Multi response simulation and optimization of gas

Applied Mathematical Modelling 42 (2017) 540–553

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Multi response simulation and optimization of gas tungsten arc welding Mukundraj V. Patil∗ Modern Education Society’s College of Engineering, Savitribai Phule Pune University, Pune, Mahrashtra 411001, India

a r t i c l e

i n f o

Article history: Received 5 November 2015 Revised 15 September 2016 Accepted 10 October 2016 Available online 22 October 2016 Keywords: Best TIG welding setting GTAW welding Definitive screening design Welding optimization Central composite design Multi criteria optimization

a b s t r a c t In the fabrication of a pressure vessel, the successful bending operation (after welding) demands higher tensile strength of weld bead. Therefore, to achieve typical tensile strength and hardness is the primary objective of this paper. Stainless steel 304 is widely used material in almost all the industrial applications, hence it is selected as a candidate material for study of tungsten inert gas (TIG) welding process. In order to produce, a high quality and reliable welding, the welding process needs to be robust in performance. A recently developed popular experimental approach known as definitive screening design (DSD) is used for process improvement. These optimum variable settings necessary for consistent welding are obtained through the application of simulation by using central composite design. The typical values of tensile strength and hardness are obtained at a low value of purging gas flow rate, filler rod dia.; intermediate values of root gap, plate thickness; and at high values of electrode dia., current, and gas flow rate. © 2016 Elsevier Inc. All rights reserved.

1. Introduction Tungsten inert gas (TIG) welding, is also known as gas tungsten arc welding (GTAW) or Heliarc welding. The latter name is due to Russell Meredith, who perfected this process in 1941 [1]. TIG welding utilizes non-consumable tungsten electrode for producing high quality weld in which, arc is shielded by inert gas such as Ar or He or N2 , or their combinations. Mechanical properties of weld are considered as a function of input and process variables. In TIG welding of Al-Mg alloy (thickness 2.14 mm), A. Kumar and S. Sundarrajan [2] used four process parameters: peak welding current, base welding current, pulse frequency, and travel speed. These four variables were used at two levels by applying Taguchi L8 (27 ) design. Significant factors are identified by using ANOVA, whereas mathematical relation modeled using regression analysis. M. Yousefieh et al. [3] used super duplex stainless steel (SDSS) of thickness 7 mm with process variables such as, pulse welding current, background welding current, pulse frequency, and % on time. According to their observation, % on time is the most influencing factor. H. Lin [4] used Inconel 718 alloy of 6.35 mm thickness for optimizing activated TIG welding process. Taguchi design of L18 orthogonal array (OA) is implemented for improving quality characteristics by minimizing the causes of variation. Arc length, travel speed, welding current, gas flow rate, angle of electrode tip, and mixed flux type are considered as the process variables. Gray relational analysis (GRA) is used to convert multiple responses into single response by assigning gray relational grade (GRG) to individual responses. R. Adalarasan and M. Santhanakumar [5] studied the response variables such as yield strength, ultimate tensile strength, and microhardness of AA

∗

Corresponding author. E-mail addresses: [email protected], [email protected]

http://dx.doi.org/10.1016/j.apm.2016.10.033 0307-904X/© 2016 Elsevier Inc. All rights reserved.

M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553

541

For single butt weld, σ t = P / (t x l), where σ t = allowable tensile strength, l = weld length P = transverse load applied, t = weld throat,

Fig. 1. Ishikawa diagram for manual TIG welding.

