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Time-frequency-analysis-based minor cutting edge fracture detection during end milling
ARTICLE IN PRESS
Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing 18 (2004) 1485–1496 www.elsevier.com/locate/jnlabr/ymssp
Time-frequency-analysis-based minor cutting edge fracture detection during end milling Xiaoli Li*, X.P. Guan Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China Received 7 February 2003; received in revised form 2 June 2003; accepted 8 July 2003
Abstract Successful application of tool condition detection during end milling can ensure high-quality parts and safeguard the machining system. This paper proposes an effective algorithm that consists of wavelet-based de-noising, discrete time-frequency analysis, FFT and second differencing for the detection of minor cutting edge fracture during end milling. The algorithm can be successfully applied to extract marked features from the feed-motor current signals to indicate the minor cutting edge fracture. Some typical experiments, the cutter run-out, entry/exit cuts and cutting parameters-variation, have been performed to confirm the robustness of the algorithm. The results show that the new approach has an excellent potential for practical and real-time application at low cost for the detection of minor cutting edge fracture during end milling. r 2003 Elsevier Ltd. All rights reserved.
1. Introduction End milling has been widely employed in automobile, aircraft, and military industries for machining thin-wall sections, slotting as well as contouring. The successful application of tool fracture detection during end milling can ensure high-quality parts and safeguard the machining system. Tool fracture is subtle in nature and might be undetected for a period of time during end milling. The undetected tool fracture, however, increases the potential for further tool damage but also has a negative effect on the surface finish of the machined part. Thus, a real-time detection of tool fracture may prevent excessive damage to the workpiece and machining system. Research to date has presented four main approaches to detect tool fracture during end milling [1]. A large amount of significant research has been done on force-based tool fracture detection [2,3]. Force measurements are commonly taken by using a dynamometer mounted on a worktable or a tool holder of a machine tool. The physical characteristics of the dynamometer mounted on a worktable, however, can seriously limit the size of the workpiece; if the dynamometer mounted on *Corresponding author. E-mail address: [email protected] (X. Li). 0888-3270/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0888-3270(03)00096-7
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a tool holder will interrupt the exchange of cutting tools; and the cost of the dynamometer also is too high by comparison with the alternative sensors [4]. Another important approach to detect tool fracture during end milling is based on acoustic emission (AE) sensor. Experimental results show that large AE bursts are generated at the instance of tool fracture, so the AE-based approach has been very successful in its application to tool fracture monitoring in single-point cutting, such as a turning operation [5], and micro-endmilling operation [6]. Its application to end milling, however, has been less straightforward. The reason is that the end milling process is an interrupted cutting operation, pulse shock loading occurs during the entry and exit of each individual tooth to the workpiece. The magnitude of these shock pulses possibly is equivalent to those generated by tool fracture during end milling. The other is that locating AE sensor to get a reasonable constant transmission path between the sensor and the rotating cutting tool is hard. Though, Hutten and Hu [7] developed a liquid-coupled sensor system mounted on the end of spindle to collect AE signals derived from the cutter through the tool holder; Li and Yuan [8] also developed a simple device to collect AE signals from the tool holder through magneto-fluid. These simple devices all alter the structure of machine tool more or less. Additionally, AE signals highly depend upon cutting parameters, tool and workpiece material/geometry, so as to require trial cuts in order to determine a proper threshold value. Accordingly, AE-based tool fracture detection leads to miss fracture events and excessive false alarms during end milling [9]. Spindle or feed motor current-based tool fracture detection has been presented in the end milling operations for overcoming the disadvantages of cutting force and AE signatures based on [10–12]. These methods first estimate cutting force by means of the motor current, and then the estimated cutting force is employed to detect tool fracture during end milling. Because the feed system contains screw and gears, the non-linearity of friction, cogging and temperature of the feed drive make it very hard to estimate an accurate cutting force from the motor current. Meanwhile, the dynamic characteristics of the current feedback control loop of the feed-drive system limit the bandwidth of the current sensing system, so the motor current cannot track the cutting force under the high-speed condition. In this paper, the wavelet analysis, discrete time-frequency analysis, FFT and second differencing are employed to construct a new algorithm, which can be used to indicate minor cutting edge fracture during end milling by sensing the feed-motor current signals. The proposed detection algorithm demonstrated by the experiments can meet the following general requirements: reliable detection of tool failures; real-time application; independence of the cutting condition and tool/ workpiece material; insensitivity to the cutting parameter-variations; low incidence of false alarms. These tests include the entry/exit cuts, the minor cutting edge fracture during steady-state cutting, the minor cutting edge fracture during entry/exit cutting and the effect of cutting parameters.
