Optimization of laser spiral welding using Response surface methodology and genetic algorithms

Abstract

In the laser spiral welding (LSW) process, the welding parameters have a significant impact on the weld quality. In this paper, experiments were conducted and experimental data were collected on galvanized steel sheets using the LSW process, and mathematical models were developed using response surface methodology (RSM) and genetic algorithm (GA) to verify the specific effects of each process parameter on the weld and to perform process optimization. Laser power, welding speed, gap and focal length were selected as the influencing factors, and melt depth, melt width and concave as the output results. In the RSM model we found that the laser power was positively correlated with the weld depth and width, while the welding speed was inversely correlated with the weld depth and width, the gap was positively correlated with the amount of concave, and the focal length had no significant effect on the weld. In the GA model we use a large amount of experimental data for BP neural network training and iterative optimization using a genetic algorithm. Validation experiments were conducted on two models, and the results indicated that the two models had higher accuracy in predicting the welding depth and width compared to predicting the concave. The GA model had an 8% increase in tensile strength and a 25% increase in plasticity of the weld joint obtained from the optimal process compared to the RSM model. The GA model has higher accuracy in optimizing the LSW process.

Keywords

Laser spiral welding response surface methodology genetic algorithm process optimization mechanical property

1 Introduction

When investigating a new welding process, it is often necessary to establish mathematical relationships between the weld geometry and process parameters to predict and control the weld quality, thus reducing the number of experiments and increasing production efficiency. With the development of statistical and mathematical analysis tools, there are various methods, such as, Response surface methods, Taguchi methods, neural networks, and genetic algorithms, that can be used to build relationships between the weld geometry and process parameters, and to predict and optimize solutions [1]. Laser spiral welding is a high-speed laser welding method that has become the preferred alternative to traditional resistance spot welding of body-in-white joints due to its high welding efficiency, ease of automation, and consistent weld quality [2].

Laser spiral welding is a welding technique in which a high-power laser is deflected by a high-speed oscillator to follow a predetermined waveform. This process produces circular weldments, and the geometry and quality of the weld joint are usually influenced by both the welding process and the welding materials [3]. When the laser spiral welding is applied to the welding galvanized steel, the laser power, welding speed, welding path, the gap between the dressings, and a number of these factors outside the focal point shall affect the formation of the weld joint, and the varying degrees of influence by these factors make it hard to identify the relationship between process conditions and weld quality. Therefore, the use of mathematical analysis tools to assist to the analysis of process data has become a profound work [4].

Two mathematical analysis methods, Response surface method (RSM) and BP neural network (GA) optimized by the genetic algorithm were selected to investigate the effectiveness of different optimization methods in this experiment. Response surface method based on experimental design is one of the techniques for optimizing the design of experimental parameters. This method constructs a series of deterministic experiments by setting a range of multiple input variables and approximating the implicit limit state function by a polynomial function [5]. Experimental points and iteration strategies are chosen to ensure that the polynomial function converges to the true implicit limit state function in terms of the failure probability, and a model is built and the results predicted based on the responses obtained. Box and Wilson proposed the Response surface method in the 1950 s [6, 7], and this method has been widely used in the process optimization across various fields, such as food, engineering, and environmental science. For example, some scholars have used the model of RSM in the study of the effect of wood processing process on wood quality, demonstrating the application of the model in process optimization [8 –10]. Many researchers also use this method to predict the welding performance and identify the best welding process. Neural networks are a way to create a mapping between the input and output, train and learn from several samples, and ultimately create a model that meets the expectations for later prediction [11]. Genetic algorithms can be used to optimize the weights and thresholds of a neural network by constructing fitness functions to calculate individual fitness values and finding the individual with the optimal fitness value after selection, crossover, and variation operations. After the genetic algorithm optimization, the neural network prediction is more accurate and can be a nonlinear function of extreme value optimization, which shall be very helpful for the prediction and optimization of the welding process.

