Experimental study of quality respones during Gas metal arc welding in industrial welding robots by using Response surface method

RSM is a comprehensive optimization method using modern mathematical statistical methods. This paper investigates the combined effects of current, wire feed rate and welding speed of an industrial robot on the geometry of weld bead, and the input parameters of GMAW welding process were optimized using Box–Behnken design in conjunction with RSM method.

To optimize with the RSM approach, you must first build a statistical experiment, then examine the coefficients in the mathematical model you've chosen, and then forecast the response and confirm the mathematical model's appropriateness inside the experimental setting [7].

For example, the speed of a race car is calculated by distance covered A and time taken to cover the distance B. Speed of various cars in the race will differ by combination of influence by A and B. Hence, distance covered, and time taken can vary continuously at any point of time. When there is an influence from a continuous range of values, then a Response Surface Methodology is useful to develop and optimize the response variable involved.

As stated in equation (1), the response variable in the situation mentioned above is the speed of the racing vehicle, or 'r,' and it depends on both the distance travelled and the amount of time required. You may say it like this:

$$\begin{eqnarray}&&{\rm{r}}={\rm{f}}\left({\rm{A}},{\rm{B}}\right)+\varepsilon \end{eqnarray} \tag{ 1 }$$

The regression model for expected response value can be recognized by using the least-squares method and since we have finite number of influential input parameters to fit the function an appropriate model for second order polynomial regression is required, where y is the expected output variable, pi and pj are the supplied input parameters, k is the total number of input factors, the intercept coefficient is βa, the linear term coefficient is βb, the squared term coefficient is βc, the interaction term coefficient is βd, and the possible errors of observation is ε. The relevance of the associated regression model was analysed and graded using the MINITAB version 19.1 software tool.

$$\begin{eqnarray}&&{\rm{y}}={\beta }_{a}+\displaystyle \sum _{i=1}^{k}{\beta }_{{\rm{b}}}{{\rm{p}}}_{{\rm{i}}}+\displaystyle \sum _{i=1}^{k}{\beta }_{{\rm{c}}}{{{\rm{p}}}_{{\rm{i}}}}^{2}+\displaystyle \sum _{i\lt j}^{k}{\beta }_{{\rm{d}}}{{\rm{p}}}_{{\rm{i}}}{{\rm{p}}}_{{\rm{ij}}}+\varepsilon \end{eqnarray} \tag{ 2 }$$

With help of literature review [8–10], the GMAW input variables that have the greatest impact upon bead geometry have now been found, and the influential input variables which are considered to this empirical approach i.e., current, filler wire feed rate and welded robot arm travel speed.

Electrode Filler rods which are recommended, during welding of grade 409 steels are Grade 430SS and 409, according to recommendation by AS 1554.6. grade 309SS electrodes or filler rods can be used. Ductility of the grade 409 material is excellent in sheet metal condition and widely used in manufacturing industries.

Working limitations for GMAW are determined by the material composition and thickness. To determine the possible operating limit band of the gas metal arc welding parameters contained in this research, a few experimental runs were performed on SS409 stainless ferritic steel plate with a thickness of 1.2mm. To conduct out early trial runs, several sets of MIG process settings are used. The operating range limitations of the work piece are set for input parameters using visual assessment of weld shape. Observations of matching responses made during the experimental trial runs are listed below:

When the current input is less than 140 Amp, there is insufficient metal fusion at the base material. Weld base metal melting (burn through) is noticed when the current input is more than 180 Amps. Insufficient bead penetration and a larger weld bead may be noticed in the work piece when the robot arm travels slower than 79 cm min⁻¹. When the travel speed is raised to 81 cm min⁻¹, the welded material deposition rate at the weld zone is reduced. Filler wire feeding rates more than 8.5 m min⁻¹ result in improperly shaped irregular weld bead geometry and welding spatters, whilst feed rates less than 7.4 m min⁻¹ result in insufficient penetration and incomplete weld bead fusion flaws.

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Other setup settings that do not directly affect weld bead shape are set to the following limitations. Visually, the flow velocity of the shielding gas combination was less than 10 lpm, and there were blow hole defect in the bead region and porosity. Gas entrapment happens, nevertheless, if the shielding gas input rate of flow is held over 18 lpm. At voltages lower than 17 V, welding pin holes and overlap of weld edge joint were found. When the voltage is higher than 20 V, the bead porosity increases, resulting in spatter all over the weld surface and undercut. With the foregoing experiments, the working range boundary of the work piece has been established, and the research has progressed accordingly.

