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Sensitivity analysis of submerged arc welding process parameters
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 500–507
journal homepage: www.elsevier.com/locate/jmatprotec
Sensitivity analysis of submerged arc welding process parameters ˘ a,∗ , Abdullah Sec¸gin b Serdar Karaoglu a b
Ege University, Faculty of Engineering, Department of Mechanical Engineering, 35100 Bornova, Izmir, Turkey Dokuz Eylul University, Faculty of Engineering, Department of Mechanical Engineering, 35100 Bornova, Izmir, Turkey
a r t i c l e
i n f o
a b s t r a c t
Article history:
Selection of process parameters has great influence on the quality of a welded connection.
Received 1 May 2007
Mathematical modelling can be utilized in the optimization and control procedure of param-
Received in revised form
eters. Rather than the well-known effects of main process parameters, this study focuses
28 September 2007
on the sensitivity analysis of parameters and fine tuning requirements of the parameters
Accepted 10 October 2007
for optimum weld bead geometry. Changeable process parameters such as welding current, welding voltage and welding speed are used as design variables. The objective function is formed using width, height and penetration of the weld bead. Experimental part of the study
Keywords:
is based on three level factorial design of three process parameters. In order to investigate
Submerged arc welding
the effects of input (process) parameters on output parameters, which determine the weld
Sensitivity analysis
bead geometry, a mathematical model is constructed by using multiple curvilinear regres-
Weld bead geometry
sion analysis. After carrying out a sensitivity analysis using developed empirical equations,
Mathematical modelling
relative effects of input parameters on output parameters are obtained. Effects of all three
Regression analysis
design parameters on the bead width and bead height show that even small changes in these parameters play an important role in the quality of welding operation. The results also reveal that the penetration is almost non-sensitive to the variations in voltage and speed. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Submerged Arc Welding (SAW) is a high quality welding process with a very high deposition rate. It is commonly used to join thick sections in the flat position. SAW is usually operated either as fully mechanized or automatically processed. However, it can be used semi-automatically as well. During SAW process, operator cannot observe the weld pool and not directly interfere with the welding process. As the automation in the SAW process increases, direct effect of the operator decreases and the precise setting of parameters become much more important than manual welding processes. In order to obtain high quality welds in automated welding pro-
∗
Corresponding author. Tel.: +90 232 388 85 62; fax: +90 232 388 85 62. ˘ E-mail address: [email protected] (S. Karaoglu). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.10.035
cesses, selection of optimum parameters should be performed according to engineering facts. Generally, welding parameters are determined by trial and error, based on handbook values, and manufacturers’ recommendations. However, this selection may not yield optimal or in the vicinity of optimal welding performance. Furthermore, it may cause additional energy and material consumption resulting in low quality welding. Besides, in the industrial welding robots, even smaller changes in the welding process parameters may cause unexpected welding performance. Therefore, it is important to study stability of welding parameters to achieve high quality welding. Optimum process parameters selection has been investigated by some significant studies via establishing a
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 500–507
mathematical model correlating welding parameters with quality characteristics using different approaches. In principle, weld bead geometry (weld bead characteristic) is one of the major quality properties mainly due to its influence on energy and electrode consumption. Determination of SAW process parameters to achieve desired weld bead geometry and the prediction of weld bead characteristics, such as bead width, bead height and penetration for the given input parameters, have been accomplished (Tarng et al., 2000; Chandel and Bala, 1988; Gupta and Parmar, 1989; Chan et al., 1994; Gunaraj and Murugan, 1999a, 2000a; Kim et al., 2003; Tarng et al., 2002). Additionally, the area of Heat Affected Zone (HAZ) has also been used as a performance characteristic for parameter optimizations in SAW (Gunaraj and Murugan, 1999b, 2002; Lee et al., 2000). Predicting the effects of small changes in design parameters provide very important information in engineering design. Therefore, by using a mathematically modeled prediction system, effect of any changes in the parameters on the overall design objective can be determined. This kind of analysis is known as Design Sensitivity Analysis (DSA). Basically, Sensitivity Analysis (SA) yields information about the increment and decrement tendency of design objective function with respect to design parameters. There are few studies performed sensitivity analysis using mathematical model for different welding methods. For example, Kim et al. (2003) conducted a sensitivity analysis in order to compare relative impact of process parameters on bead geometry of Gas Metal Arc (GMA) welding using a mathematical model. They found that width and height of weld bead are more sensitive to changes in process parameters relative to penetration. Gunaraj and Murugan (2000b) carried out a different procedure to optimize bead volume formed by SAW process. They used sensitivity analysis as a post optimization procedure to calculate variations in the objective function due to the small changes from the optimum values of constraints. In addition to these investigations, there is still need for optimization studies in all welding processes, especially for automated welding systems. Because of its simplicity in implementing to all mathematical models and inclusion of cross tendency information between process parameters, sensitivity analysis is a very useful tool. In this study, mathematical relations (empirical equations) between SAW process parameters and weld bead characteristics (SAW mathematical models) were constructed based upon the experimental data obtained by three parameters-three levels factorial analysis. The empirical equations, simulating the SAW process approximately, were carried out by Multiple Regression Analysis (MRA) and sensitivity equations were derived from these basic models. An analysis generally requires a definition of an objective function and design parameters. In this study, the objective function (quality function) was chosen as weld bead characteristics (the width, height and penetration of the weld bead) whereas process parameters (arc current, voltage and welding speed) were selected as the design variables. The methodology used in this paper for SAW is similar to that used by Kim et al. (2003) for GMA welding. The present study mainly focuses on the determination of sensitivity characteristics of design parameters and the prediction of fine-tuning requirements
501
of these parameters in SAW process. The results revealed considerable information about process parameter tendencies and optimum welding conditions. Similar process parameter behaviors were obtained for GMA welding by Kim et al. (2003). However, our study does not only provide valuable results for SAW like for GMA welding (Kim et al., 2003), but also aims to present a sensitivity characteristic map for SAW process.
