Modeling of ball-end micromilled surface roughness and geometry in ultrafine-grained and dual-phase steels using interpretable machine learning

Modeling of ball-end micromilled surface roughness and geometry in ultrafine-grained and dual-phase steels using interpretable machine learning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Modeling of ball-end micromilled surface roughness and geometry in ultrafine-grained and dual-phase steels using interpretable machine learning Cleiton Lazaro Fazolo de Assis, Alessandro Roger Rodrigues This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6753887/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Oct, 2025 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted 5 You are reading this latest preprint version Abstract This study presents an integrated experimental and computational approach to analyze surface integrity in ball-end micromilling of two low-carbon steels with distinct microstructures: dual-phase (DPh) and ultrafine-grained (UFG). The influence of tool diameter, neck length, feed per tooth, and milling strategy (up- and down-milling) on surface roughness (Ra, Rz, skewness, kurtosis), burr formation, and profile accuracy was systematically investigated. Tool deflection effects, more critical in UFG due to its higher ductility, were quantified through geometrical deviation metrics. Predictive models using Random Forest (RF) and Multilayer Perceptron neural networks (MLP) were developed to estimate surface roughness based on machining parameters. The MLP model showed superior performance for UFG steel (R² = 0.71), indicating enhanced prediction capability for homogeneous microstructures. Feature importance analysis highlighted the dominant effect of tool diameter and feed per tooth. The results advance the understanding of process-material interaction in micromilling and demonstrate the potential of interpretable machine learning for surface quality prediction in ultrafine-grained steels. Ball-end micromilling Ultrafine-grained low-carbon steel Surface roughness prediction Profile accuracy Machine learning Tool deflection Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 1. Introduction Micromilling has gained attention for its precision and efficiency, with research focusing on microstructure effects, tool wear, forces, surface quality, and burrs [ 1 , 2 ]. Integrating micromilling with other techniques shows promise for new materials and tools [ 3 ]. Micromilling cutting tools have significant influence on the quality of parts [ 4 ]. Geometry of microgrooves, machined surface and burrs formation are heavily affected by tools geometry and cutting parameters [ 5 ]. In conventional milling, the tools’ stiffness helps to predict the roughness due to low influence of deflections caused by machining forces [ 6 ]. Tool miniaturization increases deflection risks due to imbalance, size effects, and premature edge failure [ 7 ]. These tool conditions influence surface formation, making a thorough understanding of the tool–workpiece interaction essential for improving the micromilling process [ 8 ]. While flat-end mills are common, ball-end mills are preferred for intricate geometries and 3D features [ 9 , 10 ]. Usually ball-end milling operations apply tool inclinations or tilt angle of cutter to produce machined surfaces due to a varying cutting speed, despite constant spindle rotation, along the cutting-edge tools [ 11 ]. Push- and pull-milling strategies are also commonly used but require a 4- or 5-axis machining center [ 12 ]. Cutting speed in the spherical end-mill center is near to zero and machined surface is affected by tool rubbing, resulting in a workpiece surface degeneration and accelerated tool wear [ 13 ]. Applications like microfluidics and surface texturing require hemispherical grooves for wettability and lubrication [ 14 , 15 ]. In ball-end milling, a minimum surface roughness depends on cutting parameters feed per tooth (ft) and width of cut (ae) when milling steels [ 16 ]. Thus, investigations of feed per tooth influence upon surface roughness are relevant for considerations about maximum and minimum feed acceleration to machine free-forms surfaces in conventional milling and more significant during micromilling due to effects of workpiece microstructure and tool cutting-edge radius [ 17 ]. Cutting-edge radius effect has been tested by the most researchers using flat-end mills [ 18 ]. In steels, studies still indicate lower R a roughness at uncut chip thickness to cutting-edge raiuds ratios near 1, especially in precision machining conditions [ 19 ]. Other authors using ball-end mills with 1 mm diameter reported that feed per tooth close to cutting-edge radius tends to lower S a roughness, while increasing width of cut resulted higher S a [ 4 ]. The findings indicate that there is a relation between cutting-edge radius and width of cut to define surface formation. In ball-end milling, the width of cut corresponds to the effective diameter, which depends on the relationship between the tool's radius and the depth of cut [ 20 ]. The neck length of ball-end mills significantly affects the machining of steels, especially in precision and deep-cavity applications. Studies indicate that modifying the neck length of small radius ball-end mills significantly impacts tool rigidity, which in turn influences cutting accuracy and surface finishing [ 21 ]. Increased neck length often results in higher tool deflection, leading to machining errors such as reduced depth accuracy and dimensional deviations [ 22 ]. Furthermore, authors still affirm that excessive tool deflection can reduce the effectiveness of micromilling operations, particularly in materials with dual-phase microstructures like low-carbon steel, where deviations in microchannel depth have been observed. Thus, optimizing the neck length of ball-end mills is relevant to maintaining machining precision while minimizing deflection-related errors. The diameter of ball-end mills and the feed per tooth significantly influence the efficiency and accuracy of steel machining. Studies have shown that increasing the tool diameter generally reduces tool deflection, leading to improved surface finishing and dimensional accuracy [ 16 ]. Additionally, larger tool diameters facilitate allow for higher feed rates without compromising surface integrity, thus enhancing productivity [ 23 ]. However, the feed per tooth must be optimized carefully, as excessive feed rates can lead to poor surface finishing and increased cutting forces, ultimately accelerating tool wear [ 6 , 24 ]. Conversely, insufficient feed rates can cause ploughing effects, increasing specific cutting energy and reducing material removal efficiency [ 25 ]. Therefore, achieving an optimal balance between ball-end mill diameter and feed per tooth is a key factor for maintaining high-quality machining performance and tool longevity. Regarding the workpiece material, the effect of different phases on the microstructure has been studied by several researchers [ 26 , 27 ]. The studies include different machining scales (milling and micromilling) using homogeneous materials aiming at reducing surface defects, improving roughness and minimizing material deformation beneath the machined surface [ 28 , 29 ]. The results of those studies showed that the ultrafine grain material presents improved machinability at conventional and microscale cutting conditions using flat-end mills overcoming size effect problems due to the differences between cutting parameters and microstructure scale. Scientifical researches about grain refinement in low-carbon steels and its potential to reduce carbon consumption in steels production increased in the two last decades [ 30 ]. The microstructural characteristics and mechanical behaviour of this class of steels can be optimized, aiming to expand applications previously restricted [ 31 , 32 ]. A microstructure with ultrafine ferrite can provides an improvement of mechanical properties such as yield strength and toughness in an outstanding combination [ 33 ]. One way to achieve an excellent combination of strength and plasticity by microstructural grain refinement in a low-carbon steel is applying a thermomechanical processing, which the material is subjected to severe plastic deformation and heat treatments routes [ 34 ]. The result is a homogeneous microstructure with grain size reduced to even less than 1 µm [ 35 ]. In addition to structural applications in the automotive industry and improved weldability promoted by an ultrafine grained microstructure in low-carbon steels, the micromachining also would be beneficed by ultrafine grained microstructure due to reducing the size effect and the anisotropic feature while surface formation quality is allowed to control [ 36 ]. However, new issues arise and need to be investigated. Material mechanical properties can cause instability during microcutting due to small size of the cutting tools and low material removal rate, resulting in tool deflection, geometrical deviations and degradation of machined surface [ 37 , 38 ]. Thus, efforts to investigate suitable micromachining conditions for low-carbon steels with ultrafine grained microstructure is advantageous for provide new applications. Burrs control is an important issue in micromilling due to effects upon part quality and time of production, mainly by need of deburring operations [ 39 ]. Flat-end mills tend to form top burrs on up side of microgrooves and slots milling side (up- and down-milling) affects burr formation in steels [ 40 ]. Higher side-edge angles reduce burr formation, as shown with tapered tools, a concept extendable to ball-end milling [ 41 ]. The authors identified this effect during machining tests with tapered milling tools but no research was found in literature by extrapolating this application to ball-end milling. In other words, this side edge angle can also be obtained by combination between tool spherical top and effective tool diameter. Thus, once found an optimal relationship, burr formation could be avoided or minimized when milling microgrooves or micro slots. Artifical Inteligence (AI) models have enhanced micromilling by predicting cutting forces, roughness, and tool wear, supporting real-time optimization and sustainability [ 42 , 43 ]. Random Forest Regressor (RFR) and Multilayer Perceptron (MLP) neural networks have proven to be highly effective in modeling and predicting machining process behaviors due to their ability to capture nonlinear and complex relationships in manufacturing data. In tool wear prediction, RFR demonstrated remarkable performance by outperforming traditional models like decision trees and support vector machines in both accuracy and robustness, thanks to its ensemble learning approach that mitigates overfitting [ 44 ]. Similarly, in modeling metal removal rate (MRR) and surface roughness in non-traditional machining, RFR provided predictions with high reliability compared to linear models, highlighting its strength in dealing with noise and high-dimensional data sets [ 45 ]. MLPs, on the other hand, excel in capturing intricate dependencies through deep-layered representations, making them suitable for machining processes in which parameters like cutting force, tool deflection, and temperature gradients interact in complex ways. In hybrid machining environments, MLPs have shown higher generalization ability in predicting process outcomes like surface roughness and cutting force compared to multiple linear regression or gradient-boosted models [ 46 ]. Notably, MLPs effectively modeled mechanical outputs such as ultimate tensile strength and hardness across varying materials and machining conditions [ 47 ]. Together, RFR and MLP outperform conventional AI tools by offering ensemble-based reliability and deep-function approximation, relevant for adapting to the nonlinear, dynamic nature of machining processes. Although micro-milling has been extensively studied in recent years, most investigations have focused on traditional roughness parameters (e.g., Ra, Rz) under limited material conditions. Moreover, while some studies address tool deflection qualitatively, few works quantitatively examine the combined influence of tool geometry (diameter and neck length), cutting strategy, and material microstructure on both surface integrity and cross-sectional profile fidelity. Furthermore, there is a lack of studies integrating interpretable machine learning models with statistical analysis to predict and explain surface roughness outcomes in low-carbon steels with contrasting metallurgical behaviors. To fill this gap, the present study investigates the micro-milling of two steels with distinct microstructures, a conventional dual-phase steel (ferrite–pearlite) and an ultrafine-grained (single-phase ferrite) steel, under varying cutting conditions. The effects of machining parameters on surface roughness (Ra, Rz, skewness, kurtosis), burr formation, and profile accuracy are systematically analyzed. In addition, machine learning models (Random Forest and MLP) are employed not only to predict roughness values but also to interpret variable influence using feature importance analysis, providing a comprehensive view of surface generation mechanisms. This integrated approach represents an original contribution to the field of micro-manufacturing of low-carbon steels and predictive modeling of surface integrity. 2. Experimental procedures 2.1. Experimental setup Micro end-milling operations were performed to produce microgrooves using a vertical CNC machining centre Kern model D-824118 (50,000 rpm maximum speed) with dry cutting condition. Workpieces were clamped with working surface on the XY-plan with a precision vise. Each machining condition was performed four times. Figure 1 demonstrates the experimental setup. 2.2. Cutting tools Carbide ball-end mills with 400, 600 and 800 µm diameter were used. These cutter diameters were chosen because they are the most commonly used for slots production. Three values were selected in order to keep the total number of experiments and analyse within reasonable limits (total of 72 tests, included 3 replications). Tool edge raddi were measured via an Olympus 3D Laser Microscopy OLS4100, using 10 measurements per tool (Fig. 2 ). The cutting tool position control in relation to workpiece was made by a Laser Control NT Blum High-Tech Laser Systems with a precision probe and thermal compensation in all machine axis. 2.3. Workpiece material The workpiece materials used in this study consist of two different metallurgical conditions: a dual-phase and an ultrafine-grained steels. The dual-phase steel was characterized by an average grain size of 11 µm, a hardness of 192 HV, a yield strength of 474 MPa, and a Charpy impact energy of 176 J. The ultrafine-grained steel, produced through severe plastic deformation, exhibited a significantly refined microstructure with an average grain size of 0.7 µm. This refinement resulted in increased hardness (216 HV) and yield strength (510 MPa), as well as enhanced toughness, as indicated by a Charpy impact energy of 285 J. The mechanical properties of both materials were determined following standardized procedures. Hardness measurements were performed using a Vickers hardness tester, while yield strength was obtained from uniaxial tensile tests conducted at room temperature, in accordance with ASTM E8/E8M. Impact toughness was assessed using Charpy V-notch tests, following the ASTM E23 standard. Deeper descriptions about mechanical properties and microstructure analysis are presented in previously research [ 29 , 48 ]. These characterizations provided an understanding of the mechanical behavior of the selected workpiece materials, serving as a basis for further analysis of their machinability. 2.4. Experimental design In this study, the experimental design was structured to determine specifically the effects of ball-end mill diameter, tool neck length, feed per tooth, and milling sides (up- and down-milling sides) on microgroove geometry and surface roughness. To ensure a focused and statistically robust analysis, the spindle speed and depth of cut were intentionally kept constant throughout all experiments. This decision aimed to reduce the number of experimental variables and allow a more precise identification of the direct influence of the selected parameters. Table 1 presents the input variables to cut the microgrooves by using ball-end mills. Values of feed per tooth (ft) around and higher than tool cutting-edge radius were selected to evaluate the interaction between cutting tool microgeometry and workpiece metallurgical condition. Spindle rotation, feed per tooth and depth of cut (ap) limits were established for each ball-end mill size after machining pre-tests to avoid premature tool breaking due to tool rigidity. Further, depth of cut was also chosen to keep an equivalent proportion of tool penetration and tool diameter (⁓10%). Figure 3 presents the workpiece with schematic toolpath. The workpieces are formed as a sandwich with DPh and UFG steels. This setup was applied to be sure that the same cutting tool performed the machining conditions in both workpiece materials. A short cutting length (2.5 mm per workpiece material) was chosen, as tool wear was not the focus of this study. Table 1 Machining conditions to the micro end-milling operations. Group Parameter Ball-end mill diameter (µm) 400 600 800 Micromilling process Spindle rotation [rpm] 30,000 20,000 15,000 Feed [µm/tooth] 0.5, 2 and 5 0.5, 2 and 5 0.5, 2 and 5 Length of cut [mm] 2.5 2.5 2.5 Depth of cut [µm] 35 50 80 Width of cut [µm] 226 332 480 Cutting tool Edge radius [µm] 1.752 ± 0.27 1.541 ± 0.43 1.482 ± 0.15 Neck length [mm] 2 8 6 2.5. Measurement and statistical analysis Cross-sectional profiles, roughness profiles and roughness values of the microgrooves were assessed using an Olympus 3D Measuring Laser Microscopy OLS4100. Figure 4 presents the upper view of a microgroove and surface. Left side of the microgroove was cut under up-milling (chip starts to be formed with null thickness) and right side corresponds to the down-milling (chip starts to be formed with maximum thickness). Both regions were compared to investigate any effect of microgroove milling sides. Profiles were obtained by means of cross-section of the microgrooves perpendicular to the cutting tool feed direction. The evaluation of burr formation in the machined microgrooves was conducted through a combination of visual inspection, laser microscopy images, and the analysis of experimental cross-sectional profiles. Visual inspection of the workpieces was used to preliminarily identify the presence and morphology of burrs at the microgroove edges. High-resolution laser microscopy provided detailed surface topography, enabling the observation of localized plastic deformation and burr accumulation along the microgroove boundaries. Additionally, the cross-sectional profiles were examined to assess burr geometry, asymmetry, and distribution, allowing for the identification of differences in burr formation across varying machining conditions. This multi-modal evaluation ensured a comprehensive characterization of burr types and their relation to machining conditions. Roughness parameters i.e. average (Ra), root mean square (Rq), maximum height (Rz), maximum profile peak height (Rp), maximum profile valley depth (Rv), RMS slope of the profile (Rdq), skewness and kurtosis were measured twice in each milling side reaching eight roughness lines for cutting conditions and microgroove milling sides since four grooves were milled for each machining condition. These roughness parameters were chosen to reveal more sensitive effects of the aforementioned input variables upon part surface formation. To validate the machining results, various statistical tools were employed to assess geometrical accuracy, surface roughness, and width of cut deviations. The methodologies applied in this study include hypothesis testing, error analysis, confidence intervals, and determination coefficients (R 2 ), which allowed for a comprehensive assessment of the experimental data. All hypothesis tests used 95% confidence level (α = 0.05), standard in engineering research. One-sample t-test was performed to evaluate whether the experimentally measured width of cut (ae) significantly deviated from the expected nominal values for each combination of cutting parameters. The same was applied to skewness and kurtosis, but using reference values to evaluate surface characteristics (0 for skewness and 3 for kurtosis). The tests was conducted separately for DPh and UFG steels, as well as for different ball-end mill sizes and feed per tooth values. The statistical significance was determined based on the p-value. The accuracy of the machined microgroove profiles was quantitatively evaluated using Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), which measured the deviation between experimentally obtained and theoretical cross-sectional profiles. MAE provides the average absolute deviation between the measured and expected values, offering an intuitive measure of overall accuracy. RMSE penalizes larger deviations more strongly than MAE, as it squares the differences before averaging them. This metric is particularly useful for identifying extreme deviations and localized errors in the microgroove geometry. To evaluate the statistical reliability of the roughness and geometrical deviation measurements, 95% confidence intervals (CI) for the mean values were calculated. The confidence interval provides an estimate of the range within which the true mean is expected to fall, considering sample variability. By incorporating confidence intervals, the study ensured that the reported mean values accurately represented the underlying distributions, mitigating the impact of random fluctuations in experimental data. To quantify the agreement between experimental and theoretical profiles, the coefficient of determination was employed. This metric evaluates the proportion of variance in the experimental data that can be explained by the theoretical model. Higher R 2 values indicate strong agreement between theoretical and experimental cross-sectional profiles, while lower values suggest higher deviations. The statistical tools applied in this study provided a multi-level approach to evaluate machining performance. The combination of t-tests, error metrics, confidence intervals, and R 2 analysis ensured a comprehensive validation of the machining results, allowing for a deeper understanding of the effects of material properties, tool geometry, and process parameters on surface integrity and dimensional accuracy. 