Process Parameter Optimization of A-TIG Welding on P22 Steel

Abstract

In the present study, the Activated Tungsten Inert Gas (A-TIG) welding process parameters for welding of 2.25Cr-1Mo (P22) steel have been optimized to attain desired weld bead geometry. Before fabricating weld joints, it is essential to understand the effect of A-TIG welding process parameters in producing quality weld joints. It is proposed to employ the Response Surface Methodology (RSM) of the design of experiments (DOE) approach to determine the optimum parameters in P22 steel weld joint. First, using RSM, a design matrix will be generated by considering various input variables such as welding current, arc gap, torch velocity and electrode tip angle and the output responses such as depth of penetration (DOP), bead area and heat-affected zone (HAZ) width. Further, regression models were generated to correlate the input variables and output responses. The optimum process parameters to obtain the desired DOP, bead area and HAZ width have been determined mainly by utilizing the regression equations and the desirability approach. The Root Mean Square Error (RMSE) of the predicted and measured DOP, HAZ width, and bead area was minimum 0.2571 mm, 0.1776 mm and 6.628 mm², respectively. TIG current from 235 to 270 A, arc gap from 2.2 to 2.9 mm and welding speed from 60 to 75 mm/min is obtained from RSM analysis as an optimum process parameter. The study manifest that there is an excellent agreement between the predicted and measured values.

Annexure

Table 9 presents the data resulting from an investigation into the effect of three variables current (A), arc gap (B) and torch speed (C) with the respective response depth of penetration (DOP) (y). To improve the optimization process design of experiment was chosen. At first, numbers of experiments were defined based on the most important variables. The quadratic model was used to fit the result to current, arc gap and temperature.

Table 9 Experimental design matrix for response DOP with natural and coded variables

Quadratic equation for this model is shown in Eq. 5

$${\text{Y}} = {\text{b}}_{0} + {\text{b}}_{1} {\text{x}}_{1} + {\text{b}}_{2} {\text{x}}_{2} + {\text{b}}_{3} {\text{x}}_{3} + {\text{b}}_{4} {\text{x}}_{1}^{2} + {\text{b}}_{5} {\text{x}}_{2}^{2} + {\text{b}}_{6} {\text{x}}_{3}^{2} + {\text{b}}_{7} {\text{x}}_{1} {\text{x}}_{2} + {\text{b}}_{8} {\text{x}}_{1} {\text{x}}_{3} + {\text{b}}_{9} {\text{x}}_{2} {\text{x}}_{3}$$

(5)

This optimization process is performed using central composite design (CCD), and it is most widely used for fitting a second-order response surface. The CCD consists of 8 runs at the corners of a square, 6 axial runs and 6 runs at the center of the square and overall 20 runs. In terms of the coded variables the corners of the square are (x₁, x_2, x₃) = (−1, −1, −1), (−1, 1, −1), (1, 1, −1), (−1, −1, 1), (1, −1, 1), (−1, 1, 1), (1, −1, −1) and (1, 1, 1); the axial runs are at (x₁, x₂, x₃) = (0, 0, −1.681), (1.681, 0, 0), (0, 0, 1.681), (−1.681, 0, 0), (0, −1.681, 0) and (0, 1.681, 0) the center points are at (x₁, x₂, x₃) = (0, 0, 0). The second-order model can be fitted using the coded variables.

The coefficients of b₀ to b₉ can be estimated by using the methods of least squares, b = (X¹X)⁻¹X¹y

For a second-order model with 20 sets of the experiment, the matrix of independent variables X and y vector for this data is

$${\text{X}} = \left( {\begin{array}{*{20}l} {} \hfill & {{\text{x}}_{1} } \hfill & {{\text{x}}_{2} } \hfill & {{\text{x}}_{3} } \hfill & {{\text{x}}_{1}^{2} } \hfill & {{\text{x}}_{2}^{2} } \hfill & {{\text{x}}_{3}^{2} } \hfill & {{\text{x}}_{1} {\text{x}}_{2} } \hfill & {{\text{x}}_{1} {\text{x}}_{3} } \hfill & {{\text{x}}_{2} {\text{x}}_{3} } \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill & { - 1.681} \hfill & 0 \hfill & 0 \hfill & {2.828} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & { - 1.681} \hfill & 0 \hfill & 0 \hfill & {2.828} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & { - 1} \hfill & 1 \hfill & { - 1} \hfill & 1 \hfill & 1 \hfill & 1 \hfill & { - 1} \hfill & 1 \hfill & { - 1} \hfill \\ 1 \hfill & 1 \hfill & 1 \hfill & { - 1} \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & { - 1} \hfill & { - 1} \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill & {1.681} \hfill & 0 \hfill & 0 \hfill & {2.828} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & { - 1} \hfill & { - 1} \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & { - 1} \hfill & { - 1} \hfill \\ 1 \hfill & 1 \hfill & { - 1} \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & { - 1} \hfill & 1 \hfill & { - 1} \hfill \\ 1 \hfill & { - 1} \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & { - 1} \hfill & { - 1} \hfill & 1 \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & { - 1.681} \hfill & 0 \hfill & 0 \hfill & {2.828} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & { - 1} \hfill & { - 1} \hfill & { - 1} \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill \\ 1 \hfill & 0 \hfill & { - 1.681} \hfill & 0 \hfill & 0 \hfill & {2.828} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & 0 \hfill & { - 1.681} \hfill & 0 \hfill & 0 \hfill & {2.828} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & 1 \hfill & { - 1} \hfill & { - 1} \hfill & 1 \hfill & 1 \hfill & 1 \hfill & { - 1} \hfill & { - 1} \hfill & 1 \hfill \\ 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill & 1 \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ \end{array} } \right)\quad {\text{Y}} = \left( {\begin{array}{*{20}l} {4.72} \hfill \\ {5.333} \hfill \\ {2.936} \hfill \\ {6.303} \hfill \\ {4.47} \hfill \\ {4.904} \hfill \\ {3.943} \hfill \\ {4.892} \hfill \\ {4.943} \hfill \\ {3.587} \hfill \\ {2.798} \hfill \\ {5.063} \hfill \\ {2.016} \hfill \\ {4.987} \hfill \\ {3.517} \hfill \\ {4.873} \hfill \\ {4.457} \hfill \\ {5.322} \hfill \\ {4.222} \hfill \\ {5.172} \hfill \\ \end{array} } \right)$$

