# A Machine Learning Approach to Optimize, Model, and Predict the Machining Factors in Dry Drilling of Nimonic C263

Authors: S. Lakshmana Kumar; V. Jacintha; A. Mahendran; R. M. Bommi; M. Nagaraj; Umamahesawari Kandasamy
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

In this present paper, the machine learning approach is used to optimize, model, and predict the factors during drilling Nimonic C263 under dry mode. Nimonic C263 is tough to machine aero alloys, and it is required to find a predictive model and to optimize the factors in drilling this alloy before the actual machining process. It helps to avoid the actual machining cost and material cost. Experimental trails are planned based on Taguchi analysis, and L27 orthogonal array was chosen. Speed, feed, and approach angle of drill were considered as controlling factors, and cutting force and surface roughness were considered as responses. The feed forward neural network (FFNN) was used to develop a predictive model. The prediction capability was validated with a predictive model developed by Taguchi analysis. Furthermore, ANOVA (analysis of variance) analysis was done to find out the most influence factor on the responses.


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## Body

## 1. Introduction

Nimonic C263 material is an aero material. It has great mechanical properties, and it finds usage in aeronautical parts manufacturing sectors. However, it is tough to machine owing to low thermal conductivity [1]. Therefore, suitable machining factors and cutting tools to machine this alloy are to be found out to improve the product quality. Modeling and optimization of the machining factors are an important task in machining domain. Optimization of these factors with suitable optimization tool would increase the efficiency of the machining performances and improve the product quality [2]. In manufacturing sectors, machine learning reduces cost, time, and wastages and increases the quality of the parts. It also develops systems to manage human behavior. Different machine learning algorithms are available, namely, genetic algorithm, nondominated sorting genetic algorithm, particle swarm optimization, biogeography-based optimization algorithm, firefly algorithm, artificial bee colony, gray-based Taguchi analysis, and ant colony algorithm [3, 4]. Furthermore, it also important that the machined surface may get affected severely unless the insert wear rate is controlled. The cutting fluids majorly influence to reduce the temperature in the cutting zone and control the insert wear rate. The lubrication of the machine zone with the nano-MQL (minimum quantity lubrication) lubricant system produces improved machined surface and minimum insert wear rate [5]. It is also important to note that, owing to friction in the cutting zone, temperature will be increased, and this affects tool edge and other machining performances [6]. Data set was prepared by conducting milling experiments on AA7075 alloy, and the recorded data were used to develop the ANN model to predict the surface roughness. The predicted value by ANN (artificial neural network) using the small data set was compared by the Taguchi method, and the result has shown that the developed ANN model has shown best results. In ANN, back propagation and BR algorithm were used to train the data [7].The tool wear during machining is needed to monitor in the modern machining system. Baig et al. [8] considered the vibration sign during machining and proved it as best indicators for the tool wear assessment. The ANN tool was used to predict the tool life in turning EN9 and EN24 steel with help of recorded experimental data. The ANN model was found to be effective with a coefficient of 0.99 in predicting the tool wear.Alajmi and Almeshal [9] said that the machining performance data would be used for the prediction of the responses. They have predicted the cutting force and optimized the factors to get minimum of cutting force in turning AISI 4340 alloy. The prediction was done using Gaussian process regression, support vector machines, and artificial neural networks, and they have reported that the GPR tool has produced best prediction compared to other two prediction tools.Uhlmann et al. [10] said that the machining process and wear of the insert have a significant impact on surface in milling process. Many approaches have been found to get models to predict surface properties during machining. However, those approaches are to be verified with a good number of experimental trails. They have suggested that the manual experimental parameterization would not be feasible; hence, a highly automated approach for the relation between tool wear and machining factors was developed using the machine learning approach. Murua et al. [11] said that the process controlling factors can be optimized with help of predictive models, and they have developed a regression model by extracting values in face turning of inconel 718. The high-pressure coolant has reduced the wear and improves the coolant purpose compared to the traditional lubrication system.Fertig et al. [12] presented a novel approach to predict the improvement of machined work piece during milling processes. The machine tool data were recorded, and these values were used for the development of the machine learning approach, and slicing algorithm was applied to predict the quality of the machined surface. Dubey et al. [13] have used the minimum quantity lubrication approach to turn the AISI 304 steel to determine the surface finish. Linear regression (LR), random forest (RF), and support vector machine (SVM) machine learning algorithm were used for the prediction of roughness, and the predicted values were compared with experimental results. It was finally concluded that particle size effect on surface finish and machine learning techniques were found to be far to predict roughness with minimum error.Seleznev et al. [14] have used ceramic-based composites inserts that were used to machine nickel alloys, and they have highlighted SiAlON as best one. Furthermore, they have suggested that the new tool geometry, machining methods, and tool materials would be useful to assess the machining performance. Wei et al. [15] said that the machine learning methods are the best tool to predict the performances or characteristics of thermal transport properties. Dahbi et al. [16] have presented modeling of machining performances in turning 2017A aluminum. The data obtained in machining were used to develop the neural network, and network architecture was chosen based on R2, MSE (mean squared error), and APE (average percentage error). Nickel-based superalloys and titanium alloy are very difficult to cut by traditional machining process because of extreme toughness and work-hardening characteristics [17–19]. When turning to Nimonic C263 superalloy, a predictive model based on DEFORM 3D was made to predict machining properties such as cutting force and the temperature of the insert cutting edge [20]. The 2D wavelet transform can break up an image of a machined surface into pictures with different levels of detail for many different surface properties, and it can be used to evaluate surfaces [21].From the literature, it is important to develop a predictive model, and there is need to optimize the process controlling factors to achieve better machining performance. Therefore, an attempt has been taken to develop a predictive model based on the machine learning algorithm using MATLAB, namely, ANN, and the model results were validated with the help of regression.