The following range has been evaluated for the working parameters: the welding was accomplished without any fundamental visual faults for input current (140–180V), Robot arm travel speed (79–81 cm min⁻¹), and welding feed rate (7.4 m min⁻¹ to 8.5 m min⁻¹). Due to large variety of process parameters, the experimental condition was designed using 3 parameters with 3 levels and a Box Behnken design matrix with 12 experimental runs. Table 3 lists the process parameters that were examined, as well as their levels and codes. The DOE table trail runs of welding are shown in table 5.

The experiment has been conducted using Yaskawa Motoman (figure 1) is an industrial welding, the arc welder is commonly employed. This robot is employed in the welding process in this project. The robot's specifications are shown in table 4.

After generating the input values for robotic welding, the input values are fed into a welding machine and many trials are carried out. The results are then tabulated and entered Minitab software. Then, using Minitab software, the collection of values is optimized.

Next procedure is to simulate the experimental robot welding process using Industrial Robot Setup available and teach it to the robot using teach pendent. Specimen of SS 409 material of dimensions 100 × 100 × 1.2 mm is setup in Lap joint formation (figure 2) for the experiment.

Shielding gas mixture which is selected for the welding experiment is of Inert & reactive gas. Argon as inert gas + Carbon di oxide as reactive gas (CO²⁺ Argon) at 80:20 mixture ratio. Electrode filler wire material which is fed into weld pool is Stainless steel 409Ti is of 1.2 mm thick in diameter.

$$\begin{eqnarray*}&&\begin{array}{l}{\rm{BH}}=-411+0.151\,{\rm{CR}}+14.52\,{\rm{WF}}+8.5\,{\rm{RS}}-0.000424\,{\rm{CR}}* {\rm{CR}}\\ \,-\,0.453\,{\rm{WF}}* {\rm{WF}}-0.0496\,{\rm{RS}}* {\rm{RS}}-0.00227\,{\rm{CR}}* {\rm{WF}}\\ \,+\,0.00013\,{\rm{CR}}* {\rm{RS}}-0.082\,{\rm{WF}}* {\rm{RS}}\end{array}\end{eqnarray*}$$

Regression analysis of bead height can be derived by substituting the coefficients in above equation. Table 6 shows the results of for the response surface CCD (cubic model) for BH, do an analysis of variance (ANOVA) (bead height) using second order regression analysis. The model's F-value of 5.2 indicated that it is significant. A large F-Value only has a 0.01 percent probability of happening due to noise. If the 'Prob > F' value is less than 0.05, the Model Statics terms are important. Important model names in this context are A, B, C, AA, BB, CC, AB, AC, and BC [8]. If the value is more than 0.1, the statistical model terms are not significant. If the model has a large number of irrelevant terms, model reduction may improve the model. A lack of fit has no impact on the pure error, according to the 'Lack of Fit F-value' of 0.59. A significant F-value of lack of fit is likely to happen as a result of noise in 67.7% of cases. It's OK if there's a little mismatch. The Summary of Bead height statistical model results are shown in table 7.

The anticipated R square value 'Pred. R-squared' of 0.9034 is in close agreement with the neighboring R squared value 'Adj. R-squared' of 0.7295, as shown in table 7. The signal to noise ratio (S/N ratio) is calculated using 'Adeq precision.'

A ratio of more than 4 is preferable [12], but the value of 'Adeq precision' in this case is 15.77, indicating a good signal. As a result, this model may be utilised for further experimental research and is sufficient. Figure 3 depicts the relationship between predicted and actual bead height.

