The detection of tool breakage and tool wear during cutting has been studied using various methods. In past research, touch and direct measurement using a dynamometer, touch and indirect measurement using vibration/acoustic emission sensors, and non-touch and indirect measurement using the motor power/current measurement of each operating axis have been examined [1] [2] [3] [4] . Studies on tool breakage and tool wear as target anomalies for detection using motor data with a neural network have achieved a 97% accuracy with aerospace materials [5] [6] . Image processing based on machine learning has recently been studied in various processes including machining [7] [8] [9] . However, many practical issues remain. Chief among these is the target anomalies. Anomaly phenomena such as chip biting, tool vibration (excluding chattering), and material deviation often occur in mass production, but these have not received adequate research attention. Another issue is how to clarify the anomaly correlation: as the correlation between cutting phenomena and obtained data has not been formalized, it is difficult to apply correlation to anomaly detection in a mass production context. A third issue relates to anomaly detection methodology. While machine learning and pattern recognition techniques, which are frequently used, are excellent for gaining insight from the acquired data, parameter tuning is required for waveform discretization and feature extraction, which requires specialized knowledge of data processing.
Our objective in this study is to solve the un-formalized (tacit knowing) problem, which previously relied on machining experts and data scientists, and to propose anomaly detection methods that can easily be applied to mass production. To this end, we first focused on machining anomalies that occur in mass production finish cutting, especially for low mix high volume and with stainless steel, and endeavored to clarify this phenomenon during cutting by using reference data for target anomalies. Next, we adopted the motor current value of each operating axis for detecting machining anomalies and investigated the correlation between target anomalies and motor data. We developed a formalized anomaly detection method using waveform
The detection of tool breakage and tool wear during cutting has been studied using various methods. In past research, touch and direct measurement using a dynamometer, touch and indirect measurement using vibration/acoustic emission sensors, and non-touch and indirect measurement using the motor power/current measurement of each operating axis have been examined [1] [2] [3] [4] . Studies on tool breakage and tool wear as target anomalies for detection using motor data with a neural network have achieved a 97% accuracy with aerospace materials [5] [6] . Image processing based on machine learning has recently been studied in various processes including machining [7] [8] [9] . However, many practical issues remain. Chief among these is the target anomalies. Anomaly phenomena such as chip biting, tool vibration (excluding chattering), and material deviation often occur in mass production, but these have not received adequate research attention. Another issue is how to clarify the anomaly correlation: as the correlation between cutting phenomena and obtained data has not been formalized, it is difficult to apply correlation to anomaly detection in a mass production context. A third issue relates to anomaly detection methodology. While machine learning and pattern recognition techniques, which are frequently used, are excellent for gaining insight from the acquired data, parameter tuning is required for waveform discretization and feature extraction, which requires specialized knowledge of data processing.
Our objective in this study is to solve the un-formalized (tacit knowing) problem, which previously relied on machining experts and data scientists, and to propose anomaly detection methods that can easily be applied to mass production. To this end, we first focused on machining anomalies that occur in mass production finish cutting, especially for low mix high volume and with stainless steel, and endeavored to clarify this phenomenon during cutting by using reference data for target anomalies. Next, we adopted the motor current value of each operating axis for detecting machining anomalies and investigated the correlation between target anomalies and motor data. We developed a formalized anomaly detection method using waveform Abstract A cutting anomaly can be detected by using machine learning and pattern recognition in addition to the conventional method of using cutting knowledge to determine the criteria of detection. However, it is difficult to guarantee that all cutting anomalies can be detected during mass production due to various events that can occur. Moreover, machine learning and pattern recognition are not systemized for use in mass production. In this work, we investigated the detection of turning anomalies during mass production under optimized cutting conditions. We applied a method that utilizes the motor current of each operating axis to monitor the machining state without affecting the machining process and determines the correlation between turning anomalies and motor data. Our target was the unsteady anomalies that appear in mass production, such as chip biting and tool vibration. On the basis of the obtained correlation, we developed a formalized anomaly detection method using traditional statistics and a systemized anomaly detection method using discretization and pattern recognition based on the Mahalanobis Taguchi method with auto parameter tuning to eliminate the need for detailed analysis based on knowledge of cutting phenomena. Both methods achieved a detection accuracy of over 98%.
