A mathematical model of gas tungsten arc welding considering the cathode and the free surface of the weld pool

A two-dimensional axisymmetric numerical model, including the influence of the cathode and the free surface of the weld pool, is developed to describe the heat transfer and fluid flow in gas tungsten arc (GTA) welding. In the model, a boundary-fitted coordinate system is adopted to precisely describe the cathode shape and deformed weld-pool surface. The current continuity equation has been solved with the combined arc plasma-cathode system, independent of the assumption of current density distribution on the cathode surface, which was essential in the previous studies of arc plasma. It has been shown that the temperature profile, the current, and the heat flux to the anode show good agreement with the experimental data. Moreover, the current and the heat-flux distributions may be affected by the shape of the cathode and the free surface of the weld pool.     

A unified numerical modeling of stationary tungsten-inert-gas welding process

In order to clarify the formative mechanism of weld penetration in an arc welding process, the development of a numerical model of the process is quite useful for understanding quantitative values of the balances of mass, energy, and force in the welding phenomena because there is still lack of experimentally understanding of the quantitative values of them because of the existence of complicated interactive phenomena between the arc plasma and the weld pool. The present article is focused on a stationary tungsten-inert-gas (TIG) welding process for simplification, but the whole region of TIG arc welding, namely, tungsten cathode, arc plasma, workpiece, and weld pool is treated in a unified numerical model, taking into account the close interaction between the arc plasma and the weld pool. Calculations in a steady state are made for stationary TIG welding in an argon atmosphere at a current of 150 A. The anode is assumed to be a stainless steel, SUS304, with its negative temperature coefficient of surface tension. The two-dimensional distributions of temperature and velocity in the whole region of TIG welding process are predicted. The weld-penetration geometry is also predicted. Furthermore, quantitative values of the energy balance for the various plasma and electrode regions are given. The predicted temperatures of the arc plasma and the tungsten-cathode surface are in good agreement with the experiments. There is also approximate agreement of the weld shape with experiment, although there is a difference between the calculated and experimental volumes of the weld. The calculated convective flow in the weld pool is mainly dominated by the drag force of the cathode jet and the Marangoni force as compared with the other two driving forces, namely, the buoyancy force and the electromagnetic force.     

Modeling of fluid flow and heat transfer in the plasma region of the dc electric arc furnace

A mathematical model describing the transport processes in the plasma arc in dc electric arc furnaces has been developed. The equations of conservation of mass, momentum, and energy are solved numerically in conjunction with Maxwell's equations of the electromagnetic field to calculate the velocity and temperature distributions in the plasma region. The heat transfer from the arc to a rigid anode surface is calculated. The model is applied to obtain quantitative results on the relative importance of the various modes of heat transfer from the electric arc to the anode surface. Computational results were obtained for varying arc current magnitudes and anode-cathode distances. The model predicts higher arc jet velocity and a broader arc core at higher arc current. The shorter arc length is more efficient for transferring heat to the anode.     

A new finite element model for welding heat sources

A mathematical model for weld heat sources based on a Gaussian distribution of power density in space is presented. In particular a double ellipsoidal geometry is proposed so that the size and shape of the heat source can be easily changed to model both the shallow penetration arc welding processes and the deeper penetration laser and electron beam processes. In addition, it has the versatility and flexibility to handle non-axisymmetric cases such as strip electrodes or dissimilar metal joining. Previous models assumed circular or spherical symmetry. The computations are performed with ASGARD, a nonlinear transient finite element (FEM) heat flow program developed for the thermal stress analysis of welds.* Computed temperature distributions for submerged arc welds in thick workpieces are compared to the measured values reported by Christensen¹ and the FEM calculated values (surface heat source model) of Krutz and Segerlind.² In addition the computed thermal history of deep penetration electron beam welds are compared to measured values reported by Chong.³ The agreement between the computed and measured values is shown to be excellent.     

