Drilling Forces

8/3/2019 Drilling Forces

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MethodologyforDataProcessing:CalculationofCutting

Force,MomentandPeak-to-ValleyduringDrillingProcesses

M.Tash1,2,F.H.Samuel

1,F.Mucciardi

3,H.W.Doty,

4

S.Valtierra5

1UniversitduQubecaChicoutimi,Chicoutimi,Qubec,Canada

2CairoUniversity,Giza,Egypt

3McGillUniversity,Montreal,Qubec,Canada

4GeneralMotorsPowertrainGroup,MetalCastingTechnology,Inc.,Milford,NH,

USA5CorporativoNemak,S.A.deC.V.,ResearchandDevelopment,

P.O.Box100,BosquesdelValle

GarzaGarcia,N.L.66221,Mexico

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ABSTRACT

HeattreatedAl-Si-MgandAl-Si-Cu-Mgcastalloys,belongingtotheAl-Sialloy

systemandrepresentedrespectivelyby356(M1)and319(M2,M3,M4andM5)alloys

containingmainly-Fe-intermetallicandrelatedtohardnesslevelsof(10010HB),were

selected for the machinability study, due to the high demand of these alloys in the

automobileindustryInthispaper,onewasprovidedwithanintroductiontotheforceand

momentcalculationsthatwereusedtoevaluatethedrillingprocessesasareoutlinedina

previouswork.1

Anewtechniquewasdevelopedwherebyalowpassfilterwasincorporatedinthe

signalprocessingalgorithmwhichwas used incalculatingthemeancutting forceand

moment during the drilling processes. All signals were independently monitored,

digitizedandrecordedintoLabView.UniversalKistlerDynoWaresoftwarewasusedfor

forcemeasurementsanddataprocessingofcuttingforceandmoments.Matlabprograms

weredevelopedfordataprocessingandforcalculatingthemeanvalueofcuttingforce

andmomentandtheirstandarddeviationsindrillingtests.

Therawcuttingforcedatawereanalysedusingtheapplicationofalowpassfilter

andfollowingthedetectionofpointswithineachcycleinthesignalinthedrillingtests.

1600samplepointspercyclewereacquiredforcalculatingthemeanvalueofcuttingfeed

force(Fz)and1200samplepointspercyclefor theotherfivecomponentsofforceand

moment(Fx, Fy,Mx,My, andMz)in each signal(115 cycleor hole/signal) however,



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only 200 sample points per cyclewere used for standard deviation or peak-to-valley

calculations.

1 INTRODUCTION

Inthispaper is presented an introduction to theforceandmomentcalculations

whichareusedasaway of evaluatingdifferent kindsofmachiningprocesses suchas

drilling.Anewtechniquewasdevelopedwherebya lowpass filterwas incorporatedin

thesignalprocessingalgorithmwhichwasusedincalculatingthemeancuttingforceand

moment during the drilling processes. Evaluating machinability based on the cutting

forces requires adequate piezoelectric sensor technology. The piezoelectric force

measuringsystemdiffersconsiderablyfromothermethodsofmeasurement.Theforces

actingonthequartzcrystalelementareconvertedtoaproportionalelectriccharge.The

chargeamplifierconvertsthischargeintostandardizedvoltageandcurrentsignals,which

canthenbeevaluatedbysignalprocessing.

A Kistler 6-component piezoelectric quartz crystal dynamometer (type 9255B)

wasusedfor6-componentforceandmoment(Fx,Fy,Fz,Mx,MyandMz)measurement

during drilling tests.AKistlermulti-channel charge amplifier type (5017B18) with8

independentmeasuringchannelswasusedincombinedforceandmomentmeasurement

using piezoelectricmulti-componentdynamometers.The eight output signalswere fed

directly to the eight charge amplifiers by the eight-core connecting cable type

1677A5/1679A5.Allsignalswereindependentlymonitored,digitizedandrecordedinto

Lab View where DynoWare software was used for force measurements and data

processingofcuttingforcesandmoments.TheMatlaboutputresultsforallcomponents

offorceandmomentandtheirstandarddeviationsindrillingtestswereputintoanExcel



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data sheet and followed by calculations to arrive at the total meancutting force and

moment,andtheirstandarddeviationsaswellasthepeak-to-valleyrange.

