Surface Integrity of Additively Manufactured and Machined AISI 316L: Experimental and Machine Learning Analysis via PCA-RBFN and SVM

Abstract

This work investigates the surface integrity of AISI 316L produced by additive manufacturing (AM) and subsequently machined, with an emphasis on residual stresses. A full factorial design was applied to evaluate the influence of laser power from AM and milling parameters, including cutting speed, cutting depth, feed rate, and cutting fluid. Eight samples were selected for Vickers microhardness characterization. Machined surfaces were examined by scanning electron microscopy. Microhardness results showed higher values at top surfaces, reaching increases of up to 22.7%. Variations in machining parameters significantly affected residual stresses, with changes of up to 500 MPa; all measured values were tensile. Surface roughness Rt ranged from 1.59 to 4.34 µm. The best surface integrity was achieved using 160 W laser power, 170 m/min cutting speed, 0.1 mm/tooth feed rate, 0.35 mm cutting depth, and cutting fluid. ANOVA identified feed rate as the most influential factor, followed by laser power and cutting depth. Machine learning models were developed for residual stress prediction, with PCA-RBFN showing superior performance for parallel residual stress (R² = 94,53%) and SVM for perpendicular residual stress (R² = 89.85%). The hybrid approach enabled isolation of individual parameter effects while minimizing interactions between AM and machining.

Keywords:
surface integrity; additive manufacturing; residual stress

1. Introduction

Additive manufacturing (AM), also known as 3D printing, has attracted significant attention for its ability to design products with diverse functions¹,². This process, unlike a subtractive process such as machining, produces pieces layer by layer from the bottom up³. Bertolini et al.⁴ consider AM an innovative technology that can improve material performance in the biomedical area. In addition, Zhang et al.⁵ say that AM is expected to revolutionize manufacturing and biomedicine since it allows customized prostheses to be designed for each patient as a function of their characteristics⁶. Hwa et al.⁷ also discuss its use in jet engines, surgical implants, and automotive components. Given the important applications of AM in biomedical, aerospace, automotive, and energy areas, its processes can produce near-net-shaped pieces with reduced material waste⁸,⁹ and pieces with complex geometries, such as internal channels and other features that are not possible with other processes¹⁰. In addition to these advantages, the quality and structure of the materials are preserved, as in other conventional processes¹¹. However, some disadvantages, such as porosity, voids, surface roughness, residual stress, reduced ductility, and part distortion, affect the specimen's performance and limit the applicability of AM processes¹². Therefore, depending on the surface quality and geometrical tolerances, the surfaces generated by AM must be finished by another process⁸. According to Li et al.¹³, the surface integrity of AM is unpredictable, mainly because residual stresses are considerably higher than in wrought materials, which provides an opportunity to contribute to this important topic.

On the other hand, processes such as machining, grinding, and polishing after AM improve the surface quality and help close the pores produced by the AM process on the surface¹⁴. Bruschi et al.¹⁵ point out that this finishing process also changes the residual stresses, microstructure, and hardness depending on the cutting parameters used. Studying the surface integrity of AM plus another process is important because the performance of the pieces is influenced by these characteristics¹.

Regarding the metallic materials manufactured using AM, one of the most used stainless steels in the industry is 316L, which provides a combination of high corrosion resistance and mechanical properties¹⁶. Austenitic stainless steels are widely used in several industrial applications, including nuclear power, petrochemical, and chemical industries, where exceptional corrosion resistance and excellent mechanical properties at elevated temperatures are required¹⁷. 316L is a stainless steel with a high chromium content (up to 18%), which contributes to exceptional corrosion resistance. In contrast, the low carbon content (denoted by the letter 'L') reduces susceptibility to carbide formation, which may cause corrosion cracking. 316L contains a deliberate amount of molybdenum, which increases its general corrosion resistance and significantly improves its pitting resistance in chloride-ion solutions. They are widely used in exhaust manifolds, heat exchangers, pharmaceutical equipment, cryogenic piping, valve and pump trims, chemical and petrochemical processes, pulp and paper, and food industries¹⁸,¹⁹. Wang et al.²⁰ also point out its good mechanical properties, corrosion resistance, and extremely low ductile-brittle transition temperature. Zhao et al.²¹ state that 316L has high strength, excellent toughness, and ideal corrosion resistance at high temperatures, and can be used to resist oxidation and thermal shock²²,²³. However, heat treatment procedures cannot strengthen 316L and other low-carbon SS because they cannot form strengthening precipitates at low carbon levels. Therefore, work hardening is the only way to strengthen the 316L alloy²⁴. Machining can be an option for generating better surfaces in this type of material, given its characteristics.

In turn, focusing on discussions concerning the different manufacturing processes, it is important to define the surface integrity that refers to the condition of the surface of the workpiece, such as its topographical characteristics (surface roughness and topography), mechanical properties (subsurface microhardness, residual stress, etc.), and metallurgical aspects (microstructure variation, phase transformation, etc.). Especially when high reliability of the pieces is required, as in the aerospace industry or for finished surfaces used in biomedical applications, surface integrity is used to evaluate quality²⁵. The parameters used in AM and in a secondary process influence the surface integrity, including surface qualities and defects²⁶,²⁷. When machining is used as a second process, work hardening, as a function of the cutting parameters, affects residual stress and other surface integrity characteristics²⁸.

