Multi response optimization of machining parameters for an annealed Monel K 500 alloy in drilling using Machine learning techniques and ANN

Abstract

Manufacturing companies are focusing on continuous process development to thrive in today’s quality-conscious market. It is particularly relevant to investigate machining processes for advanced materials such as superalloys. Drilling is a major operation that is used in the majority of manufacturing processes. Hence, this research work is focused on investigating the drilling performance of the Monel K500. The output responses under consideration are metal removal rate (MRR), surface roughness, and tool wear. Various contemporary techniques were utilized in this work, namely machine learning methods, artificial neural networks, principal component analysis, and grey relation analysis using uncoated, coated, and HSS (high-speed steel) drills. After annealing, the softened material can be easily machined to increase the MRR and decrease tool wear and surface roughness. The experimental results show that, after annealing, the surface roughness values for HSS drills have been reduced by 23.86%, uncoated drills by 27.29%, and coated drills by 29.27%, respectively. Moreover, tool wear values for HSS drills decreased by 28.51%, uncoated drills by 34.7%, and coated drills by 33.71%, based on the relative error approach. MRR values for HSS drills increased by 20.51 %, uncoated drills by 23.08%, and coated drills by 23.5%, respectively. For PCA (principal component analysis), feed (47%), and for GRA (gray relation analysis), feed (40.1%) will be the significant parameter followed by speed, and both methods have identified the same experimental run values for optimization of cutting parameters. The theoretical values were predicted using machine learning methods, which utilized the Python language using the Google Colab and then validated with experimental values. The predicted values obtained by the decision tree are close to the measured values as compared to support vector regression and K-nearest neighbor based on relative error. The estimated values obtained by the ANN (artificial neural networks) approach, using Easy NN plus software, match well with the actual values, with a slight deviation.

Keywords

Monel K500 principal component analysis grey relation analysis with S/N ratio machine learning methods ANN

1 Introduction

Customers’ demands are changing day by day, and to keep fulfilling them, manufacturing companies are improving their capabilities. It is essential to select appropriate machining conditions to enhance the quality of the machined part and machining efficiency. They are focusing on utilizing advanced materials that possess unique properties, such as superalloys. Though these materials are difficult to machine and Monel K 500 is one such material [1]. It is a nonmagnetic material and can be further strengthened by cold work before precipitation hardening. It is extensively used in various technological industries, such as the medical, marine, aerospace, chemicals, the automobile sector, and manufacturing. The different parts that are manufactured are expandable rib cages, finger and toe replacement, fasteners, springs, chains, gas turbine engines, oil well drilling, pumps, impellers, and valve components, dental implants, marine bearings, airframes, surgical blades, and vessels [2]. Due to its advanced properties, important factors may be considered while machining this material, namely machine tool capacity, the rigidity of the tool and workpiece, and sharpening of the tools. Drilling operations necessitate cutting different contours with different sizes of drills, but drill wear, the temperature in the cutting zone, and hole quality are all critical factors [3]. The hardness of the drill tool material should be strong as compared to the work material, and the use of lubricants will be an important factor. Many industries are using artificial intelligence techniques to enable smart automated manufacturing systems. Therefore, to satisfy manufacturing requirements in industry 4.0, expert systems, machine learning-based prediction models, and optimum cutting parameters are fundamental requirements. However, there is a need to understand the machining of these alloys for different engineering applications. It is worth noting that certain Monel alloys are considered difficult to machine materials, implying that machining these materials is a difficult task [4, 5].

The heating process has been widely adopted in the last 50 years in petroleum and marine applications to obtain resistance to corrosion, high strength, and fracture toughness. As a result, temperature will be the most important factor to consider when machining this type of alloy, affecting cutting performance. To make softened material, the material can be heated externally before or during the cutting process to get better machining performance indicators. Resistance heating with gas burners, oven heating with electric arcs, and other methods such as induction, radiation, and laser assistance can all be used. A few researchers have proposed heating techniques for difficult to machine materials, namely plasma assisting cutting [6], heating by induction [7], hardening by flame [8, 9], laser heating [10], cryogenic machining [11], and the Al₃Cr₃ Sn alloy hot ultrasonic method [12]. Sun et al. [13] proposed a review of thermally enhanced machining processes focusing on laser and plasma theory for materials such as MMC (metal matrix composite) and ceramics. It includes temperature distribution, material-removing mechanisms, and tool wear. Sukumaran et al. [14] studied different heat treatment cycles ranging from temperatures of 625°C to 1025°C for the 625 alloy to obtain optimum mechanical properties. At room temperature, there will be a decrease in strength and hardness, and at heat treatment temperature, ductility will increase. Parida et al. [15] studied chip formation, tool life, and tool wear in hot turning, using flame heating at room and hot temperature conditions of 300°C–600°C. It is observed that there is a significant reduction in response parameters for all three nickel-based alloys under heating conditions.

Though Monel K500 is a vital material, there is not yet much research conducted, especially when it is annealed, creating a research gap. The primary goal of this work is to investigate the effect of machining conditions and temperature on response parameters and select optimal cutting conditions using PCA (principal component analysis) and GRA (grey relation analysis). The experimental results are compared at annealing and room temperature for three types of drills: HSS (High-speed steel), uncoated, and coated drills. Though a few researchers did some experimental investigations and modeling for the K 500 alloy, none of them utilized machine learning algorithms and an artificial neural network approach. According to the literature, most of the research work investigated the microstructure and mechanical properties of the Monel K 500 material. The novelty of this research work lies in the fact that, to the best of the authors’ knowledge, either none of the researchers or very few have studied the annealed super alloys machining comprehensively, which has tremendous potential in the aerospace, automobile, nuclear, chemical, and marine industries. Annealing is the technique of heating the workpiece before the actual cutting operation. As a result, the softened material can be easily machined to increase metal removal and decrease surface roughness and tool wear.

