Multi-response optimization for laser transmission welding of PMMA to ABS using Taguchi-based TOPSIS method

Abstract

Recently, the usage of laser transmission welding (LTW) technology in the automotive industry has been rising for joining thermoplastic parts regarding its superior properties in comparison to other welding technologies. However, specifying the process parameters is a crucial step to obtain satisfactory welding quality for the vehicle parts. In this context, this paper addresses the LTW process of Polimetil metakrilat (PMMA) to Akrilonitril bütadien stiren (ABS) materials for the production of taillights in an automotive company and proposes a new multi-response Taguchi-Based TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method to optimize machining parameters in the laser welding process. In the proposed solution methodology, the main effects of the parameters on different outputs are identified by using the $L_{16}$ orthogonal array of the Taguchi method. Regarding the best parameter set for each output, the best parameter set for multi-response is identified by using the TOPSIS method, in which alternatives are evaluated through the interrelated quality measures. To optimize welding process in taillight production, PMMA and ABS samples with the dimensions of $40 mm$ in width, $85 mm$ in length, and $2.7 mm$ in thickness are used in the experiments. The samples are welded by using LPKF Twinweld 3D 6000^® laser welding machine. For the welding process, laser power, welding speed, and pressure force are taken into account as the input parameters to optimize three responses: weld strength, breaking strain, and weld width. To identify the best process parameter values, the Taguchi Method is initially employed to calculate the main effects of LTW parameters for each output. Then, the TOPSIS method is carried out to evaluate a number of alternative parameter sets generated through the Taguchi results. As a consequence of the TOPSIS ranking scores, the best parameter set that jointly optimizes three outputs of the LTW process is identified for the taillight production as $60 W$ power, $100 mm / s$ speed, and $150 N$ pressure force. Based on the conducted experiments, this parameter setting achieves the highest weld strength, breaking strain level, and above-average weld width. The results of the experiments show that the proposed methodology is capable of optimizing LTW parameters for a multi-response with fewer experiments in the joining of plastic vehicle parts.

Keywords

Laser transmission welding thermoplastics Taguchi method TOPSIS multi-response optimization

Introduction

With the development of high-performance polymers, the use of thermoplastic materials in the automotive industry has been increasing over the last decades since they provide a considerable reduction in production cost.¹ In addition to their low cost, thermoplastic materials have been utilized in many vehicle parts due to their low weight, high strength, and superior corrosion resistance.² As a result of their lightweight structure and cost-efficiency in manufacturing processes, thermoplastics have been increasingly replaced by metallic components in vehicle parts.³

Although thermoplastic materials provide excellent mechanical properties according to various material types, one of the most critical issues is joining these parts with similar or other materials since the performance of a structure fundamentally depends on the behavior of the joints. In this context, several joining techniques have been employed in different fields, where these techniques are classified into three main categories: mechanical joining, adhesive bonding, and fusion bonding. Among these techniques, laser transmission welding (LTW) is one of the most useful methods for joining thermoplastic materials, particularly for thin parts.^4,5 In particular, laser welding is becoming an attractive and economically advantageous joining technique in the automotive industry due to much superiority over conventional welding techniques, such as non-contact and single-side access welding, low process cost, and the suitability of automation.^6–10 The LTW uses a laser beam to connect the surfaces of two materials having different optical characteristics. The thermal energy provided by the laser beam melts the materials at the interface and joins with each other due to heat diffusion.¹¹ With the help of laser technology, the LTW enables a fast and efficient joining for thermoplastics. However, the performance of the LTW is strongly bound up with the machining parameters, such as welding speed, laser power, and standoff distance.¹² Therefore, identifying the significant parameters and their optimal values for the LTW is a crucial activity to achieve a good result for a set of quality metrics. In accordance with this purpose, various methods have been introduced in the literature based on finite element, experimental design, or artificial intelligence.^1,12–16

Design of experiments (DOE) based approaches have been one of the most widely used methods to optimize LTW parameters in literature because the effects of a number of input parameters on a desired response can be efficiently analyzed. Regarding the full or fractional factorial design in DEO, many studies used the response surface methodology (RSM) to optimize the LTW parameters.^17–19 The RSM is a collection of mathematical and statistical techniques to provide an empirical model that allows determining the relation between the input parameters and the response. By using the obtained empirical model, a sensitivity analysis of response with respect to an input parameter can be done through the partial derivative of the function. Additionally, meta-heuristic methods are implemented in a number of studies to find the best parameter set. Based on the thermoplastic materials, Acherjee et al.²⁰ used the flower pollination algorithm to identify the best parameter set for two different responses: weld strength and weld width. For these outputs, the authors considered the laser power, the welding speed, the standoff distance, and the clamping pressure as input parameters to be optimized. The empirical model optimized by the flower pollination algorithm is obtained by RSM with a four-factor and five-level central composite rotatable experimental design. For the same responses, Kumar et al.²¹ considered the beam wobbling strategy in LTW and employed the particle swarm optimization method to identify the best value of five controllable parameters: the laser power, the welding frequency, the welding speed, the wobble width, and the wobble frequency. The same responses and input parameters are taken into account by Kumar et al.,²² where the teaching learning-based optimization algorithm is used for the optimization of RSM models.

