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AssessmentoftheBehaviourofPotatoesinaCup-beltPlanter

H.Buitenwerf，W.B.Hoogmoed，P.LerinkandJ.Müller.AssementoftheBehaviorofPotatoinaCup-beltPlanter.Biosytems.Engineering,Volume95,Issue,September2006:35—41

Thefunctioningofmostpotatoplantersisbasedontransportandplacementoftheseedpotatoesbyacup-belt.Thecapacityofthisprocessisratherlowwhenplantingaccuracyhastostayatacceptablelevels.Themainlimitationsaresetbythespeedofthecup-beltandthenumberandpositioningofthecups.Itwashypothesisedthattheinaccuracyinplantingdistance,thatisthedeviationfromuniformplantingdistances,mainlyiscreatedbytheconstructionofthecup-beltplanter.

Todeterminetheoriginofthedeviationsinuniformityofplacementofthepotatoesatheoreticalmodelwasbuilt.Themodelcalculatesthetimeintervalbetweeneachsuccessivepotatotouchingtheground.Referringtotheresultsofthemodel,twohypotheseswereposed,onewithrespecttotheeffectofbeltspeed,andonewithrespecttotheinfluenceofpotatoshape.Aplanterunitwasinstalledinalaboratorytotestthesetwohypotheses.Ahigh-speedcamerawasusedtomeasurethetimeintervalbetweeneachsuccessivepotatojustbeforetheyreachthesoilsurfaceandtovisualizethebehaviorofthepotato.

Theresultsshowedthat:(a)thehigherthespeedofthecup-belt,themoreuniformisthedepositionofthepotatoes;and(b)amoreregularpotatoshapedidnotresultinahigherplantingaccuracy.

Majorimprovementscanbeachievedbyreducingtheopeningtimeatthebottomoftheductandbyimprovingthedesignofthecupsanditspositionrelativetotheduct.Thiswillallowmoreroomforchangesinthecup-beltspeedswhilekeepingahighplantingaccuracy.

Introduction

Thecup-beltplanter(Fig.1)isthemostcommonlyusedmachinetoplantpotatoes.Theseedpotatoesaretransferredfromahoppertotheconveyorbeltwithcupssizedtoholdonetuber.Thisbeltmovesupwardstoliftthepotatoesoutofthehopperandturnsovertheuppersheave.Atthispoint,thepotatoesfallonthebackofthenextcupandareconfinedinasheet-metalduct.Atthebottom,thebeltturnsovertheroller,creatingtheopeningfordroppingthepotatointoafurrowinthesoil.

Fig.1.Workingcomponentsofthecup-beltplanter:(1)potatoesinhopper;(2)cup-belt;(3)cup;(4)uppersheave;(5)duct;(6)potatoonbackofcup;(7)furrower;(8)roller;(9)releaseopening;(10)groundlevel

Capacityandaccuracyofplantspacingarethemainparametersofmachineperformance.Highaccuracyofplantspacingresultsinhighyieldandauniformsortingofthetubersatharvest(McPheeetal.,1996;Pavek&Thornton,2003).Fieldmeasurements(unpublisheddata)ofplantingdistanceinTheNetherlandsrevealedacoefficientofvariation(CV)ofaround20%.EarlierstudiesinCanadaandtheUSAshowedevenhigherCVsofupto69%(Misener,1982;Entz&LaCroix,1983;Sieczkaetal.,1986),indicatingthattheaccuracyislowcomparedtoprecisionplantersforbeetormaize.

Travellingspeedandaccuracyofplantingshowaninversecorrelation.Therefore,thepresentcup-beltplantersareequippedwithtwoparallelrowsofcupsperbeltinsteadofone.Doublingthecuprowallowsdoublethetravelspeedwithoutincreasingthebeltspeedandthus,ahighercapacityatthesameaccuracyisexpected.

Theobjectiveofthisstudywastoinvestigatethereasonsforthelowaccuracyofcup-beltplantersandtousethisknowledgetoderiverecommendationsfordesignmodifications,e.g.inbeltspeedsorshapeandnumberofcups.