1.1 Literature review

Research work on drilling for coated and uncoated drills using a coolant and dry machining has been conducted for superalloys and other materials for investigating machining parameters by a few researchers. Kivak et al. [16] used drilling tests for Inconel 718 under wet, dry, and cryogenic conditions by carbide drills based on cutting factors to evaluate torque, thrust force, and cutting temperature. Thakur et al. [17] investigated the machinability of Incoloy 825 under various process conditions and evaluated response parameters such as coefficient of friction, chip type, and temperature. Swain et al. [18] conducted micro-drilling experiments to study holes’ tool life and surface quality using coated and uncoated micro drills of 0.8 mm for nickel-based superalloy Nimonic 80 A. Depending on different machining conditions, the coated micro drill performs better than the uncoated drills. Amini et al. [19] conducted an experimental analysis of turning for Monel K500 using ceramic tools with ordinary and wiper inserts under dry machining to study cutting temperature, surface roughness, and cutting force. Jayaganth et al. [20] proposed drilling experiments with HSS drill of 10 mm on a 5 mm thickness of plate SS 410 material to analyze surface roughness and tool wear with three cutting fluids: castor kerosene, and coconut oil.

Statistical optimization techniques have been used by a few researchers using GRA, PCA, and RSM (response surface methodology) for different materials in traditional and nontraditional cutting processes [21]. Tosun [22] presented GRA in drilling for reducing surface roughness and burr height based on process parameters, as well as analyzing optimal machining parameters for multi-performance features. Palanisamy et al. [23] developed two different models in milling, such as ANN (artificial neural network) and regression analysis based on the design of experiments for AISI 1020 steel for prediction of tool wear by a carbide cutter using six sigma software. Ranganathan et al. [24] suggested multi-response optimization by the Taguchi technique and GRA for stainless steel in hot turning based on cutting factors such as feed, workpiece temperature, and speed. The experimental results show that feed and speed are the dominant variables. Pramanik et al. [25] proposed fiber laser drilling process performance studies for Monel k-500 using input parameters such as trepanning speed, pulse frequency, power setting, duty cycle, and sawing angle with the help of RSM. Dewangana et al. [26] used optimum cutting factors for machining complex and critical shapes, namely surface roughness, crack density, and layer thickness in electro-discharge machining for surface integrity using PCA-based grey relation analysis. Caggianoa [27] developed monitoring of drill wear based on sensor technology made of two carbon fiber reinforced plastic laminates for predicting vibration signals, thrust force, and torque using ANN and PCA. Ezilarasan et al. [28] presented experimental work using ceramic tools in turning Nimonic C-263 to investigate the effects on surface integrity, micro hardness, residual stress, and mechanical properties. Prasanna et al. [29] suggested drilling experimental analysis using GRA and Taguchi’s design of carbide drills of 0.4 mm in Ti–6Al–4 V material to understand the significance of process parameters such as speed and air pressure on the quality of holes.

Machine learning methods have been adopted by some researchers for the theoretical prediction of response parameters for different materials. Pan Dong et al. [30] conducted experimental work and comprehensive analysis of optimization methods for underground mines for blasting parameters using a backpropagation neural network using Easy NN-plus software based on process parameters. Zong et al. [31] used various network architectures and activation functions to estimate surface roughness using carbide and diamond cutting tools. Kant et al. [32] developed an optimization model using a genetic algorithm and ANN in milling for the reduction of surface roughness for AISI 1060 steel. Abu-Mahfouz et al. [31] introduced support vector regression, K nearest neighbor, and types of decision trees for the prediction of surface roughness. Unune et al. [33] have suggested ANN and a central composite rotatable design in the grinding operation for analyzing MRR and surface roughness in EDM (electrical discharge machining) based on pulse current, wheel speed, and powder concentration for the Monel K-500. Mia et al. [34] presented two predictive methods based on RSM and SVR (support vector regression) for turning AISI 1060 steel for surface roughness estimation. Barrios et al. [35] carried out experimental work on glycol parts manufactured using 3 D printing with three models of a decision tree algorithm for analyzing surface roughness. Alsamhan et al. [36] proposed experimental work in sheet metal forming to estimate formation force by ANFIS, ANN, and a regression model using four cutting conditions, such as step size, the thickness of the sheet, and feed rate. Zacharia et al. [37] analyzed the influence of chatter occurrence during the machining of titanium alloys using a machine learning algorithm based on vibration signals from a decision tree, ANN, and support vector machines. Nicholas et al. [37] compared ANN models and machine learning methods to estimate surface roughness for copper materials. Hamed et al. [38] presented a new hybrid model using support vector regression and the K-nearest neighbor method. The model was used for general and local estimation of behaviors in pipeline corrosion measurements. Alharthi et al. [39] suggested different ANN models and traditional regression analysis for the AZ61 magnesium alloy to optimize surface roughness.

This paper is organized as follows: The materials and methods section is presented first after the introduction section. It includes work piece materials, their mechanical and physical properties, composition, schematic representation of experimentation, levels and controls, equipment used, and experimental data. Section 3 represents the methodology used, such as PCA, GRA, machine learning methods, and ANN. Finally, the paper concludes with results, discussions, conclusions, and future directions for further research.

2 Materials and methods

Experimental work was conducted as per the L9 orthogonal array for analyzing tool wear, surface roughness, and MRR for Monel K-500. The types of drills opted were uncoated, PVD TiAIN coated, and HSS drills of diameter 10 mm were selected, and the diameter of the workpiece was 70 mm. The thickness was maintained at 15 mm, on a CNC drilling machine, DMG 635 V Ecoline. For surface roughness, Surtronic 25, Taylor Hobson, was used. An optical microscope (1000 X magnification) for measuring tool wear. The MRR (material removal rate) was calculated using an electronic weighing balance with the actual weight divided by density and cutting time. The mechanical, physical properties, and composition of Monel K 500 are presented in Tables 1 2. The schematic representation of experimentation, control parameters, and the levels are shown in Fig. 1 and Table 3, respectively.