6061 with TIG and metal inert gas (MIG) welding. These multiple responses are handled by using integration of desirability function and GRA. In their study, welding current is found to be a major contributing variable. Moreover, it is proved that the results of TIG welding are better than MIG welding. G. Magudeeswaran et al. [6] used Taguchi design with L9 (34 ) OA for optimizing TIG process parameters on duplex stainless steel (DSS) of 6 mm thickness. Electrode gap, travel speed, welding current and voltage are considered as process variables. These authors found that the optimum condition corresponds to an aspect ratio of 1.24. A. K. Srirangan and S. Paulraj [7] used three welding variables current, welding speed, and voltage. Two responses yield strength and ultimate tensile strength are optimized using GRA. However, the input variables are correlated, so it cannot be guessed, whether the true optimum is achieved. Since, input variables are correlated, it is highly possible that the interaction has greater impact on the response. Definitive screening design is the most promising experimental design approach invented by B. Jones and C. Nachtsheim in 2011 [8]. This design reveals main effect, quadratic and interaction effect in minimum number of runs by using three levels of variables. Through above review, it is observed that the different variables in TIG welding affects the weld properties in different manner. Ishikawa diagram for manual TIG welding process, which is regarded as a system representing the welding process is shown in Fig. 1 and various factors affecting the process are enlisted. The root gap, if kept at too low level weakens the weld, whereas too high a level allows the weld to pass without any bondage. Thus, root gap plays an important role in the formation of weld, thereby it affects the mechanical properties and hence it is considered as a one of the variable. Since the weld strength is a function of throat thickness which depends upon the plate thickness [9]. Generally, the filler rod diameter is selected based on the parent metal composition and the thickness to be welded [10]. Therefore, filler rod diameter and plate thickness are estimated to be probable input variables [9,11,12]. If the gas flow rate during welding operation is continuous and uniform then it provides a better shielding to the weld pool and thus strengthens it. While the oxidizing gases formed on the opposite side of the weld can introduce porosity in the weld [4,10,11], which results into decrease in the weld strength. Therefore, to remove these oxidizing gases, a uniform flow of purging gas is required [10,13,14]. Thus, gas flow rate and purging gas flow rate are also considered as probable variables. The current is correlated with travel speed [15] and voltage, hence, only current is taken as input variable. Moreover, travel speed is a function of thickness [16], thus thickness is independent variable, hence, considered as system variable for process study. Electrode diameter is generally chosen of higher size for longer life, but it requires high current for starting arc [16]. The final list of input and process variables for study are shown in Fig. 2. This paper attempts to use DSD for screening and central composite design (CCD) for optimization, and desirability function for simultaneous optimization of multi response variables. This strategy is not used previously and hence it is implemented in this paper. Moreover, simultaneous study of effect of seven variables on response variables is novelty of this paper. From robustness viewpoint, the properties of weld should be consistent that will yield typical tensile strength and typical hardness. The problem formulated in this paper is: To find the optimum values of input and process variables in TIG welding, which will yield the typical tensile strength and the typical hardness. Tensile strength (primary objective) and hardness (secondary objective) are correlated properties [17]. This implies that when tensile strength is achieved the hardness should not increase sporadically resulting into brittleness of weld bead.

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M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553

Fig. 2. TIG welding process-schematic diagram.

TIG Welding

Literature Survey

Process Variables

Definitive Screening Design

Data Collection using DSD Simulation using CCD Multiresponse Optimization

Desirability Function

Select Optimal Setting

Sensitivity Analysis

Confirmation Run

Result and Discussion

Conclusions

Fig. 3. Research methodology. Table 1 Tensile strength and hardness for SS 304 [18,19]. Description

Tensile strength (MPa)

Hardness (HRB)

Minimum Typical

505 620

70 95

2. Research methodology The research methodology is depicted in Fig. 3 below. Literature survey provided useful insights regarding use of important variables. DSD provides screening and optimization of seven factors. With reference of DSD, TIG welding is performed and the test results are obtained for two response variables: tensile strength and hardness. The results obtained from DSD are further used for simulation using CCD for optimization. Desirability function approach is used for simultaneous optimization of multiple responses. Finally, the confirmation runs are conducted to ascertain the optimum results. 3. Material and experimental set-up The material SS 304 is an austenitic stainless steel and it is used in almost all industrial application including heavy fabrication industries. Therefore, it is selected as a material for experimentation. Mechanical properties of SS 304 are tabulated below (Table 1). The sample pieces (Fig. 4) were prepared in the size of 100 mm × 100 mm for both the tensile and hardness tests. The experimental setup consists of manual welding installation at Ador welding academy (AWA, Pune, India) as shown in Fig. 5. The major components in the setup are highlighted. Because of manual welding operation, ASME qualified welder is utilized for uniform and consistent welding. Argon gas with 99.99% purity is used throughout the welding process.

M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553

543

Fig. 4. Tensile test specimen.

Fig. 5. Welding setup at Ador welding academy.

Single butt joint is prepared in accordance with ISO 9692 (2003). Initially, a tack is produced at both ends by establishing a root gap with use of U-bent electrodes of same size in clamped condition of plates, then regular welding is performed. For 5 mm thick plate, two weld passes were found to be sufficient to fill the weld gap completely; whereas for 8 mm and 10 mm thick plates, three weld passes were required. After root pass is performed and before, performing the next welding pass, the weld bead was allowed to cool below 150 °C, so that chromium will remain in free form. This precaution is necessary to ensure that chromium carbide would not form at grain boundaries, which may result into crack. Thermal stick was used to ensure that interpass temperature is well below 150 °C. If the mark of thermal stick appears on the weld, then the temperature is considered to be above 150 °C, and vice-versa. Before the start of next welding operation, electrode sharpening condition was checked and confirmed, that it is within specification; if it is not, then sharpening was carried out. Tensile test specimen (Fig. 6) was obtained by cutting the weld piece, followed by the machining of weld on both the sides till the general plane of sample piece. Tensile test was executed on TUNF-600 ultimate tensile testing machine according to IS 1608 (2005) [20]. UTS was evaluated as quotient of the maximum load divided by the original cross-section area. Broken tensile test piece is shown in Fig. 7, after conduction of tensile test. Hardness was measured at weld and heat affected zone (HAZ) on both sides of the weld according to IS 1586-2 (2012) [21]. Ball of diameter 1.588 mm used with applied force of 100 kgf (980.7 N) on RASN (M)-Rockwell hardness tester. Three repetitive readings were recorded for each piece and average value of three reading on weld is presented as the hardness at weld.