In addition to the RSM, the Taguchi method has been alternatively used in the literature to optimize LTW parameters. The Taguchi method is employed in various studies since fewer experiments are required in the method to analyze the main effects of the parameters on a desired response. Anawa and Olabi²³optimized the weld strength by using the Taguchi $L_{25}$ orthogonal array for three parameters with five levels. Similarly, Acherjee et al.²⁴optimized the weld strength in LTW of acrylics using the Taguchi method. Another study based on the Taguchi method was carried out by Huang et al.²⁵ to improve the welding quality of PMMA to steel connection. Similar to the studies given above, there are many works that use the Taguchi method to optimize a single response. On the other hand, a few studies take multiple responses into account to improve welding quality by using the Taguchi method. In this context, the grey relational analysis is integrated into the Taguchi method in order to convert multiple quality characteristics to a single performance measure. The multi-response of the weld strength and the weld width is investigated in different studies with different parameter sets, such as current – standoff distance – clamping pressure,²⁶ power – welding speed – defocal position,²⁷ and laser power – welding speed – standoff distance – clamping pressure.²⁸ Distinct from the multi-response of weld strength and weld width, Hubeatir¹² analyzed the effects of the part thickness and welding speed on the multi-response of the weld with and weld depth through the grey relational analysis based Taguchi method. Similar methodology is used by Parimanik et al.²⁹ to optimize parameter set for LTW of Nitinol wires regarding multi-response of micro-hardness and tensile strength.

This study considers the LTW process in the production of taillights in an automotive company. The company uses PMMA and ABS materials to form taillights, where two thermoplastic materials are combined by using LTW. Although laser welding technology provides superior performance to other welding technologies, the welding quality of the LTW depends on the machining parameters. Therefore, a good welding quality can be observed with optimized parameter settings. On the other hand, the welding quality on the customer’s side of the company is determined through more than one criterion, such as welding strength, breaking strain, and weld width. Since the change of a certain LTW parameter has a different effect on these quality metrics, optimizing the parameters for a single response may not provide the best parameter value for the other responses. Therefore, a multi-response optimization approach is required to jointly improve all responses. In this context, this paper introduces a new multi-response solution methodology to solve the LTW parameter optimization problem of the company. The proposed method integrates the Taguchi method into the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) approach, which is called the Taguchi-Based TOPSIS method. In the Taguchi-Based TOPSIS method, first, the main effects of the LTW parameters are identified using the Taguchi method. Then a number of alternative parameter sets are generated through the Taguchi results. Finally, these alternatives are ranked using the TOPSIS method by taking into account the responses. The best parameter set is specified according to the TOPSIS ranking. The list of nomenclatures used in the article is presented in Table 1.

Table 1.

The list of nomenclatures used in the study.

Abbreviations
ABS	Akrilonitril Bütadien Stiren
DOE	Design of Experiments
LTW	Laser Transmission Welding
PMMA	Polimetil Metakrilat
RSM	Response Surface Methodology
TOPSIS	Technique for Order of Preference by Similarity to Ideal Solution
Notations
A1,…,A7	Parameter set alternatives considered in the TOPSIS method
C1, C2, C3	Criteria considered to evaluate the laser welding outputs
$c_{i}^{+}$	The relative closeness of alternative $i$ to the ideal solution
$L_{16}$	An orthogonal array of the Taguchi method
$p_{1}, p_{2}$ , $p_{3}$	Random points on the weld seam area
$r_{ij}$	Normalized scores of alternative $i$ for criterion $j$
$S / N$	Signal-to-ratio value
$s_{i}^{+}$	Separation measure from the positive ideal solution for alternative $i$
$s_{i}^{+}$	Separation measure from the negative ideal solution for alternative $i$
$v_{ij}$	Weighted normalized scores of alternative $i$ for criterion $j$
$v_{j}^{+}$	Positive ideal solution for criterion $j$
$v_{j}^{-}$	Negative ideal solution for criterion $j$
$w_{j}$	Weight of criterion $j$
$X_{ij}$	Decision matrix value of alternative $i$ for criterion $j$

Based on the aforementioned outline of the study, the main contributions of this paper are threefold. First, a real-life LTW parameter optimization problem for a vehicle part is taken into account to optimize a number of responses, where the welding of PMMA to ABS is realized on an industrial laser welding machine. Next, a new two-stage multi-response optimization approach is proposed to obtain the best parameter set, in which the well-known Taguchi method is integrated into the TOPSIS method. To the best of our knowledge, this is the first study that integrates Taguchi and TOPSIS methods to optimize LTW parameters. Lastly, no research has addressed the multi-response of weld strength, breaking strain, and weld width before. Therefore, the results of the methodology have the potential to provide crucial managerial insight for similar LTW applications.

The remainder of the paper is organized as follows. In Section “Materials and methods,” the materials and methods for the multi-response optimization of LTW parameters are introduced. Section “Results and discussion” presents the results of the application of the proposed methodology. Finally, conclusions and suggestions for future research are summarized in Section “Conclusions.”

Materials and methods

The proposed solution methodology for the LTW parameter optimization problem of the automotive company contains six main steps, as shown in Figure 1. In the first step, the experimental environment for the welding and testing process is identified. Then the LTW parameters and the outputs to be optimized are specified. In the third step, the Taguchi Method is carried out through the $L_{16}$ orthogonal array. The following step is implemented to generate alternative parameter sets regarding the Taguchi results. In the fifth step, the alternative sets are evaluated by using the TOPSIS method. In the last step, the best parameter set for the LTW is specified. The details of the solution methodology are given in the following sub-sections.

Figure 1.

The main steps of the solution methodology.

Experimental environment

The LTW process in the automotive company is carried out to join PMMA and ABS materials using the LPKF Twinweld 3D 6000^® laser welding machine, where the maximum beam source and laser wavelength of the machine are $100 W$ and $980 nm$ , respectively. In the LTW machine, the plastic welding process is done with a hybrid welding head connected to the robot arm. A tensioning roller on the arm provides a constant vertical clamping pressure to create a strong reliable joint, where the pressure force is automatically controlled by the machine control unit. In this context, Figure 2 presents the working principle of the LTW machine.

