Optimization of Femtosecond Laser Drilling Process for DD6 Single Crystal Alloy

Abstract

In this paper, we explore the optimal combination of femtosecond laser drilling parameters for micro-hole processing on DD6 single-crystal high-temperature alloy and analyze the significance of parameter variations on the microstructure characteristics of the holes. The L25(56) orthogonal test was performed by controlling six parameters during femtosecond laser ring processing: average power; overlap rate; defocus rate; feed amount; gas pressure; and end position. The significance of the influence of the factors was analyzed by ANOVA, and the parameters were optimized by genetic algorithm. Scanning electron microscopy was performed on the micropores and the salient features of the pores were analyzed. Finally, we calculated the extreme differences and conducted single-factor effect analysis. We conclude that the defocus rate has the most significant level on the hole drilling by femtosecond laser ring processing for DD6 single crystal high-temperature alloy; and the effect of the end position is smaller than others. The optimized parameters are power 6.73 W; overlap 99%, defocus 0 mm; pressure 0.2 MPa; feed 0.02 mm, and end −0.4 mm.

1. Introduction

DD6 single crystal high-temperature alloy has become a key material in the aerospace industry because of its high-temperature strength, good organizational stability, and excellent overall performance, and is widely used in turbine blades and other hot-end components of aero engines [1,2]. As aircraft engines continue to develop to a higher level, the efficiency and thrust-to-weight ratio continue to improve the service temperature of the turbine blades and has put forward higher requirements [3]. The air film hole cooling technology is the main cooling technology applied to engine blades at this stage. However, the air film hole processing is prone to thermal effects, forming micro-cracks, remelting recast layers, and other defects, causing some damage to the surface integrity of the air film cooling hole [4,5,6,7]. Femtosecond laser pulse widths are extremely short, thus preventing thermal diffusion, and it has a minimal thermal effect on the material compared to conventional processes. For DD6 alloy, the electrical discharge machining process is prone to fatigue cracks on both sides of the gas film hole, while the laser hole-making process is more likely to have one-sided fatigue cracks. Internal defects in the recast layer and radial cracks are the most important factors leading to failure [8]. So, the femtosecond laser can process small holes without significant impact around the hole, and unique small hole features can be obtained by controlling the laser parameters. Therefore, for complex hot-end components inside aero-engines, such as high-pressure turbine blades where thousands of gas film holes need to be prepared, micro-hole processing by femtosecond laser on DD6 nickel-based single crystal alloy is of interest [9,10,11].

The effect of current femtosecond laser parameters on single-crystal high-temperature alloys has been studied by scholars to some extent. It has been shown that the diameter increases with increasing single pulse energy in the range of 80 μJ to 130 μJ [12]. The entrance and exit diameters and roundness tend to be stable, while the taper exhibits a slight variation. The defocus rate has a significant effect on the characteristics of the micropores. With the increase of the defocusing rate, the diameter changed considerably. Zhai [13] et al. found a good linear relationship between the number of pulses of the femtosecond laser and the size of the processed nickel-based single crystal material in their study, with the hole diameter becoming larger with an increasing number of pulses. By observing the surface morphology of the sample after the action of femtosecond laser with DD6 single crystal high-temperature alloy, Yu [14] et al. divided the orifice of the small hole processed by femtosecond laser into four regions: ablation region, melting region, laser-induced region, and radiation region, and the mechanism of laser action in different regions is different. In the actual processing, it is not only necessary to select reasonable laser parameters to ensure the processing quality of the micro-hole, but also to select a suitable processing method according to the characteristics of the material and the requirements for the micro-hole [15]. However, the influence law of each laser parameter on the micro-hole quality (such as taper, orifice morphology, etc.) when processing small holes on DD6 alloy by femtosecond laser is still unclear and needs to be studied systematically.