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M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553

Fig. 6. Tensile test specimen.

Fig. 7. Broken tensile test specimen after testing.

4. Definitive screening design (DSD) Definitive screening design is preferred design over fractional factorial and Plackett Burman design, nowadays. It consists of three level of factors and accommodates large number of factors, which makes it useful not only for screening, but also for optimization. The center run added in the design, helps in identifying the quadratic as well as interaction effects. Since, welding process is characterized by interaction of process variables, definitive screening design is a right choice of experimental design. In this design of experiment, main effects and quadratic effects are not confounded with interaction effects. However, an interaction effect is confounded with few other two factor interactions. This problem can be overcome with the dummy variables that adds extra runs in the design, and later on removing these dummy factors from the design. The beauty of this design is that total number of runs required is (2m + 1), where m is the number of factors [8]. This design can also be created using conference matrix [22]. However, blocking [23] can add extra runs to the original design. In this design (Table 2), replication is taken into account by adding extra runs for three dummy factors in addition to seven design factors and then removing these three columns. Whole experiment is divided into two blocks, half the runs for block of low welding speed (100 mm/min) and half the runs for block of high welding speed (160 mm/min). Blocking is added to remove the extraneous effect from the response. DSD design (Table 2) is created for ten variables with two blocks each containing center run. This design created twenty two runs, finally, last three dummy columns removed from the design. 5. Desirability function Desirability function is used to convert multiple objectives into single objective. Desirability value is assigned to each individual reference in proportion to the preference given to it. The individual desirability may fall in any one of following three cases [24] (Table 3). The composite desirability is calculated as geometric mean of all individual desirability’s. The weight and importance depends on subjective preference of the user. As weight decreases (1–0.1) or increases (1–10), the probability of achieving an optimum is either facilitated or hampered respectively. Importance value determines the preference of response achievement, if achievement of an optimum for a certain response is necessary then it is given a higher importance. Importance varies from 1 to 10, the importance value 1 represents the neutral case. 6. DSD and CCD analysis The regression equation for both Y1 and Y2 obtained from DSD and used for creating CCD (Table 8). CCD design reveals unconfounded factor interactions and quadratic effects and hence chosen for optimization. CCD design is more useful, because it offers the following advantages: 1) Estimates quadratic effects and interaction effects upto fourth order, 2) Provides accurate and precise model, 3) Allows efficient estimation of response surface, and 4) The design is rotatable [25]. Central composite design with five levels and 35 center runs used, thus resulting into 177 runs. All these factors are used at five levels (Table 4): The Table 5 shows the central composite design.

Table 2 Definitive screening design with actual values of variables.

Block 1

2

Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Root gap 1.6 3.2 mm A

Filler dia. 1.6 2.4 mm B

Welding current 90 140 A C

Purging gas flow rate 6 10 L/min. D

Plate thickness 5 10 mm E

Electrode dia. 1.6 3.2 mm F

Gas flow rate 8 12 L/min. G

Ultimate tensile strength – – MPa Y1

Hardness at weld – – HRB Y2

2.4 3.2 3.2 3.2 3.2 1.6 2.4 2.4 1.6 1.6 1.6 1.6 1.6 1.6 3.2 1.6 2.4 3.2 3.2 3.2 1.6 3.2

1.6 1.6 1.6 2.4 2.4 1.6 2 2.4 2.4 2.4 1.6 2 2.4 2.4 2.4 1.6 2 2 1.6 1.6 1.6 2.4

90 115 140 140 90 140 115 140 115 90 90 140 140 90 90 90 115 90 90 140 140 140

6 6 10 6 10 6 8 10 10 6 10 10 8 6 10 10 8 6 8 10 6 6

5 10 8 5 5 10 8 10 5 8 10 10 5 10 10 5 8 5 10 5 5 10

1.6 3.2 1.6 3.2 3.2 1.6 2.4 3.2 1.6 3.2 1.6 3.2 1.6 2.4 1.6 3.2 2.4 1.6 3.2 2.4 3.2 1.6

8 8 8 8 10 10 10 12 12 12 12 8 8 8 8 8 10 12 12 12 12 12

573 489 413 528 546 306 493 276 496 363 168 269 435 210 181 446 493 554 350 516 487 222

76.57 74.33 96.88 56.33 77.06 84.68 76.20 81.84 76.75 94.72 62.40 83.72 100.67 58.44 76.44 80.92 76.20 73.69 98.07 56.31 82.30 77.82

M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553

Description Low (1) High (2) Units Variable Symbol (→)

A = Root gap, B = Filler dia., C = Current, D = Purging gas flow rate, E = Plate thickness, F = Electrode dia., G = Gas flow rate, Y1 = Tensile strength, Y2 = Hardness.

