Milling cutter breakage detection by the discretewavelet transform

\PERGAMON Mechatronics 8 "0888# 114Ð123

9846!3047:88: ! see front matter Þ 0887 Elsevier Science Ltd[ All rights reserved[PII] S9846!3047 "87#99938!X

Milling cutter breakage detection by the discretewavelet transform0

B[Y[ Leea\ Y[S[ Tarngb\�a Department of Mechanical Manufacture En`ineerin`\ National Huwei Institute of Technolo`y\ Yunlin\

Taiwan 521b Department of Mechanical En`ineerin`\ National Taiwan University of Science and Technolo`y\

Taipei\ Taiwan 095

Received 04 January 0887^ received in revised form 0 October 0887^ accepted 8 October 0887

Abstract

The paper describes the use of cutting force to detect milling cutter breakage based onthe discrete wavelet transform[ The discrete wavelet transform performs a multi!level signaldecomposition of the cutting force so that cutter breakage features can be extracted[ Millingcutter breakage can then be detected from the cutting force with or without the cutter breakagefeatures[ Experimental results have indicated that milling cutter breakage can be successfullydetected even under di}erent cutting conditions[ Þ 0887 Elsevier Science Ltd[ All rightsreserved[

Keywords] Milling^ Cutter breakage^ Discrete wavelet transform^ Cutting force

0[ Introduction

Detection of cutter breakage in milling operations has been considered a keytechnology to achieving the full automation of milling operations ð0Ł[ To detectthe occurrence of cutter breakage correctly\ the selection of an appropriate signalprocessing algorithm is very important[ The Fourier transform is a commonly usedsignal processing tool for the application of cutter breakage detection ð1Ł[ A signalcan be transformed from the time domain to the frequency domain by using theFourier transform[ However\ the Fourier transform has an inherent drawback[ Non!stationary transient information in the time domain cannot be clearly identi_ed in the

0 This paper has not been published elsewhere nor has it been submitted for publication elsewhere� Corresponding author[ Tel[] ¦775 1 1626 5345^ fax] ¦775 1 1626 5359^ e!mail] ystarngÝmail[

ntust[edu[tw

B[Y[ Lee\ Y[S[ Tarn`:Mechatronics 8 "0888# 114Ð123115

frequency domain when the Fourier transform is used[ As a result\ it is very di.cultto tell us when a particular event " for example\ cutter breakage# takes place from thefrequency domain[ To correct this de_ciency\ a windowing technique has been appliedto the Fourier transform of a small section of the signal at a time\ that is also calledshort!time Fourier transform ð2Ł[ The use of short!time Fourier transform to detectcutter breakage in milling has been studied ð3Ł[ However\ precision of the short!timeFourier transform is still limited and greatly dependent on the size of the window[ Inrecent years\ a more ~exible approach\ called the wavelet transform ð4\5Ł\ has beendeveloped to decompose the signal into various components at di}erent time windowsand frequency bands using a family of wavelets as basis functions[ Applications ofthe wavelet transform for the monitoring of machining operations have also beenreported ð6\7\8Ł[

In this paper\ the use of cutting force as a sensing signal to the detection of cutterbreakage in milling operations has been studied[ To detect cutter breakage accurately\the cutting force signal is processed by the discrete wavelet transform ð09Ł[ Based onthe discrete wavelet transform\ the cutting force signal is decomposed into a set ofapproximation and detail of the signal[ The approximation is the low!frequencycomponent of the signal and the detail is the high!frequency components of the signal[This decomposition process can be iterated so that the cutting force signal is brokeninto a hierarchical set of approximations and details\ that is also called a multi!levelsignal decomposition ð00Ł[ The results of the multi!level signal decomposition can beused to detect cutter breakage in milling operations accurately[

In the following\ the discrete wavelet transform is introduced to perform a multi!level signal decomposition[ Then\ the experimental setup for the detection of cutterbreakage in milling operations is discussed[ Experimental veri_cation of the cutterbreakage detection is shown and a summary of this study is given[

1[ The discrete wavelet transform

The wavelet transform of a signal f"t# is de_ned as the sum over all time of thesignal f"t# multiplied by scaled and shifted version of the wavelet function c"t#[ Thecoe.cients C"a\ b# of the wavelet transform of the signal f"t# can be expressed as]

C"a\b#�g�

−�

f "t#0

zac0

t−ba 1dt "0#

where a and b are the scaling and shifting parameters in the wavelet transform[Basically\ a small scaling parameter corresponds to a compressed wavelet function[

As a result\ the rapidly changing features in the signal f"t#\ i[e[ high frequency com!ponents\ can be obtained from the wavelet transform by using a small scalingparameter[ On the other hand\ low frequency features in the signal f"t# can be extractedby using a large scaling parameter with a stretched wavelet function[ In other words\a small scaling value is used for local analysis\ a large scaling value is used for globalanalysis[

