the presence of imperfections (defects) in welded joints can contribute to the increase in local stress, resulting in crack initiation. Recently, standards that are related to acceptable dimensions of various types of defects in welded joints started taking fatigue loading into account as well. For the purpose of this research, a 3D numerical model was made, of a welded joint with different types of defects (linear misalignment and a crack in the weld metal), based on the previous work, which involved static loading of the same specimen. In this case, fatigue was taken into account, and the simulation was performed using ABAQUS software, as well as Morfeo, an add-on used for determining the fatigue behaviour of structures via XFEM (extended finite element method). The welded joint was made using steel P460NL1 as the parent material, and EPP2NiMo2 wire was used for the weld metal. An additional model was made, whose defects included a crack and an overhang. Fatigue crack growth analysis was performed for this model as well, and the results for stress intensity factors and stress/strain distribution were compared in order to obtain information about how different defects can affect the integrity of a welded joint

The influence of oxide deposits on the remaining life and integrity of pressure vessels equipment

In this paper is presented the principle of application of fracture mechanics parameters in determining the integrity of rotary equipment. The behavior of rotary equipment depends on presence of cracks and basically determines the integrity and life of such equipment. The locations of stress concentration (i.e. radius changes) represent a particular problem in rotary equipment, and they are the most suitable places for the occurrence of microcracks i.e. cracks due to fatigue load. This problem is most common in the shaft of relatively large dimensions, for example, turbine shafts in hydropower plants made of high-strength carbon steel with relatively low fracture toughness, and relatively low resistance to crack formation and growth. Having in mind that rotary equipment represents the great risk in the exploitation, whose occasional failures often had severe consequences, it is necessary detail study of their integrity. For this purpose, it is necessary application of parameters of linear-elastic fracture mechanics, such as stress intensity factor, which range defines the rate of crack growth (Parisian law), and its critical value (fracture toughness) determines the critical crack length. The procedures for determining the critical crack length will be described using the fracture mechanics parameters

Using the fracture mechanics parameters in assessment of integrity of rotary equipment

In this paper is presented the principle of application of fracture mechanics parameters in determining the integrity of rotary equipment. The behavior of rotary equipment depends on presence of cracks and basically determines the integrity and life of such equipment. The locations of stress concentration (i.e. radius changes) represent a particular problem in rotary equipment, and they are the most suitable places for the occurrence of microcracks i.e. cracks due to fatigue load. This problem is most common in the shaft of relatively large dimensions, for example, turbine shafts in hydropower plants made of high-strength carbon steel with relatively low fracture toughness, and relatively low resistance to crack formation and growth. Having in mind that rotary equipment represents the great risk in the exploitation, whose occasional failures often had severe consequences, it is necessary detail study of their integrity. For this purpose, it is necessary application of parameters of linear-elastic fracture mechanics, such as stress intensity factor, which range defines the rate of crack growth (Parisian law), and its critical value (fracture toughness) determines the critical crack length. The procedures for determining the critical crack length will be described using the fracture mechanics parameters

Mathematical Modeling and Simulation in Mechanics and Dynamic Systems

The present book contains the 16 papers accepted and published in the Special Issue “Mathematical Modeling and Simulation in Mechanics and Dynamic Systems” of the MDPI “Mathematics” journal, which cover a wide range of topics connected to the theory and applications of Modeling and Simulation of Dynamic Systems in different field. These topics include, among others, methods to model and simulate mechanical system in real engineering. It is hopped that the book will find interest and be useful for those working in the area of Modeling and Simulation of the Dynamic Systems, as well as for those with the proper mathematical background and willing to become familiar with recent advances in Dynamic Systems, which has nowadays entered almost all sectors of human life and activity

Towards a hybrid approach for diagnostics and prognostics of planetary gearboxes

The reliable operation of planetary gearboxes is critical for the sustained operation of many machines such as wind turbines and helicopter transmissions. Hybrid methods that make use of the respective advantages of physics-based and data-driven models can be valuable in addressing the unique challenges associated with the condition monitoring of planetary gearboxes. In this dissertation, a hybrid framework for diagnostics and prognostics of planetary gearboxes is proposed. The proposed framework aims to diagnose and predict the root crack length in a planet gear tooth from accelerometer measurements. Physics-based and data-driven models are combined to exploit their respective advantages, and it is assumed that no failure data is available for training these models. Components required for the implementation of the proposed framework are studied separately and challenges associated with each component are discussed. The proposed hybrid framework comprises a health state estimation and health state prediction part. In the health state estimation part of the proposed framework, the crack length is diagnosed from the measured vibration response. To do this, the following model components are implemented: A first finite element model is used to simulate the crack growth path in the planet gear tooth. Thereafter, a second finite element model is used to establish a relationship between the gearbox time varying mesh stiffness, and the crack length in the planet gear tooth. A lumped mass model is then used to model the vibration response of the gearbox housing subject to the gearbox time varying mesh stiffness excitation. The measurements from an accelerometer mounted on the gearbox housing are processed by computing the synchronous average. Finally, these model components are combined with an additional data-driven model for diagnosing the crack length from the measured vibration response through the solution of an inverse problem. After the crack length is diagnosed through the health state estimation model, the Paris crack propagation law and Bayesian state estimation techniques are used to predict the remaining useful life of the gearbox. To validate the proposed hybrid framework, an experimental setup is developed. The experimental setup allows for the measurement of the vibration response of a planetary gearbox with different tooth root crack lengths in the planet gear. However, challenges in reliably detecting the damage in the experimental setup lead to the use of simulated data for studying the respective components of the hybrid method. Studies conducted using simulated data highlighted interesting challenges that need to be overcome before a hybrid diagnostics and prognostics framework for planetary gearboxes can be applied in practice.Dissertation (MSc)--University of Pretoria, 2021.Eskom EPPEIMechanical and Aeronautical EngineeringMscUnrestricte