2.6. Machine Learning and Predictive Modeling of Surface Roughness To investigate the influence of machining parameters on surface roughness in micro end-milled steel components, machine learning techniques were applied. The predictive models were designed to estimate Ra based on key process variables, including ball-end mill diameter, feed per tooth, and microgroove milling sides (up- and down-milling). The approach involved a combination of data preprocessing, dimensionality reduction, and the implementation of machine learning algorithms and artificial neural networks, ensuring a deep analysis of roughness formation mechanisms. The dataset consisted of roughness measurements obtained from DPh and UFG steels, each subjected to 36 distinct machining conditions, combining three tool diameters, three feed per tooth values, and two microgroove milling sides. Each condition was evaluated through repeated measurements. After preprocessing and filtering, 324 observations were available for DPh and 306 for UFG, considering the exclusion of the the 800 µm tool diameter and 0.5 µm/tooth feed condition in UFG due to high plastic deformation and surface inconsistency. Before model training, categorical variables (e.g., microgroove milling sides) were converted to numerical format using one-hot encoding. Numerical variables were standardized using z-score normalization to eliminate scale bias. To reduce dimensionality and minimize multicollinearity, Principal Component Analysis (PCA) was applied. Cumulative variance analysis showed that the first two principal components (PC1 and PC2) retained over 95% of the total variance, making them suitable as input for modeling. To develop accurate predictive models for roughness, two machine learning approaches were implemented and trained independently for DPh and UFG: Random Forest Regressor (RFR): An ensemble learning algorithm based on decision trees, chosen for its ability to capture complex, nonlinear relationships between machining parameters and roughness. Multilayer Perceptron (MLP) Neural Network: A feedforward artificial neural network with three hidden layers (100, 50, and 25 neurons, respectively). ReLU activation was used in the hidden layers, combined with the Adam optimizer for weight updates. The model was trained for a maximum of 1,000 iterations, with early stopping (patience = 20) to prevent overfitting. For model evaluation, the dataset was split using a stratified 80/20 train-test split, ensuring representative distributions of all machining conditions across training and test sets. Additionally, a 5-fold cross-validation was applied on the training set to assess model stability. Hyperparameter tuning was performed for both models: For the Random Forest Regressor, a grid search was conducted over the number of estimators (100, 200, 500), maximum depth (None, 10, 20), and minimum samples split (2, 5), selecting the best combination based on the lowest cross-validated MAE. For the MLP, the number of layers and neurons per layer were defined based on empirical testing and validation performance. The final model used a learning rate of 0.001 and a batch size of 8. Model performance was evaluated using two metrics: Mean Absolute Error (MAE), which was employed to assess the average prediction error in Ra values, and the coefficient of determination, which measured the proportion of variance in Ra explained by the model. These metrics enabled direct comparison between algorithms and across different materials, supporting the assessment of model generalization and providing insights into the relationship between machining parameters and roughness. 3. Results and discussion 3.1. Microgroove topography and roughness profile analysis Microgooves machined in different workpiece metallurgical and cutting conditions are presented. Aiming to simplify the analysis, ball-end mill sizes are indicated as D400 (400 µm diameter), D600 (600 µm diameter) and D800 (400 µm diameter). The tool tip resulted in a flat surface at the bottom of all microgrooves due to the tool chisel edge, in order to minimize the effect of reducing the speed cutting near the centre of the grooves. Top burrs on the sides of the microgrooves were evaluated using a qualitative analysis of intensity images. Figure 5 to 10 present the top-view intensity images and the corresponding roughness profiles of the machined microgrooves for both DPh) and UFG steels, machined with D400, D600, and D800 ball-end mills. The roughness profiles were extracted from both up- and down-milling sides, allowing for a detailed evaluation of the effects of tool diameter, neck length, workpiece microstructure, and feed per tooth on the resulting surface topography. A direct comparison between different tool sizes initially suggested a progressive improvement in surface integrity with increasing ball-end mill size. However, the analysis must also consider the neck length of each tool, which directly influences its rigidity and potential deflection. The D400 (Figs. 5 and 6 ), with a 2 mm neck length, exhibits pronounced irregularities in the roughness profiles, likely due to the small tool diameter (size effect). The D600 (Figs. 7 and 8 ), with an 8 mm neck length, also displays irregularities in the roughness profile in some zones and showed signs of increased lateral tool deflection (curves on the microgroove top), leading to irregularities that may have counteracted the expected improvements in surface quality. Despite the larger tool size, this suggests that the extended neck length increases tool flexibility, making it more susceptible to deflection-related surface deviations. In contrast, the D800 (Figs. 9 and 10 ), with a 6 mm neck length, showed no apparent signals of tool defletion on the microgrove top. While it is well established that longer neck lengths tend to reduce tool stiffness and increase deflection (thereby compromising dimensional accuracy), some conditions in this study may suggest that the D800 exhibited comparable quality than D400 (UFG at 2 and 5 µm/tooth). The neck length-to-diameter ratio is 5 for the D400 tool and 7.5 for the D800 tool, both considerably lower than that of the D600 tool, which is 13. This indicates that the stiffness of the D400 and D800 tools is comparable, exhibiting similar behavior during machining and higher resistance to deflection. The influence of workpiece microstructure on the roughness profiles is also noticed. The DPh exhibits higher roughness variation between microgroove milling sides, which may be exacerbated by uneven material removal due to greater tool flexibility and minimum cutting thickness effect, respectively. Conversely, the UFG produced more similar roughness profiles in both microgroove milling sides, benefiting from its homogeneous microstructure, which ensured a more stable cutting process. The roughness profiles also highlighted the influence of feed per tooth on surface characteristics. The results indicated that higher ft values generally lead to increased surface irregularities, while lower ft values contribute to a more consistent surface finishing. At 0.5 µm/tooth, the tool-workpiece interaction was more continuous, reducing abrupt height variations in the microgroove roughness profile. At 2 µm/tooth, a moderate increase in roughness amplitude is observed, though it remains within a relatively stable range. However, at 5 µm/tooth, there was a significant increase in roughness, attributed to the larger chip thickness, leading to increased instability. These effects were more pronounced in the D600, whose the combination of a higher ft and an extended neck length likely exacerbates tool deflection, further deteriorating machined surface quality. The analysis of microgroove milling sides further confirms the role of cutting dynamics in surface formation. Up-milling sides tended to produce higher roughness amplitudes, which may be associated with increased plowing effects and higher tool-workpiece friction forces at the start of the cutting process. Conversely, down-milling sides exhibited smoother surfaces, as the gradual tool engagement reduces impact forces and promotes better machined surface integrity. The interaction between microgroove milling side and tool size is particularly relevant for the D600, in which the long neck length increases flexibility, making the tool more susceptible to vibrations and deviations in up-milling sides. In Fig. 10 is presented 2D laser microscopy image of the microgroove machined with the D800 at 0.5 µm/tooth. The central slot of the microgroove exhibited severe plastic deformation, culminating in material rupture. This phenomenon is attributed to the reduction in cutting speed near the tool center, which increases the difficulty of material removal. As the cutting tool traverses this zone, it compresses the material beyond its plastic limit, leading to failure and lateral displacement of the deformed material towards the microgroove edges. The deformation was more pronounced on the up-milling side, where the cutting-edge must gradually reach the minimum chip thickness before initiating effective material removal. As a result, the tool-plowing effect intensifies, generating higher localized strains that contribute to excessive deformation. This phenomenon compromised the integrity of the machined surface on the up-milling side, as evidenced in the 2D laser microscopy image. The higher toughness of the ultrafine-grained steel (285 J) exacerbated this effect compared to the dual-phase steel (176 J), where material failure was less pronounced. The ultrafine microstructure, characterized by a higher resistance to crack propagation, allows for higher plastic deformation before rupture, thus favoring material displacement rather than brittle fracture [ 49 , 50 ]. Considering classification of Gillespie [ 51 ], minor burrs were observed on both lateral tops of the microgrooves. The depth of cut (ap) was not independently varied in this study; however, its effect is inherently linked to the ball-end mill radius (R) and workpiece interaction geometry. This relationship directly influences the edge angle (θ Edge ), which in turn affects chip formation and burr minimization. Previous studies on edge angle effects in micro end-milling have demonstrated that θ Edge values higher than 90° up to approximately 150° help minimize burr formation and improve machining stability [ 41 ]. This behavior was also observed in this study, where minor burrs were detected in all machining conditions, suggesting that the combination of R and ap led to an edge angle of approximately 145°, contributing to a stable cutting process (Fig. 11 ). Furthermore, the results confirmed that even when the ft was lower than the cutting edge radius, no significant top burrs were produced. This finding aligns with previous research that suggests that appropriate tool geometry can prevent burr formation without requiring modifications to the workpiece geometry [ 52 ]. 3.2. Geometrical deviation of machined microgrooves Figure 12 to 14 present the experimental and theoretical cross-sectional profiles of the machined microgrooves for D400, D600, and D800 ball-end mills, at different feed per tooth values for both DPh and UFG steels. The theoretical profiles are shown in black, while the experimentally obtained microgroove profiles are represented in red. Additionally, the coefficient of determination and statistical deviation values are provided to quantify the degree of geometric agreement between the theoretical and experimental profiles. The results indicated that DPh exhibited similar geometrical accuracy compared to UFG, as evidenced for D400 and D600. However, D800 showed better agreement between profiles for DPh, as seen by higher R 2 values and lower statistical deviations. Despite its heterogeneous microstructure, the machining process resulted in microgrooves that closely followed the theoretical geometry. The UFG steel exhibited higher deviations from the theoretical profiles, likely due to its higher toughness than DPh, which increased the tendency for plastic deformation rather than brittle material removal, making the final microgroove geometry more susceptible to variations. Although the D800 tool features a longer neck length compared to D400, its geometrical accuracy and surface roughness outcomes were not always inferior. This can be explained by the fact that neck length alone does not determine tool rigidity, but rather its relationship with tool diameter. In this case, the neck length-to-diameter ratio was more favorable for D800 (7.5) than for D600 (13), resulting in lower effective flexibility. In addition, the larger core diameter of the D800 tool enhances its structural stiffness, helping to counterbalance the increased unsupported length. Consequently, the improved performance observed with the D800 tool under specific machining conditions should not be attributed to the neck length itself, but to the combined effect of diameter, neck length, feed per tooth, and workpiece material behavior. This reinforces the importance of evaluating deflection susceptibility based on geometric ratios and process interactions rather than on neck length in isolation. Although the D600 presented the highest neck-to-diameter ratio among all tested tools, typically associated with increased flexibility and geometric inaccuracy, it exhibited the lowest median values and variability for both MAE and RMSE (Fig. 15 ). This behavior suggests that geometric stiffness alone does not fully explain the profile accuracy in micromilling. A possible explanation lies in the balanced configuration of the D600, which combines an intermediate diameter with cutting conditions that may have favored more consistent elastic deformation, reducing localized distortions. In contrast, the D400, despite having a shorter neck, showed higher geometric errors at increased feed per tooth, likely due to stress concentration over its reduced cross-sectional area. The D800, on the other hand, although stiffer in terms of diameter, combined a longer neck and higher tool-workpiece engagement, especially in UFG steel, which may have amplified structural deformation and deflection-induced deviations. While cutting forces were not directly measured in this study, the observed geometric deviations and systematic errors suggest that tool deflection dynamics are significantly affected by the interaction between tool geometry and material behavior. The comparison between MAE and RMSE revealed minimal differences between the two metrics as well. Since RMSE penalizes larger errors quadratically, this similarity suggests that the individual errors are uniformly distributed, without significant outliers (*) that could disproportionately influence the mean error. The absence of extreme values reinforces the reliability of both error metrics and suggests that no substantial deviations affect the accuracy assessment. The MAE and RMSE results also indicated that D400 was more suscetible to tool deflexion against the feed motion at higher ft value, while D800 showed higher error medians and variability for both steels at 0.5 µm/tooth and higher error medians for UFG at 2 and 5 µm/tooth. The possible increase of cutting forces during machining with D400 at higher feed per tooth favoured tool deflection, resulting in higher error medians. By other hand, for D800, UFG steel showed more difficulty to cutting process than DPh due to mechanical properties. In micromilling processes, maintaining dimensional accuracy is challenging due to tool deflection, which can lead to deviations in the machined width. The boxplot analysis of the MAE for width of cut showed variations across different cutting conditions, particularly at higher ft values and with larger tool sizes (Fig. 16 ). One of the factors contributing to this variation is the deflection of micro ball-end mills, which is influenced by their geometric characteristics. As presented, the tools used in this study exhibit a neck length, affecting their flexibility. This structural feature for greater neck-to-diameter ratio makes them more susceptible to bending under cutting forces. As a result, the actual width of cut often deviates from the nominal value, increasing process variability. The observed machining instability is primarily associated with the elastic deformation of the tool rather than random process fluctuations. This behavior is evident in the increased spread of MAE values for certain cutting conditions, suggesting a loss of predictability in the width of cut. The presence of outliers supports the idea that deflection-related variations occur sporadically under certain machining conditions. A one-sample t-test was then applied to compare the experimental ae values with the nominal values for different machining conditions (Table 2 ). Data normality was assessed using the Shapiro-Wilk test, and all datasets exhibited normal distribution (p > 0.05), what validate the test. The statistical analysis confirmed that the workpiece material significantly influenced the deviation of ae from the expected values. In particular, UFG exhibited statistically significant deviations (p < 0.05) for D600 and D800, suggesting that its higher toughness led to more pronounced variations in width of cut, likely due to increased plastic deformation. In contrast, DPh demonstrated more stability. The influence of feed per tooth on ae accuracy was also evident. At 5 µm/tooth, significant deviations were observed, especially in UFG steel, where t-values reached extreme values (-19.92 for D400 and 28.44 for D600, both with p < 0.05). This suggests that increased material removal rates introduced machining instability, leading to higher deviations from expected values. Conversely, 0.5 µm/tooth resulted in negative t-values for D400 and D800 in both materials, indicating that the actual ae was systematically smaller than the nominal values. Regarding tool size, D400 demonstrated more stable results for both workpiece materials, where at 2 µm/tooth, the t-statistic was the lowest and p > 0.05, indicating an experimental ae closer to nominal value. This suggests that smaller tools at moderate feed per tooth favor more consistent ae values. Table 2 Results of one-sample t-tests comparing experimental width of cut values to the nominal reference values under different machining conditions. Size Material ft t-statistic p-value 400 DPh 0.5 -3.5130 0.0170 2.0 -0.9569 0.3825 5.0 -5.9848 0.0018 UFG 0.5 -4.4530 0.0066 2.0 0.6214 0.5615 5.0 -19.9247 0.0000 600 DPh 0.5 0.9009 0.4089 2.0 17.9353 0.0000 5.0 7.0770 0.0008 UFG 0.5 -3.8690 0.0117 2.0 7.5465 0.0006 5.0 28.4482 0.0000 800 DPh 0.5 -28.4827 0.0000 2.0 -2.0236 0.0989 5.0 5.7646 0.0022 UFG 0.5 -14.1577 0.0000 2.0 -28.9983 0.0000 5.0 -7.9536 0.0005 3.3. Roughness analysis The machined microgrooves were evaluated using commonly applied roughness parameters to assess the topography of machined surfaces. However, the parameters selected for this study were determined based on statistical correlation analysis to ensure that each parameter was statistically independent, describing different aspects of the surface roughness [ 53 ]. The roughness parameters chosen were those exhibiting low data redundancy, as indicated by the R 2 . Table 3 presents the results of the statistical correlation analysis between roughness parameters, showing a strong correlation among Ra, Rq, Rz, Rdq, Rv, and Rp, while Rsk and Rku displayed low correlation with each other and with the other parameters. Table 3 The values of the linear correlation coefficient (R 2 ) between roughness parameters describing topography of the machined surface. Parameter Ra Rq Rz Rdq Rp Rv Rsk Rku Ra 1.00 Rq 0.99 1.00 Rz 0.98 0.98 1.00 Rdq 0.98 0.98 0.99 1.00 Rp 0.94 0.94 0.96 0.95 1.00 Rv 0.98 0.97 0.98 0.97 0.90 1.00 Rsk 0.00 0.00 0.00 0.00 0.03 0.02 1.00 Rku 0.02 0.03 0.05 0.04 0.05 0.04 0.00 1.00 Although the parameters exhibited similar trends, certain characteristics of the machined surface can be identified through the analysis of strongly correlated parameter pairs, as illustrated in Fig. 17 . The correlation between Rq and Ra indicated that Rq was 27% higher than Ra, meaning that the deviation from the mean line of the roughness profile remained relatively constant. The relationship between Rdq and Rz showed that the increase in surface steepness (Rdq) corresponded to 2.8% of Rz, while Ra accounted for 22% of Rz. Additionally, the ratio between Rp and Rv was 0.9, as seen in the graph of general relationship between Rp and Rv, indicating a balanced distribution of maximum peak height and maximum valley depth. However, when analyzed by tool size, it was observed that D600 produced Rp values 12% higher than Rv, whereas D800 exhibited Rp values 18% lower than Rv. Due to its higher sensitivity to surface texture variations compared to Ra, Rz was selected as the primary parameter to evaluate the height of the roughness profile. Figure 18 presents a boxplot with the effect of cutting parameters on Rz. For D400, although a tendency for increasing median and variability with feed per tooth was observed, the high dispersion of values limits a conclusive interpretation regarding roughness escalation. In the case of D600, median values remained relatively stable across feed rates, but the ultrafine-grained steel exhibited substantial variability, which may reflect microstructural influences or instability in the cutting process. For D800, a slight increase in Rz with feed per tooth was noted for DPh. However, due to the pronounced variability, particularly at lower feed per tooth for UFG, this trend should be interpreted with caution, as it does not consistently hold across all conditions. These observations underscore the complexity in establishing direct relationships between feed per tooth and roughness when high data variability is present. To further investigate surface texture characteristics beyond average roughness values, additional parameters such as skewness and kurtosis were evaluated to capture profile asymmetry and peak distribution. The low correlation between Rsk and Rku suggests that the machined surface did not exhibit stratitication, i.e., it lacked clustered zones of extreme peaks or valleys, indicanting that the surface texture resulted from a relatively continuous material removal process across the toolpath. Figure 19 presents a boxplot with the effect of