Forbetterunderstanding,amodelwasdeveloped,describingthepotatomovementfromthemomentthepotatoenterstheductuptothemomentittouchestheground.Thus,thebehaviourofthepotatoatthebottomofthesoilfurrowwasnottakenintoaccount.Asphysicalpropertiesstronglyinfluencetheefficiencyofagriculturalequipment(Kutzbach,1989),theshapeofthepotatoeswasalsoconsideredinthemodel.

Twonullhypotheseswereformulated:(1)theplantingaccuracyisnotrelatedtothespeedofthecup-belt;and(2)theplantingaccuracyisnotrelatedtothedimensions(expressedbyashapefactor)ofthepotatoes.Thehypothesesweretestedboththeoreticallywiththemodelandempiricallyinthelaboratory.

Materialsandmethods

2.1.Plantmaterial

Seedpotatoesofthecultivars(cv.)Sante,ArindaandMarfonahavebeenusedfortestingthecup-beltplanter,becausetheyshowdifferentshapecharacteristics.Theshapeofthepotatotuberisanimportantcharacteristicforhandlingandtransporting.Manyshapefeatures,usuallycombinedwithsizemeasurements,canbedistinguished(Du&Sun,2004;Taoetal.,1995;Zo¨dler,1969).IntheNetherlandsgradingofpotatoesismostlydonebyusingthesquaremeshsize(Koningdeetal.,1994),whichisdeterminedonlybythewidthandheight(largestandleastbreadth)ofthepotato.Forthetransportprocessesinsidetheplanter,thelengthofthepotatoisadecisivefactoraswell.

AshapefactorSbasedonallthreedimensionswasintroduced:

(1)

wherelisthelength,wthewidthandhtheheightofthepotatoinmm,withhowol.Asareference,alsosphericalgolfballs(withaboutthesamedensityaspotatoes),representingashapefactorSof100wereused.ShapecharacteristicsofthepotatoesusedinthisstudyaregiveninTable1.

2.2.Mathematicalmodeloftheprocess

Amathematicalmodelwasbuilttopredictplantingaccuracyandplantingcapacityofthecup-beltplanter.Themodeltookintoconsiderationradiusandspeedoftheroller,thedimensionsandspacingofthecups,theirpositioningwithrespecttotheductwallandtheheightoftheplanterabovethesoilsurface(Fig.2).Itwasassumedthatthepotatoesdidnotmoverelativetothecuporrotateduringtheirdownwardmovement.

Fig.2.Processsimulatedbymodel,simulationstartingwhenthecupcrosseslineA;releasetimerepresentstimeneededtocreateanopeningsufficientlylargeforapotatotopass;modelalsocalculatestimebetweenreleaseofthepotatoandthemomentitreachesthesoilsurface(freefall);rc,sumoftheradiusoftheroller,thicknessofthebeltandlengthofthecup;xclear,clearancebetweencupandductwall;xrelease,releaseclearance;arelease,releaseangle;o,angularspeedofroller;lineC,groundlevel,endofsimulation

Thefieldspeedandcup-beltspeedcanbesettoachievetheaimedplantspacing.Thefrequencyfpotofpotatoesleavingtheductatthebottomiscalculatedas

Wherevcisthecup-beltspeedinms?1andxcisthedistanceinmbetweenthecupsonthebelt.Theangularspeedoftherollerωrinrads?1withradiusrrinmiscalculatedas

Thegapintheducthastobelargeenoughforapotatotopassandbereleased.Thisgapxreleaseinmisreachedatacertainangleαreleaseinradofacuppassingtheroller.Thisreleaseangleαrelease(Fig.2)iscalculatedas

where:rcisthesuminmoftheradiusoftheroller,thethicknessofthebeltandthelengthofthecup;andxclearistheclearanceinmbetweenthetipofthecupandthewalloftheduct.

