Modeling and multi-objective optimization of drilling performance in Mg(OH) 2 -filled flax/kenaf hybrid biocomposites

Overview

The experimental methodology applied (and adopted herein) consists of three major stages: composite fabrication, drilling experimentation, and process optimization. A schematic summary of the methodology is described in Figure 1, which presents the sequential flow of methodology from the selection of materials, fabrication of composite, multi-response modelling, and optimization using RSM and ANN.OPEN IN VIEWER

Workpiece material and composite fabrication

The workpiece material in the case of the current drilling investigation consisted of a hybrid natural fiber-reinforced polymer composite made from flax and kenaf fiber incorporated with magnesium hydroxide (Mg(OH)₂) as a mineral filler. This composite formulation choice was based on optimized mechanical performance as demonstrated by the authors in a prior study in which the hybrid configuration showed better tensile and yield strength when compared to other filler systems. The composite had been composed of 20 wt% Flax fibers, 20 wt% Kenaf fibers, and 5 wt% of Mg(OH)₂ filler, and the rest of the proportion was made up of an epoxy resin matrix. Flax fibers were mainly used to improve load transfer and vibration damping, whereas kenaf fibers helped to improve the stiffness and impact resistance. Magnesium hydroxide was used as the flame-retardant filler and to enhance the interfacial bonding in the hybrid system. The matrix system was based on a low-viscosity epoxy resin (EPOLAM 2040) cross-linked with an amine-based hardener (EPOLAM 2042) with a ratio of 100:32 as recommended by the manufacturer to obtain the best cross-link density and mechanical stability. Prior to fabrication, flax and kenaf fibers were alkali-treated, which removed surface impurities, increased the roughness of the fiber, and improved the adhesion between fiber and matrix. Composite laminates were created from the compression moulding process. The treated woven flax and kenaf fibers were impregnated with the epoxy-Mg(OH)₂ mixture and stacked inside a steel mold of the dimensions 300 × 300 × 5 mm. Consolidation took place under the constant hydraulic pressure of 10 MPa at the ambient temperature for 24 h to ensure homogeneous wetting of the fibers and the thickness of the laminate. Post-curing at 60°C for 6 h subsequently was done to relieve residual stresses and complete the polymerization. The fabricated composite material showed a tensile strength of 54.05 MPa, a yield strength of 39.01 MPa, and an elongation at break of 1.26%, which proved it is suitable for load-bearing and structural applications. These properties also warranted being selected for an in-depth drilling-induced damage and machinability investigation.

Cutting tools

Drilling experiments were performed with three different 8 mm diameter twist drills, chosen so as to systematically assess the impact of tool material on drill-induced damage and hole quality.

Cutting tools used were HSS (traditional high-speed steel drill used as a baseline); M35 (cobalt-alloyed high-speed steel drill with about 5% that has high thermal resistance); and M42 (high-speed steel drill with a cobalt alloying element of about 8%, superior red-hardness, high thermal stability, and superior wear resistance at the cutting edge). All drills had the same geometrical features to eliminate the effects of any other factors (in this case, the tool material) on the drilling responses. A representative image of the cutting tools and experimental setup is presented in Figure 2.OPEN IN VIEWER

Experimental design and input parameters

A structured Design of Experiments (DoE) methodology was taken up for finding the combined effects of drilling parameters on the quality of the holes made. Considering both continuous elements and the addition of a categorical element, an FCCCD has been chosen because of its suitability for quadratic modelling and with respect to practical conditions for machining. The experimental design was set with 30 experimental trials (drilling) (Figure 2(a)) with three independent input parameters: Spindle Speed (SS), Feed Rate (FR), and Tool Material (TM). To minimize variation due to batch and to isolate the effect of tool material, the design was blocked by tool material, and a total of three blocks were used, corresponding to the three types of drills, HSS, M35, and M42 drills (Figure 2(c)). Two centerpoint replications per block were also used to determine the pure experimental error and assess the repeatability of the process. In this way, any systematic variation in manufacture between types of tools (e.g., small manufacturing differences) is included in the statistical model and not confused with the spindle speed and feed rate. The FCCCD was enforced on the condition of equal axial distance, α = 1.0, so that all the axial points align with the actual high or low levels of the continuous factors. This selection made it possible to maintain reasonable spindle speeds and feeds and to provide good estimation of the quadratic effects. The input parameters selected and the respective levels are summarized in Table 1.

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Table 1.

Drilling input parameters and their levels.

Factor	Parameter	Units	Type	−1	0	+1
A	Spindle speed (SS)	rpm	Continuous	1000	2000	3000
B	Feed rate (FR)	mm/rev	Continuous	0.20	0.40	0.60
C	Tool material (TM)	—	Categorical	HSS	M35	M42

For statistical modeling, the continuous variables were transformed into coded values using the following relationships (Equations (1) and (2)):

A coded = S S − 2000 1000

(1)

B coded = F R − 0.4 0.2

(2)

Selection of cutting parameters (namely, Spindle Speed (1000−3000 rpm) and Feed Rate (0.20−0.60 mm/rev)) was carried out in a very rationed and systematic manner to achieve direct industrial applicability in view of the latest advancements in the field of composite machining. Despite its many advantages, the challenge of drilling natural fiber composite materials is related to the material properties, namely the anisotropy and heterogeneity, which tend to cause delamination, thermal damage, and poor surface finish. ²⁴ High spindle speeds create high friction and heat, thus affecting the epoxy matrix. Optimal windows that are used to prevent thermal degradation are similar to the selected rotational speeds, as previous biocomposite study has varied from 800 to 2400 rpm. ³³ Moreover, the chosen feed and speeds are deliberately high in order to meet the stringent requirements on industrial production. While numerous studies maintain highly conservative feed ranges to artificially suppress defect generation, such as 0.04 to 0.2 mm/rev ³⁴ or 0.025 to 0.2 mm/rev, ³⁵ this study tests limits up to 0.60 mm/rev. Utilizing elevated feed rates, comparable to aggressive studies reaching 0.4 mm/rev, ³⁶ is essential to simulate demanding, high-throughput manufacturing conditions and establish the true operational boundaries of the Mg(OH)₂-reinforced system.

Response variables and measurement techniques

Drilling performance and the quality of a hole were assessed by three response variables that were considered critical: Delamination Factor (DF), Surface Roughness (SR), and Circularity Error (CE). These responses were selected because they have a direct impact on structural integrity, dimensional accuracy, and service performance of mechanically fastened composite components. While in-situ dynamometer measurements of cutting forces provide valuable real-time kinematic data, the ultimate viability of a drilled composite component in structural assemblies is dictated entirely by its post-machining dimensional and surface integrity. In aerospace and automotive quality assurance, components are accepted or rejected based on the presence of stress-concentrating defects that compromise mechanical fastening. Thus, instead of cutting forces considered time-dependent, the clear intent of this work is to quantify and optimize the physical manifestations of machining damage. As a result, the following three highly critical post-machining quality metrics were deemed as the primary response variables.

Delamination factor (DF)

As there is no universally accepted ISO standard to assess delamination in composites due to drilling, this study strictly followed the well-known and accepted formulation by Chen (1997). ³⁷ It is defined as the ratio of the maximal damaged diameter to the nominal drill diameter, as expressed in equation (3).

