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Vibration singularity analysis for milling tool condition monitoring
International Journal of Mechanical Sciences 166 (2020) 105254
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International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
Vibration singularity analysis for milling tool condition monitoring Chang’an Zhou a,b, Bin Yang a,b, Kai Guo a,b,∗, Jiangwei Liu a,b, Jie Sun a,b, Ge Song c, Shaowei Zhu c, Chao Sun c, Zhenxi Jiang c a
Key Laboratory of High-efficiency and Clean Mechanical Manufacture, National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Ji’nan 250061, China b Research Center for Aeronautical Component Manufacturing Technology & Equipment, Shandong University, Ji’nan 250061, China c Chengdu Aircraft Industrial (Group) Co., Ltd, Chengdu 610091, China
a r t i c l e
i n f o
Keywords: Vibrations Tool condition monitoring Singularity Transition points Support Vector Machine
a b s t r a c t Tool condition monitoring (TCM) is a very effective way to enhance productivity and ensure work-piece quality. This paper introduces a cutting condition independent TCM approach for milling with vibration singularity analysis. Holder Exponents (HE) are chosen as index to estimate the singularity of vibration signals. Wavelet transform modulus maxima (WTMM) are employed to estimate HEs. A wavelet basis selection method is established to select the optimal wavelet bases for the estimation of HEs. Means of HE values and Number of singular points of feed direction vibration components are found to be the most correlated with tool conditions based on experimental study. The sensitivity between these HE features and the transition points of different tool wear states is discovered. Verified by a public database, this sensitivity is found independent of the cutting conditions. Then a TCM approach is proposed which utilized a Support Vector Machine (SVM) model and a transition point identification method (TPIM). Experiment results indicate that this approach is efficient and the TPIM helps to reach more precise classification results.
1. Introduction With the increasingly fierce competition in the global manufacturing industry in recent years, it becomes urgent to further improve production efficiency, product quality, and reduce production costs. In the high-speed CNC manufacturing industry, the expense of cutting tools is one of the major manufacturing costs. However, tool wear is an inevitable and common issue, which affects the surface quality and dimensional accuracy directly. An efficient and robust online system that can monitor tool conditions continuously becomes necessary to enhance productivity and ensure work-piece quality [1]. To fulfill the TCM tasks properly, a great amount of the TCM models published recently are focused on empirical analysis [2], or sensory data-driven methods such as cutting forces [3–7], spindle current [8,9], vibration [10,11], and acoustic emission (AE) [12,13]. The related studies have been summarized in several comprehensive reviews [14,15]. Typically, the TCM system employs sensing systems to monitor the process, and then extract most relevant information from the sensory signals to identify and classify the tool conditions, to reduce the cost increased by tool failure. As sensing technology continues to mature and advance, how to extract the most relevant information has become a vital issue for
∗
TCM. However, discontinuous cutting is one of the remarkable features of the milling process, and this would result in nonstationary sensory signals. The commonly-used time-domain statistical features, frequencydomain features [16,17] are sensitive to the variation of cutting conditions [7] in milling; this would limit the applications of the proposed TCM systems. Wavelet analysis has strong time-frequency analysis capability to analyze nonstationary signals effectively [15,18]. Singularity analysis is applied early in image processing, and the correspondence between singularity and abrupt shift in pixel point mutations is often used to identify boundaries in images [18]. These similar singularities are also be observed in sensory signals collected in the machining process, especially as tipping and tool breakage occur [19]. Fourier transform and wavelet analysis are commonly used singularity analysis tools, but wavelets can provide a better time-frequency localization property. Chen and Li [20] first presented singularity analysis base on wavelet transform to cope with TCM in machining, the wavelet coefficient norm and statistical features of AE signals were selected as data samples to classify tool conditions in turning. Fractal property is one of the important attributes of singularity analysis; it was also employed to classify the variation of tool conditions in turning [21], they established a recurrent neural network to connect the fractal features of
Corresponding author at: School of Mechanical Engineering, Shandong University, 17923 Jingshi Road, Ji’nan 250061, China. E-mail address: [email protected] (K. Guo).
https://doi.org/10.1016/j.ijmecsci.2019.105254 Received 19 August 2019; Received in revised form 16 October 2019; Accepted 16 October 2019 Available online 17 October 2019 0020-7403/© 2019 Elsevier Ltd. All rights reserved.
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International Journal of Mechanical Sciences 166 (2020) 105254
Whereas, the blunt tool has smoother waveforms with fewer singularities. This waveform disorder and their singularities can be quantified by Holder Exponent (HE) [18]. 2.2. Singularity estimation with HE If a function f(t) is not differentiable at t0 , then the f(t) is said to be singular at t0 [18]. The HEs are useful index to quantize the singularity. Generally, a small HE means a singular point while a large HE represents a regular one. If A > 0 and a polynomial pv (t) of degree m exist, where m is the largest integer and m ≤ 𝛼 is satisfied, such that |𝑓 (𝑡) − 𝑝𝑣 (𝑡)| ≤ 𝐴|𝑡 − 𝑣|𝛼 | |
Fig. 1. Vibration waveform shapes under different tool wears. The variation of tool condition are correlated to changes of the vibration waveforms.
machining dynamics with flank wear. Zhu et al. [6,22] introduced the probability density functions of singularity estimated from cutting force in micro-milling to correlate with different tool conditions, and the insensitivity to cutting conditions such as work-piece material, federate, depth of cut, etc. was verified by experiment studies. In summary, the recent TCM studies with singularity analysis [6,21,22] were focusing on cutting force, AE in turning or micro-milling process experimentally or theoretically. As a result of the non-stationarity and the sophistication of the vibration signal of the milling process, the TCM approaches based on singularity analysis of vibration signals are rarely established. The purpose of the present paper is to analyze the singularities of vibration waveforms in milling systematically, which can be used to fulfill the TCM task. The highlights of this paper are summarized as follows: 1 A wavelet basis selection method is presented to pick the optimal wavelet bases for the sensor signals. The wavelet bases with 2 vanishing moments are found most effective to estimate the singularity of vibration signals in milling. 2 HE features, including Means of estimated HE values and Number of singular points of feed direction vibration components, are found most related to different tool conditions. And they are highly sensitive to the transition points of different wear states defined by VB′. This sensitivity is independent of the values of VB, the type of milling tools, the material of work-pieces, and the processing parameters. 3 A TCM approach is proposed which utilized an SVM model and a transition point identification method (TPIM). The TPIM can modify the outcomes of the SVM model and help to reach more precise classification results. The rest of this paper is organized as follows. Section 2 discusses the theoretical basis of singularity analysis. The full tool life-cycle milling experiment setups, results analysis and the public database verification are presented in Section 3. Then online TCM approaches are proposed and discussed in Section 4. Conclusion and future studies are summarized in Section 5. 2. Tool condition estimation from vibration singularity 2.1. Vibration waveforms and tool conditions Vibration shows a keen sensitivity to tool conditions [11], and it is quite convenient to be acquired during milling. As mentioned above, the underlying assumption is that with the proceeding of the milling process, the variation of tool condition is correlated to changes of the vibration waveforms, as can be seen in Fig. 1. The waveform of the fresh tool is relatively more disorder, which means stronger singularity.
(1)
where is A is an invariable, then this upper bound is depend on this 𝛼. When the 𝛼 in function |f(t) − Pv (t)| ≤ A|t − v|𝛼 (1) reaches the supremum, we say this 𝛼 is the HE of f(t) at t = v. If f(t) is n-time differentiable and the nth derivative is singular at v (with n < 𝛼 < n ++ 1), then 𝛼 can represent this singularity. The computation of HEs is complicated. It was discovered that HEs could be calculated by estimating their wavelet transform modulus maxima (WTMM) and checking the decay of the WTMMs in the time-scale plane[18]. Firstly, to estimate the WTMMs along the scale at position u, the partial differentiation of wavelet transform WTf(u, s) is calculated, make it equal to zero: 𝜕𝑊 𝑇 𝑓 (𝑢, 𝑠) = 0. 𝜕𝑢
(2)
where s is scale. In the scale-space (s, u), we call any connected lines, along which all points are modulus maxima, a maxima line [18]. Along the maxima line, the coefficients of wavelet transform WTf(u, s) have the scaling ability around t, such that: |𝑊 𝑇 𝑓 (𝑡)|𝐴 ≤ 𝑠𝛼+1∕2 . 𝑠 | |
(3)
where A is decided on the selection of the wavelet basis 𝜓(t). To reduce the amount of calculation, the discrete scale s == 2j was used as follows: log2 ||𝑊 𝑇2𝑗 𝑓 (𝑡)|| ≤ log2 𝐴 + 𝑗(𝛼 + 1∕2).