Whentheparametersofthepotatoesareknown,theanglerequiredforreleasingapotatocanbecalculated.Apartfromitsshapeandsize,thepositionofthepotatoonthebackofthecupisdeterminative.Therefore,themodeldistinguishestwopositions:(a)minimumrequiredgap,equaltotheheightofapotato;and(b)maximumrequiredgapequaltothelengthofapotato.

Thetimetreleaseinsneededtoformareleaseangleaoiscalculatedas

Calculatingtreleasefordifferentpotatoesandpossiblepositionsonthecupyieldsthedeviationfromtheaveragetimeintervalbetweenconsecutivepotatoes.Combinedwiththedurationofthefreefallandthefieldspeedoftheplanter,thisgivestheplantingaccuracy.

Whenthepotatoisreleased,itfallstowardsthesoilsurface.Aseachpotatoisreleasedonauniqueangularposition,italsohasauniqueheightabovethesoilsurfaceatthatmoment(Fig.2).Asmallpotatowillbereleasedearlierandthusatahigherpointthanalargeone.

Themodelcalculatesthevelocityofthepotatojustbeforeithitsthesoilsurfaceuendinms.1.Theinitialverticalvelocityofthepotatou0inms.1isassumedtoequaltheverticalcomponentofthetrackspeedofthetipofthecup:

Thereleaseheightyreleaseinmiscalculatedas

whereyrinmisthedistancebetweenthecentreoftheroller(lineAinFig.2)andthesoilsurface.

Thetimeoffreefalltfallinsiscalculatedwith

wheregisthegravitationalacceleration(9.8m

s?2)andthefinalvelocityvendiscalculatedas

withv0inms.1beingtheverticaldownwardspeedofthepotatoatthemomentofrelease.

ThetimeforthepotatotomovefromLineAtothereleasepointtreleasehastobeaddedtotfall.

Themodelcalculatesthetimeintervalbetweentwoconsecutivepotatoesthatmaybepositionedindifferentwaysonthecups.Thelargestdeviationsinintervalswilloccurwhenapotatopositionedlengthwiseisfollowedbyonepositionedheightwise,andviceversa.

2.3.Thelaboratoryarrangement

Astandardplanterunit(MiedemaHassiaSL4(6))wasmodifiedbyreplacingpartofthebottomendofthesheetmetalductwithsimilarlyshapedtransparentacrylicmaterial(Fig.3).Thecup-beltwasdrivenviatheroller(8inFig.1),byavariablespeedelectricmotor.Thespeedwasmeasuredwithaninfraredrevolutionmeter.Onlyonerowofcupswasobservedinthisarrangement.

Fig.3.Laboratorytest-rig;lowerright—partofthebottomendofthesheetmetalductwasreplacedwithtransparentacrylicsheet;upperright—segmentfacedbythehigh-speedcamera

Ahigh-speedvideocamera(SpeedCamPro,Wein-bergerAG,Dietikon,Switzerland)wasusedtovisualisethebehaviourofthepotatoesinthetransparentductandtomeasurethetimeintervalbetweenconsecutivepotatoes.Asheetwithacoordinatesystemwasplacedbehindtheopeningoftheduct,theXaxisrepresentingthegroundlevel.Timewasregisteredwhenthemidpointofapotatopassedthegroundline.Standarddeviationofthetimeintervalbetweenconsecutivepotatoeswasusedasmeasureforplantspacingaccuracy.Forthemeasurementsthecamerasystemwassettoarecordingrateof1000framespersecond.Withanaveragefreefallvelocityof2.5ms?1,thepotatomovesapprox.2.5mmbetweentwoframes,sufficientlysmalltoallowanaccurateplacementregistration.

Thefeedingratesforthetestoftheeffectofthespeedofthebeltweresetat300,400and500potatoesmin-1(fpot?5,6.7and8.3s.1)correspondingtobeltspeedsof0.33,0.45and0.56ms-1.Thesespeedswouldbetypicalforbeltswith3,2and1rowsofcups,respectively.Afixedfeedingrateof400potatoesmin-1(cup-beltspeedof0.45ms-1)wasusedtoassesstheeffectofthepotatoshape.

