Gaussian Heat Flux Distribution Research Articles

Numerical modelling and experimental investigations to predict the tool wear of copper electrodes during µ-EDM process

The micro electrical discharge machining (µ-EDM) process is one of the most widely used techniques to produce miniaturized components in micro-electro mechanical system (MEMS) applications due to its inherent advantages. This work investigates the wear phenomena and the morphology of the copper electrodes during the micro-die sinking process. A numerical model of a single spark is developed assuming the Gaussian distribution of heat flux to estimate the crater dimensions formed in the copper tool electrode (tool wear) used as a result of electric discharge. The crater dimension attained from the ABAQUS finite element model is validated with experimental results using a single spark test setup. Moreover, the effect of input parameters namely capacitance and voltage on the electrode wear rate and surface roughness is also studied. The crater dimensions from the single discharge study are used to formulate the wear model for different possibilities of crater distribution, such as non-overlapping craters, craters with less than 30 % overlap, and 50 % overlap. The electrode wear rate (EWR) also displayed a decline from 20.4 % to 11.6 % and further to 8 % when the overlap was permitted up to 30 % and up to 50 % for the wear model respectively. The developed model results are further compared with experimental results in terms of the electrode wear rate and depth of erosion and the deviations are found to be 20.33 % and 20.55 % respectively

Computational fluid dynamics based multi-species transport simulation of auxiliary energy systems for friction stir welding of dissimilar materials

This research compares auxiliary energy-assisted friction stir welding (FSW) techniques with conventional FSW when joining dissimilar materials. Specifically, it conducts numerical modeling and experimental validation for the effectiveness of plasma-assisted FSW and induction-assisted FSW for DH36 steel and 6061-T6 aluminum alloy. Fully coupled 3D computational fluid dynamics (CFD) models, incorporating the multi-species transport method, were developed, where the species mass fractions of the workpieces are transported through diffusion, convection, and reaction sources for individual species. Based on the temperature validation, the dedicated heat flux based on the rectangular heat flux and Gaussian heat flux distribution were considered for induction coil and plasma arc heating on the DH36 steel side, respectively. The established conventional and auxiliary energy-assisted FSW models were validated against experimentally observed temperature fields and the joints’ material features. Results indicate that the assistance of plasma and induction auxiliary energy sources increased the temperature field, strain rate, and flow velocity without forming stagnant zones on the steel side caused by reduced dynamic viscosity. In plasma arc-assisted FSW, the steel could not extrude effectively from the base steel sheet due to deficient heat and flow velocity input; therefore, defect-prone coarse steel fragments were blended with the Al matrix. In induction-assisted FSW, the uninterrupted steel layer was extruded from the steel side and placed on the Al side, which was caused by enhanced heat build-up and flow velocity. Moreover, induction-assisted FSW achieved symmetric material flow on both advancing and retreating sides, resulting in defect-free welds.

Analyzing Thermal Processes in Laser Welding of Multi- Component Heat-Resistant Alloy Thin-Walled Butt Joints: A Comprehensive Modeling Approach

Niobium-based alloys are vital in high-temperature environments due to their unique chemical composition, phase structure, high density, and oxidation resistance. These alloys find extensive applications in industries such as medicine, engine manufacturing, and space technology. This study delves into the complexities of modeling laser welding processes, necessitated by the multitude of dynamic parameters specific to each surface configuration. Finite element modeling was conducted using COMSOL Multiphysics to analyze the heat transfer in butt joints between Nb-15W-5Mo-1Zr alloy plates under 400 W laser radiation power. The research employed finite element modeling to analyze heat transfer in Nb-15W-5Mo-1Zr alloy plates, considering non-uniform movement at the start and end of the welding process, Gaussian heat flux distribution along the laser spot radius, and temperature-dependent reflection coefficient. The models accounted for non-uniform movement, Gaussian heat flux distribution, and temperature-dependent reflection coefficient. The study demonstrated that thin plates of Nb-15W-5Mo-1Zr alloy can be effectively welded using specific laser processing modes, leveraging their high initial cooling rate of 1.2-1.3 s. Successful welding of Nb-15W-5Mo-1Zr alloy plates requires careful consideration of laser processing parameters. While the alloy's thermodynamic properties allow for effective welding, ensuring weld quality mandates additional production processes aimed at preventing potential part failure.