(4)
By making equality in log2 |𝑊 𝑇2𝑗 𝑓 (𝑡)| ≤ log2 𝐴 + 𝑗(𝛼 + 1∕2) (4), A and 𝛼 can be obtained. The connection between j and 𝛼 is established by log2 |𝑊 𝑇2𝑗 𝑓 (𝑡)| ≤ log2 𝐴 + 𝑗(𝛼 + 1∕2) (4). The function also connects WTMM and j or s. A higher value of 𝛼 indicates that f(t) is less singular [18]. The HEs estimated by WTMMs was first introduced to analyze selfsimilar phenomena [23]. After that, it was employed to build a diagnosis system for machinery faults [24,25]. 2.3. Signal de-noising based on wavelet modulus maxima Comparing Fig. 2(a) and (b), it can be found that the raw vibration signal, which is taken from the 10th milling experiment in feed direction detailed in Section 3.1, is contaminated by noises. Considering the spindle speed of 1273.27 r/min and sampling frequency of 8192 Hz, there are about 386 points in total for one rotation of the spindle. Since the singularity of noise is usually negative [18], when the HE value generated by the signal is positive, the presence of noise will reduce the sum. Generally, the effective signal collected during cutting has the lowfrequency property, and the noise is high-frequency signal. Therefore, low-pass filters, wavelet filters, etc., which are commonly used by engineers, are taking advantage of these features for de-noise. Although they can effectively remove the high-frequency noise, they can also result in losing some important information of the signal, as shown in Fig. 2(b). Since the noises generate negative singularities, the WTMMs produced by noises can be told apart from those generated by effective signals. When estimating the WTMMs, if the value of the detected WTMM increases with the decrease of the scale notably, we would say that this
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International Journal of Mechanical Sciences 166 (2020) 105254
Fig. 2. (a) Raw vibration signal of the 10th milling experiment. (b) Signal de-noised by wavelet filter with db3. (c) Signal de-noised by WTMM by Haar wavelet, which has 1 vanishing moment. (d) Signal de-noised by WTMM by 2nd derivative of Gaussian wavelet with 2 vanishing moments. (e) Signal de-noised by WTMM by 3th derivative of Gaussian wavelet with 3 vanishing moments. (f), (g), (h), (i), (j) are the corresponding frequency spectrum of (a), (b), (c), (d), (e).
point is dominated by noise and setting it zero. After checking all the data points, we rebuild the signal by means of Mallat’s method [18]. By comparing Fig. 2(b)–(e), it can be seen that the de-noising algorithms by estimating WTMMs can effectively remove the noise and obtain a
smoother curve. In order to verify the de-noising effect of WTMM algorithm, the signal-to-noise ratios (SNR) of different algorithms were estimated for more randomly selected data sets from the experiments presented in Section 3.1, as shown in Table 1.
Table 1 SNR (db) of different de-noising algorithms. Experiment No.
Wavelet filter
WTMM by 1st derivative of Gaussian wavelet
WTMM by 2nd derivative of Gaussian wavelet
WTMM by 3th derivative of Gaussian wavelet
5th 10th 21th 50th
−5.2791 −4.3495 −3.6263 −15.0404
−1.4358 −1.1541 −0.4606 −5.517
−3.1063 −2.0729 −0.7248 −6.9737
−3.6901 −2.1235 −1.1681 −7.3791
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International Journal of Mechanical Sciences 166 (2020) 105254
ments [18]. Therefore, in this paper, we used the Gaussian wavelet as the wavelet basis. It is worth noting that large vanishing moments can increase the number of WTMMs at a particular scale. Considering computational efficiency, we desire the least quantity of maxima necessary to estimate the needed singularity in the signal. Therefore, we have to select a wavelet basis with as few vanishing moments as possible, but enough to perceive the HE of the highest order. Comparing subgraphs (c) and (d) of Fig. 2, it can be found that the smoothness of the de-noised signal with 2 vanishing moments is improved. This is mainly due to the fact that the wavelet basis with 2 vanishing moments could find both Type Ⅰ singular points and Type Ⅱ singular points, i.e. the discontinuities in the 1st derivative of the signal. Consequently, more points could be assessed to check which are preponderated by noise or not. Further eliminating noise components can obtain a smoother curve. A significant reduction in SNR also indicates that more noise is removed. To verify the de-noising effect, the frequency spectrum analyses are carried out on the de-noised samples. The energy of the effective vibration signal is mainly concentrated around the tooth passing frequency (TPF) and its integral multiples [27,28]. 𝑇𝑃𝐹 = 𝑁 × Fig. 3. Correspondence relationship between singularity and modulus maxima lines.(a) is a Type Ⅰ singular point, wavelet bases with 1 or 2 vanishing moments all can create WTMMs. (b) is Type Ⅱ singular point, only a wavelet basis with more than 2 vanishing moments can create WTMM here.
2.4. Wavelet basis selection method Heretofore, there is still a lack of wavelet basis selection methods for vibration signals of machining. Since some properties of the wavelet basis are interrelated and constrained, it is necessary to select the wavelet basis according to the characteristics of the milling vibration. The wavelet bases selected for HEs’ estimation must possess the following attributes: continuously differentiable, with suitable vanishing moments, symmetry or anti-symmetry [18]. There are two kinds of singularities in real signals: Type Ⅰ, which are the discontinuities of the signal at point c; Type Ⅱ, which are the discontinuities of the nth derivative of the signal at point c, as shown in Fig. 3. Reasonable selection of wavelet basis can help us to preserve the useful information in the raw signals. And the selection is closely related to the vanishing moments. A wavelet basis 𝜓(t) is with n vanishing moments, if and only if for all positive integer k < n, it satisfies [26] +∞
∫−∞
𝑡𝑘 𝜓(𝑡)𝑑𝑡 = 0.
(5)
When the selected 𝜓(t) has n vanishing moments with small compact +∞ support 𝜃, then 𝜓(t) can be written as𝜓 = ( − 1)n 𝜃 (n) with ∫−∞ 𝜃(𝑡)𝑑𝑡 ≠ 0. The WTf(u, s) can be rewritten as follows: ) 𝑑𝑛 ( 𝑊 𝑓 (𝑢, 𝑠) = 𝑠 𝑓 × 𝜃̄𝑠 (𝑢). 𝑑𝑢𝑛 𝑛
(6)
If 𝜓 = −𝜃′, it has 1 vanishing moment, the WTMM is the maximum of the 1st derivative of f smoothed by 𝜃̄𝑠 . The WTMM could find abrupt 2 shifting points. If 𝜓 = 𝜃′′, the WTMM of 𝑊2 𝑓 (𝑢, 𝑠) = 𝑠2 𝑑 2 (𝑓 ∗ 𝜃̄𝑠 )(𝑢) 𝑑𝑢
meets with local maximum curvatures. In addition, it is perceived that the WTMM of local maximum curvity is correlated to the singularity of sharp shifting point. However, when we do not know which type of singularity the signal has beforehand, we cannot choose the suitable vanishing moment. Based on the results of repeated trials, we propose a wavelet basis selection method: At first, the wavelet bases with various vanishing moments are used to de-noise the raw signals; after that by evaluating the noise reduction effect, we can judge which type of singularity signal has. The Gaussian wavelet is a commonly used wavelet basis for singularity detection, and its nth derivative is a wavelet basis with n vanishing mo-
1273.27 𝑛 =4× = 84.88(Hz). 60 60
(7)
where N is the number of cutting edges, here it is 4. And n is the spindle speed with 1273.27 (r/min). By observing Fig. 2(h) and (i), it can be seen that 2nd derivative of Gaussian wavelet can eliminate more energy of high-frequency noises and preserve the energy around integral multiples of TPF. This proves that there are two types of singularities in the milling vibration signal again. Comparing Fig. 2(d), (e), (i) and (j), it is perceived that the wavelet basis with 3 vanishing moments could make the curve of the de-noised signal smoother, but not significantly. And the similar conditions occur in the results of SNR and frequency spectrums. Given a comprehensive consideration of the cost of calculation and de-noising effect, the wavelet basis with 2 vanishing moments is effective enough to estimate the singularity of vibration signals in milling. Here, the 2nd derivative of Gaussian wavelet (also named Mexican Hat wavelet) is used for denoising and estimating singularities, which is shown as follows: 1( ) 𝑡2 2 𝜓(𝑡) = √ 𝜋 − 4 1 − 𝑡2 𝑒− 2 . 3
(8)
Remark 1. A wavelet basis selection method is presented to pick the optimal wavelet bases for the sensor signals. The wavelet bases with 2 vanishing moments are found most effective to estimate the singularity of vibration signals in milling. 2.5. HE estimation Since the estimation of WTMMs is the same process for HE estimation and de-noising, we integrated the de-noising algorithm into the HE estimation. The HE estimating process is shown in Fig. 4. In the de-noising algorithm with the estimation of WTMMs, because the number of WTMMs of noise decreases as the scale (2j ) increases [18], a relatively large scale is necessary to ensure the useful signal dominant, j = 4–5 is selected usually [22]. After estimating WTMMs for all (u,s), a threshold T of the WTMM at the largest scale would be set, which is used to locate the WTMMs dominated by the noise. The WTMMs below T would be deleted. The T is set as ( √ ) 1 + 2 𝑃𝑁 × 𝑀. (9) 𝑇 = log2 𝐽 +𝑍 where Z is invariable, here it is 2 [22]. J is the maximum for the discrete scale s = 2j (j = 0,1,2…J) . PN is the power of noise. M is the maximum WTMM, 𝑀 = max |𝑊2𝐽 (𝑥𝑖 )|.
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International Journal of Mechanical Sciences 166 (2020) 105254
Fig. 6. Variation of flank wear. The wear curve can be clearly divided into three regions: the initial wear state (A), the steady state region (B) and the accelerated wear zone (C).
Fig. 4. HE estimation procedure.
divided into three regions: the initial wear state (A), the steady state region (B) and the accelerated wear zone (C), which is consistent with the typical wear pattern [1].
3.2. Holder exponent analysis
Fig. 5. Experiment setup.