machining conditions on skewness and kurtosis. In the skewness analysis, both workpiece materials exhibited similar trends in median values and dispersion. Although most conditions resulted in skewness values near zero, indicating an approximately symmetrical peak-to-valley distribution, variability was notable across several cases. For instance, surfaces machined with D800 at 0.5 and 2 µm/tooth showed a tendency toward peak predominance (positive skewness), whereas D400 at 2 µm/tooth and D800 at 5 µm/tooth displayed a shift toward valley predominance (negative skewness). However, due to the spread in the data, these tendencies should be interpreted with caution and not as definitive trends. Regarding kurtosis, values close to 3 were observed primarily at higher feed rates, which may indicate a profile distribution resembling a Gaussian shape. In contrast, other machining conditions resulted in kurtosis values generally below 3, suggesting flatter distributions with fewer extreme peaks and valleys. Nevertheless, the considerable variability across measurements limits the ability to generalize these findings, and the results should be seen as indicative rather than conclusive. To provide statistical support for these observations and further assess whether the skewness and kurtosis values significantly deviated from ideal reference values (0 and 3, respectively), one-sample t-tests were conducted for each machining condition. This approach enabled the identification of significant asymmetries or deviations from normality in the roughness distributions, accounting for data variability across tool sizes, materials, and feed per tooth. Data normality was assessed using the Shapiro-Wilk test, and datasets exhibited normal distribution (p > 0.05), validating the test. Table 4 summarizes the one-sample t-test results. Table 4 Statistical significance of skewness and kurtosis deviations based on t-test results. Size Material ft Skewness t-statistic Skewness p-value Kurtosis t-statistic Kurtosis p-value 400 DPh 0.5 1.6464 0.1104 -7.2924 0.0000 2.0 -2.8612 0.0077 -4.4826 0.0001 5.0 -0.8092 0.4249 -4.6132 0.0000 UFG 0.5 1.6823 0.1032 -10.9772 0.0000 2.0 -1.9060 0.0665 -3.3073 0.0025 5.0 -0.0969 0.9234 -4.8255 0.0000 600 DPh 0.5 0.9537 0.3480 -8.9778 0.0000 2.0 -0.2155 0.8308 -4.2983 0.0001 5.0 1.3292 0.1941 -1.5318 0.1363 UFG 0.5 0.0937 0.9259 -8.6846 0.0000 2.0 0.3971 0.6941 -8.5020 0.0000 5.0 0.4651 0.6452 -0.3598 0.7215 800 DPh 0.5 3.3237 0.0024 -7.7387 0.0000 2.0 3.4222 0.0018 -3.5110 0.0014 5.0 -5.8839 0.0000 -4.2758 0.0001 UFG 0.5 1.8931 0.0683 -10.5780 0.0000 2.0 2.0220 0.0524 -5.7993 0.0000 5.0 -2.1488 0.0401 -6.6554 0.0000 The skewness analysis confirmed that, under most machining conditions, the roughness distributions did not significantly deviate from symmetry (p ≥ 0.05), suggesting that peaks and valleys were approximately balanced. However, for DPh in specific conditions, particularly at D400 and 2 µm/tooth, and D800 (all feed per tooth), statistically significant deviations were observed (p < 0.05), indicating a higher tendency for valley formation (negative skewness) or peak generation (positive skewness). The occurrence of negative skewness under certain conditions may be attributed to plastic deformation mechanisms like ploughing, where the ductility favors valley formation instead of chip removal. Conversely, positive skewness observed for D800 at lower feed per tooth may indicate the presence of residual peaks due to insufficient chip thickness and material accumulation near the cutting edge. The statistical analysis of kurtosis (Table 4 ) revealed that most machining conditions resulted in significantly lower values than the reference Gaussian distribution (kurtosis < 3), indicating flatter surface profiles with fewer extreme peaks and valleys. This behavior is consistent with stable material removal mechanisms, especially at lower feed per tooth and with smaller tool diameters (D400). For the D600 tool, both UFG and DPh steels presented kurtosis values statistically equivalent to 3 at 5 µm/tooth, which may reflect increased variability in chip formation or the emergence of localized surface instabilities under higher cutting loads. In contrast, the D800 consistently produced platykurtic surfaces, possibly due to the larger effective cutting area distributing forces more evenly across the surface. These results indicate that tool size, feed per tooth, and workpiece microstructure interact to influence not only the amplitude of surface roughness but also the statistical distribution of texture features. 3.3. Machine learning-based roughness prediction The predictive models for surface roughness (Ra) were separately evaluated for DPh and UFG steels, using Random Forest Regressor (RFR) and Multilayer Perceptron (MLP) Neural Network. The objective was to analyze the influence of machining parameters on roughness formation and assess the predictive capability of machine learning techniques. By this sense, Table 5 presents the comparative performance of the models for materials. Table 5 Model performance for workpiece materials. Material Model MAE (nm) R 2 DPh Random Forest 13.16 0.470 MLP Neural Network 12.73 0.480 UFG Random Forest 7.53 0.664 MLP Neural Network 7.25 0.717 For the DPh steel, the models exhibited moderate accuracy, suggesting that additional parameters beyond those considered might be more significant in determining roughness. The Random Forest model resulted in a MAE of 13.16 nm and an R 2 of 0.47, indicating that 47% of the roughness variation was explained by the model. Meanwhile, the MLP Neural Network achieved a slightly better performance, with an MAE of 12.73 nm and an R 2 of 0.48, demonstrating that machine learning techniques can partially predict roughness in dual-phase steel but with limited reliability. The results indicated that the alternating ferrite-pearlite microstructure of DPh steel might introduce higher variability in surface formation, reducing the effectiveness of purely data-driven predictive models. The complex interaction between material properties and tool engagement may require additional behaviour of tool deflections during cutting to enhance the precision of the predictions. For the UFG steel, the predictive performance significantly improved, indicating a more stable relationship between machining parameters and roughness outcomes. The Random Forest model achieved a MAE of 7.53 nm and an R 2 of 0.66, demonstrating that 66.4% of the roughness variation could be explained by the input parameters. The MLP Neural Network further improved the prediction, reducing the error to 7.25 nm and increasing R 2 to 0.71, explaining 71% of the roughness variability. These results highlight that the homogeneous microstructure of UFG contributes to a more predictable roughness formation process, allowing machine learning models to better capture the relationships between process variables and surface characteristics. The fact that the MLP model outperformed the Random Forest approach showed that non-linear interactions exist between the machining parameters and roughness, which neural networks can better account for. However, it is worth noting that the MLP model reached the maximum number of iterations without full convergence, indicating that further hyperparameter tuning, such as adjusting the learning rate and optimizing the number of hidden layers, could lead to even higher improvements. In addition to performance metrics, a feature importance analysis was carried out using the Random Forest model to assess the contribution of each input variable to the roughness prediction. The results revealed that the tool size was the most influential factor, followed by the feed per tooth and the microgroove milling side. Among the microgroove milling side, the down-milling side contributed more significantly to roughness variations than the up-milling side. These findings are consistent with the domain knowledge that tool geometry and chip engagement conditions strongly influence the surface generation mechanisms in micromilling [ 4 , 54 ]. While the Random Forest model provided interpretability by quantifying the relative importance of each input variable in predicting surface roughness (a process known as feature importance ranking), the MLP model demonstrated superior predictive power, likely due to its enhanced capacity to capture complex, multivariate nonlinear interactions. These findings suggest that although tree-based models such as Random Forest offer valuable insights into which machining parameters most influence the outcome, neural networks are more suitable for achieving high predictive accuracy in scenarios involving intricate and interdependent machining dynamics. The predictive capability of the machine learning models was notably higher for UFG steel than for DPh steel, reinforcing the idea that materials with homogeneous microstructures produce more consistent machining responses. In contrast, the higher microstructural complexity of DPh steel introduces additional variability in the roughness formation process, which remains challenging for AI-based modeling. Despite this, the results indicated that machine learning techniques, particularly neural networks, hold significant potential for roughness prediction in micromilling. The higher accuracy observed for UFG showed that AI-based process control strategies could be successfully applied to optimize surface quality for homogeneous microstructure steels. Furthermore, roughness in UFG varied more significantly with changes in cutting parameters, while in DPh steel, roughness remained more uniform and predictable. AI models tend to perform better when there is a broad range of variation in the data, as this allows the identification of complex patterns that explain the relationships between input parameters and system response. In the case of DPh, since the roughness values were more predictable and less dispersed, the models struggled to identify unique patterns that explained the variation in Ra. As a result, the lower dispersion of roughness values in DPh reduced the AI’s ability to capture deeper and more complex patterns, limiting the predictive performance of the model. To contextualize the scientific contributions of this work, Table 6 presents a comparative summary of recent studies (2018–2025) that employed machine learning techniques for predicting surface roughness in machining processes, with a particular focus on micro-milling and precision milling. The table highlights key aspects such as the machined material, roughness parameters considered, type of machining process, adopted artificial intelligence (AI) models, whether transverse profile accuracy was evaluated, and the main contributions or limitations of each study. Compared to previous works, the present research uniquely integrates the prediction of surface roughness with the analysis of geometrical accuracy of microgrooves using ball-end micromilling, considering different microstructural conditions of low-carbon steels. Furthermore, it distinguishes itself by combining interpretable machine learning models, Random Forest and Multilayer Perceptron, with feature importance analysis, offering deeper insights into the influence of tool geometry and microstructure on surface formation mechanisms. Table 6 Comparative summary of recent studies (2018–2025) using machine learning techniques for surface roughness prediction in micro-milling and precision machining. Study Material Process Roughness parameters AI Techniques Profile accuracy Main Contribution /Limitation Lu et al. (2019) [55] Single-crystal copper Micro-milling Ra SVR No Integrated crystallographic orientation in roughness modeling; limited to single-crystal copper. Shang et al . (2023) [ 56 ] Tool steel Ultra-precision micro-milling Ra Extreme Learning Machine (ELM) No Applied ELM with feature fusion for high-accuracy Ra prediction (~ 1.6% MAPE); limited to one material and test setup. Zeng and Pi (2023) [ 57 ] S45C steel; W78Cu22 alloy Milling (incl. micro-milling) Ra CNN-GRU (Physics-informed) No Physics-guided DL model improved prediction accuracy; complexity added by physical modeling. Tsai et al . (2023) [ 58 ] Stainless steel SUS304 CNC milling Ra DNN, CNN, LSTM Yes Predicted Ra and profile accuracy from force signals; CNN showed low computation time; classification step not beneficial. Kosarac et al . (2023) [ 59 ] Ti-6Al-4V Conventional milling Ra Random Forest, ANN, SVR No RF performed best in small datasets; dataset size limited generalization. Present study Low-carbon steel (UFG and Dual-Phase) Micro-milling (Ball-end) Ra, Rz, Rsk, Rku Random Forest, MLP Neural Network Yes Integrated Ra and profile accuracy prediction with ML and feature importance; unique focus on microstructural effects. 4. Conclusions This study investigated the influence of tool geometry, particularly ball-end mill size and neck length, feed per tooth, and microgroove milling side on the machining accuracy and surface roughness of microgrooves fabricated in dual-phase and ultrafine-grained low-carbon steels. The integration of statistical analysis and machine learning techniques enabled a comprehensive evaluation of tool–workpiece interactions and the predictive modeling of surface characteristics. The following conclusions can be drawn: Tool deflection was a critical factor affecting dimensional accuracy. While larger tools size inherently improved stiffness, excessive neck length (as seen with the D600 tool) introduced significant flexibility, leading to increased profile deviations. The D400 tool exhibited the lowest geometric errors at moderate feed rates due to its shorter unsupported length. Feed per tooth significantly influenced surface integrity. Lower feed values (0.5 µm/tooth) promoted smoother profiles and minimized surface irregularities, while higher feeds increased roughness amplitude and deformation, especially in up-milling sides. Workpiece microstructure is the main influence in machining outcomes. Ultrafine-grained steel, with its homogeneous and though structure, exhibited more stable surface formation and higher predictability of roughness, while dua-phase steel demonstrated better dimensional consistency due to its resistance to plastic deformation. Burr formation was minimal across all conditions, attributed to favorable edge angles (~ 145°) formed by the interaction between tool radius and depth of cut. This edge geometry contributed to stable chip formation even at low feed rates. The Multilayer Perceptron outperformed the Random Forest Regressor in predicting surface roughness, particularly for ultrafine-grained steel, achieving an R² of 0.711. This superior performance is attributed to the microstructural homogeneity of ultrafine-graned steel, which promotes stable machining behavior and reduces data variability, enhancing the accuracy of nonlinear learning models. In contrast, the dual-phase steel exhibited higher response variability, limiting predictive precision despite the interpretability advantages offered by RFR. These findings highlight the importance of selecting appropriate tool geometry and feed strategies tailored to the material’s microstructure. Moreover, the demonstrated effectiveness of machine learning in roughness prediction supports its integration into micromachining process planning, particularly for homogeneous microstructured steels in which AI models can enhance surface quality control. In contrast to prior studies that typically address roughness or profile accuracy in isolation, the present work provides an integrated modeling framework supported by interpretable AI techniques. This dual focus, combined with the consideration of metallurgical variability, represents a novel contribution to the predictive modeling of surface integrity in micromachining of low-carbon steels. Declarations Conflict of interest The authors declare that they have no known competing financial interests or personal relationships which have, or could be perceived to have, influenced the research reported in this article. Acknowledgements The authors would like to express their gratitude to the Technological Research Institute of São Paulo (IPT) for providing access to laboratory facilities and to Mitsubishi Materials for supplying the cutting tools used in this study. Funding: This work was supported by the National Council of Scientific and Technological Development (CNPq) [grant number 468309/2014-4]. Author Contribution Statement Cleiton Lazaro Fazolo de Assis: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Writing-original draft, Visualization, Supervision, Project administration, Funding acquisition. Alessandro Roger Rodrigues: Methodology, Formal analysis, Resources, Writing-reviewing and editing. References Gao S, Duan X, Zhu K, Zhang Y (2024) Investigation of the tool flank wear influence on cutter-workpiece engagement and cutting force in micro milling processes. Mech Syst and Signal Proc 209:111104. https://doi.org/10.1016/j.ymssp.2024.111104 Sun Y, Sun Y, Huang Y, Gong S, Sun M, Liu M (2025) Study on developing predicted system model of cutting-edge trajectory for micro-milling process based on tool runout error, chip thickness and force signal. Mech Syst and Signal Proc 228:112410. https://doi.org/10.1016/j.ymssp.2025.112410 Basile V, Modica F, Rebaioli L, Surace R, Fassi I (2023) Process Chains for Micro-Manufacturing: Modeling and Case Studies. J Manuf and Mat Proc 7(6):215. https://doi.org/10.3390/jmmp7060215 Biondani FG, Bissacco G (2019) Effect of cutting edge micro geometry on surface generation in ball end milling. CIRP annals 68(1):571-574. https://doi.org/10.1016/j.cirp.2019.04.017 Oliaei SNB, Karpat Y, Davim JP, Perveen A (2018) Micro tool design and fabrication: A review. J Manuf Proc 36:496-519. https://doi.org/10.1016/j.jmapro.2018.10.038 Sekulic M, Pejic V, Brezocnik M, Gostimirović M, Hadzistevic M (2018) Prediction of surface roughness in the ball-end milling process using response surface methodology, genetic algorithms, and grey wolf optimizer algorithm. Adv in Prod Eng & Manag 13(1):18-30. https://doi.org/10.14743/apem2018.1.270 Jia Z, Lu X, Gu H, Ruan F, Liang SY (2021) Deflection prediction of micro-milling Inconel 718 thin-walled parts. J Mat Proc Tech 291:117003. https://doi.org/10.1016/j.jmatprotec.2020.117003 Wojciechowski S, Wiackiewicz M, Krolczyk GM (2018) Study on metrological relations between instant tool displacements and surface roughness during precise ball end milling. Measurement 129:686-694. https://doi.org/10.1016/j.measurement.2018.07.058 Celis P, Vazquez E, Soria-Hernández CG, Bargnani D, Rodriguez CA, Ceretti E, García-López E (2022) Evaluation of ball end micromilling for Ti6Al4V ELI microneedles using a nanoadditive under MQL condition. Int J Prec Eng and Manuf-Green Tech 9(5):1231-1246. https://doi.org/10.1007/s40684-021-00383-y Guo Q, Liu Z, Yang Z, et al (2024) Development, challenges and future trends on the fabrication of micro-textured surfaces using milling technology. J Manuf Proc 126:285-331. https://doi.org/10.1016/j.jmapro.2024.07.112 Klauer K, Eifler M, Kirsch B, Seewig J, Aurich JC (2020) Ball end micro milling of areal material measures: influence of the tilt angle on the resulting surface topography. Prod Eng 14(2):239-252. https://doi.org/10.1007/s11740-019-00943-x Balázs BZ, Geier N, Pereszlai C, Poór DI, Takács M (2021) Analysis of cutting force and vibration at micro-milling of a hardened steel. Procedia CIRP 99:177-182. https://doi.org/10.1016/j.procir.2021.03.025 Imani BM, Elbestawi MA (2001) Geometric simulation of ball-end milling operations. J. Manuf Sci Eng 123(2):177-184. https://doi.org/10.1115/1.1347034 Pratap T, Patra K (2018) Micro ball-end milling—an emerging manufacturing technology for micro-feature patterns. Int J Adv Manuf Tech 94(5-8):2821-2845. https://doi.org/10.1007/s00170-017-1064-9 Song B, Zhang D, Jing X, Shi B, Wang F, Li H (2024) Cleaner production of multi-scale surface textures using integrated ball-end and vibration-assisted milling. J Cleaner Prod 484:144316. https://doi.org/10.1016/j.jclepro.2024.144316 Zhang J, Zhang S, Jiang D, Wang J, Lu S (2020) Surface topography model with considering corner radius and diameter of ball-nose end miller. Int J Adv Manuf Tech 106:3975-3984. https://doi.org/10.1007/s00170-019-04897-3 Herraz M, Redonnet JM, Mongeau M, Sbihi M (2020) A new method for choosing between ball-end cutter and toroidal cutter when machining free-form surfaces. Int J Adv Manuf Tech 111(5):1425-1443. https://doi.org/10.1007/s00170-020-06087-y Venkatesh V, Swain N, Srinivas G, Kumar P, Barshilia HC (2017) Review on the machining characteristics and research prospects of conventional microscale machining operations. Mat and Manuf Proc 32(3):235-262. https://doi.org/10.1080/10426914.2016.1151045 Wojciechowski S (2021) Estimation of minimum uncut chip thickness during precision and micro-machining processes of various materials—a critical review. Materials 15(1):59. https://doi.org/10.3390/ma15010059 Mikó B, Zentay P (2019) A geometric approach of working tool diameter in 3-axis ball-end milling. Int J Adv Manuf Tech 104(1-4):1497-1507. https://doi.org/10.1007/s00170-019-03968-9 Akamatsu T, Kitajima K, Ueda A (2004) Cutting Accuracy of the Small Radius Ball Endmill in Deep Precision Machining. Key Eng Mat 257-258:565-570. https://doi.org/10.4028/www.scientific.net/kem.257-258.565 Assis CL, Jasinevicius RG (2019) Influence of tool neck length on tool deflections during micromilling of an ultrafine grained low-carbon steel. In: Leach RK, Billington D, Nisbet C, Phillips D. editors: Proceedings of the 19th Euspen Conference, Bilbao, Spain. 