B[Y[ Lee\ Y[S[ Tarn`:Mechatronics 8 "0888# 114Ð123 116

For a digital signal f"k#\ k�9\ 0\ 1\ [ [ [\ the discrete wavelet transform should beconsidered[ The most commonly used algorithm for the discrete wavelet transform isthe scaling and shifting parameters with powers of two[ That is]

a�1 j "1#

b�ka�k1 j "2#

where j is the number of levels in the discrete wavelet transform[The coe.cients C"a\ b# of the discrete wavelet transform can be divided into two

parts] one is the approximation coe.cients and the other is the detail coe.cients[ Theapproximation coe.cients are the high!scale\ low!frequency components of the signalf"k#[ On the other hand\ the detail coe.cients are the low!scale\ high!frequencycomponents of the signal f"k#[ The approximation coe.cients of the discrete wavelettransform for the digital signal f"k# at level j can be expressed as]

Aj� sn�9

�

f"n#fj\k"n#� sn�9

�

f"n#0

z1 jf0

n−k1 j

1 j 1 "3#

where fj\k"n# is the scaling function associated with the wavelet function cj\k"n#[Similarly\ the detail coe.cients of the discrete wavelet transform for the digital

signal f"k# at level j can be expressed as]

Dj� sn�9

�

f"n#cj\k"n#� sn�9

�

f"n#0

z1 jc0

n−k1 j

1 j 1 "4#

Based on Eqs[ "3# and "4#\ the decomposition of the signal f"k# can be iterated as thenumber of levels increases[ As a result\ a hierarchical set of approximations anddetails can be obtained through the multi!level signal decomposition[ A waveletdecomposition tree can then be obtained through this transformation process[ Usefulinformation for the signal f"k# can be yielded from the multi!level wavelet signaldecomposition[ In the next section\ the use of multi!level wavelet signal decompositionof the cutting force for the cutter breakage detection in milling is reported[

2[ Experimental setup and wavelet decomposition

Fig[ 0 shows the schematic diagram of the experimental setup for the cutter breakagedetection in milling operations[ A machining center with a four!inch "091[3mm#diameter double!negative Carbaloy milling cutter with eight inserts was used[ Theworkpiece material was gray cast iron blocks mounted on a table type of dynamometer"Kistler 8144B#[ The dynamometer signal was transmitted through a charge ampli_er"Kistler 4996# from which the cutting force signal was obtained and recorded in thePC workstation through a data acquisition board "DT1717#[ A multi!level signaldecomposition of the cutting force was then performed by the discrete wavelet trans!form for the cutter breakage detection in milling operations[ In the PC workstation\


Fig[ 0[ Schematic diagram for the detection of cutter breakage in milling[

the cutting force signal was processed by the discrete wavelet transform using onetransformation per two revolutions of spindle speed[

Basically\ the cutting force signal for the runout free cutter is periodic with thetooth frequency ft[ The tooth frequency ft can be expressed as]

ft�frz "5#

where z is the number of inserts on cutter and fr is the spindle speed in revolutionsper second "rps#[

As one of the inserts is broken\ the insert following the broken one will have abigger chip load to remove the material left by the broken one[ Therefore\ the cuttingforce signal which decreases\ then increases\ forms a special cutter breakage featuredue to the existence of cutter breakage[ Since the broken insert engages with theworkpiece once per revolution\ the cutting force variation due to cutter breakageappears once per revolution in the cutting force signal[ In other words\ the cuttingforce variation due to cutter breakage is a once per revolution fr signal[ As shown inEq[ "5#\ the frequency fr of cutting force variation due to cutter breakage is smallerthan the frequency ft of cutting force variation due to the tooth frequency[ Therefore\there is a frequency change in the cutting force at the occurrence of cutter breakage[To detect the occurrence of cutter breakage clearly\ the discrete wavelet transformuses Daubechies wavelets for performing the multi!level wavelet signal decompositionin this study[ This is because the Daubechies wavelets are suitable for the detectionof a sudden frequency change in a signal[ The names of the Daubechies wavelets arewritten dbN\ where N is the order of the wavelet[ Usually\ the higher order of thewavelet\ the more complicated signal processing is required[ It was found that N equalto 1 is clear enough for the detection of cutter breakage[ The scaling function andwavelet function for the db1 wavelet are shown in Fig[ 1[

Fig[ 2 shows an experimental result of the occurrence of cutter breakage using thefour!level wavelet signal decomposition[ Fig[ 3 shows an expanded view of the cuttingforce signal and the detail coe.cients D3[ In the entry transient\ the cutter graduallyenters the workpiece and the cutting force signal starts to increase[ As to the steady


