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International Journal of Machine Tools & Manufacture 48 (2008) 1637–1645

Contents lists available at ScienceDirect

International Journal of Machine Tools & Manufacture

0890-69

doi:10.1

� Corr

E-m

quim.ci

journal homepage: www.elsevier.com/locate/ijmactool

A new experimental methodology for identification of stability lobes diagramin milling operations

Guillem Quintana, Joaquim Ciurana �, Daniel Teixidor

Department of Mechanical Engineering and Civil Construction, Universitat de Girona, Avenue Lluis Santalo s/n, 17071 Girona, Spain

a r t i c l e i n f o

Article history:

Received 26 June 2008

Received in revised form

10 July 2008

Accepted 12 July 2008Available online 22 July 2008

Keywords:

Milling processes

Stability lobes diagram

55/$ - see front matter & 2008 Elsevier Ltd. A

016/j.ijmachtools.2008.07.006

esponding author. Tel.: +34 972 418 265; fax:

ail addresses: guillem.quintana@udg.edu (G. Q

urana@udg.edu (J. Ciurana), dani.teixidor@ud

a b s t r a c t

Chatter is a self-excited vibration that can occur during machining operations. This undesirable

phenomenon is one of the most common limitations when it comes to improving productivity and part

quality. For this reason, several methods have been developed with the aim of preventing, avoiding,

reducing, suppressing or controlling the occurrence of chatter.

A stability lobes diagram (SLD) shows the boundary between chatter-free machining operations and

unstable processes, in terms of axial depth of cut as a function of spindle speed. These diagrams are used

to select chatter-free combinations of machining parameters.

This paper presents an experimental method for identifying SLDs in milling operations. The

methodology is based on empirical tests where the workpiece permits a gradual increase of the axial

depth of cut in the feed direction, which represents the y coordinate of the SLD while the spindle speed

(the x coordinate of the SLD) is increased between passes. This is possible thanks to the inclined plane

shape presented by the workpiece. The cutting process is interrupted as soon as chatter is detected and

the frontier between stable and unstable cutting, i.e. the stability lobes diagram, is identified. This

permits to obtain the SLD physically machined onto the workpiece. The methodology is good for those

small and medium enterprises which have no technical knowledge and sophisticated resources, because

the SLD can be identified with a microphone and prepared workpiece.

At first, we present the results obtained when chatter is detected by the operator by analyzing the

sound emission. Then, in order to eliminate the subjective component of the human hearing

intervention, a computer application is presented. It permits to monitor the milling process sound

and analyze its amplitudes and frequencies to identify chatter as soon as its occurrence starts. The

results provided by the computer application are quite better.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Milling, and especially high-speed milling (HSM), operationsare widely used in present day manufacturing to obtain the finalshapes of mechanical parts. Examples of this metal-cuttingprocess can be found in the production of moulds and dies, andin the automotive, aerospace or aeronautical industries, wherelarge amounts of material are removed from large metalstructures in procedures that require high productivity andaccuracy.

Chatter is a self-excited vibration that can occur duringmachining operations and becomes a common limitation toproductivity and part quality. This phenomenon has severalnegative effects such as poor surface quality, unacceptable

ll rights reserved.

+34 972 418 098.

uintana),

g.edu (D. Teixidor).

inaccuracy, excessive noise and tool wear, machine tool damage,reduced material removal rate (MRR), increased costs in terms oftime, materials and energy, as well as the environmental impact ofdumping non-valid final parts and having to repeat the manu-facturing process.

In workshops, machine tool operators often select conservativecutting parameters to avoid chatter. Moreover, in some cases,additional manual operations are required to clean chatter marksleft on the part surface. In academic environments, severalmethodologies have been developed to predict, avoid, reduce,suppress or control the occurrence of chatter and its negativeconsequences. A great deal of literature has been generated sincethe late 1950s regarding the chatter problem. However, the initialworks carried out by Tobias [1] and Tlusty [2] remain, even now,indispensable references.