2.
Mathematical modelling
2.1.
Experimental data
In the experimental part of this study, welding process parameters, namely, arc current (I), voltage (U) and welding speed (S) were used as input parameters. Bead width (W), bead height (H) and bead penetration (P) (Fig. 1) were measured and used as output parameters. Contact tube-to-work distance was kept constant (25 mm) throughout the experiment. Performed SAW conditions and corresponding weld bead values are presented in Table 1. The 33 factorial designs including main and interactive effects of three parameters with three levels were used for experimentation. Number of welds required to obtain data for mathematical modeling is 27. Bead-on-plate type welds were made by using 3.2 mm diameter wire electrodes. Mild steel plates with dimensions of 180 mm × 80 mm × 10 mm were utilized as the test material. A semi-automatic submerged arcwelding machine with a constant-current power source was employed in this study. After cutting transverse sections of the welds, metallographic samples were prepared using standard methods such as grinding, polishing and etching. Sections of welds were examined using an optical microscope. Magnified photographs were taken and images were processed digitally to measure the weld bead geometry parameters including bead width, bead height and depth of penetration.
2.2. Construction of the mathematical models of SAW process and statistical evaluation Mathematical modeling of SAW process may be constructed using multiple curvilinear regression analysis. In this regard, first, a mathematical form simulating the relation between weld bead characteristics (bead width, bead height and penetration) and process parameters (welding current, welding voltage, welding speed) should be selected. The regression coefficients are calculated based on this selected form by
Fig. 1 – A schematic representation of weld bead geometry parameters (W: width, H: height, P: penetration).
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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 500–507
Table 1 – Welding conditions and measured weld bead values Specimen number
Current (A)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Voltage (V)
400 400 400 400 400 400 400 400 400 500 500 500 500 500 500 500 500 500 600 600 600 600 600 600 600 600 600
20 20 20 25 25 25 30 30 30 20 20 20 25 25 25 30 30 30 20 20 20 25 25 25 30 30 30
Speed (mm/s)
Bead width (mm)
6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333
9.1890 7.9610 6.6200 11.3530 10.1000 8.6220 12.9370 10.7880 9.5640 10.8350 8.7620 7.9200 12.7830 10.8140 9.3700 15.0070 12.1420 9.8340 12.1440 9.7410 8.6860 14.9020 11.6270 10.6990 17.1260 14.5700 12.2010
correlating the experimental data series. In this study, a mathematical form was assumed as the following;
fi (I, U, S) = ai Ibi Uci Sdi ,
i=
⎧ ⎨ W for bead width H
⎩P
for bead height for penetration
Bead height (mm)
(1)
3.0870 2.2520 1.9890 2.2970 1.9210 1.6270 2.0590 1.5070 1.6000 3.2560 2.6130 2.2400 2.1990 2.4130 1.8900 2.1240 1.9140 1.5930 3.5580 2.7590 2.2860 3.2370 2.8090 2.4930 2.6830 2.4680 1.5890
¯ = a¯ i + bi ¯I + ci U ¯ + di S¯ ¯ S) fi (¯I, U,
(2)
3.0460 2.7940 2.2420 2.5840 2.8380 2.7060 3.0940 3.3470 2.6870 3.9540 3.4330 3.8810 4.2550 3.8880 4.3730 4.5270 5.0360 4.7760 5.4470 5.2610 4.8460 6.2020 6.2940 5.8000 5.9640 5.9790 5.7900
rithm. Noting that ai is equal to exp(a¯ i ). Calculated regression coefficients were presented in Table 2. Substituting these regression coefficients shown in Table 2 into Eq. (1), three SAW mathematical models were obtained for each weld bead characteristics: I0.6005 U0.8174 S0.4729
(Bead Width Model)
(3)
I0.6464 U0.7788 S0.4882
(Bead Height Model)
(4)
fW (I, U, S) = 0.0549 where fi (I,U,S) is weld bead function for index i (the value of this function is the bead width, bead height and bead penetration in mm at any welding conditions). I is current, U is voltage, S is welding speed and ai , bi , ci , di are coefficients. Taking natural logarithm of Eq. (1) gives a regression analysis form such as;
Bead penetration (mm)
fH (I, U, S) = 1.4978
fP (I, U, S) = 0.0000235
I1.7628 U0.4114 S0.0838
(Bead Penetration Model) (5)
Natural logarithms of the variables are denoted by bars over the associated letters. By performing multiple curvilinear regression analysis correlating Eq. (2) with the experimental data series given in Table 1, the regression coefficients a¯ i , bi , ci , di can be calculated by utilizing a simple regression algo-
In respect of the mathematical models, sufficient accuracy for a sensitivity study was obtained and this accuracy was presented in Figs. 2–4 for each model. Regarding sensitivity concept, in which the tendency behavior of an objective func-
Table 2 – Calculated regression coefficients for weld bead characteristic models Weld bead characteristics
Width (i = W) Height (i = H) Penetration (i = P)
Regression coefficients ai = exp(a¯ i )
bi
ci
di
0.0549 1.4978 0.0000235
0.6005 0.6464 1.7628
0.8174 −0.7788 0.4114
−0.4729 −0.4882 −0.0838
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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 500–507
Table 3 – Statistical evaluation of the weld bead characteristic models
Fig. 2 – Accuracy of the calculated bead width (fW ) values with respect to measured data.