Figure 2.

The working principle of the LTW machine.

To optimize the LTW parameters, PMMA and ABS samples with the dimensions of $40 mm$ in width, $85 mm$ in length, and $2.7 mm$ in thickness are used to perform experiments. The samples are obtained from the raw material sheet of PMMA/ABS and formed by using a laser cutting machine. For the welding process, the overlap surface of two materials is set to $30 mm$ , where the laser beam is moved through the center of the overlapped area. Figure 3 illustrates the schematic view of the PMMA and ABS samples used in the experiments. To ensure consistency in experiments, burrs on the sample edges are removed to avoid gaps between the surfaces. Additionally, the surfaces of the parts are cleaned with alcohol-based chemicals to purify from possible residues.

Figure 3.

Schematic view of the PMMA and ABS samples.

After the preparation of the samples, the welding process is carried out on the LTW machine using a specific fixture designed according to the part dimensions, as shown in Figure 4. The part-specific slot and the upper clamps avoid the axial movements of the parts during the welding process.

Figure 4.

The fixture designed for the experiments.

In order to determine the welding quality, three different responses are taken into account: weld strength, breaking strain, and weld width. For the response analysis, each welded part is labeled to indicate at which parameter levels it was obtained. Figure 5 presents an illustration of the labeled parts. The weld strength and breaking strain of the parts are analyzed on the Zwick/Roell Z010^® machine with a load of $10 kN$ and a speed of $5 mm / \min$ . In addition to the tensile test, the weld width is measured using Stemi 508^® optic microscope with an objective lens of $50 X$ magnification. For the measurement, three random points ( $p_{1}, p_{2}$ , $p_{3}$ ) on the weld seam area are specified as presented in Figure 6. The weld width of the part is identified by calculating the mean of the weld width of three specific points.

Figure 5.

Illustration of the welded parts.

Figure 6.

Determination of the weld width.

Identification of LTW parameters and outputs

To optimize joining quality of parts on LTW, several control parameters have been studied in the literature, such as laser power, welding speed, clamping pressure, standoff distance, laser wavelength, laser beam diameter, etc. From these parameters, the four major parameters that significantly affect the output are laser power, welding speed, standoff distance, and clamping pressure.^30–32 In this study, three controllable parameters of the LPKF Twinweld 3D 6000^® laser welding machine are taken into account to optimize LTW quality. In this context, the considered parameters are the laser power ( $W$ ), the welding speed ( $mm / s$ ), and the pressure force ( $N$ ) of the laser beam.

As in the input parameters, there exist a number of output metrics to analyze the welding quality. However, optimizing a parameter set for a single output may not always improve the other outputs. In this context, it should be expressed that considering multi-response for parameter optimization would be a more effective approach to improve LTW process. Herewith, three different measures, which are the weld strength ( $N$ ), breaking strain ( $%$ ), and weld width ( $mm$ ), are identified as the outputs of the experiments.

Taguchi method

In order to identify the main effects of three LTW parameters on three responses (weld strength, breaking strain, and weld width), the Taguchi method is used. Taguchi method allows to analyze how different process parameters affect the mean and variance of the process performance metrics and identify the parameters that significantly contribute to performance.^33,34 Distinct from the factorial design and RSM, the Taguchi method considers only a limited number of collections of parameter values for experiments by using orthogonal arrays, which provides less time and resource usage to analyze main effects. To measure the main effects of the parameters and their contribution to performance metrics, the Taguchi method uses the signal-to-noise ratio ( $S / N$ ) based on three different objective functions: larger-the-better, smaller-the-better, and nominal-the-best.³⁵

In the present work, the $L_{16}$ orthogonal array of the Taguchi method with a random order is taken into account, and four levels are identified for each parameter to perform 16 experiments. Table 2 presents the parameter levels used in the Taguchi method. In this context, considering the existing studies on LTW parameter optimization, different parameter values have been taken into account for the laser power, welding speed, and pressure force. Here, it should be noted that there is no exact parameter value range for these parameters in the literature since the materials to be welded or LTW machine specifications are different in each study. Therefore, the parameter levels given in Table 2 are specified according to the experience of the preliminary experiments on the LTW machine. It was observed during the preliminary experiments that insufficient welding occurred when an out-of-the-specified bound value was selected.

Table 2.

LTW parameters and their levels used in experiments.

Parameter	Unit	Level 1	Level 2	Level 3	Level 4
Laser power	$W$	30	50	70	90
Welding speed	$mm / s$	80	100	120	140
Pressure force	$N$	150	200	250	300

For the weld strength and breaking strain outputs, the $S / R$ is considered as the larger-the-better and calculated by using equation (1) where $n$ is the number of parameters and $y_{i}$ is the output response of the experiment. On the other hand, for the weld width, the $S / R$ is considered as the smaller-the-better and calculated by using equation (2).

\begin{matrix} \frac{S}{N} = - 10 \log_{10} [\frac{1}{n} \sum_{i = 1}^{n} \frac{1}{y_{i}^{2}}] \end{matrix}

(1)

\frac{S}{N} = - 10 \log_{10} [\frac{1}{n} \sum_{i = 1}^{n} y_{i}^{2}]

(2)

Generation of alternative parameter sets

Taguchi method results described in the previous sub-section allow analyzing the main effects of the parameters on a specific output over 16 different parameter sets. Based on the $S / N$ ratio for each parameter, the parameter level that has the most positive impact on the output can be described as the best value. However, this methodology is insufficient to jointly analyze different responses. In this context, the response-based best parameter set calculated for each output is identified as an alternative to be evaluated in the TOPSIS method. At this stage, although 16 different parameter levels are taken into account in the Taguchi method to analyze each output, only the best parameter set is selected as an alternative for the TOPSIS method. The remaining parameter sets are ignored for the TOPSIS evaluation since they would provide less benefit than the best one. However, considering that a better parameter set can be valid between the specified parameter level, additional alternatives (distinct from the parameter levels used in the $L_{16}$ orthogonal array) are generated to be evaluated in the TOPSIS method by taking the average of selected parameter levels.

