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Abstract

Laser processing of materials finds application in micro-nano devices mainly because of its accuracy, flexibility, and ability to machine almost any material. Although it offers numerous advantages, it is a complex process involving a large number of factors. The quality of machining often depends on the appropriate selection of parameters. Moreover, the output responses in machining processes have conflicting nature; some are to be minimized, and others have to be maximized. This work uses grey relationship analysis coupled with principal component analysis for multi-response optimization of conflicting responses during laser machining of micro-channels. Micro-channels with a cross-sectional size of 200 × 100 µm were created using Nd:YAG laser beam micro-milling in steel alloy (AISI 1045). The scan speed, layer thickness, and scan strategy were found to have a significant effect on the dimensional accuracy of the microchannel. At the same time, the material removal rate was mostly influenced by layer thickness. Multi-response optimization results suggest low pulse frequency, high scan speed, low layer thickness, and S3 scan strategy for accurately fabricating micro-channels.

Keywords

Nd-YAG laser micro-machining micro-channels multi-objective optimization steel

Introduction

With the micro and nano system-based sector booming, capacities are sky-rocketing, and costs are nose-diving; thus, a plethora of avenues and equally large challenges are being witnessed. Laser is, in fact, one of the most potential routes as it is optic power, easy to maneuver, compatible with automation, noncontact operation, and free from electromagnetic residue. Ablation of material from a part’s surface about a laser path directly generated from the computer-aided design (CAD) data makes the laser machining very effective for micromachining. But, many process parameters and machining strategies that affect the performance characteristics complicate the machining process.^1,2 While the pulse frequency, scanning speed, scanning strategy, peak power, and pulse width are among the significant parameters, the ratio of scanning speed to pulse frequency is a composite parameter (termed as overlap) which also significantly affects the vital responses, including roughness and accuracy. The machining application in sophisticated and high-end applications such as micro-fluidics and stents for biomedical use, components for MEMS, optical elements for photonics applications, etc., require the creation of precise micro-feature.³ The production of precise features of micro-scale requires machining with very tight tolerances, and machining accuracy becomes prime most important.^4–6

Conversely, long pulse lasers generate large-sized heat-affected zone (HAZ) due to greater heat accumulation during machining and multiple recast layers.⁷ Besides pulse length or duration, the laser scan track path is another critical parameter affecting heat accumulation apart from texture. Hung et al. machined medical needles 5.112 mm in diameter and 0.234 mm in thickness made from NiTi shape memory alloy. In addition, it demonstrated the ablation mechanism altered with the change in the laser scan path. Specific laser machining paths produced wider kerf widths enabling debris removal easier, significantly enhancing the ablation rate, and reducing the energy accumulation to less than 50%.⁸

Furthermore, while machining precision requires short pulse duration and high power density textured surfaces, the surface texture has also become an important response. The large-area-microstructured surfaces greatly increase contact angle at the liquid interface and enhance wettability in various liquid media, including water, oil, and oil-contaminated water. Ultra short pulses coupled with ultra-high power density and scanning pattern can effectively control the wettability of the machined surfaces.^9,10 Typical nano-structured surfaces on thin materials are important to photon exchange required in solar energy harnessing and proton exchange membrane fuel cells (PEMFC). The laser micromachining, thus, is vital for functional and functionally graded surface creation.¹¹

Change in wettability becomes important to micro/nanofluidics, which finds increasing application in the modern systems (micro-resonators, micro-sensors, micro-motors, micro-turbine, and micro-pumps, etc).^12,13 Lu et al.¹⁴ investigated the micro-texturing on cemented carbide workpiece using Nd:YAG laser. The friction performance of micro-textured surfaces was examined for different laser incident angles. It was reported that there was a reduction in the depth of micro textures, laser machining temperature, and residual compressive stress inside the micro textures were decreased. Monocrystalline diamonds were studied for micro-machining using a picosecond pulsed laser.¹⁵ The results revealed that the cracks propagated in a direction parallel to the top surface of the workpiece. The researchers suggested a method that can be utilized for low-cost polishing of diamond surfaces using laser micro-machining. Bhandari et al.¹⁶ presented a comparative study for the fabrication of micro-channels on Ti6Al4V using the laser ablation method and Laser-Induced Plasma Micro-Machining (LIPMM). It was reported that LIPMM resulted in better micro-channels fabrication in terms of aspect ratio and channel depth. Calabrese et al.¹⁷ compared the micro-milling process using laser and electrical discharge machining (EDM). Machining of various metals such as aluminum, titanium alloys, and stainless steel was performed. It was reported that laser machining showed better results in terms of material removal rate, though EDM provides good results in terms of geometrical accuracy. Vora et al.¹⁸ investigated the laser cutting process of Ti6Al4V. Taguchi design and Pareto techniques were utilized for multi-objective parameters optimization. Input parameters under consideration were laser power, cutting speed, and gas pressure. The output variables were kerf width, dross height, surface roughness, and material removal rate. The optimized values of the parameters were presented in the results.

Balachninaitė et al.¹⁹ utilized the Yb:KGW femtosecond laser system for micro-machining of steel and copper specimens. It was examined how the fluence affected the specific removal rates for steel and copper for single pulses and pulse bursts with various internal energy distributions. It was discovered that, in comparison to grooves ablated with single pulses, bursts generally result in much lower specific removal rates for steel and copper samples. In an another study of laser micro-machining to fabricate micro-channels, CO₂ laser system was employed.²⁰ To create straight microchannels, four laser system parameters—speed, power, focal distance, and number of passes were varied. The channels dimensional performance measures were studied for three different bio-compatible materials. The results revealed that polydimethylsiloxane (PDMS), and microscope glass micro-channels performed better than the polymethyl methacrylate (PMMA), in rapid cell adhesion experiments. Few comprehensive literature reviews about micro-channels fabrication,²¹ and use of laser for precise machining of engineering materials,²² also reported that laser machining is a viable and good option for micro-channels fabrication.

Micro-channels are required in several applications such as heat exchangers in aerospace, biomedical devices, automotive, gas-turbine blades, air-conditioning and refrigeration, micro-electronics, etc.²³ Laser machining, due to its advantages such as high material removal rate, ability to machine a wide range of machining, and precision, is a good choice for machining micro-channels, especially in difficult-to-cut materials.²⁴ The high-quality surfaces that may be achieved with laser machining, in particular, reduce liquid flow turbulence and prevent the formation of micro cavities, which are crucial for bacteria multiplication, is an added advantage in bio-medical device fabrications.²⁵ However, laser machining has its challenges also, such as more heat-affected zone.²⁶ Especially in micro-machining, where features are minuscule, the heat-affected zone is an important issue.²⁷ Therefore, it is crucial to investigate the laser input parameters for optimized results.