Fig. 3 – Accuracy of the calculated bead height (fH ) values with respect to measured data.
tion is more informative than its exact value at any design parameter, it may be stated that the weld bead characteristic models in Eqs. (3)–(5) well represent the experimental results indicated in Table 1. Moreover, Table 3 presents this accuracy by means of the statistical evaluation. Definitions of the statistical evaluation parameters are given as follows: Sum of Squares due to Error (SSE): This statistic measures the total deviation of the response values from the fit to the
Fig. 4 – Accuracy of the calculated bead penetration (fP ) values with respect to measured data.
Statistics
SSE
R-square
Width Height Penetration
3.125 1.054 2.134
0.9803 0.8686 0.9502
Adjusted R-square 0.9795 0.8634 0.9482
RMSE 0.3535 0.2053 0.2922
response values. It is also called the summed square of residuals and is usually labeled as SSE. A value closer to 0 indicates a better fit. R-square: It is defined as the ratio of the sum of squares of the regression and the total sum of squares. It can take on any value between 0 and 1, with a value closer to 1 indicating a better fit. Adjusted R-square (Degrees of Freedom Adjusted R-Square): This statistic uses the R-square statistic defined above, and adjusts it based on the residual degrees of freedom. The adjusted R-square statistic is generally the best indicator of the fit quality when one adds additional coefficients to your model. The adjusted R-square statistic can take on any value less than or equal to 1, with a value closer to 1 indicating a better fit. Root Mean Squared Error (RMSE): This statistic is also known as the fit standard error and the standard error of the regression and a RMSE value closer to 0 indicates a better fit.
3.
Sensitivity analysis
3.1.
The derivations of sensitivity equations
“Sensitivity analysis is the first and the most important step in the optimization problems, because it yields the information about the increment or decrement tendency of the design objective function with respect to the design parameter. Therefore, sensitivity analysis plays an important role in determining which parameter of the process should be mod¨ and Sec¸gin, 2004). ified for effective improvement” (Sarıgul Mathematically, sensitivity of a design objective function with respect to a design variable is the partial derivative of that function with respect to its variables. In this study, it is aimed to predict the tendency of weld bead characteristics due to a small change in process parameters (change in arc current, voltage and welding speed) for SAW processes. The weld bead characteristic models can be interpreted as design objective functions and their variables as design parameters. In this regard, sensitivity equations of Eqs. (3)–(5) can be derived for each process parameters. Thus, bead width sensitivities with respect to arc current I, voltage U and speed S are: ∂fW (I, U, S) U0.8174 = 0.033 0.3995 0.4729 ∂I I S
(6)
I0.6005 ∂fW (I, U, S) = 0.0449 0.1826 0.4729 ∂U U S
(7)
I0.6005 U0.8174 ∂fW (I, U, S) = −0.026 ∂S S1.4729
(8)
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respectively. Bead height sensitivities with respect to arc current I, voltage U, and speed S are: ∂fH (I, U, S) 0.9682 = 0.3536 0.7788 0.4882 ∂I I U S
(9)
∂fH (I, U, S) I0.6464 = −1.1665 1.7788 0.4882 ∂U U S
(10)
∂fH (I, U, S) I0.6464 = −0.7312 0.7788 1.4882 ∂S U S
(11)
respectively. Bead penetration sensitivities with respect to arc current I, voltage U and speed S are: I0.7628 U0.4114 ∂fP (I, U, S) = 0.0000414 ∂I S0.0838
(12)
∂fP (I, U, S) I1.7628 = 0.00000966 0.5886 0.0838 ∂U U S
(13)
∂fP (I, U, S) I1.7628 U0.4114 = 0.00000197 ∂S S1.0838
(14)
respectively. Sensitivities derived in Eqs. (6)–(14) imply increment or decrement tendencies of weld bead characteristics with respect to change in one of their process parameters.
3.2.
Evaluation of sensitivity analysis results
The sensitivity analysis results are depicted in Figs. 5–7 by solid bars corresponding discrete welding conditions given in Table 1.
Sensitivity information should be interpreted using mathematical definition of derivatives. Namely, positive sensitivity values imply an increment in the objective function by a small change in design parameter whereas negative values state the opposite. Sensitivity results in Fig. 5 show that current sensitivity of bead width and penetration are greater than current sensitivity of bead height. Since the bead width and penetration are more sensitive to current variations, arc current can be used effectively for any adjustment in bead width and penetration. Current sensitivity of all three weld bead characteristics are positive sense. Thus, any increase in arc current, voltage and welding speed increases the bead width, bead height, and penetration in different rates depending on their sensitivity values. As shown in Fig. 5(a), current sensitivity of bead width decreases with increasing current and increasing speed, and increases with increasing voltage. In other words, current sensitivity of bead width is maximum at lower current (400 A), higher voltage (30 V) and lower welding speed values (6.6667 mm/s). Increasing values of all welding parameters decreases the current sensitivity of bead height (Fig. 5(b)). The most sensitive bead height value is obtained at 400 A, 20 V, 6.6667 mm/s welding conditions. It is clearly seen from Fig. 5(c) that, current and voltage have positive effects on current sensitivity of penetration, whereas the effect of speed is negative. Maximum current sensitivity of penetration is observed at higher levels of current (600 A) and voltage (30 V), and lower level of welding speed (6.6667 mm/s), (i.e., maximum heat input level). It is exposed from Fig. 6 that voltage sensitivity of bead width and penetration are positive sense, while voltage sen-
Fig. 5 – Current sensitivity of: (a) width, (b) height, and (c) penetration.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 500–507
505
Fig. 6 – Voltage sensitivity of: (a) width, (b) height, and (c) penetration.
