Tool Wear Prediction Based on Artificial Neural Network during Aluminum Matrix Composite Milling †

This article deals with the phenomenon of tool wear prediction in face milling of aluminum matrix composite materials (AMC), class as hard-to-cut materials. Artificial neural networks (ANN) are one of the tools used to predict tool wear or surface roughness in machining. Model development is applicable when regression models do not give satisfactory results. Because of their mechanical properties based on SiC or Al2O3 reinforcement, AMCs are applied in the automotive and aerospace industry. Due to these materials’ abrasive nature, a three-edged end mill with diamond coating was selected to carry out milling tests. In this work, multilayer perceptron (MLP) models were used to predict the tool flank wear VBB and tool corner wear VBC during milling of AMC with 10% SiC content. The signals of vibration acceleration and cutting forces were selected as input to the network, and the tests were carried out with three cutting speeds. Based on the analysis of the developed models, the models with the best efficiency were selected, and the quality of wear prediction was assessed. The main criterion for evaluating the quality of the developed models was the mean square error (MSE) in order to compare measured and predicted value of tool wear.


Introduction
Aluminum matrix composites (AMCs) are a class of hard-to-cut metal matrix composite materials. The ingredients of AMCs are Al alloys with the most popular reinforcement materials such as SiC, Al 2 O 3 , B 4 C, and TiC. A combination of Al alloy with diverse reinforcement gives a unique blend of mechanical properties [1,2]. The reinforcement can take the separate form particulates, particulate complexes, continuous fibers, short fibers, or whiskers. The strength of these materials depends upon grain size and microstructure. AMCs offer better stiffness values and strength, lower weight, and thermic expansion coefficients compared to monolithic alloy. For example, the SiC reinforcement improves the density, hardness, tensile strength, and wear resistance of Al alloys. According to [3,4], revealed that reducing the Al 2 O 3 size affects the increase of Al matrix composite wear resistance. Kumar [5] described that, during studies of AMC with Al 2 O 3 particulates, the hardness of composites and tensile strength increased, but the relative elongation decreased. Particulate-based metal matrix composites (PMMCs) prove lower anisotropy and higher ductility than MMCs with fibers. These materials are made by dispersing the reinforcements in the metal matrix. The fabrication process also affects stiff cutting force. Monitoring or detecting tool wear and sudden tool failure are essential for improving manufacturing processes' reliability. The monitor tool wear methods could be divided into two types: direct (optical, microscope, electrical resistance, etc.) and indirect (vibration, force, torque, acoustic emission, etc.) [20][21][22]. Basically, in tool condition monitoring (TCM), the tool state is determined by analyzing the signals from sensors/multi-sensors. Based on sensor signals, the correlation between feature parameters and the tool states effectively adapts [23]. The use of sensors for measuring cutting forces, acoustic emission, mechanical vibrations, or acoustic vibrations (noise) is expected. In machining, mainly strain gauges, piezoelectric sensors, and integrated and multi-component sensors are used, while fast Fourier transform (FFT) is most commonly used for digital signal processing [24,25]. Azmi [26] developed a tool condition monitoring technique based on measured machining force data and adaptive network-based fuzzy inference systems during end milling of the GFRP composites. The results revealed that the ANFIS models matched the nonlinear relationship of tool wear and feed force highly effective compared to that of the simple power law of regression trend. In addition to the right selection of tool material, unconventional machining improved cutting performance is common. One of the used methods is the electrical discharge machining (EDM), laser machining (LAM), electrochemical machining, ultrasonic machining (USM), and high-speed machining [27][28][29]. According to [30], Chwalczuk et al. shows the optimization of heating and cutting parameters during turning of Inconel 718 under laser-assisted machining (LAM) conditions. They proved that the dendritic structure appears in the laser affected zone of the Ni-based alloy for sequential LAM. Due to surface softening kind of microstructures cause better machinability of hard to cut Inconel 718.
In addition to the use of unconventional machining methods to improve MMC materials' machinability, modern research is based on optimization methods and tools to generate a solution for engineering problems. The most frequently used optimization methods to improve the surface quality or minimize tool wear are the Taguchi method, response surface methods (RSM), adaptive network-based fuzzy inference systems (ANFISs), analysis of variance (ANOVA), and artificial neural networks (ANN) [31][32][33]. According to [34] studies, Basheer et al. investigated the surface roughness prediction model in precise machining of MMCs using PCD tools considering volume and size of reinforcement, tool nose radius or feed rate, and depth cut based on ANN. Arokiadass et al. [35] developed the empirical relationship to predict tool flank wear during end milling of Al/SiCp composites considering process parameters. The developed model (using ANOVA analysis) effectively predicts the tool flank wear of carbide end mill at 95%. Based on researches, the cutting parameter with the most significant impact on tool wear or surface roughness can be found. For example, Karabulut et al. [36] observed improvement of the surface roughness Ra during milling of AMCs using higher cutting speeds and lower feed rates. In this study, the experiment was performed based on the Taguchi method, and ANN evaluated the prediction error. Four layers network was constructed to predict the optimal output data in the propagation phase. The prediction model was developed with the prediction performance of over 97%. The effectiveness of the model results from the usefulness of the ANN in difficult to cut materials milling. In Chandrasekaran et al. [37] work, ANN was applied to the surface roughness prediction model during cylindrical grinding of LM25/SiC/4p MMC. 4-12-1 ANN model with logistic transfer function was created with 94.20% prediction accuracy. The independent input machining parameters on surface roughness were checked with the percentage of wheel velocity contribution −32.47%, feed −26.50%, and workpiece velocity −25.08%. Moreover, Devarasiddappa et al. [38] describe the surface roughness prediction model in end milling of Al-SiCp MMC using ANN. In this investigation, the average error of predictive performance equals 0.31% against 0.53% using RMS models. According to [39], Tsao et al. investigated the radial basis function network (RBFN) and the Taguchi's method with three factors (spindle speed, feed rate, and drill diameter) to predict surface roughness and thrust force in the drilling of WFC200 fabric carbon fiber/epoxy matrix (CFRP). The correlations were received by RBFN and multi-variable regression analysis and compared with experimental data. In general, RBFN is more effective than the multi-variable regression analysis. In Marani et al. [40] research, various adaptive network-based fuzzy inference systems (ANFISs) were applied to predict surface Sensors 2020, 20, 5798 4 of 17 roughness and cutting force during milling of Al-20Mg2Si MMC. The authors selected the two most precise models, and as a result, the root means square error (RMSE) value of surface roughness predicting was 0.2846 and 2.4053 for cutting force. It also means that these models can significantly predict the machinability of MMC. In paper [41], Wu et al. developed the convolutional neural network (CNN) model to automatically identify tool wear during the face milling process of high-temperature alloy Inconel 718. To pre-train, the network model convolutional automatic encoder (CAE) was used. In these studies, the experimental results indicate the model's average recognition precision rate at the level of 96.20%.
The problem of MMCs milling and real-time tool wear assessment is still significant, so optimization and predictive solutions are continually being sought. In most of the work on the machinability of AMCs, the prediction models are based on cutting parameters, size of reinforcement, or cutting tool parameters. There is a lack of work focused on prediction models based on cutting forces and acceleration of vibrations signals during milling of hard to cut Al/SiC (10%) composite. The aim of research involved the diagnosis of tool wear, based on the vibration acceleration and cutting force measurement during end milling of difficult-to-cut AMC with 10% SiC content. The research's essential element was checking the effectiveness of diagnosing the tool condition based on the developed artificial neural networks (ANN) models. For this purpose, MLP networks with different activation functions were selected based on cutting force and vibration acceleration measures in the time domain and frequency domain. Testing models of various structures allowed establishing the most effective networks for predicting tool flank and corner wear.

Materials and Methods
The study used a hard-to-cut material, the Al/SiC matrix composite, as a workpiece. The reinforcement of aluminum cast alloy with the silicon carbide particles (approximately 10% SiC) improves mechanical properties. The metallographic microsections of the AMC composite is shown in Figure 1. Moreover, Table 1 depicts the chemical decomposition of the Al/SiC composite workpiece. A three-edge end mill with diamond coating was selected to carry out milling tests. Table 2 shows the tool characteristics. The problem of MMCs milling and real-time tool wear assessment is still significant, so optimization and predictive solutions are continually being sought. In most of the work on the machinability of AMCs, the prediction models are based on cutting parameters, size of reinforcement, or cutting tool parameters. There is a lack of work focused on prediction models based on cutting forces and acceleration of vibrations signals during milling of hard to cut Al/SiC (10%) composite. The aim of research involved the diagnosis of tool wear, based on the vibration acceleration and cutting force measurement during end milling of difficult-to-cut AMC with 10% SiC content. The research's essential element was checking the effectiveness of diagnosing the tool condition based on the developed artificial neural networks (ANN) models. For this purpose, MLP networks with different activation functions were selected based on cutting force and vibration acceleration measures in the time domain and frequency domain. Testing models of various structures allowed establishing the most effective networks for predicting tool flank and corner wear.