Thus, a very wide variety of quality and response parameters are essential for numerous applications, several of which belong to micro-products. There are also many laser machining parameters, which typically affect response characteristics and their contribution, and the influence on every response is different. Given this situation, comprehensive investigations with specific laser machining parameters shall be important to facilitate the development, progress, and effective use of laser machining on micro-products. The present research has been planned to investigate important Nd-YAG laser machining process parameters on responses while micro-machining AISI 1045 steel, and a multi-response optimization was also performed to arrive at a unitary index, which may be indicative of the overall optimized response set on a large number of input laser machining factors.

Materials and methods

Lasertec 40 from DMG (Deckel Maho Gildemeister, Germany) equipped with Q-switched Nd:YAG laser with a wavelength of 1064 nm and a maximum laser output of 30 W was employed for machining of AISI 1045 steel. In either the normalized or hot-rolled condition, AISI 1045 steel exhibits great strength and impact qualities as well as good weldability and machinability. It is widely employed in all industrial applications that call for greater wear resistance and strength, including crankshafts, gears, axles, torsion bars, connecting rods, sockets, studs, etc. The laser beam was operated in fundamental Gaussian mode (TEM₀₀) and was focused on the workpiece with the help of a Galvano scanner. The experimental setup is shown in Figure 1. The laser spot size and pulse width were kept constant at 30 μm and 10 μs, respectively. Table 1 shows the Lasertec 40 machining parameters.

Figure 1.

(a) DMG Lasertec 40 utilized in this research work and (b) schematic diagram of the laser setup.

Table 1.

Lasertec 40 specifications and parameters.

Machine type	Laser type	Laser source	Laser power	Pulse duration	Wavelength	Laser spot	Aperture size
Laser-based milling machine	Q-switched (pulsed)	Solid state (Nd:YAG)	30 W	10 µs	1064 nm	30 µm	30 µm
Focal length	Scanning field	Traverse speed (X/Y/Z)	Traverse acceleration	Work Area (X/Y/Z)	Focusing axis	Programming software	Control
100 mm	60 × 60 mm	250/250/200 mm/s	0.3 g	400/300/500 mm	Z	LpsWin	LaserSoft 3D

The micro-channel was designed in CAD software that was CATIA and later exported as stereolithographic (STL) format to Deskartes software and then to the machine software Lpswin for machine programming. The flow of file processing is depicted in Figure 2.

Figure 2.

The flow of file processing in various software for laser micro-machining.

Because the incoming laser beam focuses on the top surface of the workpiece during laser beam machining (LBM), the flatter the surface is, the more consistency in laser focusing is ensured. The focus distance is significantly unequal throughout the work surface when the workpiece has a high surface roughness. As a result, all of the specimens were mechanically ground to reduce the surface roughness to a level that would not cause severe unevenness during laser focusing. Following sample preparation, the samples were mounted on the machine table with the use of a fixture, and preliminary settings such as calibration, machine zero setup, and workpiece zero setup were completed.

Based on the IV optimal design methodology, 65 experimental runs were performed to determine the effect of laser process parameters on the quality of micromachining. The selected parameters and their respective levels are shown in Table 2.

Table 2.

Laser machining process parameters and their levels.

Factor	Name	Units	Levels of factors
Factor	Name	Units	1	2	3	4
A	Frequency	kHz	25	35	40
B	Scanning speed	mm/s	200	400	600
C	Layer thickness	μm	1	2	3
D	Track displacement	μm	8	10	12
E	Scan strategy	–	S1	S2	S3	S4

In order to determine the laser intensity that can achieve the desired layer thickness in each experimental run, preliminary tests were performed. After setting up the input process parameters viz frequency, scan speed, track displacement, and scan strategy, a test square cavity was machined with initial laser intensity for 20 laser scans. The resulting depth and depth per scan were evaluated using an automated touch probe. The laser intensity was varied accordingly until the desired layer thickness was achieved with good repeatability. The process flowchart is shown in Figure 3.

Figure 3.

Determining the laser intensity for the desired layer thickness and input parameter.

Frequency is the number of laser pulses per second, the scanning speed is the speed of laser beam scanning in mm/s, the layer thickness is the thickness of material removed during one complete scan, track displacement is the distance between two consecutive laser scan lines, and the scan strategy is the manner in which laser scans are maneuvered over the work surface. The scan strategy used in this work is in terms of hatch angles of the laser scans, as shown in Figure 4.

Figure 4.

Selected scan strategies and their respective angular orientations.

To systematically investigate the effects of laser process parameters on the quality of micro-channels, Optimal Design IV-based robust methodology was employed, and 65 laser-machining runs were performed. The micro-channels of dimension 0.2 × 0.1 × 5 mm were machined by simultaneously varying selected factors. The range of variables and levels is shown in Table 3.

Table 3.

Experiment design and measured responses.

