Int. J. Computational Materials Science and Surface Engineering, Vol. 5, No. 2, 2013
Development of a regression model relating experimentally measured arc parameters and gas tungsten arc welding process variables Sanjivi Arul* and R. Sellamuthu Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham (Amrita University), Coimbatore – 641 112, Tamilnadu, India E-mail:
[email protected] E-mail:
[email protected] *Corresponding author Abstract: In order to solve the heat transfer model of GTA welding process, the physical and the thermal properties of the workpiece, the heat source efficiency and the area of heat incident on the workpiece surface are required. In this work, the arc dimensions were measured experimentally with respect to current, speed, electrode tip angle and electrode distance for autogenous GTA welding. The arc parameters were fitted against welding variables using regression analysis. The projected arc area is found to increase with current and electrode distance and to decrease with electrode tip angle whereas it is found to be independent of speed. The shape of the projected arc area is observed to be semi-circular in the front and semi-elliptical in the rear for moving heat source. The regression equation developed can be readily applied in estimating the area of heat incident for solving the heat transfer equation. Keywords: gas tungsten arc welding; GTAW; numerical simulation; heat distribution parameter; arc parameters; electrode distance; electrode tip angle; welding current; welding speed; regression analysis; computational materials science; surface engineering. Reference to this paper should be made as follows: Arul, S. and Sellamuthu, R. (2013) ‘Development of a regression model relating experimentally measured arc parameters and gas tungsten arc welding process variables’, Int. J. Computational Materials Science and Surface Engineering, Vol. 5, No. 2, pp.177–188. Biographical notes: Sanjivi Arul is working as an Assistant Professor at Amrita Vishwa Vidyapeetham (Amrita University). He has 25 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 is a Professor in the Department of Mechanical Engineering at Amrita Vishwa Vidyapeetham (Amrita University). His research interests are in the areas of materials, casting and welding. He is actively involved in the funded research at the university. He received his Doctoral degree from the University of Pittsburgh and has published several papers in international journals.
Copyright © 2013 Inderscience Enterprises Ltd.
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Introduction
Modelling of thermal cycles occurring during gas tungsten arc welding (GTAW) and thereby predicting the microstructure and the properties of the weldment has been under investigation recently. A generalised heat transfer model of the process to predict the thermal cycle has been reported previously by several researchers including Kermanpur et al. (2008) and Bag and De (2008). In order to solve the model, the physical and thermal properties of the workpiece, the heat source efficiency and the area of heat incident on the workpiece surface are required. Therefore, it becomes apparent that the characterisation of the heat source is necessary. The heat source is characterised by three parameters; namely, the efficiency, the geometry of the arc and the heat distribution within the arc column. Rosenthal has considered the geometry of the heat source to be a point or a line whereas Pavelic et al. (1969) used a disc model. In contrast, Goldak et al. (1984) have shown that ellipsoidal models are more realistic for autogenous welding. Instead of assuming an uniform heat distribution within the arc as taken by Rosenthal, Pavelic et al. (1969) proposed a Gaussian distribution model for the heat that is incident on the surface of the work piece and the variation of the heat intensity (flux) on the surface as a function of position is expressed as: q(r ) = q (0).e −Cr
2
(1)
where q(r) – flux on the workpiece surface at radius r (W/m2); q(0) – peak intensity at the centre of the heat source (W/m2); C – distribution width coefficient (m–2); r – radial distance (m) from the centre of the heat source. The circular disc-shaped geometry along with Gaussian heat distribution on the surface proposed by Pavelic et al. (1969), Friedman (1975) and Krutz and Segerlind (1978) has not been fully successful in estimating the thermal cycles for shallow penetration welding such as GTAW. In contrast, Goldak et al. (1984) have proposed a generalised ellipsoidal heat intensity model which is applicable for both shallow and deep penetration welding, such as electron beam and laser welding. Figure 1
Schematic of the bead-on-plate welding process
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Since the digging action is not significant in the case of GTAW, the double-ellipsoidal geometric model of Goldak et al. (1984) can be considered to be double-elliptical. A schematic diagram of the surface model is shown in Figure 1 for the bead on plate welding process. Assuming that the peak intensity falls at the boundary of the ellipse to 5% of its value, the positional variation of the heat flux under a set of welding parameters can now be expressed as below: 2
3ηVI −a32x −b32y q ( x, y ) = .e .e πab
2
(2)
where η – the arc efficiency; V – voltage; I – welding current; a, b – the geometric parameters of the arc, where a is af and ar for forward and rear portion of the arc, respectively; a = b for the stationary arc. These parameters are also called the heat distribution parameters in the literature. Several studies have been conducted to estimate the arc parameters (refer to Figure 1) af, ar and b by using four different methods viz. by relating them to the weld pool dimensions, split anode calorimetric method, theoretical models (genetic algorithm, etc.) and vision-based measurement of the arc.
