外文翻译--采矿作业的机械化及自动化采石挖掘机工作装置的模型 英文版.pdf

MECHANIZATIONANDAUTOMATIONOFMININGOPERATIONSAMODELOFTHEWORKINGOPERATIONSOFAQUARRYEXCAVATORE.V.Gaisler,A.P.Mattis,E.A.Mochalov,andS.V.ShishaevWedevelopamethematicalmodeloftheprocessofopen-pitminingwithaquarryex-cavatorusingabucketthathasactivebladesdrivenbyimpactblocksinstalledinthefrontwall.Thebucketoperatesasfollows.Whenthebucketcomesincontactwitharockareathatcanbebrokenbyaforcegreaterthanthesumoftheforcesoffrictionofthetoolonthesleeveandtheforceofactivationofthestartingdevice,theimpactblocksareenergized.TheactionoftheseblockscausesthebucketbladestoentertherocktoadepthX,weakeningthezonelocateddirectlyunderthebladesandformingtheso-called"disruptedbondingzone"i.Thiszonerequiresmuchlessforcetobebrokenthananin-tactmass.Withsuchactivebuckets,strongrockscanbeexcavatedwithoutpreloosening.Themainparametersdescribingthemovementsofthebucketduringexcavationincludethemechanicalpropertiesoftherock,thevariationofthesepropertiesundertheeffectoftheimpact,theworkingcharacteristicsofthedrivesoftheactuatormechanisms,andtheparametersoftheequipment.Twotypesofdestructiontakeplaceduringthecourseofexcavation:cuttingandimpactbreaking.Thegeometricsumofforcesactingonallthefacesofabladerepresentstheresist-ancetointrusion.TheprojectionofthissumontotheaxisoftheimpactblockisPl；theprojectionontothedirectionperpendiculartotheaxisisP2.Thesumofforcesact-ingperpendicularlytothebucket-travelingplaneisequaltozerobecauseblockfracturingismainlyperformed.Thefollowingassumptionsaremadeforamathematicalmodeldescribingthemotionsofthebucket:?-thecenterofmassoftherockinthebucketisstationaryrelativetothebucket；-chipsareseparatedcontinuously；-theloadsonthebucketbladesareequal；-thebladespenetratetherockinstantaneouslyuponimpact；-theresistancetothebucket-fillingisdisregarded；-themomentoffrictionrelativetotherotationaxisofthearmisdisregarded.Withtheseassumptions,themotionofthebucketcanbeinterpretedasthemotionofatwo-dimensionalmechanismundertheeffectofexternalforces,whichincludestheforcedevelopedbythedrivesofthepressuremechanismandtheliftmechanism,thegravityforce,andtheresistanceforceoftherockface.Thepositionofthebucketateachpointintimeisdefinedbythecoordinater(t),thedistance(OC),and(t)-theanglebetweentheboomandthebucketstick.Thekineticenergyofthismechanismisexpressedas"=(+m"),-+JT(1)wherem1istherockmassandthebucket；m2isthemassofthestickandtheemptybucket；Jisthemomentof"inertiaofthebucketwithrockandthestickrelativetoitsrotationaxisInstituteofMining,SiberianBranch,AcademyofSciencesoftheUSSR,Novosibirsk.Trans-latedfromFiziko-TekhnicheskieProblemyRazrabotkiPo!eznykhIskopaemykh,No.2,pp.60-67,March-April,1991.Originalarticle.submittedSeptember25,1990.0038-5581/91/2702-0131512.5091992PlenumPublishingCorporation131Y=ml(r+lCBii)+J+mi(r-rl)2+IGA),(2)whereJ1isthemomentofinertiaofanemptybucketandthestickrelativetothecenterofmassandr-rlisthecoordinateofthecenterofmassoftheemptybucketwiththestick.Therockmassinthebucketmdependsonthepathtraveledbythefrontedgeofthebucketandtheinitialshapeoftherockface.Inordertowriteanexpressionfortherateofmassincrement,wewillconsidertheschemeinFig.2.Supposethatthepathtraveledbythebucketedgebythetimetisdescribedbythecurvef2(r2,2)"Theini-tialshapeofthefacebythecurvef3(r3,3),wherer2,r3,3arepolarcoordinateswiththeoriginatzero.DuringthetimedtthebucketedgetravelsadistanceICDI；inthatcase,sinced2=d3themassincrementwithinthetimedtisspecifiedbyIdm=T,B(IOCl"IODI-IOA.IOBI)sinda2,where0istherockdensityandBisthewidthofthebucketedge.Weseefromthediagramthatloci=r,ION=r=§dr,IOAI=r,IOBI=r§dr3.Consideringthatsindada2anddisregardingthesquaresoftheinfinitesimalvariables,wewrite1a,=r,z(,-d)a.Theincrementd2isequaltotheproductattheangularspeedofthestickatthetimetandtheincrementdt,i.e.,d2=da3=&dt.Therateofincrementofthemassisnowex-pressedasdNlo"",=.