3. Experiments and discussions 3.1. Full tool life-cycle milling experiments The full tool life-cycle milling experiments were performed on a CNC machine center (Hartford CNC-168). The setup of the experiments is displayed in Fig. 5. The work-piece material was Ti–6Al–4V. The tool was a 20-mm diameter 4-flute YG solid cemented carbide end mill with a helix angle of 38°. 60 sets of data acquisition experiments were carried out with identical cutting parameters: the spindle speed was 1273.27 r/min, the feedrate was 80 m/min, the X depth of cut (radial) was 0.8 mm, and the Z depth of cut (axial) was 18 mm. A triaxial piezoelectric accelerometers (PCB -356A15) was mounted on the spindle with a magnetic base to measure the vibration during the data acquisition experiments. The vibration signals were recorded by a NI cDAQ-9171 with a sample frequency of 8192 Hz. The tool wear is measured after each data acquisition experiment by a digital microscope (Dino-Lite AM3113). Due to the limited size of the work-piece, 15 sets of milling experiment were performed on scraps between each data acquisition experiment with the same cutting parameters to wear the tool. Fig. 6 shows the variation of maximum flank wears through the entire cutting process. It can be observed that the wear curve can be clearly
As a case study, Fig. 7(a)–(c) shows the HE variations of three typical tool conditions (Fresh - cut 2, Partly worn - cut 32 and Worn cut 53) from vibration. The calculation process used vibration samples contained in 30 rotation cycles for a total 11,550 points. It can be observed that the HEs of 3 vibration components are concentrated in narrow bands, and their fluctuation ranges overlap significantly. Therefore, the HEs itself cannot be directly used as input samples for TCM tasks. Whereas, Zhu et al. [22] discovered that the probability densities distribution of HEs showed a strong relationship with tool conditions. Fig. 8 shows HEs’ probability densities of identical data displayed in Fig. 7. Comparing the Fig. 8(a)–(c), it can be observed clearly that there is a more obvious difference in the probability density distributions of the HE value in the feed direction (Y direction) of three different tool conditions. In the same time, it can be seen that all these probability densities of HEs are consistent with the characteristics of Gaussian distribution. To provide quantitative features for TCM, we extracted the basic parameters of the Gaussian distribution of HEs in the feed direction (Y direction), i.e. 𝜇 (means), and 𝜎 (standard deviations). While estimating WTMMs, under the same amount of data, the variation of the number of singular points was found correlated to the change of tool conditions. Finally, we extracted the Means, Standard deviations of HEs, and Number of singular points in the feed direction, which are shown in Fig. 9(a)–(c). As shown in Fig. 9, it can be found that the change of Means and Number is more related to the variation of VB than standard deviations. After adding the boundary lines of different wear states in Fig. 9(b) and (c), we found another very interesting phenomenon that the Means of HE values and Number of singular points are quite sensitive to the transition points of different wear states, the transition points are determined by the variations of wear rate, i.e. VB′ [30]. Although the transition point of the different wear states is not an indicator of whether the tool is blunt or not. Once the tool reaches the transition point from the steady state to the accelerated wear zone, it would decay rapidly afterward until blunt. Therefore, this phenomenon can be employed as a feature to forewarn the termination of tool life.
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International Journal of Mechanical Sciences 166 (2020) 105254
Fig. 7. HE variations of three typical tool conditions. (a) HE variation of vibration in X direction, (b) HE variation of vibration in Y direction, (c) HE variation of vibration in Z direction.
Fig. 8. HEs’ probability densities of three typical tool conditions. (a) HEs’ probability densities of vibration in X direction, (b) HEs’ probability densities of vibration in Y direction, (c) HEs’ probability densities of vibration in Z direction.
It can be perceived that when the tool begins to breaking-in, Means of HE values start to increase. This is because that there are lots of burrs on the edge of a brand-new tool, and the initial wear state is to grind off the inhomogeneous burrs on the blade, making the tool become nominal sharper [31]. This produces more singular points in the vibration signals, which leads to a low HE profile in turn at the very beginning, as shown in Fig. 9(c). From Fig. 9(e) to (d), as the tool reaches the sharpest state after the breaking-in period, Means also reaches a high value and Number of singular points touch the bottom as shown from Fig. 9(b) and (c). In order to give a reasonable explanation for the transition point from the steady state to the accelerated wear zone, we observed the tool wear process before and after the transition point (about 48th cut) from the steady wear state to the accelerated wear zone in the experiment detailed in Section 3.1, as shown in Fig. 10. After entering the steady wear state, the mechanical interactions and frictions between tool and workpiece result in the abrasive wear on the tool, the tool wear is uniform and increasing slowly. Along with the cutting process, some materials of the work-piece are adhered to the cutting edge due to the accumulation of intense heat [27], as the marked region by a green ellipse in (a) of Fig. 10. Subsequently, the tool materials on the cutting edges are taken away gradually by the bonded work-piece materials and formed the adhesion wear. The bonded materials and the gradual losses of the edges lead to the increase the degree of the singularity of the vibration and result in more singular points, which can be seen from Fig. 9(b) and (c). By the end of this state, the original cutting edges are worn out, as shown in (b) of Fig. 10. This would accelerate tool wear and damage, resulting in the tool entering the accelerated wear zone. When the original cutting edges wear out, the friction force in the tool-work-piece interface and the contact area of the wear land will increase, which result
in a significant increase in the amplitudes of vibration [27,29,31], as displayed from Fig. 9(g) to (f). Increased amplitudes of vibration will suppress the degree of signal fluctuation, resulting in a reduction in the Number of singular points and increasing the Means of HEs. Remark 2. HE features, including Means of estimated HE values and Number of singular points of feed direction vibration components, are found most correlated with tool conditions. 3.3. Public database verification In order to verify the phenomenon, we accessed a public database from a similar experiment [32]. The public database employed three 10-mm diameter 3-flute ball-nose cutters to machine the work-piece (Inconel 718) until a significant wear land. The vibration signals in three mutually orthogonal directions were monitored by three Kistler piezo accelerometers continuously. The sampling frequency was set as 50 kHz/channel. And the amount of wear was measured after each cut for three experiments (each set with 315 passes). The three experiments were labeled as cutter1, cutter2, and cutter3. The cutting parameters were constant for all the experiments: the spindle speed was 10,400 rpm, the feed rate was 1555 mm/min, the Y depth of cut (radial) was 0.125 mm and the Z depth of cut (axial) was 0.2 mm. Using the same data processing algorithm, HE values of vibration data contained in 10 rotation cycles in the feed direction of 3 cutters were estimated, then Means and Number were extracted as features to verify the relationship with tool wears, as shown in Figs. 11–13. By observing the trend of the wear curves of the three cutters, it can be found that they all match the typical tool life curve basically. However, due to the tool run-out effect and milling system dynamics in machining processes, the flank wear of three cutters is different from
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International Journal of Mechanical Sciences 166 (2020) 105254
Fig. 9. HE variations of the three typical tool conditions. (a) Standard deviations of HE values, (b) Number of HE values, (c) Means of HE values, (d)~(g) De-noised vibration waveforms containing one rotation of cut 2, 5, 47 and 51.
Fig. 10. Tool wear process. (a) after 47th cut, (b) after 48th cut.
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International Journal of Mechanical Sciences 166 (2020) 105254
Fig. 11. Relationship between HE features and tool wear of cutter1. (a) Means, (b) and Number. Fig. 12. Relationship between HE features and tool wear of cutter2. (a) Means, (b) and Number.
220 8
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10 760 740 720 700 680 660 640 620 600 580 560 540 520 500
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(a)
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(b)
Fig. 13. Relationship between HE features and tool wear of cutter3. (a) Means, (b) and Number.
each other even with identical cutting conditions. However, based on the variation of wear rates, the transition points of cutter2 and cutter3 are quite similar to the experiment in Section 3.1, as marked by the green box in Figs. 12 and 13. As for the cutter1, only the transition point from the initial zone to the steady state is evident, as indicated by the green box in Fig. 11. After that, the wear rate of cutter1 showed a significant increase, but the wear rate subsequently decreased, and no
abrupt changes occurred again. This may be related to the potential abnormal wear process of cutter1. The similar situation can also be found in the literature, which employed the same public database [5,33]. For the transition point after the breaking-in, the Means and Number have the identification ability, but with large fluctuations, which are obvious in Figs. 11–13. For the transition point from steady state region to the accelerated wear zone, both Means and Number show a
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International Journal of Mechanical Sciences 166 (2020) 105254
sensitive and robust recognition capability. It is observed clearly that the local maxima of Means, local minima of Number are directly related to this transition point, as shown in Figs. 12 and 13. It can be observed that the variation trends of Means and Numbers are similar to those of the experiment detailed in Section 3.1. However, due to the differences in the cutting process and the vibration acquisition process, the continuity of the vibration collected in our experiment is poorer than the public database, especially when the wear rate changes abruptly. After reaching the transition point (48th cut), the contact between cutting edge and work-piece starts to deteriorate, which increase the wear rate rapidly. However, the duration of the 15 sets of milling experiment is about 7 min; it is long enough to cause a significant change on the cutting edges under these circumstances. And this accounts for the abrupt changes of Means and Numbers after the transition point in Fig. 9(b) and (c). Anyway, these sensitivities are consistent with this paper’s experiment. Because the cutting tools, material properties and dimensions of work-pieces, machining centers, and processing parameters, etc. used in the public database are totally different from this paper’s experiment, the existence of same phenomena further proves that these two HE features (Means and Number) has robust recognition ability to the transition points of different wear states. And this sensitivity is independent of the values of VB, the type of milling tools, the material of work-pieces, and the processing parameters. Remark 3. These HE features are highly sensitive to the transition points of different wear states defined by VB, especially from the steady state region to the accelerated wear zone. In addition, this sensitivity is independent of the values of VB, the type of milling tools, the material of work-pieces, and the processing parameters. 4. TCM approach with HE features Based on the above analysis, this paper proposes a TCM approach based on a machine learning model and a transition points identification method (TPIM). Fig. 15 details the entire online TCM process. After the start of TCM, the vibration signal is continuously collected. At time t == i, we extract the vibration signal contained in 10 rotation cycles and estimate the HE features (Means and Number). Next, they are used as inputs into the machine learning model and TPIM simultaneously. Then outputs of above two units would be analyzed comprehensively to decide which state the tool belongs to. The proposed TCM approach would employ the raw data from the public database [32] to do training and classification. This paper refers to the Taylor’s tool life curve to establish the tool conditions [1], the cross-over points of the 2nd derivative of the curve are selected to divide the different wear states. For the sake of brevity, we use the closest 10 𝜇m as the threshold. Therefore, this paper establishes three tool conditions categories as follows: State 1 is the initial wear zone with 0–60 𝜇m; state 2 is steady wear state with 60–120 𝜇m; state 3 is accelerated wear state with ≥120 𝜇m [5,34]. 4.1. Machine learning models In this paper, Several commonly-used machine learning models were employed for classification, such as Support Vector Machine (SVM), kNearest Neighbor (KNN), Decision Tree, Ensemble Learning, etc. Data of the two experiments (cutter1 and cutter2) are selected as training samples, and data of the rest experiment (cutter3) is employed as the test sample. The optimal kernel parameters of each machine learning model are selected by the grid search with cross validation. The test accuracy and the optimal kernel parameters of these models are shown in Table 2. The results show that the SVM model has the highest test accuracy. Afterward, this model would be used to cooperate with the TPIM in Section 4.3.
