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二〇一四年三月十五日

Measurement40（2007）791–796

Continuousweighingonamulti-stageconveyorbeltwithFIRfilter

RyosukeTasaki,TakanoriYamazaki,HideoOhnishi,MasaakiKobayashi,ShigeruKurosu

DepartmentofMechanicalEngineering,KyotoInstituteofTechnology,Japan

DepartmentofMechanicalEngineering,OyamaNationalCollegeofTechnology,771Nakakuki,Oyama323-0806,Japan

DepartmentofEngineering,ShinkoCo.,Ltd.,4219-71Takasai,Shimotsuma304-0031,Japan

ResearchInstitute,Crotech,Japan

Received13January2006;

receivedinrevisedform23March2006;

accepted11May2006Availableonline2June2006

Abstract

Todayhigherspeedofoperationandhighlyaccurateweighingofpackagesduringcrossingaconveyorbelthasbeengettingmoreimportantinthefoodanddistributionindustriesetc.Continuousweighingmeansthatmassesofdiscretepackagesonaconveyorbeltareautomaticallydeterminedinsequence.Makingtheproperuseofnewweighingscalecalledamulti-stageconveyorbeltscalewhichcanbecreatedsoastoadjusttheconveyorbeltlengthtotheproductlength,weproposeasimplifiedandeffectivemassestimationalgorithmunderpracticalvibrationmodes.Conveyorbeltscalesusuallyhavemaximumcapacitiesoflessthan80kgand140cm,andachievemeasuringratesof150packagesperminuteandmore.Theoutputsignalsfromtheconveyorbeltscalesarealwayscontaminatedwithnoisesduetovibrationsoftheconveyorbeltandtheproductinmotion.Inthispaperdigitalfilteroffinite-durationimpulseresponse（FEB）typeisdesignedtoprovideadequateaccuracy.Theexperimentalresultsonconveyorbeltscalessuggestthatthefilteringalgorithmproposedhereiseffectiveenoughtopracticalapplications.Aslongasspacesbetweensuccessiveproductsaresetwithinaspecifiedrange,theproductscanbeweighedcorrectlyevenifproductshavingdifferentlengthsaretransportedinrandommanner.

Keywords:

Massmeasurement;

Continuousweighing;

Conveyorbelt;

FIRfilter

*Correspondingauthor.Tel.:

+81285202212;

fax:

+81285202884.

E-mailaddresses:

yama@oyama-ct.ac.jp（T.Yamazaki）,oonishi@vibra.co.jp（H.Ohnishi）,mkobayas@vibra.co.jp（M.Kobayashi）,kurosu_shi@yahoo.co.jp（S.Kurosu）.

1Tel.:

+81296432001;

+81296432130.

2Tel./fax:

+81296284476.

0263-2241/$-seefrontmatter©

2006PublishedbyElsevierLtd.

doi:

10.1016/j.measurement.2006.05.010

1.Introduction

Conveyorbeltscalesamongthesearemostimportantfortheproductionofagreatvarietyofprepackagedproducts[1].Whenaproductisputonaconveyorbelt,ameasuredsignalfromtheconveyorbeltscaleisalwayscontaminatedbynoises.Sincethemeasuredsignalisusuallyinthelowerfrequencyrange,afilterwhichwilleffectivelycutdownnoisesatthehigh-frequencyendcanbeeasilydesigned.If,however,theproduct（likeacardboardboxandaparceletc.）hasalowfrequencycomponent,wherethenoiseintensityishigh,itispracticallyimpossibletoseparatethemeasuredsignalfromnoise.Therestillexistrealproblemsforwhichengineeringdevelopmentinnoise-filteringisneeded.

Therecenttechniquesofdynamicmassmeasurementhavebeeninvestigatedtofindawaytoobtainmassoftheproductunderdynamicconditions.Thekeyideaofdynamicmeasurementisthatwetakeintoconsiderationthevariousdynamicfactorsthataffectthemeasuredsignalintheinstrumenttoderiveanestimationalgorithm[2].Ono[3]proposed

amethodthatdeterminesmassofdynamicmeasurementusingdynamicquantitiesofthesensingelementactuatedbygravitationalforce.Also,Lee[4]proposedthealgorithmofrecursiveleastsquaresregressionforthemeasuringsystemsimulatedasadynamicmodeltoobtainthemassbeingweighed.Successfuldynamicmassmeasurementdependsmainlyonamathematicalmodeltoachieveaccuratemeasurement.Buteventhesimplestructureofaconveyorbeltscalemakesitdifficulttoobtaintheexactmodel.

Ontheotherhand,somefilteringtechniqueshavebeenappliedtoasignalprocessingfortheconveyorbeltscale[5].Inordertoreducetheinfluenceofdynamicsandtoimprovetheaccuracyofmassmeasurementwithoutlosingthequickness,wehaveproposedasimplifiedandeffectivealgorithmfordataprocessingunderpracticalconveyorbelt’svibrations[6–9].

2.Basicconfiguration

Outlineofconveyorbeltscales

ThefundamentalconfigurationoftheconveyorbeltscalesmayberepresentedschematicallyasshowninFig.1.Theloadreceivingelementisabeltconveyorsupportedbyaloadcellattheedgeoftheframe.ThedetectedsignalbytheloadcellissentintoaFIRdigitalfilterthroughaDCamplifier.Themassoftheproductcanbeestimatedasthemaximumvalueevaluatedfromthesmoothedsignal.

