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4.5. FEM Based Design of MUDD Process
The basic deformation characteristics were clarified in Section 4. It can be seen that the material flow control by the ultra high pressure and punch displacement and the control of deformation area by constraint of blank deformation is important to achieve the high aspect ratio in MUDD process.
They strongly depends on the tooling and process parameters. In MUDD, there are many parameters in MUDD and its relationship is not clarified. In this section, the effect of tooling and process parameters in MUDD are investigated and the forming condition is optimized.
4.5.1. Effect of friction coefficient on deformation behavior
Fig. 4.12 shows the effect of friction coefficient between the blank, the 1st and 2nd punches on change of strain distribution in thickness direction. For the low friction coefficient, the thickness reduces with repeating the cycles. In addition, the position of cup edge is almost the same during MUDD process. It is because the blank edge does not flow into the die cavity but moves upward at pressurization process as shown in Fig. 4.10. As a result, the excessive thinning occurs at punch shoulder due to no material flow and the concentration of deformation area at punch shoulder. On the other hand, for high friction coefficient, the thickness reduction occurs during at punch shoulder MUDD process, but is not significant. In addition, after the blank contacts with the 2nd punch, the thickness does not reduce as shown in Figs. 4.12 (b) and 4.13. It is because the friction holding effect occurs and it restricts the thickness reduction at the contact area between the blank and the 2nd punch. Thus, the high friction coefficients between the blank, the 1st and 2nd punches are important to restrict the thickness reduction at punch shoulder by the friction holding effect.
However, because MUDD uses the fluid medium to apply ultra high pressure, there is some possibility of inserting the fluid medium into the gap between the blank and punches. It is difficult to keep the dry friction between the blank and punches. Furthermore, the tensile stress in meridional direction occurs at the punch shoulder at pressurization stage as shown in Fig. 4.14. The tensile stress at punch shoulder can be reduced in the case of high friction coefficient; however, the tensile stress in meridional direction cannot be zero. It means that this process possibly has the risks of thickness reduction and fracture. It shows that the quite high forming limit cannot be achieved using high friction coefficient alone.
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(a) Low friction coefficient between the blank, the 1st and 2nd punches (𝜇𝑠 =0.02, 𝜇𝑘=0.01)
(b) High friction coefficient between the blank, the 1st and 2nd punches (𝜇𝑠=0.35, 𝜇𝑘=0.30) Fig. 4.12 Effect of friction coefficient between the blank, the 1st and 2nd punches on strain
distribution in thickness direction at pressurization process in MUDD (𝐷𝑅 =5.4, taper punch, 𝑟𝑝𝑖1=0.05mm, without stopper, ∆𝑠 =0.05mm, 𝑝𝑐= 𝑝𝑟=200~380MPa, 𝑡 =50μm).
2ndcycle
1stcycle 3rdcycle
Excessive thinning Initial
2ndcycle
Initial 4thcycle 6thcycle 8thcycle 10thcycle
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Fig. 4.13 Change of thickness strain distribution during MUDD process (𝐷𝑅 =5.4, taper punch, 𝑟𝑝𝑖1=0.05mm, without stopper, 𝜇𝑠 =0.35, 𝜇𝑘=0.30 (Blank-1st and 2nd punches),
∆𝑠 =0.05mm, 𝑝𝑐= 𝑝𝑟=200~380MPa, 𝑡 =50μm).
(a) Low friction coefficient between blank, 1st and 2nd punches (𝜇𝑠 =0.05, 𝜇𝑘 =0.03)
(b) High friction coefficient between blank, 1st and 2nd punches (𝜇𝑠 =0.35, 𝜇𝑘=0.30) Fig. 4.14 Effect of friction coefficient between blank, 1st and 2nd punches on meridional stress
distribution during MUDD (𝐷𝑅 =5.4, taper punch, 𝑟𝑝𝑖1=0.05mm, without stopper,
∆𝑠 =0.05mm, 𝑝𝑐= 𝑝𝑟=200~380MPa, 𝑡 =50μm).