sitivity of bead height is negative. It means that an increase in welding process parameters creates an increase in bead width and penetration, and it decreases bead height. Bead width seems to be more sensitive to voltage variations than bead height and penetration. As shown in Fig. 6(a), voltage sensitivity of bead width increases with increasing current. It predicts that bead width is more sensitive to voltage varia-
tions at higher currents. On the other hand voltage sensitivity decreases with increasing voltage and speed. Maximum voltage sensitivity of bead width is observed at higher current (600 A), lower voltage (20 V) and lower welding speed values (6.6667 mm/s). Negative voltage sensitivity values of bead height in Fig. 6(b) imply that an increase in voltage decreases the bead height. According to this information, predicted min-
Fig. 7 – Speed sensitivity of: (a) width, (b) height, and (c) penetration.
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imum bead height is observed at higher current (600 A), lower voltage (20 V) and lower speed (6.6667 mm/s) combination. Voltage sensitivity of penetration (Fig. 6(c)) is very low compared to the bead width (Fig. 6(a)), which indicates a limited effect of voltage variations on penetration. Therefore, it can be said that welding voltage is not an efective parameter to control penetration. However, combination of 600 A, 20 V, and 6.6667 mm/s can be interpreted as more sensitive welding conditions for penetration. As shown in Fig. 7, welding speed sensitivity of bead width, bead height and penetration are negative sense. These sensitivities imply decrement tendency in the predictive values of bead width, bead height and penetration. It is clearly seen that the bead width is highly affected by welding speed variations, while penetration seems to be nonsensitive. Negative welding speed sensitivity of bead width increases with increasing current and voltage, whereas it decreases with increasing speed (Fig. 7(a)). Bead width is most sensitive to welding speed at higher current (600 A), higher voltage (30 V) and lower speed values (6.6667 mm/s) (i.e. maximum heat input). As shown in Fig. 7(b), a parameter setting of higher current (600 A), lower voltage (20 V) and lower speed (6.6667 mm/s) combination predicts the minimum bead height due to maximum negative sensitivity results. Penetration is said to be non-sensitive to the variations in speed in all welding conditions (Fig. 7(c)). Thus, welding speed cannot be effectively used to control penetration. Generally the results of sensitivity analysis are similar to the ones obtained by Kim et al. (2003) for GMA welding process. Current sensitivity of bead width and bead height increase with increasing current, while current sensitivity of penetration decreases with increasing current for GMA welding (Kim et al., 2003) and SAW processes. Beside current sensitivity, similarities in voltage and speed sensitivity values of GMA welding with SAW process have been observed. The signs of sensitivity values are the same in both analyses, for example; all of the current sensitivities are positive and speed sensitivities are negative. After obtaining relatively low current sensitivity values, Kim et al. (2003) concluded that, change of process parameters of GMA welding affected the bead width and bead height more strongly than penetration. However, in the present study (SAW), penetration has been found to be very sensitive to variations especially in current. This difference can be attributed to the different characteristics of the welding processes and different conditions of the experiments.
4.
Conclusions
In the first part of this study, mathematical modelling using curvilinear regression equations were developed from experimental data. Then, sensitivity analysis of weld bead parameters such as bead width, bead height, and penetration to variations in current, voltage, and speed in submerged arc welding process were performed. Welding process parameters, required for desired weld bead geometry, can effectively be predicted using mathematical models developed in this study. These mathematical
models can also be used to optimize processes and to develop automatic control systems for welding power sources. Following conclusions can be drawn from this sensitivity analysis: • Bead width is very sensitive to all process parameters. Current, voltage and speed are the determining parameters for bead width. • Bead width is more sensitive to voltage and speed variations than that of bead height and penetration. • All three process parameters have effects in determining the bead height. • In order to decrease the bead height, higher values of voltage and speed can be considered. • Since bead width and penetration are more sensitive to current variations than bead height, arc current can be used effectively for any adjustment in bead width and penetration. • Current is the most important parameter in determining the penetration. Penetration is almost non-sensitive to variations in voltage and speed. Therefore, voltage and speed cannot be efectively used to control penetration. • At maximum heat input level (higher levels of current and voltage, and lower level of welding speed), current sensitivity of penetration, and speed sensitivity of bead width reach their maximum values.
references
Chan, B., Chandel, R.S., Yang, L.J., Bibly, M.J., 1994. Software system for anticipating the size and shape of submerged arc welds. J. Mater. Process. Technol. 40 (3–4), 249–262. Chandel, R.S., Bala, S., 1998. Relationship between submerged arc welding parameters and weld bead size. Schweissen Schneiden 40(2), 28–31 (88–91). Gunaraj, V., Murugan, N., 1999a. Application of response surface methodology for predicting weld bead quality in submerged arc welding of pipes. J. Mater. Proc. Technol. 88, 266–275. Gunaraj, V., Murugan, N., 1999b. Prediction and comparison of the area of the heat-effected zone for the bead-on-plate and bead-on-joint in submerged welding of pipes. J. Mater. Proc. Technol. 95, 246–261. Gunaraj, V., Murugan, N., 2000a. Prediction and optimization of weld bead volume for the submerged arc process. Part 1. Weld. J. 79 (10), 286s–294s. Gunaraj, V., Murugan, N., 2000b. Prediction and optimization of weld bead volume for the submerged arc process. Part 2. Weld. J. 79 (11), 331s–338s. Gunaraj, V., Murugan, N., 2002. Prediction of heat-affected zone characteristics in submerged arc welding of structural steel pipes. Weld. J., 94s–98s. Gupta, V.K., Parmar, R.S., 1989. Fractional factorial technique to predict dimensions of the weld bead in automatic submerged arc welding. J. Institut. Eng. (India), Part ME 70 (pt. 4), 67–75. Kim, I.S., Son, K.J., Yang, Y.S., Yaragada, P.K.D.V., 2003. Sensitivity analysis for process parameters in GMA welding processes using a factorial design method. Int. J. Mach. Tools Manuf. 43, 763–769. Lee, C.S., Chandel, R.S., Seow, H.P., 2000. Effect of welding parameters on the size of heat affected zone of submerged arc welding. Mater. Manuf. Proc. 15 (5), 649–666.