Related studies have shown that changes in important parameters, such as the average power of the laser, overlap rate, and defocus amount, affect the quality of small holes when processing them with femtosecond lasers [16,17,18,19,20,21,22,23,24,25]. There are many factors that affect the quality of laser hole making during processing, and the test could not test all combinations of factors at the same time. So, in this paper, five different sets of test variables under six parameters (average power A, overlap rate B, defocus rate C, feed amount D, gas pressure E, and end position F) were mainly chosen for the experimental study. The relationship between the structural characteristics of the small holes and the femtosecond laser parameters was investigated using the orthogonal test method, and the optimized parameters were subsequently obtained by processing the laser parameters. The experimental results can provide a theoretical basis and guidance for small-hole processing by femtosecond laser on DD6 single-crystal high-temperature alloy.

2. Materials and Methods

2.1. Experiment Material

In this experiment, DD6 single crystal high-temperature alloy of 20 mm in length, 15 mm in width, and 2 mm in thickness was chosen as the base material, and its chemical composition (in mass fraction) is shown in

Table 1. Chemical composition of the DD6 single crystal alloy used in this study.

Element	Cr	Ta	W	Mo	Re	Al	Nb	Hf	Ni
Content	4.50	6.78	7.36	2.00	2.04	5.68	1.01	0.10	bal

.

The microscopic morphology of the sample was observed under the scanning electron microscope (SEM), as shown in Figure 1. It can be observed that the DD6 single crystal high-temperature alloy is mainly composed of γ’ phase and γ phase, where the size of γ’ phase is relatively uniform and no fine secondary γ’ phase is precipitated.

2.2. Hole-Making Process

The experiment uses a femtosecond laser processing system developed solely by Xi’an Institute of Optical Precision, which consists of four main parts: lasers equipment, processing table equipment, computer control equipment, and software system. The optical path diagram is shown in Figure 2. The laser output device is mainly responsible for the laser beam output, as well as the focusing process at the processing platform, which is the core part to realize the micro processing of materials. The processing table is responsible for carrying the sample, which is fixed on the platform. The computer control equipment sends corresponding commands, which can control the table to move along the X, Y, and Z axes, control the on and off of the beam through the optical switch. We use the software system to realize various processing methods, such as micro-hole processing and surface processing. The laser used in the processing is the PHAROS series (Light Conversion Inc, Vilnius, Lithuania).

The experimental laser hole-making method is spiral processing, the main processing process is shown in Figure 3. The test was performed in three stages, where the laser beam was emitted from the top accompanied by an auxiliary gas, and the sample was placed on a movable stage, where the holes were processed sequentially with radius R1, R2, and R3, and at the end of which the holes were processed at the bottom at a set speed for 10 s. In this paper, repeated orthogonal tests were conducted according to the parameters in the factor level table in

Table 2. Factors and levels.

Levels	Factors
	Power A (W)	Overlap B (%)	Defocus C (mm)	Pressure D (MPa)	Feed E (mm)	End F (mm)
1	6.73	87	−0.4	0.20	0.010	−0.4
2	7.84	90	−0.2	0.25	0.015	−0.2
3	8.96	93	0.0	0.30	0.020	0.0
4	10.05	96	0.2	0.35	0.025	0.2
5	11.18	99	0.4	0.40	0.030	0.4

, and each group of experiments was repeated three times. The results of the tests were measured, and the average values of the entrance and exit diameters were taken as the resultant hole diameters, respectively, while the taper values were derived using Figure 4 and Equation (1).

Taper = Arctan[(d1 − d2)⁄2L]

(1)

2.3. Data Design and Processing Methods

Genetic algorithm (GA) is an adaptive search technique that evolved according to the evolutionary laws of biological reproduction in nature. The GA as a general global solution to the problem of finding the best parameter, as shown in Figure 5, can calculate the fitness value of the population, then rank the fitness of the individuals, and finally find the optimal parameters by selection, crossover, and mutation operations. It is fully feasible and effective in solving global optimization problems under complex situations, such as large-scale, with peaked polymorphic functions, and containing discrete variables. The search approach of GA starts from the population and has the ability to process the problem in parallel, allowing comparisons between multiple individuals to be made simultaneously. The advantage of this over traditional optimization algorithms is that it avoids the possibility of falling into a local optimum solution because of individual solving for the optimal value.