Fig. 14. Scheme of the transition points identification method.
4.2. The transition points identification method Fig. 14 shows the scheme of the transition points identification method. Since the high volatility of vibration HE features, which can be observed in Fig. 11, the curve fitting method is employed to smooth curves. According to the analysis of experimental data of cutter1 and cutter2, it is found that the cubic polynomial can well fit the trends of HE features in all time. To realize real-time searching for extreme points on the curve accurately and quickly, this paper adopts a sliding window polynomial fitting method. In the actual production of factories, engineers are most concerned about whether the tool is blunt or damaged. Therefore, we are only interested in transition points from steady state region to the accelerated wear zone; in other words, we only search for the minima of Means and maxima of Number. As the experiment proceeds, at time t == i, the new features (Mean(i) and Number(i)) would form new data sequences with the previous features according to the width of the sliding window. Then a cubic polynomial would be used to curve fit these sequences. Fitting errors are analyzed based on Least-square principle. After that, we would search the local extrema by calculating the first and second derivatives of the fitted curves. If we find the extreme points (minima of Means and maxima of Number) on both curves simultaneously, we continue to search for extreme points. Then if we find the extreme points for specific consecutive times, and the position coordinates of the extrema fluctuate within a narrow range. At this point, we can be sure that the transition point is found.
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Table 2 Test accuracy of machine learning models. Machine learning models
Kernel parameters
Test accuracy
Support Vector Machine
Kernel function Kernel scale
Gaussian 0.35
81.9%
k-Nearest Neighbor
Number of neighbors Distance metric
10 Minkowski (cubic)
81.3%
Decision Tree
Max number of sploits Split criterion
20 Gini’s diversity index
79.3%
Ensemble Learning
Ensemble method Max number of splits Number of learners
AdaBoost 20 30
78.1%
Table 3 Decision strategy. Output of SVM
Output of Transition point
Final decision
1 2 3 1 2 3
No No No Yes Yes Yes
1 2 2 2 2/3 3
Tool wear state
3
Defined tool wear state Estimated tool wear state Modified tool wear state
2
1 0
50
100
150
200
250
300
Cuts Fig. 16. Estimated and modified tool wear states.
Fig. 15. Scheme of the TCM approach.
The width of the sliding window and specific consecutive times depend on sampling intervals and tool life. In this case, they are set as 20 and 10. Without loss of generality, we assume that the first several passes would not blunt the tool. So we started TPIM from the 21st pass, which corresponds to the sliding window width.
Table 4 Accuracy performance of studies published on TCM with vibration in milling. Authors
Sample features
Test accuracy
Zhou et al. [34] Xie et al. [35] Aghazadeh et al. [36] P. Krishnakumar et al. [37]
Singularity features wavelet packets features wavelet packets features Wavelet features
86.2% 92.4% 84.6% 88.89%
4.3. Tool condition estimation results By observing Figs. 11–13, it is found that state 3 begins to appear only after the transition point occurs. Therefore, the outcome of TPIM would modify three estimated outcomes of SVM model: if the transition point is not identified, result ‘3’ of SVM model would be modified by ‘2’; if the transition point has been identified, result ‘1’ would be modified by ‘2’. In addition, after the transition point is identified, once the result of SVM is ‘3’, the subsequent estimation results would be fixed to ‘3’, the scheme of the TCM approach is illustrated in Fig. 15. Table 3 illustrates the decision strategy of the final estimation results. Fig. 16 shows the estimated tool wear states of the SVM model and the modified tool wear states by TPIM. It shows that the TCM approach has more accurate classification results, which can reach a classification rate of 90.8%. The classification rate of the SVM model without TPIM is 81.9%. Table 4 shows the classification accuracy performance of the state of the art studies on TCM with vibration signals in milling. It can be observed that the classification result of the proposed TCM approach
is comparable to the above studies. Although the classification rate is not so good, it is enough to guide the tools’ replacement in the factory. Remark 4. A TCM approach is proposed which utilized an SVM model and a TPIM. The proposed TPIM would help to modify the classification results of the SVM model, which can help reach a total classification rate of 90.8%. 5. Conclusion In the present study, a vibration singularity analysis approach is proposed for tool condition monitoring in milling. A wavelet basis selection method is presented to pick the optimal wavelet bases for the sensor signals. Both the Type Ⅰ and Type Ⅱ singularities are found in the vibration signals of the milling. The 2nd derivative of Gaussian wavelet with 2 vanishing moments is found most effective to estimate the singularity
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of vibration signals in milling. The Holder Exponents (HE) were used to estimate the singularity of vibration signals. It was found that Means of HE values and Number of singular points in the feed direction of vibration signals are the most relevant and effective features. And these HE features are highly sensitive to the transition points of different wear states defined by VB, especially from the steady state region to the accelerated wear zone. It is proven that this sensitivity is independent of the values of VB, the type of milling tools, the material of work-pieces, and the processing parameters. A TCM approach is proposed which utilized an SVM model and a transition points identification method (TPIM). Experimental results show that the modification of TPIM helps to reach more accurate classification results. It is shown that the proposed approach is efficient enough to guide the tools’ replacement in the factory. Future researches would be focusing on accommodating this approach with other types of cutting. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant 51975335 in part by the Major Scientific and Technological Project of Shandong Province under Grant 2019GGX104008, and in part by the Key Laboratory of High-efficiency and Clean Mechanical Manufacture at Shandong University, Ministry of Education. References [1] Shaw MC. Metal cutting principles. 2nd ed. New York: Oxford University Press; 2005. [2] Rahman M, Kumar AS, Prakash JRS. Micro milling of pure copper. J Mater Process Techol 2001;1(116):39–43. doi:10.1016/S0924-0136(01)00848-2. [3] Altintas Y, Yellowley I. In-process detection of tool failure in milling using cutting force models. J Eng Ind 1989;2(111):149–57. doi:10.1115/1.3188744. [4] Piotr G. The manipulator tool state classification based on inertia forces analysis. Mech Syst Signal Process 2018;107:122–36. doi:10.1016/j.ymssp.2018.01.002. [5] Zhu KP, Liu TS. Online tool wear monitoring via hidden semi-markov model with dependent durations. IEEE Trans Ind Inf 2018;1(14):69–78. doi:10.1109/TII.2017.2723943. [6] Kunpeng Z, Soon HG, San WY. Multiscale singularity analysis of cutting forces for micromilling tool-wear monitoring. IEEE Trans Ind Electron 2011;58(6):2512–21. doi:10.1109/TIE.2010.2062476. [7] Nouri M, Fussell BK, Ziniti BL, Linder E. Real-time tool wear monitoring in milling using a cutting condition independent method. Int J Mach Tool Manuf 2015;89:1– 13. doi:10.1016/j.ijmachtools.2014.10.011. [8] Li XL, Tso SK, Wang J. Real-time tool condition monitoring using wavelet transforms and fuzzy techniques. IEEE Trans Syst Man Cybern: Syst 2000;3(30):352–7. doi:10.1109/5326.885116. [9] Tonshoff HK, Li XL, Lapp C. Application of fast Haartrans form and concurrent learning to tool-breakage detection in milling. IEEE-ASME Trans Mech 2003;3(8):414–17. doi:10.1109/TMECH.2003.816830. [10] García Plaza E, Núñez López PJ. Application of the wavelet packet transform to vibration signals for surface roughness monitoring in CNC turning operations. Mech Syst Signal Process 2018;98:902–29. doi:10.1016/j.ymssp.2017.05.028. [11] Albertelli P, Braghieri L, Torta M, Monno M. Development of a generalized chatter detection methodology for variable speed machining. Mech Syst Signal Process 2019;123:26–42. doi:10.1016/j.ymssp.2019.01.002. [12] Zhou JH, Pang CK, Zhong ZW, Lewis L. Tool wear monitoring using acoustic emissions for dominant-feature identification. IEEE Trans Instrum Meas 2010;2(60):547– 59. doi:10.1016/10.1109/TIM.2010.2050974. [13] Ai CS, Sun YJ, He GW, Ze XB, Li W, Mao K. The milling tool wear monitoring using the acoustic spectrum. Int J Adv Manuf Techol 2012;5-8(61):457–63. doi:10.1007/s00170-011-3738-z. [14] Rehorn AG, Jiang J, Orban PE. State-of-the-art methods and results in tool condition monitoring: a review. Int J Adv Manuf Techol 2005;7-8(26):693–710. doi:10.1007/s00170-004-2038-2.