## 2. Materials and Methods

The work piece Nimonic C263 contains chemical composition such as 52.49 Ni, 0.19 Si, 0.46 Mn, 20 Cr, 6.29 Mo, 0.07 Cu, 1.0 Fe, 16.7 Co, 1.94 Ti, 0.48 Al, 0.04 Nb, 0.15 W, 0.02 V, 0.02 C, 0.001 S, and 0.007 Ta. The cutting force and surface roughness were considered as responses. The cutting force and surface roughness were measured using a piezo-electric dynamometer and Surfcom 1500 roughness tester. Taguchi analysis is implemented to design the experiments, and L27 orthogonal array was used to conduct the experiment. AlCrN-coated carbide drill is used to drill the work. The drilling factors and their levels are given in Table1. The results of the experiment are shown in Table 2.Table 1
Process parameters and their levels.
Sl. no.Process parametersUnitSymbolLevels1231Spindle speedrpmN1250150017502Feed ratemm/revf0.100.1550.1983Point angleDegree2ρ120140145Table 2
Experiment’s results.
Exp. no.InputOutputsN (rev/min)f (mm/rev)2ρ (degree)Fz (N)Ra (μm)112500.1012012500.576212500.1014013000.585312500.1014513750.592412500.15512012650.582512500.15514013600.592612500.15514514200.621712500.19812013850.595812500.19814014000.622912500.19814514300.6411015000.101209500.6561115000.1014011000.5981215000.1014511500.6351315000.1551209900.5861415000.15514011100.6421515000.15514512000.6851615000.19812010600.5521715000.19814011200.6721815000.19814511750.6951917500.101209000.5852017500.101409700.6122117500.1014510000.6512217500.1551209250.5352317500.15514010100.5462417500.15514510500.5642517500.1981209750.5712617500.1981409900.5892717500.19814510300.635


