A simple method to determine pressure curve for sheet hydro-forming and experimental verification

Journal of Materials Processing Technology 169 (2005) 134–142

A simple method to determine pressure curve for sheethydro-forming and experimental verification

Hyunbo Shima,∗, Dong Yol Yangb

a School of Mechanical Engineering, Yeungnam University, 214-1 Daedong, Gyongsan 712-749, Republic of Koreab Department of Mechanical Engineering, KAIST, Daejeon, Republic of Korea

Received 12 November 2002; accepted 14 February 2005

Abstract

A simple method to determine optimal pressure curve for sheet hydro-forming has been proposed. The determination of the pressure curveis carried out by characterizing the curve three parameters, e.g. initial pressure, final pressure and pressure path. Through the study of previousworks, general shape of the pressure curve for hydro-forming is monotonically increasing with respect to a punch stroke. Since the penetrationvolume to a pressure chamber by a punch is of the similar characteristics as the punch stroke, and the shape of the pressure–stroke curve isn roke. Duringt rom a dies pressure,t ard manners.T ve has beend ro-formingp trol system.T sful formings©

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on-linear in general, the pressure path is assumed to be proportional to the penetration volume by a punch, rather than punch sthe hydro-forming experiment, it is observed that the major cause of failures in the early forming stage is related to lifting of a blank furface due to the penetration of punch. Now the initial pressure is determined from the lifting-prevention condition. From the initialhe assumption of pressure path and some chosen trial final pressure values, the pressure curves are interpolated in a straightforwhen, FE analyses are carried out to predict whether failure occurs or not. From the result of FE analysis, optimal final pressure curetermined among the trial final pressure curves. The corresponding experiment has been carried out with an experimental hydress where the pressure is controlled by a proportional relief valve. The press is relatively inexpensive, under an open-loop conhrough the comparison of experiment and analysis, the predicted pressure curve has been verified an optimal for the succesince no defect has been observed.2005 Elsevier B.V. All rights reserved.

eywords: Sheet hydro-forming; Optimal pressure curve; Open-loop control

. Introduction

The hydro-forming is considered as one of core technolo-ies for the Ultra Light Steel Automotive Body (ULSAB)roject together with the tailor welded blank technology.he hydro-forming process is a kind of sophisticated form-

ng process utilizing fluid as pressure media. The success ofhe hydro-forming process is mainly determined by pressureath.Fig. 1 shows a schematic diagram of the sheet hydro-

orming process.Initial pressure is the most significant parameter, since

he initial condition determines whether the process will suc-ess or fail. Too low initial pressure causes lifting of blank

∗ Corresponding author. Tel.: +82 53 810 2573; fax: +82 53 813 3703.E-mail address: [email protected] (H. Shim).

and makes the process instable from an early forming sExcessive initial pressure causes necking at the unsuppregion between punch and die. Insufficient pressure cawrinkling of flange. On the other hand, too high presscauses necking near the punch shoulder. Therefore, thesure should be carefully maneuvered between the wrincondition and the necking condition so as to avoid faithroughout the process.

Even though the pressure versus the punch stroke relaship is a crucial factor, no general method to determinerelationship for this process has been established yet,research works have been made only by a few researchethis process.

Tirosh et al. [1] found an appropriate relationship fpressure versus punch stroke so as to maintain the tness unchanged for the hydro-forming of axisymme

924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2005.02.268

H. Shim, D.Y. Yang / Journal of Materials Processing Technology 169 (2005) 134–142 135

Fig. 1. Sheet hydro-forming process.

shapes by using the upper bound method. Yossifon etal. [2] derived a theoretical relationship for wrinkling foraxisymmetric hydro-forming. Yossifon and Tirosh[3] con-sidered normal anisotropy in the analysis of the instability inhydro-forming.

The first research for the hydro-forming of arbitraryshaped-cup is carried out by Noh and Yang[4,5]. They pro-posed a kinematically admissible velocity field for regularpolygonal boxes, based on the assumption of zero thicknessstrain similar to the Tirosh’s work. Optimal pressure curvehas been derived with the UBET. In order to validate the pre-dicted pressure curve experimentally, they developed hydro-forming machine for which closed-loop control of pressurewith an electro-magnetic relief valve is employed.

The reason why the zero thickness strain condition, in allthe above method is utilized, is not clear though. since thethickness is of small values compared to the other dimen-sions and is not good enough to become a main constraintfor the description of the process with the upper boundmethod.

