Tool condition monitoring based on the fractal analysis of current and cutting force signals during CFRP trimming

Carbon fiber–reinforced plastic (CFRP) is becoming more popular in the aerospace industry due to its high strength-to-weight ratio and low weight. Machining CFRP to achieve the required surface quality, on the other hand, remains a challenge. High temperature in the cutting zone area affects the tool life and surface quality of the machined part. A thermally affected matrix makes an inaccurate interpretation of the surface quality. Then, the roughness parameters cannot be an appropriate indicator for surface evaluation of the CFRP. In the aerospace industry, however, ensuring the acceptable surface quality of a part is essential. Minimizing and controlling tool wear are necessary to avoid degrading the finished surface and losing the dimensional accuracy of the final part. Early detection of tool wear and appropriate surface quality in finishing operations can be achieved using online tool condition monitoring. Cutting forces and electric current signals related to the spindle during machining are very responsive to cutting conditions and can accurately represent tool condition changes. Fractal analysis, as a new approach in the online tool condition monitoring, can assess the tool condition during machining. This research investigates the fractal analysis of the spindle electric current signal and the total cutting force signal while trimming CFRP using a CVD end mill through three different tool life conditions, e.g. new tool, moderately worn tool, and severely worn tool. The empirical fractal index is also introduced to assess the tool condition and ensure the acceptable surface qualities in the finishing operations. The effectiveness of fractal analysis as a decision-making method in the tool condition monitoring was successfully proven in this study.


Introduction
The utilization of carbon fiber-reinforced plastic (CFRP) is increasing in the aerospace industry due to its high strengthto-weight ratio and low weight [1]. However, machining of CFRP to achieve the required surface quality remains a challenge. During machining of CFRP, abrasion and chipping are known as the major tool wear issues. Tool wear affects the rate of material removal and the quality of the machined surface [2]. While machining CFRP, the cutting tool must maintain a suitable level of edge sharpness in order to provide a clean cut at the end. During composite machining, minimizing and controlling tool wear are critical to avoid degrading the finished surface and losing dimensional accuracy of the final part [2]. Any failure may result in workpieces being rejected in the production line. Fiber pull-out or breakage, matrix smearing, or delamination may occur during the machining of CFRP [3]. To ensure product quality at the end of the finishing operation, direct or indirect methods of tool condition monitoring can be used [4]. In the direct method, the geometric parameters of the cutting tool are measured using an optical microscope with a high degree of accuracy [5]. This method has real-time limitations since it requires interrupting the cutting process to estimate the tool wear. Moreover, the direct method requires appropriate laboratory equipment, which is a limitation in harsh industrial machining applications [4]. The indirect method for tool wear monitoring is instead based on real-time analysis of signal acquisition during machining. This online approach is more appropriate for industrial applications that require few laboratory equipment and seek for automation of production processes to increase product quality and decrease operating costs [6]. It has been shown that such tool condition monitoring in an automated machining center can lead to early detection of tool wear, boost cutting processes speed by 50%, and lower the manufacturing costs from 10 to 40% [7,8].
Due to the sensitivity of cutting forces related to cutting conditions, the force signals have been widely used in tool condition monitoring [7]. Hu et al. [9] could predict distinct tool wear states, using statistical features of cutting force and acoustic emission signals during machining titanium alloy. This study employed mutual information (MI) and ν-support vector machine (ν-SVM) for model training and prediction. The proposed strategy could successfully predict different tool wear states, with a prediction accuracy of 98.9%. Despite the capability of cutting force signal to detect tool wear, the acquisition of cutting forces requires sensors, such as dynamometers, which are not practical or cost-effective to use in production line [7]. Alternatively, any changes in the cutting state can be reflected in the electric current signal of machine tools. Jeong and Cho [10] succeeded in estimating the cutting forces normal to a machined surface using the stationary feed motor current with less than 20% error. Current sensors are generally inexpensive and reliable and can be located far from the machining area [11].
The process of extracting reliable, intelligible data from enormous data sets to enhance decision-making is known as data mining. There are numerous approaches for data mining and extracting information from a particular signal [12]. Hassan et al. [13] developed the wavelet scattering convolution neural network (WSCNN) technique to extract distortion-stable features from vibration signals generated by tool wear. Large-scale experimental validation tests under various cutting conditions revealed that the WSCNN method could achieve 98% detection accuracy in tool conditions and minimize system training by up to 97%. Recently, an artificial neural network (ANN) was applied during machining to classify the tool wear states in real time using acceleration data [14] and acoustic emission signals [15]. Fuzzy logic was also introduced as another possible approach for tool condition monitoring by analyzing the uncertainties in acoustic emission signals [16]. The combination of time and frequency domain analysis [17], genetic algorithms [18], fast Fourier transform [19], and other methods has been used to analyze the acquired signals in the online tool condition monitoring. However, the robustness of these methods needs to be examined, though, as any modifications to the cutting condition or process parameters can change the result. Fractal analysis was recently developed as a new approach in tool condition monitoring. For the first time, the concept of fractal was used by B.B. Mandelbrot to estimate the length of the British coastline. Fractal objects are irregular shapes with affine structure and a sort of self-similarity. They have a fractal dimension that is greater than the topological dimension [20]. Fractal analysis was widely applied in advanced surface roughness evaluation [21], and it was also utilized in machine maintenance and diagnosis improvement [22]. Rimpault et al. [23] proved that fractal analysis of cutting force signal is more efficient to estimate the tool wear than the statistical parameters can be. In this study, different sets of cutting condition (speed and feed) were investigated. It has been demonstrated that the fractal parameters are less dependent on the cutting parameters than the statistical parameters during machining of CFRP. Moreover, recently, Jamshidi et al. [24] analyzed the cutting force signal using fractal analysis to monitor the tool condition. In this study, fractal parameters of cutting force signals while drilling CFRP/titanium stacks of material were estimated to identify distinct wear stages of the cutting tool.
The present study investigates the online tool condition monitoring using fractal analysis of the spindle electric current signal and the total cutting force signal while trimming carbon fiber-reinforced plastics (CFRP). For industrial applications, using the machine tool's internal data, such as electric current signal, is more practical due to the quick data acquisition and lack of external sensors. In this study, it is indicated that, in the integrated system that complies with industrial restrictions, the machine tool spindle electric current signal or total cutting force signal is used to predict the tool condition. This method is an innovation since it enables online tool condition monitoring, utilizing fractal parameters of the electric current signal or cutting force signal, as shown in Fig. 1. This study aims to demonstrate the robustness of the fractal analysis as a decision-making system in tool condition monitoring.

