Open Access
Issue
Manufacturing Rev.
Volume 11, 2024
Article Number 14
Number of page(s) 15
DOI https://doi.org/10.1051/mfreview/2024012
Published online 30 May 2024

© K. Doan Tat et al., Published by EDP Sciences 2024

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

Laser direct metal deposition (LDMD) is a metal additive manufacturing (AM) technology that sprays metal powder with a laser source coaxially via a nozzle to melt powder and directly deposit into the workpiece layer-by-layer [13]. The thickness of layers normally ranges from 0.1 mm to 2 mm. Based on the layer deposition principle, LDMD can build near-net shape and complex parts without the need of cutting tools and other additional resources as in traditional manufacturing processes (e.g., machining) [4,5]. Nowadays, LDMD is a promising AM technology applied in many fields, for example aeronautics, automobile, molds and dies, repairing of parts, and rapid manufacturing of spare parts [6,7].

In LDMD processes, to create a robust and tightly bonded thick clad layer on the substrate, it is essential to meticulously manage the geometric attributes of an individual deposited track [813]. Furthermore, optimizing the processing parameters is important, especially concerning the percentage of porosity and the geometric qualities, to guarantee superior clad performance during the deposition [911,1417]. There are several process parameters that directly influence the quality of single tracks, for example, the laser power Pl (W), the powder feeding rate fp (g/min), the scanning speed of the nozzle Vs (mm/s), the size of the laser beam spot, the amount of carrying and shielding gas, the powder size, and so on. However, the key process variables identified by previous studies are the laser power Pl (W), the powder feeding rate fp (g/min), the scanning speed of the nozzle Vs (mm/s) [14,18,19].

Numerous studies have been conducted to explore how the key parameters influence both the geometry of single deposited tracks and the deposited materials' integrity. For example, Errico et al. [20] examined the impact of parameters, including Pl, fp, Vs and the carrying gas flow rate on microstructures and porosity of SS 304 deposited by LDMD. Ascari et al. [21] conducted an extensive series of analysis to study how process parameters influence geometries, surface roughness, microstructures, tensile strengths, hardness, and productivity in the deposition of bulk materials of SS 316L. Campanelli et al. [22] investigated the effects of Pl, fp, Vs, and the overlapping distance between successive tracks in assessing the properties of deposited 18 Ni 300 maraging steel. To develop analytical models, which present the relationship between geometry attributes of single deposited tracks (e.g., width, height, penetration, and contact angle) and the process parameters Pl, fp, and Vs, several authors have adopted the linear model Y = a * X + b with [14,18,19]. The coefficients of the models were determined based on the experimental data with the help of Excel and Matlab software. However, the method to estimate (α, β, and γ) was not detailed in these studies. Most of these works adopted the “trial and error” method so that the determination coefficient of the models (R2) reach a maximum value possible [18].

Concerning the Optimization of the single deposited tracks in the LDMD process, Vaughan et al. [23] proposed a framework for optimizing single tracks considering the laser power, the scanning speed, and the powder feed rate, to obtain a dense bulk components of high strength steels. Zardoshtian et al. [23] adopted the response surface methodology (RSM) to optimize the single-track geometry of CuCrZr alloy deposited by LDMD. They stated that the estimated optimal parameter, including the scanning speed of 4.5 mm/s, the laser power of 1550 W, and the powder feed rate of 12 g/min enabled producing single track geometries with a good shape, sufficient dilution, and at the maximum rate of deposition. Recently, Javidrad et al. [11] performed a study on the optimization of the process parameter for the LDED process of Inconel 738LC. The authors aimed at minimizing the porosity, while maximizing the production rate and using the RSM method to resolve such a multi-objective optimization problem. Pandey et al. [24] also used the RSM method to optimize the single tracks' geometries when depositing 15Cr5Ni stainless steel. Meanwhile, Du et al. [23] employed the combination of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and GRA (Grey-Relational Analysis) for optimizing single tracks in laser cladding of 15-5PH steel.

