Int. J. Computational Materials Science and Surface Engineering, Vol. 4, No. 3, 2011
Application of a simplified simulation method to the determination of arc efficiency of gas tungsten arc welding (GTAW) and experimental validation Sanjivi Arul* and R. Sellamuthu Department of Mechancial Engineering, Amrita Vishwa Vidyapeetham (Amrita University), Coimbatore – 641 105, Tamilnadu, India E-mail:
[email protected] E-mail:
[email protected] *Corresponding author Abstract: To overcome the difficulty of solving a complex heat and fluid flow model of GTAW for predicting temperature distribution, cooling rate and weld pool geometry, a simplified simulation method has been followed in this study. The arc parameters as a measure of the heat distribution required for simulation were experimentally obtained from the arc images. The net heat flux was determined by the application of a simplified simulation method as opposed to calorimetric/genetic algorithm techniques used previously and validated experimentally. The arc efficiency was calculated as the ratio of net heat flux to the input power. The heat distribution parameter is found to be a function of current and independent of speed whereas the arc efficiency is independent of both current and travel speed. The value of arc efficiency determined in this study compares well with the data of previous studies, confirming the viability of the simulation method. Keywords: gas tungsten arc welding; GTAW; numerical simulation; heat flow; arc efficiency; heat distribution parameter; computational method; weld pool. Reference to this paper should be made as follows: Arul, S. and Sellamuthu, R. (2011) ‘Application of a simplified simulation method to the determination of arc efficiency of gas tungsten arc welding (GTAW) and experimental validation’, Int. J. Computational Materials Science and Surface Engineering, Vol. 4, No. 3, pp.265–280. Biographical notes: Sanjivi Arul is working as an Assistant Professor at Amrita Vishwa Vidyapeetham (Amrita University). He has 23 years of teaching experience to his credit. He is also a co-investigator in projects funded by Government of India. He is currently pursuing his doctoral studies in the area of welding. R. Sellamuthu has received his Doctoral degree from the University of Pittsburgh. He has published several papers in international journals and a patent to his credit. Further, he has acquired expertise in casting, welding and materials by working in several industries in the USA and executed several industrial projects. Currently, he is working as a Professor in the Department of Mechanical Engineering at Amrita Vishwa Vidyapeetham (Amrita University) and actively involved in research. He has set up a state of the art welding research laboratory at the institute with the funding received from the organisations of the Government of India. Further, he has been a consultant to foundries.
Copyright © 2011 Inderscience Enterprises Ltd.
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Introduction
Gas tungsten arc welding (GTAW) is one of the most widely employed welding processes for welding ferrous and non-ferrous metals. A heat transfer model of this process is generally used to predict temperature distribution, cooling rate and weld pool geometry which are useful in understanding microstructure, mechanical properties, segregation, residual stress, etc., of the resulting weldment (Maran et al., 2008; Tanaka et al., 2002; Zacharia et al., 1995). The process model generally involves the estimation of heat input to the workpiece from the arc source and the distribution of heat within the workpiece while accounting for the losses through radiation and convection. The net heat flux reaching the workpiece is utilised in forming the weld pool and subsequently it is lost through the outer boundaries of the workpiece. This process is further complicated by the convection occurring in the weld pool due to arc, magnetic and buoyancy forces, and surface tension gradient, etc. (Oreper et al., 1983). In order to overcome the difficulty of solving such a complex process model, a simplified approach has been followed. In this simplified model, the heat losses through convection and radiation from the arc, and conduction by the electrode need not be known, negating the need for arc modelling. In addition to physical and thermal properties of the workpiece material, the model parameters that need to be known are 1
the net heat flux reaching the surface of the workpiece
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the characteristic (heat) flux distribution parameters (Goldak et al., 1984).
The arc (thermal) efficiency is then calculated as a ratio of the net heat flux to the input power. Most of the works reported in the literature have followed two approaches to determine the net heat flux, namely, 1
experimental
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analytical/simulation methods.
