<p>Rolling contact fatigue (RCF) is a common cause of failure in tribological machine components such as rolling-element bearings (REBs). Steels selected for RCF applications are subject to various material processes in order to produce martensitic microstructures. An effect of such material processing is the retention of the austenitic phase within the steel microstructure. Retained austenite (RA) transformation in martensitic steels subjected to RCF is a well-established phenomenon. In this investigation, a novel approach is developed to predict martensitic transformations of RA in steels subjected to RCF. A criteria for phase transformations is developed by comparing the required thermodynamic driving force for transformations to the energy dissipation in the microstructure. The method combines principles from phase transformations in solids with a damage mechanics framework to calculate energy availability for transformations. The modeling is then extended to incorporate material alterations as a result of RA transforming within the material. A continuum damage mechanics (CDM) FEM simulation is used to capture material deterioration, phase transformations, and the formation of internal stresses as a result of RCF. Crystal lattice orientation is included to modify energy requirements for RA transformation. Damage laws are modified to consider residual stresses and different components of the stress state as the drivers of energy dissipation. The resulting model is capable of capturing microstructural evolution during RCF.</p> <p>The development and stability of internal stresses caused by RA transformation in bearing steel material was experimentally investigated. Specimens of 8620 case carburized steel were subjected to torsional fatigue at specific stress levels for a prescribed number of cycles. X-ray diffraction techniques were used to measure residual stress and RA volume fraction as a function of depth in the material. A model is set forth to predict compressive residual stress in the material as a function of RA transformation and material relaxation. Modeling results are corroborated with experimental data. In addition, varying levels of retained austenite (RA) were achieved through varying undercooling severity in uniformly treated case carburized 8620 steel. Specimens were characterized via XRD and EBSD techniques to determine RA volume fraction and material characteristics prior to rolling contact fatigue (RCF). Higher RA volume fractions did not lead to improvement in RCF lives. XRD measurements after RCF testing indicated that little RA decomposition had occurred during RCF. The previously established RCF simulations were modified to investigate the effects of RA stability on RCF. The results obtained from the CDM FEM captured similar behavior observed in the experimental results. Utilizing the developed model, a parametric study was undertaken to examine the effects of RA quantity, RA stability, and applied pressure on RCF performance. The study demonstrates that the energy requirements to transform the RA phase is critical to RCF performance.</p>

<p dir="ltr">Rolling contact fatigue (RCF) is one of the leading causes of failure in critical tribological components such as rolling element bearings (REBs), gears, cam and followers, etc. This is especially paramount for advanced aerospace applications where REB components need to operate for billions of RCF cycles before routine maintenance or inspection is performed. The rolling motion between the rolling elements and raceway produces RCF, wherein a complex, non-proportional, alternating contract stress is applied over a small material volume. Moreover, the highly localized stress occurs on the same length scale as microstructural features such as carbides, inclusions, grain size, hardness gradients from carburization, surface roughness, thereby amplifying their effect on fatigue performance. Therefore, the objective of this dissertation is to investigate critical microstructural modifications and their effects on RCF performance via experiments and computational modeling.</p><p dir="ltr">Initially, an investigation was undertaken to investigate surface roughness effects on RCF. The surface roughness of various REBs was measured through optical surface profilometry and used to construct rough surface pressure distributions, which were then used in a continuum damage mechanics (CDM) finite element (FE) framework. The results demonstrated that life is reduced as lambda ratio decreases. It was also observed that a 2-parameter Weibull cumulative distribution function can describe the relationship between the near surface orthogonal shear stress concentration and ratio of surface failures.