The interaction of a DC transferred arc with a melting metal: Experimental measurements and mathematical description

Experimental measurements are reported on the transient development of temperature profiles in a hemispherical metal anode onto which a DC plasma jet is impinging. The main process variables were the arc current, the electrode separation, and the argon flow rate. These experimental measurements were compared with the predictions of a mathematical model, which involved the statement of the turbulent heat and fluid flow equations in the plasma, coupled to the heat flow in the testpiece through the boundary conditions. The experimental measurements were in reasonable agreement with the predictions, and convective heat transfer was found to be dominant in the heat exchange between the plasma and the anode.     

Computation and validation of weld pool dimensions and temperature profiles for gamma TiAl

Previous research by the authors has shown that the welding current has a strong effect on the weld properties and microstructures of gamma TiAl. This article presents the results of experimentally measured and theoretically predicted temperature profiles of gas tungsten arc (GTA) welded gamma TiAl for welding currents of 75 and 100 A. The GTA welding model used in this study accounts for the fluid flow in the weld pool as well as conductive, convective, and phase change heat transfer processes in the solid, liquid, and mushy regions of a metal. The computed temperature fields predicted that as the welding current is increased, the maximum temperature reached in the weld pool also increases. Experimental validation of the computed temperature fields was determined by placing thermocouples at three locations on the specimen, to record the temperatures during welding using computer-based data acquisition hardware and software. The agreement between theoretical predictions and measurements was reasonably good, which provided a direct validation of the model. This article is based on a presentation made in the symposium entitled “Fundamentals of Structural Intermetallics,” presented at the 2002 TMS Annual Meeting, February 21–27, 2002, in Seattle, Washington, under the auspices of the ASM and TMS Joint Committee on Mechanical Behavior of Materials.     

Effect of Welding Speed on Gas Metal Arc Weld Pool in Commercially Pure Aluminum: Theoretically and Experimentally

Temperature and velocity fields, and weld pool geometry during gas metal arc welding (GMAW) of commercially pure aluminum were predicted by solving equations of conservation of mass, energy and momentum in a three-dimensional transient model. Influence of welding speed was studied. In order to validate the model, welding experiments were conducted under the similar conditions. The calculated geometry of the weld pool were in good agreement with the corresponding experimental results. It was found that an increase in the welding speed results in a decrease peak temperature and maximum velocity in the weld pool, weld pool dimensions and width of the heat-affected zone (HAZ). Dimensionless analyses were employed to understand the importance of heat transfer by convection and the roles of various driving forces in the weld pool. According to dimensionless analyses droplet driving force strongly affected fluid flow in the weld pool.     

On the calculation of the free surface temperature of gas-tungsten-arc weld pools from first principles: Part I. modeling the welding arc

A mathematical formulation has been developed and computed results are presented describing the temperature profiles in gas tungsten arc welding (GTAW) arcs and, hence, the net heat flux from the welding arc to the weld pool. The formulation consists of the statement of Maxwell's equations, coupled to the Navier-Stokes equations and the differential thermal energy balance equation. The theoretical predictions for the heat flux to the workpiece are in good agreement with experimental measurements — for long arcs. The results of this work provide a fundamental basis for predicting the behavior of arc welding systems from first principles.     

Thermal analysis of the arc welding process: Part I. General solutions

An analytical solution for the temperature-rise distribution in arc welding of short workpieces is developed based on the classical Jaeger’s moving heat-source theory to predict the transient thermal response. It, thus, complements the pioneering work of Rosenthal and his colleagues (and others who extended that work), which addresses quasi-stationary moving heat-source problems. The arc beam is considered as a moving plane (disc) heat source with a pseudo-Gaussian distribution of heat intensity, based on the work of Goldak et al. It is a general solution (both transient and quasi-steady state) in that it can determine the temperature-rise distribution in and around the arc beam heat source, as well as the width and depth of the melt pool (MP) and the heat-affected zone (HAZ) in welding short lengths, where quasi-stationary conditions may not have been established. A comparative study is made of the analytical approach of the transient analysis presented here with the finite-element modeling of arc welding by Tekriwal and Mazumder. The analytical model developed can determine the time required for reaching quasi-steady state and solve the equation for the temperature distribution, be it transient or quasi-steady state. It can also calculate the temperature on the surface as well as with respect to the depth at all points, including those very close to the heat source. While some agreement was found between the results of the analytical work and those of the finite-element method (FEM) model, there were differences identified due to differences in the methods of approach, the selection of the boundary conditions, the need to consider image heat sources, and the effect of variable thermal properties with temperature. The analysis presented here is exact, and the solution can be obtained quickly and in an inexpensive way compared to the FEM. The analysis also facilitates optimization of process parameters for good welding practice.     