The detection of tool breakage and tool wear during cutting has been studied using various methods. In past research, touch and direct measurement using a dynamometer, touch and indirect measurement using vibration/acoustic emission sensors, and non-touch and indirect measurement using the motor power/current measurement of each operating axis have been examined [1] [2] [3] [4] . Studies on tool breakage and tool wear as target anomalies for detection using motor data with a neural network have achieved a 97% accuracy with aerospace materials [5] [6] . Image processing based on machine learning has recently been studied in various processes including machining [7] [8] [9] . However, many practical issues remain. Chief among these is the target anomalies. Anomaly phenomena such as chip biting, tool vibration (excluding chattering), and material deviation often occur in mass production, but these have not received adequate research attention. Another issue is how to clarify the anomaly correlation: as the correlation between cutting phenomena and obtained data has not been formalized, it is difficult to apply correlation to anomaly detection in a mass production context. A third issue relates to anomaly detection methodology. While machine learning and pattern recognition techniques, which are frequently used, are excellent for gaining insight from the acquired data, parameter tuning is required for waveform discretization and feature extraction, which requires specialized knowledge of data processing.
Our objective in this study is to solve the un-formalized (tacit knowing) problem, which previously relied on machining experts and data scientists, and to propose anomaly detection methods that can easily be applied to mass production. To this end, we first focused on machining anomalies that occur in mass production finish cutting, especially for low mix high volume and with stainless steel, and endeavored to clarify this phenomenon during cutting by using reference data for target anomalies. Next, we adopted the motor current value of each operating axis for detecting machining anomalies and investigated the correlation between target anomalies and motor data. We developed a formalized anomaly detection method using waveform Abstract A cutting anomaly can be detected by using machine learning and pattern recognition in addition to the conventional method of using cutting knowledge to determine the criteria of detection. However, it is difficult to guarantee that all cutting anomalies can be detected during mass production due to various events that can occur. Moreover, machine learning and pattern recognition are not systemized for use in mass production. In this work, we investigated the detection of turning anomalies during mass production under optimized cutting conditions. We applied a method that utilizes the motor current of each operating axis to monitor the machining state without affecting the machining process and determines the correlation between turning anomalies and motor data. Our target was the unsteady anomalies that appear in mass production, such as chip biting and tool vibration. On the basis of the obtained correlation, we developed a formalized anomaly detection method using traditional statistics and a systemized anomaly detection method using discretization and pattern recognition based on the Mahalanobis Taguchi method with auto parameter tuning to eliminate the need for detailed analysis based on knowledge of cutting phenomena. Both methods achieved a detection accuracy of over 98%.
The detection of tool breakage and tool wear during cutting has been studied using various methods. In past research, touch and direct measurement using a dynamometer, touch and indirect measurement using vibration/acoustic emission sensors, and non-touch and indirect measurement using the motor power/current measurement of each operating axis have been examined [1] [2] [3] [4] . Studies on tool breakage and tool wear as target anomalies for detection using motor data with a neural network have achieved a 97% accuracy with aerospace materials [5] [6] . Image processing based on machine learning has recently been studied in various processes including machining [7] [8] [9] . However, many practical issues remain. Chief among these is the target anomalies. Anomaly phenomena such as chip biting, tool vibration (excluding chattering), and material deviation often occur in mass production, but these have not received adequate research attention. Another issue is how to clarify the anomaly correlation: as the correlation between cutting phenomena and obtained data has not been formalized, it is difficult to apply correlation to anomaly detection in a mass production context. A third issue relates to anomaly detection methodology. While machine learning and pattern recognition techniques, which are frequently used, are excellent for gaining insight from the acquired data, parameter tuning is required for waveform discretization and feature extraction, which requires specialized knowledge of data processing.
Our objective in this study is to solve the un-formalized (tacit knowing) problem, which previously relied on machining experts and data scientists, and to propose anomaly detection methods that can easily be applied to mass production. To this end, we first focused on machining anomalies that occur in mass production finish cutting, especially for low mix high volume and with stainless steel, and endeavored to clarify this phenomenon during cutting by using reference data for target anomalies. Next, we adopted the motor current value of each operating axis for detecting machining anomalies and investigated the correlation between target anomalies and motor data. We developed a formalized anomaly detection method using waveform Abstract A cutting anomaly can be detected by using machine learning and pattern recognition in addition to the conventional method of using cutting knowledge to determine the criteria of detection. However, it is difficult to guarantee that all cutting anomalies can be detected during mass production due to various events that can occur. Moreover, machine learning and pattern recognition are not systemized for use in mass production. In this work, we investigated the detection of turning anomalies during mass production under optimized cutting conditions. We applied a method that utilizes the motor current of each operating axis to monitor the machining state without affecting the machining process and determines the correlation between turning anomalies and motor data. Our target was the unsteady anomalies that appear in mass production, such as chip biting and tool vibration. On the basis of the obtained correlation, we developed a formalized anomaly detection method using traditional statistics and a systemized anomaly detection method using discretization and pattern recognition based on the Mahalanobis Taguchi method with auto parameter tuning to eliminate the need for detailed analysis based on knowledge of cutting phenomena. Both methods achieved a detection accuracy of over 98%.