### 2.1. Development of the Predictive Model Using Regression Analysis

The regression equation was developed for the experimental values based on the following equation.(1)Y=β0+∑i=1kβixi+∑i=1kβiixi2+∑i∑jβijxixj+ε,where the corresponding response is “Y,” xi is the values for the ith machining process parameters, and “k” is the no. of parameters to be modeled. The terms β and π are the regression coefficient and the residual of the experimental error of results, respectively. β coefficients utilised in the calculation can be determined using the least square method. ANOVA was calculated to estimate significant contribution of factors on each response. The R-squared value is used to identify the model’s significance at 95% confidence interval. The response table (S/N ratio and for means) for cutting force is given in Table 3, and it is observed that the cutting speed was found to be dominant on cutting force followed by point angle and feed rate.Table 3
Response tableFz.
LevelCutting speedFeed ratePoint angle(a) Response table for S/N ratio: Fz1−59.61−57.81−57.542−57.76−58.10−58.143−56.83−58.29−58.52Delta2.780.480.98Rank132(b) Response table for means: Fz1677.2555.6539.922547.8574.2575.93492.0587.3602.0Delta185.331.762.8Rank132Figures1 and 2 show the main effects plot for force and interaction plot for means of cutting force response. Figures 3(a)–3(c) shows the three-dimensional plot for cutting force. From Figures 1–3, the cutting force magnitude is increased at lower level of cutting speed and reduced as the level of cutting speed increases. It would be owing to that the higher temperature generation at the machining zone. Further, the cutting force magnitude is increased as the level of feed rate and point angle are increased, and it could be owing to rubbing action at the cutting zone as well as at higher level of point angle and the contact surface of the drill cutting edge is more.Figure 1
Main effects plot for means: cutting force.Figure 2
Interaction plot for means: cutting force.Figure 3
3D plot for cutting force: (a) cutting speed vs. feed rate, (b) cutting speed vs. point angle, and (c) feed rate vs. point angle.
(a)(b)(c)Furthermore, the regression analysis was done using Design–Expert software for cutting force and surface roughness. Table4 shows ANOVA for cutting force, in which it is observed that the cutting speed has more dominant factor followed by point angle, square of cutting speed, and feed rate. Since the model developed has F value equal to 113.34 for cutting force, it is adequate to predict the cutting force. The model efficiency is confirmed by its R-squared value of 98%. As compared to point angle and feed rate, the F value is high for cutting speed (791.17), meaning that it has significant impact for force. Equation (1) is an empirical equation to predict the force.Table 4
ANOVA for cutting force.
SourceSOSdfMSF valueP valueModel7.462E + 05982907.42113.34<0.0001N5.787E + 0515.787E + 05791.17<0.0001F20931.63120931.6328.62<0.00012ρ72323.10172323.1098.87<0.0001N∗f2087.6712087.672.850.1094N∗2ρ76.19176.190.10420.7508f∗2ρ3747.3313747.335.120.0370N232511.57132511.5744.45<0.0001f216.81116.810.02300.88132ρ23937.5713937.575.380.0330Residual12435.1117731.48Cot. total7.586E + 0526R-square: 98% and adj. R-square: 97%(2)Fz=1048−184∗N+35∗f+63.46∗2ρ−13.16∗N∗f−2.38∗N∗2ρ−16.66∗f∗2ρ+73.16∗N2−1.70∗f2+42.36∗2ρ2.The response table (S/N ratio and for means) for cutting surface roughness in given in Table5, and it is observed that the cutting speed was found to be dominant on the cutting force followed by point angle and feed rate. Figures 4 and 5 show the main effects plot for surface roughness and interaction plot for means of surface roughness response, respectively. Figures 6(a)–6(c) show the three-dimensional plot for surface roughness. From Figures 4–6, the surface roughness increases as the level of point angle and feed rate increases. However, the surface roughness is reduced at a high level of speed, low level of point angle, and at the middle level of feed. Furthermore, regression analysis was done using Design–Expert software for cutting force and surface roughness. Table 6 shows ANOVA for surface roughness, in which it is observed that the point angle has more dominant factor followed by cutting speed and feed rate.Table 5
Response table for Ra.
LevelCutting speedFeed ratePoint angleResponse (a) for S/N ratio: Ra14.4504.4474.86124.1024.5564.36034.6774.2264.008Delta0.5740.3300.854Rank231Response (b) for means: Ra10.59940.59990.571720.62560.59340.606330.58470.61630.6317Delta0.04090.02290.600Rank231Figure 4
Main effects plot for means: cutting force.Figure 5
Interaction plot for means: cutting force.Figure 6
3D plot for surface roughness: (a) cutting speed vs feed rate, (b) cutting speed vs point angle, and (c) feed rate vs point angle.
(a)(b)(c)Table 6
ANOVA for surface roughness.
SourceSOSdfMSF valueP valueModel0.033390.00375.000.0022N0.000810.00081.040.3215F0.000010.00000.03120.86192ρ0.012210.012216.460.0008N∗f0.002410.00243.300.0869N∗2ρ0.000210.00020.25560.6196f∗2ρ0.003910.00395.260.0348N20.010410.010414.010.0016f20.002510.00253.340.08532ρ20.001810.00182.430.1375Residual0.0126170.0007Cot. total0.045826R-square: 75% and adj. R-square: 60%(3)Ra=0.5939−0.0067∗N+0.0012∗f+0.0260∗2ρ−0.0142∗N∗f+0.0037∗N∗2ρ+0.0170∗f∗2ρ−0.0416∗N2+0.0206∗f2+0.0286∗2ρ2.Since the model developed hasF value equal to 5 for surface roughness, it is adequate to predict the surface roughness. The model efficiency is confirmed by its R-squared value of 75%. As compared to point angle and feed rate, the F value is high for cutting speed (791.17), meaning that it has significant impact for force. Equation (3) is an empirical equation to predict the force.