In this paper, the effect of LSW process parameters on the weld profile of DC06 galvanized steel lap joints are investigated by the response surface methodology and genetic algorithms. The experimental results predicted by the Response surface method and the following optimization by the genetic algorithm are further analyzed and verified hereafter. The results of the study can serve as a reference and basis for the selection of the optimal LSW welding process and the prediction of weld quality.

2 Experimental procedure

2.1 Experimental materials

The basic material used for the experiments was super-deep cold-drawn galvanized steel DC06 with a nominal sheet thickness of 0.7 mm and a galvanized layer thickness of 50μm. The chemical composition of DC06 galvanized steel is given in Table 1 and the mechanical properties are provided in Table 2. Where R_P0.2 represents the yield strength of the material, R_m represents the tensile strength of the material, A₈0 represents the plastic strain ratio of the material, r represents the plastic strain ratio, and n represents the strain hardening index of the material.

Table 1
Chemical composition of galvanized steel sheet DC06 (weight fraction, %)

C Si Mn P S Ti Al

≤0.005 ≤0.030 ≤0.200 ≤0.020 ≤0.015 0.030–0.080 0.010–0.060

C	Si	Mn	P	S	Ti	Al
≤0.005	≤0.030	≤0.200	≤0.020	≤0.015	0.030–0.080	0.010–0.060

Table 2

Mechanical properties of DC06 galvanized steel

R_P0.2 (Mpa)	R_m (Mpa)	A₈₀ (%)	r	n
120–170	270–350	≥41	≥2.1	≥0.220

2.2 Laser welding process

Figure 1 shows the laser welding system used in this study. The laser used in the experiments was a Trumpf TruDisk 16002 laser with a wavelength of 1030 nm, the maximum power of 8 kW, and a spot diameter of 540–840μm. The covered PFO lens was a Blackbird intelliWELD II FT with an oscillation frequency of 0–6000 Hz and a scanning range of 220×220×(±70) mm.

Fig. 1

Experimental setup used.

Before the laser experiment, the raw material was cut into 100×20 mm plates. A standard spacer was used to create a gap between the pieces, and a fixture was used to fix the two ends of the experimental platform, as shown in Fig. 1. The experimental laser scanning path is a closed loop consisting of five vortex lines R₁–R₅ in ascending order. The shielding gas was 82% Ar + 18% CO₂ with a gas flow rate of 15 L/min for side shock protection, the experimental factors are designed as shown in Table 3.

Table 3

Factors and levels of experimental design

Symbols	Factors	Level
		–1	0	1
X₁	Laser power (kW)	3	4	5
X₂	Welding speed (mm/s)	90	100	110
X₃	Gap (mm)	0	0.1	0.2
X₄	Expanded volume (mm)	0	+2	+4

2.3 Definition and weld size criterion

The characteristic dimensions of the weld, including weld depth, weld width, and surface concavity, are obtained by the inspection of metallographic photographs taken with a VHX-5000 3D microscope. The weld dimensions are defined and assessed as shown in Fig. 2. In this study, the weld depth was measured as the depth of the weld penetration on the base plate, while the weld width was defined as the weld width in the plane of the joint. In addition, the maximum concavity of the weld surface is used as the measured concavity value, as seen in Fig. 2.

Fig. 2

Definition and criteria for welding channel dimensions (BM: Base material, FZ:Fusion zone).

3 Results and discussion

3.1 Optimization methods

3.1.1 Response surface model

A four-factor, the three-level homogeneous design was used for the experiments. The coding factors here were the four aforementioned process parameters: laser power, welding speed, dressing gap, and out-of-focus volume. The limits of the selected factors were derived from preliminary experiments, and their units, symbols, and experimental design levels are listed in Table 4. The unified design matrix is shown in Table 5 with 30 different experiments, and the last experiment is the focal point. The upper and lower bounds of the parameters are coded as +1 and –1, respectively.

