A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces

In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this technique allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, stable and convergent solutions can be obtained without requiring tuning parameters defined outside this model. The tracking of moving surfaces is also included in the numerical model. This formulation has been checked in 21) and 3D tests

膜に閉じ込められた液晶系に対するアンカリングの効果

Tohoku University今井正幸課

On the Numerical Modelling of Machining Processes via the Particle Finite Element Method (PFEM)

Metal cutting or machining is a process in which a thin layer or metal, the chip, is removed by a wedge-shaped tool from a large body. Metal cutting processes are present in big industries (automotive, aerospace, home appliance, etc.) that manufacture big products, but also high tech industries where small piece but high precision is needed. The importance of machining is such that, it is the most common manufacturing processes for producing parts and obtaining specified geometrical dimensions and surface finish, its cost represent 15% of the value of all manufactured products in all industrialized countries. Cutting is a complex physical phenomena in which friction, adiabatic shear bands, excessive heating, large strains and high rate strains are present. Tool geometry, rake angle and cutting speed play an important role in chip morphology, cutting forces, energy consumption and tool wear. The study of metal cutting is difficult from an experimental point of view, because of the high speed at which it takes place under industrial machining conditions (experiments are difficult to carry out), the small scale of the phenomena which are to be observed, the continuous development of tool and workpiece materials and the continuous development of tool geometries, among others reasons. Simulation of machining processes in which the workpiece material is highly deformed on metal cutting is a major challenge of the finite element method (FEM). The principal problem in using a conventional FE model with langrangian mesh is mesh distortion in the high deformation. Traditional Langrangian approaches such as FEM cannot resolve the large deformations very well. Element distortion has been always matter of concern which limited the analysis to incipient chip formation in some studies. Instead, FEM with an Eulerian formulation require the knowledge of the chip geometry in advance, which, undoubtedly, restricts the range of cutting conditions capable of being analyzed. Furthermore serrated and discontinuous chip formation cannot be simulated. The main objective of this work is precisely to contribute to solve some of the problems described above through the extension of the Particle Finite Element Method (PFEM) to thermo-mechanical problems in solid mechanics which involve large strains and rotations, multiple contacts and generation of new surfaces, with the main focus in the numerical simulation of metal cutting process. In this work, we exploit the particle and lagrangian nature of PFEM and the advantages of finite element discretization to simulate the different chip shapes (continuous and serrated) that appear when cutting materials like steel and titanium at different cutting speeds. The new ingredients of PFEM are focused on the insertion and remotion of particles, the use of constrained Delaunay triangulation and a novel transfer operator of the internal variables. The remotion and insertion of particles circumvents the difficulties associated to element distortion, allowing the separation of chip and workpiece without using a physical or geometrical criterion. The constrained Delaunay improves mass conservation and the chip shape through the simulation, and the transfer allows us to minimize the error due to numerical diffusion. The thermo-mechanical problem, formulated in the framework of continuum mechanics, is integrated using an isothermal split in conjunction with implicit, semi-explicit and IMPLEX schemes. The tool has been discretized using a standard three-node triangle finite element. The workpiece has been discretized using a mixed displacement-pressure finite element to deal with the incompressibility constraint imposed by plasticity. The mixed finite element has been stabilized using the Polynomial Pressure Projection (PPP), initially applied in the literature to the Stokes equation in the field of fluid mechanics. The behavior of the tool is described using a Neo-Hookean Hyperelastic constitutive model. The behavior of the workpiece is described using a rate dependent, isotropic, finite strain j2 elastoplasticity with three different yields functions used to describe the strain hardening, the strain rate hardening and the thermal softening (Simo, Johnson Cook, Baker) of different materials under a wide variety of cutting conditions. The friction at the tool chip interface is modeled using the Norton-Hoff friction law. The heat transfer at the tool chip interface includes heat transfer due to conduction and friction. To validate the proposed mixed displacement-pressure formulation, we present three benchmark problems which validate the approach, namely, plain strain Cook´s membrane, the Taylor impact test and a thermo-mechanical traction test. The isothermal-IMPLEX split presented in this work has been validated using a thermo-mechanical traction test. Besides, in order to explore the possibilities of the numerical model as a tool for assisting in the design and analysis of metal cutting processes a set of representative numerical simulations are presented in this work, among them: cutting using a rate independent yield function, cutting using different rake angles, cutting with a deformable tool and a frictionless approach, cutting with a deformable tool including friction and heat transfer, the transition from continuous to serrated chip formation increasing the cutting speed. We have assembled several numerical tec niques which enable the simulation of orthogonal cutting processes. Our simulations demonstrate the ability of the PFEM to predict chip morphologies consistent with experimental observations. Also, our results show that the suitable selection of the global time integration scheme may involve savings in computation time up to 9 times. Furthermore, this work present a sensibility analysis to cutting conditions by means of a Design of Experiments (DoE). The Design of Experiments carried out with PFEM has been compared with DoE carried out with AdvantaEdge, Deform, Abaqus and Experiments. The results obtained with PFEM and other numerical simulations are very similar, while, a comparison of numerical simulations and experiments show some differences in the output variables that depend on the friction phenomena. The results suggest that is necessary to improve the modelization of the friction at the tool-chip interface