Methodology
The use of spindle electric current signal and cutting force signal to monitor tool condition was investigated in this study. Correlating relevant sensor signals to the tool wear states will be performed. During the composite machining, signals were acquired and analyzed using fractal analysis. A cutting tool in three different conditions was used to highlight the three distinct wear stages in the cutting tool lifespan. Surface quality was assessed to evaluate the effect of cutting tool condition on machined surface. An infrared camera is used to evaluate the temperature in order to examine the influence of temperature on surface quality.

Materials and experimental setup
Six carbon fiber-reinforced plastic (CFRP) plates were manufactured using the hand lay-up method and cured in an autoclave [2]. The stacking sequence of each plate was as follows: [0∕90] 5 . Three separate experiments were carried out, including trimming the CFRP plates using (1) a new end mill, (2) a moderately worn end mill, and (3) a severely worn end mill tool to provide three different tool conditions. These conditions reflect the wellknown phenomena of tool wear along with a whole lifespan of a cutting tool characterized with three distinct stages (Fig. 2). Due to the high pressure between the workpiece and a small contact area, tool wear is rapid in the first stage. Next, the wear is characterized by a relatively constant rate in the second stage. Then, the final wear stage occurs when the tool rapidly wears out until its end of life [24].
In the present study, the cutting tool was a 6-mm diameter multi-layer CVD coating end mill having four flutes. The tool wear was estimated as the average of the maximum flank tool wear on each of the tool's four cutting edges, which is represented in Table 1.
Two CFRP plates, with dimensions of 300 mm × 300 mm × 3 mm, were placed side by side in each experiment to allow a total cutting length of 5.7 m, with 3 m in the X direction and 2.7 m in the Y direction (Fig. 3). The red arrows indicate the cutting toolpath in Fig. 3. Dry trimming was performed using a K2X10 Huron® high-speed machining center equipped with a dust extraction system. The cutting speed and feed rate for all  experiments were 226 m/min (12,000 RPM) and 0.24 mm/rev (2880 mm/min), respectively, according to Bérubé [25]. The spindle electric current signal was acquired using the internal sensor of the machine tool through a static synchronized action programmed with the application programming interface (API) of the SIEMENS SINUMERIK 840D controller. The signal data was recorded with a 333 Hz frequency. The current signal can reflect any changes in the cutting condition, and it is expected that it may be utilized as an online tool condition monitoring, considering the development of an innovative analysis approach. Cutting force signals were recorded using a three-axis dynamometer table (Kistler 9255B). The cutting force signals were amplified and collected at a rate of 6 kHz. Cutting force signals are extremely sensitive to any changes in the cutting state and are widely used in tool condition monitoring, as stated in the literature review. To observe the cutting temperature, a VarioCAM® HD head 900 infrared camera with a 60-Hz frame rate was used to take a thermal image of the tool and workpiece in the same window. The infrared camera was mounted onto the spindle head to follow the cutting tool (Fig. 4). The emissivities of the cutting tool and CFRP specimens were calculated based on the ASTM international standard [26] and adjusted within the camera's settings. The emissivities of the CVD coating end mill tool and CFRP specimens were 0.52 and 0.94, respectively. The 3D images of the machined surface and areal surface roughness parameters were estimated using Keyence VR-5000 optical profiler after each experiment. The quality of the machined surface was assessed using areal surface roughness parameters.