Table 4
Unified design matrix and test results for 30 experiments

NO. Factors Mel depth (mm) Melt width (mm) Concave (mm) Aspect ratio

X1 X2 X3 X4

1 0 1 0 –1 1.263 6.241 0.143 0.202

2 0 0 0 0 1.135 6.625 0.169 0.171

3 0 0 –1 1 1.260 5.867 0.134 0.215

4 –1 0 1 0 0.852 6.014 0.274 0.142

5 –1 –1 0 0 1.109 6.438 0.146 0.172

6 0 0 1 1 1.116 6.162 0.286 0.181

7 0 –1 0 –1 1.384 6.523 0.179 0.212

8 –1 0 0 1 0.965 6.054 0.102 0.159

9 0 –1 1 0 1.224 6.821 0.284 0.179

10 1 –1 0 0 1.392 6.623 0.324 0.210

11 –1 1 0 0 0.536 6.234 0.096 0.086

12 0 0 0 0 1.129 6.713 0.163 0.168

13 0 0 –1 –1 1.090 5.430 0.164 0.201

14 0 –1 –1 0 1.313 6.150 0.254 0.213

15 0 0 0 0 1.132 6.629 0.173 0.171

16 0 0 0 0 1.138 6.625 0.165 0.172

17 1 0 0 –1 1.312 6.865 0.103 0.191

18 –1 0 –1 0 0.960 6.532 0.106 0.147

19 1 1 0 0 1.216 6.526 0.093 0.186

20 1 0 –1 0 1.265 6.525 0.106 0.194

21 0 0 0 0 1.138 6.651 0.145 0.171

22 0 1 1 0 1.056 5.862 0.286 0.180

23 1 0 0 1 1.234 6.943 0.094 0.178

24 0 0 1 –1 1.121 6.057 0.295 0.185

25 0 1 0 1 1.135 6.125 0.152 0.185

26 –1 0 0 –1 1.125 5.862 0.128 0.192

27 0 –1 0 1 1.296 6.631 0.162 0.195

28 1 0 1 0 1.325 6.814 0.293 0.194

29 0 1 –1 0 1.128 6.240 0.162 0.181

30 0 0 0 0 1.132 6.724 0.158 0.168

Average 1.149 6.384 0.178 0.180

NO.	Factors	Mel depth (mm)	Melt width (mm)	Concave (mm)	Aspect ratio
1	0	1	0	–1	1.263	6.241	0.143	0.202
2	0	0	0	0	1.135	6.625	0.169	0.171
3	0	0	–1	1	1.260	5.867	0.134	0.215
4	–1	0	1	0	0.852	6.014	0.274	0.142
5	–1	–1	0	0	1.109	6.438	0.146	0.172
6	0	0	1	1	1.116	6.162	0.286	0.181
7	0	–1	0	–1	1.384	6.523	0.179	0.212
8	–1	0	0	1	0.965	6.054	0.102	0.159
9	0	–1	1	0	1.224	6.821	0.284	0.179
10	1	–1	0	0	1.392	6.623	0.324	0.210
11	–1	1	0	0	0.536	6.234	0.096	0.086
12	0	0	0	0	1.129	6.713	0.163	0.168
13	0	0	–1	–1	1.090	5.430	0.164	0.201
14	0	–1	–1	0	1.313	6.150	0.254	0.213
15	0	0	0	0	1.132	6.629	0.173	0.171
16	0	0	0	0	1.138	6.625	0.165	0.172
17	1	0	0	–1	1.312	6.865	0.103	0.191
18	–1	0	–1	0	0.960	6.532	0.106	0.147
19	1	1	0	0	1.216	6.526	0.093	0.186
20	1	0	–1	0	1.265	6.525	0.106	0.194
21	0	0	0	0	1.138	6.651	0.145	0.171
22	0	1	1	0	1.056	5.862	0.286	0.180
23	1	0	0	1	1.234	6.943	0.094	0.178
24	0	0	1	–1	1.121	6.057	0.295	0.185
25	0	1	0	1	1.135	6.125	0.152	0.185
26	–1	0	0	–1	1.125	5.862	0.128	0.192
27	0	–1	0	1	1.296	6.631	0.162	0.195
28	1	0	1	0	1.325	6.814	0.293	0.194
29	0	1	–1	0	1.128	6.240	0.162	0.181
30	0	0	0	0	1.132	6.724	0.158	0.168
Average					1.149	6.384	0.178	0.180