Efficient simulation of non-linear kerb impact events in ground vehicle suspensions

In the increasing competition which pervades the automobile sector, it is necessary to develop simple methods to enable prediction of suspension loading level envelope in an early development stage. For this purpose, the FORD specified standard driving manoeuvres, based on kerb strike and pothole braking, inducing worst case loading scenarios are employed. The damaging nature of these tests and the relatively expensive physical prototypes make simple simulation models essential. These models should cope with an initial rudimentary assessment, but must suffice to predict the maximum wheel centre loads with a reasonable degree of accuracy. Enhanced model features are required to represent edge-type tyre deformation and impulsive bumper deflection. State of the art approaches are physical tyre models extended to rim clash modelling and rheological bumper models embedded in an multibody system (MBS) environment. These enhancements lead to increased complexity. The thesis proposes a minimal parameter vehicle model, tailored to predict vertical suspension loads caused by the FORD kerb strike manoeuvre. Since the focus is put on model simplicity, an in-plane bicycle model is extended to 7 degrees of freedom. Nonlinear and hysteretic characteristics of the bump-stop elements are included through use of a spatial map concept, based on displacement and velocity dependent hysteresis. Furthermore, a static tyre model is described to predict the radial stiffness against penetration of an edge and flat-type rigid body geometry. The full mathematical model is derived on the basis of the shell theory and represented in terms of few geometrical input parameters. A distinct tyre model, representing the tyre belt as a multi-link chain is also derived to confirm the assumptions made in the simple mathematical model. Model validation is supported through experiments at both component and system levels. It is shown that the bumper map concept provides an accurate, yet simple alternative to a rheological model, if applied to polyurethane foam type bumpers. This approach is also confirmed for the tyre model, substituting a comprehensive physical model approach

Numerical modeling of metal cutting processes using the Particle Finite Element Method