Fractal analysis
Some irregular geometries were initially represented by fractal dimensions. Mathematicians discovered that "rough" surfaces exhibit self-affine behavior and may be measured in terms of fractal dimension. It is difficult to determine the fractal dimension of an object or a curve. The Weierstrass-Mandelbrot (WM) function enables the sketching of a selfaffine curve [23,27].
Two factors, D and G, which are unaffected by sampling frequency or length, define the shape of the profile. The fractal dimension from a profile (D) can be obtained using a variety of fractal analysis approaches such as correlation analysis, information analysis, regularization analysis, and box-counting method. In different studies, some of this methodology such as box counting exhibited relatively low robustness [22,28]. Regularization analysis was used in the present study because of its reasonably strong repeatability, as demonstrated in recent works [28,29]. Roueff and Véhe [30] proposed a novel method to assess the regularity of a graph in 1998. They defined regularization dimension using following definition. Γ is defined to be the graph of a bounded function f ∶ ℝ → ℝ . (t) is defined to be a kernel function of Schwartz classS , so a (t) = 1 a t a is the dilated version of at scale a , and f a can be the convolution of f with a : Equation (2) shows that a tend to Dirac distribution and f a tend to f , when a goes to 0. Because f a ∈ S , then the length of its graph Γ a on K is finite and it can be calculated using following equation: Then the regularization dimension can be calculated as follows: is called regularization dimension which is referred as fractal dimension (D) in the present study.
The limit in this equation is calculated as the slope in the area where a tends to 0 and the R 2 of the linear regression is close to 1 [28]. The fractal dimension (D) is defined as the slope of the graph ( logl a vs. loga ) in the linear region, as shown in Fig. 5. Fractal dimension is an indication of the signal "roughness." To ensure the accuracy of the results, a common region in the logl a vs. loga graph with better linearity and sufficient points for linear regression must be chosen. Herein, the fractal parameters were calculated in the 9 to 16 points for spindle electric current signal (region 1) and 5 to 22 points for total cutting force signal (region 2) as illustrated in Fig. 6. Fractal dimension is conventionally determined as the slope in these regions where the ( a ) value is close to 0 and the R 2 of the linear regression is close to 1. Additional fractal parameters were defined to extract complementary characteristic features of the signal. The coefficient of determination of the linear regression ( R 2 ) was defined to represent the auto-scale regularity of the signal. A fractal index was Fig. 4 Infrared camera series VarioCAM® HD head 900 installed on the spindle head also introduced to support online tool condition monitoring and introducing a decision-making system. The empirical fractal index (I) was defined as follows:

Results and discussion
The results of machining CFRP utilizing three distinct tool conditions are discussed in the following section. The obtained signals, including spindle electric current and total cutting force, are examined using both conventional and fractal analyses. The analysis outputs are used in online tool condition monitoring to verify that the desired surface quality is achieved at the end of the machining process.

