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A new dataanalysis technique, the HilbertHuang transform (HHT), is used to analyse this process inthe frequency domain and time-frequency domain. This technique is also compared with thetraditional Welchs method power spectra based on the Fourier transform (FT) in the frequencydomain approach. The non-linearity and non-stationarity of the cutting process are taken intoaccount. 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 asa result of the cutter tool fault. The HHT analysis technique covers the physical nature of thecuttingprocess. Thecuttingprocessisnottreatedlikeatheoreticalprocess, whichisobviousbythe oscillation of the frequency around the fundamental frequency of the cutter tool. The breakof the cutter tool is obvious in the presented results.Keywords:cutter tool fault, spectral analysis, milling process monitoring, HilbertHuangtransform1INTRODUCTIONThe computer numerical control (CNC) machinescannot detect cutter tool conditions in an on-linemanner. Because a broken tool may continue func-tioning without being detected, the materials costswill 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 anunmanned, on-line tool breakage detection system isnecessary 1.The tool wear monitoring has been widely studiedby many different approaches. There are two majorapproaches using sensing technology for detectingtool 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: tool, and the other is the indirect method, whichmeasuresthecuttingparametersduringtheoperationprocess 2.The disadvantage of the direct processes is obviousin terms of the interruption of the cutting process aswellasinthepresenceofthecoolantfluidsonacuttertool.The Fourier transform (FT) and its modified short-time Fourier transform has been widely studied inordertodetectcuttertoolwearorcuttertoolbreak3.The lack of this method leads to the assumption thatthe 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 thepresence of harmonics as a multiple of fundamentalfrequency, which makes it difficult to recognize thereal frequency from harmonic. The Fourier transformpresentation is limited to the frequency domain.Thepossibledirectionofthestudytoolwearprocessor cutter tool break provides the wavelets trans-form 3,4, but the assumption of the data linearityfor wavelet transform makes it difficulty to reliablyProc. IMechE Vol. 224 Part B: J. Engineering ManufactureJEM1932 by guest on January 9, Downloaded from Cutter tool fault detection using a new spectral analysis method1785analyse the dynamic cutting force signal in order tomonitor the cutting process.The new method HilbertHuang transform (HHT)for time series analysis was proposed 5,6. Themethod overcomes the shortcomings of non-linearityand non-stationarity of the time series data sets. TheHHT was successfully applied for many solutions oftime series analysis: structural health monitoring,vibration, speech, bio-medical applications, and soon 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 METHODS2.1Tool wear recognitionThe tool wear is generally caused by a combinationof various processes. Tool wear can occur graduallyor in drastic breakdowns. Gradual wear may occur byadhesion, abrasion, or diffusion, and it may appearin two ways: wear on a tools face or wear on itsflank. Contact with the chip produces a crater in thetool face. Flank wear, on the other hand, is com-monly attributed to friction between the tool and theworkpiece material. In general, increasing the cut-ting speed increases the temperature at the contactzone, leading to a drastic reduction of the tools life.The milling cutting process is specified by theintensive contact between the cutter tool and theworkpiece and it leads to the tool wear or tool break-age. The described process is characterized by thechange of the cutter tool geometry. The cutting toothinduces the fluctuation part in the cutting force as aresult of the forced vibration. The change (tool wearortoolbreak)ofthecuttinggeometrycanbeobservedin the spectral analysis.The physical essence of the cutter tool wear will beneglected in the following parts of this study.2.2The HilbertHuang transform as a methodof analysisThe limitation of use of the traditional methods suchFourier and wavelet