2. Algorithm and its application 2.1. Wavelet-based de-noising In this paper, the aim of the wavelet based de-noising is to remove the influence of the nonlinear friction force and cogging force to the motor current signals. Given a time varying signal
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f ðtÞ; wavelet transform (WT) consists of computing coefficients that are inner products of the signal and a family of wavelets. The wavelet transform can be given by cj;k ðtÞ ¼ 2j=2 cð2j t kÞ; d0;0 ¼ h f ðtÞ; fðtÞi; dj;k ¼
D
E f ðtÞ; cj;k ðtÞ ;
j ¼ 1; y; N;
k ¼ 1; y; 2j1 ;
ð1Þ
where cj;k ðtÞ is the scaled and shifted version of the mother wavelet function cðtÞ; fðtÞ is the scale function, dj;k are the wavelet coefficients, and N is the number of wavelet scales over which the wavelet transform is generated, which is usually chosen as a power of 2. Wavelet-based de-noising is done by first transforming the data into the wavelet domain, then zeroing all the wavelet coefficients below a given threshold, and then inverse transforming back into the time domain. Wavelet-based de-noising method is used to process the feed-motor current signals in this paper. It was found that the best de-noising approach was to utilize a 3rd Symmlet mother wavelet function in combination with cross-validation threshold determination and soft threshold. 2.2. Discrete time-frequency analysis Wigner distribution is an important aspect of studying the signal to know how its frequency content changes with time. Unfortunately, the theory of continuous distributions cannot be used straightforwardly to the discrete time [13]. What is more unfortunate is that the above-mentioned distributions cannot treat periodic signals adequately; such signals arise in a variety of applications [14]. Recently, Richman et al. [15] proposed a new approach, period signals were given based on group representation theory, and properties that hold for continuous distribution would also hold for the discrete distribution. A common definition of the ambiguity function for continuous signal xðtÞ and yðtÞ is Z t t Ax;y ðt; nÞ ¼ x t þ y t ej2pnt dt; 2 2 or jpnt
Ax;y ðt; nÞ ¼ e
Z
xðt þ tÞy ðtÞej2pnt dt:
ð2Þ
Its bilinear form can be written as Ax;y ðt; nÞ ¼ hDðn; tÞx; yi;
ð3Þ
where ðDðn; tÞxÞðtÞ ¼ ejpðntÞ ej2pnt xðt þ tÞ: The signals of interest are elements of the space L2 ðZ=NÞ; which corresponds to finite energy, N-periodic sequences. Let UN denote the group of unitary operators on L2 ðZ=NÞ: For the discrete case, xðnÞAL2 ðZ=NÞ; tAZ=N; nAZ=N; define the time advance operator SN ðtÞand the frequency
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modulation operator MN ðnÞ to be ðSN ðtÞxÞðnÞ ¼ xððn þ tÞN Þ;
ð4Þ
ðMN ðnÞxÞðnÞ ¼ ejð2p=NÞnn xðnÞ
ð5Þ
using the notation ðaÞN ¼ a mod N: For an odd-length signal x(n), the definition of DN can be written as ðDðPÞxÞðnÞ ¼ rN ejð2p=NÞnn xððn þ tÞN Þ;
ð6Þ
where rN ¼ ej2p=Nðnt=2ÞN : For an even-length signal x(n), the definition of DN can also be written as ðDðPÞxÞðnÞ ¼ rN ejð2p=NÞnn xððn þ tÞN Þ
ð7Þ
but the rN is 8 > < ejp=Nðnt=2ÞN rN ¼ > : ejp=NððntÞN NÞ
N ifðnpÞN o ; 2 N ifðnpÞN X : 2 Thus, the form for the discrete symmetric cross-ambiguity function, Ax;y ðt; nÞ; that depends on the parity of the signal length is
ð8Þ Ax;y ðt; nÞ ¼ rN MN;n SN;t x; y : As a result, the discrete time, discrete frequency cross-Wigner distribution Wx;y ðn; kÞ is the 2-D Fourier transform of the symmetric cross-ambiguity function, Ax;y ðt; nÞ: 1 N 1 N 1 X X X 1N Wx;y ðn; kÞ ¼ ej2p=NðnnþktÞ rN ejð2t=NÞnl xððl þ tÞN Þy ðlÞ: ð9Þ N t¼0 n¼0 l¼0 2.3. Application to a feed-motor current signal The end milling process exhibits a period generation mechanism, perturbed by spindle speeds variations, tool conditions, and the effect of chips. The ideal feed-motor current signal during end milling varies periodically with frequency, which is equal to the product of spindle rotational frequency and the number of indecent cutting flutes, i.e. fc ¼ Nf Ns =60 (Nf is the number of cutter flutes, Ns is the cutter rotational speed in rev/min). A schematic illustration of an end milling process is provided in Fig. 1. Fig. 2(a) displays a feed-motor current signal without cutting edge fracture during end milling; the variation of motor current is similar to a regular periodic signal. The period of the signal is equal to the theoretical period of 0.025 s corresponding to a four-flute cutter rotating at 600 rpm. Fig. 2(b) shows the feed-motor current signals filtered by the wavelet-based filter, the noise derived from machining environment is disposed. Then, the processed signals are analyzed by the discrete time-frequency; the results are shown as in Fig. 2(c), which only includes
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Y X Spindle rotation, Ns Axial depth of cut, da Radial depth of cut, dr
Z
Table feed, Vf X
Feed-motor current (A)
3
(a)
2
1
0
0
0.05
0.1
0.15 Time (sec)
0.2
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Fig. 1. Illustration of an end milling process.
(b)
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
(c)
Fig. 2. Feed-motor current signals during end milling without the cutting edge fracture. Tool/workpiece material: HSS/ 45# steel; spindle speed: 600 rpm, radial depth of cut: 2 mm, axial depth of cut: 4 mm, feed speed: 120 mm/min; cutter diameter: 8 mm, cutter flute: 4. (a) Original signals; (b) de-noised signals; (c) discrete time–frequency analysis.
the dynamic components of the signals, because the d.c. components of the signals only correspond to the cutting powers, but have nothing to do with tool condition. According to the calculated frequency of signals based on the given spindle speed and the number of cutter flute, the primary frequency components are selected from the time-frequency plan, that is called the feature signals. The maximum value of the FFT of the feature signals is taken as a feature point for detecting cutting edge fracture. Finally, a second differencing method is used to extract a
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marked feature to indicate the tool condition from the feature point and the previous two feature points during end milling. The detailed process of extracting a marked feature from the feedmotor current signals to indicate the minor cutting edge fracture during end milling is summarized as follows: (a) Sampling current signals by frequency 1000 Hz, and collecting a segment of data of 0.064 s for processing; (b) Using wavelet based de-noising module to preprocess the segment; (c) Input the preprocessed segment to discrete time-frequency analysis module to get a timefrequency plan; (d) Calculating the frequency of the current signals in light of the spindle speed and the number of cutter flute; (e) Extracting the primary frequency components from the time-frequency plan based on the calculated frequency, called as the feature signals; (f) Using FFT to process the feature signals, and extract the maximum value from the frequency domain of the feature signals as a feature point; (g) Combining the feature point and previous two feature points to perform the second differencing, then to get a marked feature to indicate tool condition; (h) Comparing the marked feature with the threshold value, if the marked features over the threshold value, then generate an alarm signal.