2019. Nothampton: twenty10, 468-469. https://www.euspen.eu/knowledge-base/ICE19221.pdf [accessed 31 March 2025] Begic-Hajdarevic D, Cekic A, Kulenovic M (2014) Experimental study on the high speed machining of hardened steel. Procedia Eng 69:291-295. https://doi.org/10.1016/j.proeng.2014.02.234 Wang D, Penter L, Hänel A, Yang Y, Ihlenfeldt S (2022) Investigation on dynamic tool deflection and runout-dependent analysis of the micro-milling process. Mech Syst and Signal Proc 178:109282. https://doi.org/10.1016/j.ymssp.2022.109282 Pratap T, Patra K (2017) Micromilling of ti-6al-4v titanium alloy using ball-end tool. In IOP Conference Series: Mat Sci and Eng 229(1):012011. https://doi.org/10.1088/1757-899X/229/1/012011 Vogler MP, DeVor RE, Kapoor SG (2004) On the modeling and analysis of machining performance in micro-endmilling, part I: surface generation. J Manuf Sci Eng 126(4):685-694. https://doi.org/10.1115/1.1813470 Mian AJ, Driver N, Mativenga PT (2010) A comparative study of material phase effects on micro-machinability of multiphase materials. Int J Adv Manuf Tech 50(1-4):163-174. https://doi.org/10.1007/s00170-009-2506-9 Rodrigues AR, Balancin O, Gallego J et al (2012) Surface integrity analysis when milling ultrafine-grained steels. Mat Research 15(1):125-130. https://doi.org/10.1590/S1516-14392011005000094 De Assis CL, Jasinevicius RG, Rodrigues AR (2015) Micro end-milling of channels using ultrafine-grained low-carbon steel. Int J Adv Manuf Tech 77(5-8):1155-1165. https://doi.org/10.1007/s00170-014-6503-2 Shao Y, Li J, Zhang X (2022) The impact of financial development on CO2 emissions of global iron and steel industry. Envir Sci and Pollut Res 29(29):44954-44969. https://doi.org/10.1007/s11356-022-18977-7 Kim J, Sovacool BK, Bazilian M et al (2022) Decarbonizing the iron and steel industry: A systematic review of sociotechnical systems, technological innovations, and policy options. Energy Res & Soc Sci 89:102565. https://doi.org/10.1016/j.erss.2022.102565 Zhang D (2021) Ultrafine grained metals and metal matrix nanocomposites fabricated by powder processing and thermomechanical powder consolidation. Prog in Mat Sci 119:100796. https://doi.org/10.1016/j.pmatsci.2021.100796 Gao C, Wang Y, Qiu X, Chi H, Zhou J, Cai H, Cheng X (2022) Microstructure evolution and compressive properties of a low carbon-low alloy steel processed by warm rolling and subsequent annealing. Mat Charact 192:112237. https://doi.org/10.1016/j.matchar.2022.112237 Ghosh S, Kömi J, Mula S (2020) Flow stress characteristics and design of innovative 3-steps multiphase control thermomechanical processing to produce ultrafine grained bulk steels. Mat & Design 186:108297. https://doi.org/10.1016/j.matdes.2019.108297 Zhao J, Jiang Z (2018) Thermomechanical processing of advanced high strength steels. Prog in Mat Sci 94:174-242. https://doi.org/10.1016/j.pmatsci.2018.01.006 Zhao Z, To S, Wang J, Zhang G, Weng Z (2022) A review of micro/nanostructure effects on the machining of metallic materials. Mat & Design 111315. https://doi.org/10.1016/j.matdes.2022.111315 Balázs BZ, Geier N, Takács M, Davim JP (2021) A review on micro-milling: recent advances and future trends. Int J Adv Manuf Tech 112:655-684. https://doi.org/10.1007/s00170-020-06445-w Mamedov A (2021) Micro milling process modeling: a review. Manuf Review 8:3. https://doi.org/10.1051/mfreview/2021003 Jin SY, Pramanik A, Basak AK, Prakash C, Shankar S, Debnath S (2020) Burr formation and its treatments—a review. Int J Adv Manuf Tech 107:2189-2210. https://doi.org/10.1007/s00170-020-05203-2 Abdelrahman Elkaseer AM, Dimov SS, Popov KB, Minev RM (2014) Tool wear in micro-endmilling: Material microstructure effects, modeling, and experimental validation. Journal of Micro-and Nano-Manuf 2(4):044502. https://doi.org/10.1115/1.4028077 Saptaji K, Subbiah S, Dhupia JS (2012) Effect of side edge angle and effective rake angle on top burrs in micro-milling. Prec Eng 36(3):444-450. https://doi.org/10.1016/j.precisioneng.2012.01.008 El-Asfoury MS, Baraya M, El Shrief E, Abdelgawad K, Sultan M, Abass A (2024) AI-Based Prediction of Ultrasonic Vibration-Assisted Milling Performance. Sensors 24(17):5509. https://doi.org/10.3390/s24175509 Farooq MU, Kumar R, Khan A et al (2024) Sustainable machining of Inconel 718 using minimum quantity lubrication: Artificial intelligence-based process modelling. Heliyon. 10(15):e34836. https://doi.org/10.1016/j.heliyon.2024.e34836 Wu D, Jennings C, Terpenny J, Gao RX, Kumara S (2017) A comparative study on machine learning algorithms for smart manufacturing: tool wear prediction using random forests. J Manuf Sci and Eng 139(7):071018. https://doi.org/10.1115/1.4036350 Shanmugasundar G, Vanitha M, Čep R, Kumar V, Kalita K, Ramachandran M (2021) A comparative study of linear, random forest and adaboost regressions for modeling non-traditional machining. Proc 9(11):2015. https://doi.org/10.3390/pr9112015 Kumar V, Dubey V, Sharma AK (2023) Comparative analysis of different machine learning algorithms in prediction of cutting force using hybrid nanofluid enriched cutting fluid in turning operation. Mat Today: Proc. https://doi.org/10.1016/j.matpr.2023.05.216 La Fé-Perdomo I, Ramos-Grez JA, Jeria I, Guerra C, Barrionuevo GO (2022) Comparative analysis and experimental validation of statistical and machine learning-based regressors for modeling the surface roughness and mechanical properties of 316L stainless steel specimens produced by selective laser melting. J Manuf Proc 80:666-682. https://doi.org/10.1016/j.jmapro.2022.06.021 Gallego J, Rodrigues AR., Assis CLF, Montanari L (2014) Second phase precipitation in Ultrafine-grained ferrite steel. Mat Res 17:527-534. https://doi.org/10.1590/S1516-14392013005000199 Pippan R, Hohenwarter A (2016) The importance of fracture toughness in ultrafine and nanocrystalline bulk materials. Mat Res Letters 4(3):127-136. https://doi.org/10.1080/21663831.2016.1166403 Lei C, Li X, Deng X, Wang Z, Wang G (2018) Deformation mechanism and ductile fracture behavior in high strength high ductility nano/ultrafine grained Fe-17Cr-6Ni austenitic steel. Mat Sci and Eng: A 709:72-81. https://doi.org/10.1016/j.msea.2017.10.043 Gillespie LK (1999) Burr formation. In: Treloar M, Editor. Deburring and edge finishing handbook. Michigan: Society of Manufacturing Engineers, pp 53-90. O’Toole L, Kang CW, Fang FZ (2020) Precision micro-milling process: state of the art. Adv in Manuf 1-33. https://doi.org/10.1007/s40436-020-00323-0 Pawlus P, Reizer R, Wieczorowski M (2021) Functional importance of surface texture parameters. Mat 14(18):5326. https://doi.org/10.3390/ma14185326 Basso I, Voigt R, Rodrigues AR, Marin F, de Souza AF, de Lacalle LNL (2022) Influences of the workpiece material and the tool-surface engagement (TSE) on surface finishing when ball-end milling. J Manuf Proc 75:219-231. https://doi.org/10.1016/j.jmapro.2021.12.059 Lu X, Xue L, Ruan F, Yang K, Liang SY (2019) Prediction model of the surface roughness of micro-milling single crystal copper. J Mech Sci and Tech 33:5369-5374. https://doi.org/10.1007/s12206-019-1030-6 Shang S, Wang C, Liang X, Cheung CF, Zheng P (2023) Surface roughness prediction in ultra-precision milling: An extreme learning machine method with data fusion. Micromach 14(11):2016. https://doi.org/10.3390/mi14112016 Zeng S, Pi D (2023) Milling surface roughness prediction based on physics-informed machine learning. Sensors 23(10):4969. https://doi.org/10.3390/s23104969 Tsai MH, Lee JN, Tsai HD, Shie MJ, Hsu TL, Chen HS (2023) Applying a neural network to predict surface roughness and machining accuracy in the milling of SUS304. Electronics 12(4):981. https://doi.org/10.3390/electronics12040981 Kosarac A, Tabakovic S, Mladjenovic C, Zeljkovic M, Orasanin G (2023) Next-gen manufacturing: machine learning for surface roughness prediction in Ti-6Al-4V biocompatible alloy machining. J Manuf and Mat Proc 7(6):202. https://doi.org/10.3390/jmmp7060202 Cite Share Download PDF Status: Published Journal Publication published 02 Oct, 2025 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Editorial decision: Major Revisions Needed 16 Aug, 2025 Reviewers agreed at journal 01 Jul, 2025 Reviewers invited by journal 28 May, 2025 Editor assigned by journal 27 May, 2025 First submitted to journal 26 May, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6753887","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":463095552,"identity":"c1a8598a-3b9a-4502-8845-5d083dc49114","order_by":0,"name":"Cleiton Lazaro Fazolo de Assis","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIie3PMQrCMBSA4QeBdHnYNWCpV6gUHOtVIhlcgnPFQUFw8gJepLNFsEvcK10aC26C3sCYWdq6OeQfXkjIBwmAy/WHeRszaoAAvL09wEEXwaMZ3KyACsBskPYnTFoC3cQrdM3TBP3DI29eMgkoEH0r2whyEXElkFULEeWZMA+jcSxbyBT4mc12R4RKTlieEUOQDtsI+npnyeiqPmTdgzBBLYlK/JBTH3In9i9jJePokhVIScdf0J/r+pkmYViocb3MVlPf2+qmjXyJ/Hbd5XK5XF96A7b5QyZxOmuxAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-4858-1495","institution":"Instituto Federal de Educação, Ciência e Tecnologia de São Paulo","correspondingAuthor":true,"prefix":"","firstName":"Cleiton","middleName":"Lazaro Fazolo","lastName":"de Assis","suffix":""},{"id":463095553,"identity":"8ac991a1-b4c6-4d65-a62c-fff981c82511","order_by":1,"name":"Alessandro Roger Rodrigues","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Alessandro","middleName":"Roger","lastName":"Rodrigues","suffix":""}],"badges":[],"createdAt":"2025-05-26 22:35:46","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6753887/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6753887/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00170-025-16532-5","type":"published","date":"2025-10-02T15:57:40+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":83755564,"identity":"ad23aa67-84ea-4f39-98b1-6b630ef76aeb","added_by":"auto","created_at":"2025-06-02 08:14:53","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":691667,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental setup for micro end-milling tests.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/108e1faea47024e23008667b.png"},{"id":83755557,"identity":"66bfde3f-8f94-4a5b-abce-62c4d9e7ee03","added_by":"auto","created_at":"2025-06-02 08:14:53","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":640179,"visible":true,"origin":"","legend":"\u003cp\u003eBall-end mill edge image by (a) laser microscopy and (b) edge radius measurement.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/6bb90114a0fe9c6cdfb7eb7c.png"},{"id":83755559,"identity":"aa807df2-dde5-4bfa-a84e-d0eac54eae2b","added_by":"auto","created_at":"2025-06-02 08:14:53","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":241710,"visible":true,"origin":"","legend":"\u003cp\u003eWorkpieces schematic design by (a) upper and (b) 3D views with ball-end mill feed direction indication.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/fd328f9105e70f918bf8b10e.png"},{"id":83755562,"identity":"0e38dbe6-8999-49e6-b255-56450054c443","added_by":"auto","created_at":"2025-06-02 08:14:53","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1068118,"visible":true,"origin":"","legend":"\u003cp\u003eRoughness measurement upon microgrooves surface considering the microgroove milling sides.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/e380f2553b98943840c91d60.png"},{"id":83756430,"identity":"292634df-fbde-4dd4-9f7a-4215c90f4980","added_by":"auto","created_at":"2025-06-02 08:22:53","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":2183508,"visible":true,"origin":"","legend":"\u003cp\u003eTop-view intensity images and respective roughness profiles of dual-phase machined microgrooves with a D400 ball-end mill.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/579a61108d056ced9ddd12a0.png"},{"id":83756435,"identity":"255ce356-84fe-447a-bfb4-cb4a03a4d136","added_by":"auto","created_at":"2025-06-02 08:22:53","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":2021613,"visible":true,"origin":"","legend":"\u003cp\u003eTop-view intensity images and respective roughness profiles of ultrafine-grained machined microgrooves with a D400 ball-end mill.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/1659ca18b317ded1203779c0.png"},{"id":83755571,"identity":"b96b9821-5003-4162-a334-ed8c34dd0233","added_by":"auto","created_at":"2025-06-02 08:14:53","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":2604880,"visible":true,"origin":"","legend":"\u003cp\u003eTop-view intensity images and respective roughness profiles of dual-phase machined microgrooves with a D600 ball-end mill.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/f76c1a64ca0ccb0d831efce8.png"},{"id":83756436,"identity":"d2619ac3-977c-45f4-a8cf-547249e102b1","added_by":"auto","created_at":"2025-06-02 08:22:53","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":2539028,"visible":true,"origin":"","legend":"\u003cp\u003eTop-view intensity images and respective roughness profiles of ultrafine-grained machined microgrooves with a D600 ball-end mill.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/27ab251a4a2707f99ebb4712.png"},{"id":83757251,"identity":"7ad3d08a-dd30-4735-8132-20d16c744ca7","added_by":"auto","created_at":"2025-06-02 08:30:53","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":2593967,"visible":true,"origin":"","legend":"\u003cp\u003eTop-view intensity images and respective roughness profiles of dual-phase machined microgrooves with a D800 ball-end mill.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/cee44253482a5ff02229b229.png"},{"id":83758120,"identity":"9307208c-f650-431b-a5de-9993de08733a","added_by":"auto","created_at":"2025-06-02 08:38:55","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":2610340,"visible":true,"origin":"","legend":"\u003cp\u003eTop-view intensity images and respective roughness profiles of ultrafine-grained machined microgrooves with a D800 ball-end mill.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/ee5f5c2f0ea1ae27a99f1d87.png"},{"id":83756456,"identity":"fc0202fd-899d-4949-9fbb-266bac1eb86c","added_by":"auto","created_at":"2025-06-02 08:22:55","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":175107,"visible":true,"origin":"","legend":"\u003cp\u003eWorkpiece and ball-end mill interaction and edge angle (θ\u003csub\u003eEdge\u003c/sub\u003e).\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/9f56bbe5aaa5007f762191ea.png"},{"id":83755621,"identity":"7b3abb63-de8b-416e-96b7-189089727aa9","added_by":"auto","created_at":"2025-06-02 08:14:55","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":665820,"visible":true,"origin":"","legend":"\u003cp\u003eMicrogroove profiles comparison (theoretical and experimental) for a D400 ball-end mill.\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/cac205565a295d8f873adbbc.png"},{"id":83756453,"identity":"a2e6924f-abfe-4c4c-8b06-bbbac5e1f8fe","added_by":"auto","created_at":"2025-06-02 08:22:55","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":600095,"visible":true,"origin":"","legend":"\u003cp\u003eMicrogroove profiles comparison (theoretical and experimental) for a D600 ball-end mill.\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/7f350bd91567314b0920ff42.png"},{"id":83755590,"identity":"7d4883ce-ffb6-4e3a-aa6d-250b840c903d","added_by":"auto","created_at":"2025-06-02 08:14:54","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":690157,"visible":true,"origin":"","legend":"\u003cp\u003eMicrogroove profiles comparison (theoretical and experimental) for a D800 ball-end mill.\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/810fbb9cae0a969076adc640.png"},{"id":83755610,"identity":"f8f00633-a98b-4dfb-add5-c6722eacd686","added_by":"auto","created_at":"2025-06-02 08:14:55","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":85248,"visible":true,"origin":"","legend":"\u003cp\u003eBoxplots of MAE and RMSE for microgroove profiles accuracy.\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/8d910d999ac30c4ebfc7fc42.png"},{"id":83755572,"identity":"ac55beed-8096-4e97-b861-2f0fbcbccfe5","added_by":"auto","created_at":"2025-06-02 08:14:53","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":49198,"visible":true,"origin":"","legend":"\u003cp\u003eGraph of MAE for width of cut of the microgroove profiles.\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/e0c3c3cca7a2b31b3089c864.png"},{"id":83756450,"identity":"9003d69c-1191-4618-a8f8-99ae0653c716","added_by":"auto","created_at":"2025-06-02 08:22:54","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":260842,"visible":true,"origin":"","legend":"\u003cp\u003eMain dependencies between roughness parameters pairs.\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/a29c7cbb34d1247d3ad05727.png"},{"id":83757253,"identity":"b9064883-d235-4d4a-b741-83a6535a3399","added_by":"auto","created_at":"2025-06-02 08:30:54","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":48277,"visible":true,"origin":"","legend":"\u003cp\u003eBoxplot of cutting parameters effect upon roughness Rz.\u003c/p\u003e","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/b893da9ff6f77b6038e20fd1.png"},{"id":83755575,"identity":"a65000b1-5860-43d6-b9b5-254f8696557f","added_by":"auto","created_at":"2025-06-02 08:14:53","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":80768,"visible":true,"origin":"","legend":"\u003cp\u003eBoxplot of cutting parameters effect upon skewness and kurtosis\u003c/p\u003e","description":"","filename":"20.png","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/4beadeb7d2105c59757e9bcf.png"},{"id":92884641,"identity":"90a0383d-3d82-43da-870f-442a99343065","added_by":"auto","created_at":"2025-10-06 16:13:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":22321746,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6753887/v1/ccf39e35-faa1-4e1d-926e-74f51ea30708.pdf"}],"financialInterests":"","formattedTitle":"Modeling of ball-end micromilled surface roughness and geometry in ultrafine-grained and dual-phase steels using interpretable machine learning","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eMicromilling has gained attention for its precision and efficiency, with research focusing on microstructure effects, tool wear, forces, surface quality, and burrs [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Integrating micromilling with other techniques shows promise for new materials and tools [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Micromilling cutting tools have significant influence on the quality of parts [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Geometry of microgrooves, machined surface and burrs formation are heavily affected by tools geometry and cutting parameters [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In conventional milling, the tools\u0026rsquo; stiffness helps to predict the roughness due to low influence of deflections caused by machining forces [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Tool miniaturization increases deflection risks due to imbalance, size effects, and premature edge failure [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. These tool conditions influence surface formation, making a thorough understanding of the tool\u0026ndash;workpiece interaction essential for improving the micromilling process [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWhile flat-end mills are common, ball-end mills are preferred for intricate geometries and 3D features [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Usually ball-end milling operations apply tool inclinations or tilt angle of cutter to produce machined surfaces due to a varying cutting speed, despite constant spindle rotation, along the cutting-edge tools [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Push- and pull-milling strategies are also commonly used but require a 4- or 5-axis machining center [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Cutting speed in the spherical end-mill center is near to zero and machined surface is affected by tool rubbing, resulting in a workpiece surface degeneration and accelerated tool wear [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Applications like microfluidics and surface texturing require hemispherical grooves for wettability and lubrication [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn ball-end milling, a minimum surface roughness depends on cutting parameters feed per tooth (ft) and width of cut (ae) when milling steels [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Thus, investigations of feed per tooth influence upon surface roughness are relevant for considerations about maximum and minimum feed acceleration to machine free-forms surfaces in conventional milling and more significant during micromilling due to effects of workpiece microstructure and tool cutting-edge radius [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCutting-edge radius effect has been tested by the most researchers using flat-end mills [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. In steels, studies still indicate lower R\u003csub\u003ea\u003c/sub\u003e roughness at uncut chip thickness to cutting-edge raiuds ratios near 1, especially in precision machining conditions [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Other authors using ball-end mills with 1 mm diameter reported that feed per tooth close to cutting-edge radius tends to lower S\u003csub\u003ea\u003c/sub\u003e roughness, while increasing width of cut resulted higher S\u003csub\u003ea\u003c/sub\u003e [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. The findings indicate that there is a relation between cutting-edge radius and width of cut to define surface formation. In ball-end milling, the width of cut corresponds to the effective diameter, which depends on the relationship between the tool's radius and the depth of cut [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe neck length of ball-end mills significantly affects the machining of steels, especially in precision and deep-cavity applications. Studies indicate that modifying the neck length of small radius ball-end mills significantly impacts tool rigidity, which in turn influences cutting accuracy and surface finishing [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Increased neck length often results in higher tool deflection, leading to machining errors such as reduced depth accuracy and dimensional deviations [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Furthermore, authors still affirm that excessive tool deflection can reduce the effectiveness of micromilling operations, particularly in materials with dual-phase microstructures like low-carbon steel, where deviations in microchannel depth have been observed. Thus, optimizing the neck length of ball-end mills is relevant to maintaining machining precision while minimizing deflection-related errors.\u003c/p\u003e \u003cp\u003eThe diameter of ball-end mills and the feed per tooth significantly influence the efficiency and accuracy of steel machining. Studies have shown that increasing the tool diameter generally reduces tool deflection, leading to improved surface finishing and dimensional accuracy [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Additionally, larger tool diameters facilitate allow for higher feed rates without compromising surface integrity, thus enhancing productivity [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. However, the feed per tooth must be optimized carefully, as excessive feed rates can lead to poor surface finishing and increased cutting forces, ultimately accelerating tool wear [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Conversely, insufficient feed rates can cause ploughing effects, increasing specific cutting energy and reducing material removal efficiency [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Therefore, achieving an optimal balance between ball-end mill diameter and feed per tooth is a key factor for maintaining high-quality machining performance and tool longevity.