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International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
Vibration singularity analysis for milling tool condition monitoring Chang’an Zhou a,b, Bin Yang a,b, Kai Guo a,b,∗, Jiangwei Liu a,b, Jie Sun a,b, Ge Song c, Shaowei Zhu c, Chao Sun c, Zhenxi Jiang c a
Key Laboratory of High-efficiency and Clean Mechanical Manufacture, National Demonstration Center for Experimental Mechanical Engineering Education, School of Mechanical Engineering, Shandong University, Ji’nan 250061, China b Research Center for Aeronautical Component Manufacturing Technology & Equipment, Shandong University, Ji’nan 250061, China c Chengdu Aircraft Industrial (Group) Co., Ltd, Chengdu 610091, China
a r t i c l e
i n f o
Keywords: Vibrations Tool condition monitoring Singularity Transition points Support Vector Machine
a b s t r a c t Tool condition monitoring (TCM) is a very effective way to enhance productivity and ensure work-piece quality. This paper introduces a cutting condition independent TCM approach for milling with vibration singularity analysis. Holder Exponents (HE) are chosen as index to estimate the singularity of vibration signals. Wavelet transform modulus maxima (WTMM) are employed to estimate HEs. A wavelet basis selection method is established to select the optimal wavelet bases for the estimation of HEs. Means of HE values and Number of singular points of feed direction vibration components are found to be the most correlated with tool conditions based on experimental study. The sensitivity between these HE features and the transition points of different tool wear states is discovered. Verified by a public database, this sensitivity is found independent of the cutting conditions. Then a TCM approach is proposed which utilized a Support Vector Machine (SVM) model and a transition point identification method (TPIM). Experiment results indicate that this approach is efficient and the TPIM helps to reach more precise classification results.
1. Introduction With the increasingly fierce competition in the global manufacturing industry in recent years, it becomes urgent to further improve production efficiency, product quality, and reduce production costs. In the high-speed CNC manufacturing industry, the expense of cutting tools is one of the major manufacturing costs. However, tool wear is an inevitable and common issue, which affects the surface quality and dimensional accuracy directly. An efficient and robust online system that can monitor tool conditions continuously becomes necessary to enhance productivity and ensure work-piece quality [1]. To fulfill the TCM tasks properly, a great amount of the TCM models published recently are focused on empirical analysis [2], or sensory data-driven methods such as cutting forces [3–7], spindle current [8,9], vibration [10,11], and acoustic emission (AE) [12,13]. The related studies have been summarized in several comprehensive reviews [14,15]. Typically, the TCM system employs sensing systems to monitor the process, and then extract most relevant information from the sensory signals to identify and classify the tool conditions, to reduce the cost increased by tool failure. As sensing technology continues to mature and advance, how to extract the most relevant information has become a vital issue for
∗
TCM. However, discontinuous cutting is one of the remarkable features of the milling process, and this would result in nonstationary sensory signals. The commonly-used time-domain statistical features, frequencydomain features [16,17] are sensitive to the variation of cutting conditions [7] in milling; this would limit the applications of the proposed TCM systems. Wavelet analysis has strong time-frequency analysis capability to analyze nonstationary signals effectively [15,18]. Singularity analysis is applied early in image processing, and the correspondence between singularity and abrupt shift in pixel point mutations is often used to identify boundaries in images [18]. These similar singularities are also be observed in sensory signals collected in the machining process, especially as tipping and tool breakage occur [19]. Fourier transform and wavelet analysis are commonly used singularity analysis tools, but wavelets can provide a better time-frequency localization property. Chen and Li [20] first presented singularity analysis base on wavelet transform to cope with TCM in machining, the wavelet coefficient norm and statistical features of AE signals were selected as data samples to classify tool conditions in turning. Fractal property is one of the important attributes of singularity analysis; it was also employed to classify the variation of tool conditions in turning [21], they established a recurrent neural network to connect the fractal features of
Corresponding author at: School of Mechanical Engineering, Shandong University, 17923 Jingshi Road, Ji’nan 250061, China. E-mail address: [email protected] (K. Guo).
https://doi.org/10.1016/j.ijmecsci.2019.105254 Received 19 August 2019; Received in revised form 16 October 2019; Accepted 16 October 2019 Available online 17 October 2019 0020-7403/© 2019 Elsevier Ltd. All rights reserved.
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International Journal of Mechanical Sciences 166 (2020) 105254
Whereas, the blunt tool has smoother waveforms with fewer singularities. This waveform disorder and their singularities can be quantified by Holder Exponent (HE) [18]. 2.2. Singularity estimation with HE If a function f(t) is not differentiable at t0 , then the f(t) is said to be singular at t0 [18]. The HEs are useful index to quantize the singularity. Generally, a small HE means a singular point while a large HE represents a regular one. If A > 0 and a polynomial pv (t) of degree m exist, where m is the largest integer and m ≤ 𝛼 is satisfied, such that |𝑓 (𝑡) − 𝑝𝑣 (𝑡)| ≤ 𝐴|𝑡 − 𝑣|𝛼 | |
Fig. 1. Vibration waveform shapes under different tool wears. The variation of tool condition are correlated to changes of the vibration waveforms.
machining dynamics with flank wear. Zhu et al. [6,22] introduced the probability density functions of singularity estimated from cutting force in micro-milling to correlate with different tool conditions, and the insensitivity to cutting conditions such as work-piece material, federate, depth of cut, etc. was verified by experiment studies. In summary, the recent TCM studies with singularity analysis [6,21,22] were focusing on cutting force, AE in turning or micro-milling process experimentally or theoretically. As a result of the non-stationarity and the sophistication of the vibration signal of the milling process, the TCM approaches based on singularity analysis of vibration signals are rarely established. The purpose of the present paper is to analyze the singularities of vibration waveforms in milling systematically, which can be used to fulfill the TCM task. The highlights of this paper are summarized as follows: 1 A wavelet basis selection method is presented to pick the optimal wavelet bases for the sensor signals. The wavelet bases with 2 vanishing moments are found most effective to estimate the singularity of vibration signals in milling. 2 HE features, including Means of estimated HE values and Number of singular points of feed direction vibration components, are found most related to different tool conditions. And they are highly sensitive to the transition points of different wear states defined by VB′. This sensitivity is independent of the values of VB, the type of milling tools, the material of work-pieces, and the processing parameters. 3 A TCM approach is proposed which utilized an SVM model and a transition point identification method (TPIM). The TPIM can modify the outcomes of the SVM model and help to reach more precise classification results. The rest of this paper is organized as follows. Section 2 discusses the theoretical basis of singularity analysis. The full tool life-cycle milling experiment setups, results analysis and the public database verification are presented in Section 3. Then online TCM approaches are proposed and discussed in Section 4. Conclusion and future studies are summarized in Section 5. 2. Tool condition estimation from vibration singularity 2.1. Vibration waveforms and tool conditions Vibration shows a keen sensitivity to tool conditions [11], and it is quite convenient to be acquired during milling. As mentioned above, the underlying assumption is that with the proceeding of the milling process, the variation of tool condition is correlated to changes of the vibration waveforms, as can be seen in Fig. 1. The waveform of the fresh tool is relatively more disorder, which means stronger singularity.
(1)
where is A is an invariable, then this upper bound is depend on this 𝛼. When the 𝛼 in function |f(t) − Pv (t)| ≤ A|t − v|𝛼 (1) reaches the supremum, we say this 𝛼 is the HE of f(t) at t = v. If f(t) is n-time differentiable and the nth derivative is singular at v (with n < 𝛼 < n ++ 1), then 𝛼 can represent this singularity. The computation of HEs is complicated. It was discovered that HEs could be calculated by estimating their wavelet transform modulus maxima (WTMM) and checking the decay of the WTMMs in the time-scale plane[18]. Firstly, to estimate the WTMMs along the scale at position u, the partial differentiation of wavelet transform WTf(u, s) is calculated, make it equal to zero: 𝜕𝑊 𝑇 𝑓 (𝑢, 𝑠) = 0. 𝜕𝑢
(2)
where s is scale. In the scale-space (s, u), we call any connected lines, along which all points are modulus maxima, a maxima line [18]. Along the maxima line, the coefficients of wavelet transform WTf(u, s) have the scaling ability around t, such that: |𝑊 𝑇 𝑓 (𝑡)|𝐴 ≤ 𝑠𝛼+1∕2 . 𝑠 | |
(3)
where A is decided on the selection of the wavelet basis 𝜓(t). To reduce the amount of calculation, the discrete scale s == 2j was used as follows: log2 ||𝑊 𝑇2𝑗 𝑓 (𝑡)|| ≤ log2 𝐴 + 𝑗(𝛼 + 1∕2).
