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A novel technique of friction aided deep drawing using a blank-holder divided into four segments
Journal of Materials Processing Technology 139 (2003) 408–413
A novel technique of friction aided deep drawing using a blank-holder divided into four segments M.A. Hassan, N. Takakura, K. Yamaguchi∗ Department of Mechanical and System Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan
Abstract A new process of friction aided deep drawing has been developed, in which the friction force between the blank and the blank-holder is used to aid the drawing deformation of the blank. This has been achieved by using a divided blank-holder, which consists of four segments and can move radially under axial pressure. The drawing process can be combined with a supplemental punch which gives a constant punch force during the drawing process. The experimental results show that there is no fracture at the flange of deformed blank, which is often observed in Maslennikov’s process. The present new process is a very good trial to secure the advantages of deep drawing with elastic tools, but by using rigid tools. Very deep cups can be produced by repeating the drawing process. Theoretical analysis based on the energy and slab methods has also been conducted to study the possibility and the main features of this new process. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Sheet metal forming; Deep drawing; Friction aided deep drawing; Divided blank-holder
1. Introduction The forming limit in conventional deep drawing with rigid tools is qualified mainly by fracture at the punch profile portion, which occurs in general when the tensile stress at the punch profile portion exceeds the ultimate tensile strength of the material. The limiting drawing ratio obtained in the first stage of drawing is commonly about 2.0 and the total ratio seldom exceeds 3.5 even when subsequent redrawing is included. Many deep drawing processes have been proposed to increase the limiting drawing ratio of sheet metals. For example, Maslennikov’s process [1] is an approach based on friction aided deep drawing to increase the limiting drawing ratio, by using a rubber ring instead of a metal punch. The sheet is drawn radially inwards by the friction force induced at the contact surface between the blank sheet metal and the rubber ring. The Maslennikov process belongs to deep drawing group with elastic tools [2–5] and has been investigated to increase the limiting drawing ratio. In this process, very deep cups with high drawing ratios can be obtained. However, flange fracture sometimes occurs especially for thin sheets, and also sheets with high strength or large thickness cannot be drawn. Another disadvantage of the Maslennikov process is that it requires very high compressive load and ∗ Corresponding author. Fax: +81-75-724-7300. E-mail address: [email protected] (K. Yamaguchi).
that the rubber ring wears very rapidly and must be replaced after 100–10,000 strokes, depending on the workpiece material. In a good attempt to overcome these problems, Yamaguchi and coworkers [6] have proposed a new deep drawing process which uses a metal blank-holder divided into four segments instead of the rubber ring in the Maslennikov process. In the present paper the basic analysis by the energy and slab methods has been done to clarify the drawing mechanism and the main characteristics, and to find the optimum drawing conditions. Also, investigations of the process variables have been conducted using the divided blank-holder assisted with a constant punch pressure.
2. Difference between the present new process and Maslennikov’s process Figs. 1(a) and 2(a) show the principle of the present new process and the Maslennikov process. In the present process, a blank-holder divided into four segments as shown in Fig. 4 is used instead of the rubber ring in the Maslennikov process. Figs. 1(b) and 2(b) show schematically the radial velocity distributions of the divided blank-holder and the blank, and the rubber ring and the blank, respectively. As is seen, there exists a neutral point at the flange portion of the blank where the velocity distribution curves intersect. In the Maslennikov
0924-0136/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-0136(03)00514-4
M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
Nomenclature √ Cr = (2 + r)/(1 + 2r) coefficient of anisotropy Ec total energy consumed EI total energy imposed F strength coefficient of material Fb blank holding force h height of wrinkle n work-hardening exponent of material N number of drawing operations p blank holding pressure p1 pressure required to move blank-holder system r normal anisotropy of material Ra outer radius of rubber ring RB outer radius of blank-holder Ri inner die radius Rn neutral radius Ro current outer radius of blank S radial displacement of blank-holder t blank thickness TB blank-holder thickness UB radial velocity of blank-holder Um radial velocity at any radius R of flange portion Umi radial velocity of flange at inner die radius Umo radial velocity of blank periphery W initial gap between blank-holder segments Greek letters β µ µp µ1 σp σr σθ χ
409
Fig. 1. (a) Schematic diagram of the new process using a divided blank-holder; (b) radial velocity distributions.
process, the neutral point moves radially inwards to the die opening as the compression ratio of the rubber ring increases [3]. The direction of the friction force on the blank surface is inverted at the neutral point. Only the friction force in the inward direction contributes to the deformation of the blank.
current drawing ratio friction coefficient between blank and blank-holder friction force between blank and blank-holder friction coefficient between blank and die punch pressure radial stress hoop stress parameter representing the right-hand side of Eq. (4) Fig. 2. (a) Schematic diagram of Maslennikov’s process; (b) radial velocity distributions.