545

546

M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553 Table 3 Desirability function for three different cases [24]. Case-1: Target is the two sided

di (Yi ) =

⎧ 0 ⎪ ⎪ ⎨( Yi −L )r ⎪ ( ⎪ ⎩

T −L U−Yi U−T

)

r

0

Case-2: Target to be minimized

Yi ≤ L L ≤ Yi ≤ T

di (Yi ) =

T ≤ Yi ≤ U Yi ≥ USL

⎧ ⎨1 ( U−Yi )r ⎩ U−L

Case-3: Target to be maximized

Yi ≤ L L ≤ Yi ≤ U Yi ≥ U

0

di (Yi ) =

⎧ ⎨0 ( Yi −L )r ⎩ U−L 1

Yi ≤ L L ≤ Yi ≤ U Yi ≥ U

Yi = Individual response value, LSL = Lowest Y value, USL = Highest Y value, T = Target value for given response, di (Yi ) = Individual desirability value, r = weight applied on individual response. Table 4 Levels of factors in central composite design. Levels

A

B

C

D

E

F

G

−1 −0.2980 0 0.2980 1

1.6 2.1616 2.4 2.6384 3.2

1.6 1.8808 2 2.1192 2.4

90 107.5496 115 122.4504 140

6 7.4040 8 8.5960 10

5 6.7550 8 8.2450 10

1.6 2.1616 2.4 2.6384 3.2

8 9.4040 10 10.5960 12

Regression analysis is a study of dependent variable y as a function of independent variable x [26]. It has different objectives such as 1) describing the structure of data, 2) assessment of relationship between dependent and independent variable, 3) prediction of future datapoints, and 4) simulation to understand the system behavior [27,28].

y = β0 +

n 

βk xki +

k=1

n  k=1

βkk x2ki +

n−1  n 

βkl xki xli + εi j

k=1 l=k+1

This is a general form of regression model, where β 0 upto β k represents constant values, x1 upto xk represents continuous variables, and ε ij represents a random error term in the model. The analysis of the design yields the following regression equation. 2 2 2 Y1 = −3404 + 641.5A + 835.1B + 29.56C − 90.93D − 57.9E − 445.1F + 388.8G − 68.62A − 152.8B − 0.1279C 2 2 2 2 +4.954D + 1.271E + 98.56F −19.6G −121.9AB − 3.362AE.

Y2 = −192.3 + 21.64A + 318B − 8.274C + 5.214D + 7.071E − 155.2F + 107.6G − 0.7068A2 −62.2B2 +0.03615C2 −0.3095D2 −1.246E2 +32.44F2 −5.375G2 −29.32AB + 5AE. The above regression equation contains main, quadratic and interaction effects. All the two factor interactions are not confounded and therefore, this design offers better prediction of the response variable, as seen in the color map on correlations (Fig. 8). The model statistics are shown in the Table 6. Both these regression model have zero standard deviation. The R2 value is 100% that means all the variation in data is captured by both the model. R2 adjusted value is 100% which indicates that there is no unnecessary term present in both the model, also there is no exclusion of necessary term in both the model. Similarly, R2 predicted is 100% which means that both the model can very accurately predict the future scenarios. Since, R2 adjusted and R2 predicted are 100%, there is no possibility of Type-I or Type-II error, hence, statistical tests for model validation are not necessary. 7. Results and discussions The optimum result is: typical tensile strength = 618.7226 MPa, typical hardness = 87.9256 HRB; root gap = 2.83 mm, diameter of filler rod = 1.76 mm, welding current = 140 A, purging gas flow rate = 6 L/min, plate thickness = 5.48 mm, electrode dia. = 3.2 mm, gas flow rate = 11.92 L/min. The quadratic effect allows, different combination of variable setting which may be suboptimal solution. Most of the effects are linear and quadratic in nature, except the interaction AB and AE (Fig. 9). The practical approach will have following settings (Fig. 10). Surface plot shows the behavior of interaction variables as shown in Fig. 11. For AB interaction, when root gap (A) and filler rod diameter (B) are at high limit (both) yields maximum tensile strength (Y1 ), but yields low value of hardness (Y2 ). So true optimum is obtained, when both the values lie at intermediate point of their overall range. Similarly, for AE interaction, it is observed that when root gap (A) and plate thickness (E) are at high limits (both) yields maximum tensile strength (Y1 ), but yields low value of hardness (Y2 ). The true optimum in this case also lie at intermediate point of their overall range. The overall scenario of variables role and their optimum value is shown in Table 7 below.