To the best of the authors' knowledge, until now, very few authors have paid attention to the prediction and multi-objective optimization of the single deposited tracks in LDMD processes. To fill this knowledge gap, this paper aims to develop the prediction models for geometrical attributes of single tracks in LDMD of SS 316L. The models are developed by using experimental data. After that, several multi-objective optimization methods, including GRA, TOPSIS, and PSO (Particle Swarm Optimization) algorithm combined with TOPSIS are considered to identify the optimal process parameters that enable to obtain the expected attributes of single tracks for specific applications. GRA and TOPSIS methods are widely used in different fields to determine the optimal solution among a set of available alternatives [25,26]. On the other hand, PSO is a nature-inspired optimization technique used to find all the feasible optimal solutions in the search space [27].

2 Materials and methods

2.1 Materials and equipment

The DLMD system used in this study is comprised of a 0.5 kW fiber laser, a powder feeder system, a deposition nozzle, and a three-axis CNC mechanism (Fig. 1a). The SS 316L powder was utilized in the experiment. The particle size ranges from 15 to 55 μm with the average size of 25.56 μm and the standard deviation of 9.22 μm (Figs. 1b and 1c) and the chemical composition is given in Tab. 1. SS 316L plates with dimensions of 200 × 100 × 10 mm and its composition indicated in Table 2 were utilized as the substrate. Before the deposition, the metal powder was dried in a vacuum drying oven at 200 °C for 4 h to eliminate moisture. The substrate was polished with sandpaper and then cleaned with acetone and ethanol to remove grease and stains.

thumbnail Fig. 1

(a) The LDMD system, (b) a SEM image of SS 316L powder, and (c) the powder size distribution.

Table 1

Chemical composition of powder and substrate material (wt.%).

Table 2

Studied variables and their levels.

2.2 Fabrication of samples and data collection

In the LDMD process, there are many process parameters that could influence the geometry and quality of tracks, such as the laser beam spot diameter, the pressure and flowrate of carrying/shielding gas, the particle size distribution, the laser power Pl, the powder feeding rate fp, the scanning speed of the nozzle Vs, and so on [8,9,11,17,2831]. However, the laser power, the powder feeding rate, and the scanning speed are identified as the key parameters that most considerably impact on the temperature distribution, the melting pool dimensions, and the geometry of tracks [13,16]. Moreover, in the experiment, the change of these parameters is simpler and more practical than other ones, such as the laser beam spot diameter and the particle size distribution. Therefore, in this research, we consider the scanning speed Vs, the laser powder Pl, and the powder feeding rate fp for the parametric investigation and optimization, while other parameters were fixed at a constant value. To fabricate the single deposited tracks, the experimental plan was designed according to L9 orthogonal array Taguchi method with three levels for each parameter, as shown in Table 2. As a result, there are nine experimental runs. The nice single tracks were deposited and cleaned, as shown in Figure 2a. All the depositions were performed in a building chamber filled with a shielding gas of argon, where the oxygen level is less than 20 ppm. The rate of shielding and carrying gas was maintained at 6 L/min. The distance from the laser head tip to the substrate's surface was fixed at 15 mm, and the laser beam spot diameter is controlled at 1 mm.

It can be found that, on the top view (Fig. 2a), all the tracks were regular and stable. As a result, we can suppose that all these single tracks have almost constant value of track width and track height, especially in the middle region of each track. Therefore, we decided to analyze the tracks' attributes (including the width w, height h, and penetration depth p) from the middle of their length. This approach enables avoiding the impact of edge effects, and it is also widely used by previous studies in the literature [15,16,32]. Whereby, the cross-sections of each single track in the middle regions were extracted, ground, polished and chemically etched to measure the attributes (w, h, and p). The measurement of w, h, and p were performed with the help of an optical microscope (AXIO A2M, Carl Zeiss). The experimental matrix and measured data were presented in Table 3.

The measured data was used to analyze the influence of process variables on the attributes of single deposited tracks and to develop the prediction models. The development of prediction models and the analysis of variance are performed with the aid of Minitab 19 software.

thumbnail Fig. 2

(a) Deposited single tracks and (b) a cross-section of the deposited single track (6).

Table 3

Experimental runs and the collected data.

2.3 Optimization methods

In this study, we aim to find out the optimal process parameters for the building of thin-wall structures by the LDMD process. In this case, the width and the penetration of single deposited tracks are preferred to be minimized, while the height of the single deposited track is desired to be maximized. As a result, the multi-objective optimization issue is described as: “Find (Vs, P, and fp) to minimize (w and p) while maximize h, subject to 8 ≤ Vs (mm/s) ≤ 10, 230 ≤ P (W) ≤ 270, and 8 ≤ fp (g/min) ≤ 12”.

