FRACTURE LIMIT LOAD OF CONE SHAPE PART IN DRAWING PROCESS FRACTURE LIMIT LOAD OF CONE SHAPE PART IN DRAWING PROCESS

FRACTURE LIMIT LOAD OF CONE SHAPE PART IN DRAWING PROCESS

  • 期刊名字:机械工程学报(英文版)
  • 文件大小:391kb
  • 论文作者:Xu Jisheng,Gao Shiyou
  • 作者单位:College of Mechanical Engineering
  • 更新时间:2020-11-22
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论文简介

CHINESE JOURNAL OF MECHANICAL ENGINEERING●398●Vol.18,No.3, 2005FRACTURE LIMIT LOAD OF CONEXu JishengSHAPE PART IN DRAWING PROCESS*Gao ShiyouCollege of Mechanical Engineeing,Yanshan University,Abstract: The deformation characters and load status of the blank's potential fracture zone are ana-Qinhuangdao 066004, Chinalyzed at the moment when blank is approaching to punch comer in drawing process of cone shapepart Based on tension instability theory, the formula for calculating facture limit load of cone shapepart in drawing process is derived. Also, the formula is analyzed and verifed by experiment.Key words: Cone shape part Drawingess Fracture limit load0 INTRODUCTIONConical wallTypical axisymmetric parts made by drawing are cylinderRpPunch~shape part, sphere shape part, and cone shape part and the ltter isthe most typical one. In terms ofdifferent relative cone top di-9年Pameter, cone shape can be converted to cylinder shape part orsphere shape part. Shaping of cone shape part is characterized by&-A0-一xthe forming of the hanging wall with curved surface. For stampingtechnology the most important thing is to determine the fracturea)limit load of the blank in deformation. Research work is thereforekpfocused on the determination of formation limit. Up to now asignificant advance has been made in this field and the, fracturelimit loads of cylinder shape parth-sy, sphere shape parts, andcone shape part are proposedlo, 7. However, some assumptionsthat are lack of support of experiment data are adopted in the re-lated research and the results obtained are not quite practical. Es-pecially for cone shape part the shortcoming mentioned above isobvious.In drawing process of cone shape part, conical wall is de-formned in the combination of tension and bulge and the flange isin compressive deformation!8. Instability fracture usually occurs(b)in the area that is to contact punch corner. Consequently, it is con-ig. Geometric model of istabliy fracturesidered that instability fracture results from over stretch. Also,instability fracture may be regarded as the defect caused by lowerWhen point Po is in the position of point P , the straight line,strength of conical wall.In the study on fracture limit load of cone shape part ind, which is a portion of generatrix of cone, becomes a length ofdrawing process the portion of the blank that has attached toarc, AoP, as shown in Fig.b. .punch cormner is analyzed. However, instability fracture usually 1.2 Deformation characteristies and load statustakes place in the process that the blank is closing to punch cormer.If the longitudinal strain increment at point P is representedSince instability fracture may be suppressed due to friction efectby mean longitudinal strain increment of dl when dl sticks towhen blank sticks to the punch, it is concluded that the study of punch corner, theninstability should concentrate on deformation characteristics andds-dI_ dload status of potential fracture zone in the process of closing to(de,)p =dI= dl-'(1)punch cormer,Longitudinal strain increment1 DEFORMATION CHARACTERISTICS ANDLength of arc formed by dl when it sticks toLOAD STATUS OF THE BLANK CLOSINGpunch comerTO PUNCH CORNERAnd the latitudinal strain increment (de)p at point P is (Fig)1.1 Closing of blank near punch corner(do,),=xs+X,-xn(2)In drawing process of cone shape part, instability fracturexmay appear at the contact point of conical wall and punch cor-Let ds be longitudinal difrential increment of arc at point Aoner". For an instant in drawing process a minimal segment ofof punch cormer, thereforeconical wall, dl (i.e. AoPo in Fig.a), is going to stick to punch cor-ner, that is to say, point Po sticks to point P in punch cormer and atsx, =√1+ yds ~ dscosapoint P conical wall is tangential to punch comer. The coordinate中国煤化工into Eq.(2) the fllow_of point Poising equ:YHCNMHGxro=xo + dlcosa.