Mathematical modeling of aerosol emission from die sinking electrical discharge machining process

Emission of toxic gases and aerosol is an important hazard associated with the electrical discharge machining (EDM) process, one of the most widely used non-conventional manufacturing processes. These emissions can cause adverse health effects to the operators and has a direct impact on the environment. The emission from this process is directly related to the temperature at the process location. This paper was aimed at developing a model that quantifies the aerosol generated from the die sinking EDM process while machining steel workpiece with copper electrode. The model developed in this paper made use of energy balance and heat transfer equations. The modeling results were then validated using experimentally obtained values of the emission rate of aerosol from this process. The results showed a close correlation of +0.89 with experimental results. The model developed in this paper can predict the level of emissions at different process locations; thereby reducing the direct cost and time associated with experimentation.     

Modeling of EDM responses by support vector machine regression with parameters selected by particle swarm optimization

Electrical discharge machining (EDM) is inherently a stochastic process. Predicting the output of such a process with reasonable accuracy is rather difficult. Modern learning based methodologies, being capable of reading the underlying unseen effect of control factors on responses, appear to be effective in this regard. In the present work, support vector machine (SVM), one of the supervised learning methods, is applied for developing the model of EDM process. Gaussian radial basis function and ε-insensitive loss function are used as kernel function and loss function respectively. Separate models of material removal rate (MRR) and average surface roughness parameter (Ra) are developed by minimizing the mean absolute percentage error (MAPE) of training data obtained for different set of SVM parameter combinations. Particle swarm optimization (PSO) is employed for the purpose of optimizing SVM parameter combinations. Models thus developed are then tested with disjoint testing data sets. Optimum parameter settings for maximum MRR and minimum Ra are further investigated applying PSO on the developed models.     

Finite element analysis of evaporative cutting with a moving high energy pulsed laser

A computational model for simulation of pulsed laser-cutting process has been developed using a finite element method. An unsteady heat transfer model is considered that deals with the material-cutting process using a Gaussian wave laser beam in a pulsed mode. An iterative scheme is used to handle the geometric nonlinearity due to the melting region. The convergence study with mesh refinements and time steps first identifies optimal mesh and time step for the present analyses. Numerical analyses are carried out on the amount of material removal and groove smoothness with laser power (LP) and number of pulses (NPS) while other laser cutting parameters are fixed. The results show that there exist threshold values in number of pulses and laser power in order to achieve two predetermined conditions: (1) amount of material removal and (2) smoothness of groove shape. These values form an envelope called threshold curve that separate the acceptable region from unacceptable one for quality pulsed laser cutting. The effect of velocity also leads to another threshold curve which is determined from both number of pulses and velocity. Finally, the convergence of results in error domain is shown oscillating due to geometric nonlinearity.     

Mathematical modeling and process simulation of perlite grain expansion in a vertical electrical furnace

Expanded perlite is a lightweight material with remarkable thermal and acoustic insulation properties, rendering it widely useful in the construction and manufacturing industries. Currently applied perlite expansion technology suffers numerous technical disadvantages, which adversely affect product quality and limit the range of its applications. To overcome these established drawbacks, a new perlite expansion process has been designed on the basis of a vertical electrically heated expansion furnace. The novel furnace enables precise control of experimental conditions, in order to allow for efficient adjustment of particle residence time and internal temperature. The quality of expanded perlite strongly depends on raw material thermophysical properties as well as furnace operating conditions, and the experimental investigation of the isolated effect of each parameter on expanded product quality is technically cumbersome and extremely time-consuming and expensive.A mathematical model for perlite grain expansion has been developed in order to perform a detailed numerical investigation of process efficiency, toward the optimization of the expansion process in the novel pilot-scale furnace. The dynamic model consists of ordinary differential equations for both air and particle heat and momentum balances, as well as nonlinear algebraic equations for both air and perlite melt thermophysical and transport properties, probing the air temperature distribution within the vertical electrical furnace as well as the particle velocity, temperature and size along its trajectory inside the heating chamber. The effect of raw material physical properties (raw feed origin, initial particle size, effective water content) as well as operating parameters (air inlet temperature and flowrate, furnace wall temperature) on evolution of the particle state variables is presented and discussed. Model results indicate perlite expansion is strongly affected by raw ore feed origin, size and water content. Moreover, operating conditions affect expansion considerably, and furnace wall temperature has the strongest effect on the final particle expansion ratio attained. The new dynamic model is instrumental towards achieving a detailed comprehension of perlite expansion in the vertical electrical furnace towards multi-parametric sensitivity analysis, process optimization and efficient control.     

