A tool wear condition monitoring approach for end milling based on numerical simulation

Computer numerical control (CNC) milling machines, which stable and efficient operation can produce huge economic value, are the most widely used automatic production equipment in modern manufacturing industry. The milling tool is the most critical and vulnerable part in the milling process, its wear state affect directly the surface quality of the machined parts and the normal operation of the machine tool [20, 21, 37]. Therefore, it is particularly important to develop an accurate tool condition monitoring (TCM) method. The above-discussed issue has been addressed in the past few years by developing two general types of TCM methods, direct TCM method and indirect TCM method. The direct TCM method is often seldom adopted because it is greatly affected by the machining environment, such as light, cutting chips, and cutting fluid [49]. In contrast, the indirect TCM method employs certain artificial intelligence (AI) classifier to predict the wear state through collecting sensor signals associated with the tool wear state [33], such as cutting force [15, 50], vibration [6], acoustic emission (AE) [44], and motor current [47], sound [19, 46] signals. Recently, with the development of artificial intelligence (AI) algorithms, more and more scholars have applied AI algorithms in TCM, including support vector machine (SVM) [6,18], random forest (RF) [24, 32, 41], decision tree (DT) [3, 26], artificial neural network (ANN) [1, 9, 12, 22, 23, 28, 34]. However, while these AI methods have yielded encouraging achievements in TCM applications, achieving good wear state prediction performance using these methods relies heavily on large datasets of monitoring signals that are associated with all possible tool wear conditions for model training [14, 45], which is costly and time-consuming for machining processes under different cutting conditions. Although SVMs are suitable for model training with small datasets, they are invalid for sample missing as samples associated with some tool wear conditions are often missing due to the complex conditions encountered in the machining process. Therefore, a low-cost and easy-to-implement method is needed to solve the problem of sample missing and sample insufficiency. In recent years, the numerical simulation technology was promoted by the improvement of computer technology, more and more researchers have begun to pay attention to this technology [16, 27, 40, 43]. For example, Xiang et al. [42] proposed a personalized diagnosis method of shaft based on numerical simulation, combined with wavelet packet transform (WPT) and SVM model to realize the diagnosis of different shaft faults. Gao et al. [7] solved the problem of missing and insufficient samples of bearing faults by combining finite element As an important research area of modern manufacturing, tool condition monitoring (TCM) has attracted much attention, especially artificial intelligence (AI)based TCM method. However, the training samples obtained in practical experiments have the problem of sample missing and sample insufficiency. A numerical simulationbased TCM method is proposed to solve the above problem. First, a numerical model based on Johnson-Cook model is established, and the model parameters are optimized through orthogonal experiment technology, in which the KL divergence and cosine similarity are used as the evaluation indexes. Second, samples under various tool wear categories are obtained by the optimized numerical model above to provide missing samples not present in the practical experiments and expand sample size. The effectiveness of the proposed method is verified by its application in end milling TCM experiments. The results indicate the classification accuracies of four classifiers (SVM, RF, DT, and GRNN) can be improved significantly by the proposed TCM method. Highlights Abstract