Mathematical modeling of three-dimensional heat and fluid flow in a moving gas metal arc weld pool

Mathematical models capable of accurate prediction of the weld bead and weld pool geometry in gas metal arc (GMA) welding processes would be valuable for rapid development of welding procedures and empirical equations for control algorithms in automated welding applications. This article introduces a three-dimensional (3-D) model for heat and fluid flow in a moving GMA weld pool. The model takes the mass, momentum, and heat transfer of filler metal droplets into consideration and quantitatively analyzes their effects on the weld bead shape and weld pool geometry. The algorithm for calculating the weld reinforcement and weld pool surface deformation has been proved to be effective. Difficulties associated with the irregular shape of the weld bead and weld pool surface have been successfully overcome by adopting a boundary-fitted nonorthogonal coordinate system. It is found that the size and profile of the weld pool are strongly influenced by the volume of molten wire, impact of droplets, and heat content of droplets. Good agreement is demonstrated between predicted weld dimensions and experimently measured ones for bead-on-plate GMA welds on mild steel plate.     

Computational modeling of stationary gastungsten-arc weld pools and comparison to stainless steel 304 experimental results

A systematic study was carried out to verify the predictions of a transient multidimensional computational model by comparing the numerical results with the results of an experimental study. The welding parameters were chosen such that the predictions of the model could be correlated with the results of an earlier experimental investigation of the weld pool surface temperatures during spot gas-tungsten-arc (GTA) welding of Type 304 stainless steel (SS). This study represents the first time that such a comprehensive attempt has been made to experimentally verify the predictions of a numerical study of weld pool fluid flow and heat flow. The computational model considers buoyancy and electromagnetic and surface tension forces in the solution of convective heat transfer in the weld pool. In addition, the model treats the weld pool surface as a truly deformable surface. Theoretical predictions of the weld pool surface temperature distributions, the cross-sectional weld pool size and shape, and the weld pool surface topology were compared with corresponding experimental measurements. Comparison of the theoretically predicted and the experimentally obtained surface temperature profiles indicated agreement within ±8 pct for the best theoretical models. The predicted surface profiles were found to agree within ±20 pct on dome height and ±8 pct on weld pool diameter for the best theoretical models. The predicted weld cross-sectional profiles were overlaid on macrographs of the actual weld cross sections, and they were found to agree very well for the best theoretical models.     

Distribution of the heat and current fluxes in gas tungsten arcs

The distribution of heat flux on a water-cooled copper anode as a function of welding process parameters has been determined experimentally following an experimental technique developed previously. The results indicate that arc length is the primary variable governing heat distribution and that the distribution is closely approximated by a gaussian function. The half width of the heat flux is defined by a distribution parameter, σ, which was determined from the experimental data and is expressed as a function of arc length, current, and electrode tip angle. The distribution parameter, σ, increases from 1.5 mm to 3.6 mm as the arc length increases from 2 mm to 9 mm for a 100 A arc. The experimental data also show that arc energy transfer efficiency is greater than 80 pct on the water-cooled anode which is much higher than has been measured in the presence of a molten metal pool. For this reason, it is believed that the distribution of the heat flux and not the magnitude is the most useful information obtained in this study. The effect of helium additions to the argon on the heat distribution is also reported. Formerly Research Assistant, is with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA     

Effects of Electroosmosis on Soil Temperature and Hydraulic Head. II: Numerical Simulation