2. EXPERIMENTALPROCEDURES

Drilling experiments were performed on a Makino A88E machine at fixed

machiningconditionstostudy themachiningperformanceoftheSr-modifiedand-Fe

intermetallic-containing356and319alloys.ChemicalemulsionconcentrateVHPE210

(5% cutting fluid +95% liquid)was applied to avoid the effectsof the heatgenerated

during machining. Machinability test sample after 230 holes were drilled (first and

secondgroupofholes),drillandtapgeometryareshowninFigure1.CarbideGdrills

of6.5mmdiam.andwithminimum30mm length,straight fluteandcoolant fedwere

usedtodrilltworowsofthrough-holesineachribofthewaffleplatewith4mmbetween

rows.OptimumdrillingconditionsarelistedinTable2.

Drillingwascarriedoutathighspeedmachiningforallmetallurgicalconditions

(M1-M5) and all the data was recorded on to Lab View software. Each alloy/heat

treatmentconditionwastestedwiththesamedrill.Whenthedrillwasbrokenduringthe

drilling,twooptionswerefollowed:1)drillingwasstoppedthenthetestwaschangedfor

anotherconditionorseries,2)inthecasethedrillwasbrokenduetothepresenceofa

defectoralargeinclusion,thetestwasresumedwithanewdrillonthesameblock.



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3. RESULTSANDDISCUSSIONS

3.1.DRILLINGDATAPROCESSING:Methodology

Drillingwascarriedoutathighspeedmachining,all datawas recorded inLab

View softwarewith sampling rate of 1000 Hz. Matlab programswere developed for

processingthedrillingdataforallmetallurgicalconditions(M1toM5).Asanexampleof

data processing, the data after drilling of the 356 (M1 aged at 180C/2h.) alloy

machinabilitytestsamplenumber8arepresentedinthispapertoshowthemethodology

for the first group of holes (115 holes). The complete programs can be found in the

Appendix2. The datawere first separated according to each component of force and

moment followed by an applicationof signalprocessing procedure forcalculating the

meanvalueofforceandmoment, standarddeviationsand theircorrespondingpeak-to-

valleyrange.

There are two types of drift; normaldrift and contaminationdrift. The normal

driftwas0.03pC/sec(pC=picocoulomb=110-12coulomb)andforeachcycleperiod

(340seconds)thetotaldriftwas10.2pC.ThesensitivityforFx,FyandFzchannelswas

7.87, 7.87 and 3.87 pico coulombs/mechanical unit (pC/N), respectively. So for each

cyclewhichconsistedof115holesindrilling,thenormaldriftinFx,Fy,andFzwere1.3

N, 1.3N and 2.64 N respectively.3

From the signal results, it was observed that the

contaminationdriftwasmoresignificant.Thisdriftcamefromoxidationandthecoolant

and also from the finger impressions during handling. In addition, the long periodof



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acquisition can also amplify such kinds of drift. Contamination error was treated in

Matlabprograms.

Matlabgraphsrepresentingthestepsofdataprocessingforthedrillingforceand

momentaredisplayedinFigure2toFigure5.Allcomponentsofforceandmomentare

displayedinFigure2(a).Drillingfeedforce(Fzcomponent)wasseparatedand itsdata

wasanalysedandprocessed.TheFzcomponentsignalwasfilteredninetimesbyusinga

lowpassfilter(Filter(b,1,Fz),b=[11];b=b/sum)andasmoothsignalwasproduced,

see Figure 3(a). Slow changes were removed after taking the first difference for the

filteredsignal,Figure3(b).Again,theseconddifferencewastakenforthefilteredsignal

todetectonepointwithineachcycleofthesignal,Figure4(a).

Twopointsweredeterminedwithineachcyclerelativetothedetectedpoint(i.e.

theseconddifferencepositivepeakposition inthebluedottedsignal,Figure4(a)).The

first one (square point) represents the mean cutting feed force (Fzup) without error

treatment and the second (triangle point) represents the error (Fzdown), see legend in

Figure4(b).1600samplepointspercyclewereacquiredforcalculatingthemeanvalue

ofthecuttingfeedforce(800datapointsleftand800datapointsrightfromthesquared

point) and 1200 sample points per cycle for the other five components of force and

moment(Fxup,Fyup,Mxup,Myup,andMzup)ineachsignal(600datapointsleftand600

datapointsrightfromthesamepoint)however,only200samplepointspercyclewere

used for standarddeviationorpeak-to-valleycalculations(100datapoints left and100

datapointsrightfromthecircledpoint).