Table 1
Mechanical and Physical Properties

Density, g/cm³ 8.44

Melting Range °C 1315 - 1350

Poissions Ratio 0.32

Hardness Rockwell C 27

Elongation break 22 %

Yield strength MPa 655

Tensile strength MPa 1000

Reduction in area 40%

Density, g/cm³	8.44
Melting Range °C	1315 - 1350
Poissions Ratio	0.32
Hardness Rockwell C	27
Elongation break	22 %
Yield strength MPa	655
Tensile strength MPa	1000
Reduction in area	40%

Table 2

Composition of Monel K 500

Element %	S	C	Si	Mn	Ti
	0.011	0.18	0.50	1.4	0.35
	Fe	Cu	Al	Ni
	2.05	24	2.3	70

Fig. 1

Schematic representation of experimentation.

Table 3

Levels and Control Factors

Process factors	Level 1	Level 2	Level 3
Tool	HSS	uncoated	coated
Speed	60	80	100
Feed	0.15	0.20	0.25

The annealing process was carried out at a temperature of 900°C using a Nabertherm P330 Muffle furnace. The Monel-k 500 was put inside the furnace, and the temperature was raised up to 500°C within 20 minutes; the sample was kept at 500°C for 15 minutes and reached 900°C within 20 minutes, and was kept for 6 hours at 900°C. The cooling process was carried out at 100°C, decreasing every 1 hour. Figure 2 represents annealing temperature, Fig. 3 illustrates the experimental setup, and Fig. 4 indicates the workpiece, the microscope used to measure the hole’s dimensions, and various other resources utilized in this research work and measured data are shown in Table 4, respectively. The MRR for each experimental run was calculated using the following formula.

Fig. 2

Annealing process of Monel-K 500 up to 900°C.

Fig. 3

Experimental set up- CNC milling/drilling machine, DMG 635V Ecoline.

Fig. 4

(i) Work piece (ii) Electronic weighing balance (iii) Optical microscope (iv) Work piece after annealing (v) Furnace (vi) Taylor Hobson Surtronics for surface roughness measurement.

Table 4

Experimental Data

No	Tool	Speed	Feed	Ra-μm	Ra –A -μm	Absolute error -μm	Tw-mm	Tw –A mm	Absolute error mm	MRR m/min	MRR –A m/min	Absolute error m/min
1	HSS	60	0.15	2.19	1.66	0.53	0.195	0.141	0.054	22.46	27.01	4.56
2	HSS	80	0.20	2.26	1.70	0.56	0.202	0.150	0.052	39.89	48.19	8.3
3	HSS	100	0.25	2.38	1.84	0.54	0.218	0.148	0.07	62.40	75.17	12.75
4	Uncoated	60	0.2	2.32	1.72	0.6	0.207	0.140	0.067	29.98	37.12	7.15
5	Uncoated	80	0.25	2.45	1.78	0.67	0.221	0.145	0.076	49.87	61.09	11.22
6	Uncoated	100	0.15	2.58	1.84	0.74	0.236	0.140	0.096	37.46	46.05	8.59
7	Coated	60	0.25	2.02	1.40	0.62	0.183	0.122	0.061	37.55	47.17	9.62
8	Coated	80	0.15	1.92	1.36	0.56	0.178	0.120	0.058	29.93	37.21	7.28
9	Coated	100	0.20	1.85	1.31	0.54	0.180	0.116	0.064	49.92	60.18	10.26
Average						0.60			0.067			8.87

Ra A –Surface roughness annealing, Tw A –Tool wear annealing, MRR A –metal removal rate annealing.

Where, Wb-Weight before machining (gms), Wa-Weight after machining (gms), ρ= Density of the work piece material (gms), t = is the machining time (sec) $MRR = (W_{b} - W_{a}) / ρ x t_{cm} 3 / sec (a)$

3 Methodology

3.1 Principal component analysis

It converts multiple linked response data into different uncorrelated quality features, indicating the principal components [26, 27].

Step I: The arrangement of the actual multiple performance features in the cutting operation is shown by Equation (1). $A = (\begin{matrix} Z_{11} & Z_{12} & Z_{13} & \dots & Z_{1 k} \\ Z_{21} & Z_{22} & Z_{23} & \dots & Z_{2 k} \\ . & . & . & \dots & . \\ . & . & . & \dots & . \\ Z_{i 1} & Z_{i 2} & Z_{i 3} & \dots & Z_{ik} \end{matrix})$ (1)

Where i is trial number, k response number

Step II: Quality feature normalization was implemented in this step, and using Equations (2,3), Equations (2,3), the original sequence was normalized. $X_{i} (k) = \frac{max Z_{i} (k) - Z_{i} (k)}{max Z_{i} (k) - {minZ}_{i} (k)}$ (2)

Higher the better feature for MRR by Equation (3). $X_{i} (k) = \frac{Z_{i} (k) - {minZ}_{i} (k)}{max Z_{i} (k) - {minZ}_{i} (k)}$ (3)

Xi (k) is normalized data, min Zi (k) is smaller, and max Zi (k) larger value for k^th response using Equation (4) normalized array X will be obtained and output values of Step II are represented in Table 5.

Table 5

Normalization of Experiment Values

Exp. No.	Surface Roughness (μm)	Tool Wear (mm)	MRR (m/min)
1	0.374	0.000	1.000
2	0.200	0.633	0.609
3	0.896	0.933	0.375
4	0.113	0.417	0.316
5	0.000	0.833	0.141
6	1.000	0.850	0.609
7	0.487	0.617	0.000
8	0.661	1.000	0.375
9	0.800	0.567	0.141

$X = (\begin{matrix} X_{11} & X_{12} & X_{13} & \dots & X_{1 k} \\ X_{21} & X_{22} & X_{23} & \dots & X_{2 k} \\ . & . & . & \dots & . \\ . & . & . & \dots & . \\ X_{i 1} & X_{i 2} & X_{i 3} & \dots & X_{ik} \end{matrix})$ (4)

Step III: Based on the normalized data, variance-covariance matrix M will be obtained by the Equations (5, 6) respectively. $M = (\begin{matrix} N_{11} & N_{12} & N_{13} & \dots & N_{1 k} \\ N_{21} & N_{22} & N_{23} & \dots & N_{2 k} \\ . & . & . & \dots & . \\ . & . & . & \dots & . \\ N_{i 1} & N_{i 2} & {XN}_{i 3} & \dots & N_{ik} \end{matrix})$ (5) $N_{k, l} = \frac{Cov (X_{i} (k), X_{i} (l))}{\sqrt{Var (X_{i} (k)) * Var (X_{i} (l))}}$ (6)

Where l = 1, 2, 3.. k and Xi(l)) is covariance of sequences.