(山- dl)cosa(d&g)p =x + dIcosaAssume that A= xg /(dlcosax) , and bring it into the last equa-●This prject is supported by Doctoral Education Foundation of Ministy ofEducation of China (No.96021602). Received April 20, 2004; received in tion, thenrevisF亦数据I, 2005; accple June 2, 2005CHINESE JOURNAL OF MECHANICAL ENGINEERING●399Tbe expression of blank thickness is δ = S。expe, and &=(d&,)p =-;(d&,)p-(1 +a)s。is obtained from volume constancy. Therefore it is deri-It is obvious that when Po sticks to P, the strain ratioa at ved thatpointPisδ= 8,exp(-(1 + a)e.)(6)a=1+ ;(3)It is assumed that cone wall be conical surface whose genera-trix is straight line. On basis of equilibrium of axial force onBefore the cone whose generatrix is dI sticks to punch cormer, conical wall, and with aid of expression of forming load,the stress in direction along thickness should be zero and there are p = 2πδpxp(σ,)r sina(δ。is blank thickness at point P), and bylongitudinal stress σp and latitudinal stress σg in blank. Accordingvirtue of Eqs.(5), (6) and relation (e,)p =ε,the formula forto R. Hill's anisotropic plastic flow equation, it follows thatcalculating the fracture limit load p: can be obtainedds。dsgdeσ。-cσ。 σ。-coσ。 c。(σ。+σg) 。p= 2*g"5+(0(01+1-+01-1+1-1)”,(1+b)(1+r)(1-b)}+b]了where co=r/(1+r). Anisotropic cofficient in direction along thickness[1+a2+2ca 1ds- -. Increment of equivalent strainσ一. Equivalent stressa,√1+b-2cb. Strain in thickness directionSince the component of strain is only related to the instantxp (1+a)[(1+6)+(1-6)]1+(1-6),(7)stress state 4, the stress ratio b is(1+ b)(1 +r)2(1-b)2 +b]For plain strain state, (e)p=0, a=0, b= C。, and (p)= N,σ。 1+Coaδ= 8。exp(- n) , and the fracture limit load isBring Eq.(3) into the equation above, the following equationPo=2π Bxp68a,"*n*exp( -n)sinacan be obtainedUtilize all these expressions above in Eq.(7), it follows that_1+(1+ A)cg(4)P.=Ppo .(8)C。+(1+2)And Eq.(4) indicates that the stress in blank is not only re-F = exp(n)sina[(1+b2)+r(-b)}][1+r(1-b)]lated to anisotropic coficient, but also to parameter λ that repre-(1+ b)(+r91-b)°+川l xsents the deformation characteritics of the blank which is ap-proaching to punch corner.v1+a2 +2cga 72 FRACTURE LIMIT LOADa,√1+b2 -2cbThe experiment of grid method reveals that the deformationxp-a+a)[(1+bB)+r(1-b)]1+ r(-6))n(9)of conical wall is in combination of bulge (tension in two direc-(1+b)(1+r)*(1-b) +b]tions) and drawing (stretch in longitudinal direction and compres-sion in latitudinal direction), and on the wall there. is a strainPut expression of Pro and σ。 = B(n/e)" into Eq.(8), PI takesseparating circle in which longitudinal strain is zerol. This sug-the formgests that in the blank attaching to punch cormer both longitudinalstrain and latitudinal strain are tensile and in drawing processpoint Pis in tensile strain in two directions. Consequently, if in-p-=rEx,Fo.(.)(10)stability fracture occurs under this condition, according to insta-bility theory, the strain of the blank in length 司should have theApproximately, xp = R, , so thatform belowP= KFPo(11)。 [(1+b3)+r(1-6)]1+r(-6))。(1+ b)(1+r)2(1- b)^ +b]where K-- Relative cone top diameterActually, Po represents the fracture limit load of drawingwhere n-- Stain hardening exponentWhen instabilty fracture takes place at point P, the longitu-process of cylinder shape part whose forming die's inner diameterdinal strain (E。)p can be gained from the formula above. Tois the same as the forming die's of cone shape part. Since the workfor determining P1o is well done, the fracture limit load of conerefer to formulae for σ and ε and follow hardening law2]shape part can be obtained if only parameter F is determined.σ= BE"3 EXPERIMENTAL VARIFICATION OFwhere B- Hardening coefficient and letPARAMETER Fa, =1+r/V1+2rItc |中国煤化工. relationship with mate-the following equation is obtainedrial par) depends on parameterh. SincYHC N MH Gity facture 0ccurs in(1+a2 +2c,a)plane staiu slauc u.c. lusuaullly lawuc uf cylinder shape part ofo。= Ba,"√1+b2-2c。b(5) drawing during sticking to punch comer), a= 90,cosa=0,h→∞,(d&,)p=0,F =Fx=1.For drawing of cone shape part, dl is not predicable, however,●400●Xu Jisheng. et al: Fracture limit load of cone shape part in drawing processit is certain once forming process begins. Since d is far smallerthan x看, aproximately d=r, (sis radius of punch cormen), 4 CONCLUSIONSand meanwhile x的 =R-rp (Rp is radius of punch). Conse-(1) In drawing of cone shape part the increment ratio of lon-gitudinal strain to ltudinal strain of blank closing to punch cormerquently, h has the formcan be determined by referring to the parameters that comprehen-R-rsively reflect the deformation characteristics of blank near punchrp cosacomer(2) The formula for fracture limit load of drawing of conewhere λ is the geometric parameter that reflects the deformation shape part is proposed based on instability theory.characteristics of the blank at punch corner.