Fortheassessmentofanormaldistributionofthe

timeintervals,30potatoesinfiverepetitionswereused.

Intheothertests,20potatoesinthreerepetitionswere

Used.

2.4.Statisticalanalysis

ThehypothesesweretestedusingtheFishertest,as

analysisshowedthatpopulationswerenormallydis-

tributed.Theone-sideduppertailFishertestwasused

andawassetto5%representingtheprobabilityofa

type1error,whereatruenullhypothesisisincorrectly

rejected.Theconfidenceintervalisequalto(100-a)%.

Resultsanddiscussion

3.1.Cup-beltspeed

3.1.1.Empiricalresults

Themeasuredtimeintervalsbetweenconsecutivepotatoestouchinggroundshowedanormaldistribution.Standarddeviationssforfeedingrates300,400and500potatoesmin-1were33.0,20.5and12.7ms,respectively.

Fig.4.Normaldistributionofthetimeinterval(x,inms)ofdepositionofthepotatoes(pot)forthreefeedingrates

AccordingtotheF-testthedifferencesbetweenfeedingratesweresignificant.ThenormaldistributionsforallthreefeedingratesareshowninFig.4.Theaccuracyoftheplanterisincreasingwiththecup-beltspeed,withCVsof8.6%,7.1%and5.5%,respectively.

3.1.2.Resultspredictedbythemodel

Figure5showstheeffectofthebeltspeedonthetimeneededtocreateacertainopening.Alinearrelationshipwasfoundbetweencup-beltspeedandtheaccuracyofthedepositionofthepotatoesexpressedasdeviationfromthetimeinterval.Theshorterthetimeneededforcreatingtheopening,thesmallerthedeviations.ResultsofthesecalculationsaregiveninTable2.

Fig.5.Effectofbeltspeedontimeneededtocreateopening

Thespeedofthecupturningawayfromtheductwallisimportant.Insteadofahigherbeltspeed,anincreaseofthecup’scircumferentialspeedcanbeachievedbydecreasingtheradiusoftheroller.Theradiusoftherollerusedinthetestis0.055m,typicalfortheseplanters.Itwascalculatedwhattheradiusoftherollerhadtobeforlowerbeltspeeds,inordertoreachthesamecircumferentialspeedofthetipofthecupasfoundforthehighestbeltspeed.Thisresultedinaradiusof0.025mfor300potatoesmin.1andof0.041mfor400potatoesmin.1.Comparedtothisoutcome,alineartrendlinebasedontheresultsofthelaboratorymeasurementspredictsamaximumperformanceataradiusofaround0.020m.

Themathematicalmodel[Eqn(5)]predictedalinearrelationshipbetweentheradiusoftheroller(forr40.01m)andtheaccuracyofthedepositionofthepotatoes.Themodelwasusedtoestimatestandarddeviationsfordifferentradiiatafeedingrateof300potatoesmin.1.TheresultsaregiveninFig.6,showingthatthemodelpredictsamoregradualdecreaseinaccuracyincomparisonwiththemeasureddata.Aradiusof0.025m,whichisprobablythesmallestradiustechnicallypossible,shouldhavegivenadecreaseinstandarddeviationofabout75%comparedtotheoriginalradius.

Fig.6.Relationshipbetweentheradiusoftherollerandthestandarddeviationofthetimeintervalofdepositionofthepotatoes;therelationshipislinearforradiir40.01m,K,measurementdata;m,datafrommathematicalmodel;’,extendedforro0.01m;—,linearrelationship;R2,coefficientofdetermination

3.2.Dimensionandshapeofthepotatoes

TheresultsofthelaboratorytestsaregiveninTable3.Itshowsthestandarddeviationsofthetimeintervalatafixedfeedingrateof400potatoesmin.1.Theseresultswerecontrarytotheexpectationsthathigherstandarddeviationswouldbefoundwithincreasingshapefactors.Especiallythepoorresultsoftheballswereamazing.Thestandarddeviationoftheballswasabout50%higherthantheoblongpotatoesofcv.Arinda.ThenormaldistributionofthetimeintervalsisshowninFig.7.Significantdifferenceswerefoundbetweentheballsandthepotatoes.Nosignificantdifferenceswerefoundbetweenthetwopotatovarieties.