The Taguchi method is a low-cost and highly effective quality engineering method. The orthogonal table is used to select experimental parameters and arrange experiments, and more factors affecting the experimental results are evaluated through fewer parameter combinations. According to the existing research [16,17,18,19,20,21,22,23,24,25], the six parameters shown in Table 2 have a prominent impact on the processing quality. Therefore, we use the Taguchi method to design the parameters of the orthogonal test, and the resulting orthogonal table is shown in Table 2.

In order to process the data efficiently, we used analysis of variance (ANOVA) to analyze the significance of the parameters, and then used analysis of range (ANOR) to try to find the law of influence of each parameter on the quality of hole machining. The mean value of the experimental investigation index (the entrance, exit diameters, and taper) of each factor at different levels was used as the measurement factor. In this paper, we use the GA to perform the optimization search for the optimal parameters, and the entrance and exit diameters of 400 µm and the minimum taper are considered optimal factors.

3. Results

3.1. Results of ANOVA

Table 3. Orthogonal design and measurement results of DD6 single crystal superalloy.

Num	A	B	C	D	E	F	Entrance (μm)	Exit (μm)	Taper (°)
1	1	1	1	1	1	1	290.97	333.04	−0.603
2	1	2	2	2	2	2	319.07	335.37	−0.234
3	1	3	3	3	3	3	292.95	265.09	0.399
4	1	4	4	4	4	4	446.43	482.09	−0.511
5	1	5	5	5	5	5	496.18	490.08	0.087
6	2	1	2	3	4	5	282.24	386.82	−1.498
7	2	2	3	4	5	1	304.95	427.36	−1.753
8	2	3	4	5	1	2	470.45	510.33	−0.571
9	2	4	5	1	2	3	522.70	506.69	0.229
10	2	5	1	2	3	4	296.65	85.01	3.029
11	3	1	3	5	2	4	403.49	518.34	−1.645
12	3	2	4	1	3	5	462.00	505.96	−0.630
13	3	3	5	2	4	1	530.13	503.05	0.388
14	3	4	1	3	5	2	286.75	313.10	−1.809
15	3	5	2	4	1	3	352.98	497.67	−2.072
16	4	1	4	2	5	3	471.61	513.10	−0.594
17	4	2	5	3	1	4	540.53	525.18	0.220
18	4	3	1	4	2	5	292.14	450.8	−2.271
19	4	4	2	5	3	1	375.83	502.62	−1.815
20	4	5	3	1	4	2	428.53	500.58	−1.032
21	5	1	5	4	3	2	545.56	531.29	0.204
22	5	2	1	5	4	3	303.35	443.59	−2.008
23	5	3	2	1	5	4	341.63	466.54	−1.789
24	5	4	3	2	1	5	420.37	511.64	−1.307
25	5	5	4	3	2	1	496.07	514.29	−0.261

shows the specific grouping of the orthogonal test and the experimental results of each group. The entrance and the exit values are the average values of three independent repetitions of the test, and the taper value is taken from the values under the average value.

The range analysis can simply and visually give the major and minor factors and give a judgment on whether the effect of each factor on the test index is positive or not. However, ANOVA can more accurately provide a criterion for examining and judging whether the effect of each factor is significant or not. The purpose of ANOVA is to find out the factors that have a significant effect through data analysis. This paper uses the ANOVA method to study the most influential factors of the characteristics, and the ANOVA test was carried out with a 95% confidence level and a probability value of (α = 0.05). Statistically, the F-test is an important tool in ANOVA, which can be used to explore which parameters have a significant effect on the characteristics. Usually, when F > 4, it can be tentatively considered that the change of parameters has a significant effect on the characteristics.

The p-value is used to measure the magnitude of the difference with the control group, where the p-value is less than 0.05, it indicates a significant difference, and where the p-value is less than 0.01, it indicates the most significant difference. As shown in

Table 4. ANOVA results for each factor.