3. Experiments and results 3.1. Experiments All experiments were performed on a CNC Vertical Machining Centre (Mazak AJV 25/405) with the a.c. permanent magnet synchronous motors. The experimental set-up is shown in Fig. 3(a). Three current sensors (PCB Mounting Hall Effect Current Transducer, Stock No. 286327 (RS Components Ltd)) are used to measure the three-phase currents of feed-motor iu, iv, and iw, and through a low-pass (50 Hz) filter, respectively. The root mean square (rms) of feed-motor current, Irms, can be calculated as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 ð10Þ Irms ¼ ði þ iv2 þ iw2 Þ: 3 u This method, which is very simple and widely used in the industry, uses the rms value for converting the a.c. current to the equivalent d.c. current. A set of experiments was performed so as to test the reliability of cutting edge detection algorithm under actual cutting processes. These tests include the entry/exit cuts, the cutting edge fracture during steady-state cutting, the cutting parameter-variation, the cutting edge fracture on the entry/exit cuts. All of the tests was performed under dry conditions in down milling mode, the sampling frequency was set as 1 KHz. Additionally, the maximum tooth frequency used in the tests should be less than 67 Hz, this is limited by the bandwidth of feed servo system; i.e. under
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Servo system
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Hall effect current sensor A/D Converter (1KHz)
Feed motor
2 + I 2) / 3 (I 2 + IW V U
Irms
Low-passed filters (50 Hz)
Wavelet-based de-noising
Discrete T-F analysis
Feature extraction
Decision-making for tool condition
(a)
(b)
Fig. 3. (a) Experimental set-up; (b) minor cutting edge fracture.
67 Hz of tooth frequency, the motor current signals can track the cutting force signals during end milling. The tool/workpiece material selected was HSS/45# steel. A typical minor cutting edge fracture during end milling is shown in Fig. 3(b). 3.2. Results 3.2.1. Entry/exit cuts The insensitivity of the algorithm to the entry/exit cut is demonstrated by the following test. Fig. 4(a) and (c) show a plot of feed-motor current signals with the two distinct changes: from the entry cut to the steady cutting state and from the steady cutting state to the exit cut, respectively. As can be seen from the steady state of the feed-motor current signals, a high degree of run-out appears in the end milling processing as well as a high level of noise. Fig. 4(b) and (d) show a plot of the marked features derived from the feed-motor current signals under the two different cutting states. The entry cut occurs at the second of 4–5 in Fig. 4(b), and the exit cut occurs at the second of 6–7. As can be seen from Fig. 4(b) and (d), the distinct feature indicating the minor cutting edge fracture is not found. So the marked features obtained by the above algorithm are insensitive to the effect of the entry/exit cut. The robustness of the algorithm to process the feed-motor current signals with entry, exit, run out, and noise sources is demonstrated. 3.2.2. Minor cutting edge fracture during steady cutting states In this case, the minor cutting edge fracture occurs at around second 8 during the steady cutting state. The feed-motor current signals are collected, as shown in Fig. 5(a). Fig. 5(b) shows the
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Fig. 4. Entry/exit cut test in end milling. Tool/workpiece material: HSS/45# steel; spindle speed: 900 rpm, radial depth of cut: 2 mm, axial depth of cut: 4 mm, feed speed: 120 mm/min; cutter diameter: 8 mm, cutter flute: 4(a) Feed-motor current signal with entry cut; (b) marked features with entry cut; (c) feed-motor current signal with exit cut; (d) marked features with exit cut.
Amplitude of feed-motor current (A)
Tool fracture 3 2 1 0
Amplitude of marked features
(a)
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2
3
4
5 6 Time (sec)
7
8
9
10
0
1
2
3
4
5 6 Time (sec)
7
8
9
10
150
100
(b)
50
0
Fig. 5. Minor cutting edge fracture during the steady cutting states. Tool/workpiece material: HSS/45# steel; spindle speed: 600 rpm, radial depth of cut: 4 mm, axial depth of cut: 4 mm, feed speed: 120 mm/min; cutter diameter: 8 mm, cutter flute: 4(a) Feed-motor current signals with the cutting edge fracture; (b) marked features with the cutting edge fracture.
marked features derived from the feed-motor current signal, a peak at around second 8 is found to indicate the minor cutting edge fracture. Clearly, the algorithm can indicate the cutting edge fracture successfully during end milling.
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Amplitude of feed-motor current (A)
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3
Entry cut/fracture 2
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5 6 Time (second)
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Amplitude of marked features
(a) 500 400 300 200 100
(b)
0 0
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10
Fig. 6. Cutting edge fracture on the entry cut. Tool/workpiece material: HSS/45# steel; spindle speed: 600 rpm, radial depth of cut: 4 mm, axial depth of cut: 4 mm, feed speed: 90 mm/min; cutter diameter: 6 mm, cutter flute: 4(a) Feedmotor current signals with cutting edge fracture on the entry cut; (b) marked features of the feed-motor current.
3.2.3. Cutting edge fracture on the entry/exit cuts The tests comfirm the effectiveness of the algorithm to quickly and reliably indicate the cutting edge fracture during end milling. The cutting edge fracture of the cutter during end milling usually occurs on entry/exit cut. Fig. 6(a) is a plot of the feed-motor current signals, the cutter enters in the workpiece at around second 3, the cutter causing a cutting edge fracture at around second 3. The detection results are shown in Fig. 6(b). Fig. 7(a) is a plot of the feed-motor current signals, which contains information of a cutting edge fracture when the cutter exists from the workpiece at around second 9, the marked features, as shown in Fig. 7(b), also can indicate the cutting edge fracture. These two cases demonstrate that the cutting edge fracture occurring during entry/exit cuts can be sucessfully marked by the algorithm. 3.2.4. Effect of cutting parameters An effective algorithm to detect cutting edge fracture during the end milling also should be insensitive to the changes of the cutting parameters. The final tests are to verify the insensitivity of the algorithm to the changes of radial and axial depth of cut during end milling. The two typical workpieces, which result in the changes of axial and radial depth of cut, are shown in Fig. 8(a) and (c). Fig. 8(a) is to describe the influence of the axial depth, and Fig. 8(c) is to describe the influence of the radial depth of cut, it ranges from 0 to 6 mm. However, it is found that the marked features from the feed-motor current signals are insensitive to the two cutting parameters variations during end milling from the Fig. 8(b) and (d). This is because the algorithm is based on the frequency information; however the changes of axial and radial depth of cut are only related to the amplitude of the motor current. Therefore, the algorithm is insensitive to the axial and radial depth of cut during end milling.