Fig[ 1[ The db1 wavelet] "a# scaling function^ "b# wavelet function[

state\ the peak!to!peak cutting force signal becomes constant and is periodic pertooth[ However\ the periodicity of the cutting force per tooth is disturbed by thecutter breakage when one of the inserts on the cutter was broken at 2[0 sec[ As aresult\ a much bigger variation of the cutting force signal\ which decreases\ thenincreases\ is generated per revolution because of the broken insert[ As mentionedbefore\ the frequency of cutting force variation due to cutter breakage is lower thanthat due to the tooth frequency[ Therefore\ in the wavelet signal decompositionprocess\ the approximation coe.cients of the discrete wavelet transform should con!tain the cutting force variation due to cutter breakage[ This is because the approxi!mation coe.cients correspond to the low!frequency components of the cutting forcesignal[ As shown in Fig[ 2\ approximations are iteratively decomposed so that thecutting force signal is broken down into many lower!frequency components[ It isshown that the approximation coe.cients A2 clearly indicate variations of the cuttingforce signal due to cutter breakage and the periodic variation per tooth is removed[After removing the DC component of the cutting force from the approximationcoe.cients A2\ the cutting force variation due to cutter breakage stands out in thedetail coe.cients D3[ Therefore\ the use of the detail coe.cients D3 to detect cutterbreakage in milling have been considered in this study[

3[ Experimental veri_cation

In the experimental veri_cation\ di}erent cutting conditions have been consideredfor the detection of milling cutter breakage[ Fig[ 4 shows the cutting test results witha complete cutting cycle including transient\ steady\ and exit states[ The _rst rowshows the cutting force signal and the second row shows the detail coe.cients D3[For the damaged cutter\ an insert with chipped cutting edge was used to obtain thecutting force with cutter breakage[ A clear distinction of the detail coe.cients D3between Fig[ 4"c# and "d# is shown[ Fig[ 5 shows another cutting test result with acomplete cutting cycle[ However\ the spindle speed is increased to 0499 rpm[ Similar


Fig[ 2[ A four!level wavelet decomposition of the cutting force signal with cutter breakage[ "spindlespeed�599 rpm^ feed�9[14 mm:tooth^ axial depth of cut�1[4 mm^ radial depth of cut�49 mm^ samplingfrequency�619 Hz#[

results for the detection of milling cutter breakage is obtained[ Fig[ 6 shows the cuttinggeometry of milling over a hole[ Fig[ 7 shows the cutting test results for milling overa hole[ It is shown that the transient e}ect of milling over a hole is removed in thedetail coe.cients D3[ However\ the cutting force variation due to cutter breakagestill remains in the detail coe.cients D3 "Fig[ 7"d##[ Therefore\ a clear distinction ofthe detail coe.cients D3 is still available between the undamaged and damaged cutters"Fig[ 7"c# and "d##[ Thereby\ the detail coe.cients D3 can be used to detect the


Fig[ 3[ Expanded view for the cutting force signal with cutter breakage[ "a# cutting force^ "b# detailforce D3 "spindle speed�599 rpm^ feed�9[14 mm:tooth^ axial depth of cut�1[4 mm^ radial depth ofcut�49 mm^ sampling frequency�619 Hz#[

occurrence of cutter breakage successfully even under di}erent cutting conditions inmilling[

4[ Conclusions

The use of the discrete wavelet transform for the detection of cutter breakage inmilling has been reported in this paper[ The discrete wavelet transform performs afour!level signal decomposition of the cutting force signal in milling operations[ Basedon the results of the signal decomposition\ the detail coe.cients of the fourth levelcan be used to detect the occurrence of cutter breakage clearly[ It has also been foundthat the use of a Daubechies wavelet with the order of two is clear enough to


Fig[ 4[ Experimental results for the detection of cutter breakage with undamaged and damaged cutters["spindle speed�599 rpm^ feed�9[14 mm:tooth^ axial depth of cut�1[4 mm^ radial depth of cut�49 mm^sampling frequency�619 Hz#[

Fig[ 5[ Experimental results for the detection of cutter breakage with undamaged and damaged cutters["spindle speed�0499 rpm^ feed�9[14 mm:tooth^ axial depth of cut�1[4 mm^ radial depth of cut�49 mm^sampling frequency�0799 Hz#[

detect the occurrence of cutter breakage[ Experimental veri_cation has con_rmed thee}ectiveness of this proposed approach for the detection of cutter breakage in millingoperations\ even under di}erent cutting conditions[


Fig[ 6[ Cutting geometry for milling over a hole[

Fig[ 7[ Experimental results for the detection of cutter breakage with undamaged and damaged cutters formilling over a hole[ "spindle speed�599 rpm^ feed�9[14 mm:tooth^ axial depth of cut�0[1 mm^ radialdepth of cut�49 mm^ sampling frequency�619 Hz#[

Acknowledgements

Financial support from the National Science Council of the Republic of Chinaunder grant number NSC76!1105!E!900!914 is acknowledged[

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Milling cutter breakage detection by the discretewavelet transform