The background delineated herein, given the processes, materials, deformation mechanisms, and surface characterization, enables observation of the broad range of approaches that can be developed. Additionally, numerous experimental studies have been conducted on titanium alloys, focusing on the generation of surfaces in pieces produced by AM and machining. However, a few studies have used austenitic stainless steel and post-processing, such as milling (AM plus machining). Park et al.²⁸ studied the microstructural change in pieces manufactured by AM and machining, and its effects on the mechanical properties. They concluded that the amount of deformation increased after machining. Tyagi et al.²⁷ investigated electropolishing and chemical polishing (chempolishing) methods to reduce the surface roughness of the internal surface of AISI 316L steel AM pieces. Kim, Lee, and Kim²⁹ studied post-processing induction-assisted machining (IAM) to analyze the cutting forces, surface roughness, hardness, and microstructure of 304L from the AM process. They concluded that hardness increased and that this process can be used as a post-processing step for AM products, improving machinability and microstructure.

To conclude, extensive work has been conducted on the characterization of AM with respect to microstructure, residual stresses, and mechanical properties. In most of these works, heat treatment was used to relieve the residual stresses generated by the AM process. The surface integrity of machined parts has also been the primary focus of study. Few studies have been conducted on the AM and post-processing of AISI 316L, and given the material's characteristics and importance, the present paper contributes to understanding surface integrity under specific cutting parameters.

Therefore, this paper proposes to study the surface integrity of AISI 316L manufactured by AM and post-processed by milling, using a machine learning approach to residual stress.

2. Methods and Materials

The specimens were manufactured from AISI 316L stainless steel produced by SEAM–WIT (South Eastern Applied Materials Research Centre, Ireland). Fabrication was carried out using an EOSINT M280 system based on the DMLS (Direct Metal Laser Sintering) process, within the LPBF (Laser Powder Bed Fusion) framework. The specimens were subsequently separated using wire electrical discharge machining (EDM) with an Excetek V650G machine.

The present paper focused on machining workpieces received after the additive manufacturing process. In this case, the initial condition of the samples, designated as-built, resulted from the following AM parameters shown in Table 1.

Table 1
Additive manufacturing process parameters.

Parameter	Value
Laser power	160 and 190 W
Laser scanning speed	1000 mm/s
Layer thickness	20 µm
Laser efficiency	100%
Laser focus	72 µm
Laser width	5 mm
Build platform temperature	81 °C
Laser scan rotation (per layer)	67°

The properties for specimens after AM were: roughness: Ra = (13 ± 5) µm; Rz = (80 ± 20) µm; ultimate tensile strength XY direction: = (640 ± 50) MPa ; Z direction = (540 ± 55) MPa; yield stress XY direction: = (530 ± 60) MPa ; Z direction = (470 ± 90) MPa; elastic modulus: XY direction= 185 GPa ; Z direction: = 180 GPa; elongation XY direction = (40 ±15)%; Z direction = (50 ±20)%; hardness: 89 HRB. The final dimensions of the workpieces were: (20 x 20 x 15) mm. The average powder size was 34.5 µm, with extreme sizes ranging from 21.48 µm to 49.84 µm. The parts were made under a controlled argon atmosphere, and the powder chemical composition (in weight percentage) was: Fe - 64.05%; Cr - 18.88%; Ni - 11.75%; Mo - 2.06%; Mn - 1.32%; Si - 0.80%; Cu - 0.53%.

Figure 1 shows an example of a 3D-printed piece. The piece was manufactured layer by layer from the bottom up. The same image shows the position of the machined surface from the milling process, the cut plane for the microstructural analysis, and the microhardness measurements, all in the middle of the parts.

Figure 1
Specimen generated by the DMLS process, cut position for microstructural analysis, and direction of microhardness measurements.

For the machining process, an experimental factorial design was used, with the parameters shown in Table 2, resulting in 32 trials.

Table 2
Machining parameters and experimental levels (full factorial design).

Factor	Symbol	Levels (min and max)
Cutting speed	vc	170 and 210 m/min
Feed rate	fz	0.1 and 0.2 mm/tooth
Cutting depth	ap	0.35 and 0.7 mm
Cutting fluid	—	No and Yes
Laser power (AM)	—	160 and 190 W

The milling experiments were carried out in a Romi Discovery 560 machine center at the Maua Institute of Technology, using a face milling operation with the following tool specifications (carbide insert): M class, code R245-12 T3 K-MM 2030 with milling head CoroMill 245 – 45° - R245-063Q22-12M. The face milling process was applied to the tops of the parts at their centers.

A Surftest SJ-210 Series, a portable surface roughness tester, was used to measure surface roughness. Three repeated surface roughness measurements were performed along the feed direction, and the reported value is the arithmetic mean of these measurements.

The residual stresses were measured using X-ray diffraction with a PULSTEC µ-X360s on the machined surface, employing the cosβ method at the center of the piece. The incident angle was 30°, and the diffraction angle was 148.5°. Approximately 120 points were used to determine residual stress, making these measurements more precise than those from other types of X-ray diffraction equipment. The standard deviation for most measurements was ± 15%, and measurements were conducted in the same direction as the tool feed (parallel) and 90° about the feed tool (perpendicular).