D F = D max D n o m

(3)

where D max represents the maximum diameter of the delaminated region and D n o m is the nominal drill diameter (8 mm). A high-resolution digital camera was used to take pictures of the entry and exit surfaces. D max was determined using image analysis software (ImageJ). Damage at the hole entry/exit was carefully observed to assess problems pertaining to drilling in detail. The main type of failure at the entry side was peel-up delamination, which was caused by the initial contact of the drill, flute engagement forces, and peeling forces. Exit side damage, on the other hand, consisted of push-out delamination, which occurred when the drill had pushed out of the laminate, overcoming the interlaminar strength of the uncut composite due to the axial thrust force. Maximum damage diameter ( D max ) at both entry/exit points was measured through optical imaging process software, and the greatest D max value was used to calculate DF of each hole. The measurement uncertainty of DF was estimated to be less than ±0.005, and this value was determined by the digital imaging resolution and the software pixel calibration.

Experimental procedure and data collection

All the drilling experiments were performed on the vertical machining center (LuxMill- SDS2MS) under dry cutting conditions in order to avoid the moisture-induced fiber swelling and matrix softening effects, which are known to cause changes in the machining behavior in natural fiber composites and introduce an uncontrolled variable. The composite laminates were rigidly clamped so as to have minimal vibration and repeatable boundary conditions. For each experimental run placed in the specifications of the FCCCD, a new hole was drilled to avoid effects from the accumulation of tool wear. Upon completion of the drilling process, the drill holes underwent cleaning processes with compressed air, and the results of DF, SR, and CE measurements were made. The full design matrix of the experiment and the related response values are shown in Table 2. The overall experimental uncertainty was carefully estimated to ensure the reliability of the acquired data. The pure experimental error, which is derived from the center-point replications of the FCCCD, is the mathematical expression of purely stochastic variation of the drilling process and material uncertainty as well as instrumental measurement uncertainty. The mean square pure errors were very small for all the responses, which indicates that the experimental setup is very stable. Thus, the variations in hole quality observed in the experiment cannot be attributed to random experimental errors but are due to the deterministic influence of the drilling parameters.

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Table 2.

FCCCD experimental matrix and measured responses (DF, SR, and CE).

Std	Run	A: SS (rpm)	B: FR (mm/rev)	C: TM	Delamination factor (DF)	Surface roughness (SR) - µm	Circularity error (CE) - mm
11	1	1000	0.2	M35	1.142	3.854	0.065
7	2	2000	0.2	HSS	1.215	4.102	0.105
3	3	1000	0.6	HSS	1.524	9.251	0.138
19	4	2000	0.4	M35	1.282	5.923	0.112
5	5	1000	0.4	HSS	1.356	6.855	0.095
12	6	3000	0.2	M35	1.187	3.452	0.145
18	7	2000	0.6	M35	1.589	7.804	0.135
4	8	3000	0.6	HSS	1.423	8.156	0.210
25	9	1000	0.4	M42	1.224	5.153	0.058
2	10	3000	0.2	HSS	1.256	3.958	0.168
21	11	1000	0.2	M42	1.115	3.205	0.045
15	12	1000	0.4	M35	1.294	6.108	0.078
10	13	2000	0.4	HSS	1.385	6.452	0.145
20	14	2000	0.4	M35	1.279	5.886	0.115
6	15	3000	0.4	HSS	1.412	5.904	0.142
9	16	2000	0.4	HSS	1.391	6.521	0.195
13	17	1000	0.6	M35	1.456	8.452	0.110
28	18	2000	0.6	M42	1.365	6.954	0.105
8	19	2000	0.6	HSS	1.552	8.853	0.155
16	20	3000	0.4	M35	1.314	5.456	0.158
24	21	3000	0.6	M42	1.415	6.558	0.175
30	22	2000	0.4	M42	1.242	5.253	0.088
1	23	1000	0.2	HSS	1.193	4.552	0.082
29	24	2000	0.4	M42	1.238	5.281	0.090
23	25	1000	0.6	M42	1.395	7.554	0.085
17	26	2000	0.2	M35	1.162	3.654	0.092
14	27	3000	0.6	M35	1.468	7.405	0.185
27	28	2000	0.2	M42	1.135	2.854	0.062
22	29	3000	0.2	M42	1.152	3.056	0.125
26	30	3000	0.4	M42	1.264	4.852	0.148

In addition to the quantitative measurements, mechanisms by which drilling-induced damage occurs were examined by means of a ZEISS Scanning Electron Microscope (SEM) equipped with Energy-Dispersive X-ray Spectroscopy (EDS). The specimens that were subjected to drilling were sectioned perpendicularly to the axis of the drill in order to facilitate an examination of the surface damage.

Statistical modeling and optimization methodology

To interpret the experimental results systematically and find the optimum drilling conditions of the Flax/Kenaf/Mg(OH)₂ hybrid composites, a statistical model and multi-response optimization framework were used. This framework was a mixture of RSM, regression analysis, analysis of variance (ANOVA), and optimization of a desirability function. The polynomial regression models of second order were derived for each of the response variables (DF, SR, CE) based on the FCCCD experimental data (Table 2). The general form of the model is given in equation (4). ⁴⁰

Y = β 0 + ∑ i = 1 k β i X i + ∑ i = 1 k β i i X i 2 + ∑ i = 1 k − 1 ∑ j = i + 1 k β i j X i X j + ϵ

(4)

The categorical variable TM was numerically encoded (HSS = 1, M35 = 2, M42 = 3) for regression purposes. Model adequacy was checked by R², adjusted R², and lack-of-fit using ANOVA (t-test at 95% confidence level), indicating that the model is statistically significant. The significance of individual terms and interactions in the regression models was determined by the ANOVA procedure, which was used to determine which terms in the models had p-values less than 0.05; thus, they were considered statistically significant.

Multi-response optimization

Given the simultaneous objective of minimizing DF, SR, and CE, a desirability-based optimization approach was adopted. Individual desirability functions d i for individual responses were defined in equation (5). ⁴¹

d i = { 1 i f Y i ≤ Y min ( Y max − Y i Y max − Y min ) r i f Y min < Y i < Y max 0 i f Y i ≥ Y max

(5)

where Y min and Y max represent the lower and upper acceptable limits for the response, and r is the weight exponent ( r = 1 for linear desirability). The overall composite desirability D was then computed as the geometrical mean of the individual desirabilities (equation (6)). ⁴²

D = ( d D F · d S R · d C E ) 1 3

(6)

Optimization was carried out with Design-Expert 13 software searching for the combination of SS, FR, and TM required to maximize D to minimize all three responses simultaneously. Contour plots and three-dimensional surface plots were derived for visualization of the effects of the interactions of the input parameters on the response and for identification of feasible optimal regions. This systematic approach of modelling and optimizing provides a scientific approach to ensure that all important response characteristics are considered to provide a scientifically robust basis for drilling process improvement in hybrid natural fiber composites.

Machine learning modeling strategy

In order to further develop the statistical modelling approach based on RSM and to account for potential nonlinear relationships existing in the drilling of composites with hybrid natural fibers, the ML-based modelling framework, which uses ANN, has been implemented. The ANN model was developed to predict three machining quality responses, namely DF, SR, and CE, as functions of the drilling input parameters. The main objective of the increment of ANN modelling was to benchmark the predictive ability of ANN against RSM and the suitability of ANN for modelling complex interactions and non-linear effects that are seen in the composite drilling process. The experimental data set consisted of 30 runs of the FCCCD (Table 2) with three input parameters and three output responses. The ANN input-output relationship can be given by equation (7).

