Modelling metal cutting using modern ductile fracture mechanics: Quantitative explanations for some longstanding problems

The assumption that negligible work is involved in the formation of new surfaces in the machining of ductile metals, is re-examined in the light of both current Finite Element Method (FEM) simulations of cutting and modern ductile fracture mechanics. The work associated with separation criteria in FEM models is shown to be in the kJ/m2 range rather than the few J/m2 of the surface energy (surface tension) employed by Shaw in his pioneering study of 1954 following which consideration of surface work has been omitted from analyses of metal cutting. The much greater values of surface specific work are not surprising in terms of ductile fracture mechanics where kJ/m2 values of fracture toughness are typical of the ductile metals involved in machining studies. This paper shows that when even the simple Ernst–Merchant analysis is generalised to include significant surface work, many of the experimental observations for which traditional ‘plasticity and friction only’ analyses seem to have no quantitative explanation, are now given meaning. In particular, the primary shear plane angle φ becomes material-dependent. The experimental increase of φ up to a saturated level, as the uncut chip thickness is increased, is predicted. The positive intercepts found in plots of cutting force vs. depth of cut, and in plots of force resolved along the primary shear plane vs. area of shear plane, are shown to be measures of the specific surface work. It is demonstrated that neglect of these intercepts in cutting analyses is the reason why anomalously high values of shear yield stress are derived at those very small uncut chip thicknesses at which the so-called size effect becomes evident. The material toughness/strength ratio, combined with the depth of cut to form a non-dimensional parameter, is shown to control ductile cutting mechanics. The toughness/strength ratio of a given material will change with rate, temperature, and thermomechanical treatment and the influence of such changes, together with changes in depth of cut, on the character of machining is discussed. Strength or hardness alone is insufficient to describe machining. The failure of the Ernst–Merchant theory seems less to do with problems of uniqueness and the validity of minimum work, and more to do with the problem not being properly posed. The new analysis compares favourably and consistently with the wide body of experimental results available in the literature. Why considerable progress in the understanding of metal cutting has been achieved without reference to significant surface work is also discussed.

Toughness & oblique metalcutting

The implications of whether new surfaces in cutting are formed just by plastic flow past the tool or by some fracturelike separation process involving significant surface work, are discussed. Oblique metalcutting is investigated using the ideas contained in a new algebraic model for the orthogonal machining of metals (Atkins, A. G., 2003, "Modeling Metalcutting Using Modern Ductile Fracture Mechanics: Quantitative Explanations for Some Longstanding Problems," Int. J. Mech. Sci., 45, pp. 373–396) in which significant surface work (ductile fracture toughnesses) is incorporated. The model is able to predict explicit material-dependent primary shear plane angles and provides explanations for a variety of well-known effects in cutting, such as the reduction of at small uncut chip thicknesses; the quasilinear plots of cutting force versus depth of cut; the existence of a positive force intercept in such plots; why, in the size-effect regime of machining, anomalously high values of yield stress are determined; and why finite element method simulations of cutting have to employ a "separation criterion" at the tool tip. Predictions from the new analysis for oblique cutting (including an investigation of Stabler's rule for the relation between the chip flow velocity angle C and the angle of blade inclination i) compare consistently and favorably with experimental results.

Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

Numerical study of a M-cycle cross-flow heat exchanger for indirect evaporative cooling

In this paper, numerical analyses of the thermal performance of an indirect evaporative air cooler incorporating a M-cycle cross-flow heat exchanger has been carried out. The numerical model was established from solving the coupled governing equations for heat and mass transfer between the product and working air, using the finite-element method. The model was developed using the EES (Engineering Equation Solver) environment and validated by published experimental data. Correlation between the cooling (wet-bulb) effectiveness, system COP and a number of air flow/exchanger parameters was developed. It is found that lower channel air velocity, lower inlet air relative humidity, and higher working-to-product air ratio yielded higher cooling effectiveness. The recommended average air velocities in dry and wet channels should not be greater than 1.77 m/s and 0.7 m/s, respectively. The optimum flow ratio of working-to-product air for this cooler is 50%. The channel geometric sizes, i.e. channel length and height, also impose significant impact to system performance. Longer channel length and smaller channel height contribute to increase of the system cooling effectiveness but lead to reduced system COP. The recommend channel height is 4 mm and the dimensionless channel length, i.e., ratio of the channel length to height, should be in the range 100 to 300. Numerical study results indicated that this new type of M-cycle heat and mass exchanger can achieve 16.7% higher cooling effectiveness compared with the conventional cross-flow heat and mass exchanger for the indirect evaporative cooler. The model of this kind is new and not yet reported in literatures. The results of the study help with design and performance analyses of such a new type of indirect evaporative air cooler, and in further, help increasing market rating of the technology within building air conditioning sector, which is currently dominated by the conventional compression refrigeration technology.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