An electrolytic solution, a 10% oxalic acid solution, was used at 4.5 V for 50 s to reveal the microstructure for microhardness measurements, which were performed using a Mitutoyo HM-100 device with a load of 25 gf. Three measurements were taken, and the mean was used.

The surface analyses were performed using SEM with Tescan Vega 3.

3. Results and Discussion

3.1. Microhardness measurements

Table 3 shows the Vickers microhardness results and the difference between the material's upper region and core. The highest differences between the machined surface and the core were observed in the specimens produced with cutting fluid. Some differences are negative, indicating little difference between the values or regions with different crystallographic orientations, which could be due to distinct microstructural responses (e.g., contrast) during metallographic etching, as denoted in Figures 2 and 3. The term “severe cutting parameters” refers to the combination of higher levels of cutting speed (210 m/min), feed rate (0.2 mm/tooth), and depth of cut (0.7 mm), from the experimental design.

Table 3
Measurements of mean microhardness for all the tests [HV_0.025].

condition	machined upper region	core	difference
190 W; severe cutting parameters; dry cutting	279.8	267.3	4.7%
190 W; severe cutting parameters; cutting fluid	265.3	216.3	22.7%
190 W; mild cutting parameters; dry cutting	249.0	245.3	1.5%
190 W; mild cutting parameters; cutting fluid	212.5	198.5	7.1%
160 W; severe cutting parameters; dry cutting	204.5	213.3	-4.1%
160 W; severe cutting parameters; cutting fluid	215.3	225	-4.3%
160 W; mild cutting parameters; dry cutting	204.8	209.8	-2.4%
160 W; mild cutting parameters; cutting fluid	270	230.8	17%

Figure 2
Influence of cutting parameters on the microhardness in the upper region.

Figure 3
Typical microhardness profile.

Analyzing the core, there are two conditions: 160 W and 190 W laser power. The mean microhardness measurements were 219 HV at 160 W and 231.8 HV at 190 W. The results showed that the combination of the DMLS process parameters and 190 W laser power produced pieces with higher hardness, which could be related to the higher density of the sample expected for the greatest laser power of the AM process, while maintaining the other process parameters³⁰.

The ANOVA results did not indicate any statistically significant variable. Still,Figure 2 shows the mean effects plot for microhardness measurements in the upper regions of the pieces (machined affected region). Considering only the microhardness values in the upper (machined) region, the influence of cutting fluid was limited. The use of severe cutting parameters increased the microhardness. In this case, higher parameters led to greater surface work hardening and, consequently, higher microhardness values. The behavior of the material core was the same here, i.e., 190 W laser power produced pieces with higher microhardness.

Figure 3 shows the average microhardness profile from the machined surface toward the core of the material. A slight increase in microhardness is observed in the near-surface region, followed by a gradual stabilization toward the core.

This behavior is associated with the work-hardening effect induced by the machining process, which increases the hardness in the superficial layer due to plastic deformation. As the distance from the surface increases, the influence of machining diminishes, and the material properties tend to return to their original state.

Additionally, the variability observed in the measurements, reflected by the standard deviation, may be attributed to differences in crystallographic orientation and microstructural heterogeneity inherent to the DMLS process, which can influence the local hardness response²⁸.

3.2. Residual stresses analysis

Figure 4 shows the directions of the residual stress measurements in the as-built material.

Figure 4
Directions of the residual stress measurements in the as-built material.

Table 4 summarizes the residual stress values measured for the as-built material under different laser power conditions and measurement directions, as manufactured by DMLS.

Table 4
Residual stress values measured for the as-built material under different laser power conditions and measurement directions.

Laser power [W]	Location	Direction description	Residual stress [MPa]
160	Upper face	two orthogonal directions	252 / 354
160	Side 1	Parallel to base / perpendicular to base	79 / 240
160	Side 2	Parallel to base / perpendicular to base	69 / 213
190	Upper face	two orthogonal directions	204 / 312
190	Side 1	Parallel to base / perpendicular to base	58/206
190	Side 2	Parallel to base / perpendicular to base	54/188

All residual stresses were tensile, and the laser power of 160 W generated higher residual stresses. The residual stresses in the upper face were higher than in the side faces. The same behavior was reported by Chimmat et al.³¹. Therefore, the upper face was chosen for developing this work. On the side faces, elevated residual stresses were observed in the material's deposition direction, as reported by the same authors.

Figure 5 shows the directions of the residual stress measurements in the machined surfaces of the 32 parts.

Figure 5
Directions of the residual stress measurements in the machined surfaces.

Table 5 presents the results of residual stress and total height (Rt) roughness measurements for the machined surfaces.