1.1 Weld pool dimensions Goldak et al. (1984) have postulated that the three characteristic parameters af, ar and b, are related to the weld pool width (W) as below b =W / 2
(3)
af = W / 2
(4)
ar = 2W
(5)
In their study to determine GTAW efficiency, Dutta et al. (1994) measured the values of the weld pool length in the front and the rear of the electrode along with weld pool width and used them as heat distribution parameters af, ar and b respectively.
1.2 Calorimetric method By using split anode calorimetric technique, Nestor (1962) and Tsai and Eagar (1985) have determined the heat distribution parameters by assuming the geometry of the source as circular. Lu and Kou (1988) arrived at an empirical relation for heat distribution parameter as given in equation (6) while studying the effects of arc current, arc length and the electrode diameter on the power and current distributions. σ = 0.533I 0.2941
(6)
1.3 Inverse techniques – genetic algorithm and Abel’s transformation Considering the heat distribution parameter as one of the uncertain parameters, Mishra and Debroy (2005b), Bag and De (2008, 2010), Bag et al. (2009) etc., by genetic algorithm-based approach and Tsai and Eagar (1985) and Thornton (1993) by Abel’s transformation method have indirectly arrived at the distribution parameter while
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assuming circular heat source (disc model). Tsai and Eagar (1985) have estimated the arc radius as a function of arc length, current, and electrode tip angle.
1.4 Vision-based method To study the effect of electrode tip angle, Dobranszky et al. (2008) measured the arc dimensions using the arc images. Using arc images, Bisen et al. (2003) obtained a relationship between arc radius and welding current ranging 75 to 100 A for stationary GTA welding of gamma TiAl. The relationship is given in equation (7). Rc = 0.42 I 0.53
(7)
It can be noted that the area of the heat source incident on the metal surface, in most of the cases cited as above, is considered as circular. The circular geometry is applicable for stationary heat source, whereas it is double ellipsoidal or double elliptical (if digging action is neglected) for moving source as reported by Goldak et al. (1984). Further, those studies which consider the heat source as non-axisymmetric (ellipsoidal, double-ellipsoidal or double-elliptical) have approximated the weld pool dimensions as the arc parameters. Further, the arc dimensions were estimated only through indirect methods as mentioned above. The study of Bisen et al. (2003) has considered the effect of only current in a limited range on the arc radius. But, the arc shape and size are also dictated by other welding parameters like speed, electrode distance and electrode tip angle. Analytical/simulation method is cumbersome, requires various types of assumed or approximate input data. A realistic method would be to use an experimental technique to directly measure the arc dimensions and develop parametric model relating the arc dimensions to the critical welding parameters like current, speed, electrode distance and electrode tip angle. A study of this nature is not found in the literature. Recently, Arul and Sellamuthu (2011) have investigated the effect of welding current and welding speed on the arc dimensions. However, it is not comprehensive as this investigation does not include the electrode tip angle and electrode distance. In the present study, a vision-based imaging system was employed to capture the images of the arc and extract the arc dimensions during bead on plate autogenous GTAW, with the following objectives: 1
to establish a vision-based method to measure the arc dimensions
2
to study the variation of the arc parameters with welding current, welding speed, electrode distance and electrode tip angle
3
to develop a model for the behaviour of the arc characteristics
4
to establish the correlation between the weld pool width and the arc width.
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Experimental procedure
The experimental setup consists of Lincoln Electric V205T TIG welding machine, a servo motor driven manipulator controlled by a PLC and vision system with Dalsa vision appliance, a CCD grey-scale camera and Sherlock machine-vision software. The torch was held stationary in the vertically down position. The working table fixed to the
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manipulator was moved, while the torch was kept stationary. Argon was used as shielding gas at 18 lpm flow rate. The electrode used was a 2 mm diameter thoriated tungsten electrode. The welding mode used was DCEN. A photograph of the experimental setup is shown in Figure 2. Figure 2
Experimental setup
In this experiment, mild steel specimens were used (150 mm × 50 mm × 25 mm). The welding parameters and the welding conditions used are reported in Table 1. A total of 240 experiments were performed. Bead on plate welding was performed on the specimen. In each trial, welding was done for a length of 100 mm. The welded plates were cut, polished and macro-etched using the usual metallographic techniques. The weld pool widths were measured using ruled gratings. Table 1
Experimental parameters
Parameter Current Weld speed Electrode angle Electrode distance Figure 3
Unit
Values
A
100, 150, 200
mm/s
0, 2, 5, 8, 10
degrees
30, 45, 60, 180
mm
3, 4, 5, 6
(a) A typical image of the arc taken perpendicular to weld direction (b) Schematic diagram of the arc showing the arc parameters
(a)
(b)
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An image of the arc was captured for every trial. A typical arc image is shown in Figure 3 along with the characteristic parameters. The arc dimensions were extracted from the captured images using Sherlock machine vision software after proper calibration.