A Thermal Analysis of LASER Beam Welding Using Statistical Approaches

Implementing input parameters that match the experimental weld shape is challenging in LASER beam welding (LBW) simulation because the computed heat input and spot for temperature acquisition strongly affect the outcomes. Therefore, this study focuses on investigating the autogenous LBW of AISI 1020 using a three-dimensional heat transfer model that assumes a modified Gaussian heat flux distribution depending on LASER power (Qw), radius (R), and penetration (hp). The influence of such variables on the simulated weld bead was assessed through analysis of variance (ANOVA). The ANOVA returns reliable results as long as the data is normally distributed. The input radius exerts the most prominent influence. Taguchi’s design defined the studied data reducing about 65% of the simulations compared to a full factorial design. The optimum values to match the computed outcomes to lab-controlled experiments were 2400 W for power (80% efficiency), 0.50 mm for radius, and 1.64 mm for penetration. Moreover, the experimental errors regarding thermocouples positioning were corrected using linear interpolation. A parallel computing algorithm to obtain the temperature field reduces computational costs and may be applied in real-world scenarios to determine parameters that achieve the expected joint quality. The proposed methodology could reduce the required time to optimize a welding process, saving development and experimental costs.

Experimental and Numerical Analysis on TIG Arc Welding of Stainless Steel Using RSM Approach

This study involves the validating of thermal analysis during TIG Arc welding of 1.4418 steel using finite element analyses (FEA) with experimental approaches. 3D heat transfer simulation of 1.4418 stainless steel TIG arc welding is implemented using ABAQUS software (6.14, ABAQUS Inc., Johnston, RI, USA), based on non-uniform Goldak’s Gaussian heat flux distribution, using additional DFLUX subroutine written in the FORTRAN (Formula Translation). The influences of the arc current and welding speed on the heat flux density, weld bead geometry, and temperature distribution at the transverse direction are analyzed by response surface methodology (RSM). Validating numerical simulation with experimental dimensions of weld bead geometry consists of width and depth of penetration with an average of 10% deviation has been performed. Results reveal that the suggested numerical model would be appropriate for the TIG arc welding process. According to the results, as the welding speed increases, the residence time of arc shortens correspondingly, bead width and depth of penetration decrease subsequently, whilst simultaneously, the current has the reverse effect. Finally, multi-objective optimization of the process is applied by Derringer’s desirability technique to achieve the proper weld. The optimum condition is obtained with 2.7 mm/s scanning speed and 120 A current to achieve full penetration weld with minimum fusion zone (FZ) and heat-affected zone (HAZ) width.

Plasma-Assisted Hybrid Dissimilar Friction Stir Welding for Joining of DH36 Steel and AISI 1008 Steel: Thermal Modelling and Experimental Analysis

Dissimilar materials joining by hybrid FSW involve preheating the harder material ahead of the FSW tool, which reduces the vertical force and improves the weld quality by enhancing the material flow. In this work, both experimental and numerical analyses were conducted for the friction stir welding (FSW) and plasma-assisted friction stir welding (PAFSW) of dissimilar steels such as DH36 shipbuilding steel and AISI 1008 steel. The comparative study was performed on the thermal history, vertical force, mechanical and microstructural characterizations under different welding conditions. The 3D transient thermal phenomenological models were established using Abaqus/CAE 2017 finite element (FE) software package. The moving heat source models for FSW and PAFSW were successfully established, which were embedded in a Fortran code and fed to Abaqus/CAE through DFLUX subroutine. The additional heat source, i.e. plasma arc heat source, was modelled using the Gaussian distribution of heat flux. The stir zone isotherms of the developed numerical models and the transient thermal profiles in the FSW and PAFSW were matched fairly well with experimental results. For the reliable comparative study, the consequence of FSW parameters (i.e. traverse speed and rotational speed) and preheating parameters (i.e. plasma offset and preheating current) on thermal history was investigated. It was observed that the assistance of the plasma preheating ahead of FSW tool was significantly reduced the grain size and vertical force. In contrast, the hardness and the impact toughness values were increased compared to that of FSW.