	Symbol	Sum of Squares	Mean Square	F	P	Sig.
Entrance	Power A	37,997.159	18,338.69	1.075	0.376
	Overlap B	10,662.170	11,895.44	0.289	0.884
	Defocus C	560,708.462	141,549.20	102.163	0.000	**
	Pressure D	11,685.432	12,136.64	0.317	0.866
	Feed E	10,347.261	11,821.22	0.28	0.89
	End F	5173.179	10,601.61	0.139	0.967
Exit	Power A	222,670.808	64,684.83	6.174	0.000	**
	Overlap B	34,762.327	20,392.11	0.743	0.566
	Defocus C	269,519.637	75,727.76	8.072	0.000	**
	Pressure D	108,975.522	37,885.22	2.560	0.046
	Feed E	95,686.35	34,752.78	2.209	0.077
	End F	25,150.771	18,126.53	0.531	0.713
Taper	Power A	16.456	5.614	2.742	0.035	*
	Overlap B	8.894	3.831	1.383	0.249
	Defocus C	24.566	7.525	4.436	0.003	**
	Pressure D	22.610	7.065	4.002	0.006	**
	Feed E	17.995	5.977	3.043	0.023	*
	End F	7.757	3.564	1.194	0.321

The ** is the most significant level, and the * is the significant level.

, the results of the comparison of the differences in the levels of entrance, exit, and taper indicators corresponding to different levels in different contexts, respectively, show that the factors corresponding to different levels exhibit different levels of statistically significant differences.

The results of the comparison of differences in the levels of entrance indicators showed that defocus showed the most significant statistical difference (p = 0.000 <0.01), while all other factors were insignificant. The results of the comparison of differences for the level of exit indicators show that both power and defocus (p = 0.000 <0.01) show the most significant statistical difference, and combined with the results of the extreme difference analysis, although both are the most significant level, the defocus has a greater effect on exit. So, the final power is an extremely significant level and all other factors are insignificant. For taper, the defocus (p = 0.003 <0.01) reached the level of the most significant difference along with pressure (p = 0.006 <0.01). Power (p = 0.035 <0.05) and feed (p = 0.023 <0.05) reached the level of significance. A higher F-ratio value implies that the process parameter alteration has caused a significant change in the performance characteristic. Combined with the results of the extreme difference analysis, it can be obtained that the effect of defocus and pressure is the most significant, and defocus is stronger than pressure; the effect of power and feed is significant, and feed is stronger than power. So, the final pressure is at an extremely significant level and all other factors are insignificant.

3.2. Parameter Optimization

From Figure 4, it is clear that the parameter optimization of GA includes population initialization, fitness function, selection operator, crossover operator, and mutation operator. The parameters of the genetic algorithm are shown in

Table 5. Parameters of genetic algorithm.

Population Size	Maximal Hereditary Generation	Crossover Probability	Mutation Probability
40	150	0.9	0.1

, and the populations can be selected with equal probability. The regression equations corresponding to the values of the six variables with the factors are obtained by function fitting, as in Equations (2) and (3). Where ${\mathrm{E}}_{\mathrm{n}}$ is the entrance diameter and ${\mathrm{E}}_x$ is the exit diameter.

E_n = 150 + 13.57A + 1.84B + 300.5C − 35.5D − 1565E + 8.2F

(2)

(E_x⁵ − 1 ) (5 × 423.242⁴) = −169 + 27.37A + 0.71B + 208.3C+ 188D − 2399E + 5.8F

(3)

The goal of optimization is to achieve an entrance and exit diameter of 400 μm. Since the entrance diameter is usually used as a statistical object in industry, this paper sets the entrance weight to 0.6 and the exit weight to 0.4, and verifies the taper after obtaining the results. Therefore, the fitness function is:

F = 0.6 × (E_n − 400)² + 0.4 × (E_x − 400)²

(4)

In this paper, the above regression equation and parameter settings are used to implement the simulation of GA with MATLAB software. Figure 6 shows the optimization process of iterations, which, under the condition of 150 total iterations, shows that the fitness value no longer changes and reaches the minimum value at the 28th generation. The result after optimization by GA is ${\mathrm{A}}_1{\mathrm{B}}_5{\mathrm{C}}_3{\mathrm{D}}_1{\mathrm{E}}_3{\mathrm{F}}_1$, namely power 6.73 W, overlap 99%, defocus 0 mm, pressure 0.2 MPa, feed 0.02 mm, and end −0.4 mm. The entrance diameter is 387.796 μm, the exit diameter is 406.916 μm, and the taper is −0.273° for this parameter, satisfying the requirements of industrial preparation.

