Cutter tool fault detection using a new spectral.pdf

Manufacture Engineers, Part B: Journal of Engineering Proceedings of the Institution of Mechanical The online version of this article can be found at: DOI: 10.1243/09544054JEM1932 2010 224: 1784Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture T Kalvoda, Y-R Hwang and M Vrabec Cutter tool fault detection using a new spectral analysis method Published by: On behalf of: Institution of Mechanical Engineers can be found at:Manufacture Proceedings of the Institution of Mechanical Engineers, Part B: Journal of EngineeringAdditional services and information for Alerts: What is This? - Dec 1, 2010Version of Record by guest on January 9, Downloaded from 1784 Cutter tool fault detection using a new spectral analysis methodg T Kalvoda1*, Y-R Hwang1,2, and M Vrabec3 1Department of Mechanical Engineering, National Central University, Chung-Li, Taiwan, Republic of China 2Department of Mechanical Engineering and the Institute of Opto-Mechatronics Engineering, National Central University, Chung-Li, Taiwan, Republic of China 3Faculty of Mechanical Engineering, Czech Technical University of Prague, Prague, Czech Republic The manuscript was received on 10 December 2009 and was accepted after revision for publication on 22 March 2010. DOI: 10.1243/09544054JEM1932 Abstract:An investigation of milling end cutter tool fault monitoring based on dynamic force in the frequency domain and time-frequency domain is presented in this paper. A new data analysis technique, the HilbertHuang transform (HHT), is used to analyse this process in the frequency domain and time-frequency domain. This technique is also compared with the traditional Welchs method power spectra based on the Fourier transform (FT) in the frequency domain approach. The non-linearity and non-stationarity of the cutting process are taken into account. This method is designed to track the main peak in the frequency domain and time- frequency domain (HHT). The main tool break indicator is the appearance of new frequency as a result of the cutter tool fault. The HHT analysis technique covers the physical nature of the cuttingprocess. Thecuttingprocessisnottreatedlikeatheoreticalprocess, whichisobviousby the oscillation of the frequency around the fundamental frequency of the cutter tool. The break of the cutter tool is obvious in the presented results. Keywords:cutter tool fault, spectral analysis, milling process monitoring, HilbertHuang transform 1INTRODUCTION The computer numerical control (CNC) machines cannot detect cutter tool conditions in an on-line manner. Because a broken tool may continue func- tioning without being detected, the materials costs will increase and the quality of products will dimin- ish as errors are made by the broken tool in process. To reduce the materials costs and prevent dam- age to the cutting tool, detecting technology of an unmanned, on-line tool breakage detection system is necessary 1. The tool wear monitoring has been widely studied by many different approaches. There are two major approaches using sensing technology for detecting tool breakage: one is the direct method, which mea- sures and evaluates the volumetric change in the *Corresponding author: Department of Mechanical Engineer- ing, National Central University, No. 300, Jhongda Road, No. 300, Jhongda Road, Chung-Li, Taiwan, Republic of China. email: kalvoda tool, and the other is the indirect method, which measuresthecuttingparametersduringtheoperation process 2. The disadvantage of the direct processes is obvious in terms of the interruption of the cutting process as wellasinthepresenceofthecoolantfluidsonacutter tool. The Fourier transform (FT) and its modified short- time Fourier transform has been widely studied in ordertodetectcuttertoolwearorcuttertoolbreak3. The lack of this method leads to the assumption that the processed data are strictly linear and stationary, which is impossible owing to the nature of the cut- ting process. Another shortcoming of the FT is the presence of harmonics as a multiple of fundamental frequency, which makes it difficult to recognize the real frequency from harmonic. The Fourier transform presentation is limited to the frequency domain. Thepossibledirectionofthestudytoolwearprocess or cutter tool break provides the wavelets trans- form 3,4, but the assumption of the data linearity for wavelet transform makes it difficulty to reliably Proc. IMechE Vol. 