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¨ A.S., Sec¸gin, A., 2004. A study on the application of the Sarıgul, acoustic design sensitivity analysis of vibrating bodies. Appl. Acoustics 65, 1037–1056. Tarng, Y.S., Yang, W.H., Juang, S.C., 2000. The use of fuzzy logic in the Taguchi method for the optimisation of the submerged arc welding process. Int. J. Adv. Manuf. Technol. 16, 688–694.
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journal homepage: www.elsevier.com/locate/jmatprotec
Sensitivity analysis of submerged arc welding process parameters ˘ a,∗ , Abdullah Sec¸gin b Serdar Karaoglu a b
Ege University, Faculty of Engineering, Department of Mechanical Engineering, 35100 Bornova, Izmir, Turkey Dokuz Eylul University, Faculty of Engineering, Department of Mechanical Engineering, 35100 Bornova, Izmir, Turkey
a r t i c l e
i n f o
a b s t r a c t
Article history:
Selection of process parameters has great influence on the quality of a welded connection.
Received 1 May 2007
Mathematical modelling can be utilized in the optimization and control procedure of param-
Received in revised form
eters. Rather than the well-known effects of main process parameters, this study focuses
28 September 2007
on the sensitivity analysis of parameters and fine tuning requirements of the parameters
Accepted 10 October 2007
for optimum weld bead geometry. Changeable process parameters such as welding current, welding voltage and welding speed are used as design variables. The objective function is formed using width, height and penetration of the weld bead. Experimental part of the study
Keywords:
is based on three level factorial design of three process parameters. In order to investigate
Submerged arc welding
the effects of input (process) parameters on output parameters, which determine the weld
Sensitivity analysis
bead geometry, a mathematical model is constructed by using multiple curvilinear regres-
Weld bead geometry
sion analysis. After carrying out a sensitivity analysis using developed empirical equations,
Mathematical modelling
relative effects of input parameters on output parameters are obtained. Effects of all three
Regression analysis
design parameters on the bead width and bead height show that even small changes in these parameters play an important role in the quality of welding operation. The results also reveal that the penetration is almost non-sensitive to the variations in voltage and speed. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Submerged Arc Welding (SAW) is a high quality welding process with a very high deposition rate. It is commonly used to join thick sections in the flat position. SAW is usually operated either as fully mechanized or automatically processed. However, it can be used semi-automatically as well. During SAW process, operator cannot observe the weld pool and not directly interfere with the welding process. As the automation in the SAW process increases, direct effect of the operator decreases and the precise setting of parameters become much more important than manual welding processes. In order to obtain high quality welds in automated welding pro-
∗
Corresponding author. Tel.: +90 232 388 85 62; fax: +90 232 388 85 62. ˘ E-mail address: [email protected] (S. Karaoglu). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.10.035
cesses, selection of optimum parameters should be performed according to engineering facts. Generally, welding parameters are determined by trial and error, based on handbook values, and manufacturers’ recommendations. However, this selection may not yield optimal or in the vicinity of optimal welding performance. Furthermore, it may cause additional energy and material consumption resulting in low quality welding. Besides, in the industrial welding robots, even smaller changes in the welding process parameters may cause unexpected welding performance. Therefore, it is important to study stability of welding parameters to achieve high quality welding. Optimum process parameters selection has been investigated by some significant studies via establishing a
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 500–507
mathematical model correlating welding parameters with quality characteristics using different approaches. In principle, weld bead geometry (weld bead characteristic) is one of the major quality properties mainly due to its influence on energy and electrode consumption. Determination of SAW process parameters to achieve desired weld bead geometry and the prediction of weld bead characteristics, such as bead width, bead height and penetration for the given input parameters, have been accomplished (Tarng et al., 2000; Chandel and Bala, 1988; Gupta and Parmar, 1989; Chan et al., 1994; Gunaraj and Murugan, 1999a, 2000a; Kim et al., 2003; Tarng et al., 2002). Additionally, the area of Heat Affected Zone (HAZ) has also been used as a performance characteristic for parameter optimizations in SAW (Gunaraj and Murugan, 1999b, 2002; Lee et al., 2000). Predicting the effects of small changes in design parameters provide very important information in engineering design. Therefore, by using a mathematically modeled prediction system, effect of any changes in the parameters on the overall design objective can be determined. This kind of analysis is known as Design Sensitivity Analysis (DSA). Basically, Sensitivity Analysis (SA) yields information about the increment and decrement tendency of design objective function with respect to design parameters. There are few studies performed sensitivity analysis using mathematical model for different welding methods. For example, Kim et al. (2003) conducted a sensitivity analysis in order to compare relative impact of process parameters on bead geometry of Gas Metal Arc (GMA) welding using a mathematical model. They found that width and height of weld bead are more sensitive to changes in process parameters relative to penetration. Gunaraj and Murugan (2000b) carried out a different procedure to optimize bead volume formed by SAW process. They used sensitivity analysis as a post optimization procedure to calculate variations in the objective function due to the small changes from the optimum values of constraints. In addition to these investigations, there is still need for optimization studies in all welding processes, especially for automated welding systems. Because of its simplicity in implementing to all mathematical models and inclusion of cross tendency information between process parameters, sensitivity analysis is a very useful tool. In this study, mathematical relations (empirical equations) between SAW process parameters and weld bead characteristics (SAW mathematical models) were constructed based upon the experimental data obtained by three parameters-three levels factorial analysis. The empirical equations, simulating the SAW process approximately, were carried out by Multiple Regression Analysis (MRA) and sensitivity equations were derived from these basic models. An analysis generally requires a definition of an objective function and design parameters. In this study, the objective function (quality function) was chosen as weld bead characteristics (the width, height and penetration of the weld bead) whereas process parameters (arc current, voltage and welding speed) were selected as the design variables. The methodology used in this paper for SAW is similar to that used by Kim et al. (2003) for GMA welding. The present study mainly focuses on the determination of sensitivity characteristics of design parameters and the prediction of fine-tuning requirements
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of these parameters in SAW process. The results revealed considerable information about process parameter tendencies and optimum welding conditions. Similar process parameter behaviors were obtained for GMA welding by Kim et al. (2003). However, our study does not only provide valuable results for SAW like for GMA welding (Kim et al., 2003), but also aims to present a sensitivity characteristic map for SAW process.