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Exit cut/fracture 2
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(a)
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10
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2
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5 6 Time (sec)
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500 400 300 200 100 0
0
(b)
Amplitude of marked features
Fig. 7. Cutting edge fracture on the exit cut. Tool/workpiece material: HSS/45# steel; spindle speed: 600 rpm, radial depth of cut: 2 mm, axial depth of cut: 4 mm, feed speed: 120 mm/min; cutter diameter: 6 mm, cutter flute: 4(a) Feedmotor current signals with cutting edge fracture on the exit cut; (b) marked features with the cutting edge fracture.
(a)
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150
Radial depth from 0 to 6 mm
Cutter
4
Work piece
(c)
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(d)
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Fig. 8. Feed-motor current signals when cutting workpiece with grooves. Tool/workpiece material: HSS/45# steel; spindle speed: 900 rpm; radial depth of cut: 4 mm; axial depth of cut: 4 mm; feed speed: 120 mm/min; cutter diameter: 6 mm; cutter flute: 4(a) Workpiece A; (b) marked features of the feed-motor current signals for workpiece A under the axial depth of cut 4 mm; (c) Workpiece B; (d) marked features of the feed-motor current signals for workpiece B under the radial depth of cut 0–6 mm.
4. Discussion and conclusions For this tool condition monitoring system, the key issue is if it can indicate the cutting edge fracture from the feed-motor current signals during end milling in real time. According to the
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algorithm, the system needs 0.064 s to collect a segment of data and to then start to calculate a marked feature by using the algorithm. The time of computation is about 0.315 s to get a marked feature. Therefore, the monitoring system needs to take a 0.379 s to identify a tool fracture if it occurs during end milling; the time referred to is from the collections of current signals to an alarm generation. Note that the computer used is PII, CUP 433 MHz. Clearly, the time can meet the need of the practical application for detecting a cutting edge fracture during end milling. The other issue for a tool condition system is the cost and installation of the system. This approach only needs three current sensors to collect the feed-motor current signals, all of the costs add to less than 70 USA$. The sensor installation is very easy; it does not interrupt the machining system at all. Therefore, sensing the current of the feed drive to indicate the tool fracture is a much better alternative in terms of the equipment cost, unobtrusiveness, non-interference around the working zone, and retrofitting and hardware simplicity [16]. Unlike in other works, the motor current is only used to estimate cutting force using a model, and then the estimated cutting force is used to indicate tool conditions. In this paper, the feed-motor is directly applied to indicate the cutting edge fracture. In brief, the monitoring system based on the above algorithm has high robustness for application in practical end milling in real time, but also requires simple and inexpensive sensors that do not interrupt the cutting process. This approach, however, has some problems to be solved. The major one is that the dynamic characteristics of the current feedback control loop of the feed-drive system limit the bandwidth of the current sensing system. Another major problem is that the observed current signals of the servo drive motor contain undesirable components resulting from accelerating or decelerating the mass of table, and overcoming the friction force in the guide way. Final limitation of this currentmeasuring approach is that it cannot be applied for too light cuts because the magnitude of the useful signal for cutting is then small and difficult to extract the useful information for detecting tool conditions. Linear motor-based direct feed drives in high-speed machining not only are more desirable to improve productivity, but also eliminate the backlash and structural flexibility due to gear reduction mechanism. Meanwhile, the elimination of gearing gives the benefit of high-speed tracking, the cutting forces can directly be reflected to the motor currents due to the direct coupling; so that the motor current has an even stronger effect on tracking accuracy. Thus, the feed-motor current signals will be able to respond more effectively to the tool condition in manufacturing processing. In future work, the new algorithm proposed will be employed to detect tool condition through linear-motor current signals in high-speed milling. Additionally, although all experiments were limited to end milling operations, it is believed that the detection approach may be applied equally well to other milling operations.
Acknowledgements The author thanks the support provided by Alexander von Humboldt Foundation, Germany in writing the paper. The useful comments by editor and reviewers are also gratefully acknowledged.