Among experimental techniques, the calorimetric type of measurement has been widely used (Cantin and Francis, 2005; Dupont and Mardar, 1995; Fuerschbach and Knorowski, 1991; Giedt et al., 1989; Kou and Le, 1984; Orlowicz and Trytek, 2003; Smartt et al., 1986; Tsai and Eagar, 1985) whereas Dutta et al. (1994), Goncalves et al. (2006), Mishra and Debroy (2005), and recently Bag and De (2008, 2010) have used analytical/simulation methods. The calorimetric methods used to determine the net heat flux are cumbersome and have several drawbacks including its inability 1
to account for the heat loss during transfer
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to differentiate between transient and quasi-stationary energies as pointed out recently by Malin and Sciammarella (2006).
An alternate calorimetric method proposed by Malin and Sciammarella (2006) for laser welding also suffers from the fact that the heat loss from the upper surface of the workpiece cannot be fully accounted if applied to GTAW, and that a feature to include travel speed as a variable is lacking in this method. In a recent study, Pittner et al. (2009)
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have pointed out the shortcomings of solving inverse problems via genetic algorithm or simulated annealing methods, especially lack of a feature directly relating the model parameters to the welding variables. Further, the measurement of temperature while the welding is in progress as required in the inverse technique may result in inaccurate values due to the presence of arc voltage (Goncalves et al., 2006). A relationship between current and travel speed has not been fully established using the genetic algorithm method and results of various studies reported in the literature differ from each other in this regard. In lieu of these considerations, there is still a need to develop an efficient technique that would include all the welding variables in the estimation of the net flux and the arc efficiency. In contrast, a simple, straight forward, simulation method to estimate the net heat flux would be highly appropriate, provided all other data required for the numerical solution of transient heat transfer equation are available. Reliable data pertaining to the physical and the thermal properties of many metals and alloys are available. It is commonly known that the heat transfer within the molten weld pool is enhanced by the convection in the liquid metal. In order to account for the convection effect, researchers have adapted a method by which they have added an enhancement factor to the thermal conductivity of liquid (Zhang et al., 2003). Further, for any type of application, the simulation method must be easily performed by the users in both design and manufacturing environments and this requirement stipulates the use of commercial software packages, thereby eliminating the need for the development of custom software. The flux distribution parameter required for the heat transfer analysis was also determined by both experimental and simulation techniques. Mishra and Debroy (2005) using genetic algorithm, Tsai and Eagar (1985) using Abel’s transformation, Poloskov et al. (2006) by arc modelling, have estimated the flux distribution parameter. On the close examination of data reported in these studies, certain inconsistencies do exist among the data of various works. Case in point is the study of Poloskov et al. (2006) in which the distribution parameter does not significantly increase with current whereas it increases with current as reported by Tsai and Eagar (1985). The distribution parameter is found to increase with arc length as reported by Tsai and Eagar (1985) as opposed to no significant change in the study of Poloskov et al. (2006). In a recent study, Dobranszky et al. (2008) have highlighted the effect of electrode taper angle on the arc diameter. Further, in those studies, the voltage-current (V-I) characteristics of the power source, the welding variables and the distribution parameters are not explicitly correlated and therefore its use in simulating a real-world case is limited. In contrast, Bisen et al. (2003) have measured the arc diameter for current ranging 50 to 100 A for GTAW in the non-linear region and have taken it to be same as the distribution parameter, whereas Goldak et al. (1984) have taken the measured weld pool width itself to be the flux distribution parameter. Further, the shape of the distribution was taken to be circular in those studies, a model that is applicable only to stationary source whereas it is double ellipsoidal or at most can be considered to be double elliptical for moving source as reported by Goldak et al. (1984). In addition, a fully developed parametric model explicitly relating the distribution parameter and welding variables such as power, travel speed, taper angle, arc length, etc., is still not to be found in the literature. In the case of flux distribution parameter, it is not necessary to use analytical/simulation methods as it
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is cumbersome
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does not establish properly the relationship among arc parameters, welding variables and V-I characteristics of the power source
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requires various types of assumed or approximate input data.