Effects of various modeling assumptions on steady-state and transient performances of single-phase natural circulation loop

It is necessary to investigate the relative effect of various phenomena before neglecting the same for simulating the single-phase natural circulation loop to obtain an acceptable prediction. Hence, the present study focuses on the validation and effect of different assumptions related to Boussinesq approximation, property variation, bend effect, heat loss, axial fluid and wall conduction on the transient and steady-state characteristics. Effect of assumptions for different working fluids (water, brines and hybrid nanofluids), and assess the effect of different heat flux distributions, like uniform, linear, non-linear, sinusoidal and Gaussian, applied to heater are also explored. Mass flow rate (predicts heat transport capability), effectiveness (predicts heat transfer ability) and entropy generation rate (predicts irreversibility) are evaluated. The results disclose that the Boussinesq approximation with constant other properties under-predicts the steady-state mass flow rate and effectiveness and over-predicts the entropy generation rate. This assumption cannot be applied for all working fluids. The fluid and solid conduction is the crucial parameter for simulating transient characteristics. Gaussian heat flux distribution shows the highest mass flow rate and non-linear increasing heat flux shows the highest effectiveness and entropy generation rate. This study will help to consider reasonable assumptions for the numerical simulation.

Estimation of distributed heat flux parameters in localized heating processes

In this work a numerical-experimental methodology is presented based on a combined finite element model and experimental tests, for the determination of the heat flux distribution in oxy-acetylene localized heating processes commonly employed in the shipbuilding industry. The Levenberg-Marquardt algorithm is employed in the inverse conduction heat transfer problem using the results of experimental tests in thin flat circular steel plates with different thicknesses subjected to heat flux applied over the heated area, considered constant from the beginning to the end of heating, on the centre of the plates, followed by natural cooling. The transient temperatures in different points of the plate are measured by five thermocouples, affixed opposite to the oxy-acetylene flame. Additionally, the thermal analysis is performed using a non-linear two-dimensional axisymmetric finite element model to describe the heating and cooling processes, and the calculated and measured temperatures are compared. A statistical analysis is performed to demonstrate the stability of the methodology and the reliability of the results. Average residuals from the discrete in blocks and continuous Gaussian heat flux distribution models are compared. Good agreement is achieved with the use of the inverse problem methodology.

Analysis of multi-spark in wire electrical discharge machining

Electrical discharge machining plays a vital role in precision manufacturing processes. It is a non-conventional machining process in which electrical energy is converted into thermal energy by means of spark in a Di-electric fluid medium. Due to generation of temperature above melting point the material removal takes place. This paper presents the analysis performed on Aluminium 6061 – T6 Alloy with single-spark and multi-spark machining situations to predict temperature distribution and material removal rate. Gaussian heat flux distribution is used to simulate heat flux and four pulses are considered in multi-spark case in thermo-physical model. The results of single-spark and multi-spark simulated machining process were compared and it is observed that material removal rate and temperature distribution are higher in multi-spark simulated machining as compared to single spark.

Thermomechanical Simulations of Residual Stresses and Distortion in Electron Beam Melting with Experimental Validation for Ti-6Al-4V

Electron beam melting (EBM) is a relatively new process in three-dimensional (3D) printing to enable rapid manufacturing. EBM can manufacture metallic parts with thin walls, multi-layers, and complex internal structures that could not otherwise be produced for applications in aerospace, medicine, and other fields. A 3D transient coupled thermomechanical finite element (FE) model was built to simulate the temperature distribution, distortion, and residual stresses in electron beam additive manufactured Ti-6Al-4V parts. This research enhances the understanding of the EBM-based 3D printing process to achieve parts with lower levels of residual stress and distortion and hence improved quality. The model used a fine mesh in the layer deposition zone, and the mesh size was gradually increased with distance away from the deposits. Then, elements are activated layer by layer during deposition according to the desired material properties. On the top surface, a Gaussian distributed heat flux is used to model the heat source, and the temperature-dependent properties of the powder and solid are also included to improve accuracy. The current simulation has been validated by comparing the FE distortion and temperature results with the experimental results and other reported simulation studies. The residual stress results calculated by the FE analysis were also compared with the previously reported simulation studies on the EBM process. The results showed that the finite element approach can efficiently and accurately predict the temperature field of a part during the EBM process and can easily be extended to other powder bed fusion processes.