</p><p dir="ltr">Next, the enhancement to RCF life from grain size refinement of through hardened bearing steels was studied. To capture the effects of grain refinement, torsion stress-life data of various grain size were used in the RCF model. A predictive life equation for different grain sizes was constructed based on the exponential trend observed between grain size and life from the simulation data. The life equation was then used to calculate the quotient of RCF at two different grain sizes. This quotient was defined as the life improvement ratio and it was observed that this investigation’s ratios compared well with existing life improvement ratios from RCF experiments.</p><p dir="ltr">Hardness gradient is a common microstructural modification to improve RCF life of tribo-components. Variation of hardness gradients is prevalent in case hardened (i.e. case carburized) bearing materials. Therefore, the CDM-FE RCF model was modified to investigate the effects of various hardness gradient types and depths on fatigue life improvement. The simulation results enabled the identification of potentially optimal gradients aimed to mitigate manufacturing challenges and provided the foundation for the construction of a general fatigue life equation.</p><p dir="ltr">A fundamental study to understand the impact various common RCF failure criteria have on RCF life estimation was then conducted using computational modeling. To capture the variation of a material’s resistance to fatigue, the critical CDM damage parameters were assumed to follow a probabilistic distribution instead of a singular value. The CDM-FE model was modified to consider the shear reversal, the octahedral shear stress, the maximum shear stress, the Fatemi-Socie criteria, and the Dang Van multi-axial fatigue parameter as failure criteria. Simulation life results revealed that the CDM-FE model with shear reversal and Fatemi-Socie criteria best match empirical predictions from well-established RCF life theory. Notably, the Fatemi-Socie exhibited the best agreement over all operating conditions.</p><p dir="ltr">The next investigation focused on the cleanliness of aerospace-quality bearing steels. Torsion fatigue experiments established the stress-life (S-N) relation for three common aerospace quality bearing steels. The S-N data was later used to calibrate the RCF model’s damage equation, which considered the Fatemi-Socie criteria following conclusions from a previous investigation. Simulation results were observed to corroborate well with RCF experiments that were conducted for all three materials, while noting the simulations offered a significant time saving. As a result, a subsequent investigation focused on establishing the stress-life relationship for one of the aerospace quality bearing steels through a combined experimental and analytical approach. Good corroboration was observed between simulations and experiments at three contact pressures. This finding is particularly significant as it strengthens the reliability of computational RCF model as an efficient means to assess the RCF performance of bearing materials.</p><p dir="ltr">Furthermore, the detailed investigation on RCF performance of each critical microstructural modifications and their respective effect greatly improves the state-of-the-art. The findings emanating from the various investigations offer informed fatigue design recommendations that aid in the selection of rolling element bearings for critical tribological and aerospace applications.</p>

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The goal of this research is developing a computational framework to study mechanical fatigue and fracture at different length scales for a broad range of materials. The developed multiscale framework is utilized to study the details of fracture and fatigue for the rolling contact in rails, additively manufactured alloys, and bio-inspired hierarchical materials. Rolling contact fatigue (RCF) is a major source of failure and a dominant cause of maintenance and replacements in many railways around the world. The highly-localized stress in a relatively small contact area at the wheel-rail interface promotes micro-crack initiation and propagation near the surface of the rail. 2D and 3D microstructural-based computational frameworks are developed for studying the rolling contact fatigue in rail materials. The method can predict RCF life and simulate crack initiation sites under various conditions. The results obtained from studying RCF behavior in different conditions will help better maintenance of the railways and increase the safety of trains. The developed framework is employed to study the fracture and fatigue behavior in 3D printed metallic alloys fabricated by selective laser melting (SLM) method. SLM method as a part of metal additive manufacturing (AM) technologies is revolutionizing the manufacturing sector and is being utilized across a diverse array of industries, including biomedical, automotive, aerospace, energy, consumer goods, and many others. Since experiments on 3D printed alloys are considerably time-consuming and expensive, computational analysis is a proper alternative to reduce cost and time. In this research, a computational framework is developed to study fracture and fatigue in different scales in 3D printed alloys fabricated by the SLM method. Our