The detection of tool breakage and tool wear during cutting has been studied using various methods. In past research, touch and direct measurement using a dynamometer, touch and indirect measurement using vibration/acoustic emission sensors, and non-touch and indirect measurement using the motor power/current measurement of each operating axis have been examined [1] [2] [3] [4] . Studies on tool breakage and tool wear as target anomalies for detection using motor data with a neural network have achieved a 97% accuracy with aerospace materials [5] [6] . Image processing based on machine learning has recently been studied in various processes including machining [7] [8] [9] . However, many practical issues remain. Chief among these is the target anomalies. Anomaly phenomena such as chip biting, tool vibration (excluding chattering), and material deviation often occur in mass production, but these have not received adequate research attention. Another issue is how to clarify the anomaly correlation: as the correlation between cutting phenomena and obtained data has not been formalized, it is difficult to apply correlation to anomaly detection in a mass production context. A third issue relates to anomaly detection methodology. While machine learning and pattern recognition techniques, which are frequently used, are excellent for gaining insight from the acquired data, parameter tuning is required for waveform discretization and feature extraction, which requires specialized knowledge of data processing.
Our objective in this study is to solve the un-formalized (tacit knowing) problem, which previously relied on machining experts and data scientists, and to propose anomaly detection methods that can easily be applied to mass production. To this end, we first focused on machining anomalies that occur in mass production finish cutting, especially for low mix high volume and with stainless steel, and endeavored to clarify this phenomenon during cutting by using reference data for target anomalies. Next, we adopted the motor current value of each operating axis for detecting machining anomalies and investigated the correlation between target anomalies and motor data. We developed a formalized anomaly detection method using waveform 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to COVID-19) processing and traditional statistics based on the obtained correlation. We also carried out systemized anomaly detection with discretization and pattern recognition based on the Mahalanobis Taguchi method [10] in which auto parameter tuning to reduce the cutting phenomenon analysis process was applied using a pattern recognition technique. We compared the detection accuracy of both methods under mass production conditions. Table 1 lists the target turning anomalies, process conditions, and reference data used in this study. In addition to the workpiece material, we include cutting area and dimensions and machining conditions such as cutting frequency and depth of cut, as well as possible defects and their criteria. The cutting frequency is calculated as the number of workpiece revolutions [round/sec] × number of teeth. Anomaly Ⅰ is the appearance defect in outer diameter turning, and anomalies Ⅱ and Ⅲ are dimensional defects in inner diameter turning. One of the goals of this study is to capture the transition from a normal waveform to an anomaly waveform for these target anomalies. The process charts of these anomalies are described in Section 3. We analyzed the phenomena of a target anomaly to obtain the correlation between a target anomaly and the motor data and acquired reference data for clarifying the phenomena of the target anomalies. The method used for reference data acquisition for anomaly I is described in Section 3, along with a detailed diagram. For anomalies Ⅱ and Ⅲ, dimensional variations need to be determined. Therefore, in addition to internaldiameter measurement using Mitutoyo "SBM-CX", we obtained surface roughness Ra measured in the depth direction using Mitutoyo "S-3000", roundness measured on the inner diameter surface in the circumferential direction using Mitutoyo "RA-2200", and the image of the tool edge taken with "Dino Lite" as reference data. Figure 1 shows the direction of cutting force F in turning. The views in the direction of the blue and red arrows in (a) correspond to the views of (b) and (c), respectively. In cutting theory, FR is the main component force, Fz is the feed component force, and FX is the back-component force. Figure 2 shows a schematic diagram of the equipment used in the target anomaly detection process and the function of each motor installed in the equipment. The equipment consists of a turning center equipped with an automatic tool changer (ATC) that can set various tools in the tool turret in advance. The tool can be automatically changed using a numerical control program. The turning center has four operating axes: spindle, tool X-axis, tool Y-axis, and tool turret, and each axis is driven by a motor. When the motor moves to the commanded position, the control unit calculates the required torque and rotational speed. Next, the