transforms was presented above.Recent research 5,6 has brought a new approachfor non-linear and non-stationary data. The HHT hasbeen shown to perform well for these kind of data.The HHT has been successfully applied for manysolutions of non-linear and non-stationary data. Thepresentation in both frequency and time-frequencydomainsshowstheadvantageoftheothertransforms.The important event in the cutting process may beattributed to given time.The EMD method is fundamental to HHT. Usingtheensembleempiricalmodedecomposition(EEMD)method,anycomplicateddatasetcanbedecomposedintoafiniteandoftensmallnumberofcomponents:acollection of intrinsic mode functions (IMF). An IMFrepresents a generally simple oscillatory mode as acounterparttothesimpleharmonicfunction.Inorderto avoid mode mixing between the individual compo-nents, the white-noise of the given value is added intothe investigated signal (this process is referred to asEEMD). By definition, an IMF is any function with thesame number of extrema and zero crossings, with itsenvelopes 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 thespline;(c) find the mean (m1) of the upper and bottomenvelope identification.The mean is designated as m1, and the differencebetween the data and m1in the first component h1ish1= x(t) m1(1)In the second sifting process, h1is treated as thedata, thenh1 m11= h11(2)Thissiftingprocedurecanberepeatedk times,untilh1kis an IMF, that is h1(k1) m1k= h1k; thenit is designated as c1= h1k, the first IMF compo-nent from the data. To check if h1kis an IMF, thefollowing conditions must be fulfilled 5,6:(a) the difference between the numbers of extremaand zero-crossings is ?1;(b) the mean of the upper envelope (linked by localmaxima) and the lower envelope (linked by localminima) is zero at every point.The first IMF c1is subtracted from the original sig-nal r1= s c1. This difference is called the residuer1. It is now treated as the new signal and subjected tothe same sifting process. The decomposition processfinally stops when the residue rnbecomes a mono-tonic function or a function with only one extremumfrom which no more IMF can be extracted. Decom-position of the original signal into n-empirical modesand a residue is then achieved byx(t) =n?j=1cj+ rn(3)AnotherstepistoapplytheHilberttransformtothedecomposed IMFs. Each component has its Hilberttransform yiyi(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 VrabecFig.1Cutting force signal analysed by using of various approaches: (a) original data set; (b) Fouriertransform of the signal; (c) wavelet transform; (d) HHT of the original signalWith the Hilbert transform, the analytic signal isdefined asz(t) = x(t) + iy(t) = a(t)ei(t)(5)wherea(t) =?x2+ y2,(6)and(t) = arctan(y/x)(7)Here,a(t)istheinstantaneousamplitudeand(t)isthe phase function, and the instantaneous frequencyis simply =ddt(8)AfterperformingtheHilberttransformoneachcomponent,theoriginaldatacanbeexpressed as the real part Rin the followingformx(t) = ?n?j=1aj(t)exp?i?j(t)dt?(9)With the Hilbert spectrum defined, the marginalspectrum can be defined ash() =T?0H(,t)dt(10)The marginal spectrum offers a measure of thetotal amplitude (or energy) contribution from eachfrequency value. This spectrum represents the accu-mulated amplitude over the entire data span in aprobabilistic sense. All details of HHT are given inreferences 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 thex-axis (Fig. 1(a). The cutting conditions correspondProc. IMechE Vol. 224 Part B: J. Engineering ManufactureJEM1932 by guest on January 9, Downloaded from Cutter tool fault detection using a new spectral analysis method1787Table 1Cutting conditionsCuttingSpindleCutter toothFeedDepthWidthspeedrevolutionfrequencyrateof cutof cutTestVc(m/min) (r/min)ft(Hz)f (m/min)ap(mm)ae(mm)174.841985132.331.0511.51.2250.7134589.670.47811to test 1 given in Table 1; a low carbon steel wasconsidered for the cutting force simulation. The con-stants for the cutting force simulation are adoptedfrom reference 8.The presentation of the comparisons (Figs 1(b),(c), (d) is given in the time-frequency domain, whichcomparestheresultstotherealsignal(Fig.1(a)betterthan in frequency domain.Figure 1(b) shows the time-frequency presentationusing Fourier transform (Fig. 1(b) for a non-linearbut