224 Part B: J. Engineering ManufactureJEM1932 by guest on January 9, Downloaded from Cutter tool fault detection using a new spectral analysis method1785 analyse the dynamic cutting force signal in order to monitor the cutting process. The new method HilbertHuang transform (HHT) for time series analysis was proposed 5,6. The method overcomes the shortcomings of non-linearity and non-stationarity of the time series data sets. The HHT was successfully applied for many solutions of time series analysis: structural health monitoring, vibration, speech, bio-medical applications, and so on 6. The HHT consists of two fundamental steps: signal decompositions using empirical mode decom- position (EMD), which is actually a dyadic filter bank, and the instantaneous frequency computation 7. 2EXPERIMENTAL METHODS 2.1Tool wear recognition The tool wear is generally caused by a combination of various processes. Tool wear can occur gradually or in drastic breakdowns. Gradual wear may occur by adhesion, abrasion, or diffusion, and it may appear in two ways: wear on a tools face or wear on its flank. Contact with the chip produces a crater in the tool face. Flank wear, on the other hand, is com- monly attributed to friction between the tool and the workpiece material. In general, increasing the cut- ting speed increases the temperature at the contact zone, leading to a drastic reduction of the tools life. The milling cutting process is specified by the intensive contact between the cutter tool and the workpiece and it leads to the tool wear or tool break- age. The described process is characterized by the change of the cutter tool geometry. The cutting tooth induces the fluctuation part in the cutting force as a result of the forced vibration. The change (tool wear ortoolbreak)ofthecuttinggeometrycanbeobserved in the spectral analysis. The physical essence of the cutter tool wear will be neglected in the following parts of this study. 2.2The HilbertHuang transform as a method of analysis The limitation of use of the traditional methods such Fourier and wavelet transforms was presented above. Recent research 5,6 has brought a new approach for non-linear and non-stationary data. The HHT has been shown to perform well for these kind of data. The HHT has been successfully applied for many solutions of non-linear and non-stationary data. The presentation in both frequency and time-frequency domainsshowstheadvantageoftheothertransforms. The important event in the cutting process may be attributed to given time. The EMD method is fundamental to HHT. Using theensembleempiricalmodedecomposition(EEMD) method,anycomplicateddatasetcanbedecomposed intoafiniteandoftensmallnumberofcomponents:a collection of intrinsic mode functions (IMF). An IMF represents a generally simple oscillatory mode as a counterparttothesimpleharmonicfunction.Inorder to avoid mode mixing between the individual compo- nents, the white-noise of the given value is added into the investigated signal (this process is referred to as EEMD). By definition, an IMF is any function with the same number of extrema and zero crossings, with its envelopes being symmetric with respect to zero 5,6. The process of EMD is as follows: (a) identify minima and maxima; (b) connect local minima and maxima using the spline; (c) find the mean (m1) of the upper and bottom envelope identification. The mean is designated as m1, and the difference between the data and m1in the first component h1is h1= x(t) m1(1) In the second sifting process, h1is treated as the data, then h1 m11= h11(2) Thissiftingprocedurecanberepeatedk times,until h1kis an IMF, that is h1(k1) m1k= h1k; then it is designated as c1= h1k, the first IMF compo- nent from the data. To check if h1kis an IMF, the following conditions must be fulfilled 5,6: (a) the difference between the numbers of extrema and zero-crossings is ?1; (b) the mean of the upper envelope (linked by local maxima) and the lower envelope (linked by local minima) is zero at every point. The first IMF c1is subtracted from the original sig- nal r1= s c1. This difference is called the residue r1. It is now treated as the new signal and subjected to the same sifting process. The decomposition process finally stops when the residue rnbecomes a mono- tonic function or a function with only one extremum from which no more IMF can be extracted. Decom- position of the original signal into n-empirical modes and a residue is then achieved by