\u003c/p\u003e \u003cp\u003eRegarding the workpiece material, the effect of different phases on the microstructure has been studied by several researchers [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. The studies include different machining scales (milling and micromilling) using homogeneous materials aiming at reducing surface defects, improving roughness and minimizing material deformation beneath the machined surface [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The results of those studies showed that the ultrafine grain material presents improved machinability at conventional and microscale cutting conditions using flat-end mills overcoming size effect problems due to the differences between cutting parameters and microstructure scale.\u003c/p\u003e \u003cp\u003eScientifical researches about grain refinement in low-carbon steels and its potential to reduce carbon consumption in steels production increased in the two last decades [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. The microstructural characteristics and mechanical behaviour of this class of steels can be optimized, aiming to expand applications previously restricted [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. A microstructure with ultrafine ferrite can provides an improvement of mechanical properties such as yield strength and toughness in an outstanding combination [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. One way to achieve an excellent combination of strength and plasticity by microstructural grain refinement in a low-carbon steel is applying a thermomechanical processing, which the material is subjected to severe plastic deformation and heat treatments routes [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The result is a homogeneous microstructure with grain size reduced to even less than 1 \u0026micro;m [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn addition to structural applications in the automotive industry and improved weldability promoted by an ultrafine grained microstructure in low-carbon steels, the micromachining also would be beneficed by ultrafine grained microstructure due to reducing the size effect and the anisotropic feature while surface formation quality is allowed to control [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. However, new issues arise and need to be investigated. Material mechanical properties can cause instability during microcutting due to small size of the cutting tools and low material removal rate, resulting in tool deflection, geometrical deviations and degradation of machined surface [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Thus, efforts to investigate suitable micromachining conditions for low-carbon steels with ultrafine grained microstructure is advantageous for provide new applications.\u003c/p\u003e \u003cp\u003eBurrs control is an important issue in micromilling due to effects upon part quality and time of production, mainly by need of deburring operations [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Flat-end mills tend to form top burrs on up side of microgrooves and slots milling side (up- and down-milling) affects burr formation in steels [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Higher side-edge angles reduce burr formation, as shown with tapered tools, a concept extendable to ball-end milling [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The authors identified this effect during machining tests with tapered milling tools but no research was found in literature by extrapolating this application to ball-end milling. In other words, this side edge angle can also be obtained by combination between tool spherical top and effective tool diameter. Thus, once found an optimal relationship, burr formation could be avoided or minimized when milling microgrooves or micro slots.\u003c/p\u003e \u003cp\u003eArtifical Inteligence (AI) models have enhanced micromilling by predicting cutting forces, roughness, and tool wear, supporting real-time optimization and sustainability [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. Random Forest Regressor (RFR) and Multilayer Perceptron (MLP) neural networks have proven to be highly effective in modeling and predicting machining process behaviors due to their ability to capture nonlinear and complex relationships in manufacturing data. In tool wear prediction, RFR demonstrated remarkable performance by outperforming traditional models like decision trees and support vector machines in both accuracy and robustness, thanks to its ensemble learning approach that mitigates overfitting [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. Similarly, in modeling metal removal rate (MRR) and surface roughness in non-traditional machining, RFR provided predictions with high reliability compared to linear models, highlighting its strength in dealing with noise and high-dimensional data sets [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMLPs, on the other hand, excel in capturing intricate dependencies through deep-layered representations, making them suitable for machining processes in which parameters like cutting force, tool deflection, and temperature gradients interact in complex ways. In hybrid machining environments, MLPs have shown higher generalization ability in predicting process outcomes like surface roughness and cutting force compared to multiple linear regression or gradient-boosted models [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Notably, MLPs effectively modeled mechanical outputs such as ultimate tensile strength and hardness across varying materials and machining conditions [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. Together, RFR and MLP outperform conventional AI tools by offering ensemble-based reliability and deep-function approximation, relevant for adapting to the nonlinear, dynamic nature of machining processes.\u003c/p\u003e \u003cp\u003eAlthough micro-milling has been extensively studied in recent years, most investigations have focused on traditional roughness parameters (e.g., Ra, Rz) under limited material conditions. Moreover, while some studies address tool deflection qualitatively, few works quantitatively examine the combined influence of tool geometry (diameter and neck length), cutting strategy, and material microstructure on both surface integrity and cross-sectional profile fidelity. Furthermore, there is a lack of studies integrating interpretable machine learning models with statistical analysis to predict and explain surface roughness outcomes in low-carbon steels with contrasting metallurgical behaviors.\u003c/p\u003e \u003cp\u003eTo fill this gap, the present study investigates the micro-milling of two steels with distinct microstructures, a conventional dual-phase steel (ferrite\u0026ndash;pearlite) and an ultrafine-grained (single-phase ferrite) steel, under varying cutting conditions. The effects of machining parameters on surface roughness (Ra, Rz, skewness, kurtosis), burr formation, and profile accuracy are systematically analyzed. In addition, machine learning models (Random Forest and MLP) are employed not only to predict roughness values but also to interpret variable influence using feature importance analysis, providing a comprehensive view of surface generation mechanisms. This integrated approach represents an original contribution to the field of micro-manufacturing of low-carbon steels and predictive modeling of surface integrity.\u003c/p\u003e"},{"header":"2. Experimental procedures","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Experimental setup\u003c/h2\u003e \u003cp\u003eMicro end-milling operations were performed to produce microgrooves using a vertical CNC machining centre Kern model D-824118 (50,000 rpm maximum speed) with dry cutting condition. Workpieces were clamped with working surface on the XY-plan with a precision vise. Each machining condition was performed four times. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e demonstrates the experimental setup.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Cutting tools\u003c/h2\u003e \u003cp\u003eCarbide ball-end mills with 400, 600 and 800 \u0026micro;m diameter were used. These cutter diameters were chosen because they are the most commonly used for slots production. Three values were selected in order to keep the total number of experiments and analyse within reasonable limits (total of 72 tests, included 3 replications). Tool edge raddi were measured via an Olympus 3D Laser Microscopy OLS4100, using 10 measurements per tool (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The cutting tool position control in relation to workpiece was made by a Laser Control NT Blum High-Tech Laser Systems with a precision probe and thermal compensation in all machine axis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Workpiece material\u003c/h2\u003e \u003cp\u003eThe workpiece materials used in this study consist of two different metallurgical conditions: a dual-phase and an ultrafine-grained steels. The dual-phase steel was characterized by an average grain size of 11 \u0026micro;m, a hardness of 192 HV, a yield strength of 474 MPa, and a Charpy impact energy of 176 J. The ultrafine-grained steel, produced through severe plastic deformation, exhibited a significantly refined microstructure with an average grain size of 0.7 \u0026micro;m. This refinement resulted in increased hardness (216 HV) and yield strength (510 MPa), as well as enhanced toughness, as indicated by a Charpy impact energy of 285 J.\u003c/p\u003e \u003cp\u003eThe mechanical properties of both materials were determined following standardized procedures. Hardness measurements were performed using a Vickers hardness tester, while yield strength was obtained from uniaxial tensile tests conducted at room temperature, in accordance with ASTM E8/E8M. Impact toughness was assessed using Charpy V-notch tests, following the ASTM E23 standard.\u003c/p\u003e \u003cp\u003eDeeper descriptions about mechanical properties and microstructure analysis are presented in previously research [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. These characterizations provided an understanding of the mechanical behavior of the selected workpiece materials, serving as a basis for further analysis of their machinability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Experimental design\u003c/h2\u003e \u003cp\u003eIn this study, the experimental design was structured to determine specifically the effects of ball-end mill diameter, tool neck length, feed per tooth, and milling sides (up- and down-milling sides) on microgroove geometry and surface roughness. To ensure a focused and statistically robust analysis, the spindle speed and depth of cut were intentionally kept constant throughout all experiments. This decision aimed to reduce the number of experimental variables and allow a more precise identification of the direct influence of the selected parameters.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the input variables to cut the microgrooves by using ball-end mills. Values of feed per tooth (ft) around and higher than tool cutting-edge radius were selected to evaluate the interaction between cutting tool microgeometry and workpiece metallurgical condition. Spindle rotation, feed per tooth and depth of cut (ap) limits were established for each ball-end mill size after machining pre-tests to avoid premature tool breaking due to tool rigidity. Further, depth of cut was also chosen to keep an equivalent proportion of tool penetration and tool diameter (⁓10%). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the workpiece with schematic toolpath. The workpieces are formed as a sandwich with DPh and UFG steels. This setup was applied to be sure that the same cutting tool performed the machining conditions in both workpiece materials. A short cutting length (2.5 mm per workpiece material) was chosen, as tool wear was not the focus of this study.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMachining conditions to the micro end-milling operations.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eBall-end mill diameter (\u0026micro;m)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eMicromilling process\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpindle rotation [rpm]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30,000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20,000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15,000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFeed [\u0026micro;m/tooth]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.5, 2 and 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5, 2 and 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5, 2 and 5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLength of cut [mm]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDepth of cut [\u0026micro;m]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWidth of cut [\u0026micro;m]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e332\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e480\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCutting tool\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEdge radius [\u0026micro;m]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.752\u0026thinsp;\u0026plusmn;\u0026thinsp;0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.541\u0026thinsp;\u0026plusmn;\u0026thinsp;0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.482\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeck length [mm]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5. Measurement and statistical analysis\u003c/h2\u003e \u003cp\u003eCross-sectional profiles, roughness profiles and roughness values of the microgrooves were assessed using an Olympus 3D Measuring Laser Microscopy OLS4100. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the upper view of a microgroove and surface. Left side of the microgroove was cut under up-milling (chip starts to be formed with null thickness) and right side corresponds to the down-milling (chip starts to be formed with maximum thickness). Both regions were compared to investigate any effect of microgroove milling sides. Profiles were obtained by means of cross-section of the microgrooves perpendicular to the cutting tool feed direction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe evaluation of burr formation in the machined microgrooves was conducted through a combination of visual inspection, laser microscopy images, and the analysis of experimental cross-sectional profiles. Visual inspection of the workpieces was used to preliminarily identify the presence and morphology of burrs at the microgroove edges. High-resolution laser microscopy provided detailed surface topography, enabling the observation of localized plastic deformation and burr accumulation along the microgroove boundaries. Additionally, the cross-sectional profiles were examined to assess burr geometry, asymmetry, and distribution, allowing for the identification of differences in burr formation across varying machining conditions. This multi-modal evaluation ensured a comprehensive characterization of burr types and their relation to machining conditions.\u003c/p\u003e \u003cp\u003eRoughness parameters i.e. average (Ra), root mean square (Rq), maximum height (Rz), maximum profile peak height (Rp), maximum profile valley depth (Rv), RMS slope of the profile (Rdq), skewness and kurtosis were measured twice in each milling side reaching eight roughness lines for cutting conditions and microgroove milling sides since four grooves were milled for each machining condition. These roughness parameters were chosen to reveal more sensitive effects of the aforementioned input variables upon part surface formation.\u003c/p\u003e \u003cp\u003eTo validate the machining results, various statistical tools were employed to assess geometrical accuracy, surface roughness, and width of cut deviations. The methodologies applied in this study include hypothesis testing, error analysis, confidence intervals, and determination coefficients (R\u003csup\u003e2\u003c/sup\u003e), which allowed for a comprehensive assessment of the experimental data.\u003c/p\u003e \u003cp\u003eAll hypothesis tests used 95% confidence level (α\u0026thinsp;=\u0026thinsp;0.05), standard in engineering research. One-sample t-test was performed to evaluate whether the experimentally measured width of cut (ae) significantly deviated from the expected nominal values for each combination of cutting parameters. The same was applied to skewness and kurtosis, but using reference values to evaluate surface characteristics (0 for skewness and 3 for kurtosis). The tests was conducted separately for DPh and UFG steels, as well as for different ball-end mill sizes and feed per tooth values. The statistical significance was determined based on the p-value.\u003c/p\u003e \u003cp\u003eThe accuracy of the machined microgroove profiles was quantitatively evaluated using Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), which measured the deviation between experimentally obtained and theoretical cross-sectional profiles. MAE provides the average absolute deviation between the measured and expected values, offering an intuitive measure of overall accuracy. RMSE penalizes larger deviations more strongly than MAE, as it squares the differences before averaging them. This metric is particularly useful for identifying extreme deviations and localized errors in the microgroove geometry.\u003c/p\u003e \u003cp\u003eTo evaluate the statistical reliability of the roughness and geometrical deviation measurements, 95% confidence intervals (CI) for the mean values were calculated. The confidence interval provides an estimate of the range within which the true mean is expected to fall, considering sample variability. By incorporating confidence intervals, the study ensured that the reported mean values accurately represented the underlying distributions, mitigating the impact of random fluctuations in experimental data.\u003c/p\u003e \u003cp\u003eTo quantify the agreement between experimental and theoretical profiles, the coefficient of determination was employed. This metric evaluates the proportion of variance in the experimental data that can be explained by the theoretical model. Higher R\u003csup\u003e2\u003c/sup\u003e values indicate strong agreement between theoretical and experimental cross-sectional profiles, while lower values suggest higher deviations.\u003c/p\u003e \u003cp\u003eThe statistical tools applied in this study provided a multi-level approach to evaluate machining performance. The combination of t-tests, error metrics, confidence intervals, and R\u003csup\u003e2\u003c/sup\u003e analysis ensured a comprehensive validation of the machining results, allowing for a deeper understanding of the effects of material properties, tool geometry, and process parameters on surface integrity and dimensional accuracy.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.6. Machine Learning and Predictive Modeling of Surface Roughness\u003c/h2\u003e \u003cp\u003eTo investigate the influence of machining parameters on surface roughness in micro end-milled steel components, machine learning techniques were applied. The predictive models were designed to estimate Ra based on key process variables, including ball-end mill diameter, feed per tooth, and microgroove milling sides (up- and down-milling). The approach involved a combination of data preprocessing, dimensionality reduction, and the implementation of machine learning algorithms and artificial neural networks, ensuring a deep analysis of roughness formation mechanisms.\u003c/p\u003e \u003cp\u003eThe dataset consisted of roughness measurements obtained from DPh and UFG steels, each subjected to 36 distinct machining conditions, combining three tool diameters, three feed per tooth values, and two microgroove milling sides. Each condition was evaluated through repeated measurements. After preprocessing and filtering, 324 observations were available for DPh and 306 for UFG, considering the exclusion of the the 800 \u0026micro;m tool diameter and 0.5 \u0026micro;m/tooth feed condition in UFG due to high plastic deformation and surface inconsistency.\u003c/p\u003e \u003cp\u003eBefore model training, categorical variables (e.g., microgroove milling sides) were converted to numerical format using one-hot encoding. Numerical variables were standardized using z-score normalization to eliminate scale bias. To reduce dimensionality and minimize multicollinearity, Principal Component Analysis (PCA) was applied. Cumulative variance analysis showed that the first two principal components (PC1 and PC2) retained over 95% of the total variance, making them suitable as input for modeling.\u003c/p\u003e \u003cp\u003eTo develop accurate predictive models for roughness, two machine learning approaches were implemented and trained independently for DPh and UFG:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eRandom Forest Regressor (RFR): An ensemble learning algorithm based on decision trees, chosen for its ability to capture complex, nonlinear relationships between machining parameters and roughness.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eMultilayer Perceptron (MLP) Neural Network: A feedforward artificial neural network with three hidden layers (100, 50, and 25 neurons, respectively). ReLU activation was used in the hidden layers, combined with the Adam optimizer for weight updates. The model was trained for a maximum of 1,000 iterations, with early stopping (patience\u0026thinsp;=\u0026thinsp;20) to prevent overfitting.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eFor model evaluation, the dataset was split using a stratified 80/20 train-test split, ensuring representative distributions of all machining conditions across training and test sets. Additionally, a 5-fold cross-validation was applied on the training set to assess model stability.