In contrast, a direct measurement of the arc parameters is now feasible with the use of an image acquisition system with a CCD camera. Additional advantages of this method is that a parametric model between the dimensions of the projected arc area (circular and elliptical for stationary and moving sources, respectively) as a measure of flux distribution parameters and various welding variables such as arc length, power, travel speed, etc., can be readily established. In view of the of findings of the recent studies referred here (Bag and De, 2008, 2010; Dobranszky et al., 2008; Kermanpur et al., 2008; Maran et al., 2008; Pittner et al., 2009;) and reported elsewhere, it is to be noted that the weld process modelling remains to be a subject of current interest and the issues pertaining to its usage are still not fully resolved. Therefore, this present study is carried out for GTAW 1
to directly measure the arc parameters as a measure of the flux (heat) distribution parameters for both stationary and moving heat source using an image acquisition system and relate it to V-I characteristics of the power source and welding variables
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to determine the net heat flux reaching the workpiece using a simplified simulation method
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to validate the simulation as an alternate method via experimental data
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to determine the arc efficiency
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to evaluate the effect of input power, current and travel speed on the arc parameters and the arc efficiency
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to develop a parametric model relating efficiency and welding variables.
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Weld process model
2.1 Governing equation A schematic of the bead-on-plate welding process is shown in Figure 1 wherein the heat flux from the arc source falls onto a stationary workpiece while the arc source moves along the direction of welding. The heat transfer model applicable to the above process is given below (Kermanpur et al., 2008; Bag and De, 2008).
ρc
∂T ∂T ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ = ρ cU k + ⎜k ⎜k ⎟+ ⎟ ∂t ∂x ⎝ ∂x ⎠ ∂y ⎜⎝ ∂y ⎟⎠ ∂z ⎝ ∂z ⎠
(1)
where k is thermal conductivity, ρ is density, c is specific heat, T is temperature, t is time, x, y, z are coordinates, and U is travel speed.
Application of a simplified simulation method Figure 1
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Schematic of the bead-on-plate welding process
2.2 Initial and boundary conditions The initial condition is specified as below: T ( x, y, z , 0) = T0
(2)
where T0 is initial temperature of workpiece. The heat transfer from the surface of the workpiece to the ambient is convective and is specified as a boundary condition: Qc = Ac .h. (T − T∞ )
(3)
where Qc is total quantity of heat leaving through the outer surface of the workpiece; h is film coefficient (convective heat transfer coefficient); T∞ is ambient temperature, and Ac is surface area of the workpiece excluding the area of heat application. The distribution of the net heat flux reaching the workpiece is taken to be Gaussian and the net flux falls onto an area that is assumed to have a double elliptical shape (refer to Figure 1). The semi-axes, a and b are termed the flux distribution parameters by Goldak et al. (1984). The spatial variation of the net flux, q(x, y), falling onto to the workpiece from the arc source as a function of the distribution parameters, a and b, is expressed as another boundary condition as reported by Goldak et al. (1984): q ( x, y ) = Q p
−3 x 2 2 .e a
−3 y 2 2 .e b
(4)
where Qp is the peak heat intensity, a, b are (heat) flux distribution parameters, where a is equal to a1 and to a2 for forward and rear portion of the area of heat application, respectively; a = b for the stationary heat source (refer to Figure 1).