control unit inputs the current value and frequency required for torque and speed output to the motor. However, actual cutting conditions require values greater than the calculated ones depending on the actual load condition. For this purpose, the current value and frequency input to the motor are controlled by monitoring and feeding back the actual state using an angle encoder attached to the motor. A constant current continues to be output when stopping on the spot as well as when moving, and the current value and frequency are changed to suppress displacement. If each component of F is replaced with a shaft operated by a motor installed in the turning center, FR is the spindle axis, FX is the tool X-axis, and FZ corresponds to the tool Z-axis. Table 2 lists the details of the acquired data. The spindle, tool X-axis, and tool Z-axis motor currents are acquired to detect changes in F based on the feedback-current values. The data were acquired using software from a Controller manufacturer, and the sampling frequency was 250 Hz, which is at least five times faster than the cutting frequency of the target anomalies. After acquiring current waveform as time series data, the state was observed using fast Fourier transform (FFT) and short-time Fourier transform (STFT) in addition to the raw waveform. The tool-turret axis was used as an indicator of tool change. Since the tool turret rotates during tool change, the current value changes sharply during rotation. Therefore, it can be used as an indicator for tool change by extracting the peak value, and the waveform of the desired tool can be extracted from continuous process data. Figure 3 (a) shows an overview of the outer-diameter-side turning process in which anomaly Ⅰ occurs. The outer diameter finishes in a single step using a throwaway tip (shown in Fig. 2 ) as tool 1. Machining proceeds in the Z direction from the +Z direction, and the side surface on the -Z side is chucked with six chuck jaws. Figure 3 (b) illustrates the reference data acquisition method for this anomaly. Here, the anomaly is that the material surface remains after processing. We measured the height deviation by changing the reference plane described in the figures. These are used as reference data to evaluate the effects of chucking defects and material straightness. Since the height deviation (ΔHr) is based on the side of the material, it is equivalent to straightness. The height deviation (ΔHc) is based on the end face after machining, so it is equivalent to the tilt during machining. Configuration of reference data. Figure 4 shows the reference data and motor waveform during machining with tool 1. The top image in (b) shows the surface-remaining state indicated by the circle. We can see here that the waveform of the Z-axis motor has a significant correlation with anomaly Ⅰ. If ΔHr is relatively large and ΔHc is also large, it indicates that the raw material height deviation affects this anomaly. Even if the anomaly product's ΔHr is smaller than the normal product's ΔHr, an anomaly will occur. Therefore, ΔHr and ΔHc are not in a proportional relationship, so we can conclude that the straightness of the material does not affect this anomaly, and a problem during chucking is suspected. When observing this Z-axis motor waveform, we can see that vibration occurs in the anomaly waveform in (b), while it does not occur in the normal waveform in (a). In addition, the vibration is largest in the initial stage and is damped as the machining progresses from the +Z direction's end face to the chuck side. FFT analysis showed that this anomaly waveform had an extremely large peak at 20 Hz, which was equal to the cutting frequency. The observation result of the motor current waveform indicates that the vibration synchronized with the rotation because vibration of the rotation frequency was generated. Furthermore, based on the surface of the material-remaining area, this factor indicates the tilt of the workpiece. Figure 6 shows the workpiece-state-estimation diagram derived from the above estimation. Figure 6 (a) shows the normal chucked state and (b) shows the tilt chuck state. The phenomenon here is that the vibration of the motor current waveform is large in the initial stage and small in the work period. It can be explained by the fact that the difference in the depth of cut is mitigated from the right side of Fig. 6 (b) at the early stage of machining to the left side at the late stage of machining. Table 3 shows the extent to which the tilt chuck correlates with the raw, FFT, and STFT waveforms of the spindle, tool X-axis, and tool Z-axis, respectively. Best filter for raw wave -Bandpass filter with cutting frequency 1: Detection is easy 2: Detection is possible