3
Results and discussion
3.1 Variation of arc parameters Figures 4 and 5 show the measured values of af and ar plotted against the welding variables namely current, speed, electrode distance and electrode tip angle (refer to Table 1), respectively. These plots are in the form of multi-vari charts as described by Breyfogle (2003). The multi-vari chart (refer to Figure 4) pertaining to the values of af contains 15 panels arranged in three columns and five rows. In each panel, the panel variables, speed and current are kept constant. The x-axis indicates the electrode distance and the y-axis indicates af. Within each panel, there are four clusters of af values for different electrode distances. Each cluster consists of four af values, corresponding to four different tip angles. Similarly, the multi-vari chart for ar is constructed as shown in Figure 5.
3.1.1 Effect of electrode tip angle It can be noted from the first cluster of the first panel (refer to Figure 4), that the af value decreases with an increase in the tip angle. The same behaviour can be observed for all the panels in Figures 4 and 5. Goodarzi et al. (1997) performed stationary welding experiments to assess the effect of tip angle ranging 10° to 150° on the arc diameter. They have reported that an increase in tip angle shrinks the arc diameter. Dobranszky et al. (2008) experimentally captured the arc images and determined the geometry of the arc with respect to various tip angles ranging 30° to 90°. They have found out that the arc diameter decreases with an increase in the tip angle in this range. Our results are found to be consistent with the observations of Goodarzi et al. (1997) and Dobranszky et al. (2008). Therefore, it can be concluded that the af and ar values decrease with an increase in tip angle.
3.1.2 Effect of electrode distance It can be noted from the first panel (refer to Figure 4), that the mean af value for each cluster increases with an increase in the electrode distance as shown by the trend line. This behaviour is observed in all the panels shown in Figures 4 and 5. Allum (1983), and Eagar (1985) and Poloskov et al. (2006) have reported that the arc radius increases with the electrode distance whereas Mendez (1999) have reported that the arc radius remains constant with electrode distance. In this case also, our values are in agreement with the data of previous works, expect that of Mendez (1999). Therefore, it can be concluded that the af and ar values increase with an increase in electrode distance.
Development of a regression model relating experimentally measured arc Figure 4
Variation of ‘af’ and b with welding variables (see online version for colours)
Figure 5
Variation of ‘ar’ with welding variables (see online version for colours)
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3.1.3 Effect of welding current In the literature, a distribution parameter referring to the radius of the heat incident on the surface of the work piece is considered for heat transfer analysis in lieu of the arc parameters. Mendez (1999) have reported that the arc radius remains approximately constant for currents from 150 to 300 A whereas Tsai and Eagar (1985) and Bisen et al. (2003) have shown that the distribution parameter increases with current. Referring to panels 1, 2 and 3, it can be observed that the panel mean value of af (indicated by diamond) increases with an increase in current. Based on these results reported in Figures 4 and 5, it can be inferred that the af and ar values increase with current, an observation consistent with that of Tsai and Eagar (1985) and Bisen et al. (2003).
3.1.4 Effect of welding speed Figure 6 shows the variation of af and ar with welding speed for 100 A current, 3 mm electrode distance and 60° electrode tip angle. It can be observed that af decreases and ar increases with increase in welding speed, signifying that the front portion of the arc is compressed while the rear portion of the arc is elongated when the speed is increased. This finding is in agreement with that of Goldak et al. (1984). Many authors including Pavelic et al. (1969) and Mishra and Debroy (2005a, 2005b) have taken the shape of the heat source at the surface of the wokpiece to be circular for all welding speeds. Based on our experimental studies, it is inappropriate to assume the shape to be circular irrespective of the welding speed. Figure 6
Variation of af and ar with welding speed (see online version for colours)
3.2 Shape of the projected area of arc on the metal surface It was observed from the measured data that the half width, b of the arc is almost equal to af (refer to Figure 1) and hence the arc parameter b is taken to be equal to af. Therefore, it can be observed that the projected area of the arc at the surface of the metal is 1
circular for stationary heat source
2
semi-circular for the front portion and semi-elliptical for the rear portion for moving heat source.