A two-scale simulation method accounting for thermal effects during turning

During chip formation in turning processes, mechanical work is dissipated into thermal energy by plastic deformations and frictional processes. In case of dry cutting, the generated heat is in part removed with the chips while the rest flows into the tool and the workpiece. Within the latter, the temperature increases due to this heat flow, which in turn causes thermal expansions that increase the cutting depth and thus induce deviations from the nominal workpiece geometry. These effects are treated separately by a local model for the chip formation and a global model for the whole workpiece in order to determine the temperature distribution inside the workpiece and the dependent thermal expansion. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Varying Workpiece Dynamics in Milling Stability Analysis

Dynamic stability of a milling process with varying workpiece dynamics is investigated. The milling tool moves along the workpiece with a prescribed feed rate, whereby the contact point shifts. Furthermore, the workpiece dynamics is affected by material removal. The resultant varying workpiece dynamics is taken into account by parametric model order reduction including modal truncation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A three-dimensional steady state thermal fluid model of jumbo ingot casting during electron beam re-melting of Ti–6Al–4V

A 3-D coupled thermal-fluid model describing mass, momentum and energy transport within a Ti–6Al–4V rolling ingot cast in an (Electron Beam Cold Hearth Remelting) EBCHR process has been developed to describe steady state casting conditions. The model incorporates a number of the physical phenomena inherent to the industrial process, including a metal inlet in the center of one of the narrow faces, complex boundary conditions based on industrial practice, buoyancy driven flow within the liquid and flow attenuation using a Darcy momentum source term within the mushy zone. The model ignores turbulence in the liquid pool and Marangoni (surface tension) driven surface flows. The model has been validated against liquid pool depth and profile measurements made on an experimental casting seeded with insoluble dense markers and doped with dense alloy additions. Comparisons have also been made to video images taken of the top surface during casting. The results indicate that the model is able to quantitatively predict the steady state sump depth and profile and is able to qualitatively predict aspects of the top surface temperature distribution. The model has also been used to conduct a process heat balance and sensitivity analyses. The process heat balance conducted on the model domain indicates that at steady state the liquid metal inlet contributes 88% of the total power input, while the electron beam provides net 12% after accounting for radiation losses from the top surface; 62% of the heat is lost through the ingots sides and the balance is lost via bulk transport of sensible heat through the bottom of the domain. The results of the sensitivity analysis on pool depth indicate that casting rate has the largest effect followed by metal inlet superheat. The thermal, flow and pressure fields predicted by the steady state model serves as the initial conditions for a transient hot-top model, which is the subject of a forth-coming paper.     

快传播裂缝尖周围的温度场

裂缝进入快传播时,裂缝尖周围的温度升高是一个十分重要的实际问题,它不仅取决于一些材料常数,也取决于传播速度和热源的密度分布.本文讨论了裂缝尖周围塑性区形状以及热源密度,提出了一个温度场模型.对PMMA材料进行了数值计算,并将结果与其它理论和实验结果作了比较.     

Meshfree isoparametric finite point interpolation method (IFPIM) with weak and strong forms for evaporative laser drilling

An isoparametric finite point interpolation method (IFPIM) with weak and strong forms has been developed to analyze evaporative laser drilling. The method is based on isoparametric finite point representation of the unknowns in the influence domain. The local influence domains are mapped onto a master domain where the shape functions and their derivatives are known. The solution in the master domain is approximated by a linear combination of shape functions. The present method employs a simple strong form in the domain and a weak form on the boundary. Three different types of boundary conditions considered are of essential, convection, and laser irradiation type. The problem is geometrically nonlinear because the domain is not known a priori due to material removal in drilling. An iterative scheme is used to solve the nonlinear problem. The material removal is handled by redistributing points in the domain. This renders the point distribution non-uniform as in random distribution. The numerical results show excellent agreement with those by FEM and BEM in terms of groove shape, temperature and heat flux distributions, and amount of material removal. The results are superior to those from the isoparametric finite point interpolation methods with only strong forms.     

Modelado numérico del proceso de soldadura FSW incorporando una técnica de estimación de parámetros

Numerical models of heat transfer and fluid flow used in the simulation of the friction-stir welding (FSW) process have contributed to the understanding of the process. However, there are some input model parameters that cannot be easily determined from fundamental principles or the welding conditions. As a result, the model predictions are not always in agreement with experimental results. In this work, the Levenberg-Marquardt (LM) method is used in order to perform a non-linear estimation of the unknown parameters present in the heat transfer and fluid flow models, by adjusting the temperatures results obtained with the models to temperature experimental measurements. These models are implemented in a general-purpose software that uses a numerical formulation developed from the finite element method (FEM). The unknown parameters are: the friction coefficient and the amount of adhesion of material to the surface of the tool, the heat transfer coefficient on the bottom surface and the amount of viscous dissipation converted into heat. The obtained results show an improvement in the numerical model predictions from the incorporation of parameter estimation techniques.     