Very early on, it was demonstrated that during a millingprocess chatter can arise at certain combinations of axial depth ofcut and spindle speed (Fig. 1). As a function of these two cuttingparameters, the border between a stable cut (i.e. no chatter) and

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Stability Lobes Diagram

0.000.501.001.502.002.503.003.504.004.505.00

0 5000 10000 15000 20000 25000 30000Spindle Speed (rpm)

Axi

al d

epth

of c

ut (m

m)

Fig. 1. Example of a stability lobes diagram (SLD) and the stable and unstable

cutting conditions.

G. Quintana et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1637–16451638

an unstable one (i.e. with chatter) can be visualized in a chartcalled stability lobes diagram (SLD).

Several studies have been carried out in this field and severalmethods have been put forward to obtain the stability boun-dary that distinguishes chatter-free operations from unstableoperations.

The first approaches by Tobias [1,3] and Tlusty [2] identifiedthe regeneration mechanism. Their extensive studies establishedthe basis of the regeneration theory, which has become the mostcommonly accepted explanation for machine tool chatter. Regen-eration is the most powerful source of self-excitation. This effect isassociated with the dynamics of the machine tool and the cuttingforce variation due to subsequent cuts on the same cuttingsurface. The mathematical models developed to explain thesephenomena correspond to delay differential equations (DDEs).

Many researchers have attempted to predict the SLD usinganalytical methods [4–9]. Altintas and Budak [4] proposed makingstability predictions using the zeroth order Fourier term toapproximate the cutting force variation. This method, known aszeroth order approximation (ZOA), can achieve reasonably accurateSLD predictions for processes where the cutting force variesrelatively little, i.e. considerable radial immersions and largenumber of teeth. Insperger and Stepan [5,6] presented the semi-discretization (SD) method, which transforms the DDE into a seriesof autonomous ordinary differential equations (ODEs) with knownsolutions. Gradisek et al. [7] investigated stability boundariespredicted by ZOA and SD methods. The two methods producesimilar predictions for high radial immersions but, as radialimmersion decreases, boundary predictions begin to vary con-siderably. Analytical investigations led to the implementation ofthe bifurcation methods (i.e. Hopf bifurcation and period doublingor Flip bifurcation) for stability prediction in milling [8,9].

Recent developments in sensors and computers have led to therise of analytical–experimental methods and computer simulationanalyses. In Manufacturing Automation [10], Altintas explains awidely known analytical–experimental method based on the useof an impact hammer instrumented with a piezoelectric forcetransducer. Transfer functions of existing multi-degree-of-free-dom (MDOF) systems can be identified by structural dynamictests. In this case, to obtain the transfer function, the structure isexcited with an impact hammer and the resulting vibrations aremeasured with displacement, velocity or acceleration sensors.CUTPRO software simplifies the test and offers automaticpredictions of the SLD [11]. Another software program calledHarmonizer [12] scans the sound of the cutting process with amicrophone and chatter is detected if the energy of the measured

sound signal exceeds a certain threshold. Faassen et al. [13]use Harmonizer for the experimental validation of the proposedD-partitioning model, which considers the spindle speed depen-dencies. Sims et al. [14] describe the use of piezoelectric sensorsand actuators to predict milling SLDs. This approach offers morecontrol over the excitation signal than an impact hammer and ismore suitable for small tools where it is impossible to accuratelystrike the tool tip. Abele et al. [15,16] use an active magneticbearing (AMB) to identify the spindle tool system’s frequencyresponse function (FRF). This method allows a non-contactmeasurement to be made while the spindle is running. Thereare also many investigators who use finite element analysis (FEA)or the finite element method (FEM) for stability simulation andprediction [17–19].

Other methods do not need SLD prediction to seek stableregions between lobes. In some cases (e.g. where there are morethan three axes or for thin-walled workpieces) the SLD of thesystem cutting tool, machine tool and workpiece is continuouslychanging and it is difficult to make predictions in advance andschedule the correct parameters to ensure stable operations. Forsuch cases, researchers have developed methods consisting of on-line chatter detection and process interference to avoid thenegative effects. Ismail and Ziaei [20] implement an algorithmthat combines off-line scheduling of parameters and on-linespindle speed ramping. Faassen et al. [21] present a method todetect chatter online before it has fully developed. Early chatterdetection allows operators to interfere in the process, thusavoiding chatter marks on the workpiece surface. Doppenberget al. [22] use the detection algorithm presented in [21] to suggesta chatter controller that forces the machining process into aregion of chatter-free operation by adjusting the spindle speedwhen the onset of chatter is identified.