Introduction
Computer numerical control (CNC) milling machines, which stable and efficient operation can produce huge economic value, are the most widely used automatic production equipment in modern manufacturing industry. The milling tool is the most critical and vulnerable part in the milling process, its wear state affect directly the surface quality of the machined parts and the normal operation of the machine tool [20,21,37]. Therefore, it is particularly important to develop an accurate tool condition monitoring (TCM) method.
The above-discussed issue has been addressed in the past few years by developing two general types of TCM methods, direct TCM method and indirect TCM method. The direct TCM method is often seldom adopted because it is greatly affected by the machining environment, such as light, cutting chips, and cutting fluid [49]. In contrast, the indirect TCM method employs certain artificial intelligence (AI) classifier to predict the wear state through collecting sensor signals associated with the tool wear state [33], such as cutting force [15,50], vibration [6], acoustic emission (AE) [44], and motor current [47], sound [19,46] signals. Recently, with the development of artificial intelligence (AI) algorithms, more and more scholars have applied AI algorithms in TCM, including support vector machine (SVM) [6,18], random forest (RF) [24,32,41], decision tree (DT) [3,26], artificial neural network (ANN) [1,9,12,22,23,28,34]. However, while these AI methods have yielded encouraging achievements in TCM applications, achieving good wear state prediction performance using these methods relies heavily on large datasets of monitoring signals that are associated with all possible tool wear conditions for model training [14,45], which is costly and time-consuming for machining processes under different cutting conditions. Although SVMs are suitable for model training with small datasets, they are invalid for sample missing as samples associated with some tool wear conditions are often missing due to the complex conditions encountered in the machining process.
Therefore, a low-cost and easy-to-implement method is needed to solve the problem of sample missing and sample insufficiency. In recent years, the numerical simulation technology was promoted by the improvement of computer technology, more and more researchers have begun to pay attention to this technology [16,27,40,43]. For example, Xiang et al. [42] proposed a personalized diagnosis method of shaft based on numerical simulation, combined with wavelet packet transform (WPT) and SVM model to realize the diagnosis of different shaft faults. Gao et al. [7] solved the problem of missing and insufficient samples of bearing faults by combining finite element As an important research area of modern manufacturing, tool condition monitoring (TCM) has attracted much attention, especially artificial intelligence (AI)-based TCM method. However, the training samples obtained in practical experiments have the problem of sample missing and sample insufficiency. A numerical simulation-based TCM method is proposed to solve the above problem. First, a numerical model based on Johnson-Cook model is established, and the model parameters are optimized through orthogonal experiment technology, in which the KL divergence and cosine similarity are used as the evaluation indexes. Second, samples under various tool wear categories are obtained by the optimized numerical model above to provide missing samples not present in the practical experiments and expand sample size. The effectiveness of the proposed method is verified by its application in end milling TCM experiments. The results indicate the classification accuracies of four classifiers (SVM, RF, DT, and GRNN) can be improved significantly by the proposed TCM method.
The optimized model provide effectively missing • samples and expand sample size.
Experimental results show the proposed method • improves notably the performance of TCM.
A tool wear condition monitoring approach for end milling based on numerical simulation simulation (FEM) and Generative adversarial networks (GANs), and provided complete training samples for AI models. The metal cutting process can be understood as a process in which the tool and the workpiece move and collide with each other. The actual machining process can be simulated by establishing models and mathematical expressions. At present, there are a lot of commercial software (such as Deform, AdvantEdge, Abaqus.) in the market that encapsulate the above process in the software to bring convenience to users. The rich functions of these softwares provide the potentials to simulate physical signal corresponding to tool wear state, which can overcome the problem of sample missing and insufficient. Therefore, a novel tool wear condition monitoring method based on numerical simulation is proposed in this paper, and the remainder of this paper is organized as follows. Section 2 introduces the basic working principles of the proposed method, including numerical simulation based on Johnson-Cook (J-C) constitutive model, parameter optimization of the J-C model, and the framework of the proposed method. Experimental investigations with end milling TCM are given in Section 3. Section 4 analyzes the performance of the proposed method. Finally, conclusions are given in Section 5.

Numerical simulation based on J-C model
The essence of the cutting process is that the workpiece material from elastic deformation to the material yield point under the action of external forces, which causes the plastic deformation of workpiece and finally to the process of fracture. In this process, the tool contact and rub against with the workpiece surface and chips to produce wear, cutting force and heat will also be generated between the tool and workpiece. In cutting simulation, material constitutive models are employed to describe this complex process, and the J-C model is often used because it can describe the behavior of high temperature, high strain, and high strain rate in the cutting process. The formula of the J-C model is as follows [36]: where A (MPa) is the initial yield stress, B (MPa) is the strain hardening coefficient, ε is the the plastic strain, n is the stain hardening exponent, C is the strain rate sensitivity coefficient, ε' and ε 0 ' are the plastic strain rate (s −1 ) and reference plastic strain rate (s −1 ), respectively, T is the deformation temperature of the workpiece (°C), T 0 is room temperature (20°C), T melt is the melting temperature of the material (°C), and m is the temperature softening exponent [13]. the three individual terms separately enclosed within parentheses on the right side of formula (1), respectively, represent the strain strengthening effect of the material, the relationship between σ and the natural logarithm of the relative strain rate, and the exponential relationship between σ and temperature.
Because of the rich material library and the specialized cutting module in software DEFORM, it has attracted the attention of many researchers to the software. Shao et al. [35] adopted DEFORM to study the thermodynamic constitutive equation of Ti-6Al-4V and predicted the tool wear depth. Klocke et al. [17] utilized DEFORM to inverse the constitutive equations and damage criteria of AISI 1045 and Inconel 718, and verified the effectiveness of the method by comparing simulation results with experimental results. Thus, the software DEFORM is used in this paper to simulate the end milling process and obtain the missing wear samples.