(3) The result of experimental verification of formula forExperiment was conducted to verify parameter F in drawing fracture limit load is in good accordance with that obtained fomprocess of cone shape part. The mechanical property of blank calculation and the error is within 5%.used is shown in Table 1. The inner diameter of die is 160 mm.BHF is in a range of 25 kN to 124 kN, Diameter of the blankReferencesranges from 200 mm to 280 mm. Oil is used as lubricant. Theexperiment device introduced in Ref,[9] is used to conduct theLi M Q. Determination on the limit drawing ratio for the deep drawing ofdrawing of cone shape part. Fracture limit load is measured bysheet metals. Chinese Joumal of Mechanical Engineering, 1995, 31():measuring instruments at moment when fracture occurs and the78-82 (In Chinese)。2 Liang B W, Hu S G. Plasticity theory of sheet metal forming. Beijing:height of the part h at that moment is also measured.RanknererpFect torc blank and punch comer. PlasticTable 1 Mechanical properties of metal sheetWorking ofMetals, 1981, 22 (243): 393- -397 (In Japanese)Mechanical propertyHu S G. Cold forming of sheet metal and its principle. Beijing: DefenseIndustry Publishing House, 1979 (In Chinese)Hardening Hardening AnisotropyMaterial StrengthElongationKoyamahideo, Kawadakatu, Tozawayasu, Limit defomnation conditioo ofcoefficient exponentcofhcientblank in sphere forming. Plastic Working of Metals, 1986, 27(306):o:/MPa8B/MPa846-851 (In Japanese)SPCC329.55568.900.2121.3 4 06 Gao J, Boyce M C. A pedictive tool for delaying wrinking and tering-failures in sbeet metal forming. Transactions of the ASME, 1997, 11(9):374.350.263655.370.2201.183354- -3655754M210.470.145419.88,0.276Wan M, Yang Y Y, Li s B. Determination on limit loading of drawingprocess of cone shape part. Chinese Joumal of Mechanical Engineering,1997, 33(3): 80-86 (In Chinese)Since there is indentation made by punch comer on deformedSun w H, Xiong H M Study on drawing process of cone shape part.blank, point P can be identified and the radius, xp, can be meas-Joumal of Plasticity Engineering, 1997, 4(2): 42-46 (In Chinese)ured with microscope. Based on measured datum h and the rela- 9 Wan M, Ma L x, Li s B. Development and application of experimentaltion between the depth of formed cone shape part and approachingdevice for drawing of general shape parts. Forging eand Stamping Tech-die angle a, the latter can be determinedo. Subsequently, Po can10 JiaW.Gaosy. SongS D. Analysis of geometric model for drawing ofbe calculated. Table 2 shows parameter F gained from experimentcone shape part. Journal of Shenyang Instiute of Technology, 2000, 19(2):and calculation, respectively. It can be seen from Table 2 that for29- 33 (In Chinese)three brands of metal sheet parameter F obtained from calculatingis in good accordance with that gained in experiment and the er- Biographical notesrors are 4.8%, 1 .8% and 2.8% respectively.Xu Jisheng is currently an associate professor in Forging and Stamping Institute,Yanshan University, China. He engages in research of forging and stampingTable 2 Comparison between parameter F gainedtechnology and CAD/CAPP.by calculating and gained by experimentTel: +86-335-8057011; E mail: jsxu@ysu.edu.cnCornerParameter Parameter DittoDittoGao Shiyou is currently a professor in Forging and Stamping Institute, YanshanMaterial radiusrulis Approaching(alulated) (experiment) (mean)experiment)(mean,University, China. He reccived his PhD degree from College of Mechanicalangle a /radmmEngineering, Yanshan University, China. His research interests include forgingand stanping tecnologyo CAD/CAM and computer simulatin.0.896 30.75390.759 1Tel: +86-335 8050340; E-mail: gao58@sina.com0. .90710.7600.732 2SPCC10.8875748,0.70530.7492 0.723 8_0.864 70.73390.698 60.94640.785 00.85911.02930.8313 .0.834751.037 00.835 20.8226 0.8088 0.82380.928 50.77450.79821.004 60.81800.804 3.0.52420.47880.464 10.57970.524 60.56455754M 60.5332 0.548 50.571 20.57900.621 40.5580.5864中国煤化工MYHCNMHG

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