x(t) = n ? j=1 cj+ rn(3) AnotherstepistoapplytheHilberttransformtothe decomposed IMFs. Each component has its Hilbert transform yi yi(t) = 1 ? cj() t d(4) JEM1932Proc. IMechE Vol. 224 Part B: J. Engineering Manufacture by guest on January 9, Downloaded from 1786T Kalvoda, Y-R Hwang, and M Vrabec Fig.1Cutting force signal analysed by using of various approaches: (a) original data set; (b) Fourier transform of the signal; (c) wavelet transform; (d) HHT of the original signal With the Hilbert transform, the analytic signal is defined as z(t) = x(t) + iy(t) = a(t)ei(t)(5) where a(t) = ? x2+ y2,(6) and (t) = arctan(y/x)(7) Here,a(t)istheinstantaneousamplitudeand(t)is the phase function, and the instantaneous frequency is simply = d dt (8) AfterperformingtheHilberttransformon eachcomponent,theoriginaldatacanbe expressed as the real part Rin the following form x(t) = ? n ? j=1 aj(t)exp ? i ? j(t)dt ? (9) With the Hilbert spectrum defined, the marginal spectrum can be defined as h() = T ? 0 H(,t)dt(10) The marginal spectrum offers a measure of the total amplitude (or energy) contribution from each frequency value. This spectrum represents the accu- mulated amplitude over the entire data span in a probabilistic sense. All details of HHT are given in references 5 and 6. The performance of the Fourier transform, wavelet, and HHT can be demonstrated by an artificial sig- nal. The signal corresponds to the cutting force in the x-axis (Fig. 1(a). The cutting conditions correspond Proc. IMechE Vol. 224 Part B: J. Engineering ManufactureJEM1932 by guest on January 9, Downloaded from Cutter tool fault detection using a new spectral analysis method1787 Table 1Cutting conditions CuttingSpindleCutter toothFeedDepthWidth speedrevolutionfrequencyrateof cutof cut TestVc(m/min) (r/min)ft(Hz)f (m/min)ap(mm)ae(mm) 174.841985132.331.0511.51.2 250.7134589.670.47811 to test 1 given in Table 1; a low carbon steel was considered for the cutting force simulation. The con- stants for the cutting force simulation are adopted from reference 8. The presentation of the comparisons (Figs 1(b), (c), (d) is given in the time-frequency domain, which comparestheresultstotherealsignal(Fig.1(a)better than in frequency domain. Figure 1(b) shows the time-frequency presentation using Fourier transform (Fig. 1(b) for a non-linear but weak stationary signal. Figure 1(b) shows the fundamental frequency around 132Hz with three harmonics as a multiple of the fundamental fre- quency. The presence of the harmonics is typical for asymmetric signals. It does not have any phys- ical meaning in this case. With Fourier transform the frequency values are constant over the whole time span covering the range of integration. As the Fourier definition of frequency is not a function of time, it can be easily seen that the frequency con- tent would be physically meaningful only if the data were linear and stationary. That is why a cutter tool fault by use of Fourier transform was studied by increasingpowerdensity3,ratherthanbyfrequency change. Continuous wavelet transform (Fig. 1(c) was applied to the same data set (Fig. 1(a). The wavelet is extremely useful for data comparison and image processing. The wavelet approach offers the time- frequency information with an adjustable window. The frequency is actually pseudo frequency. The representation is usually shift-scale. The scale is proportional to the frequency and shift to time. The local property of the wavelet allows a change in the frequency to be detected, so it is useful for non- stationarydata. Themostseriousweaknessofwavelet analysis is again the limitation imposed by the uncer- tainty principle (product of the frequency resolution, ?,andthetimespanoverwhichthefrequencyvalue is defined, ?T, shall not be less than 1/2) to be local and a base wavelet cannot contain too many waves; yet to have fine frequency resolution, a base wavelet will have to contain many waves 7. Figure 1(c) shows very obvious peaks, and the frequency corresponds to the theoretical frequency 132Hz.Figure 1(d) shows the results computed using HHT. The continuous frequency along the time line is obvious. The process of computing the time-frequency domain is based on equations (1) to (10); however, the instantaneous frequency can be computed based on the Hilbert transform, zero crossings, or quadrature reference 7. The concept of the instantaneous frequency computation allows frequency to be computed not only in the