\u003c/p\u003e \u003cp\u003eHyperparameter tuning was performed for both models:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eFor the Random Forest Regressor, a grid search was conducted over the number of estimators (100, 200, 500), maximum depth (None, 10, 20), and minimum samples split (2, 5), selecting the best combination based on the lowest cross-validated MAE.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFor the MLP, the number of layers and neurons per layer were defined based on empirical testing and validation performance. The final model used a learning rate of 0.001 and a batch size of 8.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eModel performance was evaluated using two metrics: Mean Absolute Error (MAE), which was employed to assess the average prediction error in Ra values, and the coefficient of determination, which measured the proportion of variance in Ra explained by the model. These metrics enabled direct comparison between algorithms and across different materials, supporting the assessment of model generalization and providing insights into the relationship between machining parameters and roughness.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1. Microgroove topography and roughness profile analysis\u003c/h2\u003e\n \u003cp\u003eMicrogooves machined in different workpiece metallurgical and cutting conditions are presented. Aiming to simplify the analysis, ball-end mill sizes are indicated as D400 (400 \u0026micro;m diameter), D600 (600 \u0026micro;m diameter) and D800 (400 \u0026micro;m diameter). The tool tip resulted in a flat surface at the bottom of all microgrooves due to the tool chisel edge, in order to minimize the effect of reducing the speed cutting near the centre of the grooves. Top burrs on the sides of the microgrooves were evaluated using a qualitative analysis of intensity images.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e to \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e present the top-view intensity images and the corresponding roughness profiles of the machined microgrooves for both DPh) and UFG steels, machined with D400, D600, and D800 ball-end mills. The roughness profiles were extracted from both up- and down-milling sides, allowing for a detailed evaluation of the effects of tool diameter, neck length, workpiece microstructure, and feed per tooth on the resulting surface topography.\u003c/p\u003e\n \u003cp\u003eA direct comparison between different tool sizes initially suggested a progressive improvement in surface integrity with increasing ball-end mill size. However, the analysis must also consider the neck length of each tool, which directly influences its rigidity and potential deflection. The D400 (Figs. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e), with a 2 mm neck length, exhibits pronounced irregularities in the roughness profiles, likely due to the small tool diameter (size effect). The D600 (Figs. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e), with an 8 mm neck length, also displays irregularities in the roughness profile in some zones and showed signs of increased lateral tool deflection (curves on the microgroove top), leading to irregularities that may have counteracted the expected improvements in surface quality. Despite the larger tool size, this suggests that the extended neck length increases tool flexibility, making it more susceptible to deflection-related surface deviations. In contrast, the D800 (Figs. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e), with a 6 mm neck length, showed no apparent signals of tool defletion on the microgrove top.\u003c/p\u003e\n \u003cp\u003eWhile it is well established that longer neck lengths tend to reduce tool stiffness and increase deflection (thereby compromising dimensional accuracy), some conditions in this study may suggest that the D800 exhibited comparable quality than D400 (UFG at 2 and 5 \u0026micro;m/tooth). The neck length-to-diameter ratio is 5 for the D400 tool and 7.5 for the D800 tool, both considerably lower than that of the D600 tool, which is 13. This indicates that the stiffness of the D400 and D800 tools is comparable, exhibiting similar behavior during machining and higher resistance to deflection.\u003c/p\u003e\n \u003cp\u003eThe influence of workpiece microstructure on the roughness profiles is also noticed. The DPh exhibits higher roughness variation between microgroove milling sides, which may be exacerbated by uneven material removal due to greater tool flexibility and minimum cutting thickness effect, respectively. Conversely, the UFG produced more similar roughness profiles in both microgroove milling sides, benefiting from its homogeneous microstructure, which ensured a more stable cutting process.\u003c/p\u003e\n \u003cp\u003eThe roughness profiles also highlighted the influence of feed per tooth on surface characteristics. The results indicated that higher ft values generally lead to increased surface irregularities, while lower ft values contribute to a more consistent surface finishing. At 0.5 \u0026micro;m/tooth, the tool-workpiece interaction was more continuous, reducing abrupt height variations in the microgroove roughness profile. At 2 \u0026micro;m/tooth, a moderate increase in roughness amplitude is observed, though it remains within a relatively stable range. However, at 5 \u0026micro;m/tooth, there was a significant increase in roughness, attributed to the larger chip thickness, leading to increased instability. These effects were more pronounced in the D600, whose the combination of a higher ft and an extended neck length likely exacerbates tool deflection, further deteriorating machined surface quality.\u003c/p\u003e\n \u003cp\u003eThe analysis of microgroove milling sides further confirms the role of cutting dynamics in surface formation. Up-milling sides tended to produce higher roughness amplitudes, which may be associated with increased plowing effects and higher tool-workpiece friction forces at the start of the cutting process. Conversely, down-milling sides exhibited smoother surfaces, as the gradual tool engagement reduces impact forces and promotes better machined surface integrity. The interaction between microgroove milling side and tool size is particularly relevant for the D600, in which the long neck length increases flexibility, making the tool more susceptible to vibrations and deviations in up-milling sides.\u003c/p\u003e\n \u003cp\u003eIn Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e is presented 2D laser microscopy image of the microgroove machined with the D800 at 0.5 \u0026micro;m/tooth. The central slot of the microgroove exhibited severe plastic deformation, culminating in material rupture. This phenomenon is attributed to the reduction in cutting speed near the tool center, which increases the difficulty of material removal. As the cutting tool traverses this zone, it compresses the material beyond its plastic limit, leading to failure and lateral displacement of the deformed material towards the microgroove edges.\u003c/p\u003e\n \u003cp\u003eThe deformation was more pronounced on the up-milling side, where the cutting-edge must gradually reach the minimum chip thickness before initiating effective material removal. As a result, the tool-plowing effect intensifies, generating higher localized strains that contribute to excessive deformation. This phenomenon compromised the integrity of the machined surface on the up-milling side, as evidenced in the 2D laser microscopy image.\u003c/p\u003e\n \u003cp\u003eThe higher toughness of the ultrafine-grained steel (285 J) exacerbated this effect compared to the dual-phase steel (176 J), where material failure was less pronounced. The ultrafine microstructure, characterized by a higher resistance to crack propagation, allows for higher plastic deformation before rupture, thus favoring material displacement rather than brittle fracture [\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eConsidering classification of Gillespie [\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e], minor burrs were observed on both lateral tops of the microgrooves. The depth of cut (ap) was not independently varied in this study; however, its effect is inherently linked to the ball-end mill radius (R) and workpiece interaction geometry. This relationship directly influences the edge angle (\u0026theta;\u003csub\u003eEdge\u003c/sub\u003e), which in turn affects chip formation and burr minimization.\u003c/p\u003e\n \u003cp\u003ePrevious studies on edge angle effects in micro end-milling have demonstrated that \u0026theta;\u003csub\u003eEdge\u003c/sub\u003e values higher than 90\u0026deg; up to approximately 150\u0026deg; help minimize burr formation and improve machining stability [\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e]. This behavior was also observed in this study, where minor burrs were detected in all machining conditions, suggesting that the combination of R and ap led to an edge angle of approximately 145\u0026deg;, contributing to a stable cutting process (Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eFurthermore, the results confirmed that even when the ft was lower than the cutting edge radius, no significant top burrs were produced. This finding aligns with previous research that suggests that appropriate tool geometry can prevent burr formation without requiring modifications to the workpiece geometry [\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2. Geometrical deviation of machined microgrooves\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e to \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e present the experimental and theoretical cross-sectional profiles of the machined microgrooves for D400, D600, and D800 ball-end mills, at different feed per tooth values for both DPh and UFG steels. The theoretical profiles are shown in black, while the experimentally obtained microgroove profiles are represented in red. Additionally, the coefficient of determination and statistical deviation values are provided to quantify the degree of geometric agreement between the theoretical and experimental profiles.\u003c/p\u003e\n \u003cp\u003eThe results indicated that DPh exhibited similar geometrical accuracy compared to UFG, as evidenced for D400 and D600. However, D800 showed better agreement between profiles for DPh, as seen by higher R\u003csup\u003e2\u003c/sup\u003e values and lower statistical deviations. Despite its heterogeneous microstructure, the machining process resulted in microgrooves that closely followed the theoretical geometry. The UFG steel exhibited higher deviations from the theoretical profiles, likely due to its higher toughness than DPh, which increased the tendency for plastic deformation rather than brittle material removal, making the final microgroove geometry more susceptible to variations.\u003c/p\u003e\n \u003cp\u003eAlthough the D800 tool features a longer neck length compared to D400, its geometrical accuracy and surface roughness outcomes were not always inferior. This can be explained by the fact that neck length alone does not determine tool rigidity, but rather its relationship with tool diameter. In this case, the neck length-to-diameter ratio was more favorable for D800 (7.5) than for D600 (13), resulting in lower effective flexibility. In addition, the larger core diameter of the D800 tool enhances its structural stiffness, helping to counterbalance the increased unsupported length. Consequently, the improved performance observed with the D800 tool under specific machining conditions should not be attributed to the neck length itself, but to the combined effect of diameter, neck length, feed per tooth, and workpiece material behavior. This reinforces the importance of evaluating deflection susceptibility based on geometric ratios and process interactions rather than on neck length in isolation.\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eAlthough the D600 presented the highest neck-to-diameter ratio among all tested tools, typically associated with increased flexibility and geometric inaccuracy, it exhibited the lowest median values and variability for both MAE and RMSE (Fig. \u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e). This behavior suggests that geometric stiffness alone does not fully explain the profile accuracy in micromilling. A possible explanation lies in the balanced configuration of the D600, which combines an intermediate diameter with cutting conditions that may have favored more consistent elastic deformation, reducing localized distortions. In contrast, the D400, despite having a shorter neck, showed higher geometric errors at increased feed per tooth, likely due to stress concentration over its reduced cross-sectional area. The D800, on the other hand, although stiffer in terms of diameter, combined a longer neck and higher tool-workpiece engagement, especially in UFG steel, which may have amplified structural deformation and deflection-induced deviations. While cutting forces were not directly measured in this study, the observed geometric deviations and systematic errors suggest that tool deflection dynamics are significantly affected by the interaction between tool geometry and material behavior.\u003c/p\u003e\n \u003cp\u003eThe comparison between MAE and RMSE revealed minimal differences between the two metrics as well. Since RMSE penalizes larger errors quadratically, this similarity suggests that the individual errors are uniformly distributed, without significant outliers (*) that could disproportionately influence the mean error. The absence of extreme values reinforces the reliability of both error metrics and suggests that no substantial deviations affect the accuracy assessment.\u003c/p\u003e\n \u003cp\u003eThe MAE and RMSE results also indicated that D400 was more suscetible to tool deflexion against the feed motion at higher ft value, while D800 showed higher error medians and variability for both steels at 0.5 \u0026micro;m/tooth and higher error medians for UFG at 2 and 5 \u0026micro;m/tooth. The possible increase of cutting forces during machining with D400 at higher feed per tooth favoured tool deflection, resulting in higher error medians. By other hand, for D800, UFG steel showed more difficulty to cutting process than DPh due to mechanical properties.\u003c/p\u003e\n \u003cp\u003eIn micromilling processes, maintaining dimensional accuracy is challenging due to tool deflection, which can lead to deviations in the machined width. The boxplot analysis of the MAE for width of cut showed variations across different cutting conditions, particularly at higher ft values and with larger tool sizes (Fig. \u003cspan class=\"InternalRef\"\u003e16\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eOne of the factors contributing to this variation is the deflection of micro ball-end mills, which is influenced by their geometric characteristics. As presented, the tools used in this study exhibit a neck length, affecting their flexibility. This structural feature for greater neck-to-diameter ratio makes them more susceptible to bending under cutting forces. As a result, the actual width of cut often deviates from the nominal value, increasing process variability.\u003c/p\u003e\n \u003cp\u003eThe observed machining instability is primarily associated with the elastic deformation of the tool rather than random process fluctuations. This behavior is evident in the increased spread of MAE values for certain cutting conditions, suggesting a loss of predictability in the width of cut. The presence of outliers supports the idea that deflection-related variations occur sporadically under certain machining conditions.\u003c/p\u003e\n \u003cp\u003eA one-sample t-test was then applied to compare the experimental ae values with the nominal values for different machining conditions (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Data normality was assessed using the Shapiro-Wilk test, and all datasets exhibited normal distribution (p\u0026thinsp;\u0026gt;\u0026thinsp;0.05), what validate the test. The statistical analysis confirmed that the workpiece material significantly influenced the deviation of ae from the expected values. In particular, UFG exhibited statistically significant deviations (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05) for D600 and D800, suggesting that its higher toughness led to more pronounced variations in width of cut, likely due to increased plastic deformation. In contrast, DPh demonstrated more stability.\u003c/p\u003e\n \u003cp\u003eThe influence of feed per tooth on ae accuracy was also evident. At 5 \u0026micro;m/tooth, significant deviations were observed, especially in UFG steel, where t-values reached extreme values (-19.92 for D400 and 28.44 for D600, both with p\u0026thinsp;\u0026lt;\u0026thinsp;0.05). This suggests that increased material removal rates introduced machining instability, leading to higher deviations from expected values. Conversely, 0.5 \u0026micro;m/tooth resulted in negative t-values for D400 and D800 in both materials, indicating that the actual ae was systematically smaller than the nominal values.\u003c/p\u003e\n \u003cp\u003eRegarding tool size, D400 demonstrated more stable results for both workpiece materials, where at 2 \u0026micro;m/tooth, the t-statistic was the lowest and p\u0026thinsp;\u0026gt;\u0026thinsp;0.05, indicating an experimental ae closer to nominal value. This suggests that smaller tools at moderate feed per tooth favor more consistent ae values. \u0026nbsp;\u003c/p\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eResults of one-sample t-tests comparing experimental width of cut values to the nominal reference values under different machining conditions.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSize\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eft\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003et-statistic\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ep-value\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eDPh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-3.5130\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0170\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.9569\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3825\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-5.9848\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0018\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eUFG\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-4.4530\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0066\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.6214\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5615\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-19.9247\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eDPh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9009\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4089\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e17.9353\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.0770\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eUFG\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-3.8690\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0117\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.5465\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0006\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e28.4482\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eDPh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-28.4827\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-2.0236\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0989\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.7646\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0022\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eUFG\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-14.1577\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-28.9983\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-7.9536\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0005\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3. Roughness analysis\u003c/h2\u003e\n \u003cp\u003eThe machined microgrooves were evaluated using commonly applied roughness parameters to assess the topography of machined surfaces. However, the parameters selected for this study were determined based on statistical correlation analysis to ensure that each parameter was statistically independent, describing different aspects of the surface roughness [\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e]. The roughness parameters chosen were those exhibiting low data redundancy, as indicated by the R\u003csup\u003e2\u003c/sup\u003e. Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e presents the results of the statistical correlation analysis between roughness parameters, showing a strong correlation among Ra, Rq, Rz, Rdq, Rv, and Rp, while Rsk and Rku displayed low correlation with each other and with the other parameters. \u0026nbsp;\u003c/p\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe values of the linear correlation coefficient (R\u003csup\u003e2\u003c/sup\u003e) between roughness parameters describing topography of the machined surface.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRa\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRq\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRz\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRdq\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRp\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRv\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRsk\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRku\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRa\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRdq\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRv\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRsk\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRku\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eAlthough the parameters exhibited similar trends, certain characteristics of the machined surface can be identified through the analysis of strongly correlated parameter pairs, as illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e. The correlation between Rq and Ra indicated that Rq was 27% higher than Ra, meaning that the deviation from the mean line of the roughness profile remained relatively constant. The relationship between Rdq and Rz showed that the increase in surface steepness (Rdq) corresponded to 2.8% of Rz, while Ra accounted for 22% of Rz. Additionally, the ratio between Rp and Rv was 0.9, as seen in the graph of general relationship between Rp and Rv, indicating a balanced distribution of maximum peak height and maximum valley depth. However, when analyzed by tool size, it was observed that D600 produced Rp values 12% higher than Rv, whereas D800 exhibited Rp values 18% lower than Rv.