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In welding, so many factors contribute to good quality welds. The deposition rate is the rate of weld metal deposit at fusion zone during welding, which also is a key factors affecting the quality of welded joints. Too high or low deposition rate compromises the integrity of weld. This study was carried out with the aim of providing an approach for producing better weldments by optimizing and predicting deposition rate of low carbon steel using Response Surface Methodology (RSM). 30 sets of experiments were done, adopting the central composite experimental design. The tungsten inert gas welding equipment was used to produce the welded joints. Argon gas was supplied to the welding process to shield the weld from atmospheric interference. Mild steel coupons measuring 60 × 40 × 10 mm was used for the experiments. The results obtained show that the voltage and current have very strong influence on the deposition rate. The models developed possess a variance inflation factor of 1. And P-value is less than 0.05, indicating that the model is significant. The models also possessed a high goodness of fit with R
^{2} (Coefficient of determination) values of 91%. The model produced numerically obtained optimal solution of current of 160.00 Amp, voltage of 20 volts and a gas flow rate of 17 L/min produces a welded material having deposition rate of 0.4637 kg/hr. This solution was selected by design expert as the optimal solution with a desirability value of 98.8%. A weld simulation using the optimum value obtained produced a weld with good quality.

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Several techniques have been developed to improve the metal deposition rate beyond that of standard, single wire SAW to increase the productivity. An extensive research work on optimization of welding process was done by [

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Having a detailed review of literature, it was discovered that the optimization of Tungsten Inert Gas deposition rate of mild steel weld have not been established to the best of our knowledge. The aim of the study is to provide an approach for producing better weld joints considering deposition rate of Tungsten Inert Gas mild steel weld.

This research study is centered on the experimental study of TIG mild steel welds, employing scientific design of experiments, expert systems, statistical and mathematical models. The TIG sets of experiment were conducted at the Department of Welding and Fabrication Technology, Petroleum Training Institute (PTI), Warri, Delta State, Nigeria. 150 pieces of mild steel coupons measuring 60 × 40 × 10 was used for the experiments, the experiment was performed 30 times using 5 specimen for each run. The materials used in the experiment are TIG equipment (Miller machine), shielding gas cylinder and regulator and TIG Torch.

The key parameters considered in this work are welding current, welding speed, gas flow rate, and welding voltage. The range of the process parameters obtained from literature is shown in

Parameters | Units | symbol | lower | Higher |
---|---|---|---|---|

Gas flow rate | Lit/min | F | 12 | 23 |

Arc voltage | Volt | V | 14 | 21 |

Welding current | Amp | A | 130 | 180 |

Welding speed | mm/min | S | 2 | 5 |

The central composite design matrix was developed using the design expert software, producing 30 experimental runs. The input parameters and output parameters make up the experimental matrix, and the responses recorded from the weld samples were used as the data.

N = 2 n + 2 × n + n c

where N is the number of runs, n is the number of factors n c is the number of centre points the researcher desire

The data obtained were analysed using the Response Surface Methodology

The analysis of variance (ANOVA) was used to test the adequacy of the models developed. The statistical significance of the models developed and each term in the regression equation were examined using the sequential F-test, lack-of-fit test and other adequacy measures (i.e. R^{2}, Adj-R^{2} Pred. R^{2} and Adeq. Precision ratio) using the same software to obtain the best fit. The Prob. > F (sometimes called p-value) of the model and of each term in the model can be computed by means of ANOVA. If the Prob. > F of the model and of each term in the model does not exceed the level of significance (say a = 0.05) then the model may be considered adequate within the confidence interval of (1-a). For the lack-of-fit test, the lack of fit could be considered insignificant if the Prob. > F of the lack of fit exceeds the level of significance.