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References [1] P.W. Prickett, C. Johns, Overview of approaches to end milling tool monitoring, International Journal Machine Tools & Manufacture 39 (1999) 105–122. [2] Y. Altintas, L. Yellowley, In process detection of tool failure in milling using cutting force models, Journal of Engineering for Industry, Transaction of the ASME 111 (1989) 149–157. [3] D.J. O’Brien, J.W. Sutherland, S.G. Kapoor, A force-based approach to on-line flute breakage detection in a peripheral end milling process, ASME, Dynamic Systems and Control Division (Publication) DSC 22 (1999) 25–30. [4] X. Li, Detection of tool flute fracture in end milling using feed-motor current signatures, IEEE/ASME Transactions on Mechatronics 6 (2001) 491–498. [5] S.V. Kamarti, S.R.T. Kumara, P.H. Cohen, Flank wear estimation in turning through wavelet representation of acoustic emission signals, Journal of Manufacturing Science and Engineering, Transactions of the ASME 122 (2000) 12–19. [6] I.N. Tansel, M.E. Trujillo, W.Y. Bao, T.T. Arkan, Acoustic emission-based tool-breakage detector (TBD) for micro-end-milling operations, International Journal of Modelling and Simulation 21 (2001) 10–16. [7] D.V. Hutten, F. Hu, Acoustic emission monitoring of tool wear in end milling using time-domain averaging, Journal of Manufacturing Science and Engineering, Transactions of the ASME 121 (1999) 8–12. [8] X. Li, Z. Yuan, Tool wear monitoring with wavelet parket transform-fuzzy clustering method, Wear 219 (1998) 145–154. [9] X. Li, A brief review: acoustic emission method for tool wear monitoring during turning, International Journal of Machine Tools & Manufacture 42 (2002) 157–165. [10] K. Matsushima, P. Bertok, T. Sata, In process detection of tool breakage by monitoring the spindle current of a machine tool, ASME Journal of Measurement and Control for Batch Manufacturing 1 (1982) 145–154. [11] Y. Altintas, Prediction of cutting forces and tool breakage in milling from feed drive current measurements, Journal of Engineering for Industry, Transactions of the ASME 114 (1992) 386–392. [12] J.M. Lee, D.K. Choi, C.N. Chu, Prediction of cutting forces and tool breakage in milling from feed drive current measurements, Annals of the CIRP 44 (1995) 59–62. [13] L. Cohen, Time-Frequency Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1995. [14] T. Claasen, W. Mecklenbrauker, The Wigner distribution—a tool for time-frequency signal analysis—Part 2: discrete-time signals, Philips Journal of Research 35 (1980) 276–300. [15] M. Richman, T. Parks, R. Shenoy, Discrete-time, discrete-frequency, time–frequency analysis, IEEE Transactions on Signal Processing 46 (1998) 1517–1527. [16] X. Li, A. Djordjevich, K.V. Patri, Current sensor-based feed cutting force intelligent estimation and tool wear condition monitoring, IEEE Transactions on Industry Electronics 47 (2000) 697–702.
Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing 18 (2004) 1485–1496 www.elsevier.com/locate/jnlabr/ymssp
Time-frequency-analysis-based minor cutting edge fracture detection during end milling Xiaoli Li*, X.P. Guan Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China Received 7 February 2003; received in revised form 2 June 2003; accepted 8 July 2003
Abstract Successful application of tool condition detection during end milling can ensure high-quality parts and safeguard the machining system. This paper proposes an effective algorithm that consists of wavelet-based de-noising, discrete time-frequency analysis, FFT and second differencing for the detection of minor cutting edge fracture during end milling. The algorithm can be successfully applied to extract marked features from the feed-motor current signals to indicate the minor cutting edge fracture. Some typical experiments, the cutter run-out, entry/exit cuts and cutting parameters-variation, have been performed to confirm the robustness of the algorithm. The results show that the new approach has an excellent potential for practical and real-time application at low cost for the detection of minor cutting edge fracture during end milling. r 2003 Elsevier Ltd. All rights reserved.
1. Introduction End milling has been widely employed in automobile, aircraft, and military industries for machining thin-wall sections, slotting as well as contouring. The successful application of tool fracture detection during end milling can ensure high-quality parts and safeguard the machining system. Tool fracture is subtle in nature and might be undetected for a period of time during end milling. The undetected tool fracture, however, increases the potential for further tool damage but also has a negative effect on the surface finish of the machined part. Thus, a real-time detection of tool fracture may prevent excessive damage to the workpiece and machining system. Research to date has presented four main approaches to detect tool fracture during end milling [1]. A large amount of significant research has been done on force-based tool fracture detection [2,3]. Force measurements are commonly taken by using a dynamometer mounted on a worktable or a tool holder of a machine tool. The physical characteristics of the dynamometer mounted on a worktable, however, can seriously limit the size of the workpiece; if the dynamometer mounted on *Corresponding author. E-mail address: [email protected] (X. Li). 0888-3270/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0888-3270(03)00096-7
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a tool holder will interrupt the exchange of cutting tools; and the cost of the dynamometer also is too high by comparison with the alternative sensors [4]. Another important approach to detect tool fracture during end milling is based on acoustic emission (AE) sensor. Experimental results show that large AE bursts are generated at the instance of tool fracture, so the AE-based approach has been very successful in its application to tool fracture monitoring in single-point cutting, such as a turning operation [5], and micro-endmilling operation [6]. Its application to end milling, however, has been less straightforward. The reason is that the end milling process is an interrupted cutting operation, pulse shock loading occurs during the entry and exit of each individual tooth to the workpiece. The magnitude of these shock pulses possibly is equivalent to those generated by tool fracture during end milling. The other is that locating AE sensor to get a reasonable constant transmission path between the sensor and the rotating cutting tool is hard. Though, Hutten and Hu [7] developed a liquid-coupled sensor system mounted on the end of spindle to collect AE signals derived from the cutter through the tool holder; Li and Yuan [8] also developed a simple device to collect AE signals from the tool holder through magneto-fluid. These simple devices all alter the structure of machine tool more or less. Additionally, AE signals highly depend upon cutting parameters, tool and workpiece material/geometry, so as to require trial cuts in order to determine a proper threshold value. Accordingly, AE-based tool fracture detection leads to miss fracture events and excessive false alarms during end milling [9]. Spindle or feed motor current-based tool fracture detection has been presented in the end milling operations for overcoming the disadvantages of cutting force and AE signatures based on [10–12]. These methods first estimate cutting force by means of the motor current, and then the estimated cutting force is employed to detect tool fracture during end milling. Because the feed system contains screw and gears, the non-linearity of friction, cogging and temperature of the feed drive make it very hard to estimate an accurate cutting force from the motor current. Meanwhile, the dynamic characteristics of the current feedback control loop of the feed-drive system limit the bandwidth of the current sensing system, so the motor current cannot track the cutting force under the high-speed condition. In this paper, the wavelet analysis, discrete time-frequency analysis, FFT and second differencing are employed to construct a new algorithm, which can be used to indicate minor cutting edge fracture during end milling by sensing the feed-motor current signals. The proposed detection algorithm demonstrated by the experiments can meet the following general requirements: reliable detection of tool failures; real-time application; independence of the cutting condition and tool/ workpiece material; insensitivity to the cutting parameter-variations; low incidence of false alarms. These tests include the entry/exit cuts, the minor cutting edge fracture during steady-state cutting, the minor cutting edge fracture during entry/exit cutting and the effect of cutting parameters.