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3.1.1. TotalDrillingForce,MomentandPeak-to-ValleycalculationsandResults

Outputofresults forall componentsofdrilling forceandmomentwith (Fx,Fy,

Fz, Mx, My, and Mz) and without (Fxup, Fyup, Fzup, Mxup, Myup, and Mzup) error

treatmentforthefirstgroupofholesaredisplayedinFigure5.Theerrorwastakeninto

considerationandwasincorporatedintotheMatlabdrillingprogramasthefollowingset

ofequations;1)Fx=Fxup-Fxdown,2)Fy=Fyup-Fydown,3)Fz=Fzup-Fzdown,4)Mx=Mxup-

Mxdown,5)My=Myup-Mydown,and6)Mz=Mzup-Mzdown.

Afterobtainingeachcomponentofthemeancuttingforceandmomentasshown

inFigure5,thetotalmeancuttingforceandmoment,theirstandarddeviationsaswellas

thepeak-to-valley range indrillingwascalculated.Drillingresultsforallmetallurgical

conditions (M1toM5~60machinability testsampleseach230holes)aredisplayed in

Figure6.

These results were computed from the following set of equations. Standard

deviationcalculations for thetotal cuttingforceand total cuttingmomentwere carried

outbythefollowingmethod.4

( ) ( ) ( )( )2/1

2/1222

)(

*/*/*/

zyxf

tttfzzFyyFxxF

++=

++=

Eq.2

And the total cutting force and total cutting moment are calculated by the following

equations;

2/1222

2/1222

)(

)(

zyxt

zyxt

MMMM

FFFF

++=

++=

Eq.3



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Thestandarddeviationforforceandmomentcanbeobtained;

( )

( ) 2/12222/1222222

2/12222/1222222

)/(***

)/(***

zyxzyxfm

zyxzyxff

MMMMzMyMx

FFFFzFyFx

++++=

++++=

4. CONCLUSIONS

In thispaper, an introduction for the forceandmoment calculationswhich are

used to evaluate the different kinds ofmachining processes (i.e.drillingand tapping)

whichareoutlinedinasubsequentpaper.

1. A new technique was developed whereby a low pass filter in signal

processing was used in calculating the meancutting force and moment

duringboththedrillingandtappingprocesses.

2. Allsignalswereindependentlymonitored,digitizedandrecordedintoLab

View. Universal Kistler DynoWare software was used for force

measurementsanddataprocessingofcuttingforceandmoments.

3. Matlabprogramsweredeveloped fordataprocessingandforcalculating

themeanvalueofcuttingforceandmomentandtheirstandarddeviation

inbothdrillingandtappingtests. Contaminationdriftwastreatedinthese

programs.



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ACKNOWLEDGEMENT

FinancialsupportfromtheNaturalSciencesandEngineeringResearchCouncilof

Canada (NSERC), General Motors Powertrain Group and Corporativo Nemak is

gratefullyacknowledged.



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ListofTableCaptions

Table1 Chemicalcompositionsfor356and319alloysusedinthemachinabilitywork:a)M1-356alloy,b)M2-to-M5-319alloys.

Table2 Optimumdrillingconditions



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Table1 Chemicalcompositionsfor356and319alloysusedinthemachinabilitywork:a)M1-356alloy,b)M2-to-M5-319alloys.

Element(wt%)AlloyCode

Si Fe Mn Mg Cu Ti Sr Mn/Fe Al

356alloy-M1 6.85 0.44 0.3 0.34 0.05 0.15 0.0218 0.69 91.7

319alloys-M2 6.2 0.4 0.295 0.1 3.405 0.15 0.0234 0.73 89.3

M3 6.2 0.97 0.396 0.10 3.41 0.14 0.0236 0.405 88.6

M4 6.25 0.42 0.3 0.29 3.5 0.15 0.0133 0.725 88.7

M5 6.3 1.02 0.39 0.29 3.4 0.15 0.026 0.38 88.3

Table2 Optimumdrillingconditions

Parameters Drilling

Speed 234.458m/minor11000rpm.