{ S S , F R , T M } → { D F , S R , C E }

(7)

The categorical parameter (TM) was numerically encoded in terms of an ordinal scale (HSS = 1, M35 = 2, M42 = 3) to enable the ANN process. This encoding reflects the monotonic increase in cobalt content, hot hardness, and wear resistance, which are the main material properties affecting the machining performance, thereby providing a numerically meaningful representation of the material properties for the network in order to provide a physical meaning for the numerical representation. Prior to network training, all input and output variables were normalized within the range [0, 1] with the min-max scaling technique in order to avoid numerical dominance of any variable and also to achieve a higher stability of convergence (equation (8)). ⁴³

X n o r m = X − X min X max − X min

(8)

ANN architecture and network configuration

A Multilayer Perceptron (MLP) architecture using a feed-forward back-propagation structure was used due to its proven effectiveness in modelling non-linear machining processes. The finalized network topology was 3-10-3, which consisted of the following: input layer: 3 neurons, corresponding to SS, FR, and TM; hidden layer: 10 neurons; and an output layer: 3 neurons, corresponding to DF, SR, and CE. The hidden layer used a tangent sigmoid (tansig) activation function to capture nonlinearities, and the output layer used a linear (purelin) activation function to predict the continuous response values (Equations (9) and (10)):

f h i d d e n ( x ) = 2 1 + e − 2 x − 1

(9)

f o u t p u t ( x ) = x

(10)

The selected number of hidden neurons was obtained by iterative trial and error (so as to find a balance between getting accurate predictions and avoiding overfitting).

Training algorithm and data partitioning

Given the small size of the dataset, the training method used was the Bayesian Regularization backpropagation algorithm (trainbr). This algorithm composes the standard mean squared error objective function by adding a weight penalty term to the objective function to enhance the generalization performance without the need for a separate validation dataset (equation (11)). ⁴⁴

F = α E d + β E w

(11)

where E d is the sum of squared errors, E w is the sum of squared network weights, and α and β are adaptive regularization parameters. The dataset was randomly split into training and testing data with stratified random sampling, as 85% and 15% of the data are used for training and testing, respectively. This ensured that the testing subset had at least one representative data point from each tool material category (HSS, M35, M42) and maintained the distribution of the categorical variable so as to allow a fair evaluation of the generalization of the model for all tool types.

Performance evaluation criteria

The predictive accuracy of the ANN model was evaluated using statistical performance indices commonly adopted in machining studies:

Mean Squared Error (MSE):

M S E = 1 n ∑ i = 1 n ( Y i − Y i ^ ) 2

(12)

Regression Coefficient (R)

R = ∑ i = 1 n ( Y i − Y ¯ ) ( Y i ^ − Y ^ ¯ ) ∑ i = 1 n ( Y i − Y ¯ ) 2 ∑ i = 1 n ( Y i ^ − Y ^ ¯ ) 2

(13)

where Y i and Y i ^ are experimental and predicted values, respectively. ⁴⁵

High R-values (close to unity) and low MSE values indicated strong correlation and high predictive capability of the ANN model for DF, SR, and CE.

Overall trends in experimental responses

The overall machining performance of the hybrid composite was first investigated based on an examination of the global distribution and the variation of three response variables by the full FCCCD experimental matrix, Table 2. A statistical summary of the experimental responses is supported in Table 3, which provides insight into the sensitivity of the quality of holes to the selected drilling parameters.

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Table 3.

Summary statistics of experimental response data.

Response	Unit	Minimum	Maximum	Mean	Std. Dev.	Ratio (Max/Min)
DF	—	1.115	1.589	1.31	0.13	1.43
SR	µm	2.854	9.251	5.78	1.80	3.24
CE	mm	0.045	0.210	0.12	0.04	4.67

Among the three responses, SR showed the largest band (ranging from a minimum of 2.854 µm in Run 28 to a maximum of 9.251 µm in Run 3, as detailed in Table 2) and the highest standard deviation, which means that the quality of the hole wall surface is very sensitive to changes in drilling conditions. This trend could be attributed to the high effect of cutting kinematics and fiber–matrix interactions on the material removal mechanisms for hybrid NFRPs. The wide SR dispersion implies that the improper choice of parameters can lead to degradation of the surface integrity with rapid fiber pullout, smearing of the matrix, and microfracture. CE varied moderately, spanning from 0.045 mm (Run 11) to 0.210 mm (Run 8); the effect of tool rigidity, dynamic stability, and thrust-related deflection during drilling appears to have had an important influence. While all trials had CE within acceptable limits, some high values (for example, 0.210 mm in Run 8) were recorded under the more aggressive cutting setups, and this result is indicative of the tendency of the hybrid laminate to recover from the effects of the cut and create ovality. By contrast, DF exhibited relatively low variability, ranging from 1.115 (Run 11) to 1.589 (Run 7), and was near the mean value throughout. From the results, the behavior can be interpreted as a combined influence of a force of thrust, interlaminar strength, and tool geometry on delamination in the composite system studied rather than any one of them. However, the highest DF values obtained (such as 1.589 in Run 7) are due to insufficient control of the drilling and are still associated with significant entry/exit damage.

The ratio between the largest and the smallest value of the ratio obtained for all three responses was less than the critical value of the ratio (5.0) usually reported in literature when the degree of heteroscedasticity is severe; thus, it is concluded that the experimental data can be considered statistically adequate for the regression analysis and with no necessary transformation required. This stability is helpful to increase the reliability of the later RSM and ANN analysis. Finally, the overall experimental tendencies indicate that the hole surface integrity (SR and CE) is more sensitive than delamination to the processing parameters, demonstrating the applicability of multi-response optimization. These observations go to form a solid foundation for the detailed parametric and interaction effect analyses in the below subsections.

Statistical analysis and modeling of delamination factor (DF)

The experimental outcome of the DF was analyzed by RSM to explore the impact of the drilling parameters on the composite damage. A quadratic polynomial model was developed to select the significant relation between the input parameters and DF, and it was statistically tested by using ANOVA.

The results of the ANOVA for the model (DF quadratic) are given in Table 4 with the selected level of confidence (α = 0.05). The model has a high F-value of 28.69 and p < 0.0001, indicating statistical significance. The most significant (p < 0.0001) among input parameters were Feed Rate (B) and Tool Material (C), with the highest F-value indicating that these parameters affect the most variability. Spindle speed (A), interaction terms (AB, AC, BC), and quadratic terms (A², B²) were not statistically significant but were retained in the model hierarchy for accurate response surface modeling. It is observed that the p-value, which resulted from the Lack of Fit test, is statistically significant (p = 0.0006). In ANOVA, the Lack of Fit F-statistic is calculated as the ratio of the Mean Square of Lack of Fit to the Mean Square of Pure Error. The center-point replications exhibited very high repeatability with a Pure Error Mean Square of 0.0000 in this experimental design. This denominator is close to zero, which mathematically inflates the Lack of Fit F-value. As shown in well-established statistical design principles, if pure error is extraordinarily low, then the Lack of Fit test can be hyper-sensitive, that is, can show significance when there are good models. So, it is better judged from the physical appropriateness of the model on the basis of its predictive metrics. The model had an adequate precision (signal to noise ratio) of 17.818, comprising much more than the desirable value of 4.0, a high coefficient of determination (R² = 0.9460), and an adjusted R² of 0.9131. These statistics clearly indicate that the quadratic model accurately represents the main physics of delamination and is very useful in traversing the design space. These statistics confirm the reliability of using the model to represent the impact of drilling parameters on DF.

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Table 4.

ANOVA for DF quadratic model.