410
M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
In the Maslennikov process, the radial stress at the neutral point is tensile and maximum, and consequently flange fracture often occurs especially during the drawing of thin sheets, while for the newly proposed deep drawing with the blank-holder divided into four segments, of course the neutral point appears, but the direction of the friction force acting on the blank surface is in the opposite direction to that for the Maslennikov process. The radial stress at the neutral point becomes minimum (compressive in most cases) and cannot reach the fracture stress of the material under any circumstances as shown in Fig. 8. Therefore, flange fracture does not occur in the present process. Also, the net frictional area in the present process is larger than that in the Maslennikov process, because the neutral point appears close to the die opening.
3. Energy method analysis
+ 2πµp
Ro
Ri
4 √ 3
Ro
Ri
Um dR
R(UB − Um ) dR
(1)
From the condition of the neutral point and volume constancy: Um =
From Eqs. (2) and (3), the current velocity of the flange periphery can be calculated as Umo =
In order to determine the current location of the neutral point, energy method analysis was made based on the assumption that the total energy imposed, EI , is equal to the summation of all energies consumed, Ec . The former consists of the energy imposed by the compression tool and the energy imposed by the assistant punch, while the later includes the energy consumed for ideal deformation of the blank and the friction energy loss in slip between the blank and the blank-holder. Thus, the following equation holds: 2πP1 UB TB RB + 2πRi Umi tσp = Cr t σ¯
Fig. 3. Stresses acting on an element of flange portion of blank (Rn ≤ R ≤ Ro ).
Rn UB R
(2)
Substituting from Eq. (2) into Eq. (1) under the condition of Hill’s yield criterion and the power hardening law, the relation between the current position of the neutral point, Rn , and process variables can be obtained as follows: A − A2 − 4(P1 RB TB /µp − C2 ) (3) Rn = 2 where tσp C1 − , A = Ri (β − 1) + µp µp 2+r 2 n+1 n+1 n+1 C1 = tF √ Cr ln(β) , Cr = , 1 + 2r 3 R2 Fb C2 = i (β2 + 1), p = 2 2 πRi (β2 − 1)
A−
A2 − 4(P1 RB TB /µp − C2 ) UB 2 Ro
To predict the blank holding pressure required for the onset of drawing, it was assumed that the net frictional energy and the energy imposed by the assistant punch are equal to the ideal deformation energy of blank. Thus σp p t 2 n+1 n+1 n+1 (4) = Cr ln(β) − √ F µRi (β − 1) F 3
4. Slab method analysis Because the energy method cannot give any information about the stress distribution, the slab method is also used. Fig. 3 shows the stresses acting on an element taken from the flange portion of the blank. Equilibrium of forces in the radial direction results in the following equation: dσr σθ − σr p(µ1 ± µ) = − dR R t
(5)
where the ± sign in the fourth term of the right-hand side correspond to (+); Ri ≤ R ≤ Rn and (−); Rn ≤ R ≤ Ro . Eq. (5) can be solved simultaneously with Eq. (3) by using the fourth order Runge–Kutta method under the following boundary conditions: at R =
Ri Ro
σr = σp σr = 0
Hill’s yield criterion for normal anisotropy was taken as a yield condition, and plane strain condition (no change in thickness) was assumed for simplicity. Thus σθ − σr =
2(r + 1) σ, ¯ 1 + 2r
σ¯ = F ε¯ n
M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
411
Table 1 Experimental conditions Blank
Material Radius, Ro (mm) Thickness, t (mm) Hardening law
Soft aluminum 60 0.3, 0.6 σ¯ = 173 ε¯ 0.24
Die
Outer radius, Ro (mm) Inner radius, Ri (mm) Profile radius, Rp (mm)
120 22, 32 3, 5
Blank-holder
Outer radius, Ro (mm) Inner radius (mm) Gap, W (mm)
62 24, 35 6
Punch
Radius (mm) Assistant load (kN)
10, 15 2.0, 3.0
Lubrication
Blank–blank-holder Die-blank
None Teflon film
Fig. 5. Schematic diagram of the divided blank-holder.