Yang et al.[6] analyzed an axisymmetric hydro-formingprocess with the finite element method and verified theresult through the experiment. In the study, they used pres-sure curve predicted by Tirosh et al.[1]. Hsu and Chu[7] also analyzed a hydro-forming process with the finiteelement method and showed that hydro-forming improvess eina ngo g,t outs

ofh ller.K

In this study, a simple method, to determine optimal pres-sure curve for the sheet hydro-forming process, based on theFE analysis has been proposed and the corresponding exper-iments are carried out to verify the recommended pressurecurve.

2. Determination of pressure curve

Since the pressure curve is characterized by the threefactors, initial pressure, final pressure and pressure path, adetermination of the pressure curve means the determinationof those three factors.

During the study of previous works[3–5], an interestingfact has been recognized that the shapes of the optimal pres-sure curve are always monotonically increased with respect topunch stroke. The reason why the shape of the pressure curveis monotonically increasing is attributable to the nature of thehydro-forming process itself, because radii of curvature at theedges of hydro-formed product are always decreasing duringthe forming stage in order to get a detailed trace of die shape.Exploiting the characteristics of the pressure curve, a rathersimplified method based on FEM can be devised instead of theupper bound technique. Since the punch penetration volumeduring the forming is also monotonically increasing, similarto the pressure curve, the pressure path has been assumed tob

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train distribution and hence better formability results. Hnd co-workers[8–10] developed integrated hydro-formif sheet pair, in which performing via hydro-formin

rimming, welding and hydro-calibration are carriedimultaneously.

Lee and Cho[11] built dynamic model for the designydraulic control system and suggested CMAC controim [12] designed a fuzzy based controller.

e proportional to the punch penetration volume.During the hydro-forming experiment, it is observed

rinkling has been always occur if the blank has been lrom the die surface, especially when the punch starts totrate, in the early stage. Therefore, the lifting phenomf blank, which can be prevented by a sufficient presnough to keep the blank contact to the die surface, isidered as the major cause of failures in the early formtage. Now the initial pressure can be determined fromifting-prevention condition.

Optimal pressure curve can be interpolated in a straorward manner if a final pressure is assumed, since bonitial pressure and the shape of pressure curve havelready determined. With some chosen trial final presalues, FE analyses have been carried out and the opressure curve is determined after examining the strain

ribution and occurrence of failure from the FE result.Fig. 2(a–d) shows the geometry of the punches use

he study.Fig. 2(a) is of a hemispherical punch,Fig. 2(b) is aylindrical punch,Fig. 2(c) is a regular hexagonal prismaunch andFig. 2(d) is a concave-bottomed cylindrical punable 1shows the blank size used in the study, where draatio is somewhat higher than that of ordinary deep drawable 2shows properties of blank material, SPC-1.

.1. Initial pressure

In the very early forming stage, shearing deformaode occurs near the unsupported region between diend punch round, as punch penetrates and then dra

136 H. Shim, D.Y. Yang / Journal of Materials Processing Technology 169 (2005) 134–142

Fig. 2. Punch geometry used in the study: (a) hemispherical punch; (b) cylindrical punch; (c) hexagonal punch; (d) concave-bottomed punch.

stretching, bending or mixed deformation mode occurs after-ward.

If initial pressure is too low, then the blank tends to liftup from die surface as the punch penetrates and causes theprocess instable.

Table 1Size of blank used in the study

Punch shape Forming depth(mm)

Blank size(φ)

Drawingratio

Hemispherical punch (φ 45) 22.5 80 1.7830.0 90 2.00

Cylindrical punch (φ 45) 20.0 80 1.7825.0 90 2.00

Hexagonal punch (φ 42) 12.0 72 1.71

Concave-bottomed cylindricalpunch (φ 45)

20.0 80 1.78

25.0 90 2.00

Therefore, the initial pressure has to be enough to sup-press the blank from lifting. Now minimum required initialpressure can be determined from the condition.

Equation(1) is the punch force to cause shearing of theblank and equation(2) is blank holding force by the fluidpressure acting on a flange area, e.g. die contacting area

Fpunch= πdtσy√

3(1)

Table 2Properties of blank material (SPC-1)

Young’s modulus E = 2.21× 105 MPaPoisson’s ratio ν = 0.3Thickness t0 = 0.80 mmStress–strain curve σ̄ = 466.0(ε̄ + 0.001)0.22 MPaLankford value R = 1.37

Friction coefficient µ = 0.24 (punch/blank)µ = 0.12 (die/blank)


Fflange= π

4(D2 − d2)preq (2)

whereD is the blank diameter,d the diameter of blank contactregion to the punch at initial stage,t the blank thickness,σy thetensile yield stress of blank material andpreq is the requiredinitial pressure.