The significance of the model will be determined using analysis of variance (ANOVA), Differential Functioning of Items and Texts (DFITS) a measure of the influence of each observation on the values fitted. The significance of the input process parameters for the two responses was determined using the P-value of the lack of fit and the input process parameters were compared using a significance level of significance of Alpha α = 0.05 (

The coefficient of determination, R^{2}, was used to validate the obtained model for the weld deposition rate. While the adjusted coefficient of determination is obtained and used to validate the proposed model.

Different validation techniques were used to validate the predictions from the response surface methodology (RSM) model developed. Validation techniques used were: Desirability plots, residuals, DFITS, mean square errors (MSE), least significant difference (LSD) bars, Ramp plots, overlay plots, perturbation plots, contour plots, steepest ascent optimization comprising 3-D plots and response surface plots.

In this study, thirty experimental runs were carried out, each experimental run comprising the current, voltage, welding speed and gas flow rate, used to join two pieces of mild steel plates measuring 60 × 40× 10 mm. The weld deposition rate were measured, respectively. The results are shown in

In this study, a second order mathematical model was developed between some selected input variables, namely; current (I), voltage (V), welding speed (WS),

Variation Source | Degree of FreedomDf | Sum of Squares SS | Mean Square MS | Fisher Ratio F-value |
---|---|---|---|---|

Error of residuals | n − 2 | S S E = ∑ i = 1 c ∑ j = 1 n i ( y i j − y ^ i j ) 2 | M S E = S S E n − 2 | |

Regression | 1 | S S R = ∑ i = 1 c ∑ j = 1 n i ( y ^ i j − y ¯ ) 2 | M S R = S S R 1 | F = M S R M S E |

Lack of fit | C − 2 | S S L F i = ∑ i = 1 c ∑ j = 1 n i ( y ¯ i j − y ^ i j ) 2 | M S L F = S S L F c − 2 | F * = M S L F M S P E |

Total | n − 1 | S S T D = ∑ i = 1 c ∑ j = 1 n i ( y i j − y ¯ i j ) 2 | - | - |

gas flow rate (GFR) and weld deposition rate (WDR) using response surface methodology (RSM).

The target of the optimization model was to maximize the weld deposition rate.

The final solution of the optimization process was to determine the optimum value of each input variable namely: current (Amp), voltage (Volt), welding speed (cm/min) and gas flow rate (l/min) that will maximize the weld deposition rate (WDR).

To generate the experimental data for the optimization process:

1) First, statistical design of experiment (DOE) using the central composite design method (CCD) was done. The design and optimization was executed with the aid of statistical tool. For this particular problem, Design Expert 7.01 was employed.

2) Secondly, an experimental design matrix having six (6) center points (k), eight (8) axial points (2n) and sixteen (16) factorial points (2^{n}) resulting to 30 experimental runs was generated.

The randomized design matrix comprising of four input variables namely; current (Amp), voltage (Volt), welding speed (cm/min), gas flow rate (l/min) and weld deposition rate (kg/hr) in coded is shown in

The design matrix comprising of four input variables namely; current (Amp), voltage (Volt), welding speed (cm/min), gas flow rate (l/min) and weld deposition rate (kg/hr) in actual values is shown in

The model summary which shows the factors and their lowest and highest values including the mean and standard deviation is presented as shown in

To validate the suitability of the quadratic model in analyzing the experimental data, the sequential model sum of squares were calculated for weld deposition as presented in

The sequential model sum of squares figure shows the accumulating improvement in the model fit as terms are added. Based on the calculated sequential model sum of square, the highest order polynomial where the additional terms are significant and the model is not aliased was selected as the best fit. From the results of

To test how well the quadratic model can explain the underlying variation associated with the experimental data, the lack of fit test was estimated for each of the responses. Model with significant lack of fit cannot be employed for prediction. Results of the computed lack of fit for weld deposition rate as presented in

From the results of

The model statistics computed for weld deposition rate based on the different model sources as presented in