Table 5
Results of residual stresses and surface roughness.

test #	vc [m/min]	fz [mm/tooth]	ap [mm]	cutting fluid	laser power [W]	RS parallel [MPa]	RS perpendicular [MPa]	Rt [μm]
1	170	0.1	0.35	Yes	160	150	303	2.15
2	210	0.1	0.35	Yes	160	137	284	1.59
3	170	0.2	0.35	Yes	160	317	418	1.89
4	210	0.2	0.35	Yes	160	304	292	1.90
5	170	0.1	0.7	Yes	160	100	396	2.89
6	210	0.1	0.7	Yes	160	99	363	2.82
7	170	0.2	0.7	Yes	160	288	373	2.60
8	210	0.2	0.7	Yes	160	245	388	2.68
9	170	0.1	0.35	No	160	144	348	2.60
10	210	0.1	0.35	No	160	83	333	2.16
11	170	0.2	0.35	No	160	255	506	2.09
12	210	0.2	0.35	No	160	244	491	3.30
13	170	0.1	0.7	No	160	123	329	3.19
14	210	0.1	0.7	No	160	104	327	2.92
15	170	0.2	0.7	No	160	298	543	4.34
16	210	0.2	0.7	No	160	227	493	2.98
17	170	0.1	0.35	Yes	190	120	391	1.98
18	210	0.1	0.35	Yes	190	109	373	1.98
19	170	0.2	0.35	Yes	190	272	437	2.58
20	210	0.2	0.35	Yes	190	259	418	2.32
21	170	0.1	0.7	Yes	190	87	355	2.78
22	210	0.1	0.7	Yes	190	96	336	2.47
23	170	0.2	0.7	Yes	190	212	423	2.54
24	210	0.2	0.7	Yes	190	224	410	3.10
25	170	0.1	0.35	No	190	96	276	3.44
26	210	0.1	0.35	No	190	119	304	1.95
27	170	0.2	0.35	No	190	209	463	1.82
28	210	0.2	0.35	No	190	256	442	3.24
29	170	0.1	0.7	No	190	60	395	1.64
30	210	0.1	0.7	No	190	77	333	1.69
31	170	0.2	0.7	No	190	224	546	1.92
32	210	0.2	0.7	No	190	227	530	2.86

The results for both parallel and perpendicular residual stresses exhibited similar behavior with respect to the cutting parameters. Among the variables analyzed—feed rate, cutting fluid, and laser power—feed rate was significant. Higher feed rates led to more pronounced tensile residual stresses, whereas the other variables had no substantial influence. Figure 6 presents the main-effect plots for the residual stress measurements in the parallel direction.

Figure 6
Main effects plot for the residual stresses in the parallel direction to the tool feed rate.

Figure 7 displays the main-effect plots for the residual stress measurements in the perpendicular direction. The results for the perpendicular residual stresses followed a similar trend to those observed for the parallel direction, though with some distinctions in magnitude. Among the cutting parameters—feed rate, cutting fluid, and laser power—only the feed rate significantly impacted the perpendicular stresses. Higher feed rates resulted in more pronounced tensile residual stresses in the vertical direction, whereas the cutting fluid and laser power had minimal influence. The notably large error bars in Figure 7 may be attributed to the high variance of the other parameters, underscoring their limited effect on residual stress in both the parallel and perpendicular directions.

Figure 7
Main effects plot for the residual stresses in the perpendicular direction to the tool feed rate.

These results were consistent with those of M’Saoubi et al.³², who concluded that the feed rate significantly influences the residual stress profile. When increased, it generates higher residual stresses since the temperature also rises. Zhang et al.³³ also concluded that an increase in temperature leads to higher residual stresses, sometimes shifting them from compressive to tensile. In this work, the results show the same behavior: the feed rate leads to higher residual stresses. According to Leppert and Peng³⁴ the severe work hardening of austenitic stainless steel during chip formation, combined with its low thermal conductivity, generates high cutting forces and interfacial temperatures in the cutting zone and is the main reason for high levels of tensile residual stresses. In terms of direction, the perpendicular one exhibited higher residual stresses; this is how the tool cuts the material, resulting in more significant work hardening. These results are by Holmberg et al.³⁵.

3.2.1. ANOVA

Table 6 presents the results of the analysis of variance (ANOVA), which revealed that, except for cutting speed (vc), all main factors had significant effects (p < 0.05; α level: 5%) on the responses. Among these, tool feed (fz) stood out as the most influential parameter, with an F-statistic (F = 383.311) substantially higher than those of the other parameters, indicating its dominance in the process. A higher F-statistic suggests that the differences between group means are significant relative to random variation, meaning at least one factor has a meaningful effect. Laser power and cutting depth (ap) had a weaker but still notable impact. A less pronounced but still statistically significant interaction (p = 0.032) was found for cutting fluid.

Table 6
ANOVA results.

factor	DF	adj SS	adj MS	F-value	p-value
vc	1	657.03	657.03	1.451	0.239
fz	1	173607.78	173607.78	383.311	0.000
ap	1	4,584.03	4,584.03	10.121	0.004
cutting fluid	1	2,329.03	2,329.03	5.142	0.032
laser power	1	6,932.53	6,932.53	15.306	0.001
Residual	26	11775.81	452.96

From the ANOVA result, the model in Equation 1 was established for RS modeling with machine learning. In Equation 1 only significant factors were considered.

$model=fz+ap+cuttingfluid+laserpower$ (1)

Since this study is conducted under hybrid manufacturing conditions (AM combined with machining), with parameters from both processes merged, the analysis and modeling evaluated only the influence of isolated factors. This approach was adopted to prevent interaction effects between the processes (AM and machining) from inducing potential confounding in the responses, which would hinder obtaining unbiased evaluations free from interference.