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2.3 Evaluation of arc efficiency The net of flux input, QNet, onto the top surface of the workpiece is obtained by integrating equation (4) from x = –a to +a and y = –b to +b. QNet = ( Q p . Ai ) 3
(5)
where area of heat application, 2
∑ a .b
Ai = (π / 2).
i
(6)
i =1
The arc efficiency is expressed as:
η = QNet (V .I )
(7)
2.4 Flux distribution model In this study, the characteristic flux distribution parameters, a, b, defining the area of heat application are taken to be the same as the arc parameters as has been followed previously (Bisen et al., 2003; Mishra and Debroy, 2005). The major differences of this study are that 1
the shape of the distribution is taken to be double elliptical, a realistic model proposed by Goldak et al. (1984) as opposed to a circular geometry used previously
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these parameters are experimentally determined. In other words, they are not derived using the information obtained from welded specimens or any type of simulation. Further, this model is highly appropriate since the transfer of heat to the workpiece is mostly via the electronic current and the contribution by convection and radiation can be considered to be negligible (Poloskov et al., 2006).
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Experimental procedure
The bead-on-plate welding experiments were performed on 1005 steel plates of 150 × 50 × 25 mm, with the current values of 100, 125, 150, 175, 200 A and the travel speed values of 0, 2, 5, 8, 10 mm/s. The welding experiments were conducted using Lincoln Electric V205T TIG machine, under DCEN mode with 2 mm diameter thoriated tungsten electrode having 60° tip angle and 99.98% argon as shielding gas at 18 lpm flow rate. Figure 2 shows a photo of the experimental set-up. The workpiece was mounted on a fixture. In the case of moving source experiments, the welding process was started by applying selected current and travel speed. The arc and the weld pool were viewed and their images were recorded through a grade 11 dimmer glass using a vision system, consisting of a grey scale CCD camera, Dalsa vision appliance and Sherlock image processing software. The voltage at various current and speed were measured manually by placing the probes across the electrodes soon after the arc has been well established.
Application of a simplified simulation method Figure 2
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Experimental set-up
In the case of stationary welding experiments, the process was stopped when there was no enlargement of the weld pool width as it implies that the steady state has been reached. All of the above experiments were repeated five times for each current value to ensure consistency and to obtain reliable data. The arc parameters, width and breadth, were determined from the images captured during the above experiments by employing an edge detection method. The specimens were cut, polished and macro-etched using usual metallographic techniques. The widths and the penetrations of the weld bead (weldment) were measured using ruled gratings.
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Numerical simulation
4.1 Thermal and physical properties The values of the solidus/liquidus temperature (1,779/1,802 K), the solid/liquid density (7.8 × 103/7.2 × 103 kg/m3) and the effective thermal conductivity of liquid (109.2 J/m s K) were taken from the work of Zhang et al. (2003) while the latent heat of fusion (2.7 × 105 J/kg) was taken from the work of Zhang et al. (2002). Data pertaining to specific heat and solid conductivity were taken from Lindgren (2007).The value of film coefficient (2.5 × 10–4 W/mm2 K) was taken from Incropera et al. (2006). The liquid thermal conductivity with an enhancement factor of ~3 was used here, following the approach of Zhang et al. (2003). Since the process involves solidification of molten metal, the latent heat of fusion is handled by adding its value to the enthalpy of liquid.
4.2 Simulation In the case of moving heat source, the heat transfer model described in equation (1) is solved by applying the initial and the boundary conditions given in equations (2) to (4)
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along with the appropriate travel speed, by using the finite element procedure given in ANSYS. In the case of stationary source, both initial condition and travel speed are not used. The simulated weld pool width, Ws, and the simulated peak heat intensity, Q ps , are obtained as described in the procedure given below: 1
Assume a value for Q ps .
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Solve equation (1) by applying appropriate initial and boundary conditions to get the temperature distribution within the workpiece.
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Obtain the temperature values along the path AB (refer to Figure 1) and plot them as shown in Figure 3.
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Take the distance between the cutting points of the liquidus line on the profile to be the weld pool width.
5
Compare the simulated pool width, Ws and the experimental pool width, We values for a given current and travel speed. If they are equal, then the assumed value of Q ps is taken to be the peak value.
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Otherwise, repeat Steps 2–5 with a new value for Q ps .