method for studying the fatigue at the microstructural level of 3D printed alloys is pioneering with no similar work being available in the literature. Our studies can be used as a first step toward establishing comprehensive numerical frameworks to investigate fracture and fatigue behavior of 3D metallic devices with complex geometries, fabricated by 3D printing. Composite materials are fabricated by combining the attractive mechanical properties of materials into one system. A combination of materials with different mechanical properties, size, geometry, and order of different phases can lead to fabricating a new material with a wide range of properties. A fundamental problem in engineering is how to find the design that exhibits the best combination of these properties. Biological composites like bone, nacre, and teeth attracted much attention among the researchers. These materials are constructed from simple building blocks and show an uncommon combination of high strength and toughness. By inspiring from simple building blocks in bio-inspired materials, we have simulated fracture behavior of a pre-designed composite material consisting of soft and stiff building blocks. The results show a better performance of bio-inspired composites compared to their building blocks. Furthermore, an optimization methodology is implemented into the designing the bio-inspired composites for the first time, which enables us to perform the bio-inspired material design with the target of finding the most efficient geometries that can resist defects in their structure. This study can be used as an effective reference for creating damage-tolerant structures with improved mechanical behavior. / Doctor of Philosophy / The goal of this research is developing a multiscale framework to study the details of fracture and fatigue for the rolling contact in rails, additively manufactured alloys, and bio-inspired hierarchical materials. Rolling contact fatigue (RCF) is a major source of failure and a dominant cause of maintenance and replacements in many railways around the world. Different computational models are developed for studying rolling contact fatigue in rail materials. The method can predict RCF life and simulate crack initiation sites under various conditions and the results will help better maintenance of the railways and increase the safety of trains. The developed model is employed to study the fracture and fatigue behavior in 3D printed metals created by the selective laser melting (SLM) method. SLM method as a part of metal additive manufacturing (AM) technologies is revolutionizing industries including biomedical, automotive, aerospace, energy, and many others. Since experiments on 3D printed metals are considerably time-consuming and expensive, computational analysis is a proper alternative to reduce cost and time. Our method for studying the fatigue at the microstructural level of 3D printed alloys can help to create more fatigue and fracture resistant materials. In the last section, we have studied fracture behavior in bio-inspired materials. A fundamental problem in engineering is how to find the design that exhibits the best combination of mechanical properties. Biological materials like bone, nacre, and teeth are constructed from simple building blocks and show a surprising combination of high strength and toughness. By inspiring from these materials, we have simulated fracture behavior of a pre-designed composite material consisting of soft and stiff building blocks. The results show a better performance of bio-inspired structure compared to its building blocks. Furthermore, an optimization method is implemented into the designing the bio-inspired structures for the first time, which enables us to perform the bio-inspired material design with the target of finding the most efficient geometries that can resist defects in their structure.

Esse trabalho descreve o projeto e construção de um equipamento destinado ao estudo de fadiga de contato de rolamento e sua posterior aplicação na caracterização de ferros fundidos. O trabalho foi iniciado com a utilização de um equipamento previamente existente no Laboratório de Fenômenos de Superfície da EPUSP, a máquina I. Esse equipamento era baseado na substituição das pistas externas de um rolamento axial de esferas por corpos de prova na forma de arruelas. Ensaios preliminares mostraram que a máquina I apresentava limitações, a principal delas era não ser capaz de reproduzir integralmente o movimento de rolamento, havendo uma relação desconhecida rolamento/deslizamento no decorrer do ensaio. Com base nas dificuldades operacionais da máquina I, uma segunda máquina, também baseada em um rolamento axial, foi projetada e construída. Ensaios preliminares mostraram que o novo equipamento reproduzia mecanismos de falha por fadiga de contato de rolamento. A etapa seguinte então foi utilizar a máquina II no estudo de fadiga de contato de rolamento de dois tipos de ferro fundido com matrizes de levada dureza, um cinzento e um nodular, os quais