3.2.2. Residual stress modeling with machine learning algorithms

3.2.2.1. Introduction to PCA-RBFN and SVM Models

The Support Vector Machine (SVM) and the Radial Basis Function Network (RBFN) are two fundamental techniques in the field of machine learning, each with its distinct characteristics and specific applications³⁶-⁴¹. SVM, introduced in the early 1990s³⁶, is a powerful technique for classification and regression tasks. It seeks an optimal hyperplane that maximizes the margin between different data classes, ensuring effective generalization to new datasets. One of the key advantages of SVMs is the ability to obtain sparse solutions, where only a few samples, known as support vectors, are used to determine the classification or regression functions³⁶,³⁹.

On the other hand, the RBFN is an artificial neural network that uses radial basis functions as activation functions. These networks are known for their universal approximation capabilities and are commonly used in interpolation and classification problems³⁸,⁴¹,⁴³. Principal Component Analysis (PCA) ⁴¹,⁴⁴,⁴⁶ is a statistical technique that transforms the original data into a new set of uncorrelated variables, known as principal components, ordered by the amount of variance they explain.

The combination of PCA with RBFN, known as PCA-RBFN⁴¹, is a hybrid approach aimed at improving the efficiency and performance of machine learning models, particularly for classification and regression problems. This combination aims to reduce the data's dimensionality before feeding it into the neural network, which can improve the model's performance and computational efficiency.

The PCA-RBFN method applied to the variable factors in Equation 1 was developed considering fz, ap, cutting fluid, and laser power. RBF neurons utilize radial functions, whose centroids, in this context, were derived from the principal components generated by PCA⁴⁶. The radial Gaussian function was chosen for the RBFN model due to its strong convergence rates during the data interpolation process⁴³. The Equation 2 presents the model used in the PCA-RBFN method.

$\widehat{Y}={{\displaystyle \sum }}_{i=1}^n{\alpha }_i\cdot \exp \left(-\frac{|X-Z_i{|}^2}{2{\sigma }_i^2}\right)+b$ (2)

where α_i are the learned weights during training, X is the input matrix containing the input factor data with dimension n, vector Z_i and scalar σ_i are the receptive ith neuron centroid and the standard deviation, respectively. The vector Z_i was obtained during the PCA training stage⁴³.

The SVM setup employed the same variable factors as the PCA-RBFN model and was executed considering the cubic polynomial kernel, aiming to achieve a balance between data fitting and model complexity, ensuring a more generalizable model capacity³⁹.

The function Ŷ,Equation 3 presents the model used in the SVM fitting for the present study.

$\widehat{Y}={{\displaystyle \sum }}_{i=1}^n\left({\alpha }_i-{\alpha }_i^{*}\right)\cdot {\left(X_i^{T}X+1\right)}^3+b$ (3)

where α_i and α_i^* are the learned weights during training, X_i are the support vectors, X is the matrix containing the input factor data, and b is the bias. The support vector X_i was obtained during model training.

The overall neural network architecture for machine learning is presented in Figure 8. All the routines and modeling were implemented in Python-Version 3.12.4.

Figure 8
Machine learning neural network model architecture.

Table 5 was divided into two randomly selected datasets for training and testing, with 22 rows (approximately 70% of the data) allocated to the training phase and 10 rows (approximately 30%) to the performance testing phase. From this division, both models were trained using the same training dataset and evaluated on the same test set.

3.2.2.2. PCA-RBFN and SVM models

Figure 9 compares the experimental values for parallel RS with the estimates from the two machine learning models, PCA-RBFN and SVM. The gray bars represent experimental values, while the blue and red bars indicate the predictions made by the PCA-RBFN and SVM models, respectively. Additionally, the points and lines at the top of the figure illustrate the absolute percentage errors for each analyzed sample.

Figure 9
Comparison of experimental parallel RS versus PCA-RBFN and SVM estimates.

The training-stage assessment of the PCA-RBFN model was conducted using four metrics: R² (coefficient of determination), Equation 4; adjusted R² (R²_adj), Equation 5; Mean Absolute Error (MAE), Equation 6; and Root Mean Square Error (RMSE), Equation 7. These metrics assess the model's performance, and a comprehensive application of performance indicators can be found in Garcia-Alvarez et al.⁴⁴. The R²adj offers an advantage over the standard R² by penalizing the inclusion of unnecessary predictors, making it particularly valuable for model comparison and feature selection.

$R^2=1-\frac{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-\overline{y}\right)}^2}$ (4)

$R_{\text{adj}}^2=1-\left(\frac{\left(1-R^2\right)\left(n-1\right)}{n-p-1}\right)$ (5)

$\text{MAE}=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n\left|y_i-\widehat{y_i}\right|$ (6)

$\text{RMSE}=\sqrt{\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}$ (7)

where y_i is the actual value of the i-th observation, ŷ_i is the predicted value of the i-th observation from the model, ȳ is the average of the observed values, and n is the number of observations.

The results presented in Table 7 allow the comparison of the performance of the PCBA-RBFN and SVM on the test data. Although both methods exhibited similar performance, some differences can be observed.

Table 7
Performance comparison for the models with parallel RS using the testing dataset.

