矩形管翻领成型器曲面研究

3220044()JournalofSouthernYangtzeUniversity(NaturalScienceEdition)Vol.3No.2Apr.2004:1671-7147(2004)02-0168-05:2003-11-03;:2004-01-07.:(1954-),,,,.CADCAM.1,1,2(1.,214063;2.,214064):,,,CAD/CAM.:;;;:TQ320.52:AStudyonSurfaceoftheRectangularShoulderofPackagingMachinesZHOUYi2jie1,CAIHe2ping1,CUZhi2jun2(1.SchoolofMechanicalEngineering,SouthernYangtzeUniversity,Wuxi214063,China;2.SchoolofScience,SouthernYangtzeUniversity,Wuxi214064,China)Abstract:Byanalyzingtheformingoftheintersectioncurveandsurfaceoftheshoulderwithrectangularsectionofpackagingmachines,themathematicalmodelsofshoulder2curved2surfaceanditsedgeareestablished,andtherelationformulaoftheheightandotherparametersoftheshoulderisderived.ThosemodelsprovidefoundationforCAD/CAMofrectangularshoulderofpackagingmachines.Keywords:rectangularshoulderofpackagingmachines;shouldersurface;developablesurface;fringecurve.,[13],.,.,,,h.11.AB,,.,.(AABB),..,54,9.1Fig.1Rectangularshoulderofpackagingmachines21oxyz,Z.xoy2,44,L1L2L3L4G1G2G3G4,12341234.xoz,.2Fig.2Sectionofrectangularshouldery03:L1:x=py=ptan0arctan(q-rp)(1)L2:x=q/tany=qarctan(qp-r)-arctan(qp-r)(2)L3:x=-py=ptan-arctan(q-rp)(3)y0:G1:x=p-r+rcosty=q-r+rsint(0t/2)(4)G2:x=-(p-r+rsin)y=q-r+rcos(0/2)(5)S,x,C.Cxh,CSABDxoz.xoy.ABABT,T:(p-ecos,0,h+esin).TAABB,BBe,TPPT,PT=f,PTPT,,.3.3Fig.3Developedrectangularshoulderb=2(p+q-2r+2r)+w;w;e=(q-r)tan;tan=b-(q-r)a2.11L1BB,:1:x=py=ptanz=h0arctan(q-rp)(6)2.21G11PG1(x,y,z)=[(p-r+rcost),(q-r+rsint),z(t)](7)9612:f(t)=TPG1,f(t)=[p-r+rcost-(p-ecos)]2+(q-r+rsint)2+[z(t)-(h+esin)]2f(t)=(ecos-r+rcost)2+(q-r+rsint)2+[z(t)-(h+esin)]2(8)z(t)=h-e+[f(t)]2-(q-r+rt)2(9)(8)(9)z(t)=k1+2r(ecos-r)cost+2(q-r)rsint-(q-r+rt)22e(1+sin)(10)k1=(ecos-r)2+r2+(q-r)2+(h+esin)2-(h-e)2(11)G11x=p-r+rcosty=q-r+rsintz(t)=k1+2r(ecos-r)cost+2(q-r)rsint-(q-r+rt)22e(1+sin)(0t/2)(12)1t=/2,z(t)=h0,h0=k1+2(q-r)r-(q-r+r/2)22e(1+sin)(13)2.32L2,2.2:(p-r,q,h0),:(-(p-r),q,h1),2:x=q/tany=qz=h0-h0-h12(p-r)(p-r-q/tan)arctan(qp-r)-arctan(qp-r)(14)2.42G22PG2,PG2(x,y,z)=[-(p-r+rsin),(q-r+rcos),z()](15)TPG2[4]f().f()=[-(p-r+rsin)-(p-ecos)]2+(q-r+rcos)2+[z()-(h+esin)]2f()=(ecos-2p+r-rsin)2+(q-