The correlation was strong on the tool-axis side, and no correlation was observed on the spindle. This relationship is presumably affected by the inertial force. The spindle axis rotates at about 2000 rpm with respect to the tool axis, which operates at a speed close to stopping. We assume that a small change in F is absorbed by the inertial force in the spindle. Although there is a small difference between the tool axes, the tool Z-axis feed is easier to correlate. In the FFT and STFT waveforms, the peaks appear in the cutting frequency in the tilt chuck, but the correlation was inferior to that of the raw waveform for use in anomaly detection. On the basis of these results, we conclude that the raw waveform of the tool Z-axis is optimal for anomaly detection. For easy detection from the waveform, it is better to carry out waveform processing using a bandpass filter that extracts only the cutting frequency. Details of the waveform processing are described in Section 4.1. Figure 6 shows a process chart of a drilling operation in which anomaly Ⅱ occurs. Hole machining is carried out by roughing with tool 2, intermediate finishing with tool 3, and finishing with tool 4. Figure 7 shows the dimensiontransition diagram, which is the reference data for anomaly Ⅱ. The horizontal axis is the number of holes, the vertical axis is the dimension value, and one plot represents one workpiece. The target hole has a tolerance of 18 μm, and the upper and lower limits are as shown in Fig. 7 . The phenomenon that the hole size shrinks without any indication and then recovers can be observed multiple times. First, we observed workpieces with reduced diameter and workpieces before and after this reduction. The reference data were compared with the motor-waveform data of each axis of tools 2, 3, and 4. Tools 2 and 3 did not show any correlation with the reference data, but in the finishing of tool 4, there was a correlation with the tool X-axis motor waveform. The workpieces that have a correlation with the tool X-axis motor current waveform during finishing are marked with circles in Fig. 7 . The reference data and the transition of the tool Xaxis motor waveform for which the most noticeable correlation was obtained are shown in Fig. 8 (corresponding to the solid line circle in Fig. 7 ). In the motor waveform of each workpiece in Fig. 8 , the area surrounded by a square is the inner diameter part corresponding to the dotted line in Fig.  6 . A comparison of all reference data and waveforms revealed a correlation between the hole diameter and motor waveform, and we observed that F increased as machining progressed. The hole where anomaly Ⅱ occurs is a stepped hole, and it is estimated that chip biting will likely occur because the workpiece material is SUS, which is a ductile material with which it is easy to generate a long tip. However, there was almost no change in the transition of Ra, which is the reference data. There was also no significant difference in roundness and almost no flank wear or rake-face wear in the cutting-edge image.
The above results indicate that this anomaly is due to excessive growth of the built-up edge. A cutting-edge image was also taken as reference data, but the built-up edge could not be captured. The built-up edge typically grows and drops off, but the Best filter for raw wave -Lowpass filter with cutting frequency 1: Detection is easy 2: Detection is possible 3: Detection is not impossible 4: Detection is impossible SUS of this work material is a ductile material and tends to have a built-up edge. In this phenomenon, the first step is a built-up edge at the beginning of machining, where the edge grows without dropping as the machining progresses. In the second step, as the built-up edge grows, the cutting edge becomes covered with the built-up edge, so the sharpness decreases and F increases. In the third step, as F increases, the tool is pushed back toward the center of the hole, causing tool deflection and reducing the diameter of the hole. Therefore, the root cause of the diameter reduction is an anomaly built-up edge, which can easily be explained by the reference data and motor-waveform data simultaneously. The built-up edge had already dropped off when an image was taken because there is another process after the targetcutting phase. We assume this is why the built-up edge could not be observed. Table 4 shows the extent to which the built-up edge correlates with the raw, FFT, and STFT waveforms of the spindle, tool X-axis, and tool Z-axis, respectively. Similar to anomaly Ⅰ, the spindle axis did not correlate due to the effect of inertial force, while the tool axis was correlated. The waveform change at anomaly Ⅱ was a macroscopic waveform change and independent of the cutting frequency. Therefore, the macroscopic observation of the raw waveform was optimal. No correlation was observed in the FFT waveform, and only a change that reflected the macroscopicwaveform change was observed in the STFT waveform, so the correlation was weak. The changes in the tool X-axis and tool Z-axis showed the same tendency, with the machining load increasing and shifting as the machining progressed. We conclude that the raw waveform of the tool X-axis or tool Zaxis is optimal for anomaly detection, and therefore, to make a mechanical determination, it is better to carry out waveform processing that extracts the cutting frequency or lower with a lowpass filter. Details of the waveform processing for anomaly Ⅰ are described in Section 4.1.