TOPSIS method and identification of best parameter set

The TOPSIS method, which was introduced by Hwang and Yoon,³⁶ is one of the most used multi-criteria decision-making approaches for ranking a set of alternatives regarding a set of criteria. The TOPSIS method ranks the alternatives by determining the distance of each alternative from the ideal positive solution and the negative ideal solution. Because of its easy implementation and intuitive nature, the TOPSIS method has been widely used in various industrial applications.^36,37

The TOPSIS method initially starts with a decision matrix $X_{ij}$ ( $i = 1, \dots, m; j = 1, \dots, n$ ), where $m$ is the number of alternatives, and $n$ is the number of criteria (number of responses for LTW). After identifying the scores of the alternatives for each criterion, the decision matrix is normalized as follows

r_{ij} = \frac{X_{ij}}{\sqrt{\sum_{i = 1}^{m} X_{ij}^{2}}} i = 1, \dots, m j = 1, \dots, n

(3)

where $r_{ij}$ presents the normalized scores of the decision matrix. The procedure continues by determining the weighted normalized scores for the decision matrix ( $v_{ij}$ ) by using equation (4), where $w_{j}$ ( $j = 1, \dots, n$ ) is the weight of criterion $j$ . Here, it should be noted for the standard TOPSIS method that the sum of the weights has to be $1$ $(\sum_{j = 1}^{n} w_{j} = 1)$ .

v_{ij} = w_{j} \times r_{ij} i = 1, \dots, m j = 1, \dots, n

(4)

In the following step of the method, the positive and negative ideal solutions for each criterion ( $v_{j}^{+}$ , $v_{j}^{-}$ ) are identified. In case the criterion has a positive impact (a higher value provides a better response, such as weld strength and breaking strain), equations (5) and (6) are used to determine positive and negative ideal solutions, respectively. On the other hand, if the criterion has a negative impact (i.e. weld width), equations (7) and (8) are taken into account.

v_{j}^{+} = \max {ϑ_{ij} | 1 \leq i \leq m} j = 1, \dots, n

(5)

v_{j}^{-} = \min {ϑ_{ij} | 1 \leq i \leq m} j = 1, \dots, n

(6)

v_{j}^{+} = \min {ϑ_{ij} | 1 \leq i \leq m} j = 1, \dots, n

(7)

v_{j}^{-} = \max {ϑ_{ij} | 1 \leq i \leq m} j = 1, \dots, n

(8)

The next step of the method is the determination of separation measures for each alternative. The separation measure from positive and negative ideal solutions ( $s_{i}^{+}$ , $s_{i}^{-}$ ) are calculated by using equations (9) and (10), respectively.

s_{i}^{+} = \sqrt{\sum_{j = 1}^{n} {(v_{j}^{+} - v_{ij})}^{2}} i = 1, \dots, m

(9)

s_{i}^{-} = \sqrt{\sum_{j = 1}^{n} {(v_{j}^{-} - v_{ij})}^{2}} i = 1, \dots, m

(10)

The final step of the TOPSIS method is the determination of the relative closeness of each alternative to the ideal solution ( $c_{i}^{+}$ ) by using equation (11). The method ends by ranking the alternatives according to the descending order of the closeness value for the selection.

c_{i}^{+} = \frac{s_{i}^{-}}{s_{i}^{-} + s_{i}^{+}} i = 1, \dots, m

(11)

After all alternatives are ranked according to the relative closeness value of the TOPSIS method, the parameter set with the highest $c_{i}^{+}$ value is selected as the best parameter set for the LTW of PMMA to ABS.

Results and discussion

Regarding the proposed Taguchi-Based TOPSIS methodology for the LTW parameter optimization, this section introduces the computational results and discussions for the obtained results. In the first sub-section, the results of the Taguchi method are given. The following sub-section presents the application of the TOPSIS method and the ranking of the alternative parameter sets based on different criteria weights. In the final sub-section, the results of the TOPSIS method are discussed, and the best parameter set for the LTW is identified to obtain the best welding quality for joining the PMMA to ABS.

Results of the Taguchi method

Based on the parameters and their levels given in Table 2, the $L_{16}$ orthogonal design matrix and three responses measured from the experiments are presented in Table 3. Here it should be noted for the responses given in Table 2 that five independent experiments are done for each parameter level. One of the welded parts is used for the weld width monitoring, while the remaining parts are used for the tensile test. The weld strength and breaking strain values represented in Table 2 are the average of four experimental outputs. For each measure, the $S / N$ ratios of the LTW parameters are analyzed to identify the effects of alternatives and their significant levels on the output, which are given in Table 4. According to the observed $S / N$ ratios;

The pressure force is the most significant parameter for the weld strength at lower levels

The power is the most significant parameter for the breaking strain at medium levels

The power is the most significant parameter for the weld width at lower levels

Table 3.

Design matrix and measured responses.