Also, the relation between the effective strain and radial strain is given as 2 2+r ε¯ = √ εr 3 1 + 2r 5. Experimental work The experimental conditions are listed in Table 1. In the experiments, soft aluminum sheets of 0.3 and 0.6 mm in thickness were used. The effects of blank holding force, punch force and blank-holder displacement on the cup height and wrinkling behavior were mainly investigated. Fig. 4 shows the appearance of the newly developed blank-holder divided into four segments. Each segment can be moved radially inwards to the die opening as shown in Fig. 5. Initially, the gap, W, between the segments is 6 mm, but after one deformation step this gap reduces to 3 mm. In this process, when a blank undergoes drawing deformation, wrinkles tend to occur at the gaps between the four segments of the divided blank-holder. From the volume constancy of the blank material and the geometrical relation, the height of the wrinkles which occur between the gaps is given
Fig. 6. Schematic diagram showing the experimental procedure used to eliminate wrinkles.
as follows: √ 1/2 S2 2 h= SW − 2 2
(6)
where h is the wrinkle height at the free surface, S the blank-holder displacement and W the gap between the blank-holder segments. This wrinkling is a serious problem to be overcome. The experimental procedure used to correct and eliminate such wrinkling is shown schematically in Fig. 6. The deformed blank with wrinkles was rotated by 45◦ after each deformation step and compressed to correct the local wrinkling.
6. Results and discussion 6.1. Calculated results
Fig. 4. Photograph of the developed blank-holder divided into four segments.
The effect of lubrication condition between the blank and the blank-holder on the position of the neutral point was calculated from Eq. (3). The calculated results are shown in Fig. 7. It is clear that as the friction coefficient increases, the neutral point moves radially toward the die opening. This means that the efficiency of the drawing process increases as the friction coefficient increases.
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M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
Fig. 7. Neutral radius versus friction coefficient.
Fig. 10. Effects of blank holding force and blank-holder displacement on occurrence of wrinkle.
displacement increases. For the blank holding force of 50 kN, the experimental results show good agreement with the theoretical curve calculated from Eq. (6), but for the blank holding force of 38 kN, Eq. (6) overestimates the wrinkle height. 6.2. Experimental results
Fig. 8. Radial stress distribution and variation of neutral point with number of drawing, N.
The radial stress distributions at the flange of deformed blank are shown in Fig. 8, which are calculated from Eq. (5). It is seen that the radial stress is almost compression or slightly tension; this means that any fracture does not occur at the flange portion unlike Maslennikov’s process. This is the superior point of the present new process over the Maslennikov process. It is also recognized that the neutral point moves inward as the current outer radius of the blank Ro decreases. The effects of the blank-holder displacement and blank-holder force on the height of wrinkle are shown in Fig. 9. The height of wrinkle increases as the blank-holder
Fig. 9. Wrinkle height versus radial displacement of blank-holder.
In the present drawing process, the occurrence of wrinkles means the onset of drawing deformation. Fig. 10 shows the effects of the blank holding force and the blank-holder displacement on the occurrence of wrinkles. It is seen that when the blank holding force is lower than about 40 kN no wrinkling occurs; in other words, the drawing deformation of blank does not proceed at all because the friction force induced at the interface between the blank and the blank-holder is not sufficient. Therefore, from the practical point of view, the blank-holding force over 50 kN is recommended to achieve the successful drawing. Fig. 11 shows the increase in cup height with the number of drawing operations, N, for different blank-holder displacements, S. Observations show that the cup height increases as the blank-holder displacement increases. Fig. 12 shows examples of cups produced by the present deep drawing method, which have drawing ratios β = 3.8 and 5.5, and cup heights 48 and 75 mm, respectively. In fact, many drawing operations are required to obtain these cups, but
Fig. 11. Effect of sliding distance, S, on cup height.
M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
413
respectively, which are calculated from Eq. (4). In Fig. 13, there are two limits; one is the limit due to flange fracture as an upper limit; the other is the onset of deformation as a lower limit. The region between those two limit curves gives the forming region. While, in Fig. 14, it is clear that the flange fracture limit disappears and the only one limit exists for the onset of deformation. Therefore, the forming region becomes wide compared with that for the Maslennikov process. This is another advantage of the new process using the metal blank-holder divided into four segments instead of the rubber ring used in the Maslennikov process. Fig. 12. Examples of cups produced by the new process: (a) β = 3.8, height = 48 mm; (b) β = 5.5, height = 75 mm.