Correlation of Anomaly Ⅲ Figure 9 shows a process chart of a drilling operation in which anomaly Ⅲ occurs. Drilling is carried out by roughing with tool 5 and finishing with tool 6. Figure 10 shows the dimension-transition diagram, which is the reference data for Fig. 9 Anomaly Ⅲ process chart around target surface. anomaly Ⅲ. The horizontal axis is the number of holes, the vertical axis is the dimension value, and one plot represents one workpiece. The target hole has a tolerance of 24 μm, and the upper and lower limits are those shown in the figure. The phenomenon that the hole size shrank without any indication and recovers can be observed multiple times. However, since it was not a stepped hole, the machining was stable and the diameter did not shrink to below the lower limit. The workpiece with reduced diameter and those before and after it were observed, as shown in Fig. 10 . The reference data and motor-waveform data for each axis of tools 5 and 6 were compared. There was no correlation with tool 5, but in the finishing of tool 6, there was a correlation with the tool Xaxis motor waveform. The workpiece that correlated with the tool X-axis motor waveform in the finishing process for tool 4 is marked with a circle in Fig. 10 . Figure 11 shows the transition of the reference data and tool X-axis motor waveform for which the most significant correlation was obtained (corresponding to the solid circle in Fig. 10 ). In the motor waveform of each workpiece in Fig.  11 , the area surrounded by a square is the inner-diameter part corresponding to the dotted line in Fig. 9 . A comparison of the reference data and the waveform showed that the roundness of the workpiece with reduced diameter deteriorates and noise is generated in the waveform. Observation of the FFT waveform revealed that this noise was not a constant frequency but random. There was also almost no change in Ra, and no wear was observed from the cutting-edge image. On the basis of the above reasons and those presented in [11] , we conclude that this anomaly is due to tool vibration, and the root cause of tool vibration is presumed to be the continuous generation and dropping of the built-up edge. Sawai [11] studied the relationship between built-up edge and cutting force and found that cutting force is decreased with the built-up edge when the rake angle of the cutting tool is increased. When a built-up edge is generated, the cutting force F is decreased, so tool deflection decreases. If the builtup edge falls off after that, cutting force F will increase and tool deflection will increase. It is logical to assume that unsteady tool vibration occurs during this repetition, which would explain the transition of the reference data and tool motor waveforms. Table 5 shows the extent to which the tool vibration correlates with the raw, FFT, and STFT waveforms of the spindle, tool X-axis, and tool Z-axis, respectively. As with anomalies Ⅰ and Ⅱ, the spindle axis did not correlate due to the inertial force, while the tool axis did correlate. The waveform change at anomaly Ⅲ was a waveform change with random noise added and was independent of the cutting frequency. Due to random noise, there was also no correlation such as peaking in a specific frequency band in the FFT, and no further correlation was found in the STFT because the change was further dispersed. The change of the tool X-axis and tool Z-axis had the same mechanism and random noise was added. We conclude that the raw wave- Table 5 Correlation between tool vibration and motor-waveform data.
form of the tool X-axis or tool Z-axis is optimal for anomaly detection, and that the raw waveform should be processed without a filter for mechanical anomaly detection. The details of the waveform processing for anomalies I and II are described in Section 4.1. As mentioned earlier, we constructed a non-touch indirect measurement system using motor current for detecting anomalies that occur under mass production conditions.
This section describes a general method for mechanical detection by computing rather than human intervention for anomalies Ⅰ, Ⅱ, and Ⅲ discussed in Section 3. Figure 12 summarizes this method from input (waveform) to output (anomaly detection). Figure 12(a) shows waveform processing including filtering. In this process, various types of filtering based on FFT are carried out, starting from the segmentation, where the difference between normal and anomaly waveforms is most common. After that, envelope extraction, waveform offset, absolute waveform construction, etc. are carried out according to the waveform. Standardization is carried out when needed to simplify subsequent processing. As shown in (b), there are roughly two types of feature extraction methods for numerically treating the processed waveform. The first (Type 1 in the figure) are methods that use traditional statistics.
Tool X-axis Tool Z-axis There are seven statistics in the graph: maximum, minimum, average, maximum-minimum, area, inclination of approximate line, and intercept of approximate line. Since the entire waveform prepared by waveform processing is calculated, the number of features is small, so it is not suitable for complex waveforms. The second type (Type 2) are discretization methods. The details of the discretization method used in this study are described in Section 4.3, but briefly, the concept is to divide the waveform into individual finite elements and extract characteristic values from each individual element. Since there are as many extracted values as there are individual elements, the number of waveform characteristics increases, but this method is suitable for obtaining complex waveform characteristics. Figure 12 (c) shows two types of anomaly detection methods using extracted waveform characteristics. The first are methods used in combination with the statistics in (b) (Type 1) to detect anomalies by detecting the boundary from the normal waveform to anomaly waveform with one to three statistical values. With such methods, features are selected manually using a data processor, or the necessary waveform characteristics are selected using multiple regression analysis. If the physical meaning of the waveform change can be understood, such methods are also suitable from the viewpoint of explanation at the time of detection. The second (Type 2 in (c)) are pattern-recognition methods. These methods include supervised learning, unsupervised learning, and parametric methods with which it is assumed that the target is a normal distribution, and nonparametric methods with which a normal distribution is not assumed. We used the Mahalanobis-Taguchi pattern recognition method here, which is classified as both a supervised learning and parametric method (the details are described in Section 4.3).