Source	Sum of squares	df	Mean square	F-value	p-value	Significance
Model	0.4660	11	0.0424	28.69	<0.0001	Significant
A - Spindle speed	0.0020	1	0.0020	1.39	0.2543	Not significant
B - Feed rate	0.3843	1	0.3843	260.25	<0.0001	Significant
C - Tool material	0.0677	2	0.0338	22.91	<0.0001	Significant
AB	0.0038	1	0.0038	2.58	0.1253	Not significant
AC	0.0006	2	0.0003	0.1904	0.8283	Not significant
BC	0.0056	2	0.0028	1.90	0.1789	Not significant
A2	0.0009	1	0.0009	0.6166	0.4425	Not significant
B2	0.0014	1	0.0014	0.9643	0.3391	Not significant
Residual	0.0266	18	0.0015
Lack of fit	0.0265	15	0.0018	174.08	0.0006	Significant
Pure error	0.0000	3	0.0000
Cor total	0.4925	29

The relationship between DF and the drilling parameters is given by equation (14).

1.3125 + ( 0.0107 × A ) + ( 0.1461 × B ) + ( 0.0565 × C [ 1 ] ) + ( 0.0031 × C [ 2 ] ) DF = − ( 0.0178 × AB ) − ( 0.0077 × AC [ 1 ] ) + ( 0.0022 × AC [ 2 ] ) − ( 0.0069 × BC [ 1 ] ) + ( 0.0242 × BC [ 2 ] ) − ( 0.0114 × A 2 ) + ( 0.0143 × B 2 )

(14)

where A and B are the spindle speed and feed rate coded, respectively, and C1 and C2 are dummy variables representing the material of the tool: C1 = 1 for M35 and 0 otherwise; C2 = 1 for M42 and 0 otherwise; where HSS is the reference (C¹ = 0, C² = 0). Positive coefficients are direct relationships with DF, and the negative coefficients are inverse effects. The positive coefficient is the dominant one for feed rate (+0.1461) and validates its predominance in influencing delamination. Diagnostic plots (Figure 3) were used for the validation of the regression model. The normal probability plot of the residuals (Figure 3(a)) shows that the residuals are most closely fitted to a straight line that supports the assumptions of normality and reliability for the results of the application of the global regression model by the analysis of variance. The predicted versus actual values plot (Figure 3(b)) provides a good clustering along the 45° line, which implies a good agreement between experimental and predicted values for DF, which is in accordance with the high R².OPEN IN VIEWER

The predominant influences of the drilling parameters on DF are shown in Figure 4. Spindle speed (Figure 4(a)) is relatively irrelevant, consistent with its statistical insignificance (p = 0.2543). Feed rate (Figure 4(b)) shows a steep positive slope, which means that the higher the rate of feed, the higher the thrust forces and the more delamination occurs. Tool material (Figure 4(c)) has a great impact on the DF, ⁴⁷ where HSS produces the highest delamination, followed by M35 and M42, which is the lowest due to its superior hardness and wear resistance.OPEN IN VIEWER

Response surface and contour plots (Figure 5) of spindle speed and feed rate are showing the interactive effects on DF of tool materials. Feed rate dominates the response, where DF increases the direction of influence that shows primarily along its axis, while spindle speed has a minute effect. HSS shows higher surfaces, which are correlated with high DF, whereas M42 has the lowest surfaces, showing the highest delamination resistance. The optimum region for minimal DF occurs at the lowest feed rate (0.2 mm/rev) using M42 and is nearly independent of the spindle speed. This low delamination is ascribed to strong fiber-matrix interfacial bonding reformed as a result of the formation of hydrogen bonds among natural fibers and Mg(OH)₂ filler supported by FTIR spectroscopy. ¹³ Feed rate is the most important factor, which affects delamination, and by decreasing feed rate, the effect of DF is minimized. Tool material is the second most important factor, as M42 delivers an excellent hole quality. Spindle speed has an insignificant effect within the range tested. Overall, the developed quadratic model is statistically robust, accurately predicts DF, and well captures the relationship between the drilling parameters and the delamination of the Flax/Kenaf/Mg(OH)₂ hybrid composite.OPEN IN VIEWER

To compare these results with other published studies, the best performance obtained in this study (DF = 1.115 at 0.2 mm/rev using the M42 tool) is better than the standard natural fiber composites, which are often quoted for a DF value exceeding 1.30 to 1.50 at the same and similar aggressive feed rates.^17,18 From a phenomenological perspective, as visually captured by the steep positive slope in the main effects plot (Figure 4(b)), the increase in DF at elevated feed rates (0.6 mm/rev) is physically governed by thrust-driven cutting kinematics. Because real-time thrust force is directly proportional to the feed rate, increasing the feed proportionately thickens the uncut chip, thereby generating excessive, concentrated axial thrust forces ahead of the drill chisel edge. When this concentrated thrust force causes the local stress intensity to exceed the interlaminar fracture toughness (Mode I) of the composite, the uncut bottom plies succumb to push-out delamination. The ability of this specific Flax/Kenaf/Mg(OH)₂ system to maintain a relatively low DF, even at higher feeds, is attributed to the mineral filler reinforcing the epoxy matrix, thereby increasing the threshold energy required for crack propagation.

Statistical analysis and modeling of surface roughness (SR)

The SR of drilled holes in terms of the arithmetic average deviation (Ra) was systematically studied to determine the importance of drilling parameters on the quality of machining on the surface of the hybrid composite. A quadratic response surface model was used to describe main effects and interactions between the factors Spindle Speed (SS, A), Feed Rate (FR, B), and Tool Material (TM, C).

The ANOVA for the quadratic model of the SR is shown in Table 5. The model is quite significant with an F-value of 568.62 (p < 0.0001), which shows that the selected input factors have a considerable effect on SR. Feed rate dominates the study and explains about 86.5% of the total variance, followed by spindle speed and tool material. All of the main effects and two-factor interactions (AB, AC, BC) are statistically significant, while the squared terms (A², B²) are trivial over the investigated range. While the Lack of Fit is statistically significant (p = 0.0223), this is a mathematical artifact resulting from the extremely low variance in the center-point replicates, which generated a near-zero Pure Error Mean Square of 0.0012. This fractional denominator artificially ‘boosts’ the Lack of Fit F-statistic. An excellent goodness-of-fit of the quadratic model indicates its true physical ability in capturing the mechanisms of surface generation. The model accounts for 99.71% of the total variance (R² = 0.9971); has a predicted R² of 0.9921, which is an extremely strong ability to predict new observations; and scores a very high adequate precision score of 81.73. Thus, the RSM model is a good representation of the behavior of surface roughness obtained in the evaluated cutting parameters, which means a high level of accuracy. The quadratic regression equation in coded variables is given in equation (15).

5.81 − ( 0.3437 × A ) + ( 2.13 × B ) + ( 0.6831 × C [ 1 ] ) + ( 0.0221 × C [ 2 ] ) SR = − ( 0.1661 × AB ) − ( 0.0963 × AC [ 1 ] ) − ( 0.0064 × AC [ 2 ] ) + ( 0.1469 × BC [ 1 ] ) − ( 0.0109 × BC [ 2 ] ) − ( 0.0224 × A 2 ) − ( 0.0403 × B 2 )

(15)

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Table 5.

ANOVA for SR quadratic model.