Estimation of temperature in rubber-like materials using non-linear finite element analysis based on strain history

A finite element procedure for hyper-elastic materials such as rubber has been developed to estimate the temperature rise during cyclic loading. The irreversible mechanical work developed in rubber has been used to determine the heat generation rate for carrying out thermal analysis. The evaluation of the heat energy is dependent on the strains. The finite element analysis assumes Green–Lagrangian strain displacement relations, Mooney–Rivlin strain energy density function for constitutive relationship, incremental equilibrium equations, and Total Lagrangian approach and the stress and strain of the rubber-like materials are evaluated using a degenerated shell element with assumed strain field technique, considering both material and geometric non-linearities. A transient heat conduction analysis has been carried out to estimate the temperature rise for different time steps in rubber-like materials using Galerkin's formulations. A numerical example is presented and the computed temperature values for various load steps agree closely with the experimental results reported in the literature.     

Mathematical modelling of influence functions in computer-controlled polishing: Part I

Computer-controlled polishing (CCP) is commonly used to finish high-quality surfaces, such as optical lenses. Based on magnetorheological finishing (MRF), a mathematical model to calculate the polishing tool characteristic (influence function) was developed and verified experimentally. The first part of this paper introduces the model to predict the size and shape of an influence function. The second part of this paper describes the calculation of the distribution of material removal within the size of an influence function. The model supersedes the current cumbersome procedure for determining an influence function and thus results in considerably improved and more economical manufacture. Furthermore, the model enables the quality of the final surface to be enhanced when polishing complex, for example aspherical or free-form, workpiece geometries and provides the first step in the application of time-variant influence functions.     

An advanced dynamic process model for industrial horizontal anode baking furnace

The global aluminum industry is facing new challenges due to new technological developments. Carbon anodes, consisting of mainly petroleum coke and coal tar pitch, are used in the electrolytic production of aluminum. High amperage utilization in the electrolytic cells with the objective of increasing production requires high quality carbon anodes. The anode quality depends both on raw material quality, anode recipe as well as forming and baking conditions of anode manufacturing process. The cost of the baking process constitutes 15 to 25% of the total aluminum production cost [1]. The industrial challenge is to produce better quality anodes consuming less energy, and reducing environmental emissions.A transient two dimensional (2D⁺) process model for horizontal anode baking furnace was developed during this study. The main objective was to develop an efficient furnace model with low computation load and time, using the transient Finite Difference Method and simplified furnace geometry. The model represents several phenomena involved during the anode baking process such as heat transfer (convection, radiation and conduction), fuel combustion, volatile matter (tar, methane and hydrogen) generation and combustion, air infiltration and energy loss to the atmosphere from the walls, the top of the furnace and the foundation. The model was developed using two coupled sub-models; the first one describes the thermal conduction through the solid materials (brick refractory wall, packing coke and anode block) as well as the volatile release, and the second one describes the gas flow, heat and mass transfer as well as the combustion of fuel and volatiles in the flue. Compared to the existing process models (where the gas flow in flue is assumed as unidirectional along the horizontal furnace direction), the present model also considers the gas flow in vertical direction and uses four vertical planes per pit section to predict the temperature of the solids. The model predicts 2D temperature distribution within the flue gas (xy plane) and the pit solid materials (yz plane) allowing then the prediction of the pseudo tridimensional distribution of the solid temperature. This model is a useful tool for the continuous monitoring of anode temperature and studying of the horizontal anode baking furnace behaviour. The effect of any change in operational parameters and the energy consumption on the furnace operation can be predicted.     

On nonlinear cutting response and tool chatter in turning operation

Tool chatter in turning process is addressed with a new perspective. Turning dynamics is investigated using a 3D model that allows for simultaneous workpiece-tool deflections in response to the exertion of nonlinear regenerative force. The workpiece is modeled as a system of three rotors, namely, unmachined, being machined and machined, connected by a flexible shaft. Such a configuration enables the workpiece motion relative to the tool and tool motion relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous depth-of-cut, material removal rate and whirling. The equations of motion for the model are coupled through the nonlinear cutting force. The model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Different stages of stability for the workpiece and the tool subject to the same cutting conditions are studied. Numerical simulations reveal diverse, oftentimes inconsistent, tool behaviors described by the two models. Most notably, observations made with regard to the inconsistency in describing machining stability limits raise the concern for using 1D models to obtain stability charts.     