This pattern recognition method is often used in combination with the discretization method in Fig. 12(b) (Type 2) . In other words, this method is suitable for processing a large amount of features obtained by discretization.
In this section, we first summarize the correlation between a target anomaly and motor current waveform that we clarified. Then, we systemize the combination of waveform processing up to the threshold-setting stage so that mechanical anomaly detection can be carried out using the statistics and threshold-determination method presented in Section 4.1. Table 6 lists normal/anomaly waveform sets and the characteristics of anomaly waveforms for each anomaly type. The waveform-processing procedure for emphasizing the difference between normal and anomaly waveforms is shown in column b for each anomaly-waveform characteristic. The normal/anomaly waveform sets after the actual processing using the waveform-processing procedure are shown in column c and statistics that can be used for anomaly detection are selected and described.
Three types of anomaly-waveform characteristics are extracted from the correlation of anomalies Ⅰ-Ⅲ. The box of each waveform indicate the target cutting path. The waveform characteristic of the tilt chuck is specific band noise. First, the frequency is extracted using a bandpass filter after extracting the waveform term of the processing location. An envelope is extracted to make it easier to discriminate the transition of the frequency. Finally, the minimum envelope value is offset to 0 to eliminate the cutting-frequency Table 6 Formalized waveform processing and statistics combinations for anomaly detection. component that can be generated by a cutting process other than tilt chuck. With the above procedure, an anomaly waveform can be detected from the inclination of the approximate line in the statistics. As a physical phenomenon, the magnitude of the inclination of the approximate line is directly connected to the tilt chuck. The waveform characteristic of the component-edge failure is called the shift type. First, macroscopic changes to the waveform are easily observed using a low bandpass filter after extracting the waveform term of the processing location. Next, the minimum waveform value is offset to 0, and the negative current value that can be generated by the tool position is converted into a positive value. With this procedure, anomaly waveforms can be detected from the maximum value-side intercept of the approximate line among the statistics. As a physical phenomenon, the maximum value intercept corresponds to tool deflection, so the explanation at the time of detection is as good as the tilt chuck. The waveform characteristic of tool vibration is called random band noise. First, an envelope curve is generated after extracting the waveform term of the processing location. Next, the minimum envelope value is offset to 0. With the above procedure, anomaly waveforms can be detected from the waveform area among the statistics. However, the quantitative reduction in diameter caused by the size of the area and the tool vibration could not be obtained due to the limited number of samples. An anomaly waveform with this feature is more difficult to detect than the other two anomaly waveforms and is not easy to explain. As stated above, we formalized a series of waveform processing flows for each anomaly waveform according to its characteristics and applied a tilt-chuck anomaly to actual mass production. We report the detection accuracy under this condition in Section 4.4.
In this section, we propose a systemized anomaly detection method using the MT method for discretization and pattern recognition. The formalization discussed in Section 4.2 requires accurately detecting the phenomenon, but the discretization and pattern recognition methods eliminate the need for understanding the phenomenon. We utilized the MT method, which is a supervised learning method that uses a collection of normal data (i.e., training data) as a teacher. This method detects anomalies based on the distance between the measurement data obtained during operation and the normal data. A conceptual diagram of the MT method is shown in Fig. 13 . The discretization and pattern recognition based on the MT method are explained using Fig. 14, Table 7 , and Eq. 1. We first describe the common parts of the normal and measured data in the characteristic calculation process. Figure 14 shows the discretization based on the MT method. First, the original waveform in the horizontal (time) axis direction is subdivided on the basis of a specific time width, as shown in the graph on the left. Next, a sample line is drawn to subdivide the vertical axis (current value) direction on the basis of a specific time width. The enlarged diagram shows the area of the four sample lines, and a feature calculation method is shown with sample line 2 as an example. Sample line 2 has a portion that intersects the measured waveform, and the number of intersections is defined as a differential characteristic. In addition, the interval from the first crossing to the next crossing at a position lower than the waveform is defined as an integral characteristic. In this case, for sample line 2, the differential characteristic is 6 and the integral characteristic is 10. Since there are four sample lines, four differential characteristics and four integral characteristics can be obtained. Table 7 shows an example of the calculation results. Looking at the entire waveform in Fig. 14, differential and integral characteristics can be obtained by (the number of time divisions) × (the number of sample lines). The quantity of differential and integral characteristics in the entire waveform is defined as n, the nth differential characteristic is , the integral characteristic is , and vector composed of differential and integral characteristics is calculated by Eq. 1. The procedure up to this point is the discretization procedure. The pattern recognition procedure is described below using Eqs. 2-7 and in Fig. 15 .