DrillDia. CarbideGdrills6.5mm

Depth 31.75mm

FeedRate 44IPM(0.1016mm/rev)

Lubricant/Coolant ChemicalemulsionconcentrateVHPE210(5%cuttingfluid+95%liquid)



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ListofFigureCaptions

Figure1 Machinability test Sample, Drill and tap geometry, a) Machinability testsample after drilling 230 holes and b) Carbide G (RT 150) drill (O.A.L=

103mm,F.L=28mmanddrilldia=6.5mm)

Figure2 Dataprocessingfordrillingforceandmomentofthefirstgroupofholes(115-

holes)a)originalsixcomponentofforceandmomentb)Fzcomponent.Figure3 Data processing for drilling feed force-Fz component of the first groupof

holes(115-holes)forFzcomponenta) filtration (9-times)b)pointdetectionwithineachcycle-firstdifferenceofthefilteredFz.

Figure4 Data processing for drilling feed force-Fz component of the first groupofholes(115-holes) and pointdetectionwithin each cycle a) firstand second

difference of the filtered Fz and b) points within each cycle one representmeanFzwithouterrorconsiderationandanotherrepresenttheerrorvalue.

Figure5 Outputresultsfordrillingforceandmomentofthefirstgroupofholes(115-holes)-plotswithandwithouterrortreatmenta)Fz,b)Fx,c)Fy,d)Mz,e)

Mxandf)My.

Figure6 Meantotaldrillingcuttingforceandmomentforallmetallurgicalconditionsof Sr-modified 356 and 319 alloys containing mainly -Fe- intermetallicscorrespondingtoalloycodesM1(356alloy)andM3andM5(319alloys)(a)

mean total drilling force of 230 holes (one block) (b) mean total drillingmomentof230holes(oneblock).



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(a)

(b)

Figure1 MachinabilitytestSample,Drill andtapgeometry,a)Machinabilitytestsampleafterdrilling230 holesand b)CarbideG(RT150)drill (O.A.L=103mm,F.L=28mmand

drilldia=6.5mm).

Feed

Firstgroupofholes(115-holes)

Secondgroupof

holes(115-holes)



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0 0 .5 1 1 .5 2 2 .5 3 3 .5

x1 05

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

DrillingForce(N)andMoment(N

.m)

F xF yF zM xM yM z

T im e (m s e c )

(a)

0 0 .5 1 1 .5 2 2 .5 3 3 .5

x1 05

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

T im e (m s e c )

DrillingForce(N)

F z

(b)

Figure2 Dataprocessingfordrillingforceandmomentofthefirstgroupofholes(115-holes)a)originalsixcomponentofforceandmomentb)Fzcomponent.



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9 .3 9 .4 9 .5 9 .6 9 .7 9 .8 9 . 9 1 0 1 0 .1 1 0 .2 1 0 . 3

x1 04

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

T im e (m s e c )

DrillingForce(N)

F zm F z

(a)

3 9 6 3 9 8 4 0 0 4 0 2 4 0 4 4 0 6 4 0 8 4 1 0 4 1 2 4 1 4 4 1 6- 6 0 0

- 4 0 0

- 2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

T im e (m s e c )/N o o f filt e r in g

DrillingForce(N)

m F zd iffm F z

(b)

Figure3 Dataprocessingfordrillingfeedforce-Fzcomponentofthefirstgroupofholes(115-holes)forFzcomponenta)filtration(9-times)b)pointdetectionwithineachcycle-first

differenceofthefilteredFz.



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9 4 9 6 9 8 1 0 0 1 0 2 1 0 4 1 0 6 1 0 8 1 1 0 1 1 2-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

T im e (m s e c )/N o o ff ilt e r in g

DrillingForce(N)

m F zd iffm F zd iff(d iffm F z)

(a)

9 .3 9 .4 9 .5 9 .6 9 . 7 9 .8 9 . 9 1 0 1 0 .1 1 0 .2

x 1 04

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

T im e ( m s e c )

DrillingFor

ce(N)

F zm F z u pm F z d o w n

(b)

Figure4 Dataprocessingfordrillingfeedforce-Fzcomponentofthefirstgroupofholes(115-holes)andpointdetectionwithineachcyclea)firstandseconddifferenceofthefiltered

Fzandb)pointswithineachcycleonerepresentmeanFzwithouterrorconsiderationandanotherrepresenttheerrorvalue.