Materials and Methods
The study used a hard-to-cut material, the Al/SiC matrix composite, as a workpiece. The reinforcement of aluminum cast alloy with the silicon carbide particles (approximately 10% SiC) improves mechanical properties. The metallographic microsections of the AMC composite is shown in Figure 1. Moreover, Table 1 depicts the chemical decomposition of the Al/SiC composite workpiece. A three-edge end mill with diamond coating was selected to carry out milling tests. Table 2 shows the tool characteristics.     The cutting tests were conducted on the DECKEL-MAHO DMC 70 V machining center. The cutting speed v c was one variable parameter in tests. To check the repeatability of the measurements, three repetitions were carried out for each cutting speed. Table 3 presents the research plan. The tests were carried out as follows. During each milling pass, the vibration acceleration and cutting force were measured. Additionally, after each tenth pass, the tool flank wears VB B , and the tool corner wear VB C was inspected using a microscope. The tool wear criterium VB imax was equal to 0.3 mm.
During the end milling operation of Al/SiC composite, the following cutting force components were measured in three directions: Also, the acceleration of vibration was measured in the following different directions: • Af (X) for feed direction; • AfN (Y) for normal feed direction; • Ap (Z) for axial direction.
Triaxial piezoelectric charge accelerometer Type 4321 Brüel and Kjaer was selected to measure vibrations in three independent directions during research. This accelerometer is suited to operate temperatures up to 250 • C and measure up to 10,000 Hz. This piezoelectric accelerometer was attached to the MMC workpiece. Table 4 depicts the specifications of the 3D piezoelectric accelerometer. Measuring of cutting forces was carried out using a piezoelectric force sensor, and processing of signals was conducted with the use of Kistler Charge Meter Type 5015A. Table 5 shows the parameters of the piezoelectric dynamometer. In research, three charge meters have been applied. Each of them was applied in a different direction: X, Y, and Z. Figure 2 shows the scheme of the experimental apparatus set up.

Analysis of Tool Wear
The first step in analyzing results is to analyze measured tool flank wear VBB and tool corner wear VBC. In order to determine the relations between the tool wear and cutting time, a third degree polynomial function was selected as the most representative for the tool wear process: where VBi-tool wear, tc-cutting time.
Analysis for the corner wear VBC and the flank wear VBB was carried out separately. The tool wear criterion in both cases was 0.3 mm. The coefficient R 2 indicates an adjustment to the selected mathematical function.

Analysis of Tool Wear
The first step in analyzing results is to analyze measured tool flank wear VB B and tool corner wear VB C . In order to determine the relations between the tool wear and cutting time, a third degree polynomial function was selected as the most representative for the tool wear process: where VB i -tool wear, t c -cutting time.
Analysis for the corner wear VB C and the flank wear VB B was carried out separately. The tool wear criterion in both cases was 0.3 mm. The coefficient R 2 indicates an adjustment to the selected mathematical function.  Based on the determined equation, the average time needed for excessing the critical tool wear value has been calculated and shown in Table 6. Above this value, the unequal tool wear is caused by tool wear adhesion detected during AMC composite machining.  Based on the determined equation, the average time needed for excessing the critical tool wear value has been calculated and shown in Table 6. Above this value, the unequal tool wear is caused by tool wear adhesion detected during AMC composite machining.