#	LTW parameter levels			Responses
#	Power ( $W$ )	Speed $(mm / s$ )	Pressure force ( $N$ )	Weld strength ( $N$ )	Breaking strain (%)	Weld width ( $mm$ )
1	1	4	4	614.0	0.58	3.89
2	3	4	2	1542.7	1.46	4.69
3	4	3	2	1495.6	1.31	4.73
4	3	3	1	1610.2	1.54	4.65
5	4	1	4	708.0	0.77	4.58
6	2	2	1	1703.9	1.48	4.65
7	4	2	3	1055.0	1.27	4.96
8	1	2	2	1369.0	1.22	4.01
9	2	1	2	1519.0	1.42	4.72
10	3	2	4	1551.0	1.46	4.93
11	1	3	3	937.0	0.86	3.97
12	2	3	4	1644.5	1.51	4.31
13	4	4	1	1512.0	1.27	4.82
14	3	1	3	1309.2	1.51	5.05
15	1	1	1	1574.0	1.46	4.49
16	2	4	3	1492.6	1.41	4.58

Table 4.

Response table for $S / N$ ratios.

Response	Level	Power ( $W$ )	Speed ( $mm / s$ )	Pressure force ( $N$ )
Weld strength	1	60.47	61.73	64.07
	2	64.01	62.91	63.41
	3	63.51	62.85	61.43
	4	61.14	61.65	60.22
	Delta	3.55	1.26	3.85
	Rank	2	3	1
Breaking strain	1	−0.26	1.91	3.13
	2	3.25	2.62	2.60
	3	3.48	2.09	1.83
	4	1.06	0.90	−0.03
	Delta	3.73	1.72	3.16
	Rank	1	3	2
Weld width	1	−12.22	−13.45	−13.35
	2	−13.18	−13.29	−13.12
	3	−13.67	−12.88	−13.29
	4	−13.57	−13.03	−12.89
	Delta	1.45	0.57	0.46
	Rank	1	2	3

In addition to the $S / N$ ratios, the main effect plots for $S / N$ ratios are used to analyze the effects of each parameter on a single output parameter and identify the best parameter set for the corresponding output. In this context, Figures 7 to 9 show the main effect plots for weld strength, breaking strain, and weld width, respectively. When the main effect plots are analyzed, it is observed that each output exhibits a different pattern with respect to parameter changes. A medium level for the power is proper for the weld strength and breaking strain, while a low-level seems more appropriate for the weld width. A similar result is observed for other input parameters. In detail, raising the laser power increases both the weld strength and breaking strain until a threshold value (50 W for weld strength and 70 W for breaking strain) is reached. After the threshold value, the weld strength and breaking strain decrease since the critical temperature of decomposition is reached. Also, higher weld width measures are observed with higher laser power (i.e. 70 and 90 W) because the welded zone is directly proportional to the laser power. It is also evident from the main effect plots that increasing the welding speed drops off both the weld strength and breaking strains because the amount of energy applied per unit length decreases at high-speed levels. However, less weld strength and breaking strain are obtained at low-speed levels since the high energy applied for each unit length may cause a deterioration on the material. Therefore 100 or 120 $mm / s$ are observed as the threshold value for the weld speed and appear ideal level for all responses. For the weld width, high-speed levels provide a less welded zone. In addition to the power and speed parameters, the pressure force provides a better weld quality for the weld strength and breaking strain when the corresponding parameter is at a low level since the higher-pressure force may cause deterioration at the contact point of two materials. On the other hand, a significant correlation could not be observed between the pressure force and weld width. As a result of the analyzes on the main effect plots, it should be stated that the quality of the output depends on the input parameter level, and the optimal parameter set for each output is distinct from the others. Accordingly, based on the highest effect level of each parameter, the response-based best parameter sets are identified as;

50 $W$ power, 100 $mm / s$ speed, and 150 $N$ for weld strength

70 $W$ power, 100 $mm / s$ speed, and 150 $N$ for breaking strain

30 $W$ power, 120 $mm / s$ speed, and 300 $N$ for weld width

Figure 7.

Main effects for $S / N$ ratios for weld strength.

Figure 8.

Main effects for $S / N$ ratios for breaking strain.

Figure 9.

Main effects for $S / N$ ratios for weld width.

The last analysis made through the Taguchi results is carried out to identify the interaction effects of parameter pairs on the responses. In this context, Figures 10 to 12 represent the response surface plots for each pair of parameters on the responses, where an interaction effect with a distinctive trend is observed for each pair of input parameters on a response. For the weld strength and breaking strain, the interaction effect between the laser power and speed shows similar behavior. At lower power and higher speed, or higher power and lower speed, the quality of the corresponding measures is at low-level. However, high quality can be obtained at different levels of the parameters (i.e. at 30 $W$ power and 80 $mm / s$ speed, 90 $W$ power and 140 $mm / s$ speed, 60 $W$ power and 110 $mm / s$ speed). For the weld width, a slightly different interaction effect is achieved with respect to the other two responses. The lowest weld width is measured at 30 $W$ power and 140 $mm / s$ speed, while higher welding power extends the weld width. In terms of the interaction effect between the power and force, the weld strength and breaking strain measures are constant with respect to power changes when the force is at a low level. However, for the higher force values (i.e. 300, 320 $N$ ), the highest weld strength and breaking strain values are observed at midpoints for the power parameter (i.e. 50, 60 W). The final interaction effect analyses can be made through the speed and pressure force parameters. At the low-pressure force level, the speed does not affect any output measure. On the other hand, a maximum or minimum quality level is obtained with different speed values when the pressure force is increased. In particular, high weld strength and breaking strain values are observed at three points: 80 $mm / s$ speed and 200 $N$ force, 140 $mm / s$ speed and 200 $N$ force, and 110 $mm / s$ speed and 300 $N$ force. For the weld width, the number of minimum points is two, where the first point is at 100 $mm / s$ speed and 200 $N$ force, and the second point is at 120 $mm / s$ speed and 300 $N$ force. Regarding the existing literature in the LTW, equivalent findings are reported for similar input-output parameters.^17,18,22 As a result of these analyses, it can be summarized that the interactions of the parameters expose different patterns according to the main effect plots, particularly for the pair of speed and pressure force. For instance, the lowest level of the pressure force seems as the most significant level for the weld strength. However, similar or better strength values can be observed when the pressure force is at the highest level and the speed at medium levels. Here, the multiple peaks in the surface plots exhibit the non-linear structure in the interaction effects of the parameter pairs. Therefore, assuming that a better parameter value may be between two pre-defined levels, additional parameter sets are generated through the response-based best parameter sets to be analyzed in the TOPSIS method.