Ferramentas para análise dinâmica e estrutural de um reboque de linha leve

Neste trabalho é desenvolvida uma metodologia de projeto para identificar as regiões críticas da estrutura de um reboque de linha leve sendo tracionado em pavimentos do tipo rodovia de baixa qualidade e estrada secundária de muito baixa qualidade. Para tanto, são levantados alguns dados experimentais da estrutura, necessários para a aproximação e simulação dinâmica de um modelo simplificado. A excitação da base é realizada por atuadores que simulam as oscilações verticais de um perfil de estrada, a qual é definida de acordo com os estudos realizados por Dodds e Robson (1973). Isto permite a determinação de um histórico de carregamentos das regiões da estrutura do chassi sob a ação das molas da suspensão. Em seguida, é gerado um modelo estrutural simplificado do reboque em elementos finitos, chamado de global, no qual são determinadas as regiões sob ação das maiores tensões. Tendo identificada a região mais crítica da estrutura, é criado um modelo local desta parte, onde se pode observar a distribuição de tensões com mais detalhe, permitindo a identificação dos pontos de concentração de tensões. Desta forma, com a aplicação do método de análise global-local é possível a obtenção de resultados detalhados quanto aos esforços da estrutura com um menor custo computacional.

Análise de estruturas de superfície delgadas axissimétricas via método dos elementos finitos com utilização de elemento retilíneo

The present work deals with the linear analysis of bi-dimensional axisymmetric structures, through development and implementation of a Finite Element Method code. The structures are initially studied alone and afterwards compatibilized into coupled structures, that is, assemblages, including tanks and pressure vessels. Examples are analysed and, in order to prove accuracy, the results were compared with those furnished by the analytical solutions

Desenvolvimento de antenas de microfita e antenas DRA Broadband

The search for ever smaller device and without loss of performance has been increasingly investigated by researchers involving applied electromagnetics. Antennas using ceramics materials with a high dielectric constant, whether acting as a substract element of patch radiating or as the radiant element are in evidence in current research, that due to the numerous advantages offered, such as: low profile, ability to reduce the its dimensions when compared to other devices, high efficiency of ratiation, suitability the microwave range and/or millimeter wave, low temperature coefficient and low cost. The reason for this high efficiency is that the dielectric losses of ceramics are very low when compared to commercially materials sold used in printed circuit boards, such as fiberglass and phenolite. These characteristics make ceramic devices suitable for operation in the microwave band. Combining the design of patch antennas and/or dielectric resonator antenna (DRA) to certain materials and the method of synthesis of these powders in the manufacture of devices, it s possible choose a material with a dielectric constant appropriate for the design of an antenna with the desired size. The main aim of this work is the design of patch antennas and DRA antennas on synthesis of ceramic powders (synthesis by combustion and polymeric precursors - Pe- chini method) nanostructured with applications in the microwave band. The conventional method of mix oxides was also used to obtain nanometric powders for the preparation of tablets and dielectric resonators. The devices manufactured and studied on high dielectric constant materials make them good candidates to have their small size compared to other devices operating at the same frequency band. The structures analyzed are excited by three different techniques: i) microstrip line, ii) aperture coupling and iii) inductive coupling. The efficiency of these techniques have been investigated experimentally and compared with simulations by Ansoft HFSS, used in the accurate analysis of the electromagnetic behavior of antennas over the finite element method (FEM). In this thesis a literature study on the theory of microstrip antennas and DRA antenna is performed. The same study is performed about the materials and methods of synthesis of ceramic powders, which are used in the manufacture of tablets and dielectric cylinders that make up the devices investigated. The dielectric media which were used to support the analysis of the DRA and/or patch antennas are analyzed using accurate simulations using the finite difference time domain (FDTD) based on the relative electrical permittivity (er) and loss tangent of these means (tand). This work also presents a study on artificial neural networks, showing the network architecture used and their characteristics, as well as the training algorithms that were used in training and modeling some parameters associated with the devices investigated