(4)
By making equality in log2 |𝑊 𝑇2𝑗 𝑓 (𝑡)| ≤ log2 𝐴 + 𝑗(𝛼 + 1∕2) (4), A and 𝛼 can be obtained. The connection between j and 𝛼 is established by log2 |𝑊 𝑇2𝑗 𝑓 (𝑡)| ≤ log2 𝐴 + 𝑗(𝛼 + 1∕2) (4). The function also connects WTMM and j or s. A higher value of 𝛼 indicates that f(t) is less singular [18]. The HEs estimated by WTMMs was first introduced to analyze selfsimilar phenomena [23]. After that, it was employed to build a diagnosis system for machinery faults [24,25]. 2.3. Signal de-noising based on wavelet modulus maxima Comparing Fig. 2(a) and (b), it can be found that the raw vibration signal, which is taken from the 10th milling experiment in feed direction detailed in Section 3.1, is contaminated by noises. Considering the spindle speed of 1273.27 r/min and sampling frequency of 8192 Hz, there are about 386 points in total for one rotation of the spindle. Since the singularity of noise is usually negative [18], when the HE value generated by the signal is positive, the presence of noise will reduce the sum. Generally, the effective signal collected during cutting has the lowfrequency property, and the noise is high-frequency signal. Therefore, low-pass filters, wavelet filters, etc., which are commonly used by engineers, are taking advantage of these features for de-noise. Although they can effectively remove the high-frequency noise, they can also result in losing some important information of the signal, as shown in Fig. 2(b). Since the noises generate negative singularities, the WTMMs produced by noises can be told apart from those generated by effective signals. When estimating the WTMMs, if the value of the detected WTMM increases with the decrease of the scale notably, we would say that this
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Fig. 2. (a) Raw vibration signal of the 10th milling experiment. (b) Signal de-noised by wavelet filter with db3. (c) Signal de-noised by WTMM by Haar wavelet, which has 1 vanishing moment. (d) Signal de-noised by WTMM by 2nd derivative of Gaussian wavelet with 2 vanishing moments. (e) Signal de-noised by WTMM by 3th derivative of Gaussian wavelet with 3 vanishing moments. (f), (g), (h), (i), (j) are the corresponding frequency spectrum of (a), (b), (c), (d), (e).
point is dominated by noise and setting it zero. After checking all the data points, we rebuild the signal by means of Mallat’s method [18]. By comparing Fig. 2(b)–(e), it can be seen that the de-noising algorithms by estimating WTMMs can effectively remove the noise and obtain a
smoother curve. In order to verify the de-noising effect of WTMM algorithm, the signal-to-noise ratios (SNR) of different algorithms were estimated for more randomly selected data sets from the experiments presented in Section 3.1, as shown in Table 1.
Table 1 SNR (db) of different de-noising algorithms. Experiment No.
Wavelet filter
WTMM by 1st derivative of Gaussian wavelet
WTMM by 2nd derivative of Gaussian wavelet
WTMM by 3th derivative of Gaussian wavelet
5th 10th 21th 50th
−5.2791 −4.3495 −3.6263 −15.0404
−1.4358 −1.1541 −0.4606 −5.517
−3.1063 −2.0729 −0.7248 −6.9737
−3.6901 −2.1235 −1.1681 −7.3791
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ments [18]. Therefore, in this paper, we used the Gaussian wavelet as the wavelet basis. It is worth noting that large vanishing moments can increase the number of WTMMs at a particular scale. Considering computational efficiency, we desire the least quantity of maxima necessary to estimate the needed singularity in the signal. Therefore, we have to select a wavelet basis with as few vanishing moments as possible, but enough to perceive the HE of the highest order. Comparing subgraphs (c) and (d) of Fig. 2, it can be found that the smoothness of the de-noised signal with 2 vanishing moments is improved. This is mainly due to the fact that the wavelet basis with 2 vanishing moments could find both Type Ⅰ singular points and Type Ⅱ singular points, i.e. the discontinuities in the 1st derivative of the signal. Consequently, more points could be assessed to check which are preponderated by noise or not. Further eliminating noise components can obtain a smoother curve. A significant reduction in SNR also indicates that more noise is removed. To verify the de-noising effect, the frequency spectrum analyses are carried out on the de-noised samples. The energy of the effective vibration signal is mainly concentrated around the tooth passing frequency (TPF) and its integral multiples [27,28]. 𝑇𝑃𝐹 = 𝑁 × Fig. 3. Correspondence relationship between singularity and modulus maxima lines.(a) is a Type Ⅰ singular point, wavelet bases with 1 or 2 vanishing moments all can create WTMMs. (b) is Type Ⅱ singular point, only a wavelet basis with more than 2 vanishing moments can create WTMM here.
2.4. Wavelet basis selection method Heretofore, there is still a lack of wavelet basis selection methods for vibration signals of machining. Since some properties of the wavelet basis are interrelated and constrained, it is necessary to select the wavelet basis according to the characteristics of the milling vibration. The wavelet bases selected for HEs’ estimation must possess the following attributes: continuously differentiable, with suitable vanishing moments, symmetry or anti-symmetry [18]. There are two kinds of singularities in real signals: Type Ⅰ, which are the discontinuities of the signal at point c; Type Ⅱ, which are the discontinuities of the nth derivative of the signal at point c, as shown in Fig. 3. Reasonable selection of wavelet basis can help us to preserve the useful information in the raw signals. And the selection is closely related to the vanishing moments. A wavelet basis 𝜓(t) is with n vanishing moments, if and only if for all positive integer k < n, it satisfies [26] +∞
∫−∞
𝑡𝑘 𝜓(𝑡)𝑑𝑡 = 0.
(5)
When the selected 𝜓(t) has n vanishing moments with small compact +∞ support 𝜃, then 𝜓(t) can be written as𝜓 = ( − 1)n 𝜃 (n) with ∫−∞ 𝜃(𝑡)𝑑𝑡 ≠ 0. The WTf(u, s) can be rewritten as follows: ) 𝑑𝑛 ( 𝑊 𝑓 (𝑢, 𝑠) = 𝑠 𝑓 × 𝜃̄𝑠 (𝑢). 𝑑𝑢𝑛 𝑛
(6)
If 𝜓 = −𝜃′, it has 1 vanishing moment, the WTMM is the maximum of the 1st derivative of f smoothed by 𝜃̄𝑠 . The WTMM could find abrupt 2 shifting points. If 𝜓 = 𝜃′′, the WTMM of 𝑊2 𝑓 (𝑢, 𝑠) = 𝑠2 𝑑 2 (𝑓 ∗ 𝜃̄𝑠 )(𝑢) 𝑑𝑢
meets with local maximum curvatures. In addition, it is perceived that the WTMM of local maximum curvity is correlated to the singularity of sharp shifting point. However, when we do not know which type of singularity the signal has beforehand, we cannot choose the suitable vanishing moment. Based on the results of repeated trials, we propose a wavelet basis selection method: At first, the wavelet bases with various vanishing moments are used to de-noise the raw signals; after that by evaluating the noise reduction effect, we can judge which type of singularity signal has. The Gaussian wavelet is a commonly used wavelet basis for singularity detection, and its nth derivative is a wavelet basis with n vanishing mo-
1273.27 𝑛 =4× = 84.88(Hz). 60 60
(7)
where N is the number of cutting edges, here it is 4. And n is the spindle speed with 1273.27 (r/min). By observing Fig. 2(h) and (i), it can be seen that 2nd derivative of Gaussian wavelet can eliminate more energy of high-frequency noises and preserve the energy around integral multiples of TPF. This proves that there are two types of singularities in the milling vibration signal again. Comparing Fig. 2(d), (e), (i) and (j), it is perceived that the wavelet basis with 3 vanishing moments could make the curve of the de-noised signal smoother, but not significantly. And the similar conditions occur in the results of SNR and frequency spectrums. Given a comprehensive consideration of the cost of calculation and de-noising effect, the wavelet basis with 2 vanishing moments is effective enough to estimate the singularity of vibration signals in milling. Here, the 2nd derivative of Gaussian wavelet (also named Mexican Hat wavelet) is used for denoising and estimating singularities, which is shown as follows: 1( ) 𝑡2 2 𝜓(𝑡) = √ 𝜋 − 4 1 − 𝑡2 𝑒− 2 . 3
(8)
Remark 1. A wavelet basis selection method is presented to pick the optimal wavelet bases for the sensor signals. The wavelet bases with 2 vanishing moments are found most effective to estimate the singularity of vibration signals in milling. 2.5. HE estimation Since the estimation of WTMMs is the same process for HE estimation and de-noising, we integrated the de-noising algorithm into the HE estimation. The HE estimating process is shown in Fig. 4. In the de-noising algorithm with the estimation of WTMMs, because the number of WTMMs of noise decreases as the scale (2j ) increases [18], a relatively large scale is necessary to ensure the useful signal dominant, j = 4–5 is selected usually [22]. After estimating WTMMs for all (u,s), a threshold T of the WTMM at the largest scale would be set, which is used to locate the WTMMs dominated by the noise. The WTMMs below T would be deleted. The T is set as ( √ ) 1 + 2 𝑃𝑁 × 𝑀. (9) 𝑇 = log2 𝐽 +𝑍 where Z is invariable, here it is 2 [22]. J is the maximum for the discrete scale s = 2j (j = 0,1,2…J) . PN is the power of noise. M is the maximum WTMM, 𝑀 = max |𝑊2𝐽 (𝑥𝑖 )|.
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Fig. 6. Variation of flank wear. The wear curve can be clearly divided into three regions: the initial wear state (A), the steady state region (B) and the accelerated wear zone (C).
Fig. 4. HE estimation procedure.
divided into three regions: the initial wear state (A), the steady state region (B) and the accelerated wear zone (C), which is consistent with the typical wear pattern [1].
3.2. Holder exponent analysis
Fig. 5. Experiment setup.