Step IV: Eigenvalues and eigenvectors were analyzed for the correlation efficient matrix and represented as λ_j and V_j; step III and step IV output values are represented in Table 6.

Table 6

Eigen values, Eigen Vectors for Analysis of Covariance Matrix

	Ψ₁	Ψ₂	Ψ₃
Eigen Vector	0.68147	0.63928	–0.35625
	0.63867	–0.28181	0.71602
	–0.35734	0.71547	0.60034
Eigen Value	0.1644	0.1162	0.0369
AP	0.51765	0.36603	0.11632
CAP	0.51765	0.88368	1

Step V: Principal components ψj was evaluated by Equation (7), and the eigenvector V_j and output values of step V are as represented in Table 7.

Table 7

Principal Component of Performance Characteristics

Exp. No	Ψ₁	Ψ₂	Ψ₃
1	–0.103	0.955	0.467
2	0.323	0.385	0.748
3	1.072	0.578	0.574
4	0.230	0.181	0.448
5	0.482	–0.134	0.681
6	1.007	0.836	0.618
7	0.726	0.138	0.268
8	0.955	0.409	0.706
9	0.857	0.452	0.205

$Ψ_{j} = V_{1 j} Q_{1} + V_{2 j} Q_{2} + \dots \dots \dots + V_{jj} Q_{j}$ (7)

Where, ψ₁ indicates the 1st principal component, ψ₂ represents the 2nd central part, and ψ_j represents the main component for variation of performance features, such as AP, as indicated by the cumulative accountability portion.

Step VI: CPC for each trial was estimated and their eigenvalues as represented in Equation (8). $CPC = \sum_{j = 1}^{k} {[{(Ψ_{j})}^{2}]}^{\frac{1}{2}}$ (8)

Corresponding S/N ratios were calculated for the obtained composite primary component (CPC) values by Equations (9, 10), respectively. The output values of step VI and the results of confirmatory experiments are represented in Table 8.

Table 8

Composite Primary Components (CPC) with S/N Ratio and Results of Confirmatory Experiments

Exp. No.	CPC, Ψ	S/n Ratio	Results of confirmatory experiments
1	1.067617	0.568309
2	0.901361	–0.90202
3	1.346819	2.586188
4	0.535261	–5.42869		Optimal Settings
5	0.845116	–1.46167		Prediction
6	1.447008	3.209416	Level of Parameters	A₂ B₃ C₁
7	0.785749	–2.09432	Value of Ψ	1.252
8	1.255934	1.979339	S/N Ratio	1.953
9	0.990394	–0.08384

$η_{LB} = - 10 log [\frac{1}{n} \sum_{1}^{n} Y_{ij}^{2}] (Lower - the - better)$ (9) $η_{HB} = - 10 log [\frac{1}{n} \sum_{1}^{n} 1 / Y_{ij}^{2}] (Higher - the - better)$ (10)

Where Y_ij is i^th trial for j^th test

Step VII: The optimal level of factors will be recognized using experiment numbers and actual factors for the maximum value of the CPC, Ψ. The highest value of (CPC, Ψ) is 1.447, which is the 6th experiment and the factors are A₂, B₃, C₁ as uncoated, 100 speed, and 0.15 feed respectively. The value of Ψ (predicted Y) is obtained by performing regression for the actual factors and the (CPC, Ψ) values. The value of Ψ is recognized by identifying the maximum (highest) value of predicted Y, which is 1.252. The result can be obtained from the “Predicted Y” column, as shown in Table 9.

Table 9

Regression

Expt. no	Predicted Y	Residuals	Standard residuals
1	0.834	0.233	1.125
2	1.067	–0.165	–0.797
3	1.299	0.047	0.229
4	0.787	–0.252	–1.213
5	1.019	–0.174	–0.840
6	1.252	0.195	0.939
7	0.740	0.046	0.222
8	0.972	0.284	1.368
9	1.205	–0.214	–1.033

Finally, the S/N ratio will be obtained for the highest predicted Y value. The s/n ratio was calculated depending on the higher-the-better trait by Equation 10, and the s/n ratio obtained was 1.953.

Step VIII: Optimum settings of cutting factors will be obtained. ANOVA for means on CPC data was carried out for major significant parameters based on the performance features, and the output values of step 8 are represented in Table 10. Results of ANOVA on S/N ratios and percentage contribution of parameters on CPC for means and S/N ratio as represented in Table 11 and Fig. 5.

Table 10

ANOVA of Means (CPC)

Factors	df	Sequence SS	Adj. SS	A. MS	f	p	% contributions
speed	2	0.04010	0.0421	0.0200	0.25	0.78	5.876
feed	2	0.32618	0.3462	0.1630	2.06	0.24	47.795
RE	4	0.31617	0.3362	0.0790			46.328
Total	8	0.68246					100

Table 11

ANOVA of S/N Ratios

Factors	df	Seq. SS	Adj. SS	Adj. MS	f	p	% contribution
Speed	2	5.927	5.819	2.963	0.47	0.654	10.263
Feed	2	26.752	26.359	13.376	2.13	0.234	46.325
Residual Error	4	25.070	25.270	6.268			43.412
Total	8	57.749					100

Fig. 5

Percentage contributions of factors of (i) s/n ratios and (ii) means.

Table of S/N ratio and means and main effect plots of S/N ratio and means are represented by Table 12 and Fig. 6, respectively.

Table 12

Table of S/N Ratios and Means

Level	Speed	Feed	Level	Speed	Feed
1	1.1053	0.7962	1	0.75082	–2.31823
2	0.9425	1.0008	2	–1.22698	–0.12812
3	1.0107	1.2614	3	–0.06628	1.90392
Delta	0.1628	0.4652	Delta	1.97780	4.22215
Rank	2	1	Rank	2	1

Fig. 6

Main effect plots for (i) means and (ii) S/N ratio.