To resolve such a problem, different methods are employed and evaluated to select the best one. As mentioned earlier, the three following methods are examined, including PSO combined with TOPSIS, GRA, and TOPSIS. These methods are briefly described, as follows.

2.3.1 GRA

GRA is one of the methods widely used for the multi-objective optimization in manufacturing processes [33]. This method consists of transforming a multi-objective issue to a mono-objective one. The GRA procedure is composed of the following steps:

(1) Normalizing the kth objective using the following criteria:

(1)

if the objective respects the smallest-the-best criterion.

(2)

if the objective respects the biggest-the-best criterion.

where is the value of the kth objective measured at the ith trial, and are the highest and the smallest values of the kth objective measured in the experiment, and is the normalized value of the kth attribute measured at the ith trial. In this study, the objectives (w and p) are normalized according to equation (1) and h is normalized according to equation (2).

(2) Calculating GRCs (grey-relational coefficients) for the normalized data using equation (3):

(3)

where and θmax are calculated as equations (4), (5), and (6):

(4)

(5)

(6)

is the reference sequence, for example, , and φ is a coefficient in the range of (0, 1). In this study, φ = 0.5.

(3) Calculating the GRGs (grey-relational grades) by equation (7):

(7)

where ωj is the weight of the jth objective with ∑ωj = 1 and 0 < GRGj 1.

Finally, the optimized solution is corresponding to the maximum value of GRGj.

2.3.2 TOPSIS

As mentioned earlier, TOSIS relies on the concept that the optimal alternative is the nearest to the best solution and it is the farthest from the worst solution [34,35]. The main steps of TOPSIS method are expressed, as follows:

(1) Formulating the decision matrix {rij}nxm, where m is the objective number, n is the trial number in the experiment, and rij is the value of the jth objective at the ith trial.

(2) Normalizing the decision matrix by equation (8):

(8)

(3) Assigning the normalized matrix with the weight of each objective using equation (9):

(9)

(4) Determining the best solutions (BS) and the worst solutions (WS) using equations (10) and (11):

(10)

(11)

(5) Calculating the distance from the BSs and WSs to the feasible solutions using equations (12) and (13), respectively:

(12)

(13)

(6) Computing the closest index of the BSs using equation (14):

(14)

The values of are also in the range of (0, 1), and the optimum solution corresponds to the maximum value of .

In this study, it is remarked that the weight ωj for the jth objective in the TOPSIS and GRA is similar and calculated by the CRITIC method [36]. This approach integrates both the inherent conflict aspect and the level of contrast in determining the weight proportion of each response. The steps and equations associated with this approach are following:

(i) Normalizing the decision matrix {rij}nxm using equation (15):

(15)

where rij is the normalized value of the ith alternative for jth objective, and are the worst and the best values of the jth objective.

(ii) Calculating the standard deviation of each normalized attribute according to equation (16):

(16)

where rj is the average value of the jth normalized objective.

(iii) Constructing the matrix [Cij]nxn with the linear correlation coefficients Cij between the objectives. Cij is computed according to equation (17):

(17)

(iv) Calculating the objective information OIj by equation (18):

(18)

(v) Identifying the weight ωj or each objective using equation (19):

(19)

2.3.3 PSO algorithm

PSO is an optimization algorithm that mimics the collective behavior observed in flocks of birds or schools of fishes. This algorithm involves the initial creation of a population of particles, including their positions (Posii) and velocities (Veloi) are randomly assigned within allowable ranges. Each particle, specifically its position, represents a potential solution to the problem [28]. In essence, each position can be considered as a vector: Posii = (Posii,1, Posii,2, …, Posii,N), where ‘i’ signifies the particle index, and ‘N’ denotes the number of design variables, and the particle has a velocity: Veloi = (Veloi,1, Veloi,2, …, Veloi,N). The position of each particle can be seen as a unique point within the solution space. The objective function is used to evaluate each position's performance. During each iteration, the best position for each particle (Posiibest) and the best position among all particles (Globalbest) are updated and saved when necessary. Additionally, in each iteration, all the elements of the velocity and position vectors for all particles are updated using equations (20) and (21), respectively:

(20)

(21)

where i and j present the particle's index and the dimension of each design parameter, respectively. ωs the inertial weight. C1 and C2 are the coefficients of acceleration. R1 and R2 are the random numbers induced through a uniform distribution. When the termination criteria are satisfied, the optimum solution is the last best position of all the particles (i.e., the last Globalbest). The procedure of the PSO algorithm is drawn in Figure 3.

thumbnail Fig. 3

Flowchart of PSO algorithm.