\u003c/p\u003e\n \u003cp\u003eDue to its higher sensitivity to surface texture variations compared to Ra, Rz was selected as the primary parameter to evaluate the height of the roughness profile. Figure \u003cspan class=\"InternalRef\"\u003e18\u003c/span\u003e presents a boxplot with the effect of cutting parameters on Rz. For D400, although a tendency for increasing median and variability with feed per tooth was observed, the high dispersion of values limits a conclusive interpretation regarding roughness escalation. In the case of D600, median values remained relatively stable across feed rates, but the ultrafine-grained steel exhibited substantial variability, which may reflect microstructural influences or instability in the cutting process. For D800, a slight increase in Rz with feed per tooth was noted for DPh. However, due to the pronounced variability, particularly at lower feed per tooth for UFG, this trend should be interpreted with caution, as it does not consistently hold across all conditions.\u003c/p\u003e\n \u003cp\u003eThese observations underscore the complexity in establishing direct relationships between feed per tooth and roughness when high data variability is present. To further investigate surface texture characteristics beyond average roughness values, additional parameters such as skewness and kurtosis were evaluated to capture profile asymmetry and peak distribution. The low correlation between Rsk and Rku suggests that the machined surface did not exhibit stratitication, i.e., it lacked clustered zones of extreme peaks or valleys, indicanting that the surface texture resulted from a relatively continuous material removal process across the toolpath.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e19\u003c/span\u003e presents a boxplot with the effect of machining conditions on skewness and kurtosis. In the skewness analysis, both workpiece materials exhibited similar trends in median values and dispersion. Although most conditions resulted in skewness values near zero, indicating an approximately symmetrical peak-to-valley distribution, variability was notable across several cases. For instance, surfaces machined with D800 at 0.5 and 2 \u0026micro;m/tooth showed a tendency toward peak predominance (positive skewness), whereas D400 at 2 \u0026micro;m/tooth and D800 at 5 \u0026micro;m/tooth displayed a shift toward valley predominance (negative skewness). However, due to the spread in the data, these tendencies should be interpreted with caution and not as definitive trends.\u003c/p\u003e\n \u003cp\u003eRegarding kurtosis, values close to 3 were observed primarily at higher feed rates, which may indicate a profile distribution resembling a Gaussian shape. In contrast, other machining conditions resulted in kurtosis values generally below 3, suggesting flatter distributions with fewer extreme peaks and valleys. Nevertheless, the considerable variability across measurements limits the ability to generalize these findings, and the results should be seen as indicative rather than conclusive.\u003c/p\u003e\n \u003cp\u003eTo provide statistical support for these observations and further assess whether the skewness and kurtosis values significantly deviated from ideal reference values (0 and 3, respectively), one-sample t-tests were conducted for each machining condition. This approach enabled the identification of significant asymmetries or deviations from normality in the roughness distributions, accounting for data variability across tool sizes, materials, and feed per tooth. Data normality was assessed using the Shapiro-Wilk test, and datasets exhibited normal distribution (p\u0026thinsp;\u0026gt;\u0026thinsp;0.05), validating the test. Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e summarizes the one-sample t-test results.\u0026nbsp;\u003c/p\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eStatistical significance of skewness and kurtosis deviations based on t-test results.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSize\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eft\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSkewness\u003c/p\u003e\n \u003cp\u003et-statistic\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSkewness\u003c/p\u003e\n \u003cp\u003ep-value\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eKurtosis\u003c/p\u003e\n \u003cp\u003et-statistic\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eKurtosis\u003c/p\u003e\n \u003cp\u003ep-value\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eDPh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.6464\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1104\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-7.2924\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-2.8612\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0077\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-4.4826\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.8092\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4249\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-4.6132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eUFG\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.6823\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1032\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-10.9772\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-1.9060\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0665\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-3.3073\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0025\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.0969\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9234\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-4.8255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eDPh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9537\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3480\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-8.9778\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.2155\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8308\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-4.2983\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.3292\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1941\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-1.5318\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1363\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eUFG\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0937\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9259\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-8.6846\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3971\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.6941\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-8.5020\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4651\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.6452\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.3598\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.7215\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eDPh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.3237\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0024\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-7.7387\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.4222\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-3.5110\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0014\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-5.8839\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-4.2758\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eUFG\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.8931\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0683\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-10.5780\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0220\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0524\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-5.7993\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-2.1488\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0401\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-6.6554\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eThe skewness analysis confirmed that, under most machining conditions, the roughness distributions did not significantly deviate from symmetry (p\u0026thinsp;\u0026ge;\u0026thinsp;0.05), suggesting that peaks and valleys were approximately balanced. However, for DPh in specific conditions, particularly at D400 and 2 \u0026micro;m/tooth, and D800 (all feed per tooth), statistically significant deviations were observed (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), indicating a higher tendency for valley formation (negative skewness) or peak generation (positive skewness). The occurrence of negative skewness under certain conditions may be attributed to plastic deformation mechanisms like ploughing, where the ductility favors valley formation instead of chip removal. Conversely, positive skewness observed for D800 at lower feed per tooth may indicate the presence of residual peaks due to insufficient chip thickness and material accumulation near the cutting edge.\u003c/p\u003e\n \u003cp\u003eThe statistical analysis of kurtosis (Table \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e) revealed that most machining conditions resulted in significantly lower values than the reference Gaussian distribution (kurtosis\u0026thinsp;\u0026lt;\u0026thinsp;3), indicating flatter surface profiles with fewer extreme peaks and valleys. This behavior is consistent with stable material removal mechanisms, especially at lower feed per tooth and with smaller tool diameters (D400). For the D600 tool, both UFG and DPh steels presented kurtosis values statistically equivalent to 3 at 5 \u0026micro;m/tooth, which may reflect increased variability in chip formation or the emergence of localized surface instabilities under higher cutting loads. In contrast, the D800 consistently produced platykurtic surfaces, possibly due to the larger effective cutting area distributing forces more evenly across the surface. These results indicate that tool size, feed per tooth, and workpiece microstructure interact to influence not only the amplitude of surface roughness but also the statistical distribution of texture features.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3. Machine learning-based roughness prediction\u003c/h2\u003e\n \u003cp\u003eThe predictive models for surface roughness (Ra) were separately evaluated for DPh and UFG steels, using Random Forest Regressor (RFR) and Multilayer Perceptron (MLP) Neural Network. The objective was to analyze the influence of machining parameters on roughness formation and assess the predictive capability of machine learning techniques. By this sense, Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e presents the comparative performance of the models for materials. \u0026nbsp;\u003c/p\u003e\n \u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eModel performance for workpiece materials.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMAE (nm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eDPh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.470\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMLP Neural Network\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e12.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.480\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eUFG\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.664\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMLP Neural Network\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.717\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eFor the DPh steel, the models exhibited moderate accuracy, suggesting that additional parameters beyond those considered might be more significant in determining roughness. The Random Forest model resulted in a MAE of 13.16 nm and an R\u003csup\u003e2\u003c/sup\u003e of 0.47, indicating that 47% of the roughness variation was explained by the model. Meanwhile, the MLP Neural Network achieved a slightly better performance, with an MAE of 12.73 nm and an R\u003csup\u003e2\u003c/sup\u003e of 0.48, demonstrating that machine learning techniques can partially predict roughness in dual-phase steel but with limited reliability. The results indicated that the alternating ferrite-pearlite microstructure of DPh steel might introduce higher variability in surface formation, reducing the effectiveness of purely data-driven predictive models. The complex interaction between material properties and tool engagement may require additional behaviour of tool deflections during cutting to enhance the precision of the predictions.\u003c/p\u003e\n \u003cp\u003eFor the UFG steel, the predictive performance significantly improved, indicating a more stable relationship between machining parameters and roughness outcomes. The Random Forest model achieved a MAE of 7.53 nm and an R\u003csup\u003e2\u003c/sup\u003e of 0.66, demonstrating that 66.4% of the roughness variation could be explained by the input parameters. The MLP Neural Network further improved the prediction, reducing the error to 7.25 nm and increasing R\u003csup\u003e2\u003c/sup\u003e to 0.71, explaining 71% of the roughness variability. These results highlight that the homogeneous microstructure of UFG contributes to a more predictable roughness formation process, allowing machine learning models to better capture the relationships between process variables and surface characteristics.\u003c/p\u003e\n \u003cp\u003eThe fact that the MLP model outperformed the Random Forest approach showed that non-linear interactions exist between the machining parameters and roughness, which neural networks can better account for. However, it is worth noting that the MLP model reached the maximum number of iterations without full convergence, indicating that further hyperparameter tuning, such as adjusting the learning rate and optimizing the number of hidden layers, could lead to even higher improvements.\u003c/p\u003e\n \u003cp\u003eIn addition to performance metrics, a feature importance analysis was carried out using the Random Forest model to assess the contribution of each input variable to the roughness prediction. The results revealed that the tool size was the most influential factor, followed by the feed per tooth and the microgroove milling side. Among the microgroove milling side, the down-milling side contributed more significantly to roughness variations than the up-milling side. These findings are consistent with the domain knowledge that tool geometry and chip engagement conditions strongly influence the surface generation mechanisms in micromilling [\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eWhile the Random Forest model provided interpretability by quantifying the relative importance of each input variable in predicting surface roughness (a process known as feature importance ranking), the MLP model demonstrated superior predictive power, likely due to its enhanced capacity to capture complex, multivariate nonlinear interactions. These findings suggest that although tree-based models such as Random Forest offer valuable insights into which machining parameters most influence the outcome, neural networks are more suitable for achieving high predictive accuracy in scenarios involving intricate and interdependent machining dynamics.\u003c/p\u003e\n \u003cp\u003eThe predictive capability of the machine learning models was notably higher for UFG steel than for DPh steel, reinforcing the idea that materials with homogeneous microstructures produce more consistent machining responses. In contrast, the higher microstructural complexity of DPh steel introduces additional variability in the roughness formation process, which remains challenging for AI-based modeling. Despite this, the results indicated that machine learning techniques, particularly neural networks, hold significant potential for roughness prediction in micromilling. The higher accuracy observed for UFG showed that AI-based process control strategies could be successfully applied to optimize surface quality for homogeneous microstructure steels.\u003c/p\u003e\n \u003cp\u003eFurthermore, roughness in UFG varied more significantly with changes in cutting parameters, while in DPh steel, roughness remained more uniform and predictable. AI models tend to perform better when there is a broad range of variation in the data, as this allows the identification of complex patterns that explain the relationships between input parameters and system response. In the case of DPh, since the roughness values were more predictable and less dispersed, the models struggled to identify unique patterns that explained the variation in Ra. As a result, the lower dispersion of roughness values in DPh reduced the AI\u0026rsquo;s ability to capture deeper and more complex patterns, limiting the predictive performance of the model.\u003c/p\u003e\n \u003cp\u003eTo contextualize the scientific contributions of this work, Table \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e presents a comparative summary of recent studies (2018\u0026ndash;2025) that employed machine learning techniques for predicting surface roughness in machining processes, with a particular focus on micro-milling and precision milling. The table highlights key aspects such as the machined material, roughness parameters considered, type of machining process, adopted artificial intelligence (AI) models, whether transverse profile accuracy was evaluated, and the main contributions or limitations of each study. Compared to previous works, the present research uniquely integrates the prediction of surface roughness with the analysis of geometrical accuracy of microgrooves using ball-end micromilling, considering different microstructural conditions of low-carbon steels. Furthermore, it distinguishes itself by combining interpretable machine learning models, Random Forest and Multilayer Perceptron, with feature importance analysis, offering deeper insights into the influence of tool geometry and microstructure on surface formation mechanisms. \u0026nbsp;\u003c/p\u003e\n \u003ctable id=\"Tab6\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eComparative summary of recent studies (2018\u0026ndash;2025) using machine learning techniques for surface roughness prediction in micro-milling and precision machining.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStudy\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eProcess\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRoughness\u003c/p\u003e\n \u003cp\u003eparameters\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAI Techniques\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eProfile\u003c/p\u003e\n \u003cp\u003eaccuracy\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMain Contribution\u003c/p\u003e\n \u003cp\u003e/Limitation\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLu \u003cem\u003eet al.\u003c/em\u003e (2019) [55]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSingle-crystal copper\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMicro-milling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRa\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSVR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIntegrated crystallographic orientation in roughness modeling; limited to single-crystal copper.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eShang \u003cem\u003eet al\u003c/em\u003e. (2023) [\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTool steel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUltra-precision micro-milling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRa\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eExtreme Learning Machine (ELM)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eApplied ELM with feature fusion for high-accuracy Ra prediction (~\u0026thinsp;1.6% MAPE); limited to one material and test setup.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eZeng and Pi (2023) [\u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS45C steel; W78Cu22 alloy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMilling (incl. micro-milling)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRa\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCNN-GRU (Physics-informed)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePhysics-guided DL model improved prediction accuracy; complexity added by physical modeling.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTsai \u003cem\u003eet al\u003c/em\u003e. (2023) [\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStainless steel SUS304\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCNC milling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRa\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDNN, CNN, LSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePredicted Ra and profile accuracy from force signals; CNN showed low computation time; classification step not beneficial.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eKosarac \u003cem\u003eet al\u003c/em\u003e. (2023) [\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTi-6Al-4V\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eConventional milling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRa\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRandom Forest, ANN, SVR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRF performed best in small datasets; dataset size limited generalization.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePresent study\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLow-carbon\u003c/p\u003e\n \u003cp\u003esteel (UFG\u003c/p\u003e\n \u003cp\u003eand Dual-Phase)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMicro-milling (Ball-end)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRa, Rz, Rsk, Rku\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRandom Forest, MLP Neural Network\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIntegrated Ra and profile accuracy prediction with ML and feature importance; unique focus on microstructural effects.