The accountability proportion (AP) values of three principal components, like surface roughness (Ψ1 = 51.8), tool wear (Ψ2 = 36.6), and metal removal rate (Ψ3 = 11.6) are shown in Table 6 and portrayed in Figs. 7 8, respectively.

Fig. 7

Accountability proportion of (i) surface roughness vs tool wear and (ii) surface roughness vs MRR.

Fig. 8

Accountability proportion (AP) values of tool wear vs MRR.

3.2 Grey relational analysis

The grey relation coefficient will be obtained from theoretical responses and actual values depending on normalization by averaging the GRC (grey relation coefficient). The grades will be calculated depending on the responses. The value of GRG will indicate the performance of multiple responses, as this method may be utilized to obtain single response optimization with a higher GRG (grey relation grade) value. The optimum parametric combination will be determined, which will result in a higher grey relational grade [22 –24].

Step 1: S/N ratios

For surface roughness and tool wear, smaller the better feature, and for MRR, the higher the better feature. The respective columns show the negative value, and s/n ratio will be determined using Equation (11). $η = - 10 log [\frac{1}{n} \sum_{1}^{n} Y_{i}^{2}]$ (11)

The evaluation indicator is y_i value to i^th time and repeated trial will be n, the S/N ratios for MRR will be obtained by Equation (12). $η = - 10 log [\frac{1}{n} \sum_{1}^{n} 1 / Y_{i}^{2}]$ (12)

Step 2: Normalized S/N ratios

S/N ratio x_ij of í^th performance feature at j^th experiments represented by Equation (13). $x_{ij} = \frac{η_{ij} - \min_{j} η_{ij}}{{max}_{j} η_{ij} - \min_{j} η_{ij}}$ (13)

Where x_ij is data sequence, η_ij s/n ratio original sequence (where i = 1, 2, 3 . . . m, j = 1, 2, 3 . . . n)

Step 3: Deviation sequence (Δx_j) It can be calculated by Equation (14). $Δ x_{i} (k) = | x_{0} (k) - x_{i} (k) |$ (14)

Step 4: Grey relational coefficient The GRC ξ_ij for ξ^th performance features in the j^th trial is obtained by Equation (15). $ξ_{ij} = \frac{\min_{j} \min_{j} | x_{i}^{0} - x_{ij} | + ζ \max_{i} \max_{j} | x_{i}^{0} - x_{ij} |}{| x_{i}^{0} - x_{ij} | + ζ \max_{i} \max_{j} | x_{i}^{0} - x_{ij} |}$ (15)

Where x_i⁰ is normalized s/n ratios of ’i^th performance features and ζ, distinguish coefficient from 0≤ζ≤1.

Step 5: Grey relational grade

After averaging the GRC, the GRG r_i will be obtained by Equation (16) $r_{i} = - \frac{1}{n} \sum_{k = 1}^{n} ξ_{i} (k)$ (16)

Where n = process response number, the normalized S/N ratios, GRand GRG values are represented in Table 13. Ranks will be assigned as per the value of delta, with a higherelta value for the first rank as it indicates a significant parameter.

Table 13

Ranking of GRG

Exp.	S/N ratio			Normalized of S/N ratios			GRC			GRG	Rank
	Ra	Tw	MRR	Ra	Tw	MRR	Ra	Tw	MRR
1	–3.227	–42.607	35.440	0.2745	0.0000	1.0000	0.408009	0.333333	1	0.580447582	4
2	–4.350	–39.735	32.941	0.1379	0.5624	0.7184	0.367093	0.533269	0.639725	0.513362598	5
3	1.412	–37.953	31.003	0.8391	0.9116	0.5000	0.756564	0.849764	0.5	0.702109301	2
4	–4.861	–40.828	30.443	0.0757	0.3484	0.4368	0.351061	0.434185	0.470291	0.418512441	9
5	–5.483	–38.588	28.504	0.0000	0.7871	0.2184	0.333333	0.701322	0.390142	0.474932201	7
6	2.734	–38.486	32.941	1.0000	0.8072	0.7184	1	0.639725	0.787142757	1
7	–2.411	–39.825	26.566	0.3738	0.5449	0.0000	0.443984	0.523526	0.333333	0.43361456	8
8	–0.984	–37.501	31.003	0.5475	1.0000	0.5000	0.524945	1	0.5	0.674981542	3
9	0.355	–40.086	28.504	0.7105	0.4936	0.2184	0.633289	0.496839	0.390142	0.506756896	6

Step 6: Response table for GRG

Better performance of the process will depend on a larger value of GRG as per Table 13 and a higher GRG value of 0.787 for the 6th experiment, A₂B₃C₁. Therefore, uncoated, speed of 100, and feed of 0.15 were the optimum factors. The values for GRG for responses are represented in Table 14.

Table 14

GRG Values

	Level 1	Level 2	Level 3	Max.	Min.	Max –Min	Rank
A	0.598	0.560	0.538	0.598	0.538	0.060	3
B	0.4775	0.554	0.665	0.665	0.477	0.187	2
C	0.6808	0.479	0.536	0.680	0.479	0.201	1

Step 7: Identification of rank and ANOVA

The response table for GRG was considered as a response for further analysis. Errors between the maximum and minimum values will be calculated, and rank will be identified for parameters. The results of the analysis of variance on S/N ratios and ANOVA for means are represented in Tables 15, 16. Contribution of parameters of S/N ratios and factors of means as depicted by Fig. 9. Table of S/N ratio, means and effect plots for S/N ratios, means as represented by Table 17 and Fig. 10.

Table 15

Results of ANOVA with S/N ratios

Factors	Df	Seq. SS	Adj. SS	Adj. MS	f	p	% Cont.
Speed	2	1.724	1.914	0.8619	0.21	0.817	5.759
Feed	2	12.054	12.254	6.0272	1.49	0.328	40.263
Residual error	4	16.160	16.860	4.0401			53.978
Total	8	29.938					100

Table 16

Results of ANOVA with Means

Factors	Df	Seq. SS	Adj. SS	Adj. MS	f	p	% Cont.
Speed	2	0.0055	1.914	0.8619	0.21	0.817	5.759
Feed	2	0.0534	12.254	6.0272	1.49	0.328	40.263
Residual error	4	16.160	16.860	4.0401			53.978
Total	8	29.938					100

Table 17

S/N Ratios and Means

Level	Speed	Feed	Level	Speed	Feed
1	–4.529	–6.516	1	0.5986	0.4775
2	–5.371	–5.224	2	0.5602	0.5544
3	–5.525	–3.685	3	0.5385	0.6653
Delta	0.996	2.831	Delta	0.0602	0.1878
Rank	2	1	Rank	2	1

Fig. 9

Percentage contributions of parameters of (i) S/N ratios and (ii) factors for means.