A numerical model to simulate the distributions of the voltage, soil temperature, and hydraulic head during a field test of electroosmosis was developed. The two-dimensional governing equations for the distributions of the voltage, soil temperature, and hydraulic head within a cylindrical domain are derived based on the principles of charge, energy, and mass conservations, Darcy’s law, Ohm’s law, and Fourier’s law of heat conduction. We assumed that the voltage distribution was at steady state, whereas the soil temperature and hydraulic head were at transient states during the test. The simulated domain was segmented with a block-centered finite-difference scheme and the resulting equations were solved numerically with the successive overrelaxation method. The parameters (such as electrical, thermal, hydraulic, and electroosmotic properties of the soil, graphite, and sand) that were required by the model were measured either using core samples or slug tests. The model is able to predict the pattern as well as the magnitude of the voltage profiles observed. The simulated temperatures are similar in pattern and are within 3°C of the values observed in the four casings during 4 weeks of electroosmosis. The changes in the rates of temperature with an increase in energy input predicted by the model are in agreement with the observed changes. The output from the hydraulic head simulations showed that the model could predict patterns of hydraulic head changes in the vicinity of mesh and graphite electrodes. The model, however, underestimated the magnitude of the changes close to the anode. The simulated electroosmotic flow rate of 0.9 L/h is also consistent with the observation of 0.6–0.8 L/h.     

热风炉蓄热室内温度场的简化模型

建立了热风炉蓄热室内温度场计算的简化模型，对该模型用于预测热风炉蓄热室的热力行为是满意的。采用本模型模拟的结果表明，热风炉蓄热室内的温度分布在烧炉过程和稳定送风过程中具有较大的不同。同时，不同热物性的格砖也会极大地影响蓄热室的热交换行为。该模型对于热风炉的设计运行具有直接的工程指导意义。     

Effect of arc oscillations on the temperature distribution and microstructure in GTA tantalum welds

A two-dimensional mathematical model was developed to calculate the thermal history in thin tantalum sheets, GTA welded with arc oscillations. The model, based on the finite difference solution of the unsteady heat flow equation, was employed to calculate the temperature distribution for several arc oscillation conditions. The obtained results were used to explain experimentally observed improved microstructures in the fusion zone achieved by welding with arc oscillations. Indications are given for using the mathematical model in choosing the optimum arc oscillation conditions required for improving the microstructure of the weld. He is presently on Sabbatical leave at Lewis Research Center Cleveland, OH 44135.     

Experimental evaluation of two simple thermal models using transient temperature analysis

Thermal models are used to predict temperature distributions of heated tissues during thermal therapies. Recent interest in short duration high temperature therapeutic procedures necessitates the accurate modelling of transient temperature profiles in heated tissues. Blood flow plays an important role in tissue heat transfer and the resultant temperature distribution. This work examines the transient predictions of two simple mathematical models of heat transfer by blood flow (the bioheat transfer equation model and the effective thermal conductivity equation model) and compares their predictions to measured transient temperature data. Large differences between the two models are predicted in the tissue temperature distribution as a function of blood flow for a short heat pulse. In the experiments a hot water needle, approximately 30 degrees C above ambient, delivered a 20 s heating pulse to an excised fixed porcine kidney that was used as a flow model. Temperature profiles of a thermocouple that primarily traversed the kidney cortex were examined. Kidney locations with large vessels were avoided in the temperature profile analysis by examination of the vessel geometry using high resolution computed tomography angiography and the detection of the characteristic large vessel localized cooling or heating patterns in steady-state temperature profiles. It was found that for regions without large vessels, predictions of the Pennes bioheat transfer equation were in much better agreement with the experimental data when compared to predictions of the scalar effective thermal conductivity equation model. For example, at a location r approximately 2 mm away from the source, the measured delay time was 10.6 +/- 0.5 s compared to predictions of 9.4 s and 5.4 s of the BHTE and ETCE models, respectively. However, for the majority of measured locations, localized cooling and heating effects were detected close to large vessels when the kidney was perfused. Finally, it is shown that increasing flow in regions without large vessels minimally perturbs temperature profiles for short exposure times; regions with large vessels still have a significant effect.     