If the suppressing force due to fluid pressure is less than thepunch force, then the blank tends to lift up. The suppressingforce due to fluid pressure should be higher than punch forcefor the stable start up of the process

Fflange> Fpunch (3)

Now the minimum required initial pressure becomes,

preq = 4dtσy√3(D2 − d2)

(4)

During FE analysis with the initial pressure determined byequation(4), it is observed that wrinkling has been occurredfor hexagonal shaped cup, differently from the cylindricalcup. The reason may be attributed to the folding of walls inthe hexagonal cup. During the forming, circumferential com-pressive stress is subjected to the wall, and combined foldingand compressive stress give occasions to wrinkling. Once thewrinkling is occurred, the wrinkling is always getting biggerand never diminishing due to the circumferential compressives thee

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Table 3Required initial pressure and initial pressure setting

Punch shape Blank size (φ) preq (MPa) pini (MPa)

Hemispherical punch (φ 45) 80 0.52 190 0.41 1

Cylindrical punch (φ 45) 80 3.35 690 2.41 3

Hexagonal punch (φ 42) 72 4.00 8

Concave-bottomedpunch (φ 45)

80 3.35 15

90 2.41 10

Table 4Predicted thickness strain from FE analysis (hemispherical,φ 80)

pfinal Maximum strain (%) Minimum strain (%) Note

20 6.58 −8.20 Wrinkling21 6.51 −8.26 Wrinkling22 6.45 −8.33 Success23 6.34 −8.42 Success25 6.23 −8.63 Success30 6.01 −9.29 Success

carried out for some trial final pressure values. Optimal pres-sure curve is determined among the trial cases after examin-ing the FE results, e.g. strain distribution and occurrence offailure.

Table 4shows strain values and occurrence of failure pre-dicted at drawing depth 22.5 mm by the FE analysis with thehemispherical punch andφ 80 blank for some chosen valuesof final pressure. FE analysis has been carried out with thedynamic explicit stamping analysis S/W SAIT-Stamp[13].Wrinkling has been occurred when the final pressure is lessthan 21 MPa. As the high final pressure results in high thin-ning, the final pressure is determined as 22 MPa.

Table 5shows the same results when the blank size isφ

90 and drawing depth is 30.0 mm. While low pressure giveswrinkling similar to the result ofTable 5, excessive pressureresults in fracture. Therefore, final pressure is determined as28 MPa.

Fig. 3 shows the recommended optimal pressure curvesfor hemispherical shape forming. Although higher final pres-sure is required for larger blank, pressure is lower than thatof smaller blank at the same drawing depth because of thedifferent punch stroke.

Table 5Predicted thickness strain from FE analysis (hemispherical,φ 90)

p

222233

tress. Therefore, the wrinkling should be prevented fromarly stage of forming.

Since the initial pressure determined by equation(4) doesot consider forming characteristics, e.g. folding, the inressure is modified for a stable forming:

ini = βpreq > β4dtσy√

3(D2 − d2)(5)

herepini is the initial pressure setting andβ is the correcion factor to compensate forming difficulty due to shapross-section (β ≥ 1); circular section: 1≤ β ≤ 2; polygonaection: 2≤ β ≤ 3; sharp-radius of curvature: 4≤ β ≤ 5.

The reason why the correction factorβ is introduced ishat the polygonal section, like hexagonal section, wrinkccurs at a lower pressure than a smooth rounded circula

ion. For circular sections, such as hemispherical punchylindrical punch, the correction factorβ is small compareo the case of the hexagonal punch and concave-bottunch.

Table 3shows that required initial pressure to preventng and initial pressure setting.

For hemispherical cup forming, the correction factoβs higher than recommended value, since minimum inressure is 1 MPa for the current hydro-forming press.

.2. Final pressure

With the already determined initial pressure andssumption of pressure path for which the pressure isortional to the punch penetration volume, FE analyse

final Maximum strain (%) Minimum strain (%) Note

5 8.97 −14.30 Wrinkling6 8.73 −14.80 Wrinkling7 8.60 −15.41 Wrinkling8 8.33 −16.02 Success0 7.92 −17.81 Success5 6.01 −58.12 Fracture


Fig. 3. Recommended pressure curve (hemispherical cup).