Fig. 10

Main effect plots of (i) S/N ratios and (ii) means.

3.3 Machine learning methods

It is a multi-disciplinary area and is broadly classified depending on learning techniques, namely, supervised and unsupervised learning. These models offer a complementary approach to predictive capability by using expert knowledge and measured data to build a model. Each machine learning method is unique, tailored to a specific application, and the input and output data will differ. The commonly used methods of machine learning are ANN, SVM, KNN (k-nearest neighbor network), and decision trees. Implementation of these approaches follows some steps, namely, data collection, data reprocessing, model training, model performance evaluation, and final model prediction. The data set for this study contains 360 samples, with 80% used for training and the remaining 20% used for testing [34 , 40–44].

3.3.1 Support vector regression

It will be based on the concept of a support vector machine, which is a well-known and powerful model of a supervised technique. It can handle nonlinear data using a kernel. It maps the input vectors to high-dimensional features and rearranges the data set into a linear format. It will utilize kernels for converting data from the highest dimensional space to the lowest dimension, and the functions selected are linear, polynomial, sigmoid, and radial basis functions. The separation function, as represented by Equation (17) and constraints using 18, and its factors w and b, will be calculated during the training phase. $Optimization function : \underset{w, b}{argmin} \frac{1}{2} {∥ w ∥}^{2}$ (17) $Constraints : y_{n} ({wx}_{n} + b) ⩾ 1 \forall n,$ (18)

Where n is the number of points in training data

The separation function as represented in Equation (19) and variables w and b will be calculated in the training phase of SVM. $f (x) = wx + b$ (19)

The classification of unknown data x, either positive or negative, is estimated by Equation (20) ${\begin{matrix} y = + 1 (positive class) if f (x) > 0 \\ y = - 1 (negative class) if f (x) ⩽ 0 \end{matrix}$ (20)

The objective is to maximize the margin by $\frac{1}{W}$ solving this optimization problem by quadratic programming optimization using Equation (21) where αi is the Lagrange multiplier: $w = \sum_{i = 1}^{p} α_{i} y_{i} x_{i}$ (21)

The commonly selected kernels are polynomial, radial basis function, and Gaussian kernel and are represented by Equation (22), with p equal to 1. $k (x_{i}, x) = {(x_{i} . x + 1)}^{p}$ (22)

Slack variable ξ_i for approximate separability as represented in Equation 23. ${∥ \bar{W} ∥}^{2} + C \sum_{i - 1}^{n} ξ_{i} where ξ_{i} > 0 \forall i$ (23)

The larger valuef C will minimize errors in training that lead to a complex separation function. Evaluation of support vector regression (SVR), using different kernels as represented in Table 18.

Table 18

Root Mean Square Error as Error Measurement

Parameters	Values
Linear	1.11	Linear function
poly, degree = 2, C = 2	0.807	polynomial equation
poly, degree = 3, C = 3	0.733	polynomial equation
poly, degree = 4, C = 4	0.698	polynomial equation
Rbf C = 1	0.709	Radial Basis function
rbf, C = 2	0.599	RBF
Rbf C = 3	0.589	RBF
sigmoid	1.504	Sigmoid function
	C –Regularization parameter
	Degree –degree of polynomial function

3.3.2 k-Nearest neighbors (KNN) algorithm

This classifier uses a Euclidean distance function to find the closest neighbors to the new unknown data. The weights will be assigned to improve the performance of the KNN algorithm as the closer neighbor has a stronger vote, and the distance weighting for the neighbor will be based on the reciprocal of the distance to the neighbor’s 1/d. The most common technique for calculating the distance between neighbors is the Euclidian distance function, represented by Equation (24). $d (x, y) = ∥ x - y ∥ = \sqrt{\sum_{i = 1}^{n} {(x_{i} - y_{i})}^{2}}$ (24)

Where x = (x_{1, -- -- -- -}x_n) and y = (y_{1, -- -- -}y_n) and vector size is n, k neighbor points will have a shorter distance to an unknown point by Equation (25). $\hat{y} = \sum_{i = 1}^{n} w_{i} y_{i}$ (25) where wi is the weight of single neighbor point yi to query point $\hat{y}$ .

The simpler weig function is represented by Equation (26). $w_{i} = \frac{d_{i}}{\sum_{i = 1}^{n} d_{i}}$ (26) where di is the distance from the unknown point and its neighbor, as different weights may be obtained for KNN prediction as per equation 26, depending on neighbor points. The KNN prediction is not robust to outliers, so utmost care is required as the training data is as accurate as possible. To find the optimum number of neighbors (k) foprediction, a root mean square error (RMSE) is chosen. A graph is plotted between RMSE and k. The optimum number of the neighbor is at k = 3, as the error is minimum, and K values are as represented in Fig. 11 and Table 19.

Fig. 11

Root mean square error vs ‘K’ value.

Table 19

K-Values

Points	1	2	3	4	5
K-value	19.75	15.5	18.434	17.59	17.55

3.3.3 Decision tree regression

It is an old learning technique and is generally used for problems with categorical or nominal data. Decision trees follow a CART (Classification and Regression Trees) framework, where the training starts at the root node, and the data is progressively split into smaller and smaller subsets. The resulting classifier is a tree-like structure composed of if-then rules, with each node acting as a problem, focusing on one or more features and making a decision. This algorithm creates interpretable results, and sometimes a strong correlation between certain features and a class can be observed. The C 4.5 algorithm, developed by Quinlan in 1996, is the most widely used today [45]. It is a popular tree construction approach that produces a decision tree construction using Weka. The decision tree architecture and decision tree are represented in Figs. 12 13 respectively. To ease the calculation of the decision tree, the following values have been selected, such as D = 1, HSS = 2, uncoated = 2, coated = 3.