In contrast to all these methods, which are aimed at avoidingchatter by situating operations in chatter-free regions of the SLD,some researchers have looked at raising the stability boundary.Wang and Lee [23] describe a redesigning procedure for theweakest component of a machine tool structure. First, vibrationtests showed that the spindle was the weakest component. Second,the spindle was redesigned to change the dynamic behaviour of thewhole machine tool and obtain a higher stability boundary. Passivedampers have been used to increase the damping capacity of acutting tool system, e.g. inner friction plates [24], impact dampers[25] or mechanical dampers [26]. Some researchers use sensorsand actuators [27,28] to actively raise the SLD of a machine tool.Others analyze the use of variable pitch cutters (i.e. with irregularspacing between teeth) [29–31] or sinusoidal spindle speedvariation (S3V) [32] to disturb the regenerative mechanism.

In this paper, a simple experimental method for obtaining andidentifying SLDs in milling operations is presented. The method isbased on experiments where the workpiece shape permits agradual increase of the axial depth of cut in the feed direction untilchatter arises. The spindle speed is increased between passes inorder to obtain combinations of a spindle speed and an axial depthof cut in the stability frontier and describe the SLD. Once the SLD isidentified, the workshop operator can select the proper processparameters to perform chatter-free operations. The method, basedon empirical tests, is especially suitable for industrial environmentswhere operators are not familiar with large analytical methods.This method also allows to obtain SLD with few resources; then it isfocused to help small and medium enterprises.

2. Experimental setup

The work of Tonshoff cited by Dornfeld [33] used a workpiecewith an inclined plane to illustrate the sensitivity of forced and

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G. Quintana et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1637–1645 1639

self-excited vibrations to machining conditions. Tonshoff showedthat, at a certain depth of cut along the tool path, forced vibrationsturn into self-excited vibrations and the milling process becomesunstable (see Fig. 2).

Wang and Lee [23] used a workpiece with increasing cuttingdepth to determine the most influential machine tool componentduring chatter. They monitored the vibrations of the working table,workpiece and spindle with vibration sensors and performedseveral cutting tests to show that with a gradually increasedcutting depth a violent vibration appeared suddenly. Analyzing thevibration spectrum and the marks on the workpiece surface, theyconcluded that this vibration could be considered chatter. Wangand Lee also found that the weakest part of their machine toolstructure was the spindle and they carried out a redesigningprocess to improve the cutting capability of the machine.

Fig. 3 shows the proposed procedure in this work. Axial depthof cut increases, thanks to the inclined plane presented by theworkpiece. This allows the tool to move along the y coordinate ofthe SLD. When the cutting tool reaches the stability frontier,chatter occurs suddenly and the machine is stopped. Afterwards,the spindle speed is increased to carry out another pass movingalong the SLD x coordinate. The procedure has to be repeated untilthe SLD is physically machined onto the workpiece. Once the SLDis identified, the machining process can be optimized by seekingregions of stable cutting between lobes.

Initially, experiments were carried out first, by interrupting thecutting process as soon as the operator detected the chatteroccurrence by analyzing the sound emission. Afterwards, acomputer application was developed to analyze the milling soundon-line and detect the chatter occurrence. This permitted toeliminate subjective component of the methodology based on theoperator hearing performance. Fig. 4 shows a schematic repre-sentation of the followed procedure.