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$$\begin{eqnarray*}&&\begin{array}{l}{\rm{BW}}=-375-0.232\,{\rm{CR}}-17.8\,{\rm{WF}}+11.7\,{\rm{RS}}+0.000244\,{\rm{CR}}* {\rm{CR}}\\ \,-\,0.653\,{\rm{WF}}* {\rm{WF}}-0.093\,{\rm{RS}}* {\rm{RS}}+0.0023\,{\rm{CR}}* {\rm{WF}}\\ \,+\,0.00225\,{\rm{CR}}* {\rm{RS}}+0.345\,{\rm{WF}}* {\rm{RS}}\end{array}\end{eqnarray*}$$

Regression analysis of bead width can be derived by substituting the coefficients in above equation. The results of the analysis of variance (ANOVA) for bead width that use the response surface CCD (cubic model) and second order regression analysis are shown in table 8. The Model F-value of 13.97 in table 8 suggests that the model is significant. Due to noise considerations, this enormous Model F-Value has a 0.01 percent likelihood of happening. If 'Prob > F' is less than 0.0500, model terms are crucial. A, B, C, AA, BB, CC, AB, AC, BC are important model terms in this situation [8]. If the value is more than 0.1000, the statistical model elements are not significant. If your model has a lot of meaningless words, model reduction may improve it (not including those necessary to maintain hierarchy). According to the ANOVA table, a 'Lack of Fit F-value' of 3.21 indicates a 24.7 percent possibility of a significant 'Lack of Fit F-value' owing to noise components. If there is a serious fit issue, it is terrible. The model summary data for bead width are shown in table 9. The neighboring R squared value 'Adj R-Squared' of 0.7295 is in close agreement with the predicted R square value 'Pred R-Squared' of 0.9034. If there is a big fit issue, it is dreadful. The summary statistics for the model's bead width are shown in table 9. When a ratio of more than four is desired [12]. According to our ANOVA figure, a signal ratio of 15.77 suggests a sufficient signal. As a result, this model may be utilized for future research and experimentation. Figure 4 depicts the relationship between expected and actual bead width.

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$$\begin{eqnarray*}&&\begin{array}{l}{\rm{DP}}=-192+0.237\,{\rm{CR}}+2.67\,{\rm{WF}}+4.06\,{\rm{RS}}\\ \,-\,0.000953\,{\rm{CR}}* {\rm{CR}}-0.120\,{\rm{WF}}* {\rm{WF}}-0.0263\,{\rm{RS}}* {\rm{RS}}\\ \,-\,0.00205\,{\rm{CR}}* {\rm{WF}}+0.00112\,{\rm{CR}}* {\rm{RS}}-0.0045\,{\rm{WF}}* {\rm{RS}}\end{array}\end{eqnarray*}$$

Regression analysis of depth of penetration can be derived by substituting the coefficients in above equation.

The results of the ANOVA for the response surface CCD (cubic model) with second order regression analysis are shown in table 10 for the depth of penetration. The statistical model's F-value in table 10 of 6.89 indicates that it is significant. There is indeed a 0.01 percent chance that this enormous F-Value will occur due to noise factors. If 'Prob > F' is less than 0.05, model terms are noteworthy and important. Important model names in this context are A, B, C, AA, BB, CC, AB, AC, and BC [8]. The regression coefficients are not meaningful if the value in the table is greater than 0.1000. Model reduction may improve the model if an ANOVA table has a number of meaningful model terms. Lack of Fit is not substantial in compared to the pure error factor with a 'Lack of Fit F-value' of 0.9. Due to noise considerations, there is a 56.4 percent probability that a significant 'Lack of Fit F-value' will occur. A little lack of fit is acceptable and should be evaluated.

The summary of statistical regression equation for depth of penetration is shown in table 11. According to table 11, the Predicted R squares 'Pred R-squared' value of 0.9254 and the Adjacent R squared 'Adj R-squared' value of 0.7911 are quite similar. The 'Adeq precision' value is used to calculate the signal-to-noise ratio (S/N ratio). It is desired and recommended to have a ratio larger than 4 [12]. The stated signal ratio of 24.21 suggests that the signal is sufficient. As a result, the generated model is stated to be suitable for navigating the experimental investigation. The ANOVA findings for the weld bead geometry DP, BH, and BW are shown in tables 6, 8, and 10, respectively. As a result, the produced model for each answer is judged to be appropriate in terms of the 95 percent design space in the table. Figure 5 shows a graph of projected penetration depth versus actual penetration depth.

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The effectiveness of the created models was evaluated using the ANOVA (analysis of variance) method (ANOVA). According to the ANOVA technique, the model is judged adequate if the estimated F-ratio of the developed model is less than the F-ratio from the F-table for a certain confidence level (let's say 95 percent). The created model for each answer is deemed to be sufficient at the 95 percent confidence level in the table.