Use of the grey relational analysis to determine optimum laser cutting parameters with multi-performance characteristics

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Optics & Laser Technology 40 (2008) 987–994 www.elsevier.com/locate/optlastec

Technical Note

Use of the grey relational analysis to determine optimum laser cutting parameters with multi-performance characteristics Ulas- C - aydas-, Ahmet Hasc- alık Technical Education Faculty, Department of Manufacturing, University of Firat, 23119 Elazig, Turkey Received 23 November 2007; received in revised form 5 January 2008; accepted 6 January 2008 Available online 12 February 2008

Abstract This paper presents an effective approach for the optimization of laser cutting process of St-37 steel with multiple performance characteristics based on the grey relational analysis. Sixteen experimental runs based on the Taguchi method of orthogonal arrays were performed to determine the best factor level condition. The response table and response graph for each level of the machining parameters were obtained from the grey relational grade. In this study, the laser cutting parameters such as laser power and cutting speed are optimized with consideration of multiple-performance characteristics, such as workpiece surface roughness, top kerf width and width of heat affected zone (HAZ). By analyzing the grey relational grade, it is observed that the laser power has more effect on responses rather than cutting speed. It is clearly shown that the above performance characteristics in laser cutting process can be improved effectively through this approach. r 2008 Elsevier Ltd. All rights reserved. Keywords: Laser cutting; Grey relational analysis; Characteristics; Multi-performance characteristics

1. Introduction Laser cutting is a popular process, which finds wide application in various manufacturing industries due to its precision of operation and low cost. Laser cutting, being a non-contact process, does not involve any mechanical cutting forces and tool wear. The workpiece material is locally melted by the focused laser light [1]. The melt is then blown out of the kerf with an assist gas that flows coaxial with the laser beam. In metal cutting operations, in general, oxygen is used while argon or helium is used for wood or plastic cutting [2]. When using oxygen as assist gas, it will not only drag the melt away but will also provide exothermic reaction in the cutting section enhancing the energy available for increasing the cutting speed [3]. To maintain a high production rate and an acceptable level of quality for the cut parts, it is important to select the optimum combination of process parameters, as these Corresponding author. Tel.: +90 4242 370 000x4229; fax: +90 4242 367 064. E-mail address: ucaydas@firat.edu.tr (U. C - aydas-).

0030-3992/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2008.01.004

parameters impact on the special microscopic and macroscopic characteristics of the finished parts, as signified by the kerf width, the width of the heat affected zone (HAZ) and the surface roughness after processing [4]. Considerable research studies were carried out to improve the performance of laser cutting process previously. Ghany and Newishy [5] evaluated the optimum laser cutting parameters for 1.2 mm austenitic stainless steel sheets by using pulsed and continuous wave (CW) Nd:YAG laser beam and nitrogen or oxygen as assistant gases, each one separately. It was shown that the laser cutting quality depends mainly on the laser power, pulse frequency, cutting speed and focus positions. Although, nitrogen produced brighter and smoother cut surfaces with smaller kerf, it was more expensive compared to oxygen. The cutting speed was increased more than 8 m/min in CW mode compared with pulsed one. Chen [6] investigated the effects of gas composition on the CO2 laser cutting of mild steel. The gas mixtures used were composed of oxygen, argon, nitrogen and helium. It was found that a high purity of oxygen with a laser power of 1500 W is required for the high performance laser cutting of 3 mm mild steel. Wee and