Metal cutting or machining is a process in which a thin layer or metal, the chip, is removed by a wedge-shaped tool from a large body. Cutting is a complex physical phenomena in which friction, adiabatic shear bands, excessive heating, large strains and high rate strains are present. Tool geometry, rake angle and cutting speed play an important role in chip morphology, cutting forces, energy consumption and tool wear. The main objective of this work is precisely to contribute to solve some of the problems described above through the extension of the Particle Finite Element Method (PFEM) to thermo-mechanical problems in solid mechanics which involve large strains and rotations, multiple contacts and generation of new surfaces, with the main focus in the numerical simulation of metal cutting process. The new ingredients of PFEM are focused on the insertion and remotion of particles, the use of constrained Delaunay triangulation and a novel transfer operator of the internal variables. The thermo-mechanical problem, formulated in the framework of continuum mechanics, is integrated using an isothermal split in conjunction with implicit, semi-explicit and IMPLEX schemes. The tool has been discretized using a standard three-node triangle finite element. The workpiece has been discretized using a mixed displacement-pressure finite element to deal with the incompressibility constraint imposed by plasticity. The mixed finite element has been stabilized using the Polynomial Pressure Projection (PPP), initially applied in the literature to the Stokes equation in the field of fluid mechanics. The behavior of the tool is described using a Neo-Hookean Hyperelastic constitutive model. The behavior of the workpiece is described using a rate dependent, isotropic, finite strain j2 elastoplasticity with three different yields functions used to describe the strain hardening, the strain rate hardening and the thermal softening (Simo, Johnson Cook, Baker) of different materials under a wide variety of cutting conditions. The friction at the tool chip interface is modeled using the Norton-Hoff friction law. The heat transfer at the tool chip interface includes heat transfer due to conduction and friction. To validate the proposed mixed displacement-pressure formulation, we present three benchmark problems which validate the approach, namely, plain strain Cook ¿s membrane, the Taylor impact test and a thermo-mechanical traction test. The isothermal-IMPLEX split presented in this work has been validated using a thermo-mechanical traction test. Besides, in order to explore the possibilities of the numerical model as a tool for assisting in the design and analysis of metal cutting processes a set of representative numerical simulations are presented in this work, among them: cutting using a rate independent yield function, cutting using different rake angles, cutting with a deformable tool and a frictionless approach, cutting with a deformable tool including friction and heat transfer, the transition from continuous to serrated chip formation increasing the cutting speed. Our simulations demonstrate the ability of the PFEM to predict chip morphologies consistent with experimental observations. Also, our results show that the suitable selection of the global time integration scheme may involve savings in computation time up to 9 times. Furthermore, this work present a sensibility analysis to cutting conditions by means of a Design of Experiments (DoE). The Design of Experiments carried out with PFEM has been compared with DoE carried out with AdvantaEdge, Deform, Abaqus and Experiments. The results obtained with PFEM and other numerical simulations are very similar, while, a comparison of numerical simulations and experiments show some differences in the output variables that depend on the friction phenomena. The results suggest that is necessary to improve the modelization of the friction at the tool-chip interface.El mecanizado de metal es un proceso en el que una capa delgada de metal se retira por una herramienta en forma de cuña de un cuerpo grande. El corte es un complejo de fenómenos físicos en los que la fricción, bandas de cizalla adiabáticas, calentamiento excesivo, grandes deformaciones y de alta velocidad de las herramientas están presentes. La geometría de la herramienta, ángulo de ataque y la velocidad de corte juegan un papel importante en la morfología de la viruta, las fuerzas, el consumo de energía y desgaste de la herramienta de corte. El objetivo principal del trabajo es contribuir precisamente a resolver algunos de los problemas descritos anteriormente a travésde la extensión del PFEM a los problemas termo-mecánicos en mecánica de sólidos que implican grandes deformaciones y rotaciones, múltiples contactos y generación de nuevas superficies, con el foco principal en la simulación numérica de procesos de corte de metal. El problema termomecánico, formulado en el marco de la mecánica de medios continuos, se integra usando un esquema isotérmico junto con esquemas implícitos, semi-explícito y Implex. La herramienta ha sido discretizado utilizando un elemento finito triangular de tres nodos estándar. La pieza se discretizado utilizando un elemento finito desplazamiento presión mixta para hacer frente a la condición de incompresibilidad impuesto por la plasticidad. El elemento finito mixto se ha estabilizado mediantela proyección polinómica Presión, aplicado inicialmente en la literatura para la ecuación de Stokes. El comportamiento de la herramienta se describe usando un modelo constitutivo hiperelástico Neo Hookean. El comportamiento de la pieza de trabajo se describe usando un modelo isotrópico, con elastoplasticidad j2 y con tres funciones diferentes que se utilizan para describir el endurecimiento por deformación, endurecimiento de la velocidad de deformación y el ablandamiento térmico de diferentes materiales bajo una amplia variedad de condiciones de corte. La fricción en la interfaz de la herramienta-viruta se modela utilizando la fricción ley Norton-Hoff . La transferencia de calor en la interfase herramienta-viruta incluye la transferencia de calor por conducción y por fricción. Para validar la formulación desplazamiento presión mixto propuesto, se presentan tres problemas de referencia (la membrana de la tensión normal de Cook, la prueba de impacto Taylor y una prueba de tracción termomecánica ). La división isotérmica -IMPLEX presentada en este trabajo ha sido validado mediante un ensayo de tracción termomecánica. Además, con el fin de explorar las posibilidades del modelo como una herramienta para ayudar en el análisis de los procesos decorte de metal, un conjunto de simulaciones se presentan en este trabajo, entre ellas : corte de una material con tensión defluencia independiente de la tasa de deformación, cortando utilizando diferentes ángulos de ataque, corte con herramientas decorte deformables incluyendo la fricción y la transferencia de calor, la transición de la continua para la formación de virutadentada aumento de la velocidad de corte. Además, nuestros resultados muestran que la selección adecuada del esquema global de integración de tiempo puede suponer un ahorro en el tiempo de cálculo hasta 9 veces. Por otra parte, este trabajo presenta un análisis de sensibilidad a las condiciones de corte mediante un diseño de experimentos (DOE). El diseño de experimentos con el llevado a cabo PFEM ha sido comparada con la llevada a cabo con el DoEAdvantaEdge, deforme, Abaqus y experimentos. Los resultados obtenidos con PFEM y otras simulaciones numéricas son muy similares, mientras que, en comparación de las simulaciones numéricas y experimentos muestran algunas diferencias en las variables de salida que dependen de los fenómenos de fricción. Los resultados sugieren que es necesario mejorar la modelización de la fricción en la interfaz de la herramienta-viruta

Microgravity Science and Applications Program tasks, 1986 revision

The Microgravity Science and Applications (MSA) program is directed toward research in the science and technology of processing materials under conditions of low gravity to provide a detailed examination of the constraints imposed by gravitational forces on Earth. The program is expected to lead to the development of new materials and processes in commercial applications adding to this nation's technological base. The research studies emphasize the selected materials and processes that will best elucidate the limitations due to gravity and demonstrate the enhanced sensitivity of control of processes that may be provided by the weightless environment of space. Primary effort is devoted to a study of the specific areas of research which reveals potential value in the initial investigations of the previous decades. Examples of previous process research include crystal growth and directional solidification of metals; containerless processing of reactive materials; synthesis and separation of biological materials; etc. Additional efforts will be devoted to identifying the special requirements which drive the design of hardware to reduce risk in future developments