Source	Sum of squares	df	Mean square	F-value	p-value	Significance
Model	93.97	11	8.54	568.62	<0.0001	Significant
A - Spindle speed	2.13	1	2.13	141.54	<0.0001	Significant
B - Feed rate	81.49	1	81.49	5424.11	<0.0001	Significant
C - Tool material	9.65	2	4.82	321.00	<0.0001	Significant
AB	0.3310	1	0.3310	22.03	0.0002	Significant
AC	0.1192	2	0.0596	3.97	0.0374	Significant
BC	0.2411	2	0.1205	8.02	0.0032	Significant
A2	0.0035	1	0.0035	0.2344	0.6341	Not significant
B2	0.0113	1	0.0113	0.7552	0.3963	Not significant
Residual	0.2704	18	0.0150
Lack of fit	0.2670	15	0.0178	15.45	0.0223	Significant
Pure error	0.0035	3	0.0012
Cor total	94.25	29

In this form, C¹ and C² are dummy variables: C¹ = 1 for material M35 and C² = 1 for material M42 and C¹ = 0 and C² = 0 for reference HSS. Positive coefficients show that there is a positive association with SR, and negative coefficients show that there is an inverse association with SR. The rates at which these variables affect the response are: In order of the factors, feed rate is the most significant, spindle speed is second, and tool material is third, and there are significant interactions that also make meaningful contributions to the response. ⁴⁸

Diagnostic plots (Figure 6) give evidence of the validity of the model. The normal probability plot of the residuals (Figure 6(a)) is fairly close to the reference diagonal, so the assumption of normality is fulfilled. The predicted versus actual plot (Figure 6(b)) follows the 45° line with high fidelity; that is, there is very low deviation between experimental and predicted values of SR, and the model has good predictive ability.OPEN IN VIEWER

Figure 7 presents the major impacts of the drilling parameters on SR. Spindle speed (Figure 7(a)) shows a slightly negative slope, indicating that surface finish is slightly improved with an increase in spindle speed. Feed rate (Figure 7(b)) has a significant positive slope; the higher the feed rate, the greater SR becomes, probably because of fiber tearing and increased cutting forces. Tool material (Figure 7(c)) also influences SR, as HSS generally produces better finishes than M35 and M42. However, the influence of the tool material is influenced by interactions with the spindle speed and feed rate (AC, BC). Two-dimensional contour and three-dimensional response surface plots (Figure 8) show the combined effects of spindle speed (A) and feed rate (B) on SR for HSS, M35, and M42 tools. Feed rate is overriding the response with surfaces rising steeply along the B axis. Spindle speed does have a small moderating effect and will make SR slightly better at higher spindle speeds. Tool-specific interactions are important: the combination of M42 with a high spindle speed and low feed rate results in the smoothest surfaces and can be considered the optimal machining condition (blue zone).OPEN IN VIEWER

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Figure 8.

2D contour and 3D response surface plots for SR: HSS (a) & (b); M35 (c) & (d); M42 (e) & (f).

Feed rate becomes the most important aspect that controls the surface finish since the lower the feed rate, the fewer fibers will be damaged. Tool material greatly affects SR, especially when used in conjunction with the spinal speed and feed rate; M42 always gives the smoothest surfaces. Spindle speed has a secondary effect, which slightly improves SR at high revolutions per minute. Although the model quadratic equation attains a statistically significant lack of fit, it is still exhibiting very good prediction power (R² equal to 0.9971); hence, it is an excellent model to optimize the process parameters for getting good quality holes in hybrid composites. The strong contrast between the influences of feed rate and spindle speed on surface quality can be closely associated with the particular mechanism of chip formation inherent in the fabrication of heterogeneous biocomposites. The cutting edge mainly fractures the flax and kenaf fibers in a clean way when optimized and at a lesser feed rate (0.2 mm/rev). This creates powdery chips with no marks on the hole surface and a low hole surface roughness value. On the other hand, with the increase of the feed and uncut chip thickness, the cutting mechanism unfavourably shifts to tearing and ploughing. Intact segments of the stiff natural fibers are pulled out of the matrix rather than cleanly sheared, resulting in macro-cavities in the matrix.

In addition, the promotion of the heat created by the modulation of the spindle speed and rotation needs to be carefully monitored. Increases in spindle speeds may be expected to lead to increases in SR, but at the expense of increased localized frictional heating that will occur if the spindle spins too fast. This leads to an accumulation of heat at the tool-workpiece interface, resulting in thermal softening and viscoelastic smearing of the epoxy matrix on the machined surface because of the low thermal conductivity of the natural fibers.^49,50 This thermo-mechanical dynamic stands out as a major reason for the use of the M42 tool because the melting of the matrix and degradation of the surface due to blunt cutting edges and rubbing are avoided; this is because M42 has been developed as a highly thermally stable (red-hardness) material, which retains the sharpness of the cutting edges at higher temperatures without the occurrence of rubbing.

Statistical analysis and modeling of circularity error (CE)

CE is an important measurement of hole dimensional accuracy, as well as drill bit stability; in other words, it is a measurement of how tightly the drilled hole can be considered circular. Precise control of CE is important for high-precision machining and component assembly for the hybrid composites. A quadratic response surface model was provided using the data points of CE to understand the effects on the roundness of the hole.

Table 6 shows the results of the performed ANOVA, which shows that the overall model is highly significant (F = 13.24, p < 0.0001), confirming that the selected factors are reliable explanations of variability in CE. Of the main effects, spindle speed (A), the tool material, and feed rate (B) are the most influential (F = 83.61, p < 0.0001, F = 28.54, p < 0.0001, F = 15.84, p = 0.0001). All the interactions (AB, AC, BC) and square terms (A², B²) are statistically insignificant (p > 0.05), suggesting that the relationship between the inputs and CE is essentially linear. Model adequacy is supported by a non-significant lack of fit (p = 0.7084), a high coefficient of determination (R² = 0.89), and adequate precision (14.8728), indicating that there is a good signal to explore the design space. The fitted quadratic model in coded variables is expressed in equation (16).

0.1157 + ( 0.0389 × A ) + ( 0.0227 × B ) + ( 0.0231 × C [ 1 ] ) − ( 0.0009 × C [ 2 ] ) CE = − ( 0.0008 × AB ) − ( 0.0047 × AC [ 1 ] ) + ( 0.0003 × AC [ 2 ] ) + ( 0.0019 × BC [ 1 ] ) − ( 0.0014 × BC [ 2 ] ) + ( 0.0060 × A 2 ) + \ ( 0.0018 × B 2 )

(16)

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Table 6.

ANOVA for CE quadratic model.

Source	Sum of squares	df	Mean square	F-value	p-value	Significance
Model	0.0474	11	0.0043	13.24	<0.0001	Significant
A-Spindle speed (SS)	0.0272	1	0.0272	83.61	<0.0001	Significant
B-Feed rate (FR)	0.0093	1	0.0093	28.54	<0.0001	Significant
C-Tool material (TM)	0.0103	2	0.0052	15.84	0.0001	Significant
AB	6.750E-06	1	6.750E-06	0.0207	0.8871	Not significant
AC	0.0003	2	0.0001	0.3882	0.6838	Not significant
BC	0.0000	2	0.0000	0.0555	0.9462	Not significant
A2	0.0003	1	0.0003	0.7739	0.3906	Not significant
B2	0.0000	1	0.0000	0.0723	0.7911	Not significant
Residual	0.0059	18	0.0003	​	​	​
Lack of fit	0.0046	15	0.0003	0.7329	0.7084	Not significant
Pure error	0.0013	3	0.0004	​	​	​
Cor total	0.0533	29	​	​	​	​

As before, C¹ and C² are dummy variables denoting tool material (M35 and M42, respectively), with HSS being the reference (C¹ = 0, C² = 0). Positive values of coefficients for spindle speed and feed rate indicate that CE increases as the values of these variables increase. Tool material has a very small effect on CE (M35 positively and M42 negatively) due to the superior rigidity and wear resistance of the tool material. The very small values of the coefficients for interactions and quadratic terms show that CE behavior is mostly linear in the parameter range where it has been tested.