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Li [7] reported a two-dimensional analytic model for striation formation in laser cutting of mild steel. The multi-performance characteristics of the laser cutting process such as melt film thickness, oxidation and power absorption over the cut front were predicted based on the laser power, scan speed and spot width parameters in the model. Bagger and Olsen [8] optimized the pulsed mode laser cutting parameters for the medium strength steel GA 260 with a thickness of 1.8 mm. For quality assessment, multi-performance (the squareness, surface roughness and dross attachment of laser cut blanks) characteristics were evaluated. The optimal cutting conditions were achieved at 2.0 kW power and 3.5 m/min cutting speed settings for the tested material. Li et al. [9] reported an investigation into achieving striation-free laser cutting of EN 43 mild steel sheets of 2 mm thickness. It was shown that at cutting speeds above critical cutting speed, surface roughness got worse. Kaebernick et al. [10] developed a model to predict the kerf width at the beam entry side as a function of cutting speed for different pulse widths with the aim to identify optimal cutting conditions. The model showed that the kerf width appeared to increase slightly and then decreased after a critical cutting speed was reached. Lamikiz et al. [11] varied the main laser cutting parameters such as power, gas pressure, cutting speed and focus position in order to study their influence on the quality and geometry of cutting in the different types of AHSS sheet steels. It was advised that the power should be increased to 300 W to avoid the risk of the appearance of pitting which was higher as the cutting speed was increased. Rajaram et al. [12] investigated the CO2 laser cut quality of 4130 steel and showed that the kerf and HAZ width was influenced significantly by laser power, while cutting speed played a minor role. Prasad et al. [13] discussed the laser cutting of metallic coated sheet steels of 1 mm thickness. The kerf geometry and surface roughness were studied. It was proven that the cutting speed was a function of the input power. Chen [14] performed an experiment to investigate the effect of high-pressure assistant gas flow on CO2 laser cutting of 3 mm thick mild steel plate. It was shown that the side-burning effect always appeared on the top of the cut surface when using oxygen. Ghany et al. [15] investigated the effects of different laser cutting parameters such as laser power, cutting speed, different gas types and pressures and focus position on the cutting quality characteristics of attached dross, kerf width and cut surface roughness. It was experimentally shown that zinccoated steel material could be cut by Nd:YAG using laser powers of less than 400 W and speeds of up to 6 m/min. Dubey and Yadava [16] optimized the laser beam cutting process using a hybrid Taguchi method and response surface method with multi-performance characteristics for thin sheet of high silicon-alloy steel. A study on kerf width, kerf deviation and kerf taper when Nd:YAG laser cutting of nickel-based superaloy sheets have been studied by the same authors using Taguchi based method [17].

From the influence of operating parameters on the performance characteristics, the optimal operating parameters are very difficult controlled and greatly complicated. In such complex and multi-variate systems, the relationship between factors is unclear. The classical statistical procedures may not analyze these systems in an acceptable or reliable manner without large data sets that satisfy certain mathematical criteria. The grey relation theory, on the other hand, can handle both incomplete information and unclear problems very precisely. This theory was first proposed by Deng [18] and also has been applied to the different fields of machining processes. For example, Chiang and Chang [19] used grey relational analysis to determine optimal wire electrical discharge machining (WEDM) parameters for machining Al2O3 particle reinforced material with multiple-performance characteristics (surface removal rate and maximum surface roughness). Tosun [20] used grey relational analysis for optimizing the drilling process parameters such as feed rate, cutting speed, drill type and point angles of drill for the workpiece surface roughness and burr height. Palanikumar et al. [21] optimized the turning parameters such as cutting speed, feed rate, depth of cut and machining time based on the multiple-performance characteristics including material removal rate, tool wear, surface roughness and specific cutting pressure by using grey relational analysis method. Lin [22] applied the Taguchi method and grey relational analysis to optimize turning operations with multi-performance characteristics (tool life, cutting forces and surface roughness). Chang and Lu [23] applied a grey relational analysis to set of two-stage experiments to determine cutting parameters for optimizing the side milling process with multi-performance characteristics. Huang et al. [24] obtained optimal WEDM parameters’ setting for maximum material removal rate and minimum surface roughness by using grey relational analysis. Yang et al. [25] studied the influence of machining parameters such as cutting speed, feed rate and depth of cut on the groove width and the average surface roughness for the end-milling of high-purity graphite under dry machining conditions. An orthogonal array was used for experimentation and grey relational analysis method was then applied to determine optimal machining parameter setting. Lin and Ho [26] conducted on analysis of variance (ANOVA) on the chemical–mechanical polishing process parameters derived from the Taguchi method. They also analyzed the effect of data normalization and data integrity in grey relational analysis on the degree of sensitivity. From the review of literature, it is observed that the grey relational analysis has found wide application areas for determining the optimal parameters through different machining processes. However, optimization of laser cutting parameters relevant with the grey relation analysis method is rather lacking. The purpose of the present work is to introduce the use of grey relational analysis in selecting optimal laser cutting conditions on multiperformance characteristics, namely, workpiece surface