3. Experiments and discussions 3.1. Full tool life-cycle milling experiments The full tool life-cycle milling experiments were performed on a CNC machine center (Hartford CNC-168). The setup of the experiments is displayed in Fig. 5. The work-piece material was Ti–6Al–4V. The tool was a 20-mm diameter 4-flute YG solid cemented carbide end mill with a helix angle of 38°. 60 sets of data acquisition experiments were carried out with identical cutting parameters: the spindle speed was 1273.27 r/min, the feedrate was 80 m/min, the X depth of cut (radial) was 0.8 mm, and the Z depth of cut (axial) was 18 mm. A triaxial piezoelectric accelerometers (PCB -356A15) was mounted on the spindle with a magnetic base to measure the vibration during the data acquisition experiments. The vibration signals were recorded by a NI cDAQ-9171 with a sample frequency of 8192 Hz. The tool wear is measured after each data acquisition experiment by a digital microscope (Dino-Lite AM3113). Due to the limited size of the work-piece, 15 sets of milling experiment were performed on scraps between each data acquisition experiment with the same cutting parameters to wear the tool. Fig. 6 shows the variation of maximum flank wears through the entire cutting process. It can be observed that the wear curve can be clearly
As a case study, Fig. 7(a)–(c) shows the HE variations of three typical tool conditions (Fresh - cut 2, Partly worn - cut 32 and Worn cut 53) from vibration. The calculation process used vibration samples contained in 30 rotation cycles for a total 11,550 points. It can be observed that the HEs of 3 vibration components are concentrated in narrow bands, and their fluctuation ranges overlap significantly. Therefore, the HEs itself cannot be directly used as input samples for TCM tasks. Whereas, Zhu et al. [22] discovered that the probability densities distribution of HEs showed a strong relationship with tool conditions. Fig. 8 shows HEs’ probability densities of identical data displayed in Fig. 7. Comparing the Fig. 8(a)–(c), it can be observed clearly that there is a more obvious difference in the probability density distributions of the HE value in the feed direction (Y direction) of three different tool conditions. In the same time, it can be seen that all these probability densities of HEs are consistent with the characteristics of Gaussian distribution. To provide quantitative features for TCM, we extracted the basic parameters of the Gaussian distribution of HEs in the feed direction (Y direction), i.e. 𝜇 (means), and 𝜎 (standard deviations). While estimating WTMMs, under the same amount of data, the variation of the number of singular points was found correlated to the change of tool conditions. Finally, we extracted the Means, Standard deviations of HEs, and Number of singular points in the feed direction, which are shown in Fig. 9(a)–(c). As shown in Fig. 9, it can be found that the change of Means and Number is more related to the variation of VB than standard deviations. After adding the boundary lines of different wear states in Fig. 9(b) and (c), we found another very interesting phenomenon that the Means of HE values and Number of singular points are quite sensitive to the transition points of different wear states, the transition points are determined by the variations of wear rate, i.e. VB′ [30]. Although the transition point of the different wear states is not an indicator of whether the tool is blunt or not. Once the tool reaches the transition point from the steady state to the accelerated wear zone, it would decay rapidly afterward until blunt. Therefore, this phenomenon can be employed as a feature to forewarn the termination of tool life.
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Fig. 7. HE variations of three typical tool conditions. (a) HE variation of vibration in X direction, (b) HE variation of vibration in Y direction, (c) HE variation of vibration in Z direction.
Fig. 8. HEs’ probability densities of three typical tool conditions. (a) HEs’ probability densities of vibration in X direction, (b) HEs’ probability densities of vibration in Y direction, (c) HEs’ probability densities of vibration in Z direction.
It can be perceived that when the tool begins to breaking-in, Means of HE values start to increase. This is because that there are lots of burrs on the edge of a brand-new tool, and the initial wear state is to grind off the inhomogeneous burrs on the blade, making the tool become nominal sharper [31]. This produces more singular points in the vibration signals, which leads to a low HE profile in turn at the very beginning, as shown in Fig. 9(c). From Fig. 9(e) to (d), as the tool reaches the sharpest state after the breaking-in period, Means also reaches a high value and Number of singular points touch the bottom as shown from Fig. 9(b) and (c). In order to give a reasonable explanation for the transition point from the steady state to the accelerated wear zone, we observed the tool wear process before and after the transition point (about 48th cut) from the steady wear state to the accelerated wear zone in the experiment detailed in Section 3.1, as shown in Fig. 10. After entering the steady wear state, the mechanical interactions and frictions between tool and workpiece result in the abrasive wear on the tool, the tool wear is uniform and increasing slowly. Along with the cutting process, some materials of the work-piece are adhered to the cutting edge due to the accumulation of intense heat [27], as the marked region by a green ellipse in (a) of Fig. 10. Subsequently, the tool materials on the cutting edges are taken away gradually by the bonded work-piece materials and formed the adhesion wear. The bonded materials and the gradual losses of the edges lead to the increase the degree of the singularity of the vibration and result in more singular points, which can be seen from Fig. 9(b) and (c). By the end of this state, the original cutting edges are worn out, as shown in (b) of Fig. 10. This would accelerate tool wear and damage, resulting in the tool entering the accelerated wear zone. When the original cutting edges wear out, the friction force in the tool-work-piece interface and the contact area of the wear land will increase, which result
in a significant increase in the amplitudes of vibration [27,29,31], as displayed from Fig. 9(g) to (f). Increased amplitudes of vibration will suppress the degree of signal fluctuation, resulting in a reduction in the Number of singular points and increasing the Means of HEs. Remark 2. HE features, including Means of estimated HE values and Number of singular points of feed direction vibration components, are found most correlated with tool conditions. 3.3. Public database verification In order to verify the phenomenon, we accessed a public database from a similar experiment [32]. The public database employed three 10-mm diameter 3-flute ball-nose cutters to machine the work-piece (Inconel 718) until a significant wear land. The vibration signals in three mutually orthogonal directions were monitored by three Kistler piezo accelerometers continuously. The sampling frequency was set as 50 kHz/channel. And the amount of wear was measured after each cut for three experiments (each set with 315 passes). The three experiments were labeled as cutter1, cutter2, and cutter3. The cutting parameters were constant for all the experiments: the spindle speed was 10,400 rpm, the feed rate was 1555 mm/min, the Y depth of cut (radial) was 0.125 mm and the Z depth of cut (axial) was 0.2 mm. Using the same data processing algorithm, HE values of vibration data contained in 10 rotation cycles in the feed direction of 3 cutters were estimated, then Means and Number were extracted as features to verify the relationship with tool wears, as shown in Figs. 11–13. By observing the trend of the wear curves of the three cutters, it can be found that they all match the typical tool life curve basically. However, due to the tool run-out effect and milling system dynamics in machining processes, the flank wear of three cutters is different from
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Fig. 9. HE variations of the three typical tool conditions. (a) Standard deviations of HE values, (b) Number of HE values, (c) Means of HE values, (d)~(g) De-noised vibration waveforms containing one rotation of cut 2, 5, 47 and 51.
Fig. 10. Tool wear process. (a) after 47th cut, (b) after 48th cut.
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Fig. 11. Relationship between HE features and tool wear of cutter1. (a) Means, (b) and Number. Fig. 12. Relationship between HE features and tool wear of cutter2. (a) Means, (b) and Number.
220 8
0.5
200
140
0.3
120
6
Mean
0.4
4
0.2
100
0.1
60 0.0
40 0
50
100
150
200
250
180 160 140 120 100
2
80
Wear rate
180 160
10 760 740 720 700 680 660 640 620 600 580 560 540 520 500
VB Number Wear rate
0
300
Cuts
(a)
80 60 40 0
50
100
150
200
250
8
6
4
Wear rate
200
0.6
VB (μm)
220
VB (μm)
240
10 VB Mean Wear rate
Number
240
2
0
300
Cuts
(b)
Fig. 13. Relationship between HE features and tool wear of cutter3. (a) Means, (b) and Number.
each other even with identical cutting conditions. However, based on the variation of wear rates, the transition points of cutter2 and cutter3 are quite similar to the experiment in Section 3.1, as marked by the green box in Figs. 12 and 13. As for the cutter1, only the transition point from the initial zone to the steady state is evident, as indicated by the green box in Fig. 11. After that, the wear rate of cutter1 showed a significant increase, but the wear rate subsequently decreased, and no
abrupt changes occurred again. This may be related to the potential abnormal wear process of cutter1. The similar situation can also be found in the literature, which employed the same public database [5,33]. For the transition point after the breaking-in, the Means and Number have the identification ability, but with large fluctuations, which are obvious in Figs. 11–13. For the transition point from steady state region to the accelerated wear zone, both Means and Number show a
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sensitive and robust recognition capability. It is observed clearly that the local maxima of Means, local minima of Number are directly related to this transition point, as shown in Figs. 12 and 13. It can be observed that the variation trends of Means and Numbers are similar to those of the experiment detailed in Section 3.1. However, due to the differences in the cutting process and the vibration acquisition process, the continuity of the vibration collected in our experiment is poorer than the public database, especially when the wear rate changes abruptly. After reaching the transition point (48th cut), the contact between cutting edge and work-piece starts to deteriorate, which increase the wear rate rapidly. However, the duration of the 15 sets of milling experiment is about 7 min; it is long enough to cause a significant change on the cutting edges under these circumstances. And this accounts for the abrupt changes of Means and Numbers after the transition point in Fig. 9(b) and (c). Anyway, these sensitivities are consistent with this paper’s experiment. Because the cutting tools, material properties and dimensions of work-pieces, machining centers, and processing parameters, etc. used in the public database are totally different from this paper’s experiment, the existence of same phenomena further proves that these two HE features (Means and Number) has robust recognition ability to the transition points of different wear states. And this sensitivity is independent of the values of VB, the type of milling tools, the material of work-pieces, and the processing parameters. Remark 3. These HE features are highly sensitive to the transition points of different wear states defined by VB, especially from the steady state region to the accelerated wear zone. In addition, this sensitivity is independent of the values of VB, the type of milling tools, the material of work-pieces, and the processing parameters. 4. TCM approach with HE features Based on the above analysis, this paper proposes a TCM approach based on a machine learning model and a transition points identification method (TPIM). Fig. 15 details the entire online TCM process. After the start of TCM, the vibration signal is continuously collected. At time t == i, we extract the vibration signal contained in 10 rotation cycles and estimate the HE features (Means and Number). Next, they are used as inputs into the machine learning model and TPIM simultaneously. Then outputs of above two units would be analyzed comprehensively to decide which state the tool belongs to. The proposed TCM approach would employ the raw data from the public database [32] to do training and classification. This paper refers to the Taylor’s tool life curve to establish the tool conditions [1], the cross-over points of the 2nd derivative of the curve are selected to divide the different wear states. For the sake of brevity, we use the closest 10 𝜇m as the threshold. Therefore, this paper establishes three tool conditions categories as follows: State 1 is the initial wear zone with 0–60 𝜇m; state 2 is steady wear state with 60–120 𝜇m; state 3 is accelerated wear state with ≥120 𝜇m [5,34]. 4.1. Machine learning models In this paper, Several commonly-used machine learning models were employed for classification, such as Support Vector Machine (SVM), kNearest Neighbor (KNN), Decision Tree, Ensemble Learning, etc. Data of the two experiments (cutter1 and cutter2) are selected as training samples, and data of the rest experiment (cutter3) is employed as the test sample. The optimal kernel parameters of each machine learning model are selected by the grid search with cross validation. The test accuracy and the optimal kernel parameters of these models are shown in Table 2. The results show that the SVM model has the highest test accuracy. Afterward, this model would be used to cooperate with the TPIM in Section 4.3.