	PCBA-RBFN	SVM
R2	94.53%	84.40%
R2adj	90.16%	71.94%
MAE	13.91 MPa	18.80 MPa
RMSE	18.77 MPa	27.99 MPa

The results indicate that the PCA-RBFN model achieved an R² of 94.53% and an adjusted R² (R²adj) of 90.16%. The mean absolute error (MAE) was 13.91 MPa, while the root mean square error (RMSE) was 18.77 MPa. On the other hand, the SVM model demonstrated inferior performance, with an R² of 84.40% and an R²adj of 71.94%. The recorded MAE was 18.80 MPa, and the RMSE reached 27.99 MPa.

The error distribution highlights fluctuations in the predicted values for both models. When comparing the absolute errors of the PCA-RBFN and SVM models, both show uneven performance but with distinct patterns. The PCA-RBFN displays variability, with errors ranging from 0.6% to 24.6%, including one instance of high accuracy (0.6%) and others with significant deviations (e.g., 24.6%). The SVM model has smaller error ranges in some cases (a minimum of 0.4% and 1.1%) but exhibits the largest errors overall, reaching 25.9% and 27.8% in predicting samples #14 and #16, respectively.

A general conclusion for the modeling of parallel residual stress (RS) is that the PCA-RBFN model is better at representing the behavior of parallel RS. The inferior performance of the SVM model may be attributed to its greater sensitivity to outliers, the complexity of the nonlinear relationships involved in residual stress prediction, or the choice of the polynomial kernel.

Figure 10 compares the experimental perpendicular RS values with predictions from the two machine learning models. The bars represent the experimental and estimated values, while the points and lines at the top indicate the absolute percentage errors for each sample.

Figure 10
Comparison of experimental perpendicular RS versus PCA-RBFN and SVM estimates.

The performance of the PCBA-RBFN and SVM for perpendicular RS on the test data is presented in Table 8.

Table 8
Performance for the models with perpendicular RS using the testing dataset.

	PCBA-RBFN	SVM
R2	85.63%	89.85%
R2adj	74.14%	81.73%
MAE	29.93 MPa	24.71 MPa
RMSE	34.74 MPa	26.88 MPa

The statistical results indicate that the SVM model outperformed the PCA-RBFN model. The R² for SVM was 89.85%, and the adjusted R² (R²adj) was 81.73%, whereas PCA-RBFN showed lower values, with an R² of 85.63% and an R²adj of 74.14%. The error analysis further supports the superiority of the SVM model, which achieved an MAE of 24.71 MPa and an RMSE of 26.88 MPa, compared to the PCA-RBFN model, which had an MAE of 29.93 MPa and an RMSE of 34.74 MPa. Individual errors indicate that deviations were generally lower for both models, except for the PCA-RBFN model’s prediction in sample #2, where the error reached 28.9%. Overall, perpendicular RS predictions yielded lower errors compared to parallel RS predictions.

The SVM model demonstrated greater stability in both parallel and perpendicular RS analyses (with errors approximately of the same order of magnitude), whereas the PCA-RBFN model provided a better fit to the data for parallel RS, although the fit for perpendicular RS was not suboptimal. This observation may be attributed to the PCA-RBFN's strong capability to capture nonlinear relationships in data structures, while the margin maximization-based SVM tends to generalize better for multidirectional variations, accounting for its stability across multiple directions³⁶,³⁹.

The results in Figures 9 and 10 indicate that both models exhibit strong predictive capabilities. The SVM model demonstrates slightly higher accuracy for perpendicular RS. In contrast, the PCA-RBFN model proves more effective for predicting parallel RS, achieving greater accuracy and lower absolute error than the SVM model.

The variability in errors suggests that adjustments may be necessary to improve the robustness of the predictions, particularly for specific samples (e.g., #2, #14, and #16) that exhibited larger discrepancies from the experimental values.

3.3. Surface Roughness

The contour plot in Figure 11 shows that higher feed rates and lower cutting speeds increase total surface roughness (Rt). These elevated roughness values are consistent with the surface imperfections observed. The presence of milling chatter can be attributed to the increased vibrations and instability at higher feed rates. Similarly, material redeposition and side flow are more likely to occur under this condition. Therefore, the higher roughness values in the upper regions of the contour plot correspond to defect formation on the material surface.

Figure 11
Surface roughness contour plot for test #11, laser power = 160 W, vc = 170 m/min, no cutting fluid, ap = 0.35 mm.

This suggests that the cutting fluid helped reduce surface roughness, thereby improving surface quality. However, the plot also shows that higher cutting speeds near 210 m/min and increased feed rates slightly raised the roughness. Similarly, lower cutting speeds and reduced feed rates also led to higher roughness values. These findings correlate with the tearing surface defect observed, as this irregularity appears more frequently under test #3 conditions using cutting fluid. The tearing surface could significantly contribute to the observed increase in roughness under these machining conditions, indicating that while the fluid helps mitigate some defects, others, such as material tearing, persist depending on the chosen parameters.