Experiments were carried out in a Deckel Maho 64V linear 3axes vertical machine. The cutting tool used was a GARANT flatend mill, 8 mm of diameter, with 2 cutting edges installed in athermal cone. The workpiece material was aluminium 5083 witha hardness of 70–80 HB. Thirty experiments with spindle speedincreasing from 1000 to 9700 rpm maintaining a constant feed pertooth of 0.02 mm/tooth were planned. The operation consisted ofcutting slots along the Y-axis of the machine tool while increasingthe axial depth of cut, thanks to the inclined plane as shown inFig. 3. No kind of coolant was used.

forced vibration self-excited vibra

maximum cutti

cutting depth (slide travel)

vibr

atio

n am

plitu

de

Fig. 2. Illustration of forced and self

3. Results

3.1. Operator methodology

Maximum Y travel was directly extracted from the machinetool screen when chatter was detected by the operator and themachine tool was stopped. Maximum axial depth of cut can becalculated by applying trigonometric principles since the work-piece inclination is known. The operator had to decide when tostop the machine following his own criterion based on themachining sound. Expert operator can achieve good resultsapplying this methodology as is demonstrated along this work.Fig. 5 shows the workpiece machined.

The 30 slots correspond to 30 experiments carried outfollowing the parameters mentioned above. Results obtainedare given in Table 1. Spindle speed was increased betweenpasses from 1000 to 9700 rpm, starting on the left-hand sideof the figure. Axial depth of cut increased gradually, thanks tothe inclined plane machined previously on the workpiece.Fig. 5 also shows the stability frontier schematically drawnfitting the experimental results in order to differentiate betweenthe stable zone and the unstable zone of the SLD. Looking atFig. 7 it is possible to observe that process damping atlower spindle speeds provides stability. This phenomenon occursdue to the short undulations left on the workpiece surfaceby high-frequency cutting vibrations. Surface waves interfereand rub with the cutting tool flank face damping the cuttervibration.

3.2. Computer application performance

Labview application was used to develop a platform thatpermitted to monitor the metal removal process sound emission.A microphone mounted inside the machine enclosure collectedthe milling sound with a sampling rate of 25 kHz. The soundcollected was printed on-line in the computer screen in a time-based chart. The fast Fourier transform (FFT) was calculatedfrom the time-based audio signal to obtain the frequency-domainspectrum of the milling sound and also printed on-line in thecomputer screen (Figs. 6 and 7). After some initial experimenta-tion chatter frequencies were identified and the differencebetween stable and unstable cut could be recognized. As it is

tion

ng depth

maximum cuttingdepth

workpiece

milling slide

-excited vibration. Source: [33].

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Ω

yx

z

f

95m

m

300mm

200mm

10

0mm

a b

c

f g

d

Fig. 3. Schematic representation of the experimental procedure where axial depth of cut increases with feed. (a, b) Axial depth of cut increases along the operation until

chatter occurs. (c, d) Spindle speed is increased between passes. (f) SLD is physically marked in the workpiece. (g) Workpiece dimensions.

Fig. 4. Schematic representation of the followed procedure.

G. Quintana et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1637–16451640

shown in Fig. 2, the process changes abruptly from a stable stagedominated by forced vibrations to an unstable stage dominated bychatter when a certain depth of cut is exceeded at a certainspindle speed. These principles were used to implement thechatter detector. When the sound of the metal removal operation

exceeded a certain threshold at a certain frequency, the chatterdetector turned to red to inform the operator about the chatteroccurrence. Thanks to the warning alarm, the milling process canbe stopped by the operator and all the negative effects that anunstable cut entails can be avoided.

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G. Quintana et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1637–1645 1641

Data concerning teeth number and spindle speed are intro-duced by operator in the application designed. Tooth period iscalculated by the computer application following the equation

Ft ¼O60� z (1)

Figs. 6 and 7 shows the software main screen appearance,where Fig. 6 represents stable cutting operation. The sample issubjected to a milling operation carried out with a cutting toolwith two cutting teeth at a spindle speed of 4900 rpm. This meansa tooth period of 163.33 Hz, which can be observed in thefrequency-domain plot, where an important peak appears at thetooth passing frequency. This milling operation was chatter-freeand so the chatter detector remained green coloured.

Fig. 7 represents a milling operation carried out with a two-teeth cutting tool and spindle speed of 8200 rpm, which entails atooth passing frequency of 273.33 Hz with chatter. In this case

Spindle Speed increase (rpm)

Axi

al d

epth

of c

ut in

crea

se (m

m)

Fig. 5. SLD marked on the workpiece surface.