Análise e síntese de antenas e superfícies seletivas de frequência utilizando computação evolucionária e inteligência de enxames

The frequency selective surfaces, or FSS (Frequency Selective Surfaces), are structures consisting of periodic arrays of conductive elements, called patches, which are usually very thin and they are printed on dielectric layers, or by openings perforated on very thin metallic surfaces, for applications in bands of microwave and millimeter waves. These structures are often used in aircraft, missiles, satellites, radomes, antennae reflector, high gain antennas and microwave ovens, for example. The use of these structures has as main objective filter frequency bands that can be broadcast or rejection, depending on the specificity of the required application. In turn, the modern communication systems such as GSM (Global System for Mobile Communications), RFID (Radio Frequency Identification), Bluetooth, Wi-Fi and WiMAX, whose services are highly demanded by society, have required the development of antennas having, as its main features, and low cost profile, and reduced dimensions and weight. In this context, the microstrip antenna is presented as an excellent choice for communications systems today, because (in addition to meeting the requirements mentioned intrinsically) planar structures are easy to manufacture and integration with other components in microwave circuits. Consequently, the analysis and synthesis of these devices mainly, due to the high possibility of shapes, size and frequency of its elements has been carried out by full-wave models, such as the finite element method, the method of moments and finite difference time domain. However, these methods require an accurate despite great computational effort. In this context, computational intelligence (CI) has been used successfully in the design and optimization of microwave planar structures, as an auxiliary tool and very appropriate, given the complexity of the geometry of the antennas and the FSS considered. The computational intelligence is inspired by natural phenomena such as learning, perception and decision, using techniques such as artificial neural networks, fuzzy logic, fractal geometry and evolutionary computation. This work makes a study of application of computational intelligence using meta-heuristics such as genetic algorithms and swarm intelligence optimization of antennas and frequency selective surfaces. Genetic algorithms are computational search methods based on the theory of natural selection proposed by Darwin and genetics used to solve complex problems, eg, problems where the search space grows with the size of the problem. The particle swarm optimization characteristics including the use of intelligence collectively being applied to optimization problems in many areas of research. The main objective of this work is the use of computational intelligence, the analysis and synthesis of antennas and FSS. We considered the structures of a microstrip planar monopole, ring type, and a cross-dipole FSS. We developed algorithms and optimization results obtained for optimized geometries of antennas and FSS considered. To validate results were designed, constructed and measured several prototypes. The measured results showed excellent agreement with the simulated. Moreover, the results obtained in this study were compared to those simulated using a commercial software has been also observed an excellent agreement. Specifically, the efficiency of techniques used were CI evidenced by simulated and measured, aiming at optimizing the bandwidth of an antenna for wideband operation or UWB (Ultra Wideband), using a genetic algorithm and optimizing the bandwidth, by specifying the length of the air gap between two frequency selective surfaces, using an optimization algorithm particle swarm

Análise de antenas utilizando substrato cerâmico, zpt, produzido por síntese auto propagante para aplicações em sistemas de micro-ondas