M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553

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Table 5 Central composite design. Run

A

B

C

D

E

F

G

Y1

Y2

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 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

2.4 2.4 2.6384 2.6384 2.1616 2.6384 2.1616 2.4 2.6384 2.1616 2.1616 2.1616 2.6384 2.6384 2.4 2.6384 2.4 2.6384 2.6384 2.4 2.6384 2.6384 2.4 2.6384 2.1616 2.4 2.4 2.4 2.4 2.6384 2.6384 2.6384 2.6384 2.4 2.6384 2.1616 2.1616 1.6 2.6384 2.6384 2.1616 2.4 2.1616 2.4 2.6384 2.4 2.4 2.4 2.6384 2.6384 2.4 2.4 2.4 2.1616 2.1616 2.1616 2.4 2.4 2.1616 2.6384 2.1616 2.1616 2.6384 2.1616 2.1616 2.1616 2.6384 2.6384 2.1616 2.6384

2 2 1.8808 2.1192 2.1192 2.1192 1.8808 2 1.8808 1.8808 2.1192 2.1192 2.1192 2.1192 2 1.8808 2 2.1192 1.8808 2 2.1192 1.8808 2 2.1192 2.1192 2 2 2 2 2.1192 1.8808 2.1192 1.8808 2 1.8808 1.8808 2.1192 2 1.8808 1.8808 2.1192 2 1.8808 2 2.1192 2 2 2 1.8808 1.8808 2 1.6 2 2.1192 2.1192 2.1192 2 2 1.8808 1.8808 2.1192 1.8808 2.1192 2.1192 2.1192 1.8808 1.8808 2.1192 2.1192 2.1192

115 115 122.4504 122.4504 122.4504 122.4504 107.5496 115 107.5496 122.4504 122.4504 122.4504 122.4504 107.5496 115 122.4504 115 107.5496 122.4504 115 107.5496 122.4504 115 107.5496 122.4504 115 115 115 115 107.5496 107.5496 122.4504 122.4504 115 107.5496 107.5496 107.5496 115 122.4504 107.5496 122.4504 115 122.4504 115 122.4504 115 115 115 122.4504 122.4504 115 115 115 122.4504 107.5496 107.5496 115 115 107.5496 107.5496 107.5496 122.4504 107.5496 107.5496 122.4504 107.5496 107.5496 107.5496 107.5496 122.4504

8 8 7.4040 7.4040 7.4040 7.4040 8.5960 8 8.5960 7.4040 8.5960 7.4040 8.5960 7.4040 8 7.4040 8 8.5960 7.4040 8 7.4040 8.5960 8 8.5960 8.5960 8 8 8 10 8.5960 8.5960 8.5960 8.5960 8 7.4040 8.5960 7.4040 8 8.5960 8.5960 7.4040 8 7.4040 8 7.4040 8 8 8 7.4040 7.4040 8 8 8 8.5960 8.5960 8.5960 8 6 7.4040 8.5960 8.5960 8.5960 8.5960 8.5960 8.5960 7.4040 8.5960 7.4040 8.5960 8.5960

7.5 7.5 6.7550 6.7550 8.2450 6.7550 6.7550 7.5 6.7550 6.7550 6.7550 8.2450 8.2450 6.7550 7.5 6.7550 7.5 6.7550 8.2450 7.5 8.2450 6.7550 7.5 6.7550 6.7550 7.5 7.5 7.5 7.5 8.2450 6.7550 8.2450 8.2450 7.5 6.7550 6.7550 6.7550 7.5 8.2450 6.7550 6.7550 7.5 8.2450 7.5 8.2450 7.5 7.5 7.5 6.7550 6.7550 7.5 7.5 7.5 8.2450 6.7550 8.2450 7.5 7.5 8.2450 8.2450 8.2450 6.7550 8.2450 6.7550 8.2450 6.7550 8.2450 8.2450 6.7550 6.7550

2.4 2.4 2.6384 2.1616 2.1616 2.6384 2.6384 2.4 2.1616 2.1616 2.1616 2.1616 2.1616 2.1616 3.2 2.1616 2.4 2.6384 2.1616 2.4 2.1616 2.6384 2.4 2.1616 2.6384 2.4 2.4 1.6 2.4 2.1616 2.1616 2.1616 2.1616 2.4 2.6384 2.1616 2.1616 2.4 2.6384 2.6384 2.1616 2.4 2.6384 2.4 2.1616 2.4 2.4 2.4 2.1616 2.6384 2.4 2.4 2.4 2.6384 2.1616 2.1616 2.4 2.4 2.1616 2.1616 2.6384 2.1616 2.6384 2.6384 2.6384 2.6384 2.1616 2.6384 2.6384 2.6384