Model diagnostics are done to validate the regression assumptions (Figure 9). The normal probability plot of the residuals is almost on the diagonal line (Figure 9(a)), which indicates that normality holds. The predicted versus actual plot shows a good agreement between the experimental and predicted values (Figure 9(b)), which is consistent with the predictive power of the model (R² = 0.89). Figure 10 shows the influential impacts of the drilling parameters on CE, and it is possible to identify some evident trends. Spindle speed shows an interesting positive linear effect, where CE almost triples going from approx. 0.05 mm (1000 rpm) to 0.15 mm (3000 rpm). Feed rate also shows a positive linear relationship, showing that the higher the feed rate, the higher the CE due to deflection of the tool. Tool material has a secondary effect, with M42 yielding the lowest CE, followed by M35 and HSS. The very small curvature of the response confirms that the quadratic and interaction effects are small.OPEN IN VIEWER

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Figure 10.

Main effects of drilling parameters on CE: (a) Spindle speed; (b) Feed rate; (c) Tool material.

The 3D response surfaces show nearly planar behaviour, hence confirming the linear relationship between the CE and the two controlling process variables, spindle speed and feed rate (Figure 11). The spindle speed gradient is larger than the feed rate gradient, which is visual evidence of the spindle speed’s dominant effect. The tool-dependent surfaces further show that the M42 tool always reduces CE on the combination of parameters, thus showing superiority in achieving the dimensional accuracy. The best machining conditions are characterized by low spindle speed (1000 rpm) and low feed rate (0.2 mm/rev) while the M42 tool is used, which jointly minimizes the circularity deviations. Therefore, the spindle speed is the main factor affecting CE, and the lower the speed, the better the hole roundness. Feed rate plays a subordinate role, whose low value complements the effect of reduced spindle speed. Tool material has a supportive role, and M42 material is indispensable for the minimization of CE because of its rigidity and wear resistance. The CE response is linear for the most part, with spindle speed having a greater impact than feed rate. The obtained linear model is robust and reliable, while a simplified linear representation is able to predict the CE in hybrid-composite drilling operations very well.OPEN IN VIEWER

Multi-response optimization using desirability function

Given the competing nature of the three quality responses, namely, DF, SR, and CE, a multi-objective optimization approach was imperative. Increasing one response may lead to the degradation of another; thus, the desirability function approach was adopted to minimize DF, SR, and CE at the same time and find a single set of optimal machining parameters. In this method, each predicted response is converted into its own desirability value ranging from zero (completely undesirable) to one (fully desired). For this study the “Smaller-is-Better” criterion was used to do this across all three responses. The optimization objectives have been determined on the basis of the experimentally observed limits and practical quality requirements. DF was minimized with a target of no more than 1.115, SR with a target of 2.854 µm, and CE with a target of 0.045 mm. The factor constraints were controlled in the experimentally explored ranges of spindle speed between 1000 and 3000 rev/min, feed rate between 0.2 and 0.6 mm/rev, and tool material selected from HSS, M35, and M42. Results of the desirability-based optimization are summarized in Figure 12, which shows the individual factor desirability, response desirability, and also the composite desirability. The factor-desirability bars show that the optimized spindle speed, feed rate, and tool material all achieved a desirability of 1.000, indicating that the selected parameter levels all lie well within acceptable design limits. ⁵¹ Among the response desirability, both DF and CE got a perfect score of 1.000, which means that their predicted value met the absolute minimum targets. SR showed a desirability of 0.95855, indicating a slight trade-off needed to achieve a coincidence of optimal DF and CE. The composite desirability of 0.985988, as it is very close to unity, indicates a very successful optimization with negligible compromise among competing objectives.OPEN IN VIEWER

A more detailed representation of the optimal solution is given by the ramp function plot shown in Figure 13. The upper row of the above plot shows the optimum settings for the factors, which are associated with a spindle speed of 1295.81 rpm, a feed rate of 0.20 mm/rev, and the M42 tool material. The predicted responses at these settings are DF = 1.10862, SR = 3.11915 µm, and CE = 0.0449993 mm. The composite desirability value is 0.986, shown at the bottom of the plot, which is a confirmation that this solution is very close to a global optimum. The ramp plot gives us a clear idea that minimizing the feed rate and using a better tool material are important for the process, whereas the spindle speed is optimized up to a moderate value in order to compromise surface finish with dimensional accuracy. One of the findings of this optimization is the need to use the lowest feed rate (0.20 mm/rev) to get the best hole quality. Though this recommendation ensures that there are minimum defects, it has its own trade-off with the productivity of machining. This trade-off in industrial applications must be controlled where the time taken for drilling operations forms a part of the cost. The response and contour plots (Figures 5, 8, 11, and 14), constituting an imperative map for negotiation, are of critical importance. For example, assuming one can get away with some (but controlled) increase in delamination (e.g., DF < 1.25) for a given non-critical application, the models can be used to calculate that the expected feed rate can be increased to about 0.35 mm/rev for an M42 tool, significantly reducing the time to complete drilling while still preserving quality within a prescribed envelope. Thus, rather than a specific point, the models presented provide a quality-productivity Pareto front for the manufacturers to choose a component, depending on the specific requirements.OPEN IN VIEWER

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Figure 14.

Response surface 2D contour plots for composite and individual desirabilities: (a) Composite desirability; (b) Delamination factor; (c) Surface roughness; (d) Circularity error.

Further insight into the optimization landscape is gained from the contour plot (Figure 14). The composite desirability contour plot (Figure 14(a)) shows that the region of highest desirability (D >0.9) is concentrated at very low feed rates and low to moderate spindle speeds. Desirability drops sharply with increasing feed rate to create steep vertical gradients that provide visual proof that feed rate is the foremost controlling factor in the overall quality of the hole. This observation is strengthened by the individual response contours (Figure 14(b)–(d)). DF and SR contours are almost horizontal, indicating that feed rate has a significant influence, while CE contours have a diagonal structure, indicating that there is a combined effect between spindle speed and feed rate, with spindle speed having a slightly greater effect. The optimum point, which is marked on all the plots, is at the intersection of the areas for low response for all three quality metrics, proving that simultaneous optimization is possible at minimal feed rates combined with lower to moderate spindle speeds when using the M42 tool.

Validation of the optimal solution

The best predicted parameters obtained were excellent hole quality with DF = 1.10862, SR = 3.11915 µm, and CE = 0.045 mm. These predictions are very close to the best experimental run in the original design of experiments, therefore providing good preliminary validation for the optimization outcome. To further validate robustness, a separate validation experiment was performed, and the results are summarized in Table 7. The experimental mean values did not differ by more than 5% from the predictions for all responses, and all measurements were within the respective 95% confidence intervals, showing that there was no statistically significant difference between the predicted and the experimental values.

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Table 7.

validation experiment results versus model predictions.

Response	Predicted value	Experimental mean	Experimental std. Dev.	95% confidence interval	Percentage difference (%)
Delamination factor (DF)	1.10862	1.115	±0.008	1.107–1.123	+0.57%
Surface roughness (SR)	3.11915 µm	3.205 µm	±0.152	3.053–3.357	+2.75%
Circularity error (CE)	0.0449993 mm	0.047 mm	±0.003	0.044–0.050	+4.44%

A relative assessment between the closest experimental runs is given in Table 8. It may be seen from the above that the validation run gave the best performance overall if all three responses are considered simultaneously. The experimental composite desirability obtained by using validation data was near to approximately 0.977, which is quite close to the predicted value of 0.986, thus further confirming the reliability of this desirability-based optimization.