(m/min) 500 (m/min) 300 (m/min)
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with v c = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

(m/min) 500 (m/min) 300 (m/min)
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

(m/min) 500 (m/min) 300 (m/min)
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

(m/min) 500 (m/min) 300 (m/min)
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

(m/min) 500 (m/min) 300 (m/min)
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

(m/min) 500 (m/min) 300 (m/min)
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

(m/min) 500 (m/min) 300 (m/min)
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

≈5 ≈16
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

≈5 ≈16
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

≈5 ≈16
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

≈5 ≈16
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

≈5 ≈16
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

≈5 ≈16
The tool wear is significant in all cases; the loss of tool material and the material adhered in the corner is visible, mainly after milling with vc = 900 m/min. While the cutting tool engaged in the hard particles, stress, and forces are suddenly increased. Then, cutting edge chipping is occurs. During machining of AMC material, the secondary adhesion appears in an investigation, as it is a thermomechanical mechanism. However, due to stiff SiC reinforcement, the abrasion wear occurs and provokes flank wear. Almost throughout the tool edge, adhesion is visible, creating an adhered layer or BUL (built-up layer). Additionally, the increases of abrasion and flank wear are caused by these hard particles. Furthermore, due to friction, the rise in temperature is expected, which results in very short cutting time. In Table 7, the tool corner wear of the tool in various cutting conditions is shown. Moreover, the state of flank wear is presented in Table 8.

Analysis of Vibration in Time and Frequency Domain
The next step after the conducted tests was to correlate the tool wear values with measured accelerations of vibrations in the frequency domain and time domain. Based on the generated charts in "Analyzer" software, the tooth passing and tool revolution frequencies were identified. For cutting speeds applied in investigation, the tool revolutions frequencies are: Fr300 = 477 Hz, Fr500 = 796 Hz and, Fr900 = 1433 Hz. Figure 4 depicts the exemplary vibration chart in the time domain. Moreover, in Figure 5, the relation between the diagnosis measures of accelerations of vibrations and tool wear based on milling repetition in various cutting speed are presented.

Analysis of Vibration in Time and Frequency Domain
The next step after the conducted tests was to correlate the tool wear values with measured accelerations of vibrations in the frequency domain and time domain. Based on the generated charts in "Analyzer" software, the tooth passing and tool revolution frequencies were identified. For cutting speeds applied in investigation, the tool revolutions frequencies are: Fr300 = 477 Hz, Fr500 = 796 Hz and, Fr900 = 1433 Hz. Figure 4 depicts the exemplary vibration chart in the time domain. Moreover, in Figure 5, the relation between the diagnosis measures of accelerations of vibrations and tool wear based on milling repetition in various cutting speed are presented.

Analysis of Vibration in Time and Frequency Domain
The next step after the conducted tests was to correlate the tool wear values with measured accelerations of vibrations in the frequency domain and time domain. Based on the generated charts in "Analyzer" software, the tooth passing and tool revolution frequencies were identified. For cutting speeds applied in investigation, the tool revolutions frequencies are: Fr300 = 477 Hz, Fr500 = 796 Hz and, Fr900 = 1433 Hz. Figure 4 depicts the exemplary vibration chart in the time domain. Moreover, in Figure 5, the relation between the diagnosis measures of accelerations of vibrations and tool wear based on milling repetition in various cutting speed are presented.

Analysis of Vibration in Time and Frequency Domain
The next step after the conducted tests was to correlate the tool wear values with measured accelerations of vibrations in the frequency domain and time domain. Based on the generated charts in "Analyzer" software, the tooth passing and tool revolution frequencies were identified. For cutting speeds applied in investigation, the tool revolutions frequencies are: Fr300 = 477 Hz, Fr500 = 796 Hz and, Fr900 = 1433 Hz. Figure 4 depicts the exemplary vibration chart in the time domain. Moreover, in Figure 5, the relation between the diagnosis measures of accelerations of vibrations and tool wear based on milling repetition in various cutting speed are presented.

Analysis of Vibration in Time and Frequency Domain
The next step after the conducted tests was to correlate the tool wear values with measured accelerations of vibrations in the frequency domain and time domain. Based on the generated charts in "Analyzer" software, the tooth passing and tool revolution frequencies were identified. For cutting speeds applied in investigation, the tool revolutions frequencies are: Fr300 = 477 Hz, Fr500 = 796 Hz and, Fr900 = 1433 Hz. Figure 4 depicts the exemplary vibration chart in the time domain. Moreover, in Figure 5, the relation between the diagnosis measures of accelerations of vibrations and tool wear based on milling repetition in various cutting speed are presented.