2.
Mathematical modelling
2.1.
Experimental data
In the experimental part of this study, welding process parameters, namely, arc current (I), voltage (U) and welding speed (S) were used as input parameters. Bead width (W), bead height (H) and bead penetration (P) (Fig. 1) were measured and used as output parameters. Contact tube-to-work distance was kept constant (25 mm) throughout the experiment. Performed SAW conditions and corresponding weld bead values are presented in Table 1. The 33 factorial designs including main and interactive effects of three parameters with three levels were used for experimentation. Number of welds required to obtain data for mathematical modeling is 27. Bead-on-plate type welds were made by using 3.2 mm diameter wire electrodes. Mild steel plates with dimensions of 180 mm × 80 mm × 10 mm were utilized as the test material. A semi-automatic submerged arcwelding machine with a constant-current power source was employed in this study. After cutting transverse sections of the welds, metallographic samples were prepared using standard methods such as grinding, polishing and etching. Sections of welds were examined using an optical microscope. Magnified photographs were taken and images were processed digitally to measure the weld bead geometry parameters including bead width, bead height and depth of penetration.
2.2. Construction of the mathematical models of SAW process and statistical evaluation Mathematical modeling of SAW process may be constructed using multiple curvilinear regression analysis. In this regard, first, a mathematical form simulating the relation between weld bead characteristics (bead width, bead height and penetration) and process parameters (welding current, welding voltage, welding speed) should be selected. The regression coefficients are calculated based on this selected form by
Fig. 1 – A schematic representation of weld bead geometry parameters (W: width, H: height, P: penetration).
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Table 1 – Welding conditions and measured weld bead values Specimen number
Current (A)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Voltage (V)
400 400 400 400 400 400 400 400 400 500 500 500 500 500 500 500 500 500 600 600 600 600 600 600 600 600 600
20 20 20 25 25 25 30 30 30 20 20 20 25 25 25 30 30 30 20 20 20 25 25 25 30 30 30
Speed (mm/s)
Bead width (mm)
6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333 6.6667 10.0000 13.3333
9.1890 7.9610 6.6200 11.3530 10.1000 8.6220 12.9370 10.7880 9.5640 10.8350 8.7620 7.9200 12.7830 10.8140 9.3700 15.0070 12.1420 9.8340 12.1440 9.7410 8.6860 14.9020 11.6270 10.6990 17.1260 14.5700 12.2010
correlating the experimental data series. In this study, a mathematical form was assumed as the following;
fi (I, U, S) = ai Ibi Uci Sdi ,
i=
⎧ ⎨ W for bead width H
⎩P
for bead height for penetration
Bead height (mm)
(1)
3.0870 2.2520 1.9890 2.2970 1.9210 1.6270 2.0590 1.5070 1.6000 3.2560 2.6130 2.2400 2.1990 2.4130 1.8900 2.1240 1.9140 1.5930 3.5580 2.7590 2.2860 3.2370 2.8090 2.4930 2.6830 2.4680 1.5890
¯ = a¯ i + bi ¯I + ci U ¯ + di S¯ ¯ S) fi (¯I, U,
(2)
3.0460 2.7940 2.2420 2.5840 2.8380 2.7060 3.0940 3.3470 2.6870 3.9540 3.4330 3.8810 4.2550 3.8880 4.3730 4.5270 5.0360 4.7760 5.4470 5.2610 4.8460 6.2020 6.2940 5.8000 5.9640 5.9790 5.7900
rithm. Noting that ai is equal to exp(a¯ i ). Calculated regression coefficients were presented in Table 2. Substituting these regression coefficients shown in Table 2 into Eq. (1), three SAW mathematical models were obtained for each weld bead characteristics: I0.6005 U0.8174 S0.4729
(Bead Width Model)
(3)
I0.6464 U0.7788 S0.4882
(Bead Height Model)
(4)
fW (I, U, S) = 0.0549 where fi (I,U,S) is weld bead function for index i (the value of this function is the bead width, bead height and bead penetration in mm at any welding conditions). I is current, U is voltage, S is welding speed and ai , bi , ci , di are coefficients. Taking natural logarithm of Eq. (1) gives a regression analysis form such as;
Bead penetration (mm)
fH (I, U, S) = 1.4978
fP (I, U, S) = 0.0000235
I1.7628 U0.4114 S0.0838
(Bead Penetration Model) (5)
Natural logarithms of the variables are denoted by bars over the associated letters. By performing multiple curvilinear regression analysis correlating Eq. (2) with the experimental data series given in Table 1, the regression coefficients a¯ i , bi , ci , di can be calculated by utilizing a simple regression algo-
In respect of the mathematical models, sufficient accuracy for a sensitivity study was obtained and this accuracy was presented in Figs. 2–4 for each model. Regarding sensitivity concept, in which the tendency behavior of an objective func-
Table 2 – Calculated regression coefficients for weld bead characteristic models Weld bead characteristics
Width (i = W) Height (i = H) Penetration (i = P)
Regression coefficients ai = exp(a¯ i )
bi
ci
di
0.0549 1.4978 0.0000235
0.6005 0.6464 1.7628
0.8174 −0.7788 0.4114
−0.4729 −0.4882 −0.0838
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Table 3 – Statistical evaluation of the weld bead characteristic models
Fig. 2 – Accuracy of the calculated bead width (fW ) values with respect to measured data.