foram testados em duas condições: com e sem pré-tensionamento e analisados segundo a estatística de Weibull. Um aço também foi ensaiado como referência. A pré-tensão foi aplicada com uma ferramenta bi-partida e modelada por elementos finitos. Foram realizados ensaios lubrificados, com a aplicação de uma pressão máxima de contato de 3,6 GPa e conduzidos até a falha dos materiais por lascamento da superfície de rolamento. Em todas as condições de ensaio o ferro fundido nodular se mostrou muito superior ao ferro cinzento. Enquanto esse último que apresentou resultados similares na condição com e sem pré-tensão, o ferro fundido nodular teve a sua curva de distribuição de falhas significativamente alterada pela aplicação de tensão externa. Uma heterogeneidade na distribuição do tamanho de nódulos de grafita fez com que as falhas ocorressem sempre na mesma região do corpo-deprova evidenciando a sensibilidade do ensaio a variáveis microestruturais. / This work presents design and construction of an equipment for rolling contact fatigue studying and its use to cast irons analysis. Firstly it was used an equipment available at Surface Phenomena Laboratory, in São Paulo University, which was called machine I. The design of the system followed the well-known architecture where races of a thrust ball bearing are substituted by washers made with the material under investigation. Preliminary tests have shown that the first machine had severe limitations, but the most important was lack of ability to reproduce rolling contact fatigue mechanisms. An unknown sliding/rolling ratio always took place in its work. Then a second machine was designed and assembled. Sets up tests have shown typical mechanisms of rolling contact fatigue. The next step was to use the new machine to study two types of cast irons, a gray iron and a ductile iron, under two test conditions: with and without pre-stress. Also a steel specimen was tested as a reference. Results were subjected to Weibull analysis. A device was developed for pre-stress application, and the specimen/device system was modeled by finite elements analysis. Tests were carried out till failure, under lubrication, and with maximum contact pressure of 3.6 GPa. Ductile cast iron behavior was superior to gray iron in all tests. Gray iron specimens with and without pre-stress presented very similar results. On the other hand, ductile iron probability failure curve was strongly affected by pre-stress. An unexpected heterogeneity on graphite nodules size distribution promoted failures on just one region, which is an evidence of test sensitivity to micro structural changes.

In this thesis, the behavior of pearlitic steel was characterized under controlled wear conditions in the laboratory and service conditions in two ore mining stages, comminution and transportation. The thesis consists in three experimental chapters, divided according to the tribosystems analyzed. On all the chapters Electro Microscopy techniques for the microstructural analysis were employed. Scanning Electron Microscopy (SEM), Focused Ion Beam (FIB-SEM), Electron Backscatter Diffraction (EBSD) and Transmission Electron Microscopy (TEM) were used. The first experimental chapter shows the analysis of the pearlite under abrasive wear with loose abrasive particles in multi-events conditions. The sample was taken from Semi-Autogenous Grinding mills (SAG) and experimental simulation was carried out in laboratory using the Dry Sand Rubber Wheel Abrasion Test (DSRW). The results show a polycrystalline layer formation in both cases, characterized by ultra-fine grains of ferrite in the layer closer to the surface. It was also concluded that the DSRW can simulate the wear produced on field (superficial and microstructural features) in conditions of higher normal load than recommended by the ASTM Standard G65. The second experimental chapter explores the characterization of the microstructure after the indenter pass in scratch test using two conditions of normal load applied and five sequences of scratch. The microstructural analysis shows the formation of two subsuperficial layers identified by the level of the microstructural alterations. In the subsuperficial layer (close to the surface), the formation of new ultra-fine grains of ferrite was observed. A second layer was observed deeper in the sample and denominated as layer of the microstructure transition, characterized by the combination of deformed (reduction of the interlamellar spacing) and pearlite colonies not affected plastically by the mechanical loading. On this layer, the crystallographic texture in RD // in samples tested at 4 N (normal load) and one-pass scratch was determined. Later, on this chapter, the microstructure in a ground rail (industrial procedure characterized as a multi-event scratch test) was analyzed. Two grinding conditions were used for the analysis with variation of the grinding linear speed and load on the grinding stones (discs). The combination of low grinding speed and high load promotes a higher deformed