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0 0 .5 1 1 .5 2 2 .5 3 3 .5

x1 05

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

T im e (m s e c )

DrillingForce(N)

F zm F z u pm F z d o w nm F z

(a)

0 0 .5 1 1 .5 2 2 .5 3 3 .5

x1 05

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

T im e (m s e c )

DrillingForce(N)

F xm F xm F xu pm F x d o w n

(b)

Figure5 Output results fordrilling forceandmoment of the first groupofholes (115-holes)-

plotswithandwithouterrortreatmenta)Fz,b)Fx,c)Fy,d)Mz,e)Mxandf)My.



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0 0 .5 1 1 .5 2 2 .5 3 3 .5x1 0

5

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

T im e ( m s e c )

DrillingForce(N)

F ym F ym F y u pm F y d o w n

(c)

0 0 .5 1 1 .5 2 2 .5 3 3 .5

x1 05

- 8 0

- 6 0

- 4 0

- 2 0

0

2 0

4 0

6 0

8 0

1 0 0

T im e (m s e c )

DrillingMome

nt(N.m

)

M zm M zm M z u pm M zd o w n

(d)

Figure5 Output results fordrilling forceandmoment of the first groupofholes (115-holes)-plotswithandwithouterrortreatmenta)Fz,b)Fx,c)Fy,d)Mz,e)Mxandf)My.



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0 0 .5 1 1 .5 2 2 .5 3 3 .5x1 0

5

- 8 0

- 6 0

- 4 0

- 2 0

0

2 0

4 0

6 0

8 0

1 0 0

T im e (m s e c )

DrillingMoment(N.m

)

M xm M xm M x u pm M xd o w n

(e)

0 0 . 5 1 1 .5 2 2 .5 3 3 .5

x 1 05

- 8 0

- 6 0

- 4 0

- 2 0

0

2 0

4 0

6 0

8 0

1 0 0

DrillingMoment(N.m)

M ym M ym M yu pm M y d o w n

T im e (m s e c )

(f)

Figure5 Output results fordrilling forceandmoment of the first groupofholes (115-holes)-plotswithandwithouterrortreatmenta)Fz,b)Fx,c)Fy,d)Mz,e)Mxandf)My.



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0

100

200

300

400

500

600

700

800

900

1000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

NoofHoles(BlockNo.)

TotalDrillingForce(N

)

319-M2-0.1%Mg319-M3-0.1%Mg319-M5-0.28%Mg356-M1-0.3%Mg

(1):Polynomial-R2=0.99




(1),(2)and(3)=100HB

(4)=90HB(1)

(2) (3)

(4)

(a)

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

NoofHoles(BlockNo.)

TotalDrillingM

oment(N.m

)

319-M2-0.1%Mg319-M3-0.1%Mg319-M5-0.28%Mg356-M1-0.3%Mg





(1),(2)and(3)=100HB

(4)=90HB

(1) (2) (3)

(4)

(b)

Figure6 Mean total drilling cutting force andmoment for all metallurgicalconditions of Sr-modified356and319alloyscontainingmainly-Fe- intermetallicscorrespondingto

alloycodesM1(356alloy)andM3andM5(319alloys)(a)meantotaldrillingforceof230holes(oneblock)(b)meantotaldrillingmomentof230holes(oneblock).



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ListofSymbols

Fx1+2andFx3+4 Cuttingforcescomingfromsensor1,2,3and4inx-direction

Fy1+4andFy2+3 Cuttingforcescomingfromsensor1,2,3and4iny-direction

Fz1,Fz2,Fz3andFz4 Cuttingforcescomingfromsensor1,2,3and4inz-direction

nlevel, Numberoffilteration=9

Diffk 1stdifferenceforfilterdFz(k)

Difffk 2eddifferenceforfilterdFz(k)

nmin Miniumumnumberofpointsinfilteredsignalpercycle=5

ind,indd,tt,tt1,n,m,z,

N,M,Z,time1,time2,time3,timeupand

timedown,

Matlabvariablesindrilling

min,max,mean,

std,buffer,ones,length,filter,findandzeros

MatlabFunctions

mFx,mFyandmFz Meancuttingforcecalculatedwithincuttingperiodineachcycleduringthedrilling(witherrortreatment)

mMx,mMyandmMz Meancuttingmomentcalculatedwithincuttingperiodineach

cycleduringthedrilling(witherrortreatment)