4. Discussion

4.1. Morphological Analysis

The macroscopic morphology of the sample after femtosecond laser processing is shown in Figure 7 and the micromorphology results of each group of orifices under the SEM are shown in Figure 8 and Figure 9. Through-hole entrances machined with different process parameters were found to have good roundness, with large variations in entrance diameter, and most entrances produced a stepped structure after machining. Compared to the entrance, the exit is poorly rounded, with an increased variation in diameter and a partially elliptical shape. It can also be observed that when the defocus amount is +0.4 mm (as shown in the reverse diagonal of Figure 8 and Figure 9), the entrance, as well as the exit, always maintains essentially the same dimensions and characteristics regardless of the other parameters. At this time, the roundness is better, the diameter size variation is smaller, and there is almost no stepped structure. However, by the observation of 2-5-1-2-3-4 exits in Figure 9, it did not form an effective exit. After repeated tests, it was verified that this set of parameters could not form an effective through-hole, i.e., power 7.84 W, overlap 99%, defocus −0.4 mm, pressure 0.25 MPa, feed 0.02 mm, and end +0.2 mm. This phenomenon should be related to the Gaussian distribution of the pulsed laser in space. When the defocus is less than −1, the entrance diameter is close to the zero defocus, but the exit diameter is much smaller than the zero defocus [26], which results in a poor removal effect due to the coupling of other parameters.

For better comparative analysis, two through-hole morphologies with typical features and diameters close to 400 µm were selected for micro-area enlargement, as shown in Figure 10, Figure 11, Figure 12 and Figure 13. From the blue enlarged area in Figure 10 and Figure 12, it can be observed that there is a stepped structure at the entrance, and some material inside the hole is not removed. We note that this phenomenon is commonly seen on entrances where the defocus amount is less than 0. This is because when processing with R3, the angle of incidence of the laser increases with regard to the material. According to the Fresnel effect [27], when the angle of incidence of the laser increases, the absorption rate of the material decreases. The pore wall cannot absorb all the energy and the ablation rate gradually decreases [28]. When the energy density absorbed by the material is lower than the ablation threshold, the ablation process ends and the stepped morphology is formed. Therefore, in the actual machining process, we can consider optimizing the feed amount to improve the above situation when machining with R3. Furthermore, some crack generation was found on the internal material (as shown in Figure 10c). These cracks are defects caused by the formation of stepped structures, and the ridge-like accumulation and step-like residue of the orifice were both in the form of nanopillars, but with different orientations, which required further analysis. Figure 11 shows the exit without any accumulation of residue, while some of the edges are smoother and some are serrated. Compared with Figure 10 and Figure 12, there is no visible stepped residual material inside the hole, and the ridge-like accumulation has the same orientation of nanopillars present as the former, but its size is substantially reduced compared to the previous one. Comparing Figure 11 with Figure 13, the basic shape at the exit is consistent. However, it can be observed in Figure 13 that it possesses a notch in addition to the serrated edge. There are also some exits, such as 5-1-5-4-3-2 from Figure 9, that also possess this feature. This damage should be related to the final stopping position of the spiral processing laser rotation, which needs to be verified by further tests.

4.2. Single-Factor Influence Law Analysis

Table 6. Extreme difference analysis for each factor.

Projects		Factors
		Power A (W)	Overlap B (%)	Defocus C (mm)	Pressure D (MPa)	Feed E (mm)	End F (mm)
Entrance diameter (mm)	$k_1$	369.118	398.770	293.971	409.166	415.060	399.589
	$k_2$	367.371	385.980	334.349	407.566	406.690	410.069
	$k_3$	364.547	385.460	370.056	379.706	394.600	388.717
	$k_4$	400.047	410.420	469.311	388.410	398.130	405.745
	$k_5$	415.302	414.082	527.017	409.858	380.220	390.586
	Range	50.755	28.623	233.046	30.152	34.838	21.354
Exit diameter (mm)	$k_1$	381.134	456.522	345.106	462.562	475.572	456.072
	$k_2$	383.242	447.493	437.801	389.632	465.110	458.132
	$k_3$	467.624	439.163	444.601	420.895	377.990	445.227
	$k_4$	498.456	483.235	505.155	477.841	463.234	415.430
	$k_5$	493.470	417.528	511.258	492.990	462.030	469.059
	Range	117.322	65.7020	166.152	103.358	97.577	53.629
Taper (°)	$k_1$	−0.172	−0.827	−0.733	−0.764	−0.867	−0.809
	$k_2$	−0.113	−0.881	−1.481	0.256	−0.836	−0.688
	$k_3$	−1.154	−0.769	−1.068	−0.590	0.237	−0.809
	$k_4$	−1.098	−1.043	−0.513	−1.281	−0.932	−0.139
	$k_5$	−1.032	−0.050	0.226	−1.190	−1.172	−1.124
	Range	1.041	0.993	1.707	1.537	1.409	0.985

