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õõ(110006)(100083)(),,,,,,ApproachtotheMethodofCalculatingtheAmountofPressedBendinginStraightenerCuiFuShiDongcheng(NortheastUniversity)(BeijingScienceandTechnologyUniversity)ABSTRACTWiththeneedingofthepreciselysettingtheamountofpressedbendinginprocessingofstraightenerbycomputer.Anewkindofmethodinwhichatheoreticalornumericalmethodwasusedhasbeenprimarilyputforward.Therecoveredbendingdeflectionandremainedbendingdeflectionwascalculatedseparatelyatthecaseofgreaterpressedbending,andtheremainedbendingdeflectionwascalculatedbyane2quivalentbendingdeflectionwhichwasproducedbyanassumedforce,fuithermore,thisequivalentbendingdeflectionwasseparatedaselasticbendingdeflectionandplasticbendingdeflectionandcalculatedbynumeri2calmethod.Bymeansofthismethod,morepreciseresultcanbeacquired.Bycamparingexperiencedvalue,anpracticableresultcanbeacquired.KEYWORDSStraighteningAmountofpressedBendingSmallerdeflectionpressedbendingGeaterdeflectionpressedbending1,,[4],,,,,,,(),2,1TotalNo1113February1999METALLURGICALEQUIPMENT113199921,,,2l,I,E,Mt,M,M{(M{=MöMt):Df=l2M3EI=l2MtM{3EI=DtM{(1)DtDlf=DföDt,,:Dlf=M{(1)[1],Cqf=M{,Dlf=Cqf;,Dw=Df,Cqw=Cqf,Dlf=Cqw,,Cqw=W(Cq2)=W(Cq0+Cqw):Dlw=W(Cq0+Dlw)Dw=DlwDt(2),:Dl3w+(2Cq0-1.5)Dl2w+(Cq20-3Cq0)Dlw+0.5-1.5Cq20=0Dw=DlwDt(3),(D)(Dw),n,n-1(2);n-2,i,1a):Di=Dwi+12[Dw(i-1)+Dw(i+1)](4),,(n-1)(1b)):D2=2Dw2Dn-1=2Dw(n-1)(5),(n-1),(1c)):D1=2Dw2Dn=2Dt(6)13,,,,,:,,,,,,,(C2),(C0)(Cw),,Cq2=Cq0+Cqw,,(Cc),(Dc)Dc=Dw-Df,Dw,Df,DcDw:Dw=Df+Dc(7),Df(1)Dc,:Dc=DlcDt=CqcDt,Cqc1,Cqc121131999211)Cqc1,,:Dc=DlcDt=CqcDt=(Cqw-M{)Dt(8),:Dw=DlfDt+CqcDt=M{Dt+(Cqw-M{)Dt=CqwDt(9)2)Cqc1,,FcMclct,l-lct,DctDcs:Dc=Dct+Dcs=Mtl2ct3EI+llctCcxxdx(10)DwDfDc,DcDctDcs,(10)Dcs,,Ccxx,Mcx,McxCcxMcx=Fcxx,Mt=Fclct,M{cx=McxöMt=xölct;Cqcx=CcxöCt=CcxöMtöEIMcxCcxCqcxxölct,Cqcx=f(xölct):Dcs=llctCtCqcxxdx=Ctllctf(xlct)xdx(11)Dt=Mtl2ö3EI,(10)Dct=Dtl2ctöl2,Mc=Fcl,M{c=McöMt=FclöFclct=lölct,Dct=DtöM{2c:Dw=Df+Dct+Dcs=DtM{+DtM{2c+Ctllctf(xlct)xdx(12)Ct=3Dtöl2,Dt:Dlw=M{+1M{2c+3l2llctf(xlct)xdx(13)f(xölct),:Cqcx=(3-2xlct)-1ö2(14)xölct=W(Cqcx),(11):Dlcs=3l2llctCqcxxdx=3l22ni=0Cqcxixi$x(15)nlctln,ixi,Cqcxi,$x,$x=(l-lct)ön,xi=lct+i$x(15):llctCqcxxdx=2ni=0Cqcxi(lct+i$x)$x=$x2{Cqcx0lct+2Cqcx1(lct+$x)+2Cqcx2(lct+2$x)++2Cqcx(n-1)[lct+(n-1)$x]+Cqcxn(lct+n$x)}=S(16)S(13):Dlw=M{+1M{2c+3l2S(17)1M{M{clctx=f(Cqcx)Cq2M{Cqc=Cqw-M{M{clct=löM{cx=f(Cqcx)1.5-0.5öCq221.5-0.5öCq2cx=lct(1.5-0.5öCq2cx)2+1öCq32-2öCq222+1öCq3c-2öCq2cx=lct(2+1öCq3cx-2öCq2cx)1.6+0.2öCq32-0.8öCq221.6+0.2öCq3c-0.8öCq2cx=lct(1.6+0.2öCq3cx-