Table 5

BPNN and GA parameters

Model	Parameter	Value
BPNN	Number of inputs	4
	Number of hidden layers	9
	Number of outputs	3
	Maximum number of epochs	1000
	Speed of learning	0.05
	Accuracy	0.001
GA	Population size	40
	Generation number	100
	Probability of crossing	0.7
	Probability of mutation	0.01

In this paper, the melt depth, melt width, and undercut are defined as optimization objectives to maximize the weld depth-to-width ratio while achieving an acceptable amount of undercut. Therefore, the depth-to-width ratio and the amount of undercutting are chosen as the response. The depth ratio is used as the optimization objective, and the undercut quantity as the constraint.

The observations recorded during the experiments according to the design matrix. The experimental results show the effect of process parameters on the response. The laser power (x₁), welding speed (x₂), arc gap (x₃) and blur size (x₄) as a function of the response factor can be expressed as $y = f (x_{1}, x_{2}, x_{3}, x_{4})$ (1)

In RSM, second-order polynomials are usually used to approximate the actual relationship between the input variables and the response surface [12]. The second-order regression model has the following form: $\begin{matrix} y = a_{0} + \sum_{i = 1}^{4} a_{i} x_{i} + \sum_{i = 1}^{4} a_{ii} x_{i}^{2} + \\ \sum_{i < j} \sum_{i = 1}^{4} a_{ij} x_{i} x_{j} \end{matrix}$ (2)

Where a₀ is the response f(0,0,0), i.e., the centroid response, and a_ii and a_ij are the regression coefficients that depend on the linear term, quadratic term, and interaction term of each factor [13], respectively. The measured responses are shown in Table 4 based on the response results measured in the design matrix through metallographic tests. The Response surface method was then applied to the experimental data to obtain the regression equations for all the responses.

The agreement of the RSM model predictions with the actual values is shown in Fig. 3, where the model fit is checked using the coefficient of determination (R). The value of R² is always in the range of 0-1, indicating the goodness of fit of the RSM model. For a theoretically perfect statistical model, the value of R² is equal to 1. The more R² approaches 1, the more accurate the model is [14]. The coefficient of determination for the weld depth response (R²) is 0.9685, indicating that the model is able to predict 96.85% of the experimental data, leaving only 3.15% of the data unexplained, and the coefficients of determination for the weld width and weld concavity response (R²) are 0.9602 and 0.9518, respectively. The adequacy of the model was further analyzed using the R² value. The R² value represents the effectiveness of the regression, and larger R² values are always preferable. In this study, all R² determination coefficients were close to the value of 1, indicating that these second-order models were capable of estimating the quantitative relationship between laser parameters and response parameters. The final extracted mathematical model equations for the coding factors with the values of weld width, weld height, and concavity are given by Equations (3 –5).

Fig. 3

Comparison of predicted and actual values.

$\begin{matrix} Weld depth = 1.12 + 0.18 x_{1} - 0.12 x_{2} - 0.05 x_{3} \\ - 0.02 x_{4} + 0.32 x_{2}^{2} - 0.11 x_{1} x_{3} + 0.14 x_{1} x_{4} \end{matrix}$ (3) $\begin{matrix} Welding width = 6, 14 + 0, 47 x_{1} - 0, 43 x_{2} \\ - 1, 18 x_{3} - 0, 02 X_{4} - 0, 52 x_{2} x_{3} - 1, 34 x_{3} \\ - 0, 300 x_{4}^{2} \end{matrix}$ (4) $\begin{matrix} Concave = 0.30 + 0.40 x_{3} - 0.045 x_{1} x_{2} \\ + 0.03 x_{1}^{2} - 0.27 x_{3}^{2} \end{matrix}$ (5)

The result shows that welding speed plays the most important role in all responses, followed by laser power, gap size, and focal position. Welding speed has a strong negative effect on all responses, while laser power has a positive effect. For the gap sizes of the interest here (0, 0.10, and 0.20 mm), increasing the gap size resulted in smaller weld depth, larger weld width, and greater surface concavity, which is consistent with the results of previous experiments. The position of the focal point has little effect on all responses. Response surface plots are then used to find the optimum laser power and welding speed for the 0.7 mm thick galvanized DC06 sheet.