Thesimulationsandtheexperimentsarecarriedoutunderthefollowingconditions:

lengthofproduct:

li=20–140cm

lengthofthebeltconveyor:

Lj（L1=40cm,L2=40cm,L3=60cm）

massoftheproduct:

mi=20–80kg

distancebetweenproducts:

di=20–100cm

conveyorbeltspeed:

v=132m/

minrequiredaccuracy:

≤±

0.7%sampling

frequency:

fs=2000Hz（samplingperiod:

Ts=0.5ms）

Thetotallengthofthemulti-stageconveyorisconsideredinthefollowingpatterns:

L=L3（=60cm）:

forthesingle-stageconveyorbeltscale,

L=L1+L2（=80cm）:

forthetwo-stageconveyorbeltscalel,

L=L2+L3（=100cm）:

forthetwo-stageconveyorbeltscale2,

L=L1+L2+L3（=140cm）:

forthethree-stageconveyorbeltscale.

2.2.Minimumdistancebetweenproducts

Theminimumdistancebetweenproductsmustbeexaminedcorrectlybythegeometricalconditions.Incaseofathree-stageconveyorbeltscale,lettheminimumtravellingdistancewhichisnecessaryforreachingthesteadystatevalueofanoutputsignalbeSandtheminimumdistancewhichisshorter,di-1ordi,bedS.Thehypotheticaltimechangesof

aloadinginputcanbeshowninFig.2undertheconditionthatdS<

L-li.Whentheproductmiistransportedontotheconveyorbeltscale,theminimumtravellingdistanceSisnecessaryformeasuringthemassofproductsaccurately.AscanbeseenfromFig.2,theminimumdistancedSbetweenproductscanbeexpressedby:

2dS≤L-li+S（ds=min（di-1,di））

（1）

ByapplyingactualvaluesoftheproductlengthliandtheminimumdistanceS（=20cm）toInequality

（1）,theminimumdistancedSwithrespecttotheproductlengthlicanbeobtaineddiagrammaticallyasshowninFig.3.ItshouldbenotedthatdSissettobenotlessthan40cm.

3.DesignofFIRfilters

Thedesignofdigitalfiltersiswellestablishedandextensivelycoveredintheliterature.Therearetypicallytwokindsofdigitalfilters,i.e.infinite-durationimpulseresponse（IIR）typeandfinite-durationimpulseresponse（FIR）one.Aftertheproductpassesthroughtheconveyorbeltandtheloadinginputchangestozero,thetransientresponseinthefiltershouldbereturnedtotheinitialstatesofast[10—12].Forthisreason,FIRfiltercanbeconsideredtobeadequateforconveyorbeltscales.

Now,weexplaintheprocedurefordesigningtheFIRfilter.WritingthenormalizedfrequencyasΩ=fT,wherefisthefrequency（Hz）,andTisthesamplingperiod（s）,thedesiredtransferfunctioncanbeexpressedby

ThefilterHd（ejΩ）canbeeasilyobtainedbythewell-knownRemezalgorithm.Whentheloweredgefrequency（Ωs）ofthestopbandwidthischosenaslessthan0.05forthedesignofaFIRfilter,itbecomesgenerallyimpossibletodesignsincethenoiseattenuationeffectdecreasesrapidly,andthesamplingperiodTshouldbeadjustedthroughthedown-sampling.Thedatatobesmoothedareextractedateverydown-samplingperiodT（=nTm,inwhichnisaproperinteger）fromthemeasureddataateverysamplingperiodTm=0.5ms.Inourcase,ncanbechosenasn=4,6and8（correspondingtoT=2,3and4ms）.

ThegainplotofthefilterdesignedfortheorderM=42isshowninFig.4（a）.Fig.4（b）showstheimpulseresponseobtainedforthedesignspecificationsthatΩp=0.002and

Ωs=0.05.Also,Fig.5（a）showsthesimulationresultsobtainedafterfilteringtheoutputsignal.Itcanbeseenthatundesirablesignalsexistinginthehigh-frequencyrangecanbeeffectivelyeliminated,andbyincreasingTtheresponsecanbesmoothed.

Next,Fig.5（b）showsanexampleofdiscretedatasmoothedforthedown-samplingperiodsisprocessedateverysamplingperiod（Tm=0.5ms）.Aminorcontaminationofthesmoothedsignalbyhigh-frequencynoisebecomesseriousintheneighborhoodofmaximumpoint.ForthesamplingperiodT=4ms,theresultingfrequencyofthesampled

datecanbedeterminedhasaperiodicityoff=1/T=250Hz.Thenaturalfrequencyoftheconveyorbeltisinthevicinityof200Hz.Toreducetheeffectofnoiseasimplestfirst-orderlowpassfilter（cutoff-frequency10Hz）iscascadedwiththeFIRfilter.

4.Technicalproblems

4.1.Non-uniformlydistributedweight

Toillustrateanexampleofcrucialproblems,acombinedsetforthreeproductsinsequencepassesovertheconveyorbeltscaleundertheconditionthatli=100cm,mi=80kg,anddi=60cm.Fig.6（a）showstherealtimehistoryoftheoutputsignals.Thefirst,secondandthirdsignalsdenoteoutputsignalsfromconveyorbeltscaleL1,L2andL3the

addedsignaldenotesasumofoutputsignalsthatcorrespondstothemassofaproduct.Itisclearthatanexactdeterminationofmassesisimpossible,becausethecurveshaveseveralpeakvalueslikeawindingpath.Thesimplestcauseofthecrookedcurvesisthatthebaseplateoftheproductisslightlycurved（oruneven）orthereexistsa