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Based on our findings, a modification to the double-elliptical model of Goldak et al. (1984) is considered to be appropriate. It is also not appropriate to take the shape of the projected area to be circular for moving heat source as has been reported by many authors.
3.3 Parametric model by regression analysis The values shown in Figures 4 and 5 have been normalised using the minimum-maximum method and were used for the regression analysis. A linear regression analysis was performed to build a parametric model between the arc parameters and the welding variables namely, current, speed, electrode distance and tip angle. The regression equations are given in equations (8) and (9). a f = 2.31 + 1.16 I n – 0.21U n – 0.89Φ n + 0.67 Dn ;
(8)
ar = 2.06 + 1.35 I n + 0.62U n – 0.39Φ n + 1.04 Dn ;
(9)
where In, Un, Φn and Dn are the normalised values of the current, speed, electrode tip angle and electrode distance, respectively. The area Ai, is calculated from the values of af and ar as expressed below: Ai =
π 2 ( a f + a f .ar ) 2
(10)
Model adequacy checking was performed using residual analysis and the residual plots for af and ar are shown in Figures 7 and 8 respectively. Figure 7
Residuals versus fitted values plot for af (see online version for colours)
Figure 8
Residuals versus fitted values plot for ar (see online version for colours)
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Since no trend is observed in the residual plots it can be inferred that the linear model is adequate and no higher order term is required as reported by Montgomery et al. (2003) and Aczel and Sounderpandian (2002). The analysis of variance for af and ar is shown in Table 2. Table 2
Analysis of variance
Source
DF
SS
MS
F
P
221.35
0.000
203.13
0.000
Analysis of variance for af Regression
4
99.921
24.98
Residual error
235
26.521
0.113
Total
239
126.442 Analysis of variance for ar
Regression
4
127.5
31.8 0.157
Residual error
235
36.9
Total
239
164.4
It can be noted from the table that F(4,235) of 221.35 and 203.13 for af and ar respectively are greater than Fcritical of 2.41 and the p-value is ‘0.000’. Hence, it can be concluded that there is a strong evidence of a linear regression relationship as reported by Montgomery et al. (2003) and Aczel and Sounderpandian (2002). Based on the regression equations and the data reported in the Table 2, it can be concluded that •
both af and ar increases as the current increases
•
af decreases and ar increases as the speed increases
•
af and ar decrease as the electrode angle increases but af decreases more than ar
•
both af and ar increase as the electrode distance increases.
It is to be noted that the model is developed only for GTA welding; the model is independent of the base/substrate metal; and the applicability of the model for electrodes materials other than 2% thoriated tungsten is to be investigated but not part of this work.
3.4 Correlation between widths of arc and pool The variations of measured arc widths and the weld pool widths are plotted against speed, for a set of given current, tip angle and electrode distance, as shown in Figure 9. Figure 9 shows that both the arc width and the weld pool width increase with the increase in speed. The weld pool width is smaller than the arc width for any given speed. Goldak et al. (1984) and Nguyen et al. (1999) have assumed that the arc width is equal to the weld pool width. From Figure 9 it can be noted that the arc width and the weld pool width are not same. Therefore, from the above findings, it is not appropriate to use the weld pool width in place of arc width for heat transfer modelling.
Development of a regression model relating experimentally measured arc Figure 9
4
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Variation of arc width and weld pool width with welding speeds (see online version for colours)
Conclusions
An experimental technique using CCD grey scale camera and machine vision software Sherlock was employed in measuring GTA welding arc dimensions. In an effort to understand the behaviour of the arc with respect to welding variables, a regression model was developed using the data obtained from the measurement of arc dimensions versus welding variables, current, speed, tip angle and arc length. This regression model will facilitate the estimation of the projected area of the arc and its utilisation in solving the heat flow model. The arc area incident on the workpiece increases with current and electrode distance, decreases with electrode tip angle and remains almost constant with speed. The shape of the projected area of the arc is found to be semi-circular in the front and semi-elliptical in the rear for a moving heat source in the case of shallow GTA welding process. It has also been observed that it is inappropriate to use pool width in place of arc width in numerical simulation of GTA welding process as their values differ from each other significantly.
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