### 2.2. Implementation of the FFNN Model for the Prediction of Responses

Analysis of gradient, the individual and interacting impacts of drilling process parameters on cutting force, and surface roughness are investigated, and a quadratic regression model is built. In training a feed forward neural network, unlike Naïve computation where gradient is computed with each weight separately, in back propagation, the gradient is approximated with appropriate weights of the network for a multivariate dataset. Because of this efficiency, gradient algorithms can be used to train multilayered networks, adjusting weights to minimise loss. The back propagation algorithm works by using the chain rule to compute the gradient of the loss function with respect to each weight, one layer at a time, iterating backwards from the final layer to eliminate unnecessary calculations of intermediary terms in the chain rule, allowing it to be dynamically programmed.The experimental trial dataset is split into two parts: testing and training. The dataset for training is utilised to adjust weights of associated neurons until the desired error level is achieved. As shown in Figure7, training is conducted by providing a number of training vectors each with a corresponding target output vector.Figure 7
FFNN model flow diagram.Tables7 and 8 detail the experimental conditions and findings that were utilised to train and evaluate the network. The experimental findings were utilised to train the FFNN model, with 18 experimental trials being used for training and 9 trials being used for testing. In this investigation, the feed forward back propagation algorithm with Levenberg–Marquardt approximation is utilised to train the network. In MATLAB, the neural network toolbox (nntool) was utilised to model the FFNN model. The average prediction error of the predicted output and the target output is calculated using the percentage error formula and is depicted in Table 9.(4)percentageerror=M−PP×100,where M is the measured value and P is the predicted value.Table 7
Training dataset for LM algorithm.
Exp. no.InputsTargetN (rev/min)f (mm/rev)2ρ (degree)Fz (N)Ra (μm)112500.1012012500.576212500.1014013000.585312500.1014513750.592412500.15512012650.582512500.15514013600.592612500.15514514200.611015000.101209500.5651115000.1014011000.5981215000.1014511500.6351315000.1551209900.5861415000.15514011100.6421515000.15514512000.6851917500.101209000.5852017500.101409700.6122117500.1014510000.6512217500.1551209250.5352317500.15514010100.5452417500.15514510500.564Table 8
FFNN model results for test dataset using the LM algorithm.
Exp. no.InputsPredicted outputN (rev/min)f (mm/rev)2ρ (degree)Fz (N)Ra (μm)712500.198120787.19420.600289812500.1981401086.8990.681932912500.1981451153.7740.6514071615000.198120737.74390.5975031715000.1981401090.8560.6493991815000.1981451106.8660.6813512517500.198120738.42160.5967662617500.1981401135.1860.5555782717500.1981451159.5820.582648Table 9
Percentage prediction errors for test dataset.
S. no.Measured outputPredicted output% prediction errorFz (N)Ra (μm)Fz (N)Ra (μm)Fz (N)Ra (μm)113850.5951387.1940.6002890.1581780.881158214000.6221386.8990.6819320.9446268.788583314300.6411453.7740.6514071.6353191.597572410600.552997.74390.5975036.2396897.615499511200.6721090.8560.6493992.6716863.480324611750.6951106.8660.6813516.1556212.00320179750.569938.42160.5967663.8978634.65275789900.589987.1860.5555780.2850496.015688910300.6121159.5820.58264811.17495.037642Average prediction error4.453%3.685%It can be inferred from Table9 that the average prediction error for Fz is 4.453%, and surface roughness (Ra) is 3.685%. The neuron in the input layer corresponds to the depth of cut (d), feed rate (f), and point angle. On the other hand, the surface roughness correlates to the output layer (Ra). The outputs are linked to the hidden layer neurons, while the hidden neurons are linked to the inputs. The architecture is shown in Figure 8, with three neurons in the input layer, ten neurons in the hidden layer, and two neurons in the output layer.Figure 8
Feed forward neural network architecture.Model Specification. Data division: random; training: (trainlm); Levenberg–Marquardt; performance: mean squared error (MSE) calculations: MEXEpoch: 534 iterations; gradient: 1.41e−11; Mu: 1.00e−09; validation checks: 4; and linear transfer function: purelin.(i)
One hidden layer with ten neurons(ii)
Three neurons in the input layer representing the input variables for FFNN models(iii)
Two neurons in the output layer representing the output variables independently for each of the FFNN modelsFigure9 shows the performance plot for training work initially, and for neurons in hidden layers, the purelin transfer function yielded the best results. The maximum number of training epochs was easily determined empirically using the plot network performance function plot perform. While looking at the graph of network training, it was observed that, after 534 epochs, the network training practically comes to a standstill (Figure 8).Figure 9
Performance plot of the training network.During the training process, learning algorithms adapted the generated neural networks to the dataset. The accuracy of the fits was validated using MATLAB regression graphs (Figure10) that showed the network outputs in relation to the objectives for testing, validation, and training sets, with values above 0.99 for all data sets. The FFNN predictive value and experiment values are compared and found to be within less than 5% error. When comparing the analytical model with the neural network model in terms of measured values obtained during experimental trials, the regression coefficient R provides a high correlation. The generated FFNNs for setting up black box models can be utilised to create a decision support system for selecting optimal parameters in drilling of superalloy Nimonic C263.Figure 10
Regression plots of trained network w.r.t. target for (a) training, (b) validation, (c) test, and (d) all.
(a)(b)(c)(d)