10 12 10.5960 9.4040 10.5960 10.5960 10.5960 10 9.4040 10.5960 10.5960 9.4040 10.5960 9.4040 10 9.4040 10 9.4040 10.5960 10 9.4040 9.4040 10 10.5960 10.5960 10 10 10 10 9.4040 10.5960 9.4040 10.5960 10 10.5960 9.4040 10.5960 10 9.4040 10.5960 9.4040 10 9.4040 10 9.4040 10 10 10 10.5960 9.4040 10 10 10 10.5960 9.4040 9.4040 10 10 10.5960 9.4040 9.4040 10.5960 9.4040 10.5960 9.4040 9.4040 10.5960 10.5960 9.4040 10.5960

516 431 574 541 454 551 529 516 549 532 509 458 453 539 601 565 516 539 490 516 468 564 516 521 522 516 516 557 512 454 545 456 476 516 572 520 521 438 493 558 526 516 481 516 470 516 516 516 561 578 516 519 516 453 510 442 516 559 461 477 455 518 468 520 457 547 474 478 524 537

76.33 55.03 75.98 73.67 77.40 74.03 77.18 76.33 75.33 77.22 78.92 77.28 76.45 73.07 97.50 75.62 76.33 73.62 78.08 76.33 75.41 76.17 76.33 73.50 79.17 76.33 76.33 96.68 75.61 75.72 75.44 76.33 78.39 76.33 75.38 76.81 78.01 78.19 78.52 75.69 78.49 76.33 76.14 76.33 76.02 76.33 76.33 76.33 75.74 75.86 76.33 66.84 76.33 77.96 78.20 76.99 76.33 74.56 75.41 77.67 77.24 77.54 75.97 78.57 77.84 76.75 77.79 75.78 78.45 74.35

(continued on next page)

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M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553 Table 5 (continued) Run

A

B

C

D

E

F

G

Y1

Y2

71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140

2.4 2.4 2.6384 2.6384 2.1616 2.4 2.1616 2.6384 2.6384 2.6384 2.1616 2.4 2.4 2.1616 2.4 2.1616 2.6384 2.6384 2.6384 2.4 2.1616 2.4 2.1616 2.1616 2.6384 2.4 2.6384 2.6384 2.4 2.1616 2.1616 2.4 2.1616 2.1616 2.1616 2.6384 2.1616 2.6384 2.6384 2.6384 2.6384 2.6384 2.4 2.4 2.1616 2.1616 2.1616 2.6384 2.6384 2.4 2.1616 2.4 2.1616 2.6384 2.1616 2.6384 2.6384 2.1616 2.1616 2.6384 2.4 2.6384 2.4 2.1616 2.6384 2.6384 2.1616 2.1616 2.4 2.6384

2 2 1.8808 1.8808 1.8808 2 2.1192 2.1192 1.8808 1.8808 1.8808 2 2 2.1192 2 1.8808 2.1192 1.8808 1.8808 2 2.1192 2 1.8808 1.8808 1.8808 2 2.1192 2.1192 2 2.1192 2.1192 2 1.8808 1.8808 2.1192 2.1192 1.8808 1.8808 1.8808 1.8808 2.1192 1.8808 2.4 2 2.1192 1.8808 1.8808 1.8808 1.8808 2 1.8808 2 1.8808 2.1192 1.8808 1.8808 1.8808 1.8808 1.8808 1.8808 2 2.1192 2 1.8808 2.1192 2.1192 2.1192 2.1192 2 2.1192

115 115 107.5496 122.4504 122.4504 115 107.5496 122.4504 122.4504 107.5496 122.4504 115 115 122.4504 115 107.5496 107.5496 122.4504 122.4504 140 107.5496 115 122.4504 122.4504 107.5496 115 122.4504 122.4504 115 122.4504 107.5496 115 122.4504 107.5496 107.5496 107.5496 122.4504 122.4504 122.4504 107.5496 107.5496 122.4504 115 115 107.5496 107.5496 107.5496 107.5496 107.5496 115 122.4504 115 107.5496 122.4504 122.4504 107.5496 122.4504 107.5496 107.5496 107.5496 115 107.5496 115 107.5496 122.4504 107.5496 107.5496 107.5496 115 122.4504