Conventional analysis of spindle electric current signal
In this study, a CVD end mill tool in three different conditions was used to trim two plates of CFRP. Three separate experiments were conducted, including trimming of the CFRP using new, moderately worn, and severely worn end mill tools. The spindle electric current signal was obtained using the machine tool's internal sensor with the least noise level, as shown in Fig. 7. During the tool engagement phase, this figure illustrates four separate zones. Zone I indicates the cutting tool's engagement with the workpiece, which causes the current to increase. Zone II is the steady state where the CVD end mill is trimming the CFRP plate. The cutting tool disengages from the workpiece in zone III, where the electric current decreases until the cutting tool entirely exits the (6) I = (R 2 ) D workpiece. Zone IV represents the air-cutting section where the tool is not in contact with the workpiece.
The average of spindle electric current is shown in Fig. 8. Air-cutting sections were removed from signals, so the average of current is plotted as a function of the cutting length. During trimming, the average current using the new cutting tool was higher than when the worn cutting tool was used in some areas, as indicated in the zoom-in section in Fig. 8. It may be explained by the effect of cutting tool edge radius on the cutting forces and then the electric current. The forces involved in machining are inextricably linked to the spindle electric current, since they both reflect the amount of power used during the cutting process [31]. This higher average value for the current signal using a new tool may result from the sharper cutting edges that cut fibers in smaller chunks than those using a worn tool. This leads to high variations in the cutting force signal as well. Those cutting force high variations are often considered noise in the signal and then filtered out to extract the main shape of the cutting force signal. During the tool wear increase, composite fibers tend to be cut into bigger chunks when the cutting tool becomes dull and the edge radius increases. Then, bunches of fibers buckle or are pushed aside, delamination occurs between layers, and less power is consumed.
In this study, it is not possible to evaluate the condition of the cutting tool using the statistical parameters of the electric current signal during CFRP machining. Average, standard deviation, kurtosis, and skewness of electric current signal were calculated; however, fluctuations of these parameters did not appear to correlate with tool condition due to unexpected changes and excessive variation.

Fractal analysis of the spindle electric current signal
The fractal analysis results of the spindle electric current signal during the trimming of CFRP are filtered and illustrated  Fig. 9. Fractal parameters are less dependent on the cutting parameters than the statistical parameters during machining of CFRP as stated in the literature review. The current signal can reflect any changes in the cutting condition, and it can be used in online tool condition monitoring. Only the inherent patterns hidden in the signal need to be revealed. The fractal dimension has traditionally been used to evaluate surface or curve complexity. Fractal parameters have recently been applied in signal analysis. The degree of complexity of the signal shape and variation of signal are represented by the fractal dimension [32]. As shown in Fig. 9, the fractal dimension of the new cutting tool is greater than the worn cutting tool. When the new cutting tool trims the CFRP, more complex shapes and more significant variations can be detected in the electric current signal. The fractal dimension in the first 3 m of cutting (trimming in the X direction as shown in Fig. 3) remains constant for the worn and new cutting tools, even when the quantity of the current fluctuates, as can be seen in Fig. 9. The fractal dimension continues to decrease for the new cutting tool while trimming in the Y direction (Fig. 3). This behavior can be explained by the effect of the cutting direction on the shape of the electric current signal, and clearly, it affects the result of the fractal dimension and other fractal parameters. For the first 3 m of cutting, the coefficient of determination of the linear regression ( R 2 ) remains constant for both worn and new cutting tools, with a progressive rise in the graphs. The value of R 2 when the worn cutting tool is utilized is higher than when the new cutting tool is used. Then, even the R 2 results can reflect the tool condition. The fractal parameters calculated from trimming with a severely worn and a moderately worn cutting tool are relatively similar, particularly the R 2 results. Each fractal parameter characterizes a specific feature of the signal. Then, the combination of the fractal parameters can express more information about the electric current signal and improve the accuracy of the decision-making system. This empirical index was designed to feed the controller with a single value based on the combination of all fractal parameters. Therefore, before feeding it to the controller, an appropriate threshold value for each experiment must be chosen. The empirical index of fractal analysis of the spindle electric current signal is also shown in Fig. 9. As   Fig. 7 A The spindle electric current signals during trimming of CFRP using the new, the moderately worn, and the severely worn CVD end mill tool. B Zoom in section of the spindle electric current signals including zone I to zone IV. C Zoom in section of the spindle electric current signals the tool wear increases, all graphs show a progressive rise. The fractal index can be used as a decision-making system based on experimental data to support online tool condition monitoring. The experimental result of the fractal index while trimming with a new cutting tool is used to determine a threshold value to feed the controller. The fractal index could be adjusted to a threshold value and a warning could be sent before the wear is detected on the cutting tool. Early detection of tool wear leads to appropriate surface quality in finishing operations. This value can guarantee high machining quality at the end of the trimming operation. The threshold value of I for the spindle electric current signal could be adjusted to 0.958 or less based on tool condition (trimming using new cutting tool). This value can guarantee the cutting tool is still in perfect operating order with no signs of wear, which is essential for finishing operations of CFRP material.