The flow chart of the above procedure is shown in Figure 4. Figure 3
Temperature versus distance
Application of a simplified simulation method Figure 4
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Flowchart
Results and discussions
5.1 Heat flux distribution Figures 5 and 6 show a set of typical images of the arc captured by the vision system. Extracted arc parameters were used to calculate the area of heat application, i.e., the projected area of the arc, and the area is plotted against the input power for various speeds as shown in Figure 7. Figure 5
Typical front view of the arc
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Figure 6
Typical side view of the arc
Figure 7
Variation of projected area of arc with power (see online version for colours)
It is to be noted that the area of heat application increases linearly with the increase in power and the value ranges 15 to 35 mm2. Bisen et al. (2003) and Tsai and Eagar (1985) have shown a similar behaviour; however, the variation reported in those studies is non-linear. Further, it can be noted from Figure 7 as well as the coefficients of a regression fit [equation (8)] to the data that the impact of travel speed is not significant on the area of heat application, an observation not to be found in the literature and a valuable finding of this study. The parametric model is expressed as below: Ai = 3.29 + 10.1 P – 0.04 U
(8)
where P is power (kW).
5.2 Estimation of net heat flux The net heat flux reaching the workpiece is estimated from the simulated values of the peak intensity using equation (5) and the area of heat application plotted in Figure 7. The simulated values of the net heat flux are reported in Table 1 for various values of power and speed.
Application of a simplified simulation method Table 1
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Net heat flux (QNet), W/mm2, estimated by simulation
Power, watt
Travel speed mm/s 0
2
5
8
10
1,200
880
890
840
940
920
1,625
1,100
1,240
1,270
1,140
1,220
2,100
1,530
1,470
1,620
1,640
1,640
2,625
2,050
1,890
2,050
2,050
1,840
3,200
2,270
2,270
2,430
2,400
2,500
5.3 Experimental validation of simulation A typical temperature profile for the path OL that is obtained through simulation is illustrated in Figure 8. Similar to the method explained previously for the extraction of weld pool width, the simulated penetration is taken to be the distance between the top surface and the cutting point (refer to Figure 8). Figure 8
Temperature distribution along the path OL
In order to assess the simulation as a viable, alternate method to determine the net heat flux, the experimental penetration is plotted against the simulated values as shown in Figure 9. It is to be noted that the simulated values are shown as lines and the experimental values are shown as data points. As can be seen from the figure, there is an excellent match between the experimental data and the simulated values of penetration for various power and speed, implying that simulation can be reliably employed to determine the net heat flux reaching the workpiece from the arc for both stationary and moving sources. Further, when compared to generic algorithm, inverse methods of net heat flux
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estimation, the method used in this investigation is simple and straight forward, involving only a single unknown variable, i.e., the peak intensity. Figure 9
Experimental and simulated weld pool penetration (see online version for colours)
5.4 Sensitivity analysis The effectiveness of the simulation method depends on the accuracies of the model parameters: density, specific heat, thermal conductivity, latent heat of fusion, film coefficient and distribution parameters. The solid/liquid densities, specific heat, latent heat of fusion and solid conductivity of 1005 steel are known accurately. Varying the film coefficient from 10–4 to 10–3 (W/mm2 K), a range generally reported in the literature, has only a negligible impact on the width of the weld pool. Thermal conductivity of liquid, with and without, an enhancement factor has been used previously (Bag and De, 2008, 2010; Zhang et al., 2003). Simulation was performed with an enhancement factor in the range of two to four times and the findings are that 1
only a minor variation in the simulated width was noticed, an observation similar to that of Komanduri and Hou (2001) in which the width is nearly independent of thermal conductivity
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increasing the factor reflects in decreasing the thermal gradient within the molten pool, an observation that is in agreement with that of Bag and De (2010).
In contrast, variation in the distribution parameters has been found to have a major impact on the width. Assumed or estimated values used in the previous studies become inappropriate so as to be employed. Therefore, a direct measurement of the arc parameters as a measure of distribution parameters guarantees the type of accuracy needed in the analysis.