-7-=_,i(d-,.:,)=.(3)Themassfallingintothebucketduringthetimetisdefinedby!m,=Js()dT0ThismassmIisonlyafunctionofthetimet.Makinguseofthefundamentalequationofthedynamicsofavariable-masspoint(Mesh-cherskiisequation),wecandemonstratethatLagrangianequationsareapplicabletothemechanicalsystemthatconsistsofvariable-massmaterialpointsiftheabsolutevelocityoftheassociatedmassisequaltozero.Consideramechanicalsystemcomprisedofnmaterialpointswithmassesml,m2.mi,.,mn,thatmovewithvelocitiesvi.Lagrangianequationsformi=consthavebeenderivedin2,p.340.Considerthecaseofmi=mi(t).Infollowing2,weintroducegeneralizedcoordinatesq,suchthati=ri(ql,q2,qs,t),whereriisthepositionvectoroftheithmass.Now,i=)1)j,OliO"ijIuqjUqjOq)wherejisgeneralizedvelocity.Thekineticenergyofthemechanicalsystematanytimepointisdefinedas1-T?niViUi.Wefindpartialderivativesofkineticenergywithrespecttothegeneralizedcoordinateqjandthegeneralizedvelocityj:or=-oiaqjmiUi-r-,i=laqi132_ih,i-OriOTmivlmiviOqj=i=1Oqji=OqjWedifferentiatethisexpressionwithrespecttotime.Considernowthefirstsum,takingintoaccountthefundamentalequationofthedynamicsofvariable-masspointforthecasewheretheabsolutevelocityoftheassociatedmassisequaltozero2,p.143,amv=F,m.-7+-wherePistheresultantoftheforcesappliedtothepoint.Foranonfreematerialpointwithvariablemass,wehaveelT,idm-ml"-77+-d-fvi=F.,+7,whereRiistheresultantofthereactionsofconstraintsappliedtotheithpoint.Now,7,+m,-.,+7,+7,-,=i=1S-.Ori=(F+n)=Q+&.i=lThesecondsumis,infact,8T/Sqj2,p.342.Weobtaindt=Qj+o+OTOq)"ForasystemwithstationaryperfectconstraintsQjR=0d"OT07ItistheLagrangianequationforamechanicalsystemconsistingofvariable-massmaterialpointsundertheassumptionthattheabsolutevelocityoftheassociatedmassisequaltozero.Aswesee,itisidenticaltoaLagrangianequationderivedforaconstantmassofmaterialpointsbelongingtothemechanicalsystem.TheLagrangianmotionequationsforthismechanismare"r-u-7-=QJ"7,A,-=Q(5)whereQI,Q2aregeneralizedforcesactingondisplacements6rand6,respectively,lQ,=-,o,(-/-,-o.,/o-+:,-,.oI+(m+m).gcos(-),O,=l).r.sin(-OCD)r+ICDI/).P.sincos(n-OCD)/(6)133Fig.1Fig.i.Fig.2.CDFig.2Designschemeforanexcavatorwithanactivebucket.Evaluationoftheincrementofrockweightinthebucket.<,iocl:/-1)-1.,.sin.I,.+tCEI.-,sin+(mxgsin(%-)"+"2"gsin(%-).(,-rl)+(mj.ICBI+melCAI)gc),where8=8(r,a)istheanglebetweenthedirectionsoftheforcesFIandF=whicharegeneratedbythedrivesofthepressuremechanismandliftmechanism,respectively.Thecharacteristicsofthedrivesofthepressureandliftmechanismsoftheexcavatorestablishtherelationshipbetweenthemomentofforcesonthemotorshaftsandtherotationvelocities,soF,=/,(；.),&=/(；,).(7)Theformofthefunctionsf1()andf2(,&)dependsonthecharacteristicsofthedrivesandthegearratiosofthepressureandliftmechanisms.TheexpressionforQlandQ2includestheforcesPlandP2；theyarethecomponentsoftheresistancetodigging.Theycanbeestimatedwiththeaidofthemathematical-logicmodelsofDombrovskii,Zelenin,Vetrov,Artemev,Balovnev,orFedorov3.Generally,theresistancetodiggingdependsonthemechanicalpropertiesofthebed,thetoolgeo-metry,thecuttingangle(2),andthethicknessofthelayercut(h).WeshouldconsiderthatthelasttwoparametersdependimplicitlyOntime:sin(OCO)q-a|csin,a,=7,+arcsin1+trr.r71,r"CD2-2rlCDIcos(OCD)h=l"a()-r2(rAftercomputingthederivativesofthekineticenergyandsubstitutingthemintotheLagrangianequations,wehave(rot+m2)r+mlr-(mlr+m2(r-r,),a2=Qi,(8)whereQIandQ2aredefinedby(6).ThemotionofthismechanismisdescribedbyEqs.(8).Theinitialconditionsoftheseequationsarem(O)=O,(0)=0,:(0)=0,(0)=o,r(O)=ro.(9)134