Fig. 3 – Accuracy of the calculated bead height (fH ) values with respect to measured data.
tion is more informative than its exact value at any design parameter, it may be stated that the weld bead characteristic models in Eqs. (3)–(5) well represent the experimental results indicated in Table 1. Moreover, Table 3 presents this accuracy by means of the statistical evaluation. Definitions of the statistical evaluation parameters are given as follows: Sum of Squares due to Error (SSE): This statistic measures the total deviation of the response values from the fit to the
Fig. 4 – Accuracy of the calculated bead penetration (fP ) values with respect to measured data.
Statistics
SSE
R-square
Width Height Penetration
3.125 1.054 2.134
0.9803 0.8686 0.9502
Adjusted R-square 0.9795 0.8634 0.9482
RMSE 0.3535 0.2053 0.2922
response values. It is also called the summed square of residuals and is usually labeled as SSE. A value closer to 0 indicates a better fit. R-square: It is defined as the ratio of the sum of squares of the regression and the total sum of squares. It can take on any value between 0 and 1, with a value closer to 1 indicating a better fit. Adjusted R-square (Degrees of Freedom Adjusted R-Square): This statistic uses the R-square statistic defined above, and adjusts it based on the residual degrees of freedom. The adjusted R-square statistic is generally the best indicator of the fit quality when one adds additional coefficients to your model. The adjusted R-square statistic can take on any value less than or equal to 1, with a value closer to 1 indicating a better fit. Root Mean Squared Error (RMSE): This statistic is also known as the fit standard error and the standard error of the regression and a RMSE value closer to 0 indicates a better fit.
3.
Sensitivity analysis
3.1.
The derivations of sensitivity equations
“Sensitivity analysis is the first and the most important step in the optimization problems, because it yields the information about the increment or decrement tendency of the design objective function with respect to the design parameter. Therefore, sensitivity analysis plays an important role in determining which parameter of the process should be mod¨ and Sec¸gin, 2004). ified for effective improvement” (Sarıgul Mathematically, sensitivity of a design objective function with respect to a design variable is the partial derivative of that function with respect to its variables. In this study, it is aimed to predict the tendency of weld bead characteristics due to a small change in process parameters (change in arc current, voltage and welding speed) for SAW processes. The weld bead characteristic models can be interpreted as design objective functions and their variables as design parameters. In this regard, sensitivity equations of Eqs. (3)–(5) can be derived for each process parameters. Thus, bead width sensitivities with respect to arc current I, voltage U and speed S are: ∂fW (I, U, S) U0.8174 = 0.033 0.3995 0.4729 ∂I I S
(6)
I0.6005 ∂fW (I, U, S) = 0.0449 0.1826 0.4729 ∂U U S
(7)
I0.6005 U0.8174 ∂fW (I, U, S) = −0.026 ∂S S1.4729
(8)
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respectively. Bead height sensitivities with respect to arc current I, voltage U, and speed S are: ∂fH (I, U, S) 0.9682 = 0.3536 0.7788 0.4882 ∂I I U S
(9)
∂fH (I, U, S) I0.6464 = −1.1665 1.7788 0.4882 ∂U U S
(10)
∂fH (I, U, S) I0.6464 = −0.7312 0.7788 1.4882 ∂S U S
(11)
respectively. Bead penetration sensitivities with respect to arc current I, voltage U and speed S are: I0.7628 U0.4114 ∂fP (I, U, S) = 0.0000414 ∂I S0.0838
(12)
∂fP (I, U, S) I1.7628 = 0.00000966 0.5886 0.0838 ∂U U S
(13)
∂fP (I, U, S) I1.7628 U0.4114 = 0.00000197 ∂S S1.0838
(14)
respectively. Sensitivities derived in Eqs. (6)–(14) imply increment or decrement tendencies of weld bead characteristics with respect to change in one of their process parameters.
3.2.
Evaluation of sensitivity analysis results
The sensitivity analysis results are depicted in Figs. 5–7 by solid bars corresponding discrete welding conditions given in Table 1.