Figure 10.

Response surface plot showing the interaction effects of: (a) power and speed, (b) power and force, and (c) speed and pressure force on the weld strength.

Figure 11.

Response surface plot showing the interaction effects of: (a) power and speed, (b) power and pressure force, and (c) speed and pressure force on the breaking strain.

Figure 12.

Response surface plot showing the interaction effects of: (a) power and speed, (b) power and pressure force, and (c) speed and pressure force on the weld width.

Results of the TOPSIS method

Regarding the Taguchi results, three alternative parameter sets (A1–A3) are observed based on three different responses. Additionally, four different parameter sets (A4–A7) are generated by taking the average of parameter values identified in the base parameter sets. Totally, seven alternatives, which are presented in Table 5, are taken into account in the TOPSIS method to obtain the best parameter values for the multi-response LTW process. To evaluate these alternatives, the weights of criteria are identified based on four scenarios. In the first scenario, all criteria are weighted equally. For the remaining scenarios, the weight of one criterion is specified to be more than the others. Table 6 introduces the considered weights for each scenario.

Table 5.

Alternative parameter sets analyzed in the TOPSIS method.

Alternatives	Description	Parameter values			Responses
Alternatives	Description	Power ( $W$ )	Speed ( $mm / s$ )	Pressure force ( $N$ )	Weld strength ( $N$ )	Breaking strain ( $%$ )	Weld width ( $mm$ )
A1	Best parameter set for weld strength	50	100	150	1703.9	1.48	4.65
A2	Best parameter set for breaking strain	70	100	150	1741.0	1.86	5.11
A3	Best parameter set for weld width	30	120	300	519.3	0.61	3.82
A4	Average of A1–A2	60	100	150	1795.7	2.33	4.71
A5	Average of A1–A3	40	110	225	1531.2	1.86	4.38
A6	Average of A2–A3	50	110	225	1594.9	1.86	4.54
A7	Average of A1–A2–A3	50	∼107	200	1682.2	2.01	4.83

Table 6.

Scenarios for the criteria weights in the TOPSIS method.

Scenario	$w_{j}$
Scenario	Weld strength ( $N$ )	Breaking strain ( $%$ )	Weld width ( $mm$ )
Scenario 1	$1 / 3$	$1 / 3$	$1 / 3$
Scenario 2	$1 / 2$	$1 / 4$	$1 / 4$
Scenario 3	$1 / 4$	$1 / 2$	$1 / 4$
Scenario 4	$1 / 4$	$1 / 4$	$1 / 2$

Based on the seven parameter alternative sets (A1,…,A7) and their responses on the LTW process, the normalized decision matrix for the TOPSIS method is determined by using equation (1), where the results are given in Table 7. Here it should be noted for the TOPSIS computations that the weld strength, breaking strain, and weld width are called hereafter Criteria 1 ( $C 1$ ), Criteria 2 ( $C 2$ ), and Criteria 3 ( $C 3$ ), respectively.

Table 7.

Normalized decision matrix.

Alternatives	Weld strength ( $N$ )	Breaking strain ( $%$ )	Weld width ( $mm$ )
Alternatives	Criteria 1 ( $C 1$ )	Criteria 2 ( $C 2$ )	Criteria 3 ( $C 3$ )
A1	0.4115	0.3126	0.3827
A2	0.4204	0.3929	0.4206
A3	0.1254	0.1289	0.3144
A4	0.4337	0.4922	0.3876
A5	0.3698	0.3929	0.3605
A6	0.3852	0.3929	0.3736
A7	0.4062	0.4246	0.3975

Following the normalization of the decision matrix, the weighted normalized decision matrix is determined by using equation (2). Table 8 presents the weighted normalized decision matrix for four different scenarios based on the criteria weights given in Table 6.

Table 8.

Weighted normalized decision matrix.