Fig. 14. Scheme of the transition points identification method.
4.2. The transition points identification method Fig. 14 shows the scheme of the transition points identification method. Since the high volatility of vibration HE features, which can be observed in Fig. 11, the curve fitting method is employed to smooth curves. According to the analysis of experimental data of cutter1 and cutter2, it is found that the cubic polynomial can well fit the trends of HE features in all time. To realize real-time searching for extreme points on the curve accurately and quickly, this paper adopts a sliding window polynomial fitting method. In the actual production of factories, engineers are most concerned about whether the tool is blunt or damaged. Therefore, we are only interested in transition points from steady state region to the accelerated wear zone; in other words, we only search for the minima of Means and maxima of Number. As the experiment proceeds, at time t == i, the new features (Mean(i) and Number(i)) would form new data sequences with the previous features according to the width of the sliding window. Then a cubic polynomial would be used to curve fit these sequences. Fitting errors are analyzed based on Least-square principle. After that, we would search the local extrema by calculating the first and second derivatives of the fitted curves. If we find the extreme points (minima of Means and maxima of Number) on both curves simultaneously, we continue to search for extreme points. Then if we find the extreme points for specific consecutive times, and the position coordinates of the extrema fluctuate within a narrow range. At this point, we can be sure that the transition point is found.
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Table 2 Test accuracy of machine learning models. Machine learning models
Kernel parameters
Test accuracy
Support Vector Machine
Kernel function Kernel scale
Gaussian 0.35
81.9%
k-Nearest Neighbor
Number of neighbors Distance metric
10 Minkowski (cubic)
81.3%
Decision Tree
Max number of sploits Split criterion
20 Gini’s diversity index
79.3%
Ensemble Learning
Ensemble method Max number of splits Number of learners
AdaBoost 20 30
78.1%
Table 3 Decision strategy. Output of SVM
Output of Transition point
Final decision
1 2 3 1 2 3
No No No Yes Yes Yes
1 2 2 2 2/3 3
Tool wear state
3
Defined tool wear state Estimated tool wear state Modified tool wear state
2
1 0
50
100
150
200
250
300
Cuts Fig. 16. Estimated and modified tool wear states.
Fig. 15. Scheme of the TCM approach.
The width of the sliding window and specific consecutive times depend on sampling intervals and tool life. In this case, they are set as 20 and 10. Without loss of generality, we assume that the first several passes would not blunt the tool. So we started TPIM from the 21st pass, which corresponds to the sliding window width.
Table 4 Accuracy performance of studies published on TCM with vibration in milling. Authors
Sample features
Test accuracy
Zhou et al. [34] Xie et al. [35] Aghazadeh et al. [36] P. Krishnakumar et al. [37]
Singularity features wavelet packets features wavelet packets features Wavelet features
86.2% 92.4% 84.6% 88.89%
4.3. Tool condition estimation results By observing Figs. 11–13, it is found that state 3 begins to appear only after the transition point occurs. Therefore, the outcome of TPIM would modify three estimated outcomes of SVM model: if the transition point is not identified, result ‘3’ of SVM model would be modified by ‘2’; if the transition point has been identified, result ‘1’ would be modified by ‘2’. In addition, after the transition point is identified, once the result of SVM is ‘3’, the subsequent estimation results would be fixed to ‘3’, the scheme of the TCM approach is illustrated in Fig. 15. Table 3 illustrates the decision strategy of the final estimation results. Fig. 16 shows the estimated tool wear states of the SVM model and the modified tool wear states by TPIM. It shows that the TCM approach has more accurate classification results, which can reach a classification rate of 90.8%. The classification rate of the SVM model without TPIM is 81.9%. Table 4 shows the classification accuracy performance of the state of the art studies on TCM with vibration signals in milling. It can be observed that the classification result of the proposed TCM approach
is comparable to the above studies. Although the classification rate is not so good, it is enough to guide the tools’ replacement in the factory. Remark 4. A TCM approach is proposed which utilized an SVM model and a TPIM. The proposed TPIM would help to modify the classification results of the SVM model, which can help reach a total classification rate of 90.8%. 5. Conclusion In the present study, a vibration singularity analysis approach is proposed for tool condition monitoring in milling. A wavelet basis selection method is presented to pick the optimal wavelet bases for the sensor signals. Both the Type Ⅰ and Type Ⅱ singularities are found in the vibration signals of the milling. The 2nd derivative of Gaussian wavelet with 2 vanishing moments is found most effective to estimate the singularity
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of vibration signals in milling. The Holder Exponents (HE) were used to estimate the singularity of vibration signals. It was found that Means of HE values and Number of singular points in the feed direction of vibration signals are the most relevant and effective features. And these HE features are highly sensitive to the transition points of different wear states defined by VB, especially from the steady state region to the accelerated wear zone. It is proven that this sensitivity is independent of the values of VB, the type of milling tools, the material of work-pieces, and the processing parameters. A TCM approach is proposed which utilized an SVM model and a transition points identification method (TPIM). Experimental results show that the modification of TPIM helps to reach more accurate classification results. It is shown that the proposed approach is efficient enough to guide the tools’ replacement in the factory. Future researches would be focusing on accommodating this approach with other types of cutting. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant 51975335 in part by the Major Scientific and Technological Project of Shandong Province under Grant 2019GGX104008, and in part by the Key Laboratory of High-efficiency and Clean Mechanical Manufacture at Shandong University, Ministry of Education. References [1] Shaw MC. Metal cutting principles. 2nd ed. New York: Oxford University Press; 2005. [2] Rahman M, Kumar AS, Prakash JRS. Micro milling of pure copper. J Mater Process Techol 2001;1(116):39–43. doi:10.1016/S0924-0136(01)00848-2. [3] Altintas Y, Yellowley I. In-process detection of tool failure in milling using cutting force models. J Eng Ind 1989;2(111):149–57. doi:10.1115/1.3188744. [4] Piotr G. The manipulator tool state classification based on inertia forces analysis. Mech Syst Signal Process 2018;107:122–36. doi:10.1016/j.ymssp.2018.01.002. [5] Zhu KP, Liu TS. Online tool wear monitoring via hidden semi-markov model with dependent durations. IEEE Trans Ind Inf 2018;1(14):69–78. doi:10.1109/TII.2017.2723943. [6] Kunpeng Z, Soon HG, San WY. Multiscale singularity analysis of cutting forces for micromilling tool-wear monitoring. IEEE Trans Ind Electron 2011;58(6):2512–21. doi:10.1109/TIE.2010.2062476. [7] Nouri M, Fussell BK, Ziniti BL, Linder E. Real-time tool wear monitoring in milling using a cutting condition independent method. Int J Mach Tool Manuf 2015;89:1– 13. doi:10.1016/j.ijmachtools.2014.10.011. [8] Li XL, Tso SK, Wang J. Real-time tool condition monitoring using wavelet transforms and fuzzy techniques. IEEE Trans Syst Man Cybern: Syst 2000;3(30):352–7. doi:10.1109/5326.885116. [9] Tonshoff HK, Li XL, Lapp C. Application of fast Haartrans form and concurrent learning to tool-breakage detection in milling. IEEE-ASME Trans Mech 2003;3(8):414–17. doi:10.1109/TMECH.2003.816830. [10] García Plaza E, Núñez López PJ. Application of the wavelet packet transform to vibration signals for surface roughness monitoring in CNC turning operations. Mech Syst Signal Process 2018;98:902–29. doi:10.1016/j.ymssp.2017.05.028. [11] Albertelli P, Braghieri L, Torta M, Monno M. Development of a generalized chatter detection methodology for variable speed machining. Mech Syst Signal Process 2019;123:26–42. doi:10.1016/j.ymssp.2019.01.002. [12] Zhou JH, Pang CK, Zhong ZW, Lewis L. Tool wear monitoring using acoustic emissions for dominant-feature identification. IEEE Trans Instrum Meas 2010;2(60):547– 59. doi:10.1016/10.1109/TIM.2010.2050974. [13] Ai CS, Sun YJ, He GW, Ze XB, Li W, Mao K. The milling tool wear monitoring using the acoustic spectrum. Int J Adv Manuf Techol 2012;5-8(61):457–63. doi:10.1007/s00170-011-3738-z. [14] Rehorn AG, Jiang J, Orban PE. State-of-the-art methods and results in tool condition monitoring: a review. Int J Adv Manuf Techol 2005;7-8(26):693–710. doi:10.1007/s00170-004-2038-2.
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