电弧焊接数值模拟中热源模型的研究与发展

焊接过程的数值模拟作为一种有效的计算手段,在焊接温度场及残余应力分布的评价中获得了广泛应用,而焊接热源模型的选择及模型参数的确定直接影响到计算和评价结果的准确性.本文通过对近年来常用的电弧焊接热源模型进行梳理,介绍了其研究进展,分析了不同热源模型的特点及适用性.高斯面热源模型和双椭球体热源模型作为基础热源模型,广泛应用于较小尺寸工件和规则轨迹的焊接过程数值模拟,且具有较高的计算精度;简化热源模型和温度替代型热源模型多用于大厚工件的多层多道焊接及复杂轨迹焊接过程的数值模拟,能够实现效率和精度的统一;多丝电弧焊接热源较为复杂,采用修正后的双椭球体叠加热源模型,计算结果能保证一定的精度;结合型热源模型对熔池形状的描述更灵活,在深熔电弧焊的数值模拟中具有优势.本文可为电弧焊接过程数值模拟的热源模型选择和模型参数确定提供有益参考.      

Prediction of weld pool and reinforcement dimensions of GMA welds using a finite-element model

Mathematical models of the gas metal arc (GMA) welding process may be used to study the influence of various welding parameters on weld dimensions, to assist in the development of welding procedures, and to aid in the generation of process control algorithms for automated applications. In this work, a three-dimensional (3-D), steady-state thermal model of the GMA welding process has been formulated for a moving coordinate framework and solved using the finite-element method. The model includes temperature-dependent material properties, a new finite-element formulation for the inclusion of latent heat of fusion, a Gaussian distribution of heat flux from the arc, plus the effects of mass convection into the weld pool from the melted filler wire. The influence of weld pool convection on the pool shape was approximated using anisotropically enhanced thermal conductivity for the liquid phase. Weld bead width and reinforcement height were predicted using a unique iterative technique developed for this purpose. In this paper, the numerical model is shown to be capable of predicting GMA weld dimensions for individual welds, including those with finger penetration. Also, good agreement is demonstrated between predicted weld dimensions and experimentally derived relations that describe the effects of process variables and their influence on average weld dimensions for bead-onplate GMA welds on steel plate. E. PARDO, formerly Postdoctoral Fellow, Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1,     

Theoretical investigation of penetration characteristics in gas metal-arc welding using finite element method

In the modeling of the gas metal-arc (GMA) welding process, heat inputs to the workpiece by the arc and the metal transfers have been considered separately. The heat energy delivered due to the metal transfer has been approximated in the form of a cylindrical volumetric heat source, whose dimensions of the radius and the height are dependent on the molten metal droplet characteristics. The pinch instability theory (PIT) and the static force balance theory (SFBT) of drop detachment have independently been used to obtain the expressions for various characteristics of the drop,i.e., the drop radius, the drop velocity, and the drop frequency at various welding parameters. The occurrence or the nonoccurrence of finger penetration, routinely found in the GMA welding at high welding currents, has been satisfactorily explained by the cylindrical heat source model. The effect of various welding parameters,e.g., the welding current, the wire radiusetc., on the weld bead penetration characteristics has been investigated. In this modeling effort, the heat conduction equation has been solved in three dimensions.     

Computer modeling of heat flow in welds

This paper summarizes progress in the development of methods, models, and software for analyzing or simulating the flow of heat in welds as realistically and accurately as possible. First the fundamental equations for heat transfer are presented and then a formulation for a nonlinear transient finite element analysis (FEA) to solve them is described. Next the magnetohydrodynamics of the arc and the fluid mechanics of the weld pool are approximated by a flux or power density distribution selected to predict the temperature field as accurately as possible. To assess the accuracy of a model, the computed and experimentally determined fusion zone boundaries are compared. For arc welds, accurate results are obtained with a power density distribution in which surfaces of constant power density are ellipsoids and on radial lines the power density obeys a Gaussian distribution. Three dimensional, in-plane and cross-sectional kinematic models for heat flow are defined. Guidelines for spatial and time discretization are discussed. The FEA computed and experimentally measured temperature field,T(x, y, z, t), for several welding situations is used to demonstrate the effect of temperature dependent thermal properties, radiation, convection, and the distribution of energy in the arc.