## 2.1. Development of the Predictive Model Using Regression Analysis

The regression equation was developed for the experimental values based on the following equation.(1)Y=β0+∑i=1kβixi+∑i=1kβiixi2+∑i∑jβijxixj+ε,where the corresponding response is “Y,” xi is the values for the ith machining process parameters, and “k” is the no. of parameters to be modeled. The terms β and π are the regression coefficient and the residual of the experimental error of results, respectively. β coefficients utilised in the calculation can be determined using the least square method. ANOVA was calculated to estimate significant contribution of factors on each response. The R-squared value is used to identify the model’s significance at 95% confidence interval. The response table (S/N ratio and for means) for cutting force is given in Table 3, and it is observed that the cutting speed was found to be dominant on cutting force followed by point angle and feed rate.Table 3
Response tableFz.
LevelCutting speedFeed ratePoint angle(a) Response table for S/N ratio: Fz1−59.61−57.81−57.542−57.76−58.10−58.143−56.83−58.29−58.52Delta2.780.480.98Rank132(b) Response table for means: Fz1677.2555.6539.922547.8574.2575.93492.0587.3602.0Delta185.331.762.8Rank132Figures1 and 2 show the main effects plot for force and interaction plot for means of cutting force response. Figures 3(a)–3(c) shows the three-dimensional plot for cutting force. From Figures 1–3, the cutting force magnitude is increased at lower level of cutting speed and reduced as the level of cutting speed increases. It would be owing to that the higher temperature generation at the machining zone. Further, the cutting force magnitude is increased as the level of feed rate and point angle are increased, and it could be owing to rubbing action at the cutting zone as well as at higher level of point angle and the contact surface of the drill cutting edge is more.Figure 1
Main effects plot for means: cutting force.Figure 2
Interaction plot for means: cutting force.Figure 3
3D plot for cutting force: (a) cutting speed vs. feed rate, (b) cutting speed vs. point angle, and (c) feed rate vs. point angle.
(a)(b)(c)Furthermore, the regression analysis was done using Design–Expert software for cutting force and surface roughness. Table4 shows ANOVA for cutting force, in which it is observed that the cutting speed has more dominant factor followed by point angle, square of cutting speed, and feed rate. Since the model developed has F value equal to 113.34 for cutting force, it is adequate to predict the cutting force. The model efficiency is confirmed by its R-squared value of 98%. As compared to point angle and feed rate, the F value is high for cutting speed (791.17), meaning that it has significant impact for force. Equation (1) is an empirical equation to predict the force.Table 4
ANOVA for cutting force.