3 Results and discussion

3.1 Development of prediction models

In this study, all the prediction models of single-track attributes (i.e., the width w, the height h, and the penetration p) were developed with the aid of Minitab 19 software. The analysis of variance (ANOVA) for the models was conducted with a confidence level of 95% and a significant level of 5%.

3.1.1 The developed model of w

The prediction model of w is expressed by equation (22), and the ANOVA for the model of w is presented in Table 4. It is shown that the model and all the model terms {Vs, Pl, and fp} are significant with the P-value inferior to 0.05. Among the process variables, the laser power Pl shows the highest contribution of 71.83%, followed by the scanning speed Vs and the powder feed rate fp with a contribution of 23.85% and 2.20%, respectively. The determination coefficients of the model {R-sq = 97.89%, R-sq (adj) = 96.62%, R-sq(pred) = 92.72%} indicate a high prediction accuracy of the model. Therefore, the developed model of w can be utilized to predict the width of single tracks in the entire space of design with a high reliability level and it can be used as an objective function for the optimization problem.

(22)

Table 4

ANOVA for w.

3.1.2 The developed model of h

The prediction model of h is described by equation (23), and the ANOVA results for this model is given in Table 5. It is indicated that the model and all the model terms {Vs, Pl, and fp} show the P-value inferior to 0.05. Thus, they are significant model terms. In this model, the scanning speed Vs features the highest contribution of 49.86%, whereas the laser power Pl and the powder feed rate fp show a smaller contribution of 30.85% and 16.38%, respectively. The determination coefficients of the model {R-sq = 97.08%, R-sq (adj) = 95.33%, R-sq(pred) = 90.85%} demonstrate that the model has a high prediction accuracy level. As a result, this model can predict the height of single tracks in the entire space of design with a high reliability level, and it can be used as an objective function for the optimization problem.

(23)

Table 5

ANOVA for h.

3.1.3 The developed model of p

The prediction model of w is expressed by equation (24), and the ANOVA for the model of p is presented in Table 6. It is revealed that the model and all the model terms {Vs, Pl, and fp} are significant with the P-value inferior to 0.05. Among the process variables, the laser power Pl shows the highest contribution of 87.68%, followed by the powder feed rate fp and the travel speed Vs with a contribution of 6.72% and 4.70%, respectively. The determination coefficients of the model {R-sq = 99.11%, R-sq (adj) = 98.57%, R-sq (pred) = 97.40%} confirm that the developed model of p exhibits a high prediction accuracy. Thereby, this model can be employed to predict the penetration of single tracks in the entire design space, and it can be used for the optimization problem.

(24)

Table 6

ANOVA for p.

3.2 Parametric influence analysis

Figure 4a shows the main effects of the process parameters on the width of single deposited tracks (w). It is shown that w decreases with an increment in the scanning speed Vs. A decreasing trend in w is also observed but with a lower rate when the powder feed rate fp increases. On the other hand, w increases with an increase in the laser power Pl. Figure 5a shows the interactional effects of Pl, Vs, and fp on w. It is also revealed that w increases with the increase in Pl with all values of Vs and fp in the design space. w shows a decreasing trend with the increment in Vs for all values of Pl, while the interaction effects of (fg and Vs) and (fg and Pl) on w do not present uniform trends. This observation is in line with the ANOVA results presented in Table 4, where it is indicated that the laser power Pl shows the highest contribution of 71.83%, followed by the scanning speed Vs with a contribution of 23.85%, while the contribution of fp is only of 2.20%. The effect trend of Pl and Vs on w observed in this study agrees with the those presented in [18,37]. In the current study and the previous studies [14,18], the w also an increasing trend with an increase in fp. On the other hand, in the study of Sreekanth et al. [37] on the laser-DED of Inconel 718, the authors found that w features a decreasing trend with an increase in fp. Such a difference could be explained by the insignificant contribution (only 2.20%) of fp in the developed model of w. Theoretically, an increase in Vs leads to decreasing the interaction time of metal powder with the melting pool, resulting in a reduction of the tacking width and the deposited track width w. On the other hand, an increase in P can fuse more powder particles and enlarge the melting pool. Thus, the width track w increases.