r+rcos)2+[z()-(h+esin)]2(16)z()=h-e-[f()]2-(2p+q-3r+r/2+r)2(17)(16)(17)z()=k2+2r(q-r)cos-2r(r+ecos-2p)sin-(2p+q-3r+r/2+r)22e(1+sin)(18)k2=(r+ecos-2p)2+r2+(q-r)2+(h+esin)2-(h-e)2(19)G22x=-(p-r+rsin)y=q-r+rcosz()=k2+2r(q-r)cos-2r(r+ecos-2p)sin-(2p+q-3r+r/2+r)22e(1+sin)(0/2)(20)2=0,z()|=0=h1,h1=k2+2r(q-r)r-(2p+q-3r+r/2)22e(1+sin)(21)2=/2,z()|=/2=h2,h2=k2-2r(r+ecos-2p)-(2p+q-3r+r)22e(1+sin)(22)2.53L3,3.3:(-p,q,-r,h2),:(-p,0,0),3:y=-py=-ptanz=h2-h2q-r(q-r+ptan)-arctan(q-rp)(23)3,.ABS.[5]:,,071()3.,TPf,.TBSBTS,BS.TBTS,ABSE.[5,6],5,T,55.123,5,1233.,,(12)(20)12.F(X,Y,Z),1OF=OT+TF=OT+uTP(u1)(24),P1,(12).(24),1X=p-ecos+(ecos-r+rcost)uY=(q-r+rsint)uZ=h+esin+[z(t)-h-esin]u(0t/2)(u1)(25)z(t)(10).2X=p-ecos+(-2p+r+ecos-rsin)vY=(q-r+rcos)vZ=h+esin+[z()-h-esin]v(0t/2)(v1)(26)z()(18).4TPG1AEQ,TQTA(t),BT=l,AT=n,BPG1=s(t),TQ=m(t),:l=e/cos(27)n=a+ecos(28)s(t)=(h-z(t))2+(rt)2(29)cos=[f(t)]2+l2-[h-z(t)]2-(rt)22lf(t)(30)3,mm(t)=bsin[+(t)](31)Q(,,),(25),=p-ecos+(ecos-r+rcost)u=(q-r+rsint]u=h+esin+[z(t)-h-esin]u(0t/2)(u1)(32)m(t)=|QT|=[-(p-ecos)]2+(-0)2+[-(esin+h)]2(33)(31)(32)(33)u=bsin[+(t)]1(ecos-r+rcost)2+(q-r+rsint)2+[z(t)-h-esin]2(34)(34)u=u(t),(32)1=p-ecos+(ecos-r+rcost)u(t)=(q-r+rsint]u(t)=h+esin+[z(t)-h-esin]u(t)(0t/2)(35)2,TQTA:s()=[h-z()]2+[2p+q-3r+r/2+r-(q-r)]2(36)s()=[h-z()]2+(2p-2r+r/2+r)2(37)cos=[f()]2+l2-[h-z()]2-(2p-2r+r/2+r)22lf()(38)()=arccos[[f()]2+l2-[h-z()]2-(2p-2r+r/2+r)22lf()=p-ecos+(-2p+r+ecos+rsin)v()=(q-r+rcos]v()=h+esin+[z()-h-esin]v()(0/2)(39)v()=bsin[+()]1(-2p+r+ecos+rsin)2+(q-r+rcos)2+[z()-h-esin]2(40)55.1hh.1,TS,TS1712:TS=(2p-ecos)2+(h+esin)2(41)3TS,TSTS=(2p+2q-4r+r)2+(h-e)2(42)(41)(42)h=(2p+2q-4r+r)2-4p2+4pecos2e(1+sin)(43)3,e=a(q-r)b-q+r(44)(44)(43)h=2pcos1+sin+(2p+2q-4r+r)2-4p22a(q-r)(1+sin)(b-q+r)(45)hpqrab.,76.5.2Tp=q=r,,(45)h,T,,.,TAB,,TAB.Txoz,.64Pro/E,:a=78;p=16;q=25;r=8;b=80;=45;(h=77.56)4,4(b).,,4(a),.(a)(b)4Fig.432DModelofrectangularshoulder71)9,5;2)T,,9,5;3),,;4)hpqrab767.:[1]BOERSMAJ,MOLENAARJ.Geometryoftheshoulderofapachagingmachine[J].SiamReview,1995,37(9):406-422.[2].[M].:,1988.[3].[J].,2002,(2):10-12.[4].[M].:,1975.[5].[M].:,1979.[6].[M].:,1985.(:)271()3