SourceSOSdfMSF valueP valueModel7.462E + 05982907.42113.34<0.0001N5.787E + 0515.787E + 05791.17<0.0001F20931.63120931.6328.62<0.00012ρ72323.10172323.1098.87<0.0001N∗f2087.6712087.672.850.1094N∗2ρ76.19176.190.10420.7508f∗2ρ3747.3313747.335.120.0370N232511.57132511.5744.45<0.0001f216.81116.810.02300.88132ρ23937.5713937.575.380.0330Residual12435.1117731.48Cot. total7.586E + 0526R-square: 98% and adj. R-square: 97%(2)Fz=1048−184∗N+35∗f+63.46∗2ρ−13.16∗N∗f−2.38∗N∗2ρ−16.66∗f∗2ρ+73.16∗N2−1.70∗f2+42.36∗2ρ2.The response table (S/N ratio and for means) for cutting surface roughness in given in Table5, and it is observed that the cutting speed was found to be dominant on the cutting force followed by point angle and feed rate. Figures 4 and 5 show the main effects plot for surface roughness and interaction plot for means of surface roughness response, respectively. Figures 6(a)–6(c) show the three-dimensional plot for surface roughness. From Figures 4–6, the surface roughness increases as the level of point angle and feed rate increases. However, the surface roughness is reduced at a high level of speed, low level of point angle, and at the middle level of feed. Furthermore, regression analysis was done using Design–Expert software for cutting force and surface roughness. Table 6 shows ANOVA for surface roughness, in which it is observed that the point angle has more dominant factor followed by cutting speed and feed rate.Table 5
Response table for Ra.
LevelCutting speedFeed ratePoint angleResponse (a) for S/N ratio: Ra14.4504.4474.86124.1024.5564.36034.6774.2264.008Delta0.5740.3300.854Rank231Response (b) for means: Ra10.59940.59990.571720.62560.59340.606330.58470.61630.6317Delta0.04090.02290.600Rank231Figure 4
Main effects plot for means: cutting force.Figure 5
Interaction plot for means: cutting force.Figure 6
3D plot for surface roughness: (a) cutting speed vs feed rate, (b) cutting speed vs point angle, and (c) feed rate vs point angle.
(a)(b)(c)Table 6
ANOVA for surface roughness.
SourceSOSdfMSF valueP valueModel0.033390.00375.000.0022N0.000810.00081.040.3215F0.000010.00000.03120.86192ρ0.012210.012216.460.0008N∗f0.002410.00243.300.0869N∗2ρ0.000210.00020.25560.6196f∗2ρ0.003910.00395.260.0348N20.010410.010414.010.0016f20.002510.00253.340.08532ρ20.001810.00182.430.1375Residual0.0126170.0007Cot. total0.045826R-square: 75% and adj. R-square: 60%(3)Ra=0.5939−0.0067∗N+0.0012∗f+0.0260∗2ρ−0.0142∗N∗f+0.0037∗N∗2ρ+0.0170∗f∗2ρ−0.0416∗N2+0.0206∗f2+0.0286∗2ρ2.Since the model developed hasF value equal to 5 for surface roughness, it is adequate to predict the surface roughness. The model efficiency is confirmed by its R-squared value of 75%. As compared to point angle and feed rate, the F value is high for cutting speed (791.17), meaning that it has significant impact for force. Equation (3) is an empirical equation to predict the force.