Standard order	Run	Frequency (kHz)	Scan speed (mm/s)	Layer thickness (µm)	Track displacement (µm)	Scan strategy	Width error (µm), R1	Taper (°), R2	Recast layer (µm), R3	MRR (µm³/s), R4
34	1	40	200	2	8	S3	66.0	17.4	16.00	1,095,502.23
39	2	35	400	1	10	S3	50. 5	12.5	9.00	936,096.84
14	3	35	400	2	12	S1	35.7	12.9	10.00	1,539,979.71
19	4	40	600	1	8	S2	34.9	12.9	10.00	949,994.28
57	5	25	200	2	10	S4	73.4	17.8	12.50	1,389,905.43
54	6	35	600	3	8	S4	23.9	17.7	10.00	1,935,570.25
48	7	35	400	3	12	S3	45.4	17.6	12.00	2,258,138.77
2	8	25	600	1	8	S1	39.4	16.0	4.00	1,003,386.25
44	9	40	200	1	12	S3	60.7	14.7	12.30	727,703.00
6	10	40	600	3	8	S1	36.8	19.4	12.03	1,761,249.96
30	11	40	400	2	12	S2	57.7	15.5	14.00	2,173,317.33
7	12	40	400	1	10	S1	56.3	19.8	12.65	987,609.25
60	13	40	600	3	10	S4	50.0	18.3	17.41	2,258,399.12
16	14	40	200	3	12	S1	56.7	16. 8	30.45	2,284,041.98
58	15	40	400	2	10	S4	54. 7	14.75	19.03	1,936,700.41
8	16	40	200	2	10	S1	55.4	19. 45	23.57	1,354,951.82
56	17	25	400	1	10	S4	61.4	13.9	12.00	1,001,686.48
27	18	35	400	3	10	S2	62.7	18.9	15.82	2,247,685.38
24	19	35	600	1	10	S2	42.4	11.1	13.55	1,122,677.43
59	20	35	600	2	10	S4	54.7	17.0	14.07	1,876,653.92
51	21	35	400	1	8	S4	44.0	9.9	8.55	846,086.48
33	22	35	600	1	8	S3	28.0	9.8	6.00	896,486.37
26	23	40	200	3	10	S2	52.0	14.25	20.22	1,680,456.41
29	24	25	200	1	12	S2	59.7	14.8	8.77	859,297.42
5	25	35	400	3	8	S1	32.7	14.3	18.03	1,922,722.62
31	26	35	600	3	12	S2	22.0	16.5	12.25	2,500,966.88
49	27	40	600	3	12	S3	48.7	19.0	20.01	2,996,594.76
13	28	25	400	1	12	S1	42.0	15.7	8.07	1,204,153.72
35	29	35	400	2	8	S3	55.6	14.8	12.67	1,676,000.46
38	30	25	200	1	10	S3	58.0	10.8	10.3	878,244.24
1	31	40	200	1	8	S1	50.7	19.3	16.00	753,315.07
64	32	25	400	2	12	S4	50.0	15.2	11.12	1,831,405.96
46	33	35	200	2	12	S3	62.7	20.6	14.33	1,190,852.01
45	34	25	600	1	12	S3	31.7	10.2	10.00	999,219.44
37	35	40	400	3	8	S3	56.7	18.4	21.02	2,060,803.63
17	36	25	600	3	12	S1	66.7	21.15	8.60	2,442,676.34
10	37	25	200	3	10	S1	43.0	18.3	15.45	1,778,631.92
9	38	25	400	2	10	S1	35.3	20.8	17.89	1,500,961.43
11	39	35	600	3	10	S1	42.0	17.1	13.50	2,267,826.20
61	40	40	400	1	12	S4	78.3	16.0	14.11	1,187,618.20
43	41	25	400	3	10	S3	52.8	24.8	10.00	1,739,758.04
25	42	35	200	2	10	S2	79.3	18.4	13.66	1,392,919.94
23	43	25	400	1	10	S2	49.0	14.3	9.82	932,089.86
4	44	40	400	2	8	S1	37.0	16.8	12.72	1,519,996.45
52	45	40	600	1	8	S4	41.8	9.8	11.17	923,001.17
32	46	25	400	1	8	S3	48.0	11.1	12.77	818,002.15
12	47	35	200	1	12	S1	45.7	24.9	11.46	647,484.74
3	48	35	200	2	8	S1	44.1	21.7	14.89	1,173,458.45
21	49	35	600	2	8	S2	41.0	13.1	15.00	1,543,018.84
41	50	40	400	2	10	S3	59.0	20.0	17.53	1,756,348.72
22	51	25	400	3	8	S2	65.4	19.1	5.30	2,015,938.69
55	52	35	200	1	10	S4	80.0	17.2	17.56	850,540.72
36	53	25	600	2	8	S3	51.1	17.0	7.30	1,491,071.15
42	54	35	200	3	10	S3	88.7	16.4	19.00	1,943,411.11
40	55	40	600	1	10	S3	35.1	10.9	10.73	934,958.929
20	56	25	200	2	8	S2	80.1	19.9	13.36	1,332,910.99
65	57	25	400	3	12	S4	54.0	20.0	12.11	2,421,157.36
63	58	40	200	2	12	S4	85.4	21.1	14.27	1,600,062.98
18	59	35	200	1	8	S2	83.0	13.1	11.00	800,216.401
62	60	35	600	1	12	S4	51.0	10.1	8.90	1,133,303.76
53	61	40	200	3	8	S4	96.2	15.4	25.20	1,906,490.56
28	62	25	600	3	10	S2	54.2	22.8	15.30	2,442,450.86
15	63	40	600	2	12	S1	55.5	20.5	12.44	2,162,087.27
47	64	25	200	3	12	S3	71.9	17.6	8.00	2,293,916.13
50	65	25	200	1	8	S4	77.4	8.1	14.3	753,558.624

The machined channels were cut through the cross-section using Isomet 1000 precision saw from Buehler^®. After grinding, polishing, and etching they were viewed under Scanning Electron Microscope (SEM; JSM-6610LV, JEOL, Tokyo, Japan) in order to reveal the microstructure and thus the recast layer. The cross-sections were analyzed with respect to top width error, taper angle, recast layer thickness, and material removal rate (MRR). Top width error is the difference between the designed width and the actual measured width at the top of the channel. The taper angle is the angle of the channel wall with respect to the line perpendicular to the base surface of the channel, and recast layer thickness is the thickness of re-solidified molten material at the bottom of the channel. MRR is the volume of material removed in µm³ upon the machining time in second.

Results and analysis

Micro-channels were found to be uniform throughout the length of the channel. Figure 5 shows the laser machined specimen and sample in an epoxy mold for analysis.

Figure 5.

(a) Laser machined channels and (b) sample in the epoxy mold for analysis.

The SEM image of the channel cross-section and the recast layer on the channel base is shown in Figure 6(a) and (b), respectively.

Figure 6.

SEM images of (a) channel cross-section and (b) recast layer.

The measured responses R1, R2, R3, and R4, as mentioned in Table 3, may have a contradicting nature (i.e., some need to be maximized, whereas some need to be minimized). Moreover, a different response may be optimum for a different set of parameter combinations; consequently, a correct parameter setting that gives the best overall response is difficult to find. Under such a situation, multi-response optimization is helpful in which individual responses are suitably merged into a single multi-response characteristic. The contradicting relationship between input parameters with individual responses is tackled by converting the measured responses into a signal-to-noise ratio (S/N ratio). Consequently, the S/N ratio of these responses can be normally treated during subsequent analysis. Three methods for calculating S/N ratios depending on whether the responses should be minimized/maximized or nominal are defined as: Lower-the-better, Higher-the-better, and Nominal-the better, respectively. The method of calculation of the S/N ratio is discussed elsewhere.¹³ The S/N ratios of R1, R2, and R3 were Lower-the-better, while R4 was Higher-the-better. All measured responses and the calculated S/N ratios of every response are given in Tables 3 and 4, respectively.

Table 4.

The calculated SN ratio of the measured responses.