layer formation beneath the patch zone and low randomized orientation of the pearlite colonies. Finally, in the third experimental chapter, the pearlitic characterization was concluded with the study of samples of railway wheel and rail under wear in service and Rolling Contact Fatigue (RCF) in laboratory. The laboratorial simulation was carried out using the twin-disc rolling contact tribometer with a variation of number of cycles. The characterization of railway wheel shows that the WEL is characterized by levels of breaking and aligned cementite and zones with dissolution of the carbon atom in the ferrite to form the supersaturated carbon ferrite. The polycrystalline ferrite formation (ultra-fine grains) in the sub-superficial layer and it was identified a preferential orientation of RD // in the layer of microstructural transition. The results of the laboratory test show surface crack nucleation and propagation at low angle in the more severe deformed layer. The microstructure of the layer consists in polycrystalline ferrite and the cementite dissolution. / Nesta tese foi caracterizado o comportamento do aço perlítico em condições controladas de desgaste em laboratório e em serviço em dois estágios do processo de mineração de minério, cominução e transporte ferroviário. A tese consiste em três capítulos experimentais divididos segundo o tribosistema analisado. Em todos os capítulos do trabalho foi utilizada a técnica de microscopia eletrônica para análise microestrutural. Foi utilizado Microscopia eletrônica de varredura (MEV), Focused Ion Beam (FIB-SEM), Electron Backscatter Diffraction (EBSD) e Microscopia eletrônica de transmissão (MET). O primeiro capítulo experimental mostra a análise da perlita in condições de desgaste abrasivo com partículas soltas em eventos múltiplos. As amostras foram tiradas de um moinho semi-autógeno (SAG) e realizada uma simulação experimental do desgaste em condições controladas usando o tribômetro de roda de borracha (RWAT). Os resultados mostraram a formação de camada branca em ambas as condições de análise, consistindo em uma camada poli cristalina caracterizada pela formação de grãos ultrafinos na camada mais próxima da superfície de desgaste. Também foi concluído que a roda de borracha pode simular o desgaste produzido nos moinhos SAG tanto nas características superficiais quanto microestruturais em condições de maior severidade as comumente utilizadas na norma ASTM G65 (procedimento B). O Segundo capítulo experimental explora a caracterização da microestrutura depois da passagem do endentador no ensaio de riscamento (scratch test) utilizando duas condições de carga normal aplicada e 5 sequências de riscamento. A análise microestrutural mostrou a formação de duas camadas subsuperficiais identificadas pelo nível de alteração microestrutural. Na camada mais próxima da superfície de desgaste foi observada a formação de grãos ultrafinos de ferrita. A segunda camada identificada mais profundamente na amostra, denominada como camada de transição, é caracterizada pela combinação de colônias deformadas (redução do espaçamento interlamelar) e camadas não afetadas pelos esforços produzidos no contato. Nesta camada foi determinada a texturização em direção RD // nas amostras testadas a 4 N (carga normal aplicada) e uma passada. Posteriormente à análise de riscamento foi caracterizada a microestrutura de uma amostra tirada de um trilho esmerilhado (processo industrial que pode ser considerado como aplicação do ensaio de riscamento). Foram consideradas duas condições de esmerilhamento com variação de velocidade de esmerilhamento (deslocamento linear do veículo esmerilhador) e potência dos motores dos rebolos usada no procedimento. A combinação de baixa velocidade de esmerilhamento e alta potência nos motores controladores dos rebolos promoveu uma grande deformação nas camadas subsuperficiais na região de contato e uma baixa aleatoriedade das orientações cristalográficas das colônias de perlita. Finalmente, no capítulo três, a caracterização da microestrutura perlitica foi finalizada com o estudo de amostras de roda e trilho em condições de desgaste em campo e de Rolling Contact Fatigue (RCF) em ensaios de laboratório. A simulação experimental foi realizada utilizando o tribômetro twin-disc rolling (configuração disco-disco) com variação do número de ciclos. A caracterização da roda ferroviária mostrou a formação da camada branca caracterizada por níveis de cementita fraturada e alinhada em direção do movimento de rolamento/deslizamento com áreas de dissolução do átomo de carbono na ferrita formando uma ferrita supersaturada. Foi identificado a formação de policristais de ferrita (grãos ultrafinos) na camada mais superficial e uma orientação preferencial RD // na camada de transição. Os resultados dos ensaios de laboratório mostraram a nucleação de trincas superficiais se propagando a baixo ângulo na camada branca. A transformação microestrutural dessa camada após ensaios de laboratório consiste em policristais de ferrita e dissolução da cementita.