Figure 12 presents the surface roughness contour plot for test #3. Figure 13 presents the surface roughness Rt contour plot for test #19; the values range from 1.75 to 2.50 μm, which are higher than those observed in test #3. This increase in roughness can be attributed to the combination of higher cutting speeds and feed rates, which exacerbate surface irregularities. Figure 13 indicates that both extreme machining conditions—higher cutting speeds with increased feed rates and lower cutting speeds with reduced feed rates—yield higher roughness values. These conditions correspond with the surface defects observed.

Figure 12
Surface roughness contour plot for test #3, laser power = 160 W, vc = 170 m/min, with cutting fluid, ap = 0.35 mm.

Figure 13
Surface roughness contour plot for test #19, laser power = 190 W, vc = 170 m/min, with cutting fluid, ap = 0.35 mm.

Figure 14, the contour plot of surface roughness for test #27, shows roughness values ranging from 2.27 to 2.95 μm, making it the highest roughness Rt measured across all tests. This roughness profile is consistent with that observed in test #11, which was conducted under dry cutting conditions but with a lower AM sample laser power of 160 W. In the contour plot, roughness Rt increases at both extremes of the parameter range: higher cutting speeds near 210 m/min and higher feed rates led to a sharp rise in roughness, while lower cutting speeds with reduced feed rates resulted in a slight increase in roughness. This correlation can be explained by the recurrence of milling chatter vibration observed in test #27, which tends to increase surface roughness.

Figure 14
Surface roughness contour plot for test #27, laser power = 190W, vc = 170 m/min, no cutting fluid, ap = 0.35 mm.

3.4. Surface analysis

Figure 15 illustrates the as-built surfaces generated by the DMLS process at two different laser power levels: 160 W in 15(a) and 15(b), and 190 W in 15(c) and 15(d). In 15(a), defects such as incomplete melting spheres and pronounced melting lines are visible, indicating uneven energy distribution during the process. As shown in 15b, similar defects are observed, including incomplete spheres and more prominent melting lines. At 190 W, 15(c) shows an increase in defects, including a higher concentration of incomplete-melting spheres and more well-defined melting lines. In 15d, larger and more visible incomplete spheres are observed, along with deeper melting lines, indicating excessive surface irregularities. In all cases, the increase in defect quantities suggests a greater need for surface finishing, depending on the intended application¹³.

Figure 15
As-built top surface generated by the DMLS process with laser power 160W, (a) magnification of 100x, (b) magnification of 1000x, (c) as-built top surface generated with laser power 190W with magnification of 100x, and (d) magnification of 1000x.

Figure 16 presents two magnified SEM images, highlighting the surface defects on the machined surface of test #11. Several large-scale surface defects are visible in the 100x magnification image, 16(a). Among these defects is redeposition, characterized by the accumulation of material previously removed during the cutting process, resulting in surface imperfections. Another prominent defect is side flow, which indicates lateral displacement of material due to cutting forces, leading to surface deformation. Feed rate trails are visible, representing patterns left on the surface by the tool's movement and directly correlating with the applied feed rate. At 500x magnification, 16(b), finer details of the surface defects are more discernible. Voids are areas where material is absent, likely due to material removal or incomplete melting during the DMLS process. Evidence of milling chatter and vibration is also apparent, suggesting dynamic instabilities during machining.

Figure 16
Surface defects observed during the analysis of test #11 – Vc: 170 m/min, fz: 0.2 mm/rev, ap: 0.35 mm under dry cutting conditions. AM sample laser power of 160 W. Defect details at (a) 100x magnification and (b) 500x magnification.

These instabilities led to increased surface roughness as chatter and vibration marks generated irregular patterns on the surface; a probable explanation for this result of greater roughness and more defects may be associated with the fact that test condition #11 occurred without the use of cutting fluid, in general the roughness values for all dry machining conditions resulted in greater roughness. This behavior during machining was described by Li et al.⁴⁷.

In Figure 17, test #3, the sample was manufactured under the same conditions as in test #11, but with the use of cutting fluid. At 500x magnification (17a), feed-rate trails are visible, indicating the tool's progression during machining, similar to observations under dry-cutting conditions. However, in 17(b), at 3000x magnification, tearing surfaces become more prominent. This defect may result from material adhesion at the tool’s surface followed by tearing during cutting, likely exacerbated by localized forces and heat generated during the process. As a function of the local effect of the temperature, thermomechanical loads, and friction, the tearing surface with material extrusions can occur, in which the feed rate (higher values) seems to be the most critical machining parameter for activating this mechanism⁴⁷.

Figure 17
Surface defects observed during the analysis of test #3 – vc: 170 m/min, fz: 0.2 mm/rev, ap: 0.35 mm, and with cutting fluid. AM sample laser power of 160 W. Defect details at (a) 500x magnification and (b) 3000x magnification.

Figure 18 presents the surface defects for the cutting parameters of test #19, similar to those in test #3. The key difference in test #19 is the use of a higher AM sample laser power of 190 W, compared with the 160 W used previously in test #3.

Figure 18
Surface defects observed during the analysis of test #19 – Vc: 170 m/min, fz: 0.2 mm/rev, ap: 0.35 mm, and with cutting fluid. AM sample laser power of 190 W. Defect details at (a) 500x magnification and (b) 3000x magnification.