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\n\u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eThis study investigated the influence of tool geometry, particularly ball-end mill size and neck length, feed per tooth, and microgroove milling side on the machining accuracy and surface roughness of microgrooves fabricated in dual-phase and ultrafine-grained low-carbon steels. The integration of statistical analysis and machine learning techniques enabled a comprehensive evaluation of tool\u0026ndash;workpiece interactions and the predictive modeling of surface characteristics. The following conclusions can be drawn:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTool deflection was a critical factor affecting dimensional accuracy. While larger tools size inherently improved stiffness, excessive neck length (as seen with the D600 tool) introduced significant flexibility, leading to increased profile deviations. The D400 tool exhibited the lowest geometric errors at moderate feed rates due to its shorter unsupported length.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFeed per tooth significantly influenced surface integrity. Lower feed values (0.5 \u0026micro;m/tooth) promoted smoother profiles and minimized surface irregularities, while higher feeds increased roughness amplitude and deformation, especially in up-milling sides.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eWorkpiece microstructure is the main influence in machining outcomes. Ultrafine-grained steel, with its homogeneous and though structure, exhibited more stable surface formation and higher predictability of roughness, while dua-phase steel demonstrated better dimensional consistency due to its resistance to plastic deformation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eBurr formation was minimal across all conditions, attributed to favorable edge angles (~\u0026thinsp;145\u0026deg;) formed by the interaction between tool radius and depth of cut. This edge geometry contributed to stable chip formation even at low feed rates.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe Multilayer Perceptron outperformed the Random Forest Regressor in predicting surface roughness, particularly for ultrafine-grained steel, achieving an R\u0026sup2; of 0.711. This superior performance is attributed to the microstructural homogeneity of ultrafine-graned steel, which promotes stable machining behavior and reduces data variability, enhancing the accuracy of nonlinear learning models. In contrast, the dual-phase steel exhibited higher response variability, limiting predictive precision despite the interpretability advantages offered by RFR.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThese findings highlight the importance of selecting appropriate tool geometry and feed strategies tailored to the material\u0026rsquo;s microstructure. Moreover, the demonstrated effectiveness of machine learning in roughness prediction supports its integration into micromachining process planning, particularly for homogeneous microstructured steels in which AI models can enhance surface quality control.\u003c/p\u003e \u003cp\u003eIn contrast to prior studies that typically address roughness or profile accuracy in isolation, the present work provides an integrated modeling framework supported by interpretable AI techniques. This dual focus, combined with the consideration of metallurgical variability, represents a novel contribution to the predictive modeling of surface integrity in micromachining of low-carbon steels.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships which have, or could be perceived to have, influenced the research reported in this article.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to express their gratitude to the Technological Research Institute of S\u0026atilde;o Paulo (IPT) for providing access to laboratory facilities and to Mitsubishi Materials for supplying the cutting tools used in this study.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eFunding:\u003c/strong\u003e This work was supported by the National Council of Scientific and Technological Development (CNPq) [grant number 468309/2014-4].\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eAuthor Contribution Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCleiton Lazaro Fazolo de Assis:\u003c/strong\u003e Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Writing-original draft, Visualization, Supervision, Project administration, Funding acquisition. \u003cstrong\u003eAlessandro Roger Rodrigues:\u003c/strong\u003e Methodology, Formal analysis, Resources, Writing-reviewing and editing.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eGao S, Duan X, Zhu K, Zhang Y (2024) Investigation of the tool flank wear influence on cutter-workpiece engagement and cutting force in micro milling processes. Mech Syst and Signal Proc 209:111104. https://doi.org/10.1016/j.ymssp.2024.111104\u003c/li\u003e\n\u003cli\u003eSun Y, Sun Y, Huang Y, Gong S, Sun M, Liu M (2025) Study on developing predicted system model of cutting-edge trajectory for micro-milling process based on tool runout error, chip thickness and force signal. Mech Syst and Signal Proc 228:112410. https://doi.org/10.1016/j.ymssp.2025.112410\u003c/li\u003e\n\u003cli\u003eBasile V, Modica F, Rebaioli L, Surace R, Fassi I (2023) Process Chains for Micro-Manufacturing: Modeling and Case Studies. J Manuf and Mat Proc 7(6):215. https://doi.org/10.3390/jmmp7060215\u003c/li\u003e\n\u003cli\u003eBiondani FG, Bissacco G (2019) Effect of cutting edge micro geometry on surface generation in ball end milling. CIRP annals 68(1):571-574. https://doi.org/10.1016/j.cirp.2019.04.017\u003c/li\u003e\n\u003cli\u003eOliaei SNB, Karpat Y, Davim JP, Perveen A (2018) Micro tool design and fabrication: A review. J Manuf Proc 36:496-519. https://doi.org/10.1016/j.jmapro.2018.10.038\u003c/li\u003e\n\u003cli\u003eSekulic M, Pejic V, Brezocnik M, Gostimirović M, Hadzistevic M (2018) Prediction of surface roughness in the ball-end milling process using response surface methodology, genetic algorithms, and grey wolf optimizer algorithm. Adv in Prod Eng \u0026amp; Manag 13(1):18-30. https://doi.org/10.14743/apem2018.1.270\u003c/li\u003e\n\u003cli\u003eJia Z, Lu X, Gu H, Ruan F, Liang SY (2021) Deflection prediction of micro-milling Inconel 718 thin-walled parts. J Mat Proc Tech 291:117003. https://doi.org/10.1016/j.jmatprotec.2020.117003\u003c/li\u003e\n\u003cli\u003eWojciechowski S, Wiackiewicz M, Krolczyk GM (2018) Study on metrological relations between instant tool displacements and surface roughness during precise ball end milling. Measurement 129:686-694. https://doi.org/10.1016/j.measurement.2018.07.058\u003c/li\u003e\n\u003cli\u003eCelis P, Vazquez E, Soria-Hern\u0026aacute;ndez CG, Bargnani D, Rodriguez CA, Ceretti E, Garc\u0026iacute;a-L\u0026oacute;pez E (2022) Evaluation of ball end micromilling for Ti6Al4V ELI microneedles using a nanoadditive under MQL condition. Int J Prec Eng and Manuf-Green Tech 9(5):1231-1246. https://doi.org/10.1007/s40684-021-00383-y\u003c/li\u003e\n\u003cli\u003eGuo Q, Liu Z, Yang Z, et al (2024) Development, challenges and future trends on the fabrication of micro-textured surfaces using milling technology. J Manuf Proc 126:285-331. https://doi.org/10.1016/j.jmapro.2024.07.112\u003c/li\u003e\n\u003cli\u003eKlauer K, Eifler M, Kirsch B, Seewig J, Aurich JC (2020) Ball end micro milling of areal material measures: influence of the tilt angle on the resulting surface topography. Prod Eng 14(2):239-252. https://doi.org/10.1007/s11740-019-00943-x\u003c/li\u003e\n\u003cli\u003eBal\u0026aacute;zs BZ, Geier N, Pereszlai C, Po\u0026oacute;r DI, Tak\u0026aacute;cs M (2021) Analysis of cutting force and vibration at micro-milling of a hardened steel. Procedia CIRP 99:177-182. https://doi.org/10.1016/j.procir.2021.03.025\u003c/li\u003e\n\u003cli\u003eImani BM, Elbestawi MA (2001) Geometric simulation of ball-end milling operations. J. Manuf Sci Eng 123(2):177-184. https://doi.org/10.1115/1.1347034\u003c/li\u003e\n\u003cli\u003ePratap T, Patra K (2018) Micro ball-end milling\u0026mdash;an emerging manufacturing technology for micro-feature patterns. Int J Adv Manuf Tech 94(5-8):2821-2845. https://doi.org/10.1007/s00170-017-1064-9\u003c/li\u003e\n\u003cli\u003eSong B, Zhang D, Jing X, Shi B, Wang F, Li H (2024) Cleaner production of multi-scale surface textures using integrated ball-end and vibration-assisted milling. J Cleaner Prod 484:144316. https://doi.org/10.1016/j.jclepro.2024.144316\u003c/li\u003e\n\u003cli\u003eZhang J, Zhang S, Jiang D, Wang J, Lu S (2020) Surface topography model with considering corner radius and diameter of ball-nose end miller. Int J Adv Manuf Tech 106:3975-3984. https://doi.org/10.1007/s00170-019-04897-3\u003c/li\u003e\n\u003cli\u003eHerraz M, Redonnet JM, Mongeau M, Sbihi M (2020) A new method for choosing between ball-end cutter and toroidal cutter when machining free-form surfaces. Int J Adv Manuf Tech 111(5):1425-1443. https://doi.org/10.1007/s00170-020-06087-y\u003c/li\u003e\n\u003cli\u003eVenkatesh V, Swain N, Srinivas G, Kumar P, Barshilia HC (2017) Review on the machining characteristics and research prospects of conventional microscale machining operations. Mat and Manuf Proc 32(3):235-262. https://doi.org/10.1080/10426914.2016.1151045\u003c/li\u003e\n\u003cli\u003eWojciechowski S (2021) Estimation of minimum uncut chip thickness during precision and micro-machining processes of various materials\u0026mdash;a critical review. Materials 15(1):59. https://doi.org/10.3390/ma15010059\u003c/li\u003e\n\u003cli\u003eMik\u0026oacute; B, Zentay P (2019) A geometric approach of working tool diameter in 3-axis ball-end milling. Int J Adv Manuf Tech 104(1-4):1497-1507. https://doi.org/10.1007/s00170-019-03968-9\u003c/li\u003e\n\u003cli\u003eAkamatsu T, Kitajima K, Ueda A (2004) Cutting Accuracy of the Small Radius Ball Endmill in Deep Precision Machining. Key Eng Mat 257-258:565-570. https://doi.org/10.4028/www.scientific.net/kem.257-258.565\u003c/li\u003e\n\u003cli\u003eAssis CL, Jasinevicius RG (2019) Influence of tool neck length on tool deflections during micromilling of an ultrafine grained low-carbon steel. In: Leach RK, Billington D, Nisbet C, Phillips D. editors: Proceedings of the 19th Euspen Conference, Bilbao, Spain. 2019. Nothampton: twenty10, 468-469. https://www.euspen.eu/knowledge-base/ICE19221.pdf [accessed 31 March 2025]\u003c/li\u003e\n\u003cli\u003eBegic-Hajdarevic D, Cekic A, Kulenovic M (2014) Experimental study on the high speed machining of hardened steel. Procedia Eng 69:291-295. https://doi.org/10.1016/j.proeng.2014.02.234\u003c/li\u003e\n\u003cli\u003eWang D, Penter L, H\u0026auml;nel A, Yang Y, Ihlenfeldt S (2022) Investigation on dynamic tool deflection and runout-dependent analysis of the micro-milling process. Mech Syst and Signal Proc 178:109282. https://doi.org/10.1016/j.ymssp.2022.109282\u003c/li\u003e\n\u003cli\u003ePratap T, Patra K (2017) Micromilling of ti-6al-4v titanium alloy using ball-end tool. In IOP Conference Series: Mat Sci and Eng 229(1):012011. https://doi.org/10.1088/1757-899X/229/1/012011\u003c/li\u003e\n\u003cli\u003eVogler MP, DeVor RE, Kapoor SG (2004) On the modeling and analysis of machining performance in micro-endmilling, part I: surface generation. J Manuf Sci Eng 126(4):685-694. https://doi.org/10.1115/1.1813470\u003c/li\u003e\n\u003cli\u003eMian AJ, Driver N, Mativenga PT (2010) A comparative study of material phase effects on micro-machinability of multiphase materials. Int J Adv Manuf Tech 50(1-4):163-174. https://doi.org/10.1007/s00170-009-2506-9\u003c/li\u003e\n\u003cli\u003eRodrigues AR, Balancin O, Gallego J et al (2012) Surface integrity analysis when milling ultrafine-grained steels. Mat Research 15(1):125-130. https://doi.org/10.1590/S1516-14392011005000094\u003c/li\u003e\n\u003cli\u003eDe Assis CL, Jasinevicius RG, Rodrigues AR (2015) Micro end-milling of channels using ultrafine-grained low-carbon steel. Int J Adv Manuf Tech 77(5-8):1155-1165. https://doi.org/10.1007/s00170-014-6503-2\u003c/li\u003e\n\u003cli\u003eShao Y, Li J, Zhang X (2022) The impact of financial development on CO2 emissions of global iron and steel industry. Envir Sci and Pollut Res 29(29):44954-44969. https://doi.org/10.1007/s11356-022-18977-7\u003c/li\u003e\n\u003cli\u003eKim J, Sovacool BK, Bazilian M et al (2022) Decarbonizing the iron and steel industry: A systematic review of sociotechnical systems, technological innovations, and policy options. Energy Res \u0026amp; Soc Sci 89:102565. https://doi.org/10.1016/j.erss.2022.102565\u003c/li\u003e\n\u003cli\u003eZhang D (2021) Ultrafine grained metals and metal matrix nanocomposites fabricated by powder processing and thermomechanical powder consolidation. Prog in Mat Sci 119:100796. https://doi.org/10.1016/j.pmatsci.2021.100796\u003c/li\u003e\n\u003cli\u003eGao C, Wang Y, Qiu X, Chi H, Zhou J, Cai H, Cheng X (2022) Microstructure evolution and compressive properties of a low carbon-low alloy steel processed by warm rolling and subsequent annealing. Mat Charact 192:112237. https://doi.org/10.1016/j.matchar.2022.112237\u003c/li\u003e\n\u003cli\u003eGhosh S, K\u0026ouml;mi J, Mula S (2020) Flow stress characteristics and design of innovative 3-steps multiphase control thermomechanical processing to produce ultrafine grained bulk steels. Mat \u0026amp; Design 186:108297. https://doi.org/10.1016/j.matdes.2019.108297\u003c/li\u003e\n\u003cli\u003eZhao J, Jiang Z (2018) Thermomechanical processing of advanced high strength steels. Prog in Mat Sci 94:174-242. https://doi.org/10.1016/j.pmatsci.2018.01.006\u003c/li\u003e\n\u003cli\u003eZhao Z, To S, Wang J, Zhang G, Weng Z (2022) A review of micro/nanostructure effects on the machining of metallic materials. Mat \u0026amp; Design 111315. https://doi.org/10.1016/j.matdes.2022.111315\u003c/li\u003e\n\u003cli\u003eBal\u0026aacute;zs BZ, Geier N, Tak\u0026aacute;cs M, Davim JP (2021) A review on micro-milling: recent advances and future trends. Int J Adv Manuf Tech 112:655-684. https://doi.org/10.1007/s00170-020-06445-w\u003c/li\u003e\n\u003cli\u003eMamedov A (2021) Micro milling process modeling: a review. Manuf Review 8:3. https://doi.org/10.1051/mfreview/2021003\u003c/li\u003e\n\u003cli\u003eJin SY, Pramanik A, Basak AK, Prakash C, Shankar S, Debnath S (2020) Burr formation and its treatments\u0026mdash;a review. Int J Adv Manuf Tech 107:2189-2210. https://doi.org/10.1007/s00170-020-05203-2\u003c/li\u003e\n\u003cli\u003eAbdelrahman Elkaseer AM, Dimov SS, Popov KB, Minev RM (2014) Tool wear in micro-endmilling: Material microstructure effects, modeling, and experimental validation. Journal of Micro-and Nano-Manuf 2(4):044502. https://doi.org/10.1115/1.4028077\u003c/li\u003e\n\u003cli\u003eSaptaji K, Subbiah S, Dhupia JS (2012) Effect of side edge angle and effective rake angle on top burrs in micro-milling. Prec Eng 36(3):444-450. https://doi.org/10.1016/j.precisioneng.2012.01.008\u003c/li\u003e\n\u003cli\u003eEl-Asfoury MS, Baraya M, El Shrief E, Abdelgawad K, Sultan M, Abass A (2024) AI-Based Prediction of Ultrasonic Vibration-Assisted Milling Performance. Sensors 24(17):5509. https://doi.org/10.3390/s24175509\u003c/li\u003e\n\u003cli\u003eFarooq MU, Kumar R, Khan A et al (2024) Sustainable machining of Inconel 718 using minimum quantity lubrication: Artificial intelligence-based process modelling. Heliyon. 10(15):e34836. https://doi.org/10.1016/j.heliyon.2024.e34836\u003c/li\u003e\n\u003cli\u003eWu D, Jennings C, Terpenny J, Gao RX, Kumara S (2017) A comparative study on machine learning algorithms for smart manufacturing: tool wear prediction using random forests. J Manuf Sci and Eng 139(7):071018. https://doi.org/10.1115/1.4036350\u003c/li\u003e\n\u003cli\u003eShanmugasundar G, Vanitha M, Čep R, Kumar V, Kalita K, Ramachandran M (2021) A comparative study of linear, random forest and adaboost regressions for modeling non-traditional machining. Proc 9(11):2015. https://doi.org/10.3390/pr9112015\u003c/li\u003e\n\u003cli\u003eKumar V, Dubey V, Sharma AK (2023) Comparative analysis of different machine learning algorithms in prediction of cutting force using hybrid nanofluid enriched cutting fluid in turning operation. Mat Today: Proc. https://doi.org/10.1016/j.matpr.2023.05.216\u003c/li\u003e\n\u003cli\u003eLa F\u0026eacute;-Perdomo I, Ramos-Grez JA, Jeria I, Guerra C, Barrionuevo GO (2022) Comparative analysis and experimental validation of statistical and machine learning-based regressors for modeling the surface roughness and mechanical properties of 316L stainless steel specimens produced by selective laser melting. J Manuf Proc 80:666-682. https://doi.org/10.1016/j.jmapro.2022.06.021\u003c/li\u003e\n\u003cli\u003eGallego J, Rodrigues AR., Assis CLF, Montanari L (2014) Second phase precipitation in Ultrafine-grained ferrite steel. Mat Res 17:527-534. https://doi.org/10.1590/S1516-14392013005000199\u003c/li\u003e\n\u003cli\u003ePippan R, Hohenwarter A (2016) The importance of fracture toughness in ultrafine and nanocrystalline bulk materials. Mat Res Letters 4(3):127-136. https://doi.org/10.1080/21663831.2016.1166403\u003c/li\u003e\n\u003cli\u003eLei C, Li X, Deng X, Wang Z, Wang G (2018) Deformation mechanism and ductile fracture behavior in high strength high ductility nano/ultrafine grained Fe-17Cr-6Ni austenitic steel. Mat Sci and Eng: A 709:72-81. https://doi.org/10.1016/j.msea.2017.10.043\u003c/li\u003e\n\u003cli\u003eGillespie LK (1999) Burr formation. In: Treloar M, Editor. Deburring and edge finishing handbook. Michigan: Society of Manufacturing Engineers, pp 53-90.\u003c/li\u003e\n\u003cli\u003eO\u0026rsquo;Toole L, Kang CW, Fang FZ (2020) Precision micro-milling process: state of the art. Adv in Manuf 1-33. https://doi.org/10.1007/s40436-020-00323-0\u003c/li\u003e\n\u003cli\u003ePawlus P, Reizer R, Wieczorowski M (2021) Functional importance of surface texture parameters. Mat 14(18):5326. https://doi.org/10.3390/ma14185326\u003c/li\u003e\n\u003cli\u003eBasso I, Voigt R, Rodrigues AR, Marin F, de Souza AF, de Lacalle LNL (2022) Influences of the workpiece material and the tool-surface engagement (TSE) on surface finishing when ball-end milling. J Manuf Proc 75:219-231. https://doi.org/10.1016/j.jmapro.2021.12.059\u003c/li\u003e\n\u003cli\u003eLu X, Xue L, Ruan F, Yang K, Liang SY (2019) Prediction model of the surface roughness of micro-milling single crystal copper. J Mech Sci and Tech 33:5369-5374. https://doi.org/10.1007/s12206-019-1030-6\u003c/li\u003e\n\u003cli\u003eShang S, Wang C, Liang X, Cheung CF, Zheng P (2023) Surface roughness prediction in ultra-precision milling: An extreme learning machine method with data fusion. Micromach 14(11):2016. https://doi.org/10.3390/mi14112016\u003c/li\u003e\n\u003cli\u003eZeng S, Pi D (2023) Milling surface roughness prediction based on physics-informed machine learning. Sensors 23(10):4969. https://doi.org/10.3390/s23104969\u003c/li\u003e\n\u003cli\u003eTsai MH, Lee JN, Tsai HD, Shie MJ, Hsu TL, Chen HS (2023) Applying a neural network to predict surface roughness and machining accuracy in the milling of SUS304. Electronics 12(4):981. https://doi.org/10.3390/electronics12040981\u003c/li\u003e\n\u003cli\u003eKosarac A, Tabakovic S, Mladjenovic C, Zeljkovic M, Orasanin G (2023) Next-gen manufacturing: machine learning for surface roughness prediction in Ti-6Al-4V biocompatible alloy machining. J Manuf and Mat Proc 7(6):202. https://doi.org/10.3390/jmmp7060202\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Ball-end micromilling, Ultrafine-grained low-carbon steel, Surface roughness prediction, Profile accuracy, Machine learning, Tool deflection","lastPublishedDoi":"10.21203/rs.3.rs-6753887/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6753887/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents an integrated experimental and computational approach to analyze surface integrity in ball-end micromilling of two low-carbon steels with distinct microstructures: dual-phase (DPh) and ultrafine-grained (UFG). The influence of tool diameter, neck length, feed per tooth, and milling strategy (up- and down-milling) on surface roughness (Ra, Rz, skewness, kurtosis), burr formation, and profile accuracy was systematically investigated. Tool deflection effects, more critical in UFG due to its higher ductility, were quantified through geometrical deviation metrics. Predictive models using Random Forest (RF) and Multilayer Perceptron neural networks (MLP) were developed to estimate surface roughness based on machining parameters. The MLP model showed superior performance for UFG steel (R\u0026sup2; = 0.71), indicating enhanced prediction capability for homogeneous microstructures. Feature importance analysis highlighted the dominant effect of tool diameter and feed per tooth. The results advance the understanding of process-material interaction in micromilling and demonstrate the potential of interpretable machine learning for surface quality prediction in ultrafine-grained steels.\u003c/p\u003e","manuscriptTitle":"Modeling of ball-end micromilled surface roughness and geometry in ultrafine-grained and dual-phase steels using interpretable machine learning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-02 08:14:47","doi":"10.21203/rs.3.rs-6753887/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revisions Needed","date":"2025-08-16T09:17:12+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-07-01T13:41:05+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-28T12:52:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-28T03:47:21+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2025-05-26T18:35:16+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0c6e0b5e-b58d-46b9-a4a0-ad7d4f141cc1","owner":[],"postedDate":"June 2nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-10-06T16:11:22+00:00","versionOfRecord":{"articleIdentity":"rs-6753887","link":"https://doi.org/10.1007/s00170-025-16532-5","journal":{"identity":"the-international-journal-of-advanced-manufacturing-technology","isVorOnly":false,"title":"The International Journal of Advanced Manufacturing Technology"},"publishedOn":"2025-10-02 15:57:40","publishedOnDateReadable":"October 2nd, 2025"},"versionCreatedAt":"2025-06-02 08:14:47","video":"","vorDoi":"10.1007/s00170-025-16532-5","vorDoiUrl":"https://doi.org/10.1007/s00170-025-16532-5","workflowStages":[]},"version":"v1","identity":"rs-6753887","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6753887","identity":"rs-6753887","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}