	Scenario 1			Scenario 2			Scenario 3			Scenario 4
	$C 1$	$C 2$	$C 3$	$C 1$	$C 2$	$C 3$	$C 1$	$C 2$	$C 3$	$C 1$	$C 2$	$C 3$
A1	0.1372	0.1042	0.1276	0.2057	0.0782	0.0957	0.1029	0.1563	0.0957	0.1029	0.0782	0.1913
A2	0.1401	0.1310	0.1402	0.2102	0.0982	0.1051	0.1051	0.1965	0.1051	0.1051	0.0982	0.2103
A3	0.0418	0.0430	0.1048	0.0627	0.0322	0.0786	0.0314	0.0644	0.0786	0.0314	0.0322	0.1572
A4	0.1446	0.1641	0.1292	0.2168	0.1230	0.0969	0.1084	0.2461	0.0969	0.1084	0.1230	0.1938
A5	0.1233	0.1310	0.1202	0.1849	0.0982	0.0901	0.0924	0.1965	0.0901	0.0924	0.0982	0.1802
A6	0.1284	0.1310	0.1245	0.1926	0.0982	0.0934	0.0963	0.1965	0.0934	0.0963	0.0982	0.1868
A7	0.1354	0.1415	0.1325	0.2031	0.1061	0.0994	0.1016	0.2123	0.0994	0.1016	0.1061	0.1988

The next step of the TOPSIS method is performed to identify the positive and negative ideal solutions for the criteria, where the results are presented in Table 9. For $C 1$ and $C 2$ , the maximum weighted normalized value is specified as the positive ideal solution, while the minimum weighted normalized value is defined as the negative ideal solution. The opposite composition is taken into account for the $C 3$ since a smaller value expresses a better result for weld width.

Table 9.

Positive and negative ideal solutions.

	Scenario 1			Scenario 2			Scenario 3			Scenario 4
	$C 1$	$C 2$	$C 3$	$C 1$	$C 2$	$C 3$	$C 1$	$C 2$	$C 3$	$C 1$	$C 2$	$C 3$
$v_{j}^{+}$	0.1446	0.1641	0.1048	0.2168	0.1230	0.0786	0.1084	0.2461	0.0786	0.1084	0.1230	0.1572
$v_{j}^{-}$	0.0418	0.0430	0.1402	0.0627	0.0322	0.1051	0.0314	0.0644	0.1051	0.0314	0.0322	0.2103

The final step of the TOPSIS method is carried out to determine the relative closeness of each alternative to the ideal solution by using the separation measure from the positive and negative ideal solutions. Table 10 shows the results of applications of equations (9)–(11), where the alternative with the highest $c_{j}^{+}$ score is the best alternative for the TOPSIS method.

Table 10.

Separation measures from the positive and negative ideal solutions and the relative closeness of each alternative.

	Scenario 1			Scenario 2			Scenario 3			Scenario 4
	$s_{j}^{+}$	$s_{j}^{-}$	$c_{j}^{+}$	$s_{j}^{+}$	$s_{j}^{-}$	$c_{j}^{+}$	$s_{j}^{+}$	$s_{j}^{-}$	$c_{j}^{+}$	$s_{j}^{+}$	$s_{j}^{-}$	$c_{j}^{+}$
A1	0.0645	0.1140	0.6389	0.0493	0.1505	0.7533	0.0916	0.1168	0.5606	0.0567	0.0871	0.6058
A2	0.0487	0.1320	0.7307	0.0369	0.1616	0.8140	0.0564	0.1512	0.7284	0.0587	0.0990	0.6278
A3	0.1588	0.0354	0.1822	0.1789	0.0265	0.1292	0.1973	0.0265	0.1186	0.1191	0.0531	0.3083
A4	0.0244	0.1592	0.8670	0.0183	0.1791	0.9072	0.0183	0.1975	0.9152	0.0366	0.1203	0.7665
A5	0.0422	0.1216	0.7421	0.0421	0.1397	0.7686	0.0534	0.1462	0.7325	0.0374	0.0948	0.7169
A6	0.0418	0.1245	0.7486	0.0377	0.1462	0.7948	0.0532	0.1476	0.7350	0.0405	0.0955	0.7022
A7	0.0369	0.1362	0.7869	0.0301	0.1588	0.8407	0.0403	0.1638	0.8027	0.0454	0.1026	0.6933

The results of the TOPSIS method is validated by comparing them with the Multi-Objective Optimization Ratio Analysis (MOORA) method introduced by Brauers in 2004.³⁹ MOORA is one of the multi criteria decision making approach that can be used to evaluate alternatives through positive and negative ideal solutions as in the TOPSIS method. Table 11 presents the ranking of alternatives according to the TOPSIS and MOORA results for each scenario. It can be seen from Table 11 that the same results are obtained for the first three scenarios. On the other hand, the ranking of MOORA has a slight difference in the last scenario, where the disparities in the rankings are displayed with bold characters in the table. The results of the comparisons demonstrate the consistency of the TOPSIS method.

Table 11.

TOPSIS and MOORA rankings for four scenarios.

	Scenario 1		Scenario 2		Scenario 3		Scenario 4
	TOPSIS	MOORA	TOPSIS	MOORA	TOPSIS	MOORA	TOPSIS	MOORA
A1	6	6	6	6	6	6	6	6
A2	5	5	3	3	5	5	5	5
A3	7	7	7	7	7	7	7	7
A4	1	1	1	1	1	1	1	1
A5	4	4	5	5	4	4	2	2
A6	3	3	4	4	3	3	3	4
A7	2	2	2	2	2	2	4	3

Identification of best parameter set

The results of the TOPSIS method show that the highest relative closeness to the ideal solution is observed with A4 for each scenario. As a consequence of the computations, it should be expressed that the best parameter set for the LTW process of PMMA to ABS material in taillight production is $60 W$ power, $100 mm / s$ speed, and $150 N$ pressure force. Although there exists a better parameter setting to optimize a single response (i.e. A1 for weld strength, A2 for breaking strain, and A3 for weld width), A4 jointly optimizes three outputs with the help of the TOPSIS method. It can be observed from Table 4 that the best weld strength quality is provided by using the A4 parameter set. Similarly, the A4 parameter set allows obtaining higher breaking strain values with respect to other alternative parameter sets. However, in terms of the weld width, the A4 parameter set is in third place in the ranking. For the weld width, better performance is obtained by using A2 and A7 parameter sets. Nevertheless, it should be noted that the A4 parameter set provides a better result than the average weld width values given in Table 4. Furthermore, if the A2 or A7 alternatives were selected instead of A4, a worse quality level would have been obtained in terms of both weld strength and breaking strain responses. As a result, when the outputs obtained from the experiments are evaluated through the TOPSIS ranking scores, A4 can be described as the best alternative to jointly optimize three quality measures. Obtaining A4 as the best alternative for each scenario demonstrates the validity of the decided parameter values.