8 8 7.4040 7.4040 7.4040 8 7.4040 7.4040 8.5960 7.4040 8.5960 8 8 8.5960 8 8.5960 8.5960 8.5960 7.4040 8 8.5960 8 8.5960 7.4040 8.5960 8 7.4040 8.5960 8 7.4040 7.4040 8 8.5960 7.4040 7.4040 7.4040 7.4040 7.4040 8.5960 7.4040 8.5960 8.5960 8 8 8.5960 8.5960 7.4040 8.5960 8.5960 8 8.5960 8 8.5960 8.5960 7.4040 7.4040 8.5960 7.4040 8.5960 7.4040 8 7.4040 8 8.5960 7.4040 8.5960 7.4040 7.4040 8 7.4040

10 7.5 8.2450 8.2450 8.2450 7.5 6.7550 6.7550 8.2450 8.2450 8.2450 7.5 7.5 6.7550 7.5 8.2450 8.2450 6.7550 8.2450 7.5 6.7550 7.5 6.7550 6.7550 8.2450 7.5 8.2450 8.2450 7.5 6.7550 8.2450 7.5 8.2450 8.2450 6.7550 6.7550 6.7550 8.2450 6.7550 8.2450 6.7550 6.7550 7.5 7.5 8.2450 8.2450 6.7550 8.2450 6.7550 7.5 6.7550 7.5 6.7550 6.7550 8.2450 8.2450 8.2450 8.2450 8.2450 6.7550 5 6.7550 7.5 8.2450 6.7550 6.7550 6.7550 8.2450 7.5 8.2450

2.4 2.4 2.6384 2.1616 2.1616 2.4 2.6384 2.1616 2.6384 2.1616 2.6384 2.4 2.4 2.6384 2.4 2.1616 2.6384 2.6384 2.6384 2.4 2.1616 2.4 2.6384 2.1616 2.6384 2.4 2.6384 2.6384 2.4 2.6384 2.6384 2.4 2.6384 2.6384 2.6384 2.6384 2.6384 2.6384 2.1616 2.1616 2.1616 2.1616 2.4 2.4 2.6384 2.1616 2.1616 2.6384 2.6384 2.4 2.1616 2.4 2.1616 2.1616 2.1616 2.6384 2.1616 2.1616 2.6384 2.1616 2.4 2.6384 2.4 2.6384 2.6384 2.6384 2.1616 2.1616 2.4 2.6384

10 10 9.4040 9.4040 10.5960 10 9.4040 10.5960 10.5960 9.4040 9.4040 10 10 9.4040 10 10.5960 10.5960 10.5960 10.5960 10 10.5960 10 10.5960 9.4040 9.4040 10 9.4040 9.4040 10 9.4040 10.5960 8 10.5960 9.4040 10.5960 10.5960 10.5960 9.4040 10.5960 10.5960 9.4040 9.4040 10 10 10.5960 9.4040 10.5960 10.5960 9.4040 10 9.4040 10 10.5960 9.4040 9.4040 10.5960 9.4040 9.4040 10.5960 10.5960 10 9.4040 10 9.4040 9.4040 10.5960 9.4040 10.5960 10 10.5960

407 516 505 494 463 516 538 538 489 491 467 516 516 526 516 447 464 560 503 440 507 516 532 536 491 516 484 470 516 540 465 444 463 478 534 549 545 507 547 488 525 551 464 516 451 451 530 487 562 516 522 516 516 527 467 501 480 465 461 559 641 553 516 465 555 535 524 452 516 480

69.49 76.33 77.60 77.96 76.02 76.33 78.13 73.79 78.64 77.36 76.45 76.33 76.33 79.05 76.33 75.72 76.09 76.29 78.32 99.93 78.32 76.33 77.78 77.11 77.91 76.33 76.26 76.57 76.33 78.74 77.04 54.63 76.57 75.54 78.25 73.43 77.47 78.20 76.05 77.48 73.38 75.93 65.91 76.33 77.36 75.61 76.62 78.03 75.57 76.33 77.42 76.33 76.93 73.98 75.90 77.72 78.27 75.29 75.97 75.13 67.59 73.31 76.33 75.85 73.92 73.74 77.89 76.80 76.33 76.38

(continued on next page)

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549

Table 5 (continued) Run

A

B

C

D

E

F

G

Y1

Y2

141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177

2.1616 2.1616 2.1616 2.4 2.4 2.6384 2.1616 2.4 2.1616 2.4 2.1616 2.1616 2.4 2.6384 2.6384 2.4 2.1616 2.6384 2.1616 2.6384 2.6384 3.2 2.1616 2.1616 2.6384 2.1616 2.4 2.1616 2.6384 2.1616 2.6384 2.1616 2.6384 2.1616 2.1616 2.1616 2.1616

1.8808 2.1192 1.8808 2 2 2.1192 2.1192 2 2.1192 2 1.8808 2.1192 2 2.1192 2.1192 2 2.1192 2.1192 1.8808 1.8808 2.1192 2 1.8808 1.8808 1.8808 1.8808 2 2.1192 2.1192 1.8808 2.1192 2.1192 2.1192 2.1192 2.1192 2.1192 1.8808