weak stationary signal. Figure 1(b) shows thefundamental frequency around 132Hz with threeharmonics as a multiple of the fundamental fre-quency. The presence of the harmonics is typicalfor asymmetric signals. It does not have any phys-ical meaning in this case. With Fourier transformthe frequency values are constant over the wholetime span covering the range of integration. As theFourier definition of frequency is not a function oftime, it can be easily seen that the frequency con-tent would be physically meaningful only if the datawere linear and stationary. That is why a cutter toolfault by use of Fourier transform was studied byincreasingpowerdensity3,ratherthanbyfrequencychange.Continuous wavelet transform (Fig. 1(c) wasapplied to the same data set (Fig. 1(a). The waveletis extremely useful for data comparison and imageprocessing. The wavelet approach offers the time-frequency information with an adjustable window.The frequency is actually pseudo frequency. Therepresentation is usually shift-scale. The scale isproportional to the frequency and shift to time. Thelocal property of the wavelet allows a change in thefrequency to be detected, so it is useful for non-stationarydata. Themostseriousweaknessofwaveletanalysis is again the limitation imposed by the uncer-tainty principle (product of the frequency resolution,?,andthetimespanoverwhichthefrequencyvalueis defined, ?T, shall not be less than 1/2) to be localand a base wavelet cannot contain too many waves;yet to have fine frequency resolution, a base waveletwill have to contain many waves 7.Figure 1(c) shows very obvious peaks, and thefrequency corresponds to the theoretical frequency132Hz.Figure 1(d) shows the results computedusing HHT. The continuous frequency along thetime line is obvious. The process of computing thetime-frequency domain is based on equations (1)to (10); however, the instantaneous frequency canbe computed based on the Hilbert transform, zerocrossings, or quadrature reference 7. The conceptof the instantaneous frequency computation allowsfrequency to be computed not only in the distancebetween the two peaks, but also within one peakif the data density is high enough. The oscillations(Fig.1(d)describethefrequencychangingwithinonepeak.2.3Experimental equipment and designThe material used for the workpiece in the testwas 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 selectedwas an end-mill type manufactured from high-speed steel (HSS-Co), with a diameter of 12mm, andfour flutes. The test was performed on a five contin-uous axis milling machine centre, manufactured byChuan Liang, having a maximum spindle revolutionof 20000r/min, with a NUM 760 control system. TheNC program was created in Cam NX 4.0. Dry cuttingwas performed.The experiment was performed for two differentcutting conditions given in Table 1. Each test wasrepeated at least four times.In order to avoid misrepresentation of the toolvibration with the natural frequency of the cuttingset-up an impact test was performed. The naturalfrequency was measured by the impact hammer inall directions on the workpiece (x, y, z) and thenaturalfrequencyofthetoolwasalsomeasured. Inallcases the frequencies were higher than 2.5kHz. Thethree-axis piezoelectric dynamometer Kistler 9257Bwas connected to the charge amplifier.Vibration was picked up by the data acquisitionunit instruNET (OMEGA). The data acquisition unitwas 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-upis shown in Figure 2.All signals were recorded under loading. Somesignals were collected from different positions onJEM1932Proc. IMechE Vol. 224 Part B: J. Engineering Manufacture by guest on January 9, Downloaded from 1788T Kalvoda, Y-R Hwang, and M VrabecFig.2Experimental cutting set-upFig.3Segment of cutting force data set damaged cuttertool, time domainthe workpiece. The cutter tooth frequency ftwascalculated using the following equationft=60n(11)where is the spindle speed in r/min and n is thenumber of teeth on the cutter tool.3RESULTS3.1Time domainFigure 3 shows a segment of the data set of thedamaged cutter tool in time domain in contrast toFig. 4, where the cutter tool was undamaged. TheFig.4Segment of cutting force data set undamagedcutter tool, time domain(a)(b)Fig.5(a) Hilbert spectrum of the undamaged cutter tool.