mFxup,mFyupand

mFzup

Meancuttingforcecalculatedwithincuttingperiodineach

cycleduringthedrilling(withouterrortreatment)

mMxup,mMyupand

mMzup

Meancuttingmomentcalculatedwithincuttingperiodineach

cycleduringthedrilling(withouterrortreatment)mFxdown,mFydownand

mFzdown

Meancuttingforcecalculatedwithinnon-cuttingperiodineach

cycleduringthedrilling(representerror)

mMxdown,mMydownandmMzdown

Meancuttingmomentcalculatedwithinnon-cuttingperiodineachcycleduringthedrilling(representerror)

sFx,sFyandsFz

,smMx,smMyandsmMz

Standarddeviationforforceandmomentcalculatedwithin

cuttingperiodineachcycleduringthedrilling

f,andf Standarddeviationandcombinedfunctions(forceormoment)

x,yandz Standarddeviationcomponents

Ft Totalcuttingforceindrilling

Mt TotalcuttingmomentindrillingFt/x,Ft/yandFt/z Partialderivationoftotalcuttingforcerespecttox,yandz

Mt/x,Mt/yand

Mt/z

Partialderivationoftotalcuttingmomentrespecttox,yandz

ff Standarddeviationforcombinedfunction(totalforce)

fm Standarddeviationforcombinedfunction(totalmoment)

x,yandz Standarddeviationforforceormomentcomponents(x,yandz)



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Appendix:1)DrillingMatlabProgramcloseall;clearall,clc[fi,ch]=uigetfile('C:\machinabilityCTA\M2-drilling\*.*','Ouvrir...');

ifch==0return

end;Threshold=100;

nom=[chfi];k=load(nom);

k1=k(3,:);figure(14);plot(k1);gridon

title('originalplot(Fz=k)')xlabel('time(msec)')

ylabel('Fz(N)')b=[11];b=b/sum(b);

k2=k1;nlevel=9;

fori=1:nlevelk1=filter(b,1,k1);

k1=k1(1:2:end);end

t1=1:length(k);t2=t1(1:2^nlevel:end);

figure(15);plot(t1,k2,'b',t2-0*2^nlevel,k1,'r');gridontitle('methodofdetectionstep(1);filtering')

xlabel('time(msec)')ylabel('FzandmFz(N)')

diffk=diff(k1);figure(16),plot(1:length(k1),k1,1:length(k1)-1,diffk),gridon

title('step(2),difference(diffmFz)andcomparison')xlabel('time(msec)/Nooffiltering')

ylabel('mFzanddiffmFz(N)')diffk(diffk0)=350;difffk=diff(diffk);

figure(17);plot(1:length(k1),k1,1:length(diffk),diffk,1:length(difffk),difffk),gridontitle('step(3)diffecnce(diff(diffmFz),comparisonanddetection')

xlabel('time(msec)/Nooffiltering')ylabel('mFz,diffmFz,anddiff(diffmFz)(N)')

ind=find(difffk==350);ind=ind(1:end-1);

%numberofelementsofdiff(ind)=numberofelementsof(ind)-1min(diff(ind))

max(diff(ind))nmin=5;



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indd=zeros(1,length(ind)*nmin);fori=1:nmin

indd(i:nmin:end)=ind+i-1;end

tt=k1(indd);

tt1=buffer(tt,nmin);[mfzupjj1]=max(tt1);[mfzdownjj2]=min(tt1);

timeup=(ind+jj1+3)*2^9;timedown=(ind+jj2-2.375)*2^9;

NN=1200;MM=10;

ZZ=200;n=((0:NN)-NN/2)';

m=((0:MM)-MM/2)';z=((0:ZZ)-ZZ/2)';