Analysis of Vibration in Time and Frequency Domain
The next step after the conducted tests was to correlate the tool wear values with measured accelerations of vibrations in the frequency domain and time domain. Based on the generated charts in "Analyzer" software, the tooth passing and tool revolution frequencies were identified. For cutting speeds applied in investigation, the tool revolutions frequencies are: Fr300 = 477 Hz, Fr500 = 796 Hz and, Fr900 = 1433 Hz. Figure 4 depicts the exemplary vibration chart in the time domain. Moreover, in Figure 5, the relation between the diagnosis measures of accelerations of vibrations and tool wear based on milling repetition in various cutting speed are presented.

Analysis of Vibration in Time and Frequency Domain
The next step after the conducted tests was to correlate the tool wear values with measured accelerations of vibrations in the frequency domain and time domain. Based on the generated charts in "Analyzer" software, the tooth passing and tool revolution frequencies were identified. For cutting speeds applied in investigation, the tool revolutions frequencies are: Fr 300 = 477 Hz, Fr 500 = 796 Hz and, Fr 900 = 1433 Hz. Figure 4 depicts the exemplary vibration chart in the time domain. Moreover, in Figure 5, the relation between the diagnosis measures of accelerations of vibrations and tool wear based on milling repetition in various cutting speed are presented.

Analysis of Vibration in Time and Frequency Domain
The next step after the conducted tests was to correlate the tool wear values with measured accelerations of vibrations in the frequency domain and time domain. Based on the generated charts in "Analyzer" software, the tooth passing and tool revolution frequencies were identified. For cutting speeds applied in investigation, the tool revolutions frequencies are: Fr300 = 477 Hz, Fr500 = 796 Hz and, Fr900 = 1433 Hz. Figure 4 depicts the exemplary vibration chart in the time domain. Moreover, in Figure 5, the relation between the diagnosis measures of accelerations of vibrations and tool wear based on milling repetition in various cutting speed are presented.   Based on vibration acceleration, the best results were obtained for the exponential function for all diagnostic measures. The R 2 coefficient represents the matching of the assumed mathematical function to the experimental results. Table 9    Based on vibration acceleration, the best results were obtained for the exponential function for all diagnostic measures. The R 2 coefficient represents the matching of the assumed mathematical function to the experimental results. Table 9 shows R 2 values of diagnosis measures analyzed in the frequency domain (Aifr), and root means square value (RMS) based on the time domain. Based on vibration acceleration, the best results were obtained for the exponential function for all diagnostic measures. The R 2 coefficient represents the matching of the assumed mathematical function to the experimental results. Table 9 shows R 2 values of diagnosis measures analyzed in the frequency domain (Ai fr ), and root means square value (RMS) based on the time domain.

Analysis of Cutting Forces
The next step was to recognize the relationship between the tool wear and cutting force components measure as a diagnostic signal. Figure 6 depicts the correlation between diagnostic measures and tool wear. The R 2 coefficient represents the matching of the exponential mathematical function to the experimental results. Table 10

Analysis of Cutting Forces
The next step was to recognize the relationship between the tool wear and cutting force components measure as a diagnostic signal. Figure 6 depicts the correlation between diagnostic measures and tool wear. The R 2 coefficient represents the matching of the exponential mathematical function to the experimental results. Table 10

Diagnostic Model Based on Artificial Neural Network
Using ANN in this work was to assess the possibility of predicting tool conditions based on measured signals. The low correlation coefficient between tool wear and diagnostic measures indicates the chances of using other methods than regression models. During this work, a multilayer perceptron (MLP) was used to check the tool wear prediction effectiveness. The input data were diagnostic measures based on the analysis of the cutting forces components and vibration acceleration. One of the steps was focused on learning the neural networks using the Broyden-Fletcher-Goldfarb-Shanno algorithm (BFGS), which is considered one of the most effective. The (BFGS) training algorithm, i.e., back propagation, is characterized by high stability and low error sensitivity [21]. Due to select the best ANN, the activation functions were changed in the hidden and the initial layer: linear, logistic, tangent, and exponential. Figure 7 shows the scheme of structure two-layered MLP network model with thirteen of inputs.