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5.5 Arc efficiencies Figure 10 shows the variation of the arc efficiency, calculated from the values of power input plotted in Figure 7 and the values reported in Table 1 using equation (7), with current for various values of travel speed. As can be inferred from the plot, the arc efficiency remains almost constant and is independent of both current and travel speed. A parametric model by a regression fit to the data shown in Figure 10 is expressed as:
η = 71.8 + 0.006 I + 0.36 U
(9)
The regression analysis also indicates that the arc efficiency is constant as the coefficients of both current and travel speed are very small. However, it should be noted that other welding variables such as arc length, tip angle, etc., may influence the behaviour of the arc efficiency. Figure 10 Estimated arc efficiencies (see online version for colours)
5.6 Efficiency vs. current The first finding that 1
the efficiency is independent of current in this study is in agreement with the results of Orlowicz and Trytek (2003) (75% at low speed), and Dupont and Mardar (1995) (67%), Smartt et al. (1986) (70%) via calorimetric measurements, Bag and De (2010) and Mishra and Debroy (2005) (72%) via optimisation technique, Cantin and Francis (2005) (80%) via experiments
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our value of 74% compares well with the data of previous works.
Therefore, the simulation technique employed in this study can be considered to be reliable while it is simple and direct. In contrast, Bisen et al. (2003) and Dutta et al. (1994) have reported that the arc efficiency is a function of current. Bisen et al. (2003)
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has estimated the arc efficiency in the non-linear region of the V-I curve and it may be due to this fact that the efficiency may not be constant.
5.7 Efficiency vs. travel speed Orlowicz and Trytek (2003) has shown that the arc efficiency decreases significantly with travel speed whereas Fuerschbach and Knorowski (1991) has shown that it increases marginally with travel speed and Dutta et al. (1994) have reported that it is also a function of travel speed. Orlowicz and Trytek (2003) have used a calorimetric technique wherein the heat from the bottom of the workpiece was transferred to the calorimeter and the heat loss due to radiation and convection from the top surface is not accounted for in the calculation of efficiency. In the case of high speed, it is to be noted that the proportion of the heat loss via radiation/convection will increase as compared to the heat reaching the calorimeter due to shorter residence time of the arc over the workpiece. This phenomenon results in lower efficiency. Fuerschbach and Knorowski (1991) have used the Seebeck calorimeter wherein the heat loss during transfer of the workpiece to the calorimeter is relatively high when the workpiece temperature is high due to low travel speed, resulting in relatively low efficiency as pointed out by Malin and Sciammarella (2006). Therefore, it can be inferred from the above review of the works of Orlowicz and Trytek (2003) and Fuerschbach and Knorowski (1991) that the variation of efficiency with travel speed is due to the inadequacy of their techniques in accounting all the heat that reaches the workpiece from the arc source. Since Dutta et al. (1994) have used a very limited range of travel speed, any variation reported in their study cannot be used to draw any definitive conclusion. Yet another result of this study is to be noted, i.e., the projected area of the arc does not vary significantly with travel speed as shown in Figure 7, implying that any variation in the net heat flux will be marginal due to travel speed. Therefore, the second finding of this study is that the travel speed will not have a significant impact on the arc efficiency.
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Conclusions
Based on the investigation carried out to evaluate the viability of a simplified simulation method to determine the arc efficiency for GTAW with both stationary and moving sources, the following were concluded: 1
the value of arc efficiency determined in this study compares well with the data of previous studies, a result that confirms the viability of the simulation method adapted here
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the arc efficiency is mostly independent of current and travel speed
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the area of heat application is a function of power and is independent of travel speed.
Further, it has been found in this study that 1
measurement of the distribution parameters via imaging technique enables us to build a parametric model relating it to the welding variables
2
since the distribution parameter is obtained by an independent experiment, the estimation of the net flux via simulation becomes simple and straight forward.
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