(b) Hilbert spectrum of the damaged cutter toolProc. IMechE Vol. 224 Part B: J. Engineering ManufactureJEM1932 by guest on January 9, Downloaded from Cutter tool fault detection using a new spectral analysis method1789Fig.6Decomposed signal of the damaged cutter tool, the highest energy componentsresults correspond to the cutting conditions for test1, given in Table 1. The change of the amplitudein every fourth peak corresponds to the cutter toolbreak (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 inFig. 3. The marked period (0.032s) roughly corre-sponds to the cycle of one spindle revolution if theperiod is computed (equation (11). The presenteddata segment, however, does not represent all ofthe data set; most of the time the signal is not verysteady and tool break estimation could therefore beimpossible.The shortcoming of the Fourier transform for thepresented data set (see section 2.2) is obvious. Timedomain representation does not show all of the con-tent of the data set. Therefore a better representationis given in the frequency domain or time-frequencydomain.3.2Time-frequency domainFigure 5(a) shows Hilbert spectra of the undam-aged cutter tool. The novel approach (HHT) showsoscillations around the fundamental frequency ofthe forced vibrations,which was 132Hz.Theinstantaneous frequency can be computed by usingHHT. The slight oscillations describe the cutting pro-cess better. The cutting process by using HHT is nottreated 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 toolwas simulated by grinding one of the teeth into atriangle shape. The change of the instantaneous fre-quency is obvious. The drift into lower frequencies aswell as the higher fluctuations of the instantaneousfrequency indicates the cutter tool damage.The most obvious indicator of the cutter tool breakis the appearance of the new frequency around 32Hz.Thisfrequencycorrespondsexactlytothegap(causedby cutter tool fault) in the time domain set of thedamaged cutter tool in Fig. 3. The gap is marked inFig. 3 as a grey rectangle.The EEMD (equations (1) to (3) allows the fre-quency separation, which works like a band-passfilter. This has advantage that the filter does nothave to be used. The two significant components ofthe decomposed signal of the damaged cutter toolare shown in Fig. 6. Those frequencies correspondto the highest energy in Hilbert spectra (Fig. 5(b).The IMFs components are sorted from the highestfrequency into lowest frequency.The advantage of the data presentation in thetime-frequency domain is very straightforward. Thedifference between the Fourier transform and HHTis obvious: results can be presented in the in time-frequency domain at a high-frequency resolution,which is impossible using Fourier transform.3.3Frequency domainFigure 7 shows the Hilbert marginal spectra, whichis similar to the power spectra for Fourier transform.Figure 7 corresponds to Figs 5(a) and 5(b), but thepresentation is in the frequency-power spectra. Thetool fault is also obvious. The tool fault indicates thehigher energy in the Hilbert marginal spectra aroundthe frequency 32Hz, which also correspond to theJEM1932Proc. IMechE Vol. 224 Part B: J. Engineering Manufacture by guest on January 9, Downloaded from 1790T Kalvoda, Y-R Hwang, and M VrabecFig.7Marginal spectra: comparison between new anddamaged cutter tool, test 1Fig.8Marginal spectra: comparison between new anddamaged cutter tool, test 2gap in Fig. 3. The shift into lower frequencies iscaused by tool wear. The change in the shape of thecuttertoothintoadifferentgeometrycausesthesignalto shift into lower frequencies.The new method was used for different cuttingconditions, test 2, (Table 1) in order to confirmthe repeatability. The results (Fig. 8) correspond totheresultsabove:ashiftofthetrackedpeakintolowerfrequency and new frequency occurrence as a resultof the cutter tool fault.Figure 9 shows the comparison of the Hilbertmarginal spectra and the Fourier transform. Theadvantage is obvious: the Hilbert marginal spectrumdoes not have any harmonic it presents the datalocally, and the slight oscillations around the funda-mental frequency present the cutting process muchmore reliably.Fig.9Welchs power spectrum and marginal spectrumof the undamaged cutter t