Concept for the calculation of the distribution of heat input in the cathode area by GMA welding

Currently used approaches for the modeling of the heat input in gas metal arc (GMA) welding process simulation usually assume an axisymmetrical Gaussian distribution of heat flux in the cathode region. However, as in GMA welding, cathodic electron emission of non-refractory metals is involved; the attachment region consists of multiple highly mobile cathode spots, which have a highly concentrated current density, which cannot be explained solely by thermionic emission, as is present in refractory cathodes. In this work, a novel concept is presented to determine the distribution of the cathode spots, allowing to determine the distribution of heat flux and current density, to serve as boundary conditions in a magneto-hydrodynamic weld pool simulation. While the concept does not yet deliver a fully convergent solution, a model lies at its core, which takes into account the experimentally determined high current density and provides a relationship between the cathode surface temperature, the generated heat flux, and the current density. By applying a stochastic cellular automaton method, the weighted random walk of the movement of the cathode spots is simulated, according to a probability determined by the potentially released heat flux. Averaging over time gives a spatially resolved distribution of heat flux and current density.

Thermal modeling of single discharge in prospect of tool wear compensation in μEDM

Due to the non-isoenergetic nature of discharge pulses in resistance-capacitance (RC) based micro electrical discharge machining (μEDM), the volume of produced micro-crater by each pulse varies significantly. This fact has driven the researchers in this work to propose an electrothermal principle–based analytical model to approximate dimensional accuracies of such micro-craters. A finite element (FE) simulation considering Gaussian heat flux distribution of single discharge μEDM has been performed at significant input parameters such as discharge energy, capacitance, and open-circuit voltage and compared with analytical simulation results. Upon validation of these simulated results with experimental results, nominal dimensional inaccuracies of 2–11% for a wide range of input parameters have been noticed. This effectively predicted crater dimension from the workpiece can be incorporated in the proposed thermal modeling–based real-time tool wear monitoring and compensation system through a unique strategy, which is discussed at the end.

Finite element model for topography prediction of electrical discharge textured surfaces considering multi-discharge phenomenon

The prediction of surface topography obtained with electrical discharge texturing (EDT) process is very challenging, due to stochastic nature and complex physics in occurrence of sparks. Though there are a few models for surface texture prediction in the literature, there are still ample opportunities to improve upon by adopting more realistic assumptions and formulations for simulation. This paper presents a numerical simulation of progressive development of surface topography due to sequential application of spark discharges on an instantaneous textured surface formed by all previous spark discharges. The model incorporates major single-spark features such as, Gaussian distribution of heat flux, temperature-dependent work material properties, latent heat of melting, and operating parameter dependent variation of factors such as, cathode energy fraction, spark radius, and plasma flushing efficiency; besides the multi-spark features such as, stochastic distribution of sparks with respect to: i) location, ii) energy level, and iii) chronological order. Finite element simulation of EDT is performed in ABAQUS with the help of user-defined subroutines for the dynamic simulation of spark discharges, flagging of elements attaining evaporation temperature from further heat flux application and storage of the highest temperatures attained by each element. An evolution of surface texture through the progress of spark erosions has been studied. As EDT continues, the number of craters overlapping generally tend to increase, whereas the center-to-center distance between a crater with its nearest neighbour tends to decrease. The simulated surface textures are validated with the experimental ones using two methods: error function method and Ra distribution method, and were found to be in good agreement.