2. Algorithm and its application 2.1. Wavelet-based de-noising In this paper, the aim of the wavelet based de-noising is to remove the influence of the nonlinear friction force and cogging force to the motor current signals. Given a time varying signal
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f ðtÞ; wavelet transform (WT) consists of computing coefficients that are inner products of the signal and a family of wavelets. The wavelet transform can be given by cj;k ðtÞ ¼ 2j=2 cð2j t kÞ; d0;0 ¼ h f ðtÞ; fðtÞi; dj;k ¼
D
E f ðtÞ; cj;k ðtÞ ;
j ¼ 1; y; N;
k ¼ 1; y; 2j1 ;
ð1Þ
where cj;k ðtÞ is the scaled and shifted version of the mother wavelet function cðtÞ; fðtÞ is the scale function, dj;k are the wavelet coefficients, and N is the number of wavelet scales over which the wavelet transform is generated, which is usually chosen as a power of 2. Wavelet-based de-noising is done by first transforming the data into the wavelet domain, then zeroing all the wavelet coefficients below a given threshold, and then inverse transforming back into the time domain. Wavelet-based de-noising method is used to process the feed-motor current signals in this paper. It was found that the best de-noising approach was to utilize a 3rd Symmlet mother wavelet function in combination with cross-validation threshold determination and soft threshold. 2.2. Discrete time-frequency analysis Wigner distribution is an important aspect of studying the signal to know how its frequency content changes with time. Unfortunately, the theory of continuous distributions cannot be used straightforwardly to the discrete time [13]. What is more unfortunate is that the above-mentioned distributions cannot treat periodic signals adequately; such signals arise in a variety of applications [14]. Recently, Richman et al. [15] proposed a new approach, period signals were given based on group representation theory, and properties that hold for continuous distribution would also hold for the discrete distribution. A common definition of the ambiguity function for continuous signal xðtÞ and yðtÞ is Z t t Ax;y ðt; nÞ ¼ x t þ y t ej2pnt dt; 2 2 or jpnt
Ax;y ðt; nÞ ¼ e
Z
xðt þ tÞy ðtÞej2pnt dt:
ð2Þ
Its bilinear form can be written as Ax;y ðt; nÞ ¼ hDðn; tÞx; yi;
ð3Þ
where ðDðn; tÞxÞðtÞ ¼ ejpðntÞ ej2pnt xðt þ tÞ: The signals of interest are elements of the space L2 ðZ=NÞ; which corresponds to finite energy, N-periodic sequences. Let UN denote the group of unitary operators on L2 ðZ=NÞ: For the discrete case, xðnÞAL2 ðZ=NÞ; tAZ=N; nAZ=N; define the time advance operator SN ðtÞand the frequency
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modulation operator MN ðnÞ to be ðSN ðtÞxÞðnÞ ¼ xððn þ tÞN Þ;
ð4Þ
ðMN ðnÞxÞðnÞ ¼ ejð2p=NÞnn xðnÞ
ð5Þ
using the notation ðaÞN ¼ a mod N: For an odd-length signal x(n), the definition of DN can be written as ðDðPÞxÞðnÞ ¼ rN ejð2p=NÞnn xððn þ tÞN Þ;
ð6Þ
where rN ¼ ej2p=Nðnt=2ÞN : For an even-length signal x(n), the definition of DN can also be written as ðDðPÞxÞðnÞ ¼ rN ejð2p=NÞnn xððn þ tÞN Þ
ð7Þ
but the rN is 8 > < ejp=Nðnt=2ÞN rN ¼ > : ejp=NððntÞN NÞ
N ifðnpÞN o ; 2 N ifðnpÞN X : 2 Thus, the form for the discrete symmetric cross-ambiguity function, Ax;y ðt; nÞ; that depends on the parity of the signal length is
ð8Þ Ax;y ðt; nÞ ¼ rN MN;n SN;t x; y : As a result, the discrete time, discrete frequency cross-Wigner distribution Wx;y ðn; kÞ is the 2-D Fourier transform of the symmetric cross-ambiguity function, Ax;y ðt; nÞ: 1 N 1 N 1 X X X 1N Wx;y ðn; kÞ ¼ ej2p=NðnnþktÞ rN ejð2t=NÞnl xððl þ tÞN Þy ðlÞ: ð9Þ N t¼0 n¼0 l¼0 2.3. Application to a feed-motor current signal The end milling process exhibits a period generation mechanism, perturbed by spindle speeds variations, tool conditions, and the effect of chips. The ideal feed-motor current signal during end milling varies periodically with frequency, which is equal to the product of spindle rotational frequency and the number of indecent cutting flutes, i.e. fc ¼ Nf Ns =60 (Nf is the number of cutter flutes, Ns is the cutter rotational speed in rev/min). A schematic illustration of an end milling process is provided in Fig. 1. Fig. 2(a) displays a feed-motor current signal without cutting edge fracture during end milling; the variation of motor current is similar to a regular periodic signal. The period of the signal is equal to the theoretical period of 0.025 s corresponding to a four-flute cutter rotating at 600 rpm. Fig. 2(b) shows the feed-motor current signals filtered by the wavelet-based filter, the noise derived from machining environment is disposed. Then, the processed signals are analyzed by the discrete time-frequency; the results are shown as in Fig. 2(c), which only includes
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Y X Spindle rotation, Ns Axial depth of cut, da Radial depth of cut, dr
Z
Table feed, Vf X
Feed-motor current (A)
3
(a)
2
1
0
0
0.05
0.1
0.15 Time (sec)
0.2
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Filtered feed-motor current (A)
Fig. 1. Illustration of an end milling process.