Esse trabalho descreve o projeto e construção de um equipamento destinado ao estudo de fadiga de contato de rolamento e sua posterior aplicação na caracterização de ferros fundidos. O trabalho foi iniciado com a utilização de um equipamento previamente existente no Laboratório de Fenômenos de Superfície da EPUSP, a máquina I. Esse equipamento era baseado na substituição das pistas externas de um rolamento axial de esferas por corpos de prova na forma de arruelas. Ensaios preliminares mostraram que a máquina I apresentava limitações, a principal delas era não ser capaz de reproduzir integralmente o movimento de rolamento, havendo uma relação desconhecida rolamento/deslizamento no decorrer do ensaio. Com base nas dificuldades operacionais da máquina I, uma segunda máquina, também baseada em um rolamento axial, foi projetada e construída. Ensaios preliminares mostraram que o novo equipamento reproduzia mecanismos de falha por fadiga de contato de rolamento. A etapa seguinte então foi utilizar a máquina II no estudo de fadiga de contato de rolamento de dois tipos de ferro fundido com matrizes de levada dureza, um cinzento e um nodular, os quais foram testados em duas condições: com e sem pré-tensionamento e analisados segundo a estatística de Weibull. Um aço também foi ensaiado como referência. A pré-tensão foi aplicada com uma ferramenta bi-partida e modelada por elementos finitos. Foram realizados ensaios lubrificados, com a aplicação de uma pressão máxima de contato de 3,6 GPa e conduzidos até a falha dos materiais por lascamento da superfície de rolamento. Em todas as condições de ensaio o ferro fundido nodular se mostrou muito superior ao ferro cinzento. Enquanto esse último que apresentou resultados similares na condição com e sem pré-tensão, o ferro fundido nodular teve a sua curva de distribuição de falhas significativamente alterada pela aplicação de tensão externa. Uma heterogeneidade na distribuição do tamanho de nódulos de grafita fez com que as falhas ocorressem sempre na mesma região do corpo-deprova evidenciando a sensibilidade do ensaio a variáveis microestruturais. / This work presents design and construction of an equipment for rolling contact fatigue studying and its use to cast irons analysis. Firstly it was used an equipment available at Surface Phenomena Laboratory, in São Paulo University, which was called machine I. The design of the system followed the well-known architecture where races of a thrust ball bearing are substituted by washers made with the material under investigation. Preliminary tests have shown that the first machine had severe limitations, but the most important was lack of ability to reproduce rolling contact fatigue mechanisms. An unknown sliding/rolling ratio always took place in its work. Then a second machine was designed and assembled. Sets up tests have shown typical mechanisms of rolling contact fatigue. The next step was to use the new machine to study two types of cast irons, a gray iron and a ductile iron, under two test conditions: with and without pre-stress. Also a steel specimen was tested as a reference. Results were subjected to Weibull analysis. A device was developed for pre-stress application, and the specimen/device system was modeled by finite elements analysis. Tests were carried out till failure, under lubrication, and with maximum contact pressure of 3.6 GPa. Ductile cast iron behavior was superior to gray iron in all tests. Gray iron specimens with and without pre-stress presented very similar results. On the other hand, ductile iron probability failure curve was strongly affected by pre-stress. An unexpected heterogeneity on graphite nodules size distribution promoted failures on just one region, which is an evidence of test sensitivity to micro structural changes.