In 18(a), some regions exhibit redeposited particles adhering to the surface, which negatively affect the finish. Side plastic flow, in which material laterally displaces under cutting forces, is also observed, but on a smaller scale than in test #11. In 18(b), small tearing surfaces are still visible across the image, indicating that material tearing remains a persistent issue even with the modified laser power and cutting fluid.

An important observation in 18(b) is the presence of a void defect, attributed to the DMLS process used to manufacture the AM sample. This void was likely formed during additive manufacturing, where incomplete material fusion can create imperfections. This defect was less recurrent than those seen under machining conditions. However, it highlights the complexities of achieving a high-quality surface finish in hybrid manufacturing with AM and machining.

Figure 19 presents the surface defects observed during test #27, conducted under dry cutting conditions with a vc of 170 m/min, fz of 0.2 mm/rev, and ap of 0.35 mm. The AM sample was produced with a laser power of 190 W. At 100x magnification, 19(a) shows the presence of milling chatter vibration is evident, which is characterized by irregularities on the machined surface caused by vibrations during the milling process. This defect significantly contributes to the surface roughness observed in this test. In 19(b) at 500x magnification, additional defects, such as side flow and redeposited material, are visible.

Figure 19
Surface defects observed during the analysis of test #27 – Vc: 170 m/min, fz: 0.2 mm/rev, ap: 0.35 mm under dry cutting conditions. AM sample laser power of 190 W. Defect details at (a) 100x magnification and (b) 500x magnification.

4. CONCLUSION

This paper examined the effect of manufacturing parameters on the surface integrity of 316L stainless steel using a residual-stress machine-learning approach. The manufacturing investigated is additive manufacturing (laser powder bed fusion) and post-processing via milling. The following conclusions were drawn:

• Laser power was the most crucial variable for the microhardness measurements. High laser power, followed by cutting fluid and a set of severe cutting parameters, generated surfaces with higher microhardness (up to a 22.7% increase compared to the core material).

• Depending on the machining parameters, the residual stress changed and decreased the tractive values to generate better surfaces, partially eliminating the high values of tractive residual stress from the AM process, without heat treatments. Smaller feed rates, laser power, and cutting fluid generated surfaces with lower residual stress values.

• The surface roughness varied from 1.59 to 4.34 µm Rt. The laser power and cutting depth were the most critical variables, followed by the feed rate. Lower laser power, cutting depth, and feed rate values generated lower surface roughness (best Rt: 1.59 µm with 160 W laser power, 0.1 mm/tooth feed rate, and 0.35 mm cutting depth).

• Statistical analysis (ANOVA) confirmed tool feed (fz) as the dominant machining parameter (F = 383.311, p < 0.001), with cutting fluid and laser power also showing significant effects (p < 0.05). Machine learning modeling demonstrated that PCA-RBFN outperformed SVM for parallel residual stress prediction (R² = 94.53%, MAE = 13.91 MPa vs. R² = 84.40%, MAE = 18.80 MPa). In comparison, SVM showed better performance for perpendicular residual stress (R² = 89.85%, MAE = 24.71 MPa vs. R² = 85.63%, MAE = 29.93 MPa for PCA-RBFN).

• Among the evaluated models, SVM showed more stable performance across both parallel and perpendicular residual stress predictions. At the same time, PCA-RBFN achieved higher accuracy for parallel residual stress due to its ability to capture nonlinear relationships. This is further supported by the narrow gap between R² (94.53%) and R²adj (90.16%) observed for the PCA-RBFN model, indicating high parameter efficiency and consistency with the ANOVA results, where feed rate (fz), depth of cut (ap), cutting fluid, and laser power were identified as significant factors (p < 0.05). In contrast, the larger gap observed for SVM suggests that its cubic polynomial kernel may introduce unnecessary complexity for parallel residual stress prediction.

• For perpendicular RS, SVM's smaller R²-R²adj gap (89.85% against 81.73%) compared to PCA-RBFN (85.63% against 74.14%) implies that SVM's kernel better captures the underlying physics of stress variation. The wider gap in PCA-RBFN suggests that principal components may lose explanatory power when applied to perpendicular RS, which justifies the use of SVM despite its poorer performance in parallel RS. This trade-off underscores the need for direction-specific modeling in hybrid manufacturing.

• The conclusion is that finding a unique group of parameters for most of the best surfaces in terms of the characteristics studied was possible. Depending on the objective, one or another property may be somehow penalized.

These results provide a systematic framework for parameter selection in hybrid AM-machining systems, balancing competing surface integrity requirements while leveraging data-driven modeling to predict residual stresses.

5. Acknowledgments

The authors would like to thank the São Paulo Research Foundation - FAPESP (Process Numbers: 2020/10653-5 and 2020/09163-3) and VAS Technology for the residual stress measurements.

6. Data Availability

All the data supporting the results of this study are presented within the article itself.

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This document has an erratum: https://doi.org/10.1590/1980-5373-MR-2026-0053er

*

e-mail: [e-mail]

Associate Editor:

Aloisio Klein.

Editor-in-Chief:

Luiz Antonio Pessan.

Publication Dates

• Publication in this collection
  31 July 2026
• Date of issue
  2026

History

• Received
  12 Feb 2026
• Reviewed
  07 May 2026
• Accepted
  30 May 2026
• Corrected
  12 Sept 2026