The response surface and contour plots are created based on the mathematical model described above. Since the effects of the gap and scattering are relatively small, they are set at the mean level, and the other two factors, laser power and welding speed, can be found on the x and y axes in Fig. 3. These response profiles are helpful for predicting the optimum parameters for 0.7 mm thick galvanized steel DC06.

Figure 4(a) shows the effect of laser power and welding speed on the aspect ratio. It can be observed that the aspect ratio reaches high values in both parts of the graph within a reasonable range, where the laser power tends to be at a high level and the speed at a low to medium level. However, it is too hasty to jump to conclusions without checking the dimensions of the other three welding channels. The weld depths and widths obtained correspond to the requirements given in this part of the diagram, as seen in Fig. 4 (b) and 4(c). When the welding speeds are lower than 95 mm/s, the weld depth exceeds the 0.15 mm limit, see Fig. 4(d). Therefore, the optimal parameters would be a small flange gap, medium to high laser power, and medium welding speed.

Fig. 4

Area and contour plots showing the effect of laser power and welding speed on (a) aspect ratio, (b) weld width, (c) weld depth, and (d) undercut.

3.1.2 BP neural networks and GA models

In RSM, the specified laser power, welding speed, arc gap and out-of-focus quantity are used as input variables, the melt width, melt depth and undercut as output variables, and depth-to-width ratio as the optimization object to construct the BP neural network GA optimization algorithm model with the procedure presented in Fig. 5. And the main steps are: BP neural network structure determination, genetic algorithm optimization of weights and thresholds, BP neural network training and prediction [15]. The topology of the BP neural network is determined based on the number of input/output parameters of the sample, so that the number of optimization parameters of the genetic algorithm can be obtained, and thus the encoding length of the individuals of the population can be determined [16]. Since the optimization parameters of the genetic algorithm are the initial weights and thresholds of the BP neural network, the number of weights and thresholds shall be known if the structure of the network is known [17]. The weights and thresholds of the neural network are usually initialized by randomly setting them to random numbers in the interval [–0.5, 0.5]. The results of training the network are the same and a genetic algorithm is introduced to optimize the best initial weights and thresholds [18].

Fig. 5

Flow of the BP algorithm optimized by GA.

3.1.2.1. Creating a grid. For general pattern recognition problems, a three-layer network can be a good solution. And the structure of the BPNN is shown in Fig. 6, in which the output Hj of the j-th neuron in the hidden layer is calculated according to Equation (6) [19]: $H_{j} = f (\sum_{i = 1}^{n} w_{ij} x_{i} - a_{j}) j = 1, 2, \dots, 1$ (6)

Fig. 6

Structure of the BPNN.

where wij denotes the weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer; xi is the input of the i-th neuron in the input layer; f and aj are the transfer function and threshold of the j-th neuron in the hidden layer, respectively; and n and l are the numbers of neurons in the input and hidden layers, respectively [20]. In this case, since the sample has four input parameters, i.e., laser power, welding speed, arc gap, and out-of-focus quantity, and three output parameters i.e., melt depth, melt width, and undercut quantity, the structure of the BP neural network is set to 4 - 9 - 3, etc. With a total of 63 weights and 12 thresholds, the number of parameters optimized by the genetic algorithm is 75. 75% of the samples are used as training data for training the network and 25% of the samples are used as test data. The smaller the parameterized error of an individual is, the greater the fitness value of the individual and the better the individual is [21]. The transfer function of the neurons in the hidden layer of the neural network uses a tangent function of the S Tan-Sigmoid type according to Equation (7), and the transfer function of the neurons in the output layer uses a logarithmic function of the S Log-Sigmoid type according to Equation (8), which then satisfies the output requirements of the network as the output pattern is 0 –1 [22]. $F (x) = \frac{2}{1 + e^{- 2 x}}$ (7) $f (x) = \frac{2}{1 + e^{- x}}$ (8)

3.1.2.2. Network training and testing Network training is a process of continually adjusting weights and thresholds, by which, the output error of the network continues to decrease. The training function of a BP neural network is trained by default, i.e., the network is trained using the Levenberg-Marquardt algorithm [23], after which, the network needs to be tested. The BP model training results are shown in Fig. 7.