Parameter optimization
The benchmark value of five parameters, A, B, n, C, m, in the J-C model with certain workpiece material can be obtained from split Hopkinson pressure bar (SHPB) tests and static tensile tests [2,30]. For example, the benchmark value of the five parameters are shown in Table 1 when the workpiece material is AISI 1045. However, these values of model parameters may not conform the practical cutting process because of different cutting environment and other various factors, so it is necessary to optimize these model parameters [4]. Considering the cost and time of experiments, orthogonal experiment is adopted to select the best parameter combination.
For the metrics, Kullback-Leibler (KL) [5,8] divergence and cosine similarity are used as the evaluation indexes of the orthogonal experiment. The KL divergence measures the difference in probability distribution of two groups of signal, and the closer the value of KL is to 0, the more similar the two groups of signal are. The formula of KL divergence is as follows [5]: where p(X) and q(Y) represent the probability density of two groups of signal, respectively. The cosine similarity evaluates the similarity of two groups of signal through calculating their cosine value, and the calculation formula is as follows: The closer the value of cos(θ) is to 1, the more similar the two groups of signal are. In actual engineering, it is generally considered that cos(θ) > 0.6 meets the requirements [29].

Framework of the proposed method
In this paper, a new TCM method based on numerical simulation is proposed to compensate missing samples and expand sample size. The framework of the proposed method is show in Figure 1, and the three steps of the proposed TCM are outlined in detail as follows.
Step 1: Conduct a limited number of milling TCM experiments to obtain measured cutting force signal samples, and obtain the best parameter combination of the J-C model under normal wear state of tool .
First, cutting force signal data is obtained in the milling experiments under several selected tool wear conditions by means of a three-component dynamometer. Second, the numerical model based on the J-C model is built in DEFORM, and the best parameter combination is selected by the orthogonal experiment with the comparative analysis of the simulation signal and the experimental signal under the normal tool condition, in which the criteria is minimize KL divergence satisfying the cos(θ) > 0.6.
Step2: Simulate missing sample and obtain complete wear training samples.  Root mean square

Frequency domain
Mean of power spectrum High-low ratio of power spectrum Missing tool wear categories can be defined from the experimental results, that is, these categories not occurred in experiments are missing tool wear categories. These missing tool wear categories can be simulated based on the optimal numerical model above, and the corresponding cutting force signal could be obtained. After supple-menting missing samples, several feature parameters (shown in Table  2) of time, frequency, and time-frequency domains (wavelet energy coefficient) for each sample are extracted to form a feature parameter set [7,25,37,48]. Here, the time-frequency domain parameter was obtained using the three-layer wavelet packet transform (WPT) with the Daubechies 2 (db2) wavelet basis function.

Skewness of bandpower
Step 3: Identify tool wear condition through AI classifiers.
The training set consists of simulated samples and measured samples, and inputs to train certain AI model. The trained AI model can be employed to identify unknown wear condition of tools.

Description of experiments
The experimental setup for the end milling TCM experiments under various operating conditions is illustrated in Figure 2. The experimental platform was built on a DMTG VDL850A vertical machining center as shown in Figure 2(a). The tools used in the experiments were uncoated three-flute tungsten steel end milling cutters (Φ 10 mm), and the workpiece material was AISI 1045 steel with dimensions of 300 mm × 100 mm × 80 mm. A three-component dynamometer (Kistler 9139AA) was mounted between the workpiece and the machine table to measure the cutting forces in the form of charges (shown in Figure  2(b)). The cutting force signal (Axial force, radial force and tangential force) was collected by a charge amplifier (Kistler 5073 A4) and a data acquisition instrument (Kistler 5697 A1) with a sampling frequency of 12 kHz (shown in Figure 2(c)). As shown in Figure 2(d), the flute wear of each cutting tool was measured after each machining stage using a GP-300C optical microscope, which represented individual milling stages. It is noteworthy that we found the influence of the length of rake face wear (KB) on the surface roughness of the workpiece after milling was greater than that of flank wear (VB) and the depth of rake face wear (KT) [47]. Therefore, KB was employed as the tool wear criterion in the experiments, and the tool wear value after each cutting stage was defined as the maximum KB value of the three teeth. Figure 3 illustrates the progression of tool wear after finishing a single workpiece surface 1, 5, and 10 times (i.e., 1, 5, and 10 milling stages). The experimental measurements employed eight operational conditions comprising random combinations of three operational parameters: spindle speed, depth of cut, and feed rate. The operational parameters employed in the experiments are listed in Table 3. Each case began with a new tool under the eight operational conditions and ran 10 milling stages, and the largest tool wear value obtained after completing those milling stages in all eight conditions was 2.054 mm. Therefore, the milling tool wear condition was divided into 7 categories according to tool wear intervals of 0.3 mm, and the numbers of samples observed for all conditions in all categories are listed in Table 4. It can be found in Table 4 that samples indicative of individual tool wear categories were not always available under all cutting conditions. These represent missing samples.