## 2.2. Implementation of the FFNN Model for the Prediction of Responses

Analysis of gradient, the individual and interacting impacts of drilling process parameters on cutting force, and surface roughness are investigated, and a quadratic regression model is built. In training a feed forward neural network, unlike Naïve computation where gradient is computed with each weight separately, in back propagation, the gradient is approximated with appropriate weights of the network for a multivariate dataset. Because of this efficiency, gradient algorithms can be used to train multilayered networks, adjusting weights to minimise loss. The back propagation algorithm works by using the chain rule to compute the gradient of the loss function with respect to each weight, one layer at a time, iterating backwards from the final layer to eliminate unnecessary calculations of intermediary terms in the chain rule, allowing it to be dynamically programmed.The experimental trial dataset is split into two parts: testing and training. The dataset for training is utilised to adjust weights of associated neurons until the desired error level is achieved. As shown in Figure7, training is conducted by providing a number of training vectors each with a corresponding target output vector.Figure 7
FFNN model flow diagram.Tables7 and 8 detail the experimental conditions and findings that were utilised to train and evaluate the network. The experimental findings were utilised to train the FFNN model, with 18 experimental trials being used for training and 9 trials being used for testing. In this investigation, the feed forward back propagation algorithm with Levenberg–Marquardt approximation is utilised to train the network. In MATLAB, the neural network toolbox (nntool) was utilised to model the FFNN model. The average prediction error of the predicted output and the target output is calculated using the percentage error formula and is depicted in Table 9.(4)percentageerror=M−PP×100,where M is the measured value and P is the predicted value.Table 7
Training dataset for LM algorithm.
Exp. no.InputsTargetN (rev/min)f (mm/rev)2ρ (degree)Fz (N)Ra (μm)112500.1012012500.576212500.1014013000.585312500.1014513750.592412500.15512012650.582512500.15514013600.592612500.15514514200.611015000.101209500.5651115000.1014011000.5981215000.1014511500.6351315000.1551209900.5861415000.15514011100.6421515000.15514512000.6851917500.101209000.5852017500.101409700.6122117500.1014510000.6512217500.1551209250.5352317500.15514010100.5452417500.15514510500.564Table 8
FFNN model results for test dataset using the LM algorithm.
Exp. no.InputsPredicted outputN (rev/min)f (mm/rev)2ρ (degree)Fz (N)Ra (μm)712500.198120787.19420.600289812500.1981401086.8990.681932912500.1981451153.7740.6514071615000.198120737.74390.5975031715000.1981401090.8560.6493991815000.1981451106.8660.6813512517500.198120738.42160.5967662617500.1981401135.1860.5555782717500.1981451159.5820.582648Table 9
Percentage prediction errors for test dataset.