Fig. 12

Decision Tree Architecture.

Fig. 13

Decision Tree.

The predicted values of surface roughness and tool wear obtained by a decision tree, support vector regression, and K nearest neighbor are represented in Table 20.

Table 20

Predicted values of Ra, Tw calculated from Decision Tree (DT), SVR, KNN

No	Tool	Speed	Feed	Ra-μm.	Ra DT		Ra SVR		Ra KNN		Tw-mm	Tw DT		Tw SVR		Tw KNN
					Pred.	Rel. Err.	Pred.	Rel. Err.	Pred.	Rel. Err.		Pred.	Rel. Err.	Pred.	Rel. Err.	Pred.	Rel. Err.
1	HSS	60	0.15	2.19	2.12	3.19	2.28	4.10	2.33	6.4	0.195	0.190	2.56	0.203	4.11	0.209	7.18
2	HSS	80	0.20	2.26	2.22	1.77	2.37	4.87	2.44	7.9	0.202	0.199	1.49	0.211	4.46	0.215	6.44
3	HSS	100	0.25	2.38	2.34	1.68	2.49	6.40	2.54	6.73	0.218	0.215	1.38	0.231	5.97	0.235	7.8
4	Uncoated	60	0.2	2.32	2.27	2.16	2.46	6.03	2.53	9.0	0.207	0.204	1.45	0.217	4.84	0.225	8.7
5	Uncoated	80	0.25	2.45	2.42	1.23	2.56	4.5	2.61	6.54	0.221	0.219	0.90	0.234	5.88	0.240	8.59
6	Uncoated	100	0.15	2.58	2.53	1.94	2.71	5.04	2.76	6.98	0.236	0.232	1.70	0.246	4.25	0.255	8.05
7	Coated	60	0.25	2.02	1.98	1.98	2.15	6.44	2.27	12.3	0.183	0.180	1.65	0.197	7.65	0.20	9.29
8	Coated	80	0.15	1.92	1.89	1.56	2.08	8.3	2.16	12.5	0.178	0.175	1.69	0.187	5.05	0.193	8.43
9	Coated	100	0.20	1.85	1.82	1.62	1.96	5.95	2.07	11.7	0.180	0.177	1.67	0.187	3.89	0.196	8.88
Average						1.90		5.74		8.90			1.61		5.13		8.16

3.3.4 Artificial neural network

Analytical, empirical, and experimental models have been established for analyzing the performance of a machining operation. Artificial intelligent-based models have been established using non-conventional methods, namely genetic algorithms, support vector regression, fuzzy logic, and ANN [30 , 33]. Empirical models based on conventional approaches were developed based on response surface methodology, statistical regression, and factorial design. The software used for this analysis was the Easy NN-Plus 2015 version. Different training trials with hidden neurons, momentum value (0.8), and learning rate (0.6) were selected, and the validation error was 0.01453974, calculated at up to 6000000 learning cycles. For sensitivity analysis, the target error was 0.0100, and the average training error was 0.019749. The ANN training curves and control factors are as represented in Figs. 14 15, respectively. For the network diagram, the input nodes were selected as 2, one hidden layer, node 2, and hidden layer 2 nodes 2, and output is represented in Fig. 16. The theoretical prediction of response data is shown in Table 21.

Fig. 14

ANN Training Curves.

Fig. 15

Control Table.

Fig. 16

ANN Architecture.

Table 21

Predicted Values by ANN

No	Tool	Speed	Feed	Ra-μm	Ra-μmANN	Tw -mm	Tw –mm ANN
1	HSS	60	0.15	2.19	2.12	0.195	0.191
2	HSS	80	0.20	2.26	2.31	0.202	0.205
3	HSS	100	0.25	2.38	2.33	0.218	0.213
4	Uncoated	60	0.2	2.32	2.28	0.207	0.211
5	Uncoated	80	0.25	2.45	2.39	0.221	0.226
6	Uncoated	100	0.15	2.58	2.61	0.236	0.232
7	Coated	60	0.25	2.02	1.98	0.183	0.186
8	Coated	80	0.15	1.92	1.96	0.178	0.181
9	Coated	100	0.20	1.85	1.81	0.180	0.176

4 Results and discussion

4.1 Machining performance

This paper presents the drilling of the K500 alloy under different cutting conditions based on the L9 array using three drills. The influence of heating temperature on response parameters, namely MRR, surface roughness, and tool wear, has been studied using optimization methods such as GRA, PCA, and validation by machine learning techniques and ANN. The measured values are represented in Table 4 and are shown in Figs. 17 –19, respectively. As per Fig. 17, the surface roughness values for HSS drills are reduced by 23.86%, uncoated by 27.29%, and coated by 29.27%, respectively. As per Fig. 18, tool wear values for HSS drills decreased by 28.51%, uncoated drills by 34.7%, and coated drills by 33.71%, respectively, based on the relative error approach. As per Fig. 19, the MRR values for HSS drills have increased by 20.51% for HSS drills, uncoated drills by 23.08%, and coated drills by 23.5%, respectively. The PVD –TiALN coated drills are commonly used due to their high hardness, chemical stability, wear resistance, and better machinability and tool life.

Fig. 17

Surface roughness at room and annealed temperature.

Fig. 18

Tool wear at room and annealed temperature.

Fig. 19

MRR at room and annealed temperature.

As per Fig. 20, at room temperature, at a higher cutting speed, the presence of hard particles in the K 500 alloy will generate more pressure on the cutting tool, causing rapid tool wear. At annealed temperature, at higher speed, the cutting zone temperature increases, causing a reduction in the strength of the material and minimizing wear. Feed increases as tool wear increases based on an increase in the area of the cut, chip load, and a higher cutting zone temperature.

Fig. 20

Tool wear vs (i) cutting speed, and (ii) feed.

As per Fig. 21, machined surface quality depends on roughness values. Due to an increase in speed and feed, there will be a decrease in surface roughness values at room temperature due to minimum chip tool contact length and higher temperature at the cutting zone.