distance between the two peaks, but also within one peak if the data density is high enough. The oscillations (Fig.1(d)describethefrequencychangingwithinone peak. 2.3Experimental equipment and design The material used for the workpiece in the test was SAE 1045 carbon steel with a nominal mate- rial composition of C=0.45per cent,Mn= 0.75per cent,P=0.04per cent max,S= 0.05per cent max (wt%). The cutting tool selected was an end-mill type manufactured from high- speed steel (HSS-Co), with a diameter of 12mm, and four flutes. The test was performed on a five contin- uous axis milling machine centre, manufactured by Chuan Liang, having a maximum spindle revolution of 20000r/min, with a NUM 760 control system. The NC program was created in Cam NX 4.0. Dry cutting was performed. The experiment was performed for two different cutting conditions given in Table 1. Each test was repeated at least four times. In order to avoid misrepresentation of the tool vibration with the natural frequency of the cutting set-up an impact test was performed. The natural frequency was measured by the impact hammer in all directions on the workpiece (x, y, z) and the naturalfrequencyofthetoolwasalsomeasured. Inall cases the frequencies were higher than 2.5kHz. The three-axis piezoelectric dynamometer Kistler 9257B was connected to the charge amplifier. Vibration was picked up by the data acquisition unit instruNET (OMEGA). The data acquisition unit was connected to a PCI Bus controller card for a PC. The sampling rate was 5kHz. The data were pro- cessed using Matlab. The experimental cutting set-up is shown in Figure 2. All signals were recorded under loading. Some signals were collected from different positions on JEM1932Proc. IMechE Vol. 224 Part B: J. Engineering Manufacture by guest on January 9, Downloaded from 1788T Kalvoda, Y-R Hwang, and M Vrabec Fig.2Experimental cutting set-up Fig.3Segment of cutting force data set damaged cutter tool, time domain the workpiece. The cutter tooth frequency ftwas calculated using the following equation ft= 60n (11) where is the spindle speed in r/min and n is the number of teeth on the cutter tool. 3RESULTS 3.1Time domain Figure 3 shows a segment of the data set of the damaged cutter tool in time domain in contrast to Fig. 4, where the cutter tool was undamaged. The Fig.4Segment of cutting force data set undamaged cutter tool, time domain (a) (b) Fig.5(a) Hilbert spectrum of the undamaged cutter tool. (b) Hilbert spectrum of the damaged cutter tool Proc. IMechE Vol. 224 Part B: J. Engineering ManufactureJEM1932 by guest on January 9, Downloaded from Cutter tool fault detection using a new spectral analysis method1789 Fig.6Decomposed signal of the damaged cutter tool, the highest energy components results correspond to the cutting conditions for test 1, given in Table 1. The change of the amplitude in every fourth peak corresponds to the cutter tool break (Fig. 3). The speed of the spindle was = 1985r/min; thus the frequency of each tooth was: ft= 33Hz (equation (11). The cycle is marked in Fig. 3. The marked period (0.032s) roughly corre- sponds to the cycle of one spindle revolution if the period is computed (equation (11). The presented data segment, however, does not represent all of the data set; most of the time the signal is not very steady and tool break estimation could therefore be impossible. The shortcoming of the Fourier transform for the presented data set (see section 2.2) is obvious. Time domain representation does not show all of the con- tent of the data set. Therefore a better representation is given in the frequency domain or time-frequency domain. 3.2Time-frequency domain Figure 5(a) shows Hilbert spectra of the undam- aged cutter tool. The novel approach (HHT) shows oscillations around the fundamental frequency of the forced vibrations,which was 132Hz.The instantaneous frequency can be computed by using HHT. The slight oscillations describe the cutting pro- cess better. The cutting process by using HHT is not treated like a theoretical process. The results of the radial force Fr(x-axis in coordi- nates of the milling machine) are presented. Figure 5(b) shows the Hilbert spectra of the dam- aged cutter tool. The damage to the cutter tool was simulated by grinding one of the teeth into a triangle shape. The change of the instantaneous fre- quency is obvious. The drift into lower frequencies as well as the higher fluctuations of the instantaneous fre