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Table 8.

Performance comparison with nearest experimental runs.

Run	SS (rpm)	FR (mm/rev)	TM	DF	SR (µm)	CE (mm)	Rank
Validation	1300	0.20	M42	1.115	3.205	0.047	1
Run 11	1000	0.20	M42	1.115	3.205	0.045	2
Run 28	2000	0.20	M42	1.135	2.854	0.062	3

While the best solution requires a low feed rate (0.20 mm/rev) for supreme quality, in industrial applications, a balance must be reached for good quality versus productivity. The validated models in this study allow the quantitative evaluation of this trade-off. For example, if a relatively small increase in delamination (e.g., DF < 1.20) is acceptable for a non-critical structural application, the RSM model indicates that the feed rate can be raised to around 0.35 mm/rev with an M42 tool operating at 2000 rpm. This adjustment could reduce drilling time by over 40% while maintaining all responses within a strict, predefined quality envelope. The desirability function analysis was able to identify a strong and practical process window for high-quality drilling of the hybrid composite. Feed rate was confirmed as the most crucial factor and must be minimized to get excellent performance in terms of all quality measures. Tool material plays an enabling key role with M42, making the best trade-off between delamination and better surface finish. and improved dimensional accuracy. Spindle speed is a fine-tuning parameter where moderate values are acceptable and are a compromise between surface quality and circularity. Overall, the high composite desirability value and good experimental validation prove that the proposed multi-response optimization strategy is effective, reliable, and suitable for industrial implementation.

Validation and predictive modeling using machine learning

To validate the statistical relationships achieved by the RSM and to be able to capture the complex nonlinear relationships inherent to the drilling of hybrid fiber composites, an Artificial Neural Network (ANN) model was developed. Although RSM offers explicit polynomial relationships that are useful to understand the impacts of significant factors and general trends in the process, its predictive power is limited in situations where the underlying physical mechanisms have a high level of non-linearity. In drilling operations involving natural fiber–reinforced composites, phenomena such as tool vibration, heterogeneous fiber distribution, and tool–matrix interaction often result in non-polynomial behavior. As it is a complex system, non-linear systems can be well modeled by ML techniques, such as ANN. With this, the ANN modeling method was used as parallel and autonomous prediction methods for DF, SR, and CE.

Network architecture and training algorithm

The development of the ANN model was done using the Neural Network Toolbox of the MATLAB simulation software R2025b. Because of its universal approximation capability, ⁵² the MLP (multi-layer perceptron) architecture (with the feed-forward backpropagation algorithm) was chosen. The adopted network topology is based on a 3-10-3 structure that is an input layer, a single hidden layer, and an output layer (see Figure 15(a)). The MATLAB implementation, displaying the signal flow from inputs to outputs to the responses, is illustrated in Figure 15(b). The input layer consists of three neurons corresponding to the drilling parameters: spindle speed (N), feed rate (f), and tool material. To facilitate numerical processing, the categorical variable tool material was encoded using an ordinal scale based on increasing hardness and cutting performance: High-Speed Steel (HSS = 1), M35 cobalt-alloyed steel (2), and M42 cobalt-alloyed steel (3). The hidden layer has 10 neurons (chosen optimally, exposing some preliminary trials between prediction accuracy and computational efficiency). A tangent sigmoid (tansig) activation function was used in the hidden layer to add non-linearity and allow the network to play dynamic and complex transitions, such as the evolution of tool wear and dynamic instability. The output layer consists of three neurons corresponding to DF, SR, and CE, which are linked using a linear transfer function (purelin) in order to produce continuous values of output prediction for the experimental range.OPEN IN VIEWER

Figure 15.

(a) Schematic diagram of the 3–10–3 Artificial neural network architecture; (b) MATLAB implementation showing signal flow from inputs to outputs.

Given the relatively small experimental data set of 30 runs, the Bayesian Regularization (trainbr) algorithm was chosen to be used in the training process. Unlike conventional backpropagation algorithms that require a separate validation set to prevent overfitting, in Bayesian Regularization, a combined objective function of the sum of squared errors and the sum of squared weights in the network is minimized. ⁵³ This way, it penalizes the excessive model complexity, and the network responses are smoother. As a result, the whole data set could be effectively used for learning without losing generalization. The full architecture of ANN and training parameters is summarized in Table 9.

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Table 9.

ANN architecture and training parameters.

Parameter	Setting/Value
Network type	Feed-forward backpropagation
Training function	Bayesian regularization (trainbr)
Input neurons	3 (Spindle speed, feed rate, tool material)
Hidden layer neurons	10
Output neurons	3 (Delamination, roughness, circularity)
Hidden layer activation function	Tangent sigmoid (tansig)
Output layer activation function	Linear (purelin)
Performance metric	Mean squared error (MSE)
Maximum epochs	1000
Training ratio	0.85 (85%)
Testing ratio	0.15 (15%) (5 samples)
Validation ratio	0.00 (not required for trainbr)

Training performance and convergence

The ANN training process was monitored by the evolution of Mean Squared Error (MSE), gradient magnitude, and regularization parameter (μ). Training converged in 258 epochs, and its total execution time was ∼2 s. As can be seen from the results reported in Table 10, the training stopped when the regularization parameter reached the highest value (5 × 10⁵) that it can reach in Bayesian Regularization, meaning a good compromise of the relative importance between fitting the data and smoothness of the model had been found.

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Table 10.

Final training state parameters of the ANN model.

Parameter	Value at stop (epoch 258)	Significance
Mean squared error (MSE)	1.47 × 10−4	Indicates an extremely high-precision fit between predicted and experimental outputs.
Gradient	1.28 × 10−4	Confirms convergence of the training process and that the solution has reached a local minimum.
Mu (μ)	5.00 × 1010	Represents maximum regularization in the Levenberg–Marquardt algorithm, ensuring numerical stability and robust generalization.
Effective parameters	46.3 (total: 73)	Approximately 37% of network connections were pruned, reducing model complexity and preventing overfitting.

The final MSE value of 1.47 × 10⁻⁴ confirms the extremely high precision of the trained network, while the low gradient value is an indication of convergence to a stable solution. Importantly, the effective number of parameters was reduced to 46.3 out of 73 total weights and biases, which means that approx. 37% of the network complexity was suppressed to avoid overfitting. The convergence behaviour of the ANN is shown in Figure 16 and illustrates the evolution of the MSE for training as well as the test dataset. A sharp reduction in MSE during the initial epochs proves that dominant relationships between the drilling parameters and the hole quality metrics are learned fast. Throughout the training process, the testing curve closely follows the training curve without divergence and thus shows a good performance of generalization.OPEN IN VIEWER

Figure 16.

Mean squared error (MSE) convergence curve for training and testing datasets.

Even more information about controlling the model complexity provides the training state variables in Figure 17. The stabilization of the gradient, the maximization of the regularization parameter, and the convergence of the effective number of parameters put together prove that Bayesian Regularization was able to create a robust and generalized ANN model despite the small dataset size. ⁵⁴ OPEN IN VIEWER

Figure 17.

Training state variables showing gradient, regularization parameter (μ), and effective number of parameters.