Experimental determination of mechanical properties of cylindrical samples made by additive technology

This paper presents experimental results in determining the mechanical properties of cylindrical samples made by additive technology. In the past, additive technologies were used only for prototypes. Today, they are actively involved in the production, especially in the case of small series or parts with special geometric and mechanical requirements—the tested samples were cylindrical and printed on a printer German Rep Rap X400 (It is important to note that, during the test, the samples were not treated with acetone). The German Rep Rap X400 is an Industrial Quality 3D Printer with high precision, speed and printing volume. The test was performed in the control of displacement at a speed of 1 [mm/min], while the layer's height was 0.2 [mm]. The substrate temperature was 100oC, while the nozzle temperature was 245oC. The results presented in this paper can be used and are repeatable in practice and in further research

Experimental determination of mechanical properties of cylindrical samples made by additive technology

This paper presents experimental results in determining the mechanical properties of cylindrical samples made by additive technology. In the past, additive technologies were used only for prototypes. Today, they are actively involved in the production, especially in the case of small series or parts with special geometric and mechanical requirements—the tested samples were cylindrical and printed on a printer German Rep Rap X400 (It is important to note that, during the test, the samples were not treated with acetone). The German Rep Rap X400 is an Industrial Quality 3D Printer with high precision, speed and printing volume. The test was performed in the control of displacement at a speed of 1 [mm/min], while the layer's height was 0.2 [mm]. The substrate temperature was 100oC, while the nozzle temperature was 245oC. The results presented in this paper can be used and are repeatable in practice and in further research

Prédiction numérique de la durée de vie en fatigue de structures complexes de véhicules en aluminium

Le sujet du présent ouvrage consiste à développer une méthodologie de prédiction de la résistance en fatigue de structures complexes. Il est donc ici question d’évaluer les performances en fatigue de joints rivetés (rivet aveugle) et de joints soudés au laser à simple recouvrement de manière expérimentale et de simuler leur comportement de manière numérique. Lors de la fabrication d’un châssis d’un véhicule motorisé, plusieurs méthodes d’assemblages sont utilisées. Il est donc essentiel de connaître les limites en fatigue des assemblages fabriqués par ces méthodes, puisque les faiblesses d’une structure se situent généralement aux joints entre les divers composants de la structure complexe. Le fait d’être en mesure de prédire numériquement la durée de vie d’un assemblage complexe est d’une grande utilité pour les concepteurs, puisque cela permet de corriger tout éventuel problème lié à ce mode de bris lors de la conception du véhicule. Ceci permet également de s’assurer que celui-ci se conforme aux exigences mécaniques prescrites par la conception. Pour ce faire, plusieurs essais mécaniques comme l’essai de traction et des essais de fatigue ont été effectués afin d’évaluer les propriétés mécaniques des assemblages choisis sous des chargements monotones et dynamiques et de caractériser leur comportement en fatigue. Afin d’évaluer les performances en fatigue des joints, la technologie de détection de l’endommagement par émissions acoustiques (EA) est utilisée pour détecter l’initiation de la fissuration des échantillons. Ces données ont ensuite permis l’établissement de courbes de fatigue et modèles numériques pour ces méthodes d’assemblage. Afin d’obtenir un modèle se collant le plus possible à la réalité, l’influence du choix de plusieurs paramètres, comme l’approche de modélisation des joints ainsi que la façon d’évaluer les contraintes ont été étudiées. En outre, il est question de développer des méthodes de modélisation simples offrant le meilleur compromis entre la précision des résultats et la rapidité d’exécution. Pour atteindre cet objectif, la méthode de la contrainte structurale est utilisée conjointement au modèle probabiliste de Stüssi pour tracer les courbes de fatigue. Ces courbes sont ensuite combinées à un modèle d’éléments finis statique linéaire pour établir les modèles de prédiction numérique de la durée de vie en fatigue de structures complexes. Par la suite, les modèles développés sont utilisés pour prédire la durée de vie de plusieurs assemblages complexes soumis à des chargements à amplitudes variables. Les modèles retenus sont ici comparés aux résultats des essais expérimentaux réalisés sur ces assemblages afin de définir la méthodologie la plus prometteuse. De plus, plusieurs techniques permettant de traiter les chargements à amplitudes variables sont comparées afin de vérifier si l’ajout de certaines complexités aux modèles de prédiction, comme l’interaction entre les cycles de chargement et la chronologie du chargement, est pertinent. Bref, les travaux réalisés dans le cadre de ce projet de recherche ont permis de développer une méthodologie pertinente pour évaluer la durée de vie de structures rivetées ou soudées complexes soumises à des chargements à amplitudes variables