Same approach to determine the final pressures for eachcase has been applied and the results are summarized inTable 6.

3. Experiment

3.1. Hydro-forming machine

Fig. 4shows the CNC hydro-forming machine for exper-iment. Control system for this machine is composed of fourparts, e.g. forming part, hydraulic power system, computerinterface and measurement part.Fig. 5 shows a schematicdiagram of control system for the present hydro-formingmachine.

Since the maximum possible hydraulic pressure by thehydraulic pump is 21 MPa and the design pressure for theforming chamber is 55 MPa, a booster is used to amplify thesystem pressure required for hydro-forming.

Table 6Summary of pressure setting

Punch shape Blanksize (φ)

pini (MPa) pfinal

(MPa)

Hemispherical punch (φ 45) 80 1 22

C

H

C

Fig. 4. CNC hydro-forming press.

Fig. 5. Control system for hydro-forming press.

The recommended pressure curve is employed as a mastercurve for pressure control. During the hydro-forming process,the hydraulic pressure in the pressure chamber is controlledby tracking the given pressure–stroke curve by a electroni-cally controlled proportional relief valve based on open-loopcontrol system. The punch stroke is measured by LVDT andits signal is fed into the computer through I/O interface.

Fig. 6. Deformed specimen (φ 80, depth 22.5 mm).

90 1 28

ylindrical punch (φ 45) 80 6 3390 3 35

exagonal punch (φ 42) 72 8 41

oncave-bottomedpunch (φ 45)

80 15 40

90 10 45


Fig. 7. Pressure–stroke curve (hemispherical cup,φ 80, depth 22.5 mm).

3.2. Experiment

In order to verify the validity of the pressure–stroke curvedetermined from the current study, the corresponding exper-iment have been carried out for the hemispherical, cylindri-cal, hexagonal and concave-bottomed cylindrical punches,as shown inFig. 1. Tables 1 and 2show the shapes and thematerial properties of the blank for each experiment.Table 6shows the pressure settings that are determined by the presentstudy.

3.2.1. Hemispherical cupFig. 6 shows a successfully formed specimen using the

recommended value inTable 6. Fig. 7 compares the refer-ence pressure and an actual pressure measured at the pressurechamber to show the whether the hydraulic pressure con-troller traces the master curve well. The measured pressureseems to trace quite well to the master pressure curve, inspite of open-loop hydraulic pressure control. Since there isno feedback in the open-loop control, some deviation fromthe reference curve has been occurred. Bearing in mind thatthe hydraulic system is based on a proportional relief valve,instead of relatively expensive servo-valve, the tracing capa-bility of hydraulic pressure control system found to be quitewell. The reason why the satisfactory tracing capability beena cter-i e isa ess,t ropor-t osth

Fig. 8. Thickness strain (hemispherical cup,φ 80).

Fig. 9. Wrinkling due to insufficient pressure (φ 80).

Fig. 8 shows distribution of thickness strain along theradial direction with comparison to the FE analysis. Sincethe thickness strain lies in the range of−0.1≤ εt ≤ 0.1, thethickness strain distribution shows more uniform than theordinary deep drawing, for which the thickness strain lies in

Fig. 10. Deformed specimen (φ 80, depth 20 mm).

chieved at the proportional valve is ascribed to the charastics of hydro-forming itself. Since the forming pressurlways monotonic increasing in most hydro-forming proc

here is no need to decrease the pressure therefore pional valve is good enough for the pressure control of mydro-forming processes.


Fig. 11. Pressure curve (cylindrical cup,φ 80).

the range of−0.3≤ εt ≤ 0.2 in general. Therefore, both thereference pressure determined by the present method and thetracing capability of pressure controller are verified.

Fig. 9 shows a wrinkled specimen for which the initialand final pressures are 7 and 17 MPa, respectively, while theoptimal pressures for this process are 1 and 22 MPa, respec-tively, as listed inTable 6. Although the forming processstarted from 7 MPa, higher than the optimal initial pressure,wrinkling occurred at a lower pressure since the pressure islower than the optimal pressure.

3.2.2. Cylindrical cupFig. 10shows a successfully formed cylindrical specimen

using the recommended value inTable 6.Fig. 11 compares the master pressure curve and a mea-

sured pressure curve during the experiment to show thewhether the hydraulic pressure controller traces the mastercurve. The measured pressure traces to the master pressurecurve successfully.