Ceramic substrates have been investigated by researchers around the world and has achieved a high interest in the scientific community, because they had high dielectric constants and excellent performance in the structures employed. Such ceramics result in miniaturized structures with dimensions well reduced and high radiation efficiency. In this work, we have used a new ceramic material called lead zinc titanate in the form of Zn0,8Pb0,2TiO3, capable of being used as a dielectric substrate in the construction of various structures of antennas. The method used in constructing the ceramic combustion synthesis was Self- Sustained High Temperature (SHS - "Self-Propagating High-Temperature Synthesis") which is defined as a process that uses highly exothermic reactions to produce various materials. Once initiated the reaction area in the reaction mixture, the heat generated is sufficient to become self-sustaining combustion in the form of a wave that propagates converting the reaction mixture into the product of interest. Were analyzed aspects of the formation of the composite Zn0,8Pb0,2TiO3 by SHS powders and characterized. The analysis consisted of determining the parameters of the reaction for the formation of the composite, as the ignition temperature and reaction mechanisms. The production of composite Zn0,8Pb0,2TiO3 by SHS performed in the laboratory, was the result of a total control of combustion temperature and after obtaining the powder began the development of ceramics. The product was obtained in the form of regular, alternating layers of porous ceramics and was obtained by uniaxial pressing. 10 The product was characterized by analysis of dilatometry, X-ray diffraction analysis and scanning electron microscopy. One of the contributions typically defined in this work is the development of a new dielectric material, nevertheless presented previously in the literature. Therefore, the structures of the antennas presented in this work consisted of new dielectric ceramics based Zn0,8Pb0,2TiO3 usually used as dielectric substrate. The materials produced were characterized in the microwave range. These are dielectrics with high relative permittivity and low loss tangent. The Ansoft HFSS, commercial program employee, using the finite element method, and was used for analysis of antennas studied in this work

Estudo do efeito de substratos metamateriais em parâmetros de antenas de microfita

Microstrip antennas are subject matter in several research fields due to its numerous advantages. The discovery, at 1999, of a new class of materials called metamaterials - usually composed of metallic elements immersed in a dielectric medium, have attracted the attention of the scientific community, due to its electromagnetic properties, especially the ability to use in planar structures, such as microstrip, without interfering with their traditional geometry. The aim of this paper is to analyze the effects of one and bidimensional metamaterial substrates in microstrip antennas, with different configurations of resonance rings, SRR, in the dielectric layer. Fractal geometry is applied to these rings, in seeking to verify a multiband behavior and to reduce the resonance frequency of the antennas. The results are then given by commercial software Ansoft HFSS, used for precise analysis of the electromagnetic behavior of antennas by Finite Element Method (FEM). To reach it, this essay will first perform a literature study on fractal geometry and its generative process. This paper also presents an analysis of microstrip antennas, with emphasis on addressing different types of substrates as part of its electric and magnetic anisotropic behavior. It s performed too an approach on metamaterials and their unique properties

Otimização de forma aplicando B-splines sob critério integral de tensões

This work proposes a computational methodology to solve problems of optimization in structural design. The application develops, implements and integrates methods for structural analysis, geometric modeling, design sensitivity analysis and optimization. So, the optimum design problem is particularized for plane stress case, with the objective to minimize the structural mass subject to a stress criterion. Notice that, these constraints must be evaluated at a series of discrete points, whose distribution should be dense enough in order to minimize the chance of any significant constraint violation between specified points. Therefore, the local stress constraints are transformed into a global stress measure reducing the computational cost in deriving the optimal shape design. The problem is approximated by Finite Element Method using Lagrangian triangular elements with six nodes, and use a automatic mesh generation with a mesh quality criterion of geometric element. The geometric modeling, i.e., the contour is defined by parametric curves of type B-splines, these curves hold suitable characteristics to implement the Shape Optimization Method, that uses the key points like design variables to determine the solution of minimum problem. A reliable tool for design sensitivity analysis is a prerequisite for performing interactive structural design, synthesis and optimization. General expressions for design sensitivity analysis are derived with respect to key points of B-splines. The method of design sensitivity analysis used is the adjoin approach and the analytical method. The formulation of the optimization problem applies the Augmented Lagrangian Method, which convert an optimization problem constrained problem in an unconstrained. The solution of the Augmented Lagrangian function is achieved by determining the analysis of sensitivity. Therefore, the optimization problem reduces to the solution of a sequence of problems with lateral limits constraints, which is solved by the Memoryless Quasi-Newton Method It is demonstrated by several examples that this new approach of analytical design sensitivity analysis of integrated shape design optimization with a global stress criterion purpose is computationally efficient