Multi-spark model for predicting surface roughness of electrical discharge textured surfaces

Several models in the literature predict the average surface roughness (Ra) of electrical discharge textured surfaces using either a single-spark simulation for roughness estimation, or a multi-spark simulation with a uniform or a symmetric distribution of sparks. This paper presents an improved approach for surface roughness prediction, by generating surface profiles with the stochastic distribution of sparks with respect to the following: (i) location, (ii) energy level, and (iii) time. In addition, the formulation for single-spark adopts better assumptions, such as a Gaussian heat flux distribution for sparks, temperature dependency of material properties, and the operating parameter-dependent variation of factors, such as spark radius, cathode energy fraction, and plasma flushing efficiency. Surface profiles are simulated by the multi-spark model, considering the stochastic distribution of crater profiles, which are evaluated by the single-spark model. Unique profiles are obtained for each run of the multi-spark model, for a particular parameter combination. They vary in location, size, and shape of individual peaks and valleys, among each other due to this stochastic distribution of sparks. This variation among profiles agrees well with the variable distribution of peaks and valleys in actual EDTed surface profiles. It is observed that an increase in discharge current and pulse on-time leads to a lesser number of peaks and valleys, and a higher peak-to-valley height on the surface profile, due to increase in individual crater dimensions. The adoption of the more realistic assumptions in current model reduces the average Ra prediction error to 11.5%.

Numerical simulation of part-level temperature fields during selective laser melting of stainless steel 316L

Numerical transient thermal analysis of a part during the selective laser melting process is a great challenge due to huge computational cost. An efficient simulation scheme is proposed to estimate the temperature distribution and history in part level. The building domain is coarsely meshed at the beginning. Then, deposited elements are activated layer by layer with desired material properties. The Gaussian distributed heat flux is applied to the top surface and travels according to the predefined scanning path. With the motion of input heat flux, the mesh is continuously refined and coarsened as the laser beam moves in and out. To improve the solution accuracy, temperature-dependent thermal properties in powder and solid state are incorporated in the finite element system. To reduce the computation cost, the Gaussian line heat source with a large time step length is used to replace the traditional moving Gaussian point heat source. To achieve a compromise between the computational efficiency and the solution accuracy, the hybrid of the Gaussian line heat source and Gaussian point heat source is adopted as heat input and results are compared with that of the Gaussian point heat source. The proposed simulation scheme is validated by comparing the simulated geometry of the melt pool with experimental results. Simulation results show that the proposed simulation scheme has the ability to efficiently and accurately predict the temperature field of a part during the selective laser melting process and can be easily extended to other powder bed fusion processes.

Numerical simulation of the influence of fluid motion in mushy zone during micro-EDM on the crater surface profile of Inconel 718 alloy

The micro-EDM, due to its ability to machine any electrically conductive material, has been one of the preferred manufacturing methodologies for machining difficult to machine materials. The micro-EDM is a thermal energy-based material removal process where the material removal occurs by spark erosion. In majority of the modeling associated with micro-EDM, the effect of the fluid motion in the liquid and mushy phase of the workpiece alloy is not considered. This paper aims at numerically simulating the crater surface profile formed on Inconel 718 incorporating the effects of material movement in the mushy zone using micro-EDM. Navier–Stokes equations were used as the governing equations. Temperature-dependent specific heat, thermal conductivity, density and viscosity were incorporated, in three ranges, i.e., solid ( $${T}<1523\hbox { K}$$ ), liquid ( $$T>1609\hbox { K}$$ ) and mushy ( $$1523\hbox { K}<{T}<1609\hbox { K}$$ ). The mushy zone properties were calculated using enthalpy porosity method, and the properties were updated after each iteration. Specific boundary conditions like Gaussian distributed heat flux on the top surface, fixed percentage of heat to the anode and Marangoni stress on the top surface of the workpiece were applied. The simulations were performed using CFD package ANSYS 15.0 FLUENT for three distinct voltages 100, 125 and 150 V, keeping capacitance constant at $$0.4\,\upmu \hbox {F}$$ . User-defined functions were written in C language to incorporate the temperature-dependent properties and the boundary conditions. These simulated results were compared with the experimental values at same input condition, and the maximum calculated deviation in crater profile prediction was less than 14%.