Fig. 12. Thickness strain (cylindrical cup,φ 80, depth 20 mm).

Fig. 12shows a distribution of the thickness strain withcomparison to the analysis and the both results coincide well.The thickness strain distribution shows more uniform than theordinary deep drawing.

3.2.3. Hexagonal cupFig. 13shows a successfully formed hexagonal specimen

with blank sizeφ 72 with comparison to the deformed shapepredicted by the FE analysis. Differently from the previouscircular shape, folding at the wall lets the process instable.During the FE analysis, it has been found that sufficient form-ing pressure should be applied at initial forming stage, sincethe enough stretching at the corner of hexagonal shape makesthe process stable from the early stage of forming.

Fig. 14shows wrinkled specimen due to insufficient pres-sure for which initial and final pressure for this cup is 2 and25 MPa, respectively, which are much lower than the recom-mended values, 8 and 41 MPa, respectively. From the result,it has been known that failure occurs if the pressure doesnot follow the recommended optimal pressure curve and therecommended pressure is verified optimal.

Figs. 15 and 16show distribution of the thickness strainalong the transverse direction and diagonal direction, respec-

ed sp
Fig. 13. (a and b) Deform ecimen (φ 72, depth 12 mm).


Fig. 14. Wrinkling due to insufficient pressure (hexagonal cup).

Fig. 15. Thickness strain (hexagonal cup, traverse direction).

tively, with comparison to the analysis and the both resultscoincide well except for the wall region. However, the thick-ness strain distribution shows more uniform than the ordinarydeep drawing.

Fig. 16. Thickness strain (hexagonal cup, diagonal direction).

Fig. 17. Deformed shape (φ 90).

3.2.4. Concave-bottomed cylindrical cupFig. 17shows a hydro-formed specimen withφ 90 blank.

Earing is observed at the flange due to the planar anisotropyof the blank material. Differently from the ordinary deepdrawing, single stage forming of the concave-bottomed cup isenabled due to the action of hydraulic pressure at the bottomof the cup.

Fig. 18compares the reference pressure curve and a mea-sured pressure curve during the experiment to show thewhether the hydraulic pressure controller traces the mastercurve.Fig. 19compares thickness strain distribution and bothresults coincide well.

Fig. 18. Pressure curve (cylindrical cup with concave bottom,φ 90).


Fig. 19. Thickness strain distribution (cylindrical cup with concave bottomφ 90).

4. Conclusion

A simple method to derive an optimal pressure curvehas been proposed for sheet hydro-forming process. In themethod, the pressure curve for hydro-forming process hasbeen characterized by the three factors, initial pressure, finalpressure and pressure path. The pressure path, e.g. the shapof pressure curve is assumed to be proportional to the punchpenetration volume. The initial pressure is derived from nolifting condition of the blank and final pressure is obtainedfrom result of FE analysis.

With the determined pressure curve, the correspondingexperiments have been carried out with a CNC hydro-formingpress where pressure is controlled in an open-loop by a elec-tronically controlled proportional relief valve.

Through the comparison of experiment and analysis, thepredicted pressure curve has been verified optimal pressure

curve for the successful forming since no defect has beenobserved.

Acknowledgement

This research work has been supported by the YeungnamUniversity research grant.

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[3] S. Yossifon, J. Tirosh, Rupture instability in hydro-forming deepdrawing process, Int. J. Mech. Sci. 27 (1985) 559–570.

[4] T.S. Noh, D.Y. Yang, Analysis of hydro-forming of regular polygonalboxes, Int. J. Mech. Sci. 29 (1987) 139–148.

[5] T.S. Noh, D.Y. Yang, A general formulation for hydro-forming ofarbitrarily shaped boxes and its application to hydro-forming of anelliptic-circular box, J. Manuf. Sci. Eng., Trans. ASME 120 (1998)481–488.

[6] D.Y. Yang, H.J. Kwon, T.S. Noh, W.J. Chung, Rigid-plastic finiteelement analysis of axi-symmetric hydro-forming with controlledpressure, KSME 14 (3) (1990) 571–580 (in Korean).

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[8] P. Hein, Vollertsen, Hydro-forming of sheet metal pairs, J. MaProcess. Technol. 87 (1999) 154–164.

[9] O. Kreis, P. Hein, Manufacturing system for the integrated hyforming, trimming and welding of sheet metal pairs, J. Mater.cess. Technol. 115 (2001) 49–54.

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Documents

A simple method to determine pressure curve for sheet hydro-forming and experimental verification