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roughness, top kerf width and width of HAZ. The setting of laser cutting parameters was accomplished using the Taguchi experimental design method. Moreover, the most effective factor and the order of importance of the controllable factors to the multi-performance characteristics in the laser cutting process were determined by using grey relational grade. 2. Experimental procedure The experiments were conducted on an Amada LC-aIII laser center. This machine used a l ¼ 10.6 mm wavelength CO2 laser with a nominal power output of 2000 W at pulsed mode. Oxygen emerging from a conical nozzle and co-axially with the laser beam was used. The laser beam was focused using a 127 mm focal length lens. The nozzle–workpiece stand-off distance was controlled at 1 mm. A 10 mm thick St-37 steel was used as workpiece material. The chemical composition of the St-37 is provided in Table 1. Because of the large number of independent parameters that control the laser cutting process, some preliminary experiments were conducted by Nagarajan [27] in order to determine which parameters should be considered for

optimization. Four parameters (power, feed rate, beam frequency and duty cycle) were varied by 25% above and below their normal operating levels and it was found that any change in beam frequency and duty cycle lead to any significant gains in productivity. Therefore, the optimization of laser cutting process was obtained by varying only feed speed and power in this study. The summary of experimental conditions is listed in Table 2. The experimental results after laser cutting were evaluated in terms of the following measured machining performances: (1) surface roughness (Ra); (2) top kerf width (wt); (3) width of HAZ (see Fig. 1). Each test piece was measured 5 times and average value taken for a more accurate reading. The surface roughness of laser cut surfaces was measured from the centerline of the cut edge using a Mitutoyo SJ-201 instrument. The sampling length of each measurement was set to 5 mm. The top kerf width and width of HAZ was measured by using a stereo zoom microscope. In order to achieve best cutting quality, Taguchi’s experimental design, an efficient plan, was used for conducting experiments. For this purpose, a L16 orthogonal array was used for experiment (Table 3). The experimental results are summarized in Table 3.

3. Grey relational analysis

Table 1 Nominal chemical composition of St-37 steel C

Si

Mn

P

S

Cr

Mo

Ni

V

Fe

0.13

0.2

0.75

0.05

0.06

0.04

0.02

0.015

0.0012

Balance

Table 2 Laser cutting factors and their levels Symbol

Cutting factor

Level 1

Level 2

Level 3

Level 4

A B

Power (W) Cutting speed (mm/s)

800 21.6

1000 32.44

1200 45.5

1400 55

In grey relational analysis, black represents having no information and white represents having all information. A grey system has a level of information between black and white [20]. This analysis can be used to represent the grade of correlation between two sequences so that the distance of two factors can be measured discretely. In the case when experiments are ambiguous or when the experimental method cannot be carried out exactly, grey analysis helps to compensate for the shortcoming in statistical regression [26]. Grey relation analysis is an effective means of analyzing the relationship between sequences with less data and can analyze many factors that can overcome the disadvantages of statistical method [28].

Top kerf w

idth

HAZ

t

989

Surface roughness measurement

Fig. 1. Measurement of multi-performance responses.

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990

Table 3 Experimental layout using an L16 orthogonal array and multi-performance results Experiment no

A Power (W)

B Cutting speed (mm/s)

Surface roughness, Ra (mm)

Top kerf (mm)

HAZ (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

7.214 6.826 7.361 7.751 6.640 6.571 6.814 6.926 5.971 5.756 6.010 6.334 5.771 5.524 5.817 6.428

0.179 0.167 0.154 0.148 0.200 0.194 0.187 0.181 0.245 0.237 0.228 0.223 0.275 0.264 0.251 0.243

44.293 40.010 37.278 32.876 61.028 52.173 43.718 32.916 63.141 56.524 49.614 43.638 53.928 54.176 55.624 54.123