Figure 4b shows the direct influence of Pl, Vs, and fp on h, while Figure 5b exhibits the interaction effects of these parameters on h. It can be seen that h decreases as Vs increases from 6 mm/s to 10 mm/s while h increases as Pl increases from 200 W to 300 W. Similarly, h exhibits an increasing trend when fp increases from 6 g/min to 18 g/min. These variation trends of h with the process parameter (Vs, Pl, and fp) variation are also consistent with those observed in previous studies [19,32,38,39]. Due to Vs features the highest contribution of 49.86% to the h model (Tab. 5), Vs shows negative effects on h (i.e., h decreases when Vs increases) for all values of Pl and fp. On the other hand, the interaction effects of (fg and Vs) and (fg and Pl) are not clear. This observation agrees with the ANOVA results given in Table 5, because fg shows a small contribution to the h model (with a contribution of 16.38%). The deposited track height h decreases with an increase in Vs can be explained by the reduction of the powder amount per unit length along the deposition direction when Vs increases [14,40]. Meanwhile, h increases with an increment in the laser powder Pl. This is because when Pl increases the energy input increases and the amount of melted powder increases too, resulting in forming a great molting pool. As a result, both the w and h of the deposited track increase.

Figures 4c and 5c present the direct effects and the interactive effects of process variables on the penetration deep p of the deposited track, respectively. It can be observed that p increases for an increment in Pl (from 200 W to 300 W), while it is decreased with an augment in Vs (from 6 mm/s to 10 mm/s) and fp (from 6 g/min to 18 g/min). In this case, due to the highest contribution to the p model of Pl (with 87.68% of contribution), the effect trend of Pl on p is the strongest. p increments with an increase in Pl for all values of Vs and fp in the whole design space. On the other hand, with a small contribution value of fp and Vs to the p model (6.72% and 4.70%, respectively), the effect trend of these variables on p is not uniform. The similar observation on the effects of Pl, Vs and fp on p was reported in previous publications [14,32,38,40,41]. As explained in previous studies, when Pl increases, more laser energy input applied to the deposition process increases. As a result, p is deeper.

thumbnail Fig. 4

Direct influences of parameters on (a) w, (b) h, and (c) p.

thumbnail Fig. 5

Interaction influences of parameters on (a) w, (b) h, and (c) p.

3.3 Optimization results

3.1.1 GRA results

Table 7 presents the results obtained by the GRA method. The normalized objectives were calculated by equations (1) and (2) for {w, p} and h, respectively. The grey-relational coefficients GRC were computed using equations (3)–(6), while the GRGs were achieved using equation (7). It is noted that the weight ωj for each objective (i.e., w, p and h) was estimated from the experimental data by the CRITIC method, and the weight values were employed in both the GRA and TOPSIS methods. In this research, ωw = ωp = 0.26 and ωh = 0.48 Based on the GRGs' value, it is indicated that the run No. 7 with the highest value of GRG (0.703) is considered as the optimal solution. Hence, the optimal parameters estimated by the GRA methods are {Vs = 10 mm/s, Pl = 200 W, and fp = 18 g/min} that produce a deposited track with {w = 1.386 mm, h = 0.094 mm, and p = 0.042 mm}.

Table 7

Optimization obtained by GRA.

3.3.2 TOPSIS results

Table 8 shows the results obtained by the TOPSIS method. The normalized data and the weighted normalized data were calculated by equations (8) and (9), respectively. The values of and ere calculated by equations (12)–(14), respectively. Based on the highest value of it is found that the process variables of the run No. 3 (i.e., Vs = 6 mm/s, Pl = 300 W, and fp = 18 g/min) are considered as the optimal process variables, and they produced the deposited track with {w = 1.745 mm, h = 0.235 mm, and p = 0.116 mm}.

Table 8

Optimization obtained by TOPSIS.