shows the analytical calculation results data, which can be derived from the DD6 single crystal high-temperature alloy hole size as well as the extreme difference distribution of taper. Figure 14 shows the influence pattern of different parameters on the DD6 single crystal high-temperature alloy.

M_i is considered as the average of all experimental data under this parameter and R is the range. The relationship between R and M_i is

R = Max (M_i) − Min (M_i)

(5)

According to Figure 14a, it can be observed that as the laser power increases, both the entrance and exit diameter increase, with the exit diameter increasing more rapidly, thus leading to a decrease in the taper. Figure 14b shows that the effect of overlap on the entrance diameter is not significant, but the effect on the exit diameter and taper is large, which has no significant pattern. The comparison reveals that the relative slope of the defocus in Figure 14c is the largest, so its effect is the most significant. With the increase of the defocusing amount, both the entrance and exit diameter increase. From Figure 14d, we can see that the gas pressure has little effect on the entrance diameter, but the exit diameter has a greater effect. When observing the samples, it was observed that the exit diameter increases with increasing air pressure greater than 0.25 MPa, which is due to the fact that the larger gas pressure can carry away the plasma more efficiently after the through-hole is formed. According to Figure 14e, it was found that an increase in feed leads to a decrease in the entrance bore diameter, and the experimental results show that when feed was zero, this is beneficial to obtain a through-hole of 400 mm. When the feed is 2mm, there is a data point anomaly; we can guess that this is related to the failure of parameters 2-5-1-2-3-4 to form an effective exit. After removing this group of data and recalculating it, the average value of exit at this time was 451.24mm and the taper was −0.461, which did not affect the basic trend in Figure 14e when compared with the original data. So, the feed of 0.02 mm is beneficial for machining small taper through-holes and smaller exit holes due to increased feed. The increase in the end before 0.2 mm in Figure 14f causes a reduction in the entrance and exit diameters, but its taper has improved. This is the same as the power phenomenon, which is due to the appearance of an increase in taper due to a drop in exit more than in entrance.

5. Conclusions

In this paper, the influence law of femtosecond laser parameters on the hole making of DD6 single crystal high-temperature alloy was studied by an orthogonal test, the optimization of relevant parameters was carried out, and significance evaluation was performed using ANOVA. The following conclusions were drawn:

(1)

The optimal parameters after GA optimization are power 6.73 W, overlap 99%, defocus 0 mm, pressure 0.2 MPa, feed 0.02 mm, and end −0.4 mm. For this parameter, the entrance diameter is 387.796 μm, the exit diameter is 406.916 μm, and the taper is −0.273°.

(2)

The through-hole entrances processed under different process parameters have good roundness, but the diameters have large variations, and the exits have no accumulation of residues and are poorly rounded, almost all being elliptical in shape, while some jagged edges exist. In response to the increase in the exit diameter after the gas pressure is greater than 0.25 MPa, this is related to the fact that the larger gas pressure can carry away the plasma more effectively after the through-hole is generated.

(3)

The increase in the laser power causes an increase in the entrance and exit diameters, but the exit diameter increases more rapidly, thus leading to a decrease in the taper. The feed of 0.02 mm is beneficial for machining small taper through-holes, and the end position has less effect on the structural characteristics.

(4)

For the entrance and the exit, the defocus has the most significant level; as well as, the power, which has the most significant level for the exit. For taper, the defocus is also the most significant level, and the level of pressure is the same as the defocus. The power and feed are significant levels.