(b)
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
(c)
Fig. 2. Feed-motor current signals during end milling without the cutting edge fracture. Tool/workpiece material: HSS/ 45# steel; spindle speed: 600 rpm, radial depth of cut: 2 mm, axial depth of cut: 4 mm, feed speed: 120 mm/min; cutter diameter: 8 mm, cutter flute: 4. (a) Original signals; (b) de-noised signals; (c) discrete time–frequency analysis.
the dynamic components of the signals, because the d.c. components of the signals only correspond to the cutting powers, but have nothing to do with tool condition. According to the calculated frequency of signals based on the given spindle speed and the number of cutter flute, the primary frequency components are selected from the time-frequency plan, that is called the feature signals. The maximum value of the FFT of the feature signals is taken as a feature point for detecting cutting edge fracture. Finally, a second differencing method is used to extract a
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marked feature to indicate the tool condition from the feature point and the previous two feature points during end milling. The detailed process of extracting a marked feature from the feedmotor current signals to indicate the minor cutting edge fracture during end milling is summarized as follows: (a) Sampling current signals by frequency 1000 Hz, and collecting a segment of data of 0.064 s for processing; (b) Using wavelet based de-noising module to preprocess the segment; (c) Input the preprocessed segment to discrete time-frequency analysis module to get a timefrequency plan; (d) Calculating the frequency of the current signals in light of the spindle speed and the number of cutter flute; (e) Extracting the primary frequency components from the time-frequency plan based on the calculated frequency, called as the feature signals; (f) Using FFT to process the feature signals, and extract the maximum value from the frequency domain of the feature signals as a feature point; (g) Combining the feature point and previous two feature points to perform the second differencing, then to get a marked feature to indicate tool condition; (h) Comparing the marked feature with the threshold value, if the marked features over the threshold value, then generate an alarm signal.
3. Experiments and results 3.1. Experiments All experiments were performed on a CNC Vertical Machining Centre (Mazak AJV 25/405) with the a.c. permanent magnet synchronous motors. The experimental set-up is shown in Fig. 3(a). Three current sensors (PCB Mounting Hall Effect Current Transducer, Stock No. 286327 (RS Components Ltd)) are used to measure the three-phase currents of feed-motor iu, iv, and iw, and through a low-pass (50 Hz) filter, respectively. The root mean square (rms) of feed-motor current, Irms, can be calculated as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 ð10Þ Irms ¼ ði þ iv2 þ iw2 Þ: 3 u This method, which is very simple and widely used in the industry, uses the rms value for converting the a.c. current to the equivalent d.c. current. A set of experiments was performed so as to test the reliability of cutting edge detection algorithm under actual cutting processes. These tests include the entry/exit cuts, the cutting edge fracture during steady-state cutting, the cutting parameter-variation, the cutting edge fracture on the entry/exit cuts. All of the tests was performed under dry conditions in down milling mode, the sampling frequency was set as 1 KHz. Additionally, the maximum tooth frequency used in the tests should be less than 67 Hz, this is limited by the bandwidth of feed servo system; i.e. under
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Hall effect current sensor A/D Converter (1KHz)
Feed motor
2 + I 2) / 3 (I 2 + IW V U
Irms
Low-passed filters (50 Hz)
Wavelet-based de-noising
Discrete T-F analysis
Feature extraction
Decision-making for tool condition
(a)
(b)
Fig. 3. (a) Experimental set-up; (b) minor cutting edge fracture.
67 Hz of tooth frequency, the motor current signals can track the cutting force signals during end milling. The tool/workpiece material selected was HSS/45# steel. A typical minor cutting edge fracture during end milling is shown in Fig. 3(b). 3.2. Results 3.2.1. Entry/exit cuts The insensitivity of the algorithm to the entry/exit cut is demonstrated by the following test. Fig. 4(a) and (c) show a plot of feed-motor current signals with the two distinct changes: from the entry cut to the steady cutting state and from the steady cutting state to the exit cut, respectively. As can be seen from the steady state of the feed-motor current signals, a high degree of run-out appears in the end milling processing as well as a high level of noise. Fig. 4(b) and (d) show a plot of the marked features derived from the feed-motor current signals under the two different cutting states. The entry cut occurs at the second of 4–5 in Fig. 4(b), and the exit cut occurs at the second of 6–7. As can be seen from Fig. 4(b) and (d), the distinct feature indicating the minor cutting edge fracture is not found. So the marked features obtained by the above algorithm are insensitive to the effect of the entry/exit cut. The robustness of the algorithm to process the feed-motor current signals with entry, exit, run out, and noise sources is demonstrated. 3.2.2. Minor cutting edge fracture during steady cutting states In this case, the minor cutting edge fracture occurs at around second 8 during the steady cutting state. The feed-motor current signals are collected, as shown in Fig. 5(a). Fig. 5(b) shows the
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Fig. 4. Entry/exit cut test in end milling. Tool/workpiece material: HSS/45# steel; spindle speed: 900 rpm, radial depth of cut: 2 mm, axial depth of cut: 4 mm, feed speed: 120 mm/min; cutter diameter: 8 mm, cutter flute: 4(a) Feed-motor current signal with entry cut; (b) marked features with entry cut; (c) feed-motor current signal with exit cut; (d) marked features with exit cut.
Amplitude of feed-motor current (A)
Tool fracture 3 2 1 0
Amplitude of marked features
(a)
0
1
2
3
4
5 6 Time (sec)
7
8
9
10
0
1
2
3
4
5 6 Time (sec)
7
8
9
10
150
100
(b)
50
0
Fig. 5. Minor cutting edge fracture during the steady cutting states. Tool/workpiece material: HSS/45# steel; spindle speed: 600 rpm, radial depth of cut: 4 mm, axial depth of cut: 4 mm, feed speed: 120 mm/min; cutter diameter: 8 mm, cutter flute: 4(a) Feed-motor current signals with the cutting edge fracture; (b) marked features with the cutting edge fracture.
marked features derived from the feed-motor current signal, a peak at around second 8 is found to indicate the minor cutting edge fracture. Clearly, the algorithm can indicate the cutting edge fracture successfully during end milling.