Regression analysis and model accuracy

The predictive ability of the ANN model was quantitatively compared with the linear regression model by comparing the experimental target value and ANN results. Regression plots of the training and test as well as combined data sets are presented in Figure 19. The function of learning the experimental data is valid because there is a perfect correlation coefficient (R = 1.0000). More important, a high generalization capability (correlation coefficient R = 0.9991) was obtained from the test set (samples that were not used for updating weights). The overall regression for all the 30 experimental runs was obtained, which was very good with a correlation coefficient value of R = 0.99985, and hence, the agreement between the predicted values and experimental values was near perfection. ⁵⁵ The regression parameters, such as the values of the slope and intercept, are summarized in Table 11. The values of the slope are approximately unity, and the values of the intercepts are negligibly small for all the datasets, which is an indication of an unbiased and accurate predictive model. This high degree of precision is important for the reliable optimization of a multi-response because it ensures that the predicted optimal drilling conditions relate to physically realizable outcomes rather than numerical artifacts.OPEN IN VIEWER

Figure 19.

Regression plots for ANN predictions vs experimental targets for (a) training, (b) test, and (c) all datasets.

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Table 11.

Statistical regression metrics for the ANN model.

Dataset	Samples	Correlation (R)	Slope	Intercept	Accuracy interpretation
Training	25	1.0000	1.00	3.2 × 10−5	Perfect fit to learned data.
Test	5	0.9991	1.00	−0.015	Excellent prediction of new data.
Overall	30	0.9999	1.00	−0.0026	Robust global model.

Comparative evaluation of RSM and ANN models

A comparative evaluation between the developed models of the RSM earlier and that of the ANN model was employed to represent the best predictive model for drilling hybrid Flax/Kenaf/Mg(OH)₂ composites. The comparison of the goodness-of-fit metrics is shown in Table 12. While both the approaches showed a good predictive ability, ANN showed favourable performance compared to RSM for all the response variables.

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Table 12.

Comparison of predictive performance between RSM and ANN models.

Response variable	RSM model (R2)	ANN model (R)	Predictive improvement
Delamination factor (DF)	0.9460	0.9999	Significant (+5.7%)
Surface roughness (SR)	0.9971	0.9999	Marginal (+0.3%)
Circularity error (CE)	0.8900	0.9999	Major (+12.3%)

For DF, the ANN showed a near-perfect prediction accuracy as compared to the RSM model, which is suggestive of the capability of ANN to capture subtle non-linearity effects that are not fully expressed by quadratic equations. In the case of SR, both the models showed exceptional performance, suggesting that surface roughness is mainly deterministic and is adequately modelled by second-order polynomials. The highest level of improvement was seen in CE, where the ANN outperformed the RSM to a great extent. This result confirms that CE is controlled by complex dynamic phenomena, such as drill wandering and vibration, which are nonlinearities in complex forms and scales and are better modelled by neural networks.

The good agreement between training and testing accuracies gives more evidence that the experimental dataset has low measurement noise and high reproducibility. Overall, the ANN model has a better predictive ability and robustness in responses driven by dynamic machining behavior, while RSM still provides useful aspects to interpret the process and analyze the significance of factors. These results should be compared with the current status in biocomposite machining to clearly demonstrate the advantages of this framework in prediction. Traditional modeling using stand-alone RSM or normal feed-forward ANNs (also trained by the standard Levenberg-Marquardt or gradient descent algorithms) normally shows correlation values (R) in the range of 0.92–0.97 for natural fiber composites.^17,21 The result of this study (R >0.9999) is considered excellent, which is based on the method used. The highly non-linear, high-frequency noise generated by the abrasive fillers Mg(OH)₂ with the machining dynamics often degrades the generalization capability of the standard algorithms in practice. On the other hand, the Bayesian regularization algorithm used here will actively optimize the objective function by penalizing excessively complex network weights. This ensures a highly robust, generalized model capable of mapping the complex physical tool-wear kinematics with near-perfect fidelity, substantially outperforming conventional statistical approaches in abrasive hybrid systems.

The comparative analysis provides a key methodological consideration, however: the choice between RSM and ANN needs to be informed by the objective of the modelling exercise. RSM is therefore invaluable in the process of interpretation and screening of factors involved in liquid resist deposition and provides transparent, physically interpretable equations (Equations (14)–(16)), which explicitly describe the contribution of feed rate, spindle speed, and tool material. Its power is in the identification of dominant trends and interaction effects, which are important for fundamental understanding and preliminary process design. On the other hand, the ANN model is a good predictor in predicting high fidelity for final process optimization and applications based on digital twins, especially in situations where the response has complex, non-stationary dynamics, as demonstrated by the better performance for CE. This dual functionality makes RSM appear to offer a synergy in the workflow, as it can be used for preliminary factor analysis, analyzing data so as to design a focused experimental region where data can then be used to train a strong ANN for the precise prediction and optimization of the result. In industrial implementations of the task where the accuracy of prediction is of paramount importance (and model interpretability is of secondary importance), the ANN model developed herein is a reliable, plug-and-play solution.

Morphological analysis of machined surfaces

In order to prove the statistical results and to understand the physical mechanisms controlling the quality of the holes, an elaborate morphological analysis was conducted based on SEM-EDS. Direct physical evidence to support the trends observed in the model (RSM and ANN) results is presented in this analysis. A comparative assessment of the microstructure of the as-fabricated composite and drilled surfaces produced under contrasting cutting conditions is shown in Figure 20.OPEN IN VIEWER

Implications of the hybrid system on machinability

Compared to an optimization of the basic parameters, the results of this investigation offer a key linkage from theory to practice for the implementation of advanced hybrid biocomposites in industry. The addition of the Mg(OH)₂ filler can strengthen mechanical integrity and flame resistance of the composite between laminates in theory. However, as demonstrated in the sections “Statistical Analysis and Modeling of Delamination Factor (DF)” and “Statistical Analysis and Modeling of Surface Roughness (SR)”, this microstructural design requires a fundamental change in the manufacturing process. The strong fiber-matrix bond inhibits ply-wise separation but is accompanied by strong non-linear and abrasive tool-wear mechanisms and significant viscoelastic thermal restrictions. As it relates to applied engineering and manufacturing, from a theoretical mechanics point of view, these have three important practical consequences. The physical validation of the superiority of the M42 tool (red-hardness and prevention of sticking of Mg(OH)₂ filler) indicates that the high tool cost is compensated by the longer tool life. When bending large quantities of vehicle or aerospace components, the use of M42 for all automotive and aerospace high-speed steels can significantly reduce spindle downtime, minimize the need for tool changes, and eliminate catastrophic part rejection caused by unexpected sudden edge blunting. The global optimum requires this highly conservative feed rate (0.20 mm/rev) to ensure a high quality of the undesired holes; however, in an industrial setting, a compromise must be made between this and throughput. The mathematical models developed herein can give a quantifiable Pareto front to the manufacturing engineers. Based on the validated model, if a structure assembly has a higher dimensional tolerance (such as DF < 1.25), the engineers can safely increase the feed rate (such as to 0.35 mm/rev) for this structure, safely reduce the machining cycle time by more than 40%, and maintain the successful joint reliability. The very high predictive capability of the Bayesian-regularized ANN (with R >0.999 for non-linear quantities such as the circularity error) has an extremely relevant industrial application. This high-fidelity ANN architecture, instead of being just a laboratory model, can be very easily integrated into the Industrial Internet of Things (IIoT) platform as a digital twin. Real-time spindle speed and feed rate data will be input to the network, and manufacturers will have the ability to actively predict hole quality after the machining process to provide dynamic process control and predictive maintenance prior to structural damage, which is irreversible in the composite panel. Finally, this work reiterates the key tenet of sustainable engineering: advanced materials need to be co-optimized not only for the service that they are required to provide but also for their scalable manufacturability.