Fig. 13. Forming region for Maslennikov’s process after Yamaguchi and coworkers [6].
the possibility of the present process has been confirmed. Since this drawing process can easily be automated, the time required for production will be reduced. 6.3. Comparison of forming regions between Maslennikov’s process and the present process The forming region for Maslennikov’s process and that for the present new process are shown in Figs. 13 and 14,
7. Conclusions A new friction aided deep drawing process has been developed to overcome the problems in Maslennikov’s process. This could be achieved by using the metal blank-holder divided into four segments instead of the rubber ring. The process parameters have been studied by the energy and slab methods to obtain the optimum drawing conditions. The possibility of the process has been confirmed by obtaining successful cups with drawing ratios of β = 3.8 and 5.5, and cup heights 48 and 75 mm, respectively. This process is still under developing to prevent the local wrinkling simultaneously with the drawing process. Also, further study should be done to increase the productivity of the process. In this process drawing deformation is achieved mainly by the friction force at the flange. Thus the application of this new technique to the drawing of low-grade sheets and thin sheets can be expected.
Acknowledgements The authors would like to thank Messrs. K. Hino and R. Suenaga, graduate students of Kyoto Institute of Technology, for their cooperation in the experiment. The authors also would like to thank the Japan Science Society for financial support to complete some parts of this work.
References
Fig. 14. Forming region for present new process using a blank-holder divided into four segments.
[1] N.A. Maslennikov, Metalworking Prod. 16 (1957) 1417–1420. [2] F.L. Derweesh, P.B. Mellor, in: S.A. Tobias, F. Koenigsberger (Eds.), Proceedings of the 10th International Machine Tool Design and Research Conference, Manchester, 1969, Pergamon Press, Oxford, 1970, 499–509. [3] M. Fukuda, K. Yamaguchi, T. Nishikoji, Bull. Jpn. Soc. Mech. Eng. 17 (133) (1974) 1513–1521. [4] K. Yamaguchi, N. Takakura, M. Fukuda, J. Mech. Working Technol. 2 (4) (1979) 357–366. [5] S. Thirvarudchelvan, W. Lewis, J. Mater. Process. Technol. 87 (3) (1999) 128–130. [6] N. Takakura, K. Hino, K. Yamaguchi, Proceedings of the 47th Japanese Joint Conference on Technology of Plasticity, 1996, 341–342.
A novel technique of friction aided deep drawing using a blank-holder divided into four segments M.A. Hassan, N. Takakura, K. Yamaguchi∗ Department of Mechanical and System Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan
Abstract A new process of friction aided deep drawing has been developed, in which the friction force between the blank and the blank-holder is used to aid the drawing deformation of the blank. This has been achieved by using a divided blank-holder, which consists of four segments and can move radially under axial pressure. The drawing process can be combined with a supplemental punch which gives a constant punch force during the drawing process. The experimental results show that there is no fracture at the flange of deformed blank, which is often observed in Maslennikov’s process. The present new process is a very good trial to secure the advantages of deep drawing with elastic tools, but by using rigid tools. Very deep cups can be produced by repeating the drawing process. Theoretical analysis based on the energy and slab methods has also been conducted to study the possibility and the main features of this new process. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Sheet metal forming; Deep drawing; Friction aided deep drawing; Divided blank-holder
1. Introduction The forming limit in conventional deep drawing with rigid tools is qualified mainly by fracture at the punch profile portion, which occurs in general when the tensile stress at the punch profile portion exceeds the ultimate tensile strength of the material. The limiting drawing ratio obtained in the first stage of drawing is commonly about 2.0 and the total ratio seldom exceeds 3.5 even when subsequent redrawing is included. Many deep drawing processes have been proposed to increase the limiting drawing ratio of sheet metals. For example, Maslennikov’s process [1] is an approach based on friction aided deep drawing to increase the limiting drawing ratio, by using a rubber ring instead of a metal punch. The sheet is drawn radially inwards by the friction force induced at the contact surface between the blank sheet metal and the rubber ring. The Maslennikov process belongs to deep drawing group with elastic tools [2–5] and has been investigated to increase the limiting drawing ratio. In this process, very deep cups with high drawing ratios can be obtained. However, flange fracture sometimes occurs especially for thin sheets, and also sheets with high strength or large thickness cannot be drawn. Another disadvantage of the Maslennikov process is that it requires very high compressive load and ∗ Corresponding author. Fax: +81-75-724-7300. E-mail address: [email protected] (K. Yamaguchi).
that the rubber ring wears very rapidly and must be replaced after 100–10,000 strokes, depending on the workpiece material. In a good attempt to overcome these problems, Yamaguchi and coworkers [6] have proposed a new deep drawing process which uses a metal blank-holder divided into four segments instead of the rubber ring in the Maslennikov process. In the present paper the basic analysis by the energy and slab methods has been done to clarify the drawing mechanism and the main characteristics, and to find the optimum drawing conditions. Also, investigations of the process variables have been conducted using the divided blank-holder assisted with a constant punch pressure.