And From, $b\, = \,\left( {X^{1} X} \right)^{ - 1} X^{1} y$

$${\text{X}}^{1} .{\text{X}} = \left( {\begin{array}{*{20}l} {20} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {13.657} \hfill & {13.657} \hfill & {13.657} \hfill & 0 \hfill \\ 0 \hfill & {13.657} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & {13.657} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & {13.657} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {13.657} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & {24} \hfill & 8 \hfill & 8 \hfill & 0 \hfill \\ {13.657} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 8 \hfill & {24} \hfill & 8 \hfill & 0 \hfill \\ {13.657} \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 8 \hfill & 8 \hfill & {24} \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 8 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ \end{array} } \right)\quad {\text{X}}^{1} .{\text{y}} = \left( {\begin{array}{*{20}l} {88.46} \hfill \\ {10.81} \hfill \\ { - 1.80} \hfill \\ { - 3.85} \hfill \\ {54.41} \hfill \\ {60.01} \hfill \\ {58.15} \hfill \\ {4.34} \hfill \\ { - 5.10} \hfill \\ { - 1.91} \hfill \\ \end{array} } \right)\quad {\text{b}} = \left( {\begin{array}{*{20}l} {4.91} \hfill \\ {0.79} \hfill \\ { - 0.13} \hfill \\ { - 0.28} \hfill \\ { - 0.43} \hfill \\ { - 0.08} \hfill \\ { - 0.20} \hfill \\ { - 0.54} \hfill \\ { - 0.63} \hfill \\ { - 0.23} \hfill \\ \end{array} } \right)$$

Therefore, the Eq. 5 can be written as shown below,

y = 4.91 + 0.79x₁−0.13x₂−0.28x₃ + 0.54x₁x₂−0.63x₁x₃−0.23x₂x₃−0.43x ² ₁ −0.08x ² ₂ −0.20x ² ₃

In terms of natural variables, the model is

y = 4.91 + 0.79A−0.13B−0.28C + 0.54AB−0.64AC−0.24BC−0.43A²−0.08B²−0.20C²

Steps involved in the analysis of variance (ANOVA)

The sequence of steps involved in doing analysis of variance (ANOVA) is explained below. The ANOVA for different responses are shown in Table 4, 5 and 6 which contains the output of Design Expert. Generally, computer software will be used to fit a response surface model and to construct the contour plots. ANOVA for the selected quadratic model is an overall summary for the full model with all interactions and main effects.

• Step 1: computing the sum of squares

The model sum of squares is

$${\text{SS}}_{\text{model}} = {\text{SS}}_{\text{A}} + {\text{SS}}_{\text{B}} + {\text{SS}}_{\text{C}} + {\text{SS}}_{\text{AB}} + {\text{SS}}_{\text{AC}} + {\text{SS}}_{\text{BC}} + {\text{SS}}_{\text{A}}^{2} + {\text{SS}}_{\text{B}}^{2} + {\text{SS}}_{\text{C}}^{2}$$

$$SS_{total} \, = \,\sum {\left( {X - X^{1} } \right)^{2} }$$

$${\text{SS}}_{\text{residual}} = {\text{SS}}_{\text{total}} - {\text{SS}}_{\text{model}}$$

X—Response, X¹—average of X.

• Step 2: computing the degrees of freedom (DF)

$${\text{DF}} = {\text{N}}{-}1$$

N is a number of observations.

• Step 3: computing the mean squares (MS)

$${\text{MS}} = {\text{SS}}/{\text{DF}}$$

F = MS_model/MS_residual

The F ratio is the ratio of two mean square values. If the null hypothesis is true, then F will have a value close to 1.0. The P value is computed from the F ratio which is computed from the ANOVA table. For each ANOVA table, various R² value is presented

$${\text{R}}^{2} = {\text{SS}}_{\text{model}} /{\text{SS}}_{\text{total}} ,{\text{R}}^{2}_{\text{adj}} = \left( {{\text{SS}}_{\text{residal}} /{\text{DF}}_{\text{residual}} } \right)/\left( {{\text{SS}}_{\text{total}} /{\text{DF}}_{\text{total}} } \right)\,{\text{and}}\,{\text{R}}^{2}_{\text{pred}} 1{-}{\text{PRESS}}/{\text{SS}}_{\text{total}}$$

PRESS = prediction error sum of squares

• Step 4: a significance test

After, all the above steps are completed, the results provided in table format.