StdOrder	Run	A	B	C	D	E	S/N for responses
StdOrder	Run	A	B	C	D	E	R1	R2	R3	R4
34	1	3	1	2	1	3	−36.401	−24.815	−24.082	120.792
39	2	2	2	1	2	3	−34.065	−21.949	−19.085	119.426
14	3	2	2	2	3	1	−31.053	−22.221	−20	123.75
19	4	3	3	1	1	2	−30.847	−22.207	−20	119.554
57	5	1	1	2	2	4	−37.313	−25.008	−21.938	122.86
54	6	2	3	3	1	4	−27.553	−24.977	−20	125.736
48	7	2	2	3	3	3	−33.132	−24.89	−21.584	127.075
2	8	1	3	1	1	1	−31.9	−24.1	−12.041	120.029
44	9	3	1	1	3	3	−35.669	−23.322	−21.798	117.239
6	10	3	3	3	1	1	−31.308	−25.777	−21.605	124.916
30	11	3	2	2	3	2	−35.224	−23.828	−22.923	126.742
7	12	3	2	1	2	1	−35.016	−25.954	−22.042	119.892
60	13	3	3	3	2	4	−33.979	−25.235	−24.816	127.076
16	14	3	1	3	3	1	−35.067	−24.484	−29.67	127.174
58	15	3	2	2	2	4	−34.755	−23.334	−25.589	125.741
8	16	3	1	2	2	1	−34.862	−25.736	−27.447	122.638
56	17	1	2	1	2	4	−35.759	−22.836	−21.584	120.015
27	18	2	2	3	2	2	−35.941	−25.543	−23.984	127.035
24	19	2	3	1	2	2	−32.551	−20.92	−22.639	121.005
59	20	2	3	2	2	4	−34.755	−24.634	−22.966	125.468
51	21	2	2	1	1	4	−32.875	−19.949	−18.639	118.548
33	22	2	3	1	1	3	−28.943	−19.824	−15.563	119.051
26	23	3	1	3	2	2	−34.323	−23.031	−26.116	124.509
29	24	1	1	1	3	2	−35.515	−23.38	−18.86	118.683
5	25	2	2	3	1	1	−30.296	−23.097	−25.12	125.678
31	26	2	3	3	3	2	−26.848	−24.351	−21.763	127.962
49	27	3	3	3	3	3	−33.756	−25.551	−26.025	129.533
13	28	1	2	1	3	1	−32.466	−23.901	−18.137	121.614
35	29	2	2	2	1	3	−34.897	−23.418	−22.056	124.485
38	30	1	1	1	2	3	−35.27	−20.638	−20.257	118.872
1	31	3	1	1	1	1	−34.105	−25.726	−24.082	117.54
64	32	1	2	2	3	4	−33.982	−23.615	−20.922	125.256
46	33	2	1	2	3	3	−35.948	−26.29	−23.125	121.517
45	34	1	3	1	3	3	−30.021	−20.163	−20	119.993
37	35	3	2	3	1	3	−35.067	−25.291	−26.453	126.281
17	36	1	3	3	3	1	−36.48	−26.483	−18.69	127.757
10	37	1	1	3	2	1	−32.669	−25.266	−23.779	125.002
9	38	1	2	2	2	1	−30.965	−26.353	−25.052	123.527
11	39	2	3	3	2	1	−32.466	−24.636	−22.607	127.112
61	40	3	2	1	3	4	−37.875	−24.097	−22.991	121.494
43	41	1	2	3	2	3	−34.448	−27.9	−20	124.81
25	42	2	1	2	2	2	−37.988	−25.315	−22.709	122.879
23	43	1	2	1	2	2	−33.804	−23.083	−19.842	119.389
4	44	3	2	2	1	1	−31.376	−24.498	−22.09	123.637
52	45	3	3	1	1	4	−32.419	−19.788	−20.961	119.304
32	46	1	2	1	1	3	−33.628	−20.922	−22.124	118.255
12	47	2	1	1	3	1	−33.195	−27.912	−21.184	116.225
3	48	2	1	2	1	1	−32.88	−26.712	−23.458	121.389
21	49	2	3	2	1	2	−32.256	−22.348	−23.522	123.767
41	50	3	2	2	2	3	−35.42	−26.019	−24.876	124.892
22	51	1	2	3	1	2	−36.308	−25.642	−14.486	126.09
55	52	2	1	1	2	4	−38.062	−24.689	−24.89	118.594
36	53	1	3	2	1	3	−34.168	−24.628	−17.266	123.47
42	54	2	1	3	2	3	−38.958	−24.322	−25.575	125.771
40	55	3	3	1	2	3	−30.896	−20.75	−20.612	119.416
20	56	1	1	2	1	2	−38.068	−25.997	−22.516	122.496
65	57	1	2	3	3	4	−34.649	−26.042	−21.663	127.68
63	58	3	1	2	3	4	−38.625	−26.493	−23.088	124.083
18	59	2	1	1	1	2	−38.383	−22.378	−20.828	118.064
62	60	2	3	1	3	4	−34.151	−20.105	−18.988	121.087
53	61	3	1	3	1	4	−39.662	−23.758	−28.028	125.605
28	62	1	3	3	2	2	−34.68	−27.176	−23.694	127.757
15	63	3	3	2	3	1	−34.886	−26.256	−21.896	126.697
47	64	1	1	3	3	3	−37.135	−24.912	−18.062	127.212
50	65	1	1	1	1	4	−37.778	−18.203	−23.107	117.542

Analysis of variance

ANOVA tests with 95% confidence were performed to determine the significance of selected factors on the responses. Values of “Prob > F” less than 0.0500 indicate model terms are significant with an α of .05. Values greater than 0.1000 indicate the model terms are not significant. Table 5 shows the ANOVA results for width error. Scan speed, scan strategy, interaction of scan speed, scan strategy, and the interaction of scan speed and track displacement were found to have a significant effect on the dimensional error. Table 6 shows the ANOVA results for the taper response. Layer thickness and scan strategy were found to have significant effect on the taperness of the microchannel. In addition the interactions of layer thickness with frequency, scan speed and scan strategy were found to significantly influence the taper angle of the microchannel. Table 7 presents the ANOVA results for the response recast layer. It can be seen that scan speed and scan strategy have a significant effect on the recast layer formation. The interactions of frequency with layer thickness and track displacement in addition to the interaction of layer thickness and scan strategy have the significant effect on the recast layer. Table 8 presents the ANOVA results for MRR. Scan speed, layer thickness, and track displacement were found to have significant effect on the MRR.

Table 5.

ANOVA results for width error with respect to the selected parameters.

Source	Sum of squares	df	Mean square	F-value	p-Value
Source	Sum of squares	df	Mean square	F-value	Prob > F
Model	13,402.24	25	536.0895	6.5862	<0.0001 significant
A-frequency	132.4001	1	132.4001	1.6266	0.2097
B-scan Speed	5939.105	1	5939.1049	72.9653	<0.0001
C-layer Thickness	93.17978	1	93.1798	1.1448	0.2912
D-track displacement	19.0974	1	19.0974	0.2346	0.6308
E-scan strategy	2419.468	3	806.4893	9.9082	<0.0001
AB	205.7954	1	205.7954	2.5283	0.1199
AC	176.9848	1	176.9848	2.1744	0.1484
AD	198.2803	1	198.2803	2.4360	0.1267
AE	331.0726	3	110.3575	1.3558	0.2705
BC	14.4013	1	14.4013	0.1769	0.6763
BD	433.5097	1	433.5097	5.3259	0.0264
BE	2148.422	3	716.1407	8.7982	0.0001
CD	4.539415	1	4.5394	0.0558	0.8145
CE	461.1444	3	153.7148	1.8885	0.1475
DE	496.573	3	165.5243	2.0336	0.1250
Residual	3174.457	39	81.3963
Cor total	16,576.69	64

Table 6.