Another outcome that can be achieved from Table 10 is the effect of weights on the ranking of alternatives. Although the best parameter set is A4 for each scenario, the ranking of the alternatives varies according to the weights of the criteria. In detail, the ranking of the alternatives is $A 4 \to A 7 \to A 6 \to A 5 \to A 2 \to A 1 \to A 3$ for Scenario 1 and Scenario 3. A similar result is obtained for Scenario 2, where the order of the alternatives is $A 4 \to A 7 \to A 2 \to A 6 \to A 5 \to A 1 \to A 3$ . However, when the weld width is considered as a more important criterion, the ranking of the alternatives ( $A 4 \to A 5 \to A 6 \to A 7 \to A 2 \to A 1 \to A 3$ ) is quite different from the other results. Here, it should be noted that it may be possible to find different ranking through the TOPSIS with different criteria weights.

The final outcome of the TOPSIS result can be made through the relative closeness value of the A1, A2, and A3. For each scenario, it can be observed from Table 10 that optimizing a single performance measure adversely affects other performance measures. Particularly, A1 and A3 are successful to optimize weld strength and weld width, respectively. It could not be possible to obtain a good multi-response welding quality with these alternatives. Therefore, these sets remained in the last place in the ranking. As a result, it can be stated that the proposed solution approach provides a better solution to optimize multiple performance measures in LTW process.

Conclusions

This paper considers the optimization of laser transmission welding parameters for the production of vehicle taillight, which is formed by welding PMMA to ABS. Regarding the quality of the welding process depends on three different metrics, a multi-response Taguchi-based TOPSIS method is proposed to find the best parameter set for the machining. The proposed methodology, which is the first study that integrates Taguchi and TOPSIS methods to optimize LTW parameters, provides the best LTW parameters for a multi-response with fewer experiments in the joining of plastic vehicle parts. In the first step of the solution approach, the main effects of controllable machining parameters on three responses are determined by using the $L_{16}$ orthogonal array of the Taguchi method. Then a number of alternative sets for the parameters generated through the Taguchi results are evaluated by using the TOPSIS method. The outputs of the TOPSIS method are analyzed considering different scenarios generated with different response weights. Based on the computational results, the following conclusions are drawn:

The best parameter value for the LTW process varies according to the quality measure taken into account (i.e. $50 W$ power, $100 mm / s$ speed, and $150 N$ pressure force for weld strength, $70 W$ power, $100 mm / s$ speed, and $150 N$ pressure force for breaking strain, and $30 W$ power, $120 mm / s$ speed, and $300 N$ pressure force for weld width). Thus, the best parameter set obtained for a single response may not be the best set for the other responses. Therefore, a multi-response approach is required to obtain the best parameter settings to optimize a number of responses.

According to the $S / N$ ratios observed by the Taguchi method, the most significant machining parameter is the power for both the breaking strain and weld width, where the $S / N$ ratios are 3.73 for breaking strain, and 1.45 for weld width. On the other hand, the pressure force significantly affects the weld strength quality since the parameter has the highest $S / N$ ratio.

For the multi-response optimization, the proposed Taguchi-based TOPSIS method is capable of finding the best parameter set by taking different output criteria into account. In this context, seven alternative parameter sets are evaluated through three fundamental LTW quality measures.

Regarding four different scenario, the highest $c_{j}^{+}$ score is observed by the $A 4$ for each scenario, where the relative closeness of $A 4$ is 0.8670, 0.9072, 0.9152, and 0.7665, respectively.

Based on the TOPSIS ranking scores, the best LTW parameter set for three outputs is identified as $60 W$ power, $100 mm / s$ speed, and $150 N$ pressure force. For the findings stated above, it should be noted that the efficiency of the proposed solution methodology highly depends on the experimental environment. Considering the response surface plots observed for each output at experiments, parameter inputs and output measures have a non-linear relationship. Furthermore, the parameter levels identified for the experiments directly affect the results of the Taguchi method. Therefore, there would be a better alternative parameter set to be evaluated by the TOPSIS method. Consequently, a better welding quality may be obtained for the vehicle taillights by executing more experiments at the expense of higher resource usage.

For future research, this study can be extended in a few directions. Based on the proposed methodology, the proposed approach can be carried out for the welding of different materials. In this context, thinner thermoplastic materials can be also considered for the LTW process. On the other hand, different multi-criteria decision-making approaches can be integrated to the Taguchi method to evaluate the welding quality of PMMA to ABS. Furthermore, the additional controllable machining parameters can be integrated with the parameters considered in this paper.

Footnotes

Acknowledgements

The authors would like to sincerely thank the Odelo Automotive Signal Lights Inc. and Tofaş Automotive Inc. companies for their support on the experimental studies of the work.

Handling Editor: Chenhui Liang

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

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Ayca Kucukoglu

Fatih Karpat

Data availability

Dataset related these studies, findings, and results as reported are included in the manuscript itself.

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