Fig. 7

BPNN Convergence curve.

3.1.2.3. Implementation of genetic algorithm BP neural network optimization using genetic algorithm is to use a genetic algorithm to optimize the initial weight value and the threshold value of the BP neural network, so that the optimized BP neural network can be more suitable for the sample prediction [24]. The elements of the genetic algorithm for optimizing BP neural networks include population initialization, fitness function, selection operator, crossover operator and variation operator [25, 26]. Each individual is a binary string consisting of four parts: the connection weights between the input layer and the implicit layer, the threshold value of the implicit layer, the connection weights between the implicit layer and the output layer, and the threshold value of the output layer. In this case, the idea is to keep the residuals of the predicted value and the expected value of BP network as small as possible during prediction, thus, the parameter of the error matrix of the predicted value and the expected value of the predicted sample is chosen as the output of the objective function [27]. A fitness ranking assignment function is used in the fitness function: find = ranking(obj), where obj is the output of the objective function [28]. And random selection (sus) is used in the selection operator. In this paper, a two-point crossover is chosen, where two loci are randomly selected on each of the two selected parent chromosomes, and strings are exchanged between the pairs [29], an example of the crossover operation is provided in Fig. 8. Mutations are generated with a certain probability in a number of mutated genes, and the genes that undergo mutation are selected randomly. If the selected gene has a code of 1, it becomes 0; if not, it becomes 1. Chromosomes are selected randomly based on low mutation probabilities, usually with values between 0.001 and 0.1 [30]. An example of a mutation operation is presented in Fig. 8. The results of the GA model training test are shown in Fig. 9.

Fig. 8

Example of a crossover operation and variant handling.

Fig. 9

GA Convergence curve.

The working parameters of the genetic algorithm for this case are set according to Table 5. The variation of the simulation error of the test sample with the number of iterations is shown in Fig. 10. As the number of genetic generations increases, the variation of the error decreases from 0.586 to 0.533, and the optimal initial weight and threshold matrix can be obtained after the genetic algorithm is optimized.

Fig. 10

Error change after GA optimization.

3.2 Verification and discussion

From the results predicted by both the RSM and GA models, five sets of data are randomly selected and compared with the experimental results, and the obtained average error rates are shown in Fig. 11. It can be found that the prediction errors of both models are 0.2–0.25 for the Concave and 0.18–0.2 for the depth-to-width ratio, and the error rates of the GA model are lower than those of the RSM model when predicting the same type of results.

Fig. 11

Ratio of RSM/GA prediction errors to actual values.

The optimum parameters predicted by both models are selected and the results are verified independently using experimental methods, with both algorithmic process parameters listed in Table 6. The weld cross sections produced with the optimum process parameters are shown in Fig. 12 below. Both models control the size of the undercut to be less than 0.15 mm, and the weld size and aspect ratio at the optimum parameters are in general agreement with the predicted values. This suggests to some extent that both models can be used as potential methods for determining the relationships between process parameters and weld geometry in the LSW process, that the predictions for the depth-to-width ratios are generally better than for the undercut, and that the post-optimized GA results have better predictability compared to the RSM.

Table 6

RSM and GA optimization and validation results

		Laser	Welding	gap	Expanded	Melting	Melt	Concave	Aspect
		power (kW)	speed (mm/s)	(mm)	volume (mm)	depth (mm)	width (mm)	(mm)	ratio
RSM	Estimated value	4.683	104.720	0.102	+4.000	1.311	6.156	0.092	0.213
	Experimental value	4.683	104.720	0.102	+4.000	1.379	6.238	0.119	0.221
GA	Estimated value	4.750	109.051	0.062	+3.420	1.491	6.658	0.061	0.224
	Experimental value	4.750	109.051	0.062	+3.420	1.525	6.661	0.075	0.229

Fig. 12

Cross-section through the weld obtained with the optimum parameters.