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0 1 2 3 4 5
Thickness strain εt
Distance from cup center x/D
p1
stdrawing
MUDD (2
nddrawing)
Lifting up 1st punch stage
Pressurization stage
Lifting down 1stand 2nd punches stage
Tensile stress
Zero meridional
stress
Lifting up 1st punch stage
Pressurization stage
Lifting down 1stand 2nd punches stage
Reduction of tensile stress by friction
holding effect Zero meridional
stress
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4.5.2. Effect of tooling conditions on deformation behavior
Fig. 4.15 shows the effects of existence of stopper and punch shape on change of strain distribution in thickness direction. In flat punch without stopper, the excessive thinning occurs at punch shoulder due to the low friction holding effect at low friction coefficient between the blank, the 1st and 2nd punches as shown in Fig. 4.15.(a). By adding the stopper, the thickness reduction does not occur during MUDD process and the excessive thinning can be avoided even though the friction coefficients between the blank, 1st and 2nd punches are low as shown in Fig. 4.15.(b). However, the thickness is still reduced at 2nd punch shoulder and the excessive thickening occurs at 1st punch shoulder as shown in Fig. 4.16 (a). In the case of taper punch, the excessive thinning can also be avoided using the stopper, although it occurs without the stopper as shown in Figs. 4.15(c) and (d).
Moreover, the thinning does not occur at the 2nd punch shoulder and the excessive thickening can be restricted as shown in Fig. 4.16(b).
By using the stopper in MUDD process, the blank is subjected to the compression stress in meridional direction unlike no stopper as shown in Figs. 4.14(a) and 4.17. It is because the deformation and movement of blank at the 1st punch side wall is constrained by the stopper. Hence, the deformation area of blank is localized at the flange area and the material flows into the die cavity.
Therefore, not the tensile stress, but the compression stress occurs in flange area by using the stopper in MUDD. It is why the excessive thinning can be avoided in flat and taper punch with stopper.
However, because the compression stress occurs in pressurization stage by using the stopper, the buckling in meridional direction occurs at flange area. Particularly, the buckling is large in the case of flat punch and the insufficient material flow is resulted in area A as shown in Fig. 4.15(b). This insufficient material flow in area A causes the lack of material flow in area B and thinning at the 2nd punch shoulder is resulted. At the same time, the excessive thickening occurs because the material dose not flow from area A to the die cavity but the material flows from the 1st punch side wall to area A. As explained above, the nonuiform material flow in areas A and B causes the thinning behavior at the 2nd punch shoulder and the excessive thickening behavior at the 1st punch shoulder in the flat punch with stopper.
On the other hand, in the case of taper punch, the buckling in the meridional direction can be significantly improved and the material flow becomes uniform as shown in Fig. 4.15(d). Therefore, the thinning at the 2nd punch shoulder and the excessive thickening at the 1st punch shoulder can be avoided because the material flows into the die cavity properly. As mentioned above, the stopper and taper are effective to avoid the thinning and fracture.
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(a) Without stopper in flat punch
(b) With stopper in flat punch
(c) Without stopper in taper punch
2
ndcycle
Initial 4
thcycle 6
thcycle
Excessive thinning
2ndcycle
Initial 4thcycle 8thcycle
Excessive thickening
10thcycle 6thcycle
Buckling Node locus
B A
Nonuniform material flow
2ndcycle
1stcycle 3rdcycle
Excessive thinning Initial
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(d) With stopper in taper punch
Fig. 4.15 Effect of stopper and punch shape on strain distribution in thickness direction at pressurization process in MUDD (𝐷𝑅 =5.4, 𝑟𝑝𝑖1=0.05mm, 𝜇𝑠 =0.02, 𝜇𝑘=0.01 (Blank-1st and 2nd punches), ∆𝑠 =0.05mm, 𝑝𝑐= 𝑝𝑟=200~380MPa, 𝑡 =50μm).