Numerical simulation of end milling process
First, simulation modeling was carried out according to the dimensions of workpiece and milling tool in the experiment, then the models are imported into DEFORM for processing. Second, the general preprocessing module of DEFORM was selected in the main interface, and the unit standard was set as SI. The workpiece was set as a plastic body and the material was set as AISI 1045. The tool was set as a rigid body and the material was set as tungsten carbide steel. The mechanical characteristics of these materials were imported from the rich material library in DEFORM. Then, the J-C model was selected for the workpiece material model, and the benchmark parameters of J-C model are shown in Table 1. The number of meshes for the workpiece and tool were 40,000 and 10,000, respectively. Considering the efficiency of remeshing during calculation to reduce the time of the entire milling simulation calculation, the mesh type in the model was set to a tetrahedral mesh. And the mesh size could be set to 1/3 of feed rate per spindle speed [31,39], thus according to Table 3 the mesh size could be calculated to 0.053 mm (400/2500/3 = 0.053mm). Reasonable simulation speed and accuracy was ensured by applying local refinement to the machined surface, and the refinement ratio was 0.01. After inspection, the maximum mesh size of the workpiece and the tool is less than 1/5 of the feed. Figure 4(a), (b) and (c) show the milling tool model, meshing refinement, and simulation running in DEFORM, respectively.
For boundary conditions, the bottom of the workpiece was fixed in the three directions (X, Y, and Z), the entire surface of the workpiece and tool were selected for heat exchange with the environment, the three operational parameters (spindle speed, depth of cut, and feed rate) of cutting processing were set in according to actual conditions in Table 3. The number of simulation steps was set 24000, and the sampling interval was 8.33 × 10 -5 s and the sampling time was 1 s. In modeling the tool/workpiece contact, the friction coefficient between the tool and the workpiece was 0.6 [10], and the thermal conductivity was 45 W·m -1 ·C -1 [11]. Finally, after simulation, the cutting force data was exported and saved in the post-processing.

Parameter optimization by orthogonal experiments
In this section,three levels of each parameter in Table 1 were set as 80%, 100% and 120% of the benchmark value (shown in Table  5), and an orthogonal table of five factors and three levels (L 18 (5 3 )) was employed to conduct the orthogonal experiments, as shown in Table 6. The operational parameters (speed, depth of cut, and feed rate) used in the orthogonal experiment were 2500 rpm, 0.6 mm, and 450 mm/min, respectively. Therefore, the experimental data of the same parameters were selected to calculate the KL divergence and cosine similarity, and the comparison data is taken one second (12,000 data points) after the milling tool completely entered the workpiece. The KL divergence and cosine similarity results of the 18 cutting tests are shown in Table 6.
The KL divergence and cosine similarity results of each orthogonal experiment case were presented in Table 6, in which the values of KL divergence and cosine similarity are the average of three directions (X, Y and Z). By main effect analysis, the best parameter combination is A(2) B(1) n(2) m(2) C(2), as shown in Table 6, the corresponding average KL divergence is 2.6035, which is smaller than the other com-  binations, and the average cosine similarity values (= 0.7389) greater than 0.6. The simulated and measured time series data corresponding to the best parameter combination under normal tool condition are presented in Figure 5 in the X, Y, and Z directions. It can be seen that the simulated signals differ slightly from the measured signals.

Simulation signal verification
The validity of the simulated samples were tested by comparing 1.0 s (i.e., 12,000 sampling points) of the simulated and measured cutting force signals obtained for operational condition 6 under different tool wear categories. Figures 6-8 show the time series data and the corresponding frequency spectra of the simulated and measured signal in the X, Y, and Z directions under the 2-nd, 4-th and 10-th tool wear categories. It can be seen that, under these tool wear categories, the simulated signals differ slightly from the measured signals in terms of the amplitudes of the peaks in the frequency domain, while the frequency peak positions agree well.