The stress-strain curve for the LSW lap joint is shown in Fig. 13. It can be seen that both tensile specimens fracture away from the heat-affected zone of the weld and eventually end up tearing at the base material, with the best process predicted by GA showing an 8% increase in stress and 25% increase in strain compared to RSM, which indicates that the larger depth-to-width ratio has a positive effect on the better shear resistance of the weld [31].

Fig. 13

Stress-strain curves for the optimal RSM and GA parameters.

By comparing the two methods, RSM and GA, similarities and differences can be noticed. In terms of predictability, both mathematical models can predict the experimental results under multiple parameter combinations through a finite set of experiments; the RSM model needs to set the experimental conditions and perform characteristic experiments according to the experimental parameters given in the system; within the set parameter range, the prediction effect is good, beyond the parameter range, the prediction result is poor. The BP neural network in the GA model can learn the correlation between the given process parameters and the results, and the accuracy of the model increases as the experimental data becomes more adequate. In terms of visualization, the RSM has intuitive 3D surfaces and projection curves to visualize the effect of a parameter change on the results, and can quickly determine the process window; the effect of a particular process parameter on the results is not observed from GA. In terms of accuracy, the GA algorithm using a nonlinear fit, which is more accurate in terms of finding outliers than the RSM with a linear fit. In practice, it is possible to combine the properties of both algorithms to compensate for the shortcomings of one algorithm.

4 Conclusion

The process parameters for the optimum weld width, weld height, and undercut in the LSW process were determined using RSM and GA models, and it was found that different factors had different coefficients of influence on the results, indicating that

Laser power and welding speed on the melt depth and melt width have a more distinct response, the laser power was positively correlated with the weld depth and width, while the welding speed was inversely correlated with the weld depth and width, the gap was positively correlated with the amount of concave, and the focal length had no significant effect on the weld. The maximum depth-to-width ratio can be achieved by combining medium power at low speed and high power at high speed. Lower welding speeds and larger gaps between the dressings are not conducive to the formation of a smaller depression, and the size of the blur does not have a significant effect on all responses.

Both mathematical models developed by RSM and GA are in great agreement with the corresponding experimental results, and the predictions for aspect ratio are generally better than those for the undercut. The GA model achieves a greater depth-to-width ratio than the RSM model predicts, with an 8% increase in weld tensile strength and a 25% increase in plasticity, using the optimal process parameters to obtain the actual required high quality welds.

The best process parameters determined by GA are a laser power of 4.75 kW, a welding speed of 109.05 mm/s, an arc gap of 0.062 mm, and an out-of-focus quantity of +3.42 mm. The shear stress obtained using this process parameter is approximately 300 MPa, and the actual high-quality welds required can be obtained using the best process parameters.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

This project is supported by Scientific and technological innovation 2030 - major project of new generation artificial intelligence (2020AAA0109300), Class III Peak Discipline of Shanghai-Materials Science and Engineering (High-Energy Beam Intelligent Processing and Green Manufacturing), Professional Technology Service Platform of Shanghai Science and Technology Commission (21DZ2294200), Shanghai Local Universities Capacity Building Project of Science and Technology Innovation Action Program (20030500900)

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Optimization of laser spiral welding using Response surface methodology and genetic algorithms

Abstract

Keywords

1 Introduction

2 Experimental procedure

2.1 Experimental materials

Table 1 Chemical composition of galvanized steel sheet DC06 (weight fraction, %) C Si Mn P S Ti Al ≤0.005 ≤0.030 ≤0.200 ≤0.020 ≤0.015 0.030–0.080 0.010–0.060

3.1 Optimization methods

3.1.1 Response surface model

Declaration of conflicting interests

Funding

References

Table 1
Chemical composition of galvanized steel sheet DC06 (weight fraction, %)

C Si Mn P S Ti Al

≤0.005 ≤0.030 ≤0.200 ≤0.020 ≤0.015 0.030–0.080 0.010–0.060