Investigation of Thermal Efficiency and Depth of Penetration during GTAW Process

Abstract A numerical and experimental investigation of gas tungsten arc welding (GTAW) of AISI 304L was carried out to obtain the thermal field, depth of penetration with varying input process parameters. A three-dimensional finite element model is developed to simulate the GTAW welding process considering double ellipsoidal heat source with Gaussian heat flux distribution. A novel iso-volume approach is used to estimate the melting efficiency of the process and calculated maximum melting efficiency of the process is found 44 %. Calculated results in terms of thermal histories and depth of penetration have compared with measured results and are in good agreement.

Evaluation of Micro-EDM (μEDM) Characteristics of Conductive Silicon Carbide Using a Coupled Thermo-Structural Process Model

In this work, micro-EDM ([Formula: see text]EDM) characteristics of conductive SiC have been evaluated using the knowledge of existing coupled thermo-structural model. A simplified thermo-structural model of [Formula: see text]EDM process on conductive SiC has been used to simulate the [Formula: see text]EDM process on conductive SiC. So far, the studies have used traditional melting and evaporation removal mechanism during EDM simulation which is suitable for metals. In case of ceramics, material removal occurs by various phenomenon such as spalling, melting, evaporation and it depends on [Formula: see text]EDM energy and type of ceramic. Thus, we aim here to evaluate the characteristics of a SiC ceramic using the thermo-structural model. To make the model more realistic, Gaussian heat flux distribution has been used and transient study has been performed. The model uses process parameters (voltage, capacitance and time) and material properties as input to predict the transient temperature distribution, crater dimensions, volume of material removed and thermal residual stresses. To simulate the material removal, element death has been performed. The element death is purely based on attainment of certain temperature suitable for material removal irrespective of material removal mechanism. The transient thermal analysis was carried out in heating phase and the structural analysis was carried out in cooling phase. Observatory experiments were performed to add value to the model predictions.

A modeling study of stress and strain formation induced during melting process in powder-bed electron beam melting for Ni superalloy

In order to decrease deformation and stress in powder-bed electron beam melting, clarification of the characteristics of strain and stress formation during the melting process would be of great benefit. We developed an FE-based 3D thermal elastoplastic model with a Gaussian heat flux distribution profile in raster scanning pattern for Ni superalloy “René 80”It was confirmed that strain variation in simulation showed good agreement with values calculated by a proposed mechanical model and proved to be quantitatively valid. The stress distribution during the melting process showed anisotropy in that the stresses in the beam scanning direction were higher than those in the other directions. The anisotropy formation mechanism was explicable by plastic strain anisotropy dominated by the restraint condition in that orthogonal direction was free boundary and lengthwise direction was subjected to restraint.

FE Modeling for Single Spark in EDM Considering Plasma Flushing Efficiency

Due to complex nature of single spark phenomenon in EDM, the removal mechanism needs better comprehension and clarity. In this context, this work presents a finite element simulation of a single spark during electrical discharge machining taking into consideration significant aspects such as temperature dependency of material properties, Gaussian distribution of heat flux, plasma channel radius varying with current and discharge duration, and variability in factors such as cathode energy fraction, and plasma flushing efficiency. Such a model can offer a better prediction of the crater profile obtained on the work surface which enables it to be extended to multi-spark scenarios for predicting the surface texture obtained through EDM process. FE simulations showed that the crater radius and crater depth increases with increasing values of the operating parameters such as discharge current and pulse on-time. It is also observed that the crater aspect ratio (rc / dc), which is the ratio between crater radius and crater depth, shows a high value at low values of discharge current and pulse on-time. This is due to feeble penetration of heat through the cathode body for low values of the operating parameters. The validation of the FE model is made against experiments and it was found that the model displays improved prediction at high values of the operating parameters. The error in prediction of rc / dc by the model varies from 9.1 to 13.4 % which represents a good prediction of crater profile by the model.