Sample augmentation
As shown in Figure 6, different tool wear states were simulated based on the optimal numerical simulation model according to the tool wear lengths and wear shapes obtained during the experiments, and the linear interpolation method was applied to achieve KB values less than the threshold for missing categories according to the observed tool wear value trends. Three examples of wear categories added based on the FEM model are presented in Fig. 6 for operational condition 6.
According to Table 4, the 1-st and 7-th wear categories were generally missing under the operational conditions considered. Therefore, we consider missing samples only for the 7-th category here owing to article length limitations. Cases 2, 4, 5, 7, and 8 were employed as the training dataset because all of these are missing the 7-th wear category, and the remaining three cases 1, 3, and 6, which contain the 7-th category but not the 1-st category, were employed as the testing dataset. Then, 12,000 data points (1 s) were selected for the simulated and measured samples of each category, which are evenly divided into 20 groups. The optimal numerical simulation model model is employed to simulate the testing cases (Cases 1, 3, and 6) to increase the number of samples in the training dataset. Each simulated case contains 12 different tool KB samples involving all wear categories, and the sample sizes of the measured and simulated training sets were 900 (45×20) and 560 (28×20) not including the 1-st category, respectively. Accordingly, we employed three separate datasets to train the AI classifiers, which included the measurement dataset composed of only measured samples, the simulation dataset composed of only simulated samples, and the measurement + simulation dataset composed of measured and simulated samples, with a total of 1460 (900+560) samples.

Classification result and analysis
These feature parameters listed in Table 2 were calculated for the individual samples in the training and testing datasets, and employed as the input parameters for training and testing classifiers. Four common algorithms, SVM, RF, DT, and a generalized regression neural network (GRNN), were adopted to verify the generalized ability of the proposed method. Here, the SVM classifier selects the radial basis kernel function, and the penalty factor and kernel function radius are set to 3 and 1, respectively. The RF classifier was executed with the Randomforest-matlab open source toolbox developed by Abhishek Jaiantilal (https://github.com/ajaiantilal/ randomforest-matlab), and the number of decision trees was set to 500. The DT classifier was used the toolbox function ClassificationTree.fit in MATLAB R2016, and the parameters of 'name' and 'value' were selected as 'model' and 'graph', respectively. The value of SPREAD in the GRNN classifier was set to 0.1. Table 7 shows the classification accuracies of four classifiers with the testing dataset. It can be found from Table 7, that the average classification accuracy obtained by the classifiers based on the simula-tion dataset is greater than that based on the measurement dataset by 11.42%, although the sample size of the simulation datset is less than that of the measurement dataset. There are two reasons for this result, one is the simulation dataset makes up missing categories not occurred in experiments, the other is the cutting conditions corresponding to the simulation dataset are consistent with that to the testing dataset. In addition, the average classification accuracy obtained by the classifiers based on the measurement + simulation dataset is greater than that based on the measurement dataset by 22.83%, and the classification accuracies obtained by the SVM, RF, and DT classifiers based on the measurement + simulation dataset are above 90%. Therefore, it can be considered that the proposed TCM method can improves significantly the classification accuracies of many classifiers.
The classification accuracy of each wear category obtained using the four classifiers trained using the three different training datasets are presented in Figures 10-13, respectively. We note from the figures  b) c) a) that the classification accuracy of the four classifiers trained with the measurement dataset is not high for most of the wear categories. In contrast, the classification accuracy of the four classifiers trained with the simulation dataset and the measurement + simulation dataset are generally much greater (except for wear category 3 in RF and wear category 4 in GRNN, which are lower).

Conclusion
This paper proposed a feasible TCM method for obtaining various samples of tool wear condition by numerical simulation based on J-C model to overcome the problem of sample missing and sample insufficiency in real experiments. First, a numerical model based on Johnson-Cook model is established, and the model parameters are optimized through orthogonal experiment technology with the practical experiments, in which the Kullback-Leibler divergence and cosine similarity are used as the evaluation indexes. Second, samples under various tool wear categories are obtained by the optimized numerical model above to provide missing samples not present in the practical experiments and expand sample size. The effectiveness of the proposed method is verified by its application in end milling TCM experiments. The results indicate the classification accuracies of four classifiers (SVM, RF, DT, and GRNN) can be improved significantly by the proposed TCM method, and we believe that the proposed method has similar effects on other AI classifiers. In addition, although this study is about tool wear condition monitoring approach for end milling, the proposed method is also applicable to other machining process.