3.3.3 Results of PSO combined with TOPSIS

As mentioned earlier, the PSO algorithm generates a set of feasible optimal solutions. In this case, the prediction models of w, h, p (Eqs. (22), (23), and (24), respectively) were used as objective functions in PSO algorithms. The parameters of the PSO algorithm were chosen as follows: Both the population size and the repository size are equal to 50. The maximum generation number is 100. The inertia weight is 0.4. The individual confidence and swarm confidence factors are equal to 2. As a result, we obtained the Pareto of 50 feasible optimal solutions, as shown in Figure 6a. It can be found that it is difficult to select one feasible solution manually that satisfies the requirement (i.e., maximizing h while minimizing both w and p), because h increases with an increase in w and p (Figs. 6b and 6c). Therefore, the TOPSIS is utilized to select the most optimal solution among the feasible optimal solutions.

Table 9 shows the results of TOPSIS applied to the 50 feasible optimal solutions. It is shown that the solution No. 14 exhibits the highest value of . As a result, the most optimal solution selected by TOPSIS among the Pareto points is (Vs = 6 mm/s, Pl = 263.63 W, and fp = 18 g/min), and they produced the deposited track with {w = 1.656 mm, h = 0.208 mm, and p = 0.094 mm}.

thumbnail Fig. 6

PSO results: (a) Pareto of feasible optimal solutions, (b) w vs. h, and (c) p vs. h.

Table 9

Optimization obtained by TOPSIS from the PSO feasible optimal solutions.

3.3.4 Comparison of different optimization results

Table 10 presents the comparison between different optimization results obtained with GRA, TOPSIS, and PSO combined with TOPSIS. Herein, the difference in results between the method A vs. the method B was defined by equation (25), where the Atribute (A)  and Atribute (B)s the values of the same attribute obtained by the method A and B, respectively.

(25)

It is indicated that the optimal solution obtained by TOPSIS shows the highest value of h, followed by the (PSO + TOPSIS) and GRA, respectively. The h obtained by TOPSIS is higher than that obtained by GRA up to 150%, while the optimal solution generated by (PSO+TOPSIS) shows a higher h value of 122% compared to that of GRA. Similarly, the values of w and p in TOPSIS and (PSO+TOPSIS) are higher than those obtained by GRA.

Compared to the TOPSIS method, the optimal parameters obtained by PSO+TOPSIS method enable producing the single track with the values of w, h, and p lower than those in TOPSIS with a reduction of 5%, 11% and 19%, respectively. As a result, in terms of w and p, the PSO+TOPSIS method provides better results, meanwhile, in terms of h, the TOPSIS is better. Indeed, h is related to the distance upwards the cladding nozzle moves prior to deposing the next layer or the layer height, while the penetration depth p is related to the bonding between the deposited layers through the dilution indicator, d = 100%×p/(p + h). Higher dilutions d lead to porosity and crack generation, which ultimately deteriorates the part's bond quality and mechanical performance [24,32,42]. In the current study, although the TOPSIS method provides a better objective h than the PSO+TOPSIS method (0.235 mm vs. 0.208 mm), it also provide a higher objective p (0.116 mm vs. 0.094 mm), leading to a higher dilution d (33% vs. 31%). Due to this reason, we consider that the PSO+TOPSIS method provides a better solution.

As a conclusion, in this research, compared to GRA and TOPSIS methods, PSO + TOPSIS offers the most appropriate objectives because it gives a solution balancing the objectives in the multi-objective optimization problem − i.e., maximizing h, while minimizing both (w and p).

Finally, the optimal process variables obtained by PSO + TOPSIS (i.e., Vs = 6 mm/s, Pl= 264 W, and fp = 18 g/min) were used to build several thin-walled structures as shown in Figure 7. It can be seen that all the as-deposited components have good shape. There are also no major cracks appearing between the as-built part and the substrate, as well as between the deposited layers.

Table 10

Comparison of optimization results obtained by GRA, TOPSIS and (PSO + TOPSIS).

thumbnail Fig. 7

Thin wall structures deposited with the optimal variables obtained in PSO + TOPSIS (i.e., Vs = 6 mm/s, Pl= 264 W, and fp = 18 g/min).