The objective of this study is to develop an integrated multibody dynamics computational framework for the deterministic and reliability-based design optimization of wind turbine drivetrains to obtain an optimal wind turbine gear design that ensures a target reliability under wind load and gear manufacturing uncertainties. Gears in wind turbine drivetrains are subjected to severe cyclic loading due to variable wind loads that are stochastic in nature. Thus, the failure rate of drivetrain systems is reported to be relatively higher than the other wind turbine components. It is known in wind energy industry that improving reliability of drivetrain designs is one of the key issues to make wind energy competitive as compared to fossil fuels. Furthermore, a wind turbine is a multi-physics system involving random wind loads, rotor blade aerodynamics, gear dynamics, electromagnetic generator and control systems. This makes an accurate prediction of product life of drivetrains challenging and very limited studies have been carried out regarding design optimization including the reliability-based design optimization (RBDO) of geared systems considering wind load and manufacturing uncertainties. In order to address these essential and challenging issues on design optimization of wind turbine drivetrains under wind load and gear manufacturing uncertainties, the following issues are discussed in this study: (1) development of an efficient numerical procedure for gear dynamics simulation of complex multibody geared systems based on the multi-variable tabular contact search algorithm to account for detailed gear tooth contact geometry with profile modifications or surface imperfections; (2) development of an integrated multibody dynamics computational framework for deterministic and reliability-based design optimization of wind turbine drivetrains using the gear dynamics simulation software developed in (1) and RAMDO software by incorporating wide spatiotemporal wind load uncertainty model, pitting gear tooth contact fatigue model, and rotor blade aerodynamics model using NREL AeroDyn/FAST; and (3) deterministic and reliability-based design optimization of wind turbine drivetrain to minimize total weight of a drivetrain system while ensuring 20-year reliable service life with wind load and gear manufacturing uncertainties using the numerical procedure developed in this study. To account for the wind load uncertainty, the joint probability density function (PDF) of 10-minute mean wind speed (V₁₀) and 10-minute turbulence intensity (I₁₀) is introduced for wind turbine drivetrain dynamics simulation. To consider wide spatiotemporal wind uncertainty (i.e., wind load uncertainty for different locations and in different years), uncertainties of all the joint PDF parameters of V₁₀, I₁₀ and copula are considered, and PDF for each parameter is identified using 249 sets of wind data. This wind uncertainty model allows for the consideration of a wide range of probabilistic wind loads in the contact fatigue life prediction. For a given V₁₀ and I₁₀ obtained from the stochastic wind model, the random time-domain wind speed data is generated using NREL TurbSim, and then inputted into NREL FAST to perform the aerodynamic simulation of rotor blades to predict the transmitted torque and speed of the main shaft of the drivetrain that are sent to the multibody gear dynamics simulation as an input. In order to predict gear contact fatigue life, a high-fidelity gear dynamics simulation model that considers the detailed gear contact geometry as well as the mesh stiffness variation needs to be developed to find the variability of maximum contact stresses under wind load uncertainty. This, however, leads to a computationally intensive procedure. To eliminate the computationally intensive iterative online collision detection algorithm, a numerical procedure for the multibody gear dynamics simulation based on the tabular contact search algorithm is proposed. Look-up contact tables are generated for a pair of gear tooth profiles by the contact geometry analysis prior to the dynamics simulation and the contact points that fulfill the non-conformal contact condition and mesh stiffness at each contact point are calculated for all pairs of gears in the drivetrain model. This procedure allows for the detection of gear tooth contact in an efficient manner while retaining the precise contact geometry and mesh stiffness variation in the evaluation of mesh forces, thereby leading to a computationally efficient gear dynamics simulation suited for the design optimization procedure considering wind load uncertainty. Furthermore, the accuracy of mesh stiffness model introduced in this study and transmission error of gear tooth with tip relief are discussed, and a wind turbine drivetrain model developed using this approach is validated against test data provided in the literature. The gear contact fatigue life is predicted based on the gear tooth pitting fatigue criteria and is defined by the sum of the number of stress cycles required for the fatigue crack initiation and the number required for the crack to propagate from the initial to the critical crack length based on Paris-Erdogan equation for Mode II fracture. All the above procedures are integrated into the reliability-based design optimization software RAMDO for design optimization and reliability analysis of wind turbine drivetrains under wind load and manufacturing uncertainties. A 750kW GRC wind turbine gearbox model is used to perform the design optimization and the reliability analysis. A deterministic design optimization (DDO) is performed first using an averaged joint PDF of wind load to ensure a 20-year service life. To this end, gear face width and tip relief (profile modification) are