ANOVA results for taper with respect to the selected parameters.

Source	Sum of squares	df	Mean square	F value	P value
Source	Sum of squares	df	Mean square	F value	Prob > F
Model	696.6685	25	27.8667	4.7907	<0.0001 significant
A-frequency	0.2888	1	0.2888	0.0496	0.8248
B-scan speed	16.7702	1	16.7702	2.8830	0.0975
C-layer thickness	216.4824	1	216.4824	37.2162	<0.0001
D-track displacement	12.0463	1	12.0463	2.0709	0.1581
E-scan strategy	60.1772	3	20.0591	3.4484	0.0257
AB	4.8268	1	4.8268	0.8298	0.3679
AC	52.5410	1	52.5410	9.0325	0.0046
AD	6.4558	1	6.4558	1.1098	0.2986
AE	7.7262	3	2.5754	0.4427	0.7238
BC	54.5928	1	54.5928	9.3852	0.0040
BD	4.6525	1	4.6525	0.7998	0.3766
BE	5.1080	3	1.7027	0.2927	0.8304
CD	5.4348	1	5.4348	0.9343	0.3397
CE	118.3375	3	39.4458	6.7813	0.0009
DE	14.8685	3	4.9562	0.8520	0.4740
Residual	226.8587	39	5.8169
Cor total	923.5272	64

Table 7.

ANOVA results for recast layer with respect to the selected parameters.

Source	Sum of squares	df	Mean square	F value	P value
Source	Sum of squares	df	Mean square	F value	Prob > F
Model	3522.291	25	140.8916	4.9295	<0.0001 significant
A-frequency	34.03596	1	34.0360	1.1908	0.2819
B-scan speed	141.8904	1	141.8904	4.9645	0.0317
C-layer thickness	57.84958	1	57.8496	2.0240	0.1628
D-track displacement	6.912626	1	6.9126	0.2419	0.6256
E-scan strategy	1912.801	3	637.6002	22.3083	<0.0001
AB	94.3687	1	94.3687	3.3018	0.0769
AC	190.1961	1	190.1961	6.6546	0.0138
AD	111.8236	1	111.8236	3.9125	0.0550
AE	125.417	3	41.8057	1.4627	0.2396
BC	10.60154	1	10.6015	0.3709	0.5460
BD	81.52897	1	81.5290	2.8525	0.0992
BE	53.86206	3	17.9540	0.6282	0.6012
CD	54.3852	1	54.3852	1.9028	0.1756
CE	337.7005	3	112.5668	3.9385	0.0151
DE	135.4325	3	45.1442	1.5795	0.2098
Residual	1114.67	39	28.5813
Cor total	4636.961	64

Table 8.

ANOVA results for MRR with respect to the selected parameters.

Source	Sum of squares	df	Mean square	F value	P value
Source	Sum of squares	df	Mean square	F value	Prob > F
Model	1.93183E+13	7	2.75976E+12	80.1154	<0.0001 significant
A-frequency	27,360,439,244	1	27,360,439,244	0.7943	0.3766
B-scan speed	1.18987E+12	1	1.18987E+12	34.5417	<0.0001
C-layer thickness	1.57176E+13	1	1.57176E+13	456.2806	<0.0001
D-track displacement	1.16998E+12	1	1.16998E+12	33.9643	<0.0001
E-scan strategy	95,917,408,558	3	31,972,469,519	0.9282	0.4331
Residual	1.9635E+12	57	34,447,281,253
Cor total	2.12818E+13	64

Grey relational analysis

The S/N ratios of these can now be normally treated during conversion into a unified multi-criteria characteristic. The multi-criteria characteristic was obtained through Grey relational analysis-based principal component analysis or Grey-PCA.^28,29 Grey relational analysis obtains a normalized sequence of S/N ratios in which the data of all the responses become comparable between a normalized range of zero and one. The normalized S/N ratio x_ij for the ith performance characteristic in the jth experiment can be expressed as in equation (1).

x_{ij} = \frac{η_{ij} - {min}_{j} η_{ij}}{{max}_{j} η_{ij} - {min}_{j} η_{ij}}

(1)

In the next step of the grey relational analysis, the normalized sequence is converted into a deviation sequence by subtracting it from 1. The normalized and deviation sequences of the S/N ratios are given in Table 9. The deviation sequence is further processed to obtain a grey relational coefficient (GRC). The GRC ξ_ij for the ith response in the jth experiment can be expressed as per equation (2).

ξ_{ij} = \frac{{min}_{i} {min}_{j} | x_{i}^{o} - x_{ij} | + ξ {max}_{i} {max}_{j} | x_{i}^{o} - x_{ij} |}{| x_{i}^{o} - x_{ij} | + ξ {max}_{i} {max}_{j} | x_{i}^{o} - x_{ij} |}

(2)

Table 9.

Normalized and deviation sequences.