Sensitivity information should be interpreted using mathematical definition of derivatives. Namely, positive sensitivity values imply an increment in the objective function by a small change in design parameter whereas negative values state the opposite. Sensitivity results in Fig. 5 show that current sensitivity of bead width and penetration are greater than current sensitivity of bead height. Since the bead width and penetration are more sensitive to current variations, arc current can be used effectively for any adjustment in bead width and penetration. Current sensitivity of all three weld bead characteristics are positive sense. Thus, any increase in arc current, voltage and welding speed increases the bead width, bead height, and penetration in different rates depending on their sensitivity values. As shown in Fig. 5(a), current sensitivity of bead width decreases with increasing current and increasing speed, and increases with increasing voltage. In other words, current sensitivity of bead width is maximum at lower current (400 A), higher voltage (30 V) and lower welding speed values (6.6667 mm/s). Increasing values of all welding parameters decreases the current sensitivity of bead height (Fig. 5(b)). The most sensitive bead height value is obtained at 400 A, 20 V, 6.6667 mm/s welding conditions. It is clearly seen from Fig. 5(c) that, current and voltage have positive effects on current sensitivity of penetration, whereas the effect of speed is negative. Maximum current sensitivity of penetration is observed at higher levels of current (600 A) and voltage (30 V), and lower level of welding speed (6.6667 mm/s), (i.e., maximum heat input level). It is exposed from Fig. 6 that voltage sensitivity of bead width and penetration are positive sense, while voltage sen-
Fig. 5 – Current sensitivity of: (a) width, (b) height, and (c) penetration.
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Fig. 6 – Voltage sensitivity of: (a) width, (b) height, and (c) penetration.
sitivity of bead height is negative. It means that an increase in welding process parameters creates an increase in bead width and penetration, and it decreases bead height. Bead width seems to be more sensitive to voltage variations than bead height and penetration. As shown in Fig. 6(a), voltage sensitivity of bead width increases with increasing current. It predicts that bead width is more sensitive to voltage varia-
tions at higher currents. On the other hand voltage sensitivity decreases with increasing voltage and speed. Maximum voltage sensitivity of bead width is observed at higher current (600 A), lower voltage (20 V) and lower welding speed values (6.6667 mm/s). Negative voltage sensitivity values of bead height in Fig. 6(b) imply that an increase in voltage decreases the bead height. According to this information, predicted min-
Fig. 7 – Speed sensitivity of: (a) width, (b) height, and (c) penetration.
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imum bead height is observed at higher current (600 A), lower voltage (20 V) and lower speed (6.6667 mm/s) combination. Voltage sensitivity of penetration (Fig. 6(c)) is very low compared to the bead width (Fig. 6(a)), which indicates a limited effect of voltage variations on penetration. Therefore, it can be said that welding voltage is not an efective parameter to control penetration. However, combination of 600 A, 20 V, and 6.6667 mm/s can be interpreted as more sensitive welding conditions for penetration. As shown in Fig. 7, welding speed sensitivity of bead width, bead height and penetration are negative sense. These sensitivities imply decrement tendency in the predictive values of bead width, bead height and penetration. It is clearly seen that the bead width is highly affected by welding speed variations, while penetration seems to be nonsensitive. Negative welding speed sensitivity of bead width increases with increasing current and voltage, whereas it decreases with increasing speed (Fig. 7(a)). Bead width is most sensitive to welding speed at higher current (600 A), higher voltage (30 V) and lower speed values (6.6667 mm/s) (i.e. maximum heat input). As shown in Fig. 7(b), a parameter setting of higher current (600 A), lower voltage (20 V) and lower speed (6.6667 mm/s) combination predicts the minimum bead height due to maximum negative sensitivity results. Penetration is said to be non-sensitive to the variations in speed in all welding conditions (Fig. 7(c)). Thus, welding speed cannot be effectively used to control penetration. Generally the results of sensitivity analysis are similar to the ones obtained by Kim et al. (2003) for GMA welding process. Current sensitivity of bead width and bead height increase with increasing current, while current sensitivity of penetration decreases with increasing current for GMA welding (Kim et al., 2003) and SAW processes. Beside current sensitivity, similarities in voltage and speed sensitivity values of GMA welding with SAW process have been observed. The signs of sensitivity values are the same in both analyses, for example; all of the current sensitivities are positive and speed sensitivities are negative. After obtaining relatively low current sensitivity values, Kim et al. (2003) concluded that, change of process parameters of GMA welding affected the bead width and bead height more strongly than penetration. However, in the present study (SAW), penetration has been found to be very sensitive to variations especially in current. This difference can be attributed to the different characteristics of the welding processes and different conditions of the experiments.
4.
Conclusions
In the first part of this study, mathematical modelling using curvilinear regression equations were developed from experimental data. Then, sensitivity analysis of weld bead parameters such as bead width, bead height, and penetration to variations in current, voltage, and speed in submerged arc welding process were performed. Welding process parameters, required for desired weld bead geometry, can effectively be predicted using mathematical models developed in this study. These mathematical
models can also be used to optimize processes and to develop automatic control systems for welding power sources. Following conclusions can be drawn from this sensitivity analysis: • Bead width is very sensitive to all process parameters. Current, voltage and speed are the determining parameters for bead width. • Bead width is more sensitive to voltage and speed variations than that of bead height and penetration. • All three process parameters have effects in determining the bead height. • In order to decrease the bead height, higher values of voltage and speed can be considered. • Since bead width and penetration are more sensitive to current variations than bead height, arc current can be used effectively for any adjustment in bead width and penetration. • Current is the most important parameter in determining the penetration. Penetration is almost non-sensitive to variations in voltage and speed. Therefore, voltage and speed cannot be efectively used to control penetration. • At maximum heat input level (higher levels of current and voltage, and lower level of welding speed), current sensitivity of penetration, and speed sensitivity of bead width reach their maximum values.
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