Fig.7.Normaldistributionofthetimeinterval(x,inms)ofdepositionofthepotatoesfordifferentshapefactorsatafixedfeedingrate

Thepoorperformanceoftheballswascausedbythefactthattheseballscouldbepositionedinmanywaysonthebackofthecup.Thus,differentpositionsoftheballsinadjacentcupsresultedinaloweraccuracyofdeposition.Thethree-dimensionaldrawingofthecup-beltshowstheshapeofthegapbetweencupandductillustratingthatdifferentopeningsizesarepossible(Fig.8)

ArindatubersweredepositedwithahigheraccuracythanMarfonatubers.Analysisoftherecordedframesandthepotatoes,demonstratedthatthepotatoesofcv.Arindaalwayswerepositionedwiththeirlongestaxisparalleltothebackofthecup.Thus,apartfromtheshapefactor,ahigherratiowidth/heightwillcauseagreaterdeviation.Forcv.Arinda,thisratiowas1.09,forcv.Marfonaitwas1.15.

3.3.Modelversuslaboratorytest-rig

Themathematicalmodelpredictedtheperformanceoftheprocessunderdifferentcircumstances.Themodelsimulatedabetterperformanceforsphericalballscomparedtopotatoeswhereasthelaboratorytestshowedtheopposite.Anadditionallaboratorytestwasdonetocheckthereliabilityofthemodel.

Inthemodel,thetimeintervalbetweentwopotatoesiscalculated.StartingpointisthemomentthepotatocrosseslineAandendpointisthecrossingoflineC(Fig.2).Inthelaboratorytest-rigthetime-intervalbetweenpotatoesmovingfromlineAtoCwasmeasured(Fig.3).Thelength,widthandheightofeachpotatowasmeasuredandpotatoeswerenumbered.Duringthemeasurementitwasdeterminedhoweachpotatowaspositionedonthecup.Thispositionandthepotatodimensionswereusedasinputforthemodel.Themeasurementsweredoneatafeedingrateof400potatoesmin?1withpotatoesofcv.ArindaandMarfona.ThestandarddeviationsofthemeasuredtimeintervalsareshowninTable4.Theywereslightlydifferent(higher)fromthestandarddeviationscalculatedbythemodel.Explanationsforthesedifferencesare:(1)themodeldoesnottakeintoconsiderationsituationsasshowninFig.8,(2)thepassingmomentatlineAandCwasdisputable.Oblongpotatoessuchascv.Arindamayfallwiththetiporwiththelongestsizedown.Thismaycauseupto6msdifferenceforthepotatotoreachthebottomlineC.

4.Conclusions

Themathematicalmodelsimulatingthemovementofthepotatoesatthetimeoftheirreleasefromthecup-beltwasaveryusefultoolleadingtothehypothesestobetestedandtodesignthelaboratorytest-rig.

Boththemodelandthelaboratorytestshowedthatthehigherthespeedofthebelt,themoreuniformthedepositionofthepotatoesatzerohorizontalvelocity.Thiswasduetothefactthattheopening,allowingthepotatotodrop,iscreatedquicker.Thisleaveslesseffectofshapeofthepotatoandthepositioningofthepotatoonthecup.Arelationshipwiththebeltspeedwasfound.So,toprovidemoreroomforreductionsinthecup-beltspeedswhilekeepingahighplantingaccuracyitisrecommendedtodecreasetheradiusoftherollertillaslowastechnicallypossible.

Thisstudyshowedthattheaccuracyofplanting(distanceintheseedingfurrow)isinfluencedforalargepartbythecup-beltunitoftheplanter.

Amoreregularshape(lowershapefactor)doesnotautomaticallyresultinahigheraccuracy.Asphere(golfball)inmostcaseswasdepositedwithaloweraccuracythanapotato.Thiswascausedbytheshapesoftheguidingduc