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Entry cut/fracture 2
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Amplitude of marked features
(a) 500 400 300 200 100
(b)
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Fig. 6. Cutting edge fracture on the entry cut. Tool/workpiece material: HSS/45# steel; spindle speed: 600 rpm, radial depth of cut: 4 mm, axial depth of cut: 4 mm, feed speed: 90 mm/min; cutter diameter: 6 mm, cutter flute: 4(a) Feedmotor current signals with cutting edge fracture on the entry cut; (b) marked features of the feed-motor current.
3.2.3. Cutting edge fracture on the entry/exit cuts The tests comfirm the effectiveness of the algorithm to quickly and reliably indicate the cutting edge fracture during end milling. The cutting edge fracture of the cutter during end milling usually occurs on entry/exit cut. Fig. 6(a) is a plot of the feed-motor current signals, the cutter enters in the workpiece at around second 3, the cutter causing a cutting edge fracture at around second 3. The detection results are shown in Fig. 6(b). Fig. 7(a) is a plot of the feed-motor current signals, which contains information of a cutting edge fracture when the cutter exists from the workpiece at around second 9, the marked features, as shown in Fig. 7(b), also can indicate the cutting edge fracture. These two cases demonstrate that the cutting edge fracture occurring during entry/exit cuts can be sucessfully marked by the algorithm. 3.2.4. Effect of cutting parameters An effective algorithm to detect cutting edge fracture during the end milling also should be insensitive to the changes of the cutting parameters. The final tests are to verify the insensitivity of the algorithm to the changes of radial and axial depth of cut during end milling. The two typical workpieces, which result in the changes of axial and radial depth of cut, are shown in Fig. 8(a) and (c). Fig. 8(a) is to describe the influence of the axial depth, and Fig. 8(c) is to describe the influence of the radial depth of cut, it ranges from 0 to 6 mm. However, it is found that the marked features from the feed-motor current signals are insensitive to the two cutting parameters variations during end milling from the Fig. 8(b) and (d). This is because the algorithm is based on the frequency information; however the changes of axial and radial depth of cut are only related to the amplitude of the motor current. Therefore, the algorithm is insensitive to the axial and radial depth of cut during end milling.
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10
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2
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500 400 300 200 100 0
0
(b)
Amplitude of marked features
Fig. 7. Cutting edge fracture on the exit cut. Tool/workpiece material: HSS/45# steel; spindle speed: 600 rpm, radial depth of cut: 2 mm, axial depth of cut: 4 mm, feed speed: 120 mm/min; cutter diameter: 6 mm, cutter flute: 4(a) Feedmotor current signals with cutting edge fracture on the exit cut; (b) marked features with the cutting edge fracture.
(a)
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100
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8
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10
150
Radial depth from 0 to 6 mm
Cutter
4
Work piece
(c)
100
(d)
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Fig. 8. Feed-motor current signals when cutting workpiece with grooves. Tool/workpiece material: HSS/45# steel; spindle speed: 900 rpm; radial depth of cut: 4 mm; axial depth of cut: 4 mm; feed speed: 120 mm/min; cutter diameter: 6 mm; cutter flute: 4(a) Workpiece A; (b) marked features of the feed-motor current signals for workpiece A under the axial depth of cut 4 mm; (c) Workpiece B; (d) marked features of the feed-motor current signals for workpiece B under the radial depth of cut 0–6 mm.
4. Discussion and conclusions For this tool condition monitoring system, the key issue is if it can indicate the cutting edge fracture from the feed-motor current signals during end milling in real time. According to the
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algorithm, the system needs 0.064 s to collect a segment of data and to then start to calculate a marked feature by using the algorithm. The time of computation is about 0.315 s to get a marked feature. Therefore, the monitoring system needs to take a 0.379 s to identify a tool fracture if it occurs during end milling; the time referred to is from the collections of current signals to an alarm generation. Note that the computer used is PII, CUP 433 MHz. Clearly, the time can meet the need of the practical application for detecting a cutting edge fracture during end milling. The other issue for a tool condition system is the cost and installation of the system. This approach only needs three current sensors to collect the feed-motor current signals, all of the costs add to less than 70 USA$. The sensor installation is very easy; it does not interrupt the machining system at all. Therefore, sensing the current of the feed drive to indicate the tool fracture is a much better alternative in terms of the equipment cost, unobtrusiveness, non-interference around the working zone, and retrofitting and hardware simplicity [16]. Unlike in other works, the motor current is only used to estimate cutting force using a model, and then the estimated cutting force is used to indicate tool conditions. In this paper, the feed-motor is directly applied to indicate the cutting edge fracture. In brief, the monitoring system based on the above algorithm has high robustness for application in practical end milling in real time, but also requires simple and inexpensive sensors that do not interrupt the cutting process. This approach, however, has some problems to be solved. The major one is that the dynamic characteristics of the current feedback control loop of the feed-drive system limit the bandwidth of the current sensing system. Another major problem is that the observed current signals of the servo drive motor contain undesirable components resulting from accelerating or decelerating the mass of table, and overcoming the friction force in the guide way. Final limitation of this currentmeasuring approach is that it cannot be applied for too light cuts because the magnitude of the useful signal for cutting is then small and difficult to extract the useful information for detecting tool conditions. Linear motor-based direct feed drives in high-speed machining not only are more desirable to improve productivity, but also eliminate the backlash and structural flexibility due to gear reduction mechanism. Meanwhile, the elimination of gearing gives the benefit of high-speed tracking, the cutting forces can directly be reflected to the motor currents due to the direct coupling; so that the motor current has an even stronger effect on tracking accuracy. Thus, the feed-motor current signals will be able to respond more effectively to the tool condition in manufacturing processing. In future work, the new algorithm proposed will be employed to detect tool condition through linear-motor current signals in high-speed milling. Additionally, although all experiments were limited to end milling operations, it is believed that the detection approach may be applied equally well to other milling operations.
Acknowledgements The author thanks the support provided by Alexander von Humboldt Foundation, Germany in writing the paper. The useful comments by editor and reviewers are also gratefully acknowledged.
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