3.1. Data pre-processing In grey relational analysis, when the range of the sequence is large or the standard value is enormous, the function of factors is neglected. However, if the factors, goals and directions are different, the grey relational might produce incorrect results. Therefore, one has to pre-process the data which are related to a group of sequences, which is called ‘‘grey relational generation’’ [23]. Data pre-processing is a process of transferring the original sequence to a comparable sequence. For this purpose, the experimental results are normalized in the range between zero and one. The normalization can be done from three different approaches [29]. If the target value of original sequence is infinite, then it has a characteristic of ‘‘the-larger-the-better’’. The original sequence can be normalized as follows [30]: xi ðkÞ ¼

xi ðkÞ  min x0i ðkÞ , max x0i ðkÞ  min x0i ðkÞ

(1)

if the expectancy is the-smaller-the better, then the original sequence should be normalized as follows: xi ðkÞ ¼

max x0i ðkÞ  x0i ðkÞ . max x0i ðkÞ  min x0i ðkÞ

(2)

However, if there is a definite target value to be achieved, the original sequence will be normalized in the form xi ðkÞ ¼ 1 

jx0i ðkÞ  x0 j max x0i ðkÞ  x0

(3)

or the original sequence can be simply normalized by the most basic methodology, i.e. let the values of original sequence be divided by the first value of sequence: xi ðkÞ ¼

x0i ðkÞ , x0i ð1Þ

(4)

where xi ðkÞ is the value after the grey relational generation (data pre-processing), maxx0i ðkÞ is the largest value of x0i ðkÞ, minx0i ðkÞ is the smallest value of x0i ðkÞ and x0 is the desired value. 3.2. Grey relational coefficient and grey relational grade Following data pre-processing, a grey relational coefficient is calculated to express the relationship between the ideal and actual normalized experimental results. The grey relational coefficient can be expressed as follows [31]: xi ðkÞ ¼

Dmin þ z  Dmax , D0i ðkÞ þ z  Dmax

(5)

where D0i ðkÞ is the deviation sequence of the reference sequence x0 ðkÞ and the comparability sequence xi ðkÞ, namely D0i ðkÞ ¼ kx0 ðkÞ  xi ðkÞk, Dmax ¼ max max kx0 ðkÞ  xj ðkÞk, 8j2i

8k

Dmin ¼ min min kx0 ðkÞ  xj ðkÞk. 8j2i

8k

z is distinguishing or identification coefficient:z 2 ½0; 1. z ¼ 0:5 is generally used. After obtaining the grey relational coefficient, we normally take the average of the grey relational coefficient as the grey relational grade. The grey relational grade is defined as follows [28]: gi ¼

n 1X x ðkÞ. n k¼1 i

(6)

However, since in real application the effect of each factor on the system is not exactly same. Eq. (6) can be

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D01 ð2Þ ¼ jx0 ð2Þ  x1 ð2Þj ¼ j1:00  0:7559j ¼ 0:2441,

modified as gi ¼

n X

wk  xi ðkÞ

k¼1

991

n X

wk ¼ 1,

(7)

k¼1

where wk represents the normalized weighting value of factor k. Given the same weights, Eqs. (6) and (7) are equal. In the grey relational analysis, the grey relational grade is used to show the relationship among the sequences. If the two sequences are identical, then the value of grey relational grade is equal to 1. The grey relational grade also indicates the degree of influence that the comparability sequence could exert over the reference sequence. Therefore, if a particular comparability sequence is more important than the other comparability sequences to the reference sequence, then the grey relational grade for that comparability sequence and reference sequence will be higher than other grey relational grades [25]. 4. Analysis and discussion of experimental results In the present study, the workpiece surface roughness, top kerf width and width of HAZ in different pulsed laser cutting parameters and the experimental runs are listed in Table 3. Typically, lower values of the surface roughness, top kerf width and width of HAZ as the target values are desirable. Therefore, the data sequences have a the-smallerthe-better characteristic. The values of the surface roughness, top kerf width and width of HAZ are set to be the reference sequence x0 ðkÞ, k ¼ 1–3. Moreover, the results of 16 experiments were the comparability sequences xi ðkÞ, i ¼ 1; 2; . . . ; 16, k ¼ 1–3. Table 4 lists all of the sequences following data pre-processing using Eq. (2). Also, the deviation sequences D0i ; Dmax ðkÞ, and Dmin ðkÞ for i ¼ 1–16, k ¼ 1–3 can be calculated as follows: D01 ð1Þ ¼ jx0 ð1Þ  x1 ð1Þj ¼ j1:00  0:2411j ¼ 0:7589, Table 4 The sequences of each performance characteristic after data preprocessing