Fig. 21

Surface roughness vs (i) cutting speed, and (ii) feed.

As per Fig. 22, the MRR is a machining performance indicator. As there is an increase in speed and feed, there will be a decrease in metal removal rate at room temperature due to the higher cutting force. At annealed temperature, there will be a reduction in the shear strength of the workpiece, minimizing cutting force, and the application of heat on the surface of workpiece material and refined microstructure will enhance the removal rate.

For PCA, CPC values with S/N ratios and results of conformity experiments are represented in Table 8. The higher value of CPC will be 1.447, representing the 6th experiment. The optimum parameters will be A₂ B₃ C₁ as an uncoated drill, 100 cutting speed, and feed 0.15, respectively.

Table 10 and Fig. 5 show the results of ANOVA on CPC and the percentage contribution of parameters, representing feed (47.8%) will be a significant parameter, followed by speed (5.87%).

The ANOVA on s/n ratio is shown in Table 11, and the main effect plots are represented by Fig. 6, which indicates that feed (46.3%) will be a significant factor, followed by speed (10.26%).

From Table 6, the accountability proportion (AP) values of three principal components, like surface roughness (Ψ1 = 51.8), tool wear (Ψ2 = 36.6), and MRR (Ψ3 = 11.6), are portrayed in Figs. 7, 8 respectively.

For GRA, the normalized S/N ratios, GRC, and GRG are shown in Table 13. The largest value of GRG at 0.787, indicates the better performance of the process. The optimum cutting factors will be A₂ B₃ C₁ for the 6th experiment, indicating uncoated drill, cutting speed of 100, and feed of 0.15 mm/rev, respectively.

The results of the ANOVA on S/N ratios and the parentage contribution of the parameters represented by Table 15 and Fig. 9 indicate that feed (40.3%) will be a significant factor, followed by speed (5.76%). The ANOVA on S/N ratios and means are represented in Tables 16, 17. The main effect plots for S/N ratio/mean are represented by Fig. 10 indicates that feed (40.1%) will be a significant factor, followed by speed (4.18%).

Machine learning methods such as decision trees and architecture, as shown in Figs. 12, 13, and support vector regression, KNN, are estimated by programming in Python using Google Colab, as shown in Table 20. The values obtained by the decision tree method are found to be better among these algorithms based on the relative error approach that was used for this study and match well with the measured values.

The KNN predicts local predictions using unknown point neighbors, as the SVR prediction will be based on a general approximation of the complete dataset.

Figures 14 , and 16 show the ANN training curves, control table, and architecture, and Table 21 represents the estimated values obtained by the ANN approach that match well with measured values.

Fig. 22

MRR vs (i) cutting speed, and (ii) feed.

5 Conclusions

In the present study, machining parameters, namely MRR, surface roughness, and tool wear, are compared at room and annealed temperatures using three types of drills. It demonstrates that heating has a significant impact on machining performance.

The annealing process changes the material’s physical and sometimes chemical properties, relieving internal stresses, reducing hardness, and increasing ductility. Because this method is suitable for hard-to-cut materials, requires less tooling cost, and is a simple method. After annealing, the softened material can be easily machined to increase metal removal and decrease tool wear and surface roughness. PCA may be useful for indicating patterns in data, and principal components may reduce the number of trials. Experimental results show that feed (47%), will be a significant parameter, followed by speed. PCA can predict optimum factors for better performance of the cutting process and may be generalized to other machining processes.

GRA can estimate optimal machining factors. The results indicate that feed (40.2%) will be a significant parameter, followed by speed, and it can also be generalized to any other manufacturing process. Both methods predicted the same experimental run, the 6th for optimum cutting conditions for this study based on cutting parameters.

Data-driven models have demonstrated a high potential to predict machining parameters more accurately than analytical and statistical methods. As per the results, the decision tree is found to be a powerful classifier for estimation using the C 4.5 algorithm. It will be suitable for feature reduction and classification as the decision tree predictions are better than the SVR and KNN. ANN can be implemented for predicting response parameters in a machining operation and may be suitable for complex machining processes.

In future work, metaheuristic algorithms can be used, such as desirability function analysis (DFA) for the optimization of multi-response characteristics and multi-criteria decision-making methods such as Topsis (technique for order of preference by similarity to ideal solution), and combinative distance-based assessment (CODAS).

Declarations

Funding

The authors extend their appreciation to the Deanship of Scientific Research at King Saud University, Riyadh, for funding this work through Research Group number (RG- 1441-535).

Conflicts of interest

The authors declare that, they have no known competing financial interests that could have appeared to influence the work reported in this paper.

Availability of data and material

All available data is present in the manuscript.

Data availability statement

All data, models, and code generated or used during the study appear in the submitted article.

Authors contribution

Conceptualization by Chintakindi Sanjay (C.S.), Ali Samhan (A.S.), and Mustufa Haider Abidi (M.H.A.); Methodology by C.S., A.S., and M.H.A; Data curation by C.S. and M.H.A; Investigation by C.S. and M.H.A.; writing original draft by C.S. and A.S., writing review & editing by C.S. and M.H.A.; funding acquisition by C.S. and A.S.

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Multi response optimization of machining parameters for an annealed Monel K 500 alloy in drilling using Machine learning techniques and ANN

Abstract

Keywords

1 Introduction

1.1 Literature review

2 Materials and methods

Table 1 Mechanical and Physical Properties Density, g/cm3 8.44 Melting Range °C 1315 - 1350 Poissions Ratio 0.32 Hardness Rockwell C 27 Elongation break 22 % Yield strength MPa 655 Tensile strength MPa 1000 Reduction in area 40%

3.1 Principal component analysis

3.3.1 Support vector regression

4.1 Machining performance

Declarations

Funding

Conflicts of interest

Availability of data and material

Data availability statement

Authors contribution

References

Table 1
Mechanical and Physical Properties

Density, g/cm³ 8.44

Melting Range °C 1315 - 1350

Poissions Ratio 0.32

Hardness Rockwell C 27

Elongation break 22 %

Yield strength MPa 655

Tensile strength MPa 1000

Reduction in area 40%