4 Conclusions

In this research, the influences of process variables (including the laser power Pl, the scanning speed of the deposition nozzle Vs, and the powder feeding rate fp) on single deposited tracks' attributes in laser direct metal deposition (LDMD) of 316L stainless steel were explored and the optimum process variables for the deposition of 316L stainless steel thin-wall structures were identified, considering different multi-objective optimization problems. The main outcomes of this research can be summarized as follows:

  • The laser powder Pl exhibits the highest impact contribution to the models of the deposited track width w and the deposited track penetration p with a contribution of 71.83% and 87.68%, respectively, among the process parameters (the scanning speed Vs, the laser power Pl, and the powder feed rate fp). The scanning speed Vs exhibits the highest contribution to the models of the deposited track height h a contribution of 49.86%. Meanwhile, the powder feeding rate fp shows an insignificant impact contribution to the w and p models.

  • All the developed models of w, h, and p feature a high prediction accuracy with the values of determination coefficients R2 of 97.89%, 97.08%, 99.11%, respectively, which demonstrate that they can be used to prediction w, h, and p with high confidence and precision levels.

  • Moreover, the optimization results achieved by different methods (i.e., GRA, TOPSIS, and PSO+TOPSIS) demonstrated that the PSO combined with TOPSIS can be used to find out the most optimal process parameters (i.e., Vs = 6 mm/s, Pl = 263.63 W, and fp = 18 g/min) to build thin-walled structures in SS316L by LDMD.

  • The as-deposited part built with the optimal process variables shows smooth surfaces and a regular height, and without major cracks, validating their consistency.

Because of a significant role of the single tracks in the LDMD process, this research contributed an insight into the effects of the main process parameters (i.e., the scanning speed Vs, the laser power Pl, and the powder feed rate fp) on the single tracks and the methods determining the optimal process parameters in LDMD of SS316L, to the academic community and specific applications. However, to provide a comprehensive understanding on the impact of the process parameters on the single tracks, other variables such as the laser beam spot diameter, the pressure and flowrate of carrying/shielding gas, the stand-off distance, and the particle size, need to be considered in the future work. The process optimization could also consider other outputs of the single tracks such as surface roughness, wetting angle, porosity, microhardness, etc.

Funding

This research is funded by Vietnam National Foundation for Science and Technology Development under grant number KC4.0-15/19-25.

Conflicts of interest

The authors have no competing interests to declare that are relevant to the content of this article.

Data availability statement

All data generated and analyzed during this study are included in this article.

Author contribution statement

T.K. Doan and V.T. Le are involved in the conceptualization and methodology; T.K. Doan, V.T. Le, and V. N. Duong contributed to the formal analysis and investigation; T.K. Doan and V.T. Le contributed to writing—original draft preparation; all the authors contributed to writing, review, and editing; T.K. Doan acquired the funding.

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Cite this article as: Khoa Doan Tat , Van Thao Le, Nguy Duong Van , Prediction models and multi-objective optimization of the single deposited tracks in laser direct metal deposition of 316L stainless steel, Manufacturing Rev. 11, 14 (2024)

All Tables

Table 1

Chemical composition of powder and substrate material (wt.%).

Table 2

Studied variables and their levels.

Table 3

Experimental runs and the collected data.

Table 4

ANOVA for w.

Table 5

ANOVA for h.

Table 6

ANOVA for p.

Table 7

Optimization obtained by GRA.

Table 8

Optimization obtained by TOPSIS.

Table 9

Optimization obtained by TOPSIS from the PSO feasible optimal solutions.

Table 10

Comparison of optimization results obtained by GRA, TOPSIS and (PSO + TOPSIS).

All Figures

thumbnail Fig. 1

(a) The LDMD system, (b) a SEM image of SS 316L powder, and (c) the powder size distribution.

In the text
thumbnail Fig. 2

(a) Deposited single tracks and (b) a cross-section of the deposited single track (6).

In the text
thumbnail Fig. 3

Flowchart of PSO algorithm.

In the text
thumbnail Fig. 4

Direct influences of parameters on (a) w, (b) h, and (c) p.

In the text
thumbnail Fig. 5

Interaction influences of parameters on (a) w, (b) h, and (c) p.

In the text
thumbnail Fig. 6

PSO results: (a) Pareto of feasible optimal solutions, (b) w vs. h, and (c) p vs. h.

In the text
thumbnail Fig. 7

Thin wall structures deposited with the optimal variables obtained in PSO + TOPSIS (i.e., Vs = 6 mm/s, Pl= 264 W, and fp = 18 g/min).

In the text

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