StdOrder	Run	Normalized sequences				Deviation sequences for responses
StdOrder	Run	R1	R2	R3	R4	R1	R2	R3	R4
34	1	0.2544	0.3190	0.3170	0.3432	0.7456	0.6810	0.6830	0.6568
39	2	0.4368	0.6142	0.6005	0.2406	0.5632	0.3858	0.3995	0.7594
14	3	0.6718	0.5862	0.5485	0.5655	0.3282	0.4138	0.4515	0.4345
19	4	0.6880	0.5876	0.5485	0.2502	0.3120	0.4124	0.4515	0.7498
57	5	0.1833	0.2991	0.4386	0.4986	0.8167	0.7009	0.5614	0.5014
54	6	0.9450	0.3023	0.5485	0.7147	0.0550	0.6977	0.4515	0.2853
48	7	0.5096	0.3112	0.4587	0.8153	0.4904	0.6888	0.5413	0.1847
2	8	0.6057	0.3926	1.0000	0.2859	0.3943	0.6074	0.0000	0.7141
44	9	0.3116	0.4727	0.4465	0.0762	0.6884	0.5273	0.5535	0.9238
6	10	0.6520	0.2199	0.4575	0.6531	0.3480	0.7801	0.5425	0.3469
30	11	0.3464	0.4206	0.3828	0.7903	0.6536	0.5794	0.6172	0.2097
7	12	0.3625	0.2016	0.4327	0.2756	0.6375	0.7984	0.5673	0.7244
60	13	0.4435	0.2757	0.2754	0.8154	0.5565	0.7243	0.7246	0.1846
16	14	0.3586	0.3530	0.0000	0.8228	0.6414	0.6470	1.0000	0.1772
58	15	0.3829	0.4715	0.2315	0.7151	0.6171	0.5285	0.7685	0.2849
8	16	0.3746	0.2242	0.1261	0.4820	0.6254	0.7758	0.8739	0.5180
56	17	0.3046	0.5229	0.4587	0.2848	0.6954	0.4771	0.5413	0.7152
27	18	0.2904	0.2440	0.3225	0.8123	0.7096	0.7560	0.6775	0.1877
24	19	0.5549	0.7202	0.3989	0.3592	0.4451	0.2798	0.6011	0.6408
59	20	0.3829	0.3376	0.3803	0.6946	0.6171	0.6624	0.6197	0.3054
51	21	0.5297	0.8202	0.6257	0.1746	0.4703	0.1798	0.3743	0.8254
33	22	0.8365	0.8331	0.8002	0.2124	0.1635	0.1669	0.1998	0.7876
26	23	0.4166	0.5028	0.2016	0.6225	0.5834	0.4972	0.7984	0.3775
29	24	0.3236	0.4668	0.6132	0.1847	0.6764	0.5332	0.3868	0.8153
5	25	0.7309	0.4959	0.2581	0.7104	0.2691	0.5041	0.7419	0.2896
31	26	1.0000	0.3668	0.4486	0.8820	0.0000	0.6332	0.5514	0.1180
49	27	0.4609	0.2432	0.2068	1.0000	0.5391	0.7568	0.7932	0.0000
13	28	0.5616	0.4131	0.6542	0.4049	0.4384	0.5869	0.3458	0.5951
35	29	0.3719	0.4629	0.4319	0.6207	0.6281	0.5371	0.5681	0.3793
38	30	0.3427	0.7492	0.5340	0.1990	0.6573	0.2508	0.4660	0.8010
1	31	0.4336	0.2252	0.3170	0.0988	0.5664	0.7748	0.6830	0.9012
64	32	0.4433	0.4426	0.4962	0.6786	0.5567	0.5574	0.5038	0.3214
46	33	0.2898	0.1671	0.3713	0.3977	0.7102	0.8329	0.6287	0.6023
45	34	0.7524	0.7981	0.5485	0.2832	0.2476	0.2019	0.4515	0.7168
37	35	0.3586	0.2700	0.1825	0.7556	0.6414	0.7300	0.8175	0.2444
17	36	0.2483	0.1472	0.6229	0.8666	0.7517	0.8528	0.3771	0.1334
10	37	0.5457	0.2726	0.3342	0.6595	0.4543	0.7274	0.6658	0.3405
9	38	0.6787	0.1605	0.2620	0.5488	0.3213	0.8395	0.7380	0.4512
11	39	0.5616	0.3375	0.4007	0.8181	0.4384	0.6625	0.5993	0.1819
61	40	0.1394	0.3930	0.3789	0.3959	0.8606	0.6070	0.6211	0.6041
43	41	0.4069	0.0012	0.5485	0.6451	0.5931	0.9988	0.4515	0.3549
25	42	0.1306	0.2675	0.3949	0.5000	0.8694	0.7325	0.6051	0.5000
23	43	0.4572	0.4974	0.5575	0.2378	0.5428	0.5026	0.4425	0.7622
4	44	0.6467	0.3517	0.4300	0.5570	0.3533	0.6483	0.5700	0.4430
52	45	0.5652	0.8368	0.4940	0.2314	0.4348	0.1632	0.5060	0.7686
32	46	0.4709	0.7200	0.4281	0.1526	0.5291	0.2800	0.5719	0.8474
12	47	0.5047	0.0000	0.4814	0.0000	0.4953	1.0000	0.5186	1.0000
3	48	0.5292	0.1236	0.3524	0.3881	0.4708	0.8764	0.6476	0.6119
21	49	0.5780	0.5731	0.3488	0.5668	0.4220	0.4269	0.6512	0.4332
41	50	0.3310	0.1950	0.2720	0.6513	0.6690	0.8050	0.7280	0.3487
22	51	0.2618	0.2338	0.8613	0.7413	0.7382	0.7662	0.1387	0.2587
55	52	0.1249	0.3320	0.2711	0.1780	0.8751	0.6680	0.7289	0.8220
36	53	0.4287	0.3382	0.7036	0.5444	0.5713	0.6618	0.2964	0.4556
42	54	0.0549	0.3698	0.2323	0.7174	0.9451	0.6302	0.7677	0.2826
40	55	0.6841	0.7377	0.5138	0.2398	0.3159	0.2623	0.4862	0.7602
20	56	0.1244	0.1972	0.4058	0.4713	0.8756	0.8028	0.5942	0.5287
65	57	0.3912	0.1926	0.4542	0.8608	0.6088	0.8074	0.5458	0.1392
63	58	0.0809	0.1461	0.3734	0.5905	0.9191	0.8539	0.6266	0.4095
18	59	0.0998	0.5700	0.5016	0.1382	0.9002	0.4300	0.4984	0.8618
62	60	0.4300	0.8041	0.6060	0.3654	0.5700	0.1959	0.3940	0.6346
53	61	0.0000	0.4278	0.0932	0.7048	1.0000	0.5722	0.9068	0.2952
28	62	0.3888	0.0758	0.3390	0.8665	0.6112	0.9242	0.6610	0.1335
15	63	0.3727	0.1706	0.4410	0.7870	0.6273	0.8294	0.5590	0.2130
47	64	0.1972	0.3090	0.6585	0.8256	0.8028	0.6910	0.3415	0.1744
50	65	0.1470	1.0000	0.3723	0.0990	0.8530	0.0000	0.6277	0.9010

In equation (2), x_i^o is the ideal normalized S/N ratio for the ith performance characteristic and ξ distinguishing coefficient which is defined in the range 0 ≤ ξ ≤ 1, and it is usually taken as 0.5. The values of GRC as calculated by equation (2) and given in Table 7 although lie within the comparable range of zero-to-one but are still unique to individual responses. The GRCs of individual responses should be combined effectively to obtain a single multi-response characteristic. During aggregation of individual GRCs, weightings which commensurate with their contribution in the multi-response must be applied. There are various methods by which weightings can be established, a large number of which are subjective in nature. But the principal component analysis (PCA) effectively establishes the inherence contribution of the individual GRCs through statistical processing without subjectivity.

Thus, in this work, grey relational analysis coupled with principal component analysis (Grey-PCA) is employed to simplify the selection of input parameters, resulting in the best overall quality represented by a single multi-response characteristic.

Principal component analysis

To determine the weightings of individual responses, GRC PCA was employed. Processing of GRC for the PCA simplifies a large number of correlated variables into fewer independent principal components based on which the weighting is determined. During processing, the elements of the GRC data matrix are transformed into corresponding eigenvalues through which the principal components are calculated.