selected as design variables and optimized such that 20-year fatigue life is ensured while minimizing the total weight of drivetrains. It is important to notice here that an increase in face width leads to a decrease in the fatigue damage, but an increase in total weight. On the other hand, the tip relief has almost no effect on the total weight, but it has a major impact on the fatigue damage. It is shown in this study that the optimum tip relief allows for lowering the greatest maximum shear stresses on the tooth surface without relying heavily on face width widening to meet the 20-year fatigue life constraint and it leads to reduction of total drivetrain weight by 8.4%. However, if only face width is considered as design variable, total weight needs to be increased by 4.7% to meet the 20-year fatigue life constraint. Furthermore, the reliability analysis at the DDO optimum design is carried out considering the large spatiotemporal wind load uncertainty and gear manufacturing uncertainty. Local surrogate models at DDO optimum design are generated using Dynamic Kriging method in RAMDO software to evaluate the gear contact fatigue damage. 49.5% reliability is obtained at the DDO optimum design, indicating that the probability of failure is 50.5%, which is as expected for the DDO design. RBDO is, therefore, necessary to further improve the reliability of the wind turbine drivetrain. To this end, the sampling-based reliability analysis is carried out to evaluate the probability of failure for each design using the Monte Carlo Simulation (MCS) method. However, the use of a large number of MCS sample points leads to a large number of contact fatigue damage evaluation time using the 10-minute multibody drivetrain dynamics simulation, resulting in the RBDO calculation process being computational very intensive. In order to overcome the computational difficulty resulting from the use of high-fidelity wind turbine drivetrain dynamics simulation, intermediate surrogate models are created prior to the RBDO process using the Dynamic Kriging method in RAMDO and used throughout the entire RBDO iteration process. It is demonstrated that the RBDO optimum obtained ensures the target 97.725 % reliability (two sigma quality level) with only 1.4 % increase in the total weight from the baseline design with 8.3 % reliability. This result clearly indicates the importance of incorporating the tip relief as a design variable that prevents larger increase in the face width causing an increase in weight. This, however, does not mean that a larger tip relief is always preferred since an optimum tip relief amount depends on stochastic wind loads and an optimum tip relief cannot be found deterministically. Furthermore, accuracy of the RBDO optimum obtained using the intermediate surrogate models is verified by the reliability analysis at the RBDO optimum using the local surrogate models. It is demonstrated that the integrated design optimization procedure developed in this study enables the cost effective and reliable design of wind turbine drivetrains.

Surfaces subjected to rolling and sliding contacts maysuffer from contact fatigue. This thesisdeals with solidmechanic aspects of contact fatigue including the descriptionand verificationof explaining mechanisms. The new mechanism forsurface initiated contact fatigue is basedon tensile surfacestresses from local asperity contacts. It is also realised thatsub-surfaceinitiated contact fatigue is the result of tensileresidual stresses that emanate from plasticdeformation belowthe surface. These mechanisms clearly show that contact fatiguecracksfollow the same rules as ordinary fatigue cracks inhardened steel. The thesis contains four papers that treat a new testprocedure named Standing ContactFatigue (SCF). The results ofthe test procedure have played an important role inthedevelopment and verification of the mechanisms for surfaceand sub-surface contact fatigue. The first part of the research work was experimental. Inthis part the SCF test properties wasdecided, crack resultsconfirmed and crack detection methods developed. Herecomparativestudies were performed using some differentmaterials and mechanical properties. It wasverified that SCFcould detect differences in contact fatigue resistance. Next a finite element model of the SCF test was evaluatedthrough the general-purposeprogram MARC. The model includedgraded material properties that originate from heattreatment.The residual surface deformation and surface compliance wereverified againstexperimental results. Crack initiation wasinvestigated in two ways. Firstly, the principalstresses atcritical locations were computed and plotted in a Haighdiagram. The diagramshowed that the cracks initiate in adirection perpendicular to the principal stress with thelargeststress range provided that the principal stress is tensilesometime during the load cycle. Secondly, some high cycle multiaxial fatigue criteria,including the Haigh principal stresscriterion, was evaluatedagainst the SCF crack initiation results. The surface cracklocation waspredicted by including statistical effects using aweakest-link criterion and a three-parameterWeibulldistribution. The SCF crack propagation was investigated by numericalevaluation ofJ1 andJ2integrals. The crack initiation and propagationphases were separated with a threshold criterionand a directioncriterion. It was found that during crack propagation bothsurface andsub-surface contact fatigue cracks follow thedirection with minimum mode II loading. Key words: contact fatigue mechanism; spall; spalling;surface crack; sub-surface crack;elasto-plastic indentation;contact compliance measurement; mixed-mode fatigue;fatiguecrack growth;J-integral; multiaxial fatigue; weakest-link. / QC 20100407