S. no.Measured outputPredicted output% prediction errorFz (N)Ra (μm)Fz (N)Ra (μm)Fz (N)Ra (μm)113850.5951387.1940.6002890.1581780.881158214000.6221386.8990.6819320.9446268.788583314300.6411453.7740.6514071.6353191.597572410600.552997.74390.5975036.2396897.615499511200.6721090.8560.6493992.6716863.480324611750.6951106.8660.6813516.1556212.00320179750.569938.42160.5967663.8978634.65275789900.589987.1860.5555780.2850496.015688910300.6121159.5820.58264811.17495.037642Average prediction error4.453%3.685%It can be inferred from Table9 that the average prediction error for Fz is 4.453%, and surface roughness (Ra) is 3.685%. The neuron in the input layer corresponds to the depth of cut (d), feed rate (f), and point angle. On the other hand, the surface roughness correlates to the output layer (Ra). The outputs are linked to the hidden layer neurons, while the hidden neurons are linked to the inputs. The architecture is shown in Figure 8, with three neurons in the input layer, ten neurons in the hidden layer, and two neurons in the output layer.Figure 8
Feed forward neural network architecture.Model Specification. Data division: random; training: (trainlm); Levenberg–Marquardt; performance: mean squared error (MSE) calculations: MEXEpoch: 534 iterations; gradient: 1.41e−11; Mu: 1.00e−09; validation checks: 4; and linear transfer function: purelin.(i)
One hidden layer with ten neurons(ii)
Three neurons in the input layer representing the input variables for FFNN models(iii)
Two neurons in the output layer representing the output variables independently for each of the FFNN modelsFigure9 shows the performance plot for training work initially, and for neurons in hidden layers, the purelin transfer function yielded the best results. The maximum number of training epochs was easily determined empirically using the plot network performance function plot perform. While looking at the graph of network training, it was observed that, after 534 epochs, the network training practically comes to a standstill (Figure 8).Figure 9
Performance plot of the training network.During the training process, learning algorithms adapted the generated neural networks to the dataset. The accuracy of the fits was validated using MATLAB regression graphs (Figure10) that showed the network outputs in relation to the objectives for testing, validation, and training sets, with values above 0.99 for all data sets. The FFNN predictive value and experiment values are compared and found to be within less than 5% error. When comparing the analytical model with the neural network model in terms of measured values obtained during experimental trials, the regression coefficient R provides a high correlation. The generated FFNNs for setting up black box models can be utilised to create a decision support system for selecting optimal parameters in drilling of superalloy Nimonic C263.Figure 10
Regression plots of trained network w.r.t. target for (a) training, (b) validation, (c) test, and (d) all.
(a)(b)(c)(d)


## 3. Conclusions

The following important conclusions were arrived in drilling of Nimonic C263 using carbide drill.(i)
The developed model by FFNN is found to be effective to predict cutting force and surface roughness compared to the regression method. As indicated by the comparatively high correlation coefficientR, the modeled neural network is well matched to the experimental data. The use of FFNN allows us to forecast surface roughness performance prediction with an accuracy of 0.9–2.9%, which is the same as the measurement values obtained during the experimental trials.(ii)
In drilling Nimonic C263, the maximum cutting force and surface roughness are observed to be 1430N and 0.65µm respectively. The cutting speed was found to be a major factor in effecting cutting force followed by point angle and feed rate. The point angle was found to be a significant factor on surface roughness followed by cutting speed and feed rate.



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*Source: 4856089-2022-06-16.xml*