(a) In flat punch 2ndcycle
Initial 4thcycle 6thcycle 8thcycle 10thcycle
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0 1 2 3 4
Th ic kne ss stra in ε
tDistance from cup center x/D
p1
stdrawing
MUDD (2
nddrawing)
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(b) In taper punch
Fig. 4.16 Change of thickness strain distribution during MUDD process (𝐷𝑅 =5.4, 𝑟𝑝𝑖1=0.05mm, without stopper, 𝜇𝑠 =0.02, 𝜇𝑘=0.01 (Blank-1st and 2nd punches), ∆𝑠 =0.05mm, 𝑝𝑐= 𝑝𝑟=200~380MPa).
Fig. 4.17 Meridional stress distribution during MUDD with stopper (𝐷𝑅 =5.4, taper punch, 𝜇𝑠=0.02, 𝜇𝑘=0.01 (Blank-1st and 2nd punches), 𝑟𝑝𝑖1=0.05mm, ∆𝑠 =0.05mm, 𝑝𝑐= 𝑝𝑟=200~380MPa, 𝑡 =50μm).
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0 1 2 3 4
Th ic kne ss stra in ε
tDistance from cup center x/D
pMUDD (2
nddrawing)
1
stdrawing
Lifting up 1
stpunch stage
Pressurization stage
Lifting down 1
stand 2
ndpunches stage
Zero meridional
stress
Compression
stress
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Fig. 4.18 shows the effect of the 1st punch inner shoulder radius on strain distribution in thickness direction. Using the large the 1st punch inner shoulder radius, the blank at the 1st punch inner shoulder is subjected the reverse bulge deformation. It causes that no material flow and no deformation at flange area by applying the ultra high pressure because the stiffness at the 1st punch inner shoulder area increases. Therefore, the micro cup cannot be fabricated in the large the 1st punch inner shoulder radius. Thus, the partial high stiffness interferes the material deformation at flange area. The nouniform material flow by partial high stiffness is also resulted in the small punch shoulder radius. The small punch inner shoulder radius and large punch shoulder radius are required to obtain the uniform material flow in MUDD.
Fig. 4.19 shows the effect of foil thickness on strain distribution in thickness direction. When the thickness of 20μm is used, not only the buckling in the meridional direction, but also the wrinkling in the circumferential direction occurs. The buckling can be eliminated by compressing it using the 1st punch and die because it occurs at flange area. On the other hand, the winkling occurs at die shoulder area. Accordingly, the wrinkles cannot be eliminated by compression using the 1st punch.
By using the thickness of 50μm, the wrinkling can be prevented due to the high bending stiffness for the thick thickness. From these results, the foil thickness of 50μm is used in the MUDD.
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Fig. 4.18 Change of thickness distribution during MUDD with large 1st punch inner shoulder (𝐷𝑅 =5.4, taper punch, 𝑟𝑝𝑖1=0.10mm, with stopper, 𝜇𝑠=0.02, 𝜇𝑘=0.01 (Blank-1st and 2nd punches), ∆𝑠 =0.05mm, 𝑝𝑐= 𝑝𝑟=200~380MPa, 𝑡 =50μm).
Fig. 4.19 Change of thickness distribution during MUDD for thickness 𝑡 =20μm (𝐷𝑅 =5.4, taper punch, 𝑟𝑝𝑖1=0.10mm, with stopper, 𝜇𝑠 =0.02, 𝜇𝑘=0.01 (Blank-1st and 2nd punches),
∆𝑠 =0.05mm, 𝑝𝑐= 𝑝𝑟=200~380MPa).
2
ndcycle
Initial 4
thcycle
Partial high stiffness
2ndcycle
Initial 4thcycle 8thcycle
Wrinkling 10thcycle 6thcycle
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4.5.3. Effect of process parameters on deformation behavior
Fig. 4.20 shows the effect of punch displacement ∆𝑠 and counter and radial pressure 𝑝𝑐, 𝑝𝑟 on strain distribution in thickness direction. ∆𝑠 in Fig. 4.20(a) is twice as large as that in Fig. 4.14(d).
In this case, the deformation amount in a cycle is large and the thickness reduction at 2nd punch shoulder does not occur. In addition, the revers bulge deformation at the 2nd punch inner shoulder shown in Fig. 4.18 can be avoided due to the improvement of material flow as shown in Fig. 4.20(b).