Table 1Parameters planned and results obtained

Exp. X (mm) Spindle speed (rpm) Feed

1 10 1000 40

2 20 1300 52

3 30 1600 64

4 40 1900 76

5 50 2200 88

6 60 2500 100

7 70 2800 112

8 80 3100 124

9 90 3400 136

10 100 3700 148

11 110 4000 160

12 120 4300 172

13 130 4600 184

14 140 4900 196

15 150 5200 208

16 160 5500 220

17 170 5800 232

18 180 6100 244

19 190 6400 256

20 200 6700 268

21 210 7000 280

22 220 7300 292

23 230 7600 304

24 240 7900 316

25 250 8200 328

26 260 8500 340

27 270 8800 352

28 280 9100 364

29 290 9400 376

30 300 9700 388

chatter occurrence made the chatter detector to turn red. Chatterfrequency, as is possible to see in the FFT chart, occurred at afrequency of approximately 2100 Hz.

Parameters planned to carry out the tests in areas to designcomputer application and results obtained for those experimentsare given in Table 2.

Fig. 8 shows again the workpiece machined to obtain computerapplication. The 30 slots correspond to the 30 experiments carriedout following the parameters presented in Table 2.

3.3. Validation

A total of 600 experiments were carried out to obtain the SLDwith the same combination of cutting tool, tool holder, machinetool and workpiece material for both cases of experimentalprocess and computer application performance. Spindle speedvaried from 1000 to 9700 rpm with increases of 300 rpm. Axialdepth of cut varied from 0.25 to 5.00 mm with increases of0.25 mm. This makes a total of 30 levels of spindle speed and 20levels of axial depth of cut. Feed per tooth was maintainedconstant as in the experiments carried out with the inclined planemethodology. Linear feed rate was calculated to keep a feed pertooth of 0.02 mm/tooth.

In Fig. 9, the experimental results obtained with the inclinedplane methodology applied by the operator and the computerapplication results are compared with the SLD obtained machin-ing point by point.

It is possible to observe that between 4000 and 5000 rpm thereis no agreement between the SLD obtained with the inclinedplane and the SLD obtained point by point. This inaccuracy may bedue to an incorrect decision made by the operator. In the inclinedplane methodology operator expertise in chatter identificationplays an important role. However, for the rest of the range,verification tests present a quite accurate concordance. Results

(mm/min) Max. Y (mm) Max. depth of cut (mm)

200.000 5.000

200.000 5.000

200.000 5.000

200.000 5.000

200.000 5.000

200.000 5.000

200.000 5.000

200.000 5.000

109.848 2.746

85.081 2.127

108.779 2.719

132.879 3.322

181.691 4.542

94.703 2.368

74.949 1.874

57.208 1.430

192.231 4.806

75.577 1.889

28.966 0.724

52.390 1.310

110.159 2.754

62.119 1.553

86.807 2.170

85.788 2.145

35.340 0.884

60.543 1.514

143.454 3.586

65.916 1.648

49.603 1.240

72.911 1.823

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Fig. 6. Software main screen appearance and performance in a chatter-free milling operation.

Fig. 7. Software main screen appearance and performance in milling operation with chatter.

G. Quintana et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1637–16451642

provided by the computer application are better than the resultsobtained by the operator. In this case, concordance is accuratealong almost the whole spindle speed range. However, it ispossible to observe a certain deviation between 4000 and5000 rpm. Nevertheless, the use of computer application designedin this work permits to reduce the relevance of the operatorexpertise in the reliability of the SLD obtained.