From the results of

The summary statistics of model fit shows the standard deviation, the r-squared and adjusted r-squared, predicted r-squared and the PRESS statistic for each complete model. Low standard deviation, R-Squarednear unity and relatively low PRESS are the optimum criteria for defining the best model source. Based on the results of

Analysis of the model standard error was employed to assess the suitability of response surface methodology using the quadratic model to maximize the weld deposition rate (WDR. The computed standard errors for the selected responses is presented in

From the results of

The correlation matrix of regression coefficient is presented in

Lower values of the off diagonal matrix as observed in

To understand the influence of the individual design points on the model’s predicted value, the model leveages were computed as presented in

Leverage of a point varies from 0 to 1 and indicates how much an individual design point influences the model’s predicted values. A leverage of 1 means the predicted value at that particular case will exactly equal the observed value of the experiment, i.e., the residual will be 0. The sum of leverage values across all cases equals the number of coefficients (including the constant) fit by the model. The maximum leverage an experiment can have is 1/k, where k is the number of times the experiment was replicated. Leverages of 0.6698 and 0.6073 calculated for both the factorial and axial points coupled with 0.1663 for the center point as observed in

In assessing the strength of the quadratic model towards maximizing the weld deposition rate (WDR) one way analysis of variance (ANOVA) figure was generated for deposition rate and result obtained is presented in

Analysis of variance (ANOVA) was needed to check whether or not the model is significant and also to evaluate the significant contributions of each individual variable, the combined and quadratic effects towards each response. From the result of

“Lack of Fit F-value” of 0.48 implies the Lack of Fit is not significant relative to the pure error. There is an 84.86% chance that a “Lack of Fit F-value” this large could occur, due to noise. Non-significant lack of fit is good as it indicates a model that is significant. To validate the adequacy of the quadratic model based on its ability to maximize the weld deposition rate (WDR) the goodness of fit statistics presented in

From the result of

To obtain the optimal solution, we first consider the coefficient statistics and the corresponding standard errors. The computed standard error measures the difference between the experimental terms and the corresponding predicted terms. Coefficient statistics for weld deposition rate is presented in

The optimal equation which shows the individual effects and combine interactions of the selected input variables (current, voltage, welding speed and gas flow rate) against weld deposition rate is presented based on the coded variables in

The optimal equation which shows the individual effects and combine interactions of the selected input variables (current, voltage, welding speed and gas flow rate) agains tweld deposition rate is presented based on actual factors in

The diagnostics case statistics which shows the observed values of (weld deposition rate (WDR) against their predicted values is presented in

Lower residual values resulting to higher leverages as observed in

To asses the accuracy of prediction and established the suitability of response surface methodology using the quadratic model, a reliability plot of the observed and predicted values of weld deposition rate is presented in

The high coefficient of determination (r^{2} = 0.9538) as observed in Figures 4.26 was used to established the suitability of response surface methodology in maximizing the weld deposition rate (WDR).

To accept any model, its satisfactoriness must first be checked by an appropriate statistical analysis output. To diagnose the statistical properties of the

response surface model, the normal probability plot of residual presented in

The normal probability plot of studentized residuals was employed to assess the normality of the calculated residuals. The normal probability plot of

residuals which is the number of standard deviation of actual values based on the predicted values was employed to ascertain if the residuals (observed-predicted) follows a normal distribution. It is the most significant assumption for checking the sufficiency of a statistical model. Result of

To determine the presence of a possible outlier in the experimental data, the cook’s distance plot was generated for the different responses. The cook’s distance is a measure of how much the regression would change if the outlier is omitted from the analysis. A point that has a very high distance value relative to the other points may be an outlier and should be investigated. The generated cook’s distance for deposition rate is presented in

The cook’s distance plot has an upper bound of 1.00 and a lower bound of 0.00. Experimental values smaller than the lower bound or greater than the upper bounds are considered as outliers and must be properly investigated. Results of

To study the effects of current and voltage on deposition rate, 3D surface plots presented in

Finally, numerical optimization was performed to ascertain the desirability of the overall model. In the numerical optimization phase, we ask design expert to maximize the weld deposition rate (WDR). In addition, the optimum current, voltage, welding speed and gas flow rate was determined simultaneously.