0.8öCq2cx)4P[(1-1öCq22)1ö2õ(2.5-1öCq22)õ13+Cq22arcsin(1öCq2)]4P[(1-1öCq2c)1ö2õ(2.5-1öCq2c)õ13+Cqc2arcsin(1öCqc)]x=4Plct[(1-1öCq2cx)1ö2õ(2.5-1öCq2cx)õ13+Cqcx2arcsin(1öCqcx)]:(1)l;(2)MtCtDt;(3)C0,Cq0;(4)CwCqw,Cq2=Cq0+Cqw;(5)x=f(Cqcx)(1);(6)xCqcx;(7)(l-lct)n(n=1020),$x;(8)lct3:199921Cqcx0xi=lct+i$xCqcxi,(n+1),,S;(9)DlwDw481300mm56#,H=168mm,E=206000MPa,Rs=300MPa()2281300mmB=0.075,G=0.0863,[1]:M{=[B(1.5-0.5öCq22)+G3(1-B)Cq2]ö[B+G3(1-B)]:M{=1.488-0.496öCq22+0.00787Cq2M{=1.488-0.496ö(Cq0+Dlw)2+0.00787(Cq0+Dlw)(18):Dl3w+(1.9921Cq0-1.4998)Dl2w+(0.9841Cq20-2.9996Cq0)Dlw+0.4999-1.4898Cq20-0.0079Cq30=0Dw=DlwDt(19),+C0,0,-C0,+C0,-C0,,,Cq0=5,,,:Cq0i=Cqc(i-1)=Dlw(i-1)-Dlf(i-1)(20),Cq0=0,(18):Df(i-1)=M{(i-1)=1.488-0.4961öDl2w(i-1)+0.00787Dlw(i-1)(21)(20),(19)iCq03=Cq0=52281300mm56#Cq03=Cq02Dlw3Cq04=Cqc3Dlw4Cq05=Cqc4Dlw5Cq06=Cqc5Dlw6Cq07=Cqc6Dlw7Cqc7511528012411280109112010511105010141103010015:Dt=Mtl23EI=2Rs3EH(p4)2=230013002320600016816=0.61mmDw3=0.93mm,Dw4=0.78mm,Dw5=0.73mm,Dw6=0.68mm,Dw7=0.63mm,Dw8=0.61mm,Dw2=Dw3=0.93mm(5)(6):D2=2Dw2=1.9mm,D4=Dw4+(Dw3+Dw5)ö2=1.6mm,D6=Dw6+(Dw5+Dw7)ö2=1.4mm,D8=2Dt=1.3mm(H)015mm,-0.5mm,D2=2.4mm,D4=2.1mm,D6=1.9mm;+0.05mm,,,D8=1.3mm,[2]7081300mm,,56#34113199921,,,,,0.49mmn1.3mm,,,381300mm56#(:mm)2521912109214+0.31441321351195211+0115641511992151119-01618211510149113+0181:CqwM{max,,,,Cqwmax=2M{maxM{max=1.8,Cqwmax=3.6Cq0=3Cq2=3+3.6=6.6,(18)Cqf=M{=1.53Cqc=Cqw-Cqf=3.6-1.53=2.07,(18),:M{c=1.488-0.496öCq2c+0.00787Cqc(22)M{c=1.39,l=pö4=325mmlct=löM{c=233.7mml-lct=91.3mm91.3mm,x=f(Cqcx)1:x=lctM{cx=233.7(1.488-0.496öCq2cx+0.00787Cqcx)(23)3n=10,$x=9.13mm,xi,Cqcxi,$xxiCqcxi4S=39555.26((16)),((17)):Dlw=M{+1M{2c+3l2S=1.53+1ö1.392+339555.26ö3252=3.23Cqcxx4xiCqcxixiCqcxi$xx0x1x2x3x4x5x6x7x8x9x1023317242183251196261109270122279135288148297161306174315187325Cqcx0Cqcx1Cqcx2Cqcx3Cqcx4Cqcx5Cqcx6Cqcx7Cqcx8Cqcx9Cqcx10111042110891114311206112801137011484116251182021090x0Cqcx0$xx1Cqcx1$xx2Cqcx2$xx3Cqcx3$xx4Cqcx4$xx5Cqcx5$xx6Cqcx6$xx7Cqcx7$xx8Cqcx8$xx9Cqcx9$xx10Cqcx10$x21331682310115220511327241632975133326416036081344032129455018752481696201155:Dw=DlwDt=3.20.61=2mm(56),;(89),,,,Dw2=Dw3=Dw4=Dw5=2mmD2=D4=2Dw2=4mm,Cq06=Cqc5=Cqw5-Cqf55:199921=Dlw5-Dlf5=3.171-1.53=1.641,(19)Dlw6=1.46,Dw6=1.46Dt=0.9mmDw7=Dt=0.61mm(4)D6=Dw6+(Dw5+Dw7)ö2=0.9+(2+0.61)ö2=2.2mmD8=2Dt=1.22mm0.5mm,D2=D4=4.5mm,D6=2.7mm,D8=1.7mm[2],5581300mm56#(:mm)2121241158105415-3.554831794121415+0129671521994151217-1181801167-1.67117+3137,,,,,,,,415mm,,5[2],,,,,,,[4],,[1].().,1994[2].1300.,1986[3],.().,1993[4]..,1997.4(19981012)(31)(