D01 ð3Þ ¼ jx0 ð3Þ  x1 ð3Þj ¼ j1:00  0:6227j ¼ 0:3773. So D01 ¼ ð0:7589; 0:2441; 0:3773Þ. The results of all D0i for i ¼ 1–16 are given in Table 5. Using Table 5, Dmax and Dmin can be found as follows: Dmax ¼ D04 ð1Þ ¼ D13 ð2Þ ¼ D09 ð3Þ ¼ 1:00, Dmin ¼ D14 ð1Þ ¼ D04 ð2Þ ¼ D04 ð3Þ ¼ 0:00. The distinguishing coefficient z can be substituted for the grey relational coefficient in Eq. (5). If all the process parameters have equal weighting, z is 0.5. Table 6 lists the grey relational coefficient and grade for each experiment of the L16 orthogonal array by applying Eqs. (5) and (6). Table 5 The deviation sequences Deviation sequences

D0i (1)

D0i (2)

D0i (3)

Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp.

0.7589 0.5847 0.8249 1.0000 0.5012 0.4702 0.5793 0.6296 0.2008 0.1042 0.2183 0.3638 0.1110 0.0000 0.1316 0.4060

0.2441 0.1497 0.0473 0.0000 0.4095 0.3623 0.3071 0.2599 0.7638 0.7008 0.6300 0.5906 1.0000 0.9134 0.8111 0.7481

0.3773 0.2358 0.1455 0.0000 0.9302 0.6377 0.3583 0.0014 1.0000 0.7814 0.5531 0.3556 0.6956 0.7038 0.7517 0.7021

no. no. no. no. no. no. no. no. no. no. no. no. no. no. no. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Table 6 The calculated grey relational coefficient and grey relational grade and its orders for 16 comparability sequences Exp.

Grey relational coefficient

Experimental no.

Surface roughness

Top kerf width

HAZ

no.

Reference sequence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1.0000 0.2411 0.4153 0.1751 0.0000 0.4988 0.5298 0.4207 0.3704 0.7992 0.8958 0.7817 0.6362 0.8890 1.0000 0.8684 0.5940

1.0000 0.7559 0.8503 0.9527 1.0000 0.5905 0.6377 0.6929 0.7401 0.2362 0.2992 0.3700 0.4094 0.0000 0.0866 0.1889 0.2519

1.0000 0.6227 0.7642 0.8545 1.0000 0.0698 0.3623 0.6417 0.9986 0.0000 0.2186 0.4469 0.6444 0.3044 0.2962 0.2483 0.2979

Ra (mm)

Kerf width (mm)

HAZ (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.3971 0.4609 0.3773 0.3333 0.4994 0.5153 0.4632 0.4426 0.7134 0.8275 0.6960 0.5788 0.8183 1.0000 0.7916 0.5518

0.6719 0.7695 0.9135 1.0000 0.5497 0.5798 0.6195 0.6579 0.3956 0.4163 0.4424 0.4584 0.3333 0.3537 0.3813 0.4006

0.5699 0.6795 0.7745 1.0000 0.3496 0.4394 0.5825 0.9972 0.3333 0.3901 0.4747 0.5843 0.4182 0.4153 0.3994 0.4159

Grey relational grade

Orders

0.5463 0.6366 0.6884 0.7777 0.4662 0.5115 0.5550 0.6992 0.4807 0.5446 0.5377 0.5405 0.5232 0.5896 0.5241 0.4561