Diagnostic Model Based on Artificial Neural Network
Using ANN in this work was to assess the possibility of predicting tool conditions based on measured signals. The low correlation coefficient between tool wear and diagnostic measures indicates the chances of using other methods than regression models. During this work, a multilayer perceptron (MLP) was used to check the tool wear prediction effectiveness. The input data were diagnostic measures based on the analysis of the cutting forces components and vibration acceleration. One of the steps was focused on learning the neural networks using the Broyden-Fletcher-Goldfarb-Shanno algorithm (BFGS), which is considered one of the most effective. The (BFGS) training algorithm, i.e., back propagation, is characterized by high stability and low error sensitivity [21]. Due to select the best ANN, the activation functions were changed in the hidden and the initial layer: linear, logistic, tangent, and exponential. Figure 7 shows the scheme of structure twolayered MLP network model with thirteen of inputs. Searching for the model with the most effective quality of ANN network testing for VBC and VBB prediction, the MLP networks were selected with different activation functions and with the least validation errors. The 50 models were checked, and fourteen models with the best testing efficiency were selected. Table 11 presents the characteristics of selected MLP networks for corner tool wear prediction. The number of random samples was assumed at 70% for the training set, 15% for the test et, and 15% for the validation set. The number of epochs for data was 200. The network name means, for example, MLP 13-1-1: 13-input data, 1-hidden layer, and 1-output.
Based on new experimental data, the mean square error (MSE) was estimated to compare measured and the predicted value of VBC. Figure 8 shows a spread graph of these values for neural network MLP with the best validation quality for four models with the lower MSE. Searching for the model with the most effective quality of ANN network testing for VB C and VB B prediction, the MLP networks were selected with different activation functions and with the least validation errors. The 50 models were checked, and fourteen models with the best testing efficiency were selected. Table 11 presents the characteristics of selected MLP networks for corner tool wear prediction. The number of random samples was assumed at 70% for the training set, 15% for the test set, and 15% for the validation set. The number of epochs for data was 200. The network name means, for example, MLP 13-1-1: 13-input data, 1-hidden layer, and 1-output. Based on new experimental data, the mean square error (MSE) was estimated to compare measured and the predicted value of VB C . Figure 8 shows a spread graph of these values for neural network MLP with the best validation quality for four models with the lower MSE. presents a comparison of the errors of individual MLP networks. The highest error values were observed when the number of neurons in the hidden layer was greater than or equal to nine.
The main criterion for assessing the developed models' quality was to compare the MSE error for new data. These experimental data were not entered into the network learning process. Figure 9 presents a comparison of the errors of individual MLP networks. The highest error values were observed when the number of neurons in the hidden layer was greater than or equal to nine.  The main criterion for assessing the developed models' quality was to compare the MSE error for new data. These experimental data were not entered into the network learning process. Figure 9 presents a comparison of the errors of individual MLP networks. The highest error values were observed when the number of neurons in the hidden layer was greater than or equal to nine. The main criterion for assessing the developed models' quality was to compare the MSE error for new data. These experimental data were not entered into the network learning process. Figure 9 presents a comparison of the errors of individual MLP networks. The highest error values were observed when the number of neurons in the hidden layer was greater than or equal to nine.
The main criterion for assessing the developed models' quality was to compare the MSE error for new data. These experimental data were not entered into the network learning process. Figure 9 presents a comparison of the errors of individual MLP networks. The highest error values were observed when the number of neurons in the hidden layer was greater than or equal to nine.

Conclusions
Based on the experimental results of the present work, the following conclusions can be drawn.
• Analysis of the correlation of the diagnostic measures used, such as vibration acceleration or cutting force with tool wear, shows an unsatisfactory correlation coefficient R 2 . During normal wear of the cutting tool, higher vibration signals appear over time, which can be caused by encountering hard SiC particles in the material's matrix.

•
The use of artificial neural network models with thirteen inputs has significantly improved the correlation coefficient's value. The effectiveness of predicting wear based on forces and vibrations gave satisfactory results, and the lowest MSE error between the measured and predicted data was 0.022.

•
Based on the models, it can be seen that the tangent and logistic activation function in the hidden layer gave the best results in the learning and testing process. However, one or two neurons in the hidden layer bring the significant effects of tool wear prediction. Increasing the number of neurons in the hidden layer does not improve the performance of prediction models.
To sum up, the use of ANN models to predict tool wear during AMC materials milling is a significant prediction tool. Developed MLP models based on specific cutting conditions with input parameters: cutting speed, cutting forces, and accelerations of vibrations are satisfactory to predict tool wear. Based on these signals, effective prediction of tools with diamond coating wear's during end milling of hard-to-cut Al-SiC (10%) composite is allowed (average value of MSE equals 0.027); This enables identifying tool wear's criterium during machining.