122.4504 122.4504 122.4504 115 90 107.5496 122.4504 115 122.4504 115 107.5496 107.5496 115 122.4504 122.4504 115 122.4504 122.4504 107.5496 107.5496 107.5496 115 122.4504 122.4504 107.5496 122.4504 115 122.4504 107.5496 107.5496 122.4504 122.4504 107.5496 107.5496 122.4504 107.5496 107.5496

8.5960 8.5960 7.4040 8 8 7.4040 7.4040 8 7.4040 8 8.5960 7.4040 8 8.5960 7.4040 8 8.5960 8.5960 7.4040 7.4040 8.5960 8 7.4040 8.5960 7.4040 8.5960 8 8.5960 7.4040 7.4040 8.5960 7.4040 7.4040 7.4040 7.4040 8.5960 7.4040

8.2450 6.7550 8.2450 7.5 7.5 8.2450 6.7550 7.5 8.2450 7.5 6.7550 8.2450 7.5 6.7550 8.2450 7.5 8.2450 8.2450 6.7550 6.7550 8.2450 7.5 6.7550 6.7550 6.7550 8.2450 7.5 8.2450 6.7550 8.2450 6.7550 8.2450 8.2450 8.2450 6.7550 8.2450 6.7550

2.1616 2.1616 2.6384 2.4 2.4 2.1616 2.6384 2.4 2.6384 2.4 2.6384 2.6384 2.4 2.1616 2.1616 2.4 2.1616 2.6384 2.6384 2.1616 2.1616 2.4 2.6384 2.6384 2.6384 2.1616 2.4 2.1616 2.1616 2.6384 2.6384 2.6384 2.6384 2.1616 2.1616 2.1616 2.1616

9.4040 9.4040 10.5960 10 10 10.5960 10.5960 10 10.5960 10 9.4040 9.4040 10 10.5960 10.5960 10 10.5960 10.5960 10.5960 9.4040 10.5960 10 9.4040 9.4040 9.4040 10.5960 10 9.4040 10.5960 10.5960 9.4040 9.4040 9.4040 9.4040 10.5960 10.5960 9.4040

453 513 477 516 432 464 536 516 467 516 533 469 516 524 466 516 440 466 543 562 450 507 549 535 576 450 516 444 535 475 541 471 481 456 523 438 534

76.21 78.81 76.26 76.33 97.91 75.53 78.86 76.33 77.65 76.33 77.06 76.93 76.33 74.10 76.13 76.33 77.72 76.69 76.87 75.01 75.84 73.56 77.35 77.66 75.26 76.33 76.33 77.60 73.19 75.66 74.23 77.53 75.66 76.68 78.61 77.11 76.50

Table 6 Summary of model statistics for regression equations. Model statistic

Y1

Y2

Standard deviation, s R2 (%) R2 adjusted (%) R2 predicted (%)

0 100 100 100

0 100 100 100

Table 7 Final result summary. Variable

Too low

Optimum

Too high

Root gap Filler rod diameter Current Purging gas flow rate Plate thickness Electrode dia. Gas flow rate

Low strength High strength No arc initiation Porosity Burning of plate Low life-span Porosity

2.80 mm 1.60 mm 140 A 6 L/min 5.5 mm 3.2 mm 12 L/min

No bondage between work-pieces Low strength Arc instability, low weld quality Low penetration, poor finish (waviness) on root side Low penetration Need high starting current Increased brittleness

550

M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553

Fig. 8. Color map on correlations.

Fig. 9. Result of multiresponse optimization.

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Fig. 10. Result of multiresponse optimization (modified variable setting).

Fig. 11. Surface plot of interaction variables.

7.1. Confirmation run The purpose of confirmation run is to verify the results obtained. These tests are conducted at an optimum level of input and process variables with three replications each for Y1 and Y2 . The welding at an optimum setting of variables produced better surface finish on the weld and also full penetration of the weld bead (Fig. 12). Result of confirmation runs presented in Table 8, all the deviations are less and therefore the optimum values obtained are acceptable.

552

M.V. Patil / Applied Mathematical Modelling 42 (2017) 540–553

Fig. 12. Weld finish at optimum condition. Table 8 Result of confirmation runs. Description Units Description / symbol Typical value Optimum value Run % Deviation from optimum value

Ultimate tensile strength MPa Replications Y1

597 2.73

620 613.7805 592 3.55

Hardness at weld HRB Replications Y2

588 4.20

80.82 1.72

95 82.2317 78.98 3.95

78.51 4.53

Y1 = Tensile strength, Y2 = Hardness.

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