A step-by-step procedure of the Grey-PCA is given in Abidi et al.²⁸ As per the procedure, during PCA, the array of GRC is processed to generate the covariance coefficients (R_jl) as per equation (3).

R_{jl} = (\frac{Cov ((x_{i} (j), x_{i} (l)))}{σ_{(x_{i})} (j) \times σ_{(x_{i})} (l)}), j = 1, 2, 3, \cdot \cdot \cdot, n; l = 1, 2, 3, \cdot \cdot \cdot, n

(3)

where, in x_i_(l) is the element of GRC array, (Cov(x_i(j), x_i(l))) is the covariance of sequences x_i(j) and x_i(l); σ_(xi)(j) is the standard deviation of sequence x_i(j); σ_(xi)(l) is the standard deviation of sequence x_i(l). The covariance matrix generated by utilizing equation (3) is given in Table 10.

Table 10.

Grey relational coefficients and the grey relational coefficients and Grades.

StdOrder	Run	Grey relational coefficients				Grade	Rank
StdOrder	Run	R1	R2	R3	R4	Grade	Rank
34	1	0.4014	0.4234	0.4226	0.4322	0.4229	48
39	2	0.4703	0.5645	0.5558	0.3970	0.5565	11
14	3	0.6037	0.5472	0.5255	0.5350	0.5323	16
19	4	0.6157	0.5480	0.5255	0.4001	0.5311	17
57	5	0.3797	0.4164	0.4711	0.4993	0.4544	34
54	6	0.9009	0.4175	0.5255	0.6367	0.4945	23
48	7	0.5049	0.4206	0.4802	0.7303	0.4647	31
2	8	0.5591	0.4515	1.0000	0.4118	0.8254	1
44	9	0.4207	0.4867	0.4746	0.3512	0.4768	26
6	10	0.5896	0.3906	0.4796	0.5904	0.4538	35
30	11	0.4334	0.4632	0.4475	0.7046	0.4550	33
7	12	0.4396	0.3851	0.4685	0.4083	0.4423	41
60	13	0.4732	0.4084	0.4083	0.7304	0.4119	56
16	14	0.4381	0.4359	0.3333	0.7383	0.3691	65
58	15	0.4476	0.4862	0.3942	0.6370	0.4249	46
8	16	0.4443	0.3919	0.3639	0.4911	0.3739	64
56	17	0.4183	0.5117	0.4802	0.4115	0.4888	25
27	18	0.4133	0.3981	0.4246	0.7271	0.4197	52
24	19	0.5291	0.6412	0.4541	0.4383	0.5110	20
59	20	0.4476	0.4301	0.4466	0.6208	0.4434	40
51	21	0.5153	0.7356	0.5719	0.3772	0.6194	5
33	22	0.7536	0.7497	0.7145	0.3883	0.7217	2
26	23	0.4615	0.5014	0.3851	0.5698	0.4226	49
29	24	0.4250	0.4839	0.5638	0.3801	0.5371	15
5	25	0.6501	0.4980	0.4026	0.6332	0.4346	45
31	26	1.0000	0.4412	0.4755	0.8091	0.4697	28
49	27	0.4812	0.3978	0.3866	1.0000	0.3968	60
13	28	0.5328	0.4600	0.5912	0.4566	0.5495	13
35	29	0.4432	0.4821	0.4681	0.5687	0.4734	27
38	30	0.4321	0.6660	0.5176	0.3843	0.5611	10
1	31	0.4689	0.3922	0.4226	0.3568	0.4127	55
64	32	0.4732	0.4729	0.4981	0.6087	0.4915	24
46	33	0.4132	0.3751	0.4430	0.4536	0.4223	50
45	34	0.6688	0.7124	0.5255	0.4109	0.5814	7
37	35	0.4381	0.4065	0.3795	0.6717	0.3909	63
17	36	0.3995	0.3696	0.5700	0.7894	0.5109	21
10	37	0.5240	0.4074	0.4289	0.5949	0.4242	47
9	38	0.6088	0.3733	0.4039	0.5256	0.3962	61
11	39	0.5328	0.4301	0.4548	0.7333	0.4504	37
61	40	0.3675	0.4517	0.4460	0.4529	0.4476	38
43	41	0.4574	0.3336	0.5255	0.5849	0.4674	30
25	42	0.3651	0.4057	0.4524	0.5000	0.4385	43
23	43	0.4795	0.4987	0.5305	0.3961	0.5192	18
4	44	0.5859	0.4354	0.4673	0.5302	0.4584	32
52	45	0.5349	0.7539	0.4970	0.3941	0.5742	8
32	46	0.4858	0.6410	0.4664	0.3711	0.5186	19
12	47	0.5024	0.3333	0.4909	0.3333	0.4411	42
3	48	0.5151	0.3633	0.4357	0.4497	0.4139	53
21	49	0.5423	0.5394	0.4343	0.5358	0.4676	29
41	50	0.4277	0.3831	0.4072	0.5891	0.4018	59
22	51	0.4038	0.3949	0.7829	0.6590	0.6624	4
55	52	0.3636	0.4281	0.4069	0.3782	0.4129	54
36	53	0.4667	0.4304	0.6278	0.5233	0.5661	9
42	54	0.3460	0.4424	0.3944	0.6389	0.4115	57
40	55	0.6128	0.6559	0.5070	0.3968	0.5513	12
20	56	0.3635	0.3838	0.4570	0.4860	0.4347	44
65	57	0.4509	0.3824	0.4781	0.7823	0.4521	36
63	58	0.3523	0.3693	0.4438	0.5497	0.4220	51
18	59	0.3571	0.5376	0.5008	0.3672	0.5102	22
62	60	0.4673	0.7185	0.5593	0.4407	0.6062	6
53	61	0.3333	0.4663	0.3554	0.6288	0.3921	62
28	62	0.4500	0.3511	0.4307	0.7893	0.410	58
15	63	0.4435	0.3761	0.4721	0.7012	0.4452	39
47	64	0.3838	0.4198	0.5942	0.7414	0.5421	14
50	65	0.3695	1.0000	0.4434	0.3569	0.6756	3

The covariance matrix, as given in Table 11, was used to find eigenvectors corresponding to each eigenvalue, and the same is listed in Table 12. The eigenvectors of the eigenvalue of the covariance matrix are aligned in descending order and represent the principal components. The first principal component accounts for the most variance in the data, and its square is taken as the weighting of the corresponding performance characteristic.

Table 11.

Covariance matrix.

Response	R1	R2	R3	R4
R1	70,233.71	70,908.08	85,516.55	58,632.3
R2	70,908.08	66,107.08	83,703.52	59,195.21
R3	85,516.55	83,703.52	102,526.8	71,390.56
R4	58,632.3	59,195.21	71,390.56	1,939,699

Table 12.

Eigen values and explained variations.