However, the large ∆𝑠 causes the large buckling at 1st punch shoulder. It causes the insufficient material flow as with the flat punch shown in Fig. 4.14(b). Furthermore, the shape accuracy of the blank surface decreases due to a nonuniform flange pressing between the 1st punch and die as shown in Fig. 4.20(a) and 4.21.
On the other hand, the counter and radial pressures also affect the deformation behavior in MUDD. When the counter and radial pressures are too low, the blank cannot be deformed. The excessive counter and radial pressures, in contrast, results the reverse bulge deformation at the 2nd punch inner shoulder which causes no material flow due as shown in Fig. 4.20(c). Therefore, the appropriate counter and radial pressures are required to deform the blank and enhance the material flow.
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(a) Small punch inner shoulder (𝑟𝑝𝑖1=0.10mm, 𝑝𝑐= 𝑝𝑟=200~380MPa)
(b) Large punch inner shoulder (𝑟𝑝𝑖1=0.10mm, 𝑝𝑐= 𝑝𝑟 =200~380MPa)
(c) Large punch inner shoulder with higher pressure (𝑟𝑝𝑖1=0.10mm, 𝑝𝑐= 𝑝𝑟=400~560MPa) Fig. 4.20 Effect of process parameters on change of thickness distribution during MUDD
(𝐷𝑅 =5.4, taper punch, with stopper, 𝜇𝑠 =0.02, 𝜇𝑘=0.01 (Blank-1st and 2nd punches),
∆𝑠 =0.10mm, 𝑡 =50μm).
2ndcycle
Initial 4thcycle 6thcycle 8thcycle 10thcycle
2
ndcycle
Initial 4
thcycle 5
thcycle
2
ndcycle
Initial 4
thcycle
Partial high
stiffness
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Fig. 4.21 Change of thickness strain distribution during MUDD process (𝐷𝑅 =5.4, taper punch, 𝑟𝑝𝑖1=0.05mm, without stopper, 𝜇𝑠 =0.02, 𝜇𝑘=0.01 (Blank-1st and 2nd punches),
∆𝑠 =0.10mm, 𝑝𝑐= 𝑝𝑟=200~380MPa, 𝑡 =50μm).
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0 1 2 3 4 5
Th ic kne ss stra in ε
tDistance from cup center x/D
pMUDD (2
nddrawing)
1
stdrawing
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4.5.4. Design guideline for forming conditions in MUDD
Fig. 4.22 shows the effect of tooling and process parameters on failure types in MUDD. It was clarified that the excessive thinning and fracture at the 2nd punch shoulder is resulted by the low friction coefficient between the blank, the 1st and 2nd punches and no stopper to restrict the upward movement at blank edge. The large 1st punch inner shoulder radius and the excessive counter pressure cause no material flow and no material deformation at flange area. On the other hand, the flat punch and large punch displacement results the excessive thickening and low shape accuracy due to the nonuniform material flow. As a result, it was found that the appropriate forming condition to avoid the thickness reduction at the 2nd punch shoulder is the high friction coefficient, the use of stopper, the small 1st punch inner shoulder radius, the proper counter pressure, and the low punch displacement.
Fig. 4.22 Effect of tooling and process parameters on failure modes in MUDD.
Tooling condition
Flat punch Taper punch
Without stopper With stopper Without stopper Without stopper With stopper μs=0.02, μk=0.01 (between blank, 1stand 2ndpunches) μs=0.35, μk=0.30 μs=0.02, μk=0.01
rpi=0.05mm rpi=0.10mm
Process parameters Δs=0.05mm pc=pr=200~380MPa Δs=0.10mm pc=pr=200~380MPa
Δs=0.10mm pc=pr=400~560MPa
○
×
× △ ○
△
×
No material flow FractureFracture Thickening
Low accuracy
△
Low accuracy×
No material flowProcess Design of MUDD
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4.5.5. FEM based validation of proposed MUDD process for high aspect ratio cup
As mentioned in Section 4, the thickness reduction can be restricted and the uniform material flow and high shape accuracy can be obtained using the appropriate tooling and process parameters.
Based on this appropriate forming condition, MUDD with high drawing ratios is conducted to fabricate the micro cup with the aspect ratio.