MPM simulations of high-speed machining of Ti6Al4V titanium alloy considering dynamic recrystallization phenomenon and thermal conductivity

Ti6Al4V titanium alloy is often used in the aircraft industry due to its good strength and toughness etc. However, it is very difficult to simulate high speed machining of titanium alloy using the finite element method (FEM). The reason is that the high speed, large deformation and high strain rate of metal material at high temperature etc. will lead to the element distortions and other numerical difficulties. In contrast with FEM, material point method (MPM) has the advantage of simulating extreme large deformation, fracture and impact problems. Therefore, it is specially suitable for dealing with high speed cutting process. In many existing researches about the high speed cutting process using Johnson−Cook constitutive model, the material dynamic recrystallization softening effect under high pressure and high temperature has not been considered. For this, three modified Johnson−Cook constitutive models for Ti6Al4V titanium alloy are adopted and the parameters for these models were obtained by the split Hopkinson pressure bar (SHPB) test considering the critical strain values, high-temperature range and dynamic recrystallization phenomenon. Furthermore, to ensure the numerical accuracy, the transient heat conduction algorithm is employed in MPM implementation. Finally, comparison and discussion are carried out between the experimental and the simulation data, which show that the high speed cutting process can be better simulated using the modified Johnson−Cook constitutive models.     

Mathematical modeling of friction stir welding considering dry and viscous friction

In this paper, the investigation of a pre-immersion period of Friction Stir Welding process (FSW) from the mechanical point of view using analytical considerations is presented. This initial period is a part of the real technological process, when a FSW instrument reaches the touchdown point with the workpiece, preheats the contact zone, but does not penetrate the material. This approach enables an insight into FSW process on a level, where the system parameters are known and an experimental evaluation of theoretical results is possible. Beside these considerations an analytical estimation of the power input of dry and viscous friction during instrument rotation and translation in parallel is shown. These phenomena are investigated including friction between a FSW instrument and a workpiece. The influences of both dry and viscous friction are studied. Experiments have been done to validate the calculated results.     

Thermomechanical Simulation of the Electron Beam Melting Process for TiAl6V4

In the present contribution a nonlinear thermomechanical finite element model with temperature dependent material parameters is used to simulate the electron beam melting process for TiAl6V4. The beam is modeled as a moving heat source and the isentropic split solution scheme is applied. The temperature and stress distribution during the process were simulated and showed sound results from a qualitative point of view. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

CFD modelling of the flow and reactions in the Olympic Dam flash furnace smelter reaction shaft

The performance of flash furnace burners can be evaluated quickly and efficiently using CFD modelling. Gas flows are modelled using the conventional Eulerian approach, while Lagrangian particle tracking is used to model the flow of solid feed through the burner and into the reaction shaft. A composite particle model has been developed that considers the solid feed to be made up of single particles containing appropriate quantities of concentrate, flux and dust. Solid fuels (such as coal) can also be included in the composite particle. Reactions between the solids and gas are then modelled using standard heat and mass transfer relationships. Results from the modelling process are shown for BHP-Billiton’s Olympic Dam copper flash smelter with the burner that was used from 1998–2003. Flow patterns, temperature and gas composition distributions, particle dispersion and residence time, and overall extent of sulphur removal are predicted and used to evaluate furnace performance. However, results are sensitive to the assumed size of the composite particles, and plant measurements are required to determine the appropriate composite particle size to predict quantitative data.     

Towards the simulation of Internal Traverse Grinding – from mesoscale modelling to process simulations

The present work aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 using electro plated cBN grinding wheels. We focus on the thermomechanical behaviour resulting from the interaction of tool and workpiece in the process zone on a mesoscale. Based on topology analyses of the grinding wheel surface, two-dimensional single- and multigrain representative numerical experiments are performed to investigate the resulting load-displacement-behaviour as well as the specific heat generation due to friction and plastic dissipation. A thermoelastic-viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Based on previous work, an adaptive remeshing scheme which uses a combination of error estimation and indicator methods, is applied to overcome mesh dependence. In consequence, the formulation allows to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelo de un proceso de cristalización continua de un sorbete por medio de la metodología de momentos

Freezing is an important step in the manufacturing process of ice-cream and sorbet, since the operating conditions have a strong influence on the micro-structure, and consequently on the sensorial attributes of the final product. This steep of freezing is carried out by a scraped surface heat exchanger (SSHE) where the product quality is conditioned by process conditions as the evaporation temperature of a refrigerant fluid, the mix flow rate, the dasher speed and the cylinder pressure due to the air introduction. In order to study the relevance of a control system based on the influence of process variables on product quality, this paper presents a model for a continuous crystallization of a sorbet using the method of moments, which is validated by experimental data.The model created by this methodology has been able to represent the influence of the process conditions during the crystallization of the sorbet on the final product characteristics such as crystal size and the draw temperature in the outlet of the SSHE in absence of air. The model based in moments is studied as a reduced model of the population balance equation and includes the phenomena of heterogeneous nucleation and growth. This model developed represents minimal computational requirements and is highly adapted for optimization and/or process control tasks.