Principal components	Eigen value
First	1,554,679.111
Second	213,117.348
Third	−888.944
Fourth	2398.535

The contributions of width error, taper, recast layer, and MRR are shown in Table 13. These contributions are indicated as 0.002025, 0.304704, 0.682276, and 0.010816. The weighting coefficients (or contributions) w1, w2, w3, and w4 (i.e., w_k, k = 1–4) were thereby set as 0.002025, 0.304704, 0.682276, and 0.010816, respectively. After the weighting factors w_k the single multi-performance characteristic that is, grey relational-PCA grade GRG ( $γ_{i}$ ) is obtained as per equation (4).

γ_{i} = \sum_{k = 1}^{n} w_{k \cdot x_{i} (k)}

(4)

Table 13.

Eigenvectors for principal components and contributions of corresponding responses.

Parameter	Response	First principal components	Contributions
Width error	R1	0.045	0.002025
Taper	R2	−0.552	0.304704
Recast layer	R3	0.826	0.682276
MRR	R4	0.104	0.010816

Based on equation (4) and data listed in Table 4, the GRGs were calculated as shown in Table 10. Thus, the optimization design performed with respect to a single multi-criteria grey relational-PCA grade simplifies the complexities arising from the contradicting nature and varied levels of significance of individual responses. A plot of GRG with respect to standard experiment order is given in Figure 7, which depicts how the GRC pans out across an entire range of experiments.

Figure 7.

Scan strategy employed during laser machining.

Analysis of means (ANOM)

The single multi-criteria characteristic represented by the GRG makes optimizing the experimental conditions within the selected range of process parameters easy. Analysis of means (ANOM) was performed to find the condition for the highest GRG. The ANOM was performed by calculating the level-wise average of the GRG for all the laser micromachining process parameters. The ANOM plot is given in Figure 8. The ANOV is a simple statistical analysis technique to find optimized machining conditions by identifying the sequence of levels of factors that give the highest GRG values. The ANOM gives that the average values of GRG for the laser machining process parameters are highest for factor A at level-1, Factor-B at level-3, factor C at level-1, factor D at level-1, and factor E at level-3. Thus, the optimum process parameter condition for the laser micro machining can be identified as A1B3C1D1E3. Table 14 presents the confirmation experiments for the first few optimum process conditions based on the grey relational grade and rank.

Figure 8.

Effect of levels of laser micro machining process parameters on the RGR.

Table 14.

Confirmation experiments for the optimum process conditions.

Rank	Freq. (kHz)	Scan speed (mm/s)	Layer thick. (µm)	Track disp. (µm)	Scan stragy.	Width error (µm)		Taper (°)		Recast layer (µm)		MRR (µm³/s)
Rank	Freq. (kHz)	Scan speed (mm/s)	Layer thick. (µm)	Track disp. (µm)	Scan stragy.	Actual	Predict.	Actual	Predict.	Actual	Predict.	Actual	Predict.
1	25	600	1	8	S1	39.4	40.2	16.0	15.3	38.9	33.1	1,003,386.2	968,198.8
2	35	600	1	8	S3	28.0	34.0	9.8	10.6	55.1	54.7	896,486.4	968,198.8
3	25	200	1	8	S4	77.4	82.4	8.1	13.4	44.4	46.1	753,558.6	624,943.6
4	25	400	3	8	S2	65.4	55.3	19.1	20.1	44.1	45.2	2,015,938.7	1,989,838.5

Discussion

The laser fluence greatly varies across the focal cross-section from the center to its maximum expanse. The fluence is maximum at the center and fades out at the periphery. The ablation occurs over in the focal plane over the width where the fluence exceeds the threshold. The threshold fluence is found to depend on the pulse frequency, and the two have an inverse kind of relation.³⁰ The ablation is deeper near the center due to fluence being intense. The variation in tracks formed by the array of ablation during laser scans generates the footprints of the width and depth errors during machining.³¹ The variation in the depth for a given width results in the taper, which in turn causes variation in the surface roughness. The aggregated width and depth errors which themselves are mutually related, are also directly related to the surface roughness.³² An error in the width of the track, its depth, and taper in the wall of the track; all are responsible for the machining errors. It is found that width error is mainly affected by the scanning speed, whereas the layer thickness mainly affects taper angle and is consequently primarily responsible for the taper.

The statistically determined Grey-PCA weightings for all responses (width error, taper, recast layer, and MRR) established that the contribution of width error on the multi-response characteristics is negligible (0.002025) and that of MRR is significantly less (0.018016), whereas for rest of the two responses the contribution is high. It may be attributed to the combined effect of the individual input process parameters within the selected range. The variation in the values of levels of numeric parameters within the feasible ranges is 40%, 100%,100%, and 25% for frequency (A), scanning speed (B), layer thickness (C), and track displacement (D), respectively. Moreover, these parameters have a mutual interaction effect, some of which are cumulative and some conflicting. Evidently, rastering of beam over narrow track displacement may result in the overlap of the width of ablation between successive scans and consequently result in effects of all process parameters on the MRR and width of ablation (and hence the width error too) to reduce significantly. Narrow track displacement also results in more profound ablating action and accounts for greater variations in the taper angle. Level-wise variations in the values of scanning speed and layer thickness are the highest among all process parameters.

Further, the scan strategy is non-numeric in nature, but it has a significant impact on the total number of scans, total scan time, and the start-to-finish order of successive layers has a considerable effect on net energy input in each of the strategies. Reversal of order (of start to finish) direction of scans provides less time for energy dissipation and causes higher net energy input. The number of breaks in scans is least for hatch angles 0° and 180°, highest for 90° and 270°. The optimized scan strategy thus evens out the breaks in scans, resulting in a more stabilized energy supply during laser micro-machining.

Conclusions

Optimal design IV methodology, along with GRA and PCA, has proved to be a valuable tool in comprehending the effects of laser process parameters on the performance measures during laser machining of micro-channels in AISI 1045 steel. The following conclusion can be drawn from the study:

Scan strategy and scan speed were found to have a significant effect on the dimensional accuracy of the micro-channels.

Taper angle was found to increase significantly with an increase in layer thickness due to an increase in the laser fluence.

Low layer thickness and moderate pulse frequency resulted in micro-channels with the least recast layer thickness.

Multi-response optimization is characterized by low pulse frequency, high scan speed, low layer thickness, and S3 scan strategy.

Footnotes

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors extend their appreciation to King Saud University for funding this work through Researchers Supporting Project number (RSP2022R499), King Saud University, Riyadh, Saudi Arabia.

ORCID iD

Mustufa Haider Abidi

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Multi-objective optimization of Nd:Yag laser machining’s conflicting responses while milling micro-channels

Abstract

Keywords

Introduction

Materials and methods

Results and analysis

Analysis of variance

Grey relational analysis

Principal component analysis

Analysis of means (ANOM)

Discussion

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References