Fig. 4.23 shows the appearance of drawn micro cup for each drawing ratio. Using proper forming condition, the aspect ratio of 4.6 can be successfully fabricated in MUDD. The thickness at the 2nd punch shoulder does not significantly decreases in MUDD process even in 𝐷𝑅 =7.0. In addition, the uniform thickness distribution can be obtained at side wall in 𝐷𝑅 =5.4 and 7.0 due to the flange pressing as shown in Fig. 4.24, although it cannot be obtained at 𝐷𝑅 =3.8 because the flange are is not large enough to do the flange pressing. It shows that the desired thickness can be obtained by controlling the thickening and thinning behavior at the flange pressing stage in MUDD.
From above results, it was revealed that MUDD can significantly improve the forming limit due to the deformation localization to restrict the thickness reduction and can improve the shape accuracy to control the thickening and thinning behavior.
Fig. 4.23 Appearance of drawn micro cup with each drawing ratio.
DR=1.8 × 2.1=3.8 DR=1.8 × 3.0=5.4 DR=2.0 × 3.5=7.0 H/D=1.1
H/D=2.2
H/D=4.6
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(a) 𝐷𝑅 =1.8×2.1=3.8
(b) 𝐷𝑅 =1.8×3.0=5.4 -0.4
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
0 1 2 3
Th ic kne ss stra in ε
tDistance from cup center x/D
pMUDD (2
nddrawing)
1
stdrawing
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0 1 2 3 4 5
Th ic kne ss stra in ε
tDistance from cup center x/D
pMUDD (2
nddrawing)
1
stdrawing
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(c) 𝐷𝑅 =2.0×3.0=7.0
Fig. 4.24 Thickness strain distribution before and after MUDD.
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0 1 2 3 4 5 6 7 8
Th ic kne ss stra in ε
tDistance from cup center x/D
pMUDD (2
nddrawing)
1
stdrawing
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4.4. Concluding Remarks
In this chapter, the newly micro ultra deep drawing (MUDD) process by combining the ultra high pressure and incremental control was developed. Furthermore, the appropriate forming condition to achieve the high aspect ratio and high shape accuracy in MUDD was designed by FEM simulation. The main conclusions are as follows;
(1) The MUDD process with 1st and 2nd punches in the same axis was developed, which can fabricate the long micro cup by repeating ① making the space between the 1st punch and blank by lifting up the 1st punch, ② applying the ultra high pressure so as to disappear this space, and
③ lifting down the 1st and 2nd punches at the same time.
(2) In MUDD process, the material flow can be induced by the ultra high pressure and incremental control of punch movement. The deformation area can be controlled by the material constraint at 2nd punch side wall by friction holding effect and at 1st punch side wall by the stopper. These effects can prevent the local thinning at 2nd punch shoulder and avoid the fracture. Due to these effects, the MUDD process can achieve larger drawing ratio than the conventional MDD and MHDD.
(3) The MUDD process and forming condition for the high forming limit and high shape accuracy was designed. It was found that the thickness reduction at 2nd punch shoulder can be avoided by the high friction coefficient, the use of stopper, the small 1st punch inner shoulder radius, the proper counter pressure, and the small punch displacement. Using the appropriate forming condition, the micro cup with aspect ratio of 4.6 and uniform thickness distribution can be obtained.
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References
[4-1] J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, J. Allwood, Asymmetric single point incremental forming of sheet metal, CIRP Annals – Manufacturing Technology, 54, (2005), 88-114.
[4-2] T. Iizuka, Fabrication of ultra long cup by the deep drawing of thin sheet using press compression, The Proceedings of the 3rd Integrated Advanced Conference in the Light Metal Educational Foundation, (2013), 47-53.
[4-3] K. Kitazawa, Incremental forming for new reuse technology, Journal of the Japan Society for Technology of Plasticity (in Japanese), 42-4889, (2001), 1001-1007.
[4-4] K. Manabe, T. Shimizu, H. Koyama, M. Yang, K. Ito, Validation of FE simulation based on surface roughness model in micro-deep drawing, Journal of Materials Processing Technology, 204, (2008), 89-93.