The interphase of the numerical optimization of deposition rate showing the objective function is presented in

The constraint set for the numerical optimization algorithm is presented in

The numerical optimization produces about twenty two (22) optimal solutions which are presented in

From the results of

The ramp solution which is the graphical presentation of the optimal solution is presented in

The desirability bar graph which shows the accuracy with which the model is able to predict the values of the selected input variables and the corresponding responses is shown in

It can be deduce from the result of

To identify the region with the optimum gas flow rate and welding speed, predicting the optimum deposition rate response using contour plot is produced in

As presented in Figures the contour plot can be employed to predict the optimum values of the input variables based on the flagged response variables.

In this study, the optimization of weld deposition rate (WDR) was done using response surface methodology (RSM).The target of the optimization model was to Maximize the weld deposition rate, statistical design of experiment (DOE), using the central composite design method (CCD) was done. The design and optimization was executed with the aid of Design Expert 7.01.

The model summary, which is presented as shown in

The summary statistics of model fit shows the standard deviation, the r-squared and adjusted r-squared, predicted r-squared and the PRESS statistic for each complete model. Low standard deviation, R-Squared near unity and relatively low PRESS are the optimum criteria for defining the best model

source. Variance inflation factor (VIF) of approximately 1.0 as observed in

To understand the influence of the individual design points on the model’s predicted value, the model leverages were computed as presented in

experiment, i.e., the residual will be 0. Leverages of 0.6698 and 0.6073 calculated for both the factorial and axial points coupled with 0.1663 for the center point as observed in

In assessing the strength of the quadratic model towards maximizing the weld deposition rate (WDR), one way analysis of variance (ANOVA) figure was generated for deposition rate and result obtained is presented in

The optimal equation which shows the individual effects and combine interactions of the selected input variables (current, voltage, welding speed and gas flow rate) against weld deposition rate is presented based on actual factors in

To determine the presence of a possible outlier in the experimental data, the cook’s distance plot was generated for the different responses. The Cook’s distance is a measure of how much the regression would change, if the outlier is omitted from the analysis. A point that has a very high distance value relative to the other points may be an outlier and should be investigated. The generated cook’s distance for deposition rate is presented in

The 3D surface plot as observed in

Finally, numerical optimization was performed to ascertain the desirability of the overall model.

From the result of

The desirability bar graph, which shows the accuracy with which the model is able to predict the values of the selected input variables and the corresponding responses, is shown in

In this study, the response surface methodology to optimize the deposition rate of TIG welded joints and result shows that they are suitable models. Weld deposition rate is a very important factor that influences the integrity and quality of welded joint. The study reveals that respond surface methodology (RSM) produced a good model for predicting weld deposition rate. it was observed that a current of 160.020 amp, voltage of 20.00 vol, a welding speed of 47.460 cm/min and gas flow rate of 17.000 L/min will result in a welding process with weld deposition rate (WDR) 0.436708 kg/hr. It has been shown that the optimization and prediction of weld deposition rate has improved the quality of welded joints. A weld simulation was carried out using the optimum value obtained from the response surface methodology to produce a welded sample with good quality. It is, therefore, recommended that welding and fabrication industries should endeavor to use the optimum welding process parameters obtained in this study to produce high quality welds in Tungsten inert gas welding process, as applicable.

The authors declare no conflicts of interest regarding the publication of this paper.

Imhansoloeva, N.A., Achebo, J.I., Obahiagbon, K., Osarenmwinda, J.O. and Etin-Osa, C.E. (2018) Optimization of the Deposition Rate of Tungsten Inert Gas Mild Steel Using Response Surface Methodology. Engineering, 10, 784-804. https://doi.org/10.4236/eng.2018.1011055