4. Discussion

This methodology is especially appropriate for slotting operations.In cases where tool immersion is o100%, superposition of passes maycause a problem because tool immersion can change near the stabilityfrontier due to the length of the previous pass. The workpiece must bepreviously prepared by cutting sufficiently separated slots into the

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Table 2Parameters planned and results obtained

Exp. X (mm) Spindle speed (rpm) Feed (mm/min) Max. Y (mm) Max. depth of cut (mm)

1 10 1000 40 200,000 5,000

2 20 1300 52 200,000 5,000

3 30 1600 64 200,000 5,000

4 40 1900 76 200,000 5,000

5 50 2200 88 200,000 5,000

6 60 2500 100 200,000 5,000

7 70 2800 112 200,000 5,000

8 80 3100 124 200,000 5,000

9 90 3400 136 108,522 2,713

10 100 3700 148 82,356 2,059

11 110 4000 160 83,220 2,081

12 120 4300 172 76,523 1,913

13 130 4600 184 70,331 1,758

14 140 4900 196 85,923 2,148

15 150 5200 208 72,129 1,803

16 160 5500 220 53,263 1,332

17 170 5800 232 188,789 4,720

18 180 6100 244 72,125 1,803

19 190 6400 256 19,236 0,481

20 200 6700 268 51,850 1,296

21 210 7000 280 114,234 2,856

22 220 7300 292 59,859 1,496

23 230 7600 304 85,998 2,150

24 240 7900 316 89,128 2,228

25 250 8200 328 20,324 0,508

26 260 8500 340 56,856 1,421

27 270 8800 352 147,524 3,688

28 280 9100 364 64,152 1,604

29 290 9400 376 46,235 1,156

30 300 9700 388 75,805 1,895

Stability Lobes Diagram

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

1000

1600

2200

2800

3400

4000

4600

5200

5800

6400

7000

7600

8200

8800

9400

Spindle Speed (rpm)

Axi

al d

epth

of c

ut (m

m)

Fig. 8. SLD marked in the workpiece surface.

G. Quintana et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1637–1645 1643

workpiece. This permits the cutting tool to be introduced into the slotwith the required immersion in one of its walls.

The accuracy of the methodology and the workpiece size areinevitably related. Bigger workpieces permit to perform morepasses reducing the spindle speed, increases between passes, and

this reduces the lack of information between slots. Therefore,given a certain workpiece shape, the accuracy of the methoddecreases for big tool diameters, because the number of passeshas to be reduced to perform the methodology within a certainspindle speed range.

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Stability Lobes Diagram

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Spindle Speed (rpm)

Axi

al D

epth

of c

ut (m

m)

Stable cutting ChatterOperator identification Computer aplication identificacion

Fig. 9. Validation of the methodologies performance.

G. Quintana et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1637–16451644

When the machine tool or tool to be analyzed works within arange of spindle speeds, then the number of passes using thismethod can be reduced by planning all the passes within this range.

This method can be extrapolated to any combination of millingmachine tool, cutting tool, tool holder and workpiece materials.However, the procedure needs to be repeated for each new materialor cutting tool. This also occurs in the case of experimental modalanalyses such as the impact hammer test.

Expertise of the operator in chatter detection is a major factorin the precision of the SLD obtained in the first method proposed.Nevertheless, this has been improved in the second part, wherechatter automatically is detected with the computer applicationimplemented.

5. Conclusions

Machine tool operators often select conservative cutting para-meters to avoid the occurrence of chatter. This can negatively affectthe production system decreasing the productivity and the perfor-mance of a company. Stability lobe diagrams (SLD) show theboundary between chatter-free machining operations and unstableprocesses in terms of axial depth of cut as a function of spindle speed.

The simple experimental method for SLD identification proposedin this paper provides a practical technique for optimal processplanning of depth of cuts and spindle speeds in milling operations.The method allows us to obtain the boundary between stable andunstable processes physically captured on the workpiece.

An additional advantage of the method proposed in this workis that SLD can be identified using a microphone, preparedinclined workpiece and labview programme. The methodologywas developed to help those small- and medium-sized enterprisesfor which it is difficult to acquire specific equipment such asimpact hammers, piezoelectric transducers, specific software,sensors for chatter detection.

Acknowledgements

The authors acknowledge the generous support given bythe workshop staff of our Product, Process and Production

Engineering Research Group (GREP) and the interest shown bythe ASCAMM Technology Centre. We greatly appreciatetheir attention, responsibility and dedication. The authors alsoacknowledge the great advices and guidance given by ProfessorLuis Norberto Lopez de Lacalle and Francisco Campa from theUniversity of the Basque Country, Bilbao.

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