Equations 2-3 are used to calculate the mean value � and standard deviation in each column of vector , as Subsequently, when the normalization matrix is calculated in Eq. 4, is obtained using Eq. 5.
Up to this point, both normal (training) data and measured data are calculated. Next, a correlation matrix indicating the degree of correlation between differential and integral characteristics is defined only for normal (training) data. Since there are two types of variables, differential and integral characteristics are represented using a 2 × 2 square matrix.
Next, to quantify the anomaly signs of machining, the Mahalanobis distance MD, which is used to characterize the waveform, is obtained by where �� obtained from the training data represents an inverse matrix of , and represents a transposed matrix of the normalization matrix .
( 
Tsubasa Watanabe et al/ Procedia Manufacturing 00 (2019) 000-000 When is training data, the is 1. When is measured data, the is greater than 1, and a threshold is determined according to the degree of the magnitude to determine the normal/anomaly waveform. The MT method is a pattern recognition method, but since the discretization method is described as a high-speed calculation method and was released at the same time, they are often used as a set. Figure 15 is a conceptual diagram of how the anomaly detection is systemized using the discretization and patternrecognition procedure based on the MT method with an auto parameter-tuning function. It is roughly divided into three steps: 1) the normal/anomaly-waveform-classification process, 2) the learning process using the classified waveform, and 3) the detection process that detects anomalies during mass production using a learned model. The second step is particularly important. There are waveform-processing parameters, such as waveform extraction and filtering, and feature-extraction parameters, such as time axis separation width and number of sample lines. With the systemized method, except for waveform extraction, we adopted an algorithm that uses both normal and anomaly data and evaluates the combination of various parameters with all parameter combinations. These parameters are listed in Table 8 . For evaluation of the selected parameters, when the between the anomaly data calculated with the combined parameters and the normal space constructed with normal data is positive, the magnitude of is positive. When the is negative, it means the number of overlapping points in the space was used for anomaly detection. In actual mass production, various phenomena occur in addition to the anomalies to be detected, so complete classification is undeniably difficult. As described above, we developed a systemized anomaly detection method for detecting anomalies with high accuracy without having to understand detailed physical phenomena by systemizing anomaly detection using discretization and pattern recognition. 
For the proposed formalized and systemized methods discussed in Sections 4.2 and 4.3, we implemented an anomaly detection system in a mass production line with the tilt chuck anomaly as the target and evaluated the detection accuracy of both methods calculated using the validation method summarized in Table 9 . The total production amount for this validation was 2,829 products. We focused on the correct-detection rate obtained by dividing the total amount of "Hit" (areas (1) and (4)) by the total production amount (areas (1) to (4)). Table 10 lists the evaluation results. The correct-detection rate was 98.34% when using the method that clarifies physical phenomena and selected statistics. The misjudgment rate was 1.66%, which is probably due to the difference between normal and anomaly waveforms. Therefore, it is sufficient that the difference of correct-detection rate based on pattern recognition and that based on formalized correlation is within 0.3% and either correct-detection rate is over 98%.
Future work will need to deal with the fact that the waveform term extraction is manual and the calculation time is enormous. The calculation time is proportional to [(number of normal waveforms to create normal space) × (variable parameter level) ^ (variable parameter number)]. Figure 16 shows an overview of the anomaly detection system with the anomaly notification function and reject function for anomaly products added to the mass production line. With the reject function, we used a pre-installed function to take out the workpiece immediately after machining without stopping the operation and took measures to minimize the risk of a false alarm occurring. Fig. 16 Anomaly-detection system set up for mass production.
We proposed two anomaly-detection methods focused on the axis motor current data of equipment for detecting turning anomalies and evaluated them in a mass production line. Our main contributions are as follows.
1) Constructed a non-touch indirect measurement system using motor current that can be applied to mass production without affecting cutting process. 2) Clarified the correlation between turning anomaly and motor current data and demonstrated that small dimensional changes of about 5-10 μm can be observed.
considering cutting phenomenon for each anomalywaveform type and obtained statistics that accurately describe anomaly cutting phenomena and maximize data meaning. 4) Systemized anomaly detection using discretization and pattern recognition by auto parameter tuning to reduce reliance on experts. 5) Implemented an anomaly detection system with anomaly-corresponding function using the proposed formalized and systemized anomaly detection methods for a mass production line. Both methods achieved a correct-detection rate of 98%.