Conventional analysis of total cutting force signal
The total cutting force signal as a function of machining time and the average of the total cutting force signal as a function of cutting length during the trimming of CFRP are illustrated in Fig. 10. For the worn cutting tool, the total cutting force average is lower in some areas than for the new cutting tool. This behavior can be explained by the effect of cutting tool temperature on matrix softening, where the softer matrix requires less cutting force. Generally, due to the composite material's low thermal conductivity, the high temperature tends to stay in the cutting zone area during the machining of composite parts [33]. High temperature in the cutting zone area affects the tool life and surface quality of the machined part. The strength and properties of CFRP are degraded by matrix softening and decomposition at temperatures over the resin's glass transition temperature [33,34]. The average temperature of the CFRP in the cutting zone area and the average temperature of the cutting tool are illustrated in Fig. 11. These temperatures were estimated using the infrared camera installed on the spindle head with the frame rates of 60 Hz, and it is graphed for the first 3 m length of cut. The cutting tool temperature was estimated when the tool exited the workpiece. The average temperature of the worn cutting tool during the trimming of CFRP is higher than the average temperature of the new cutting tool, as shown in Fig. 11. Moreover, the average temperature of the CFRP (in the cutting zone area) is also higher when the worn cutting tool is utilized. Wear on the cutting tool generates a rise in temperature in the cutting area, causing the matrix to soften and burn. The temperature of a new cutting tool reaches 300 °C after 3 m of cutting; while for the moderately worn and severely worn cutting tool, the temperature reaches 320 °C and 394.1 °C, respectively. Figure 12 shows the 3D images of the surface texture for the last 50 mm of cut with the new Fig. 8 Average of the spindle electric current as a function of cutting length during trimming of CFRP using the new, the moderately worn, and the severely worn CVD end mill tool  9 Fractal analysis of the spindle electric current signal during trimming of CFRP using the new, moderately worn, and severely worn CVD end mill tool and severely worn cutting tools. The thermally impacted matrix creates a smooth surface, as seen in Fig. 12, which is a false interpretation of the surface evaluation. R a is the arithmetical mean height of a line and it estimates the roughness of a profile. S a is the extension of R a to a surface. S a is the average value of the absolute value of height at each point in the area [35]. The result of S a (arithmetical mean height) indicates that the surface improves when the worn cutting tool is utilized (Fig. 13). The moderately worn tool makes a smooth machined surface with S a less than 10 µm. However, when the surface is trimmed by the new cutting tool, the S a rises to 20 µm. High temperature in the cutting zone area leads to matrix softening and inaccurate interpretation of surface quality. It is concluded that roughness parameters cannot be an appropriate indicator for surface evaluation of the CFRP, as Hamedanianpour and Chatelain [36] and Ghidossi et al. [37] also mentioned in their studies.

Fractal analysis of total cutting force signal
Cutting force signals have frequently been used to monitor the tool condition. However, the acquisition of cutting forces needs sensors like dynamometers, which are not practical or cost-effective to utilize in production lines. Depending on equipment availability, the cutting force signal can be used as an alternate option for tool condition monitoring. Due to unforeseen changes and excessive fluctuation, the statistical   Fig. 11 A The average temperature of the workpiece in the cutting zone area and the average temperature of the cutting tool during trimming of the CFRP in the first 3 m length of cut using the new, the moderately worn, and the severely worn CVD end mill tool. B Photo taken using infrared camera during cutting in X direction. C Photo taken during cutting in Y direction. D Photo taken when the cutting tool is out of the workpiece to estimate the temperature of the cutting tool

Conclusion
Machining of CFRP is challenging due to the elevated temperature that remains in the cutting zone area. According to the results, the average temperature of the worn cutting tool during the trimming of CFRP was much higher than the new cutting tool's average temperature. A thermally affected matrix made an inaccurate interpretation of the surface quality. According to the result of S a , roughness parameters cannot be an appropriate indicator for surface evaluation of the CFRP. The tool wear was selected as a comparative factor for the results. This study investigated the online tool condition monitoring using fractal analysis of the spindle electric current signal and the total cutting force signal during the trimming of CFRP. Based on the results, fractal parameters of the total cutting force signal can be used to assess the tool condition during machining CFRP. The fractal dimension describes the regularity of the signal, while the coefficient of determination of the linear regression describes the autoscale dependency of the signal. Index computation using a combination of fractal parameters allows for merging the key detection performances of each parameter. This index provides a more precise monitoring of tool wear and surface quality during the machining of CFRP. For production environments where no force acquisition systems are implemented, this study demonstrates that fractal analysis of the spindle electric current signal is as appropriate to extract the tool wear information as the force signal is during the trimming of CFRP. This study effectively demonstrated the efficiency of fractal analysis as a decision-making method in tool condition monitoring.

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