7 4 3 1 15 13 6 2 14 8 10 9 12 5 11 16

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992

Grey relational grade

1 0.8 0.6 0.4 0.2 0 0

2

4

6 10 8 12 Experiment number

14

16

18

Fig. 2. Graph of grey relational grade.

gA1 ¼ 14ð0:5463 þ 0:6366 þ 0:6884 þ 0:7777Þ ¼ 0:6622,

Table 7 Response table for the grey relational grade Cutting parameters

A B

According to performed experiment design, it is clearly observed from Table 6 and Fig. 2 that the laser cutting parameters’ setting of experiment no. 4 has the highest grey relation grade. Thus, the fourth experiment gives the best multi-performance characteristics among the 16 experiments. The respond table of Taguchi method was employed here to calculate the average grey relational grade for each factor level. The procedure was to group the relational grades firstly by factor level for each column in the orthogonal array, and then to average them [30]. For example, the grey relational grades for factors A and B at level 1 can be calculated as follows:

gB1 ¼ 14ð0:5463 þ 0:4662 þ 0:4807 þ 0:5232Þ ¼ 0:5041.

Average grey relational grade by factor level Level 1

Level 2

Level 3

Level 4

Max–min

0.6622 0.5041

0.5579 0.5705

0.5258 0.5763

0.5232 0.6183*

0.1390 0.1142

 Optimal level.

Using the same method, calculations were performed for each factor level and response table was generated, as shown in Table 7. Since the grey relational grades represented the level of correlation between the reference and the comparability sequences, the larger grey relational grade means the comparability sequence exhibits a stronger

10 mm

10 mm

HAZ

Top kerf width

Fig. 3. The measured multi-performance characteristics of samples: (a) laser cut surface for initial cutting conditions; (b) laser cut surface for optimal cutting conditions; (c) top kerf width for initial cutting conditions; (d) top kerf width for optimal cutting conditions; (e) width of HAZ for initial cutting conditions; and (f) width of HAZ for optimal cutting conditions).

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A

993

B

0.68 0.66

Grey relational grade

0,64 0.62 0.60 0.58 0.56 0.54 0.52 0.50 A1

A2

A3 A4 B1 B2 Laser cutting parameter level

B3

B4

Fig. 4. Effect of laser cutting parameter levels on the multi-performance.

correlation with the reference sequence. Therefore, the comparability sequence has a larger value of grey relational grade for the surface roughness, top kerf width and width of HAZ. Based on this premise, this study selects the level that provides the largest average response. In Table 7, A1 and B4 show the largest value of grey relational grade for factors A and B, respectively. Therefore, A1B4 is the condition for the optimal parameter combination of the laser cutting process. Restated, laser power is 800 W and cutting speed is 55 mm/min. It is possible to find the difference between the initial and optimal machining performances in Fig. 3. The influence of each cutting parameter can be more clearly presented by means of the grey relational grade graph. The grey relational grade graph shows the change in the response, when the factors go for their level 1–level 4. The response graph for the cutting parameters of the laser cutting process is presented in Fig. 4. In this figure, the greater values give the low surface roughness, top kerf width and width of HAZ and dashed line indicates the value of the total mean of the grey relational grade. When the last column of Table 7 was compared, it is observed that the difference between the maximum and minimum value of the grey relational grade for factor A is bigger than factor B’s. This indicates that the laser power has stronger effect on the multi-performance characteristics than cutting speed factor. If the number of machining parameters increases, the importance of the controllable factors on the multi-performance characteristics will be determined by ordering max–min grade relational values. 5. Conclusion Use of the grey relational analysis to optimize the laser cutting process with the multiple-performance characteristics has been reported in this article. A grey relational analysis of the workpiece surface roughness, top kerf width

and width of HAZ obtained from the Taguchi method can convert optimization of the multiple-performance characteristics into optimization of a single performance characteristic called the grey relational grade. As a result, optimization of complicated multiple-performance characteristics can be greatly simplified through this approach. It is shown that the performance characteristics of the laser cutting process such as surface roughness, top kerf width and width of HAZ are improved together by using the method proposed by this study.

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