N=length(timeup);M=length(timedown);

time1=ones(NN+1,1)*timeup+n*ones(1,N);time2=ones(MM+1,1)*timedown+m*ones(1,M);

time3=ones(ZZ+1,1)*timeup+z*ones(1,N);mfxup=mean(buffer(k(1,time1),1201));

smfx=std(buffer(k(1,time3),201));mfyup=mean(buffer(k(2,time1),1201));

smfy=std(buffer(k(2,time3),201));smfz=std(buffer(k(3,time3),201));

mMxup=mean(buffer(k(4,time1),1201));smMx=std(buffer(k(4,time3),201));

mMyup=mean(buffer(k(5,time1),1201));smMy=std(buffer(k(5,time3),201));

mMzup=mean(buffer(k(6,time1),1201));smMz=std(buffer(k(6,time3),201));

mfxdown=mean(buffer(k(1,time2),11));mfydown=mean(buffer(k(2,time2),11));

mMxdown=mean(buffer(k(4,time2),11));mMydown=mean(buffer(k(5,time2),11));

mMzdown=mean(buffer(k(6,time2),11));mfx=(mfxup-mfxdown);

mfy=(mfyup-mfydown);mfz=(mfzup-mfzdown);

mMx=(mMxup-mMxdown);mMy=(mMyup-mMydown);

mMz=(mMzup-mMzdown);

results=[timeup;mfx;smfx;mfy;smfy;mfz;smfz;mMx;smMx;mMy;smMy;mMz;smMz];txt1=['%4.4f'char(9)'%4.4f'char(9)'%4.4f',...



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char(9)'%4.4f'char(9)'%4.4f'char(9),...'%4.4f'char(9)'%4.4f'char(9)'%4.4f'char(9),...

'%4.4f'char(9)'%4.4f'char(9)'%4.4f'char(9),...'%4.4f'char(9)'%4.4f'char(13)char(10)];

fid=fopen([fi'.xls'],'w');

txt2=['timeup'char(9)'mfx'char(9)'smfx',...char(9)'mfy'char(9)'smfy'char(9),...'mfz'char(9)'smfz'char(9)'mMx'char(9),...

'smMx'char(9)'mMy'char(9)'smMy'char(9),...'mMz'char(9)'smMz'char(13)char(10)];

fwrite(fid,txt2,'char');

fprintf(fid,txt1,results(:));fcloseall;figure;plot(t1,k(1,:),'b',timeup,mfx,'.-m',timeup,mfxup,'.-r',timedown,mfxdown,'.-y'),grid

onxlabel('Time(msec)')

ylabel('DrillingForce(N)')figure;plot(t1,k(2,:),'b',timeup,mfy,'.-m',timeup,mfyup,'.-r',timedown,mfydown,'.-y'),grid


ylabel('DrillingForce(N)')figure;plot(t1,k(3,:),'b',timeup,mfz,'.-m',timeup,mfzup,'.-r',timedown,mfzdown,'.-y'),grid


ylabel('DrillingForce(N)')figure;plot(t1,k(3,:),'b',timeup,mfzup,'.-r',timedown,mfzdown,'.-y',timeup,mfz,'.-m'),grid


ylabel('DrillingForce(N)')figure;plot(t1,k(4,:),'b',timeup,mMx,'.-m',timeup,mMxup,'.-r',timedown,mMxdown,'.-

y'),gridonxlabel('Time(msec)')

ylabel('DrillingMoment(N.m)')figure;plot(t1,k(5,:),'b',timeup,mMy,'.-m',timeup,mMyup,'.-r',timedown,mMydown,'.-


ylabel('DrillingMoment(N.m)')figure;plot(t1,k(6,:),'b',timeup,mMz,'.-m',timeup,mMzup,'.-r',timedown,mMzdown,'.-


ylabel('DrillingMoment(N.m)')figure;plot(mfx);

xlabel('Noofholes')ylabel('DrillingForce(N)')

figure;plot(mfy)xlabel('Noofholes')



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ylabel('DrillingForce(N)')figure;plot(mfz)

xlabel('Noofholes')ylabel('DrillingForce(N)')

figure;plot(mMx);

xlabel('Noofholes')ylabel('DrillingMoment(N.m)')figure;plot(mMy);

xlabel('Noofholes')ylabel('DrillingMoment(N.m)')

figure;plot(mMz);xlabel('Noofholes')

ylabel('DrillingMoment(N.m)')



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5. REFERENCES

1 M.Tash,F.H. Samuel, F.MucciardiandH.W.Doty, EffectofMetallurgicalParameters on the Machinability of Heat-Treated 356 and 319 Aluminum

Alloys, Prepared for submission to the Materials Science and Engineering,

2005.

2 http://www.mathworks.com/

3 http://www.kistler.com/

4 J.R.Taylor,An Introduction toErrorAnalysis: TheStudy ofUncertainties in

Physical Measurements, University Science Books, Mill Valley, California,1982.

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Drilling Forces

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