2. Difference between the present new process and Maslennikov’s process Figs. 1(a) and 2(a) show the principle of the present new process and the Maslennikov process. In the present process, a blank-holder divided into four segments as shown in Fig. 4 is used instead of the rubber ring in the Maslennikov process. Figs. 1(b) and 2(b) show schematically the radial velocity distributions of the divided blank-holder and the blank, and the rubber ring and the blank, respectively. As is seen, there exists a neutral point at the flange portion of the blank where the velocity distribution curves intersect. In the Maslennikov
0924-0136/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-0136(03)00514-4
M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
Nomenclature √ Cr = (2 + r)/(1 + 2r) coefficient of anisotropy Ec total energy consumed EI total energy imposed F strength coefficient of material Fb blank holding force h height of wrinkle n work-hardening exponent of material N number of drawing operations p blank holding pressure p1 pressure required to move blank-holder system r normal anisotropy of material Ra outer radius of rubber ring RB outer radius of blank-holder Ri inner die radius Rn neutral radius Ro current outer radius of blank S radial displacement of blank-holder t blank thickness TB blank-holder thickness UB radial velocity of blank-holder Um radial velocity at any radius R of flange portion Umi radial velocity of flange at inner die radius Umo radial velocity of blank periphery W initial gap between blank-holder segments Greek letters β µ µp µ1 σp σr σθ χ
409
Fig. 1. (a) Schematic diagram of the new process using a divided blank-holder; (b) radial velocity distributions.
process, the neutral point moves radially inwards to the die opening as the compression ratio of the rubber ring increases [3]. The direction of the friction force on the blank surface is inverted at the neutral point. Only the friction force in the inward direction contributes to the deformation of the blank.
current drawing ratio friction coefficient between blank and blank-holder friction force between blank and blank-holder friction coefficient between blank and die punch pressure radial stress hoop stress parameter representing the right-hand side of Eq. (4) Fig. 2. (a) Schematic diagram of Maslennikov’s process; (b) radial velocity distributions.
410
M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
In the Maslennikov process, the radial stress at the neutral point is tensile and maximum, and consequently flange fracture often occurs especially during the drawing of thin sheets, while for the newly proposed deep drawing with the blank-holder divided into four segments, of course the neutral point appears, but the direction of the friction force acting on the blank surface is in the opposite direction to that for the Maslennikov process. The radial stress at the neutral point becomes minimum (compressive in most cases) and cannot reach the fracture stress of the material under any circumstances as shown in Fig. 8. Therefore, flange fracture does not occur in the present process. Also, the net frictional area in the present process is larger than that in the Maslennikov process, because the neutral point appears close to the die opening.
3. Energy method analysis
+ 2πµp
Ro
Ri
4 √ 3
Ro
Ri
Um dR
R(UB − Um ) dR
(1)
From the condition of the neutral point and volume constancy: Um =
From Eqs. (2) and (3), the current velocity of the flange periphery can be calculated as Umo =
In order to determine the current location of the neutral point, energy method analysis was made based on the assumption that the total energy imposed, EI , is equal to the summation of all energies consumed, Ec . The former consists of the energy imposed by the compression tool and the energy imposed by the assistant punch, while the later includes the energy consumed for ideal deformation of the blank and the friction energy loss in slip between the blank and the blank-holder. Thus, the following equation holds: 2πP1 UB TB RB + 2πRi Umi tσp = Cr t σ¯
Fig. 3. Stresses acting on an element of flange portion of blank (Rn ≤ R ≤ Ro ).
Rn UB R
(2)
Substituting from Eq. (2) into Eq. (1) under the condition of Hill’s yield criterion and the power hardening law, the relation between the current position of the neutral point, Rn , and process variables can be obtained as follows: A − A2 − 4(P1 RB TB /µp − C2 ) (3) Rn = 2 where tσp C1 − , A = Ri (β − 1) + µp µp 2+r 2 n+1 n+1 n+1 C1 = tF √ Cr ln(β) , Cr = , 1 + 2r 3 R2 Fb C2 = i (β2 + 1), p = 2 2 πRi (β2 − 1)
A−
A2 − 4(P1 RB TB /µp − C2 ) UB 2 Ro
To predict the blank holding pressure required for the onset of drawing, it was assumed that the net frictional energy and the energy imposed by the assistant punch are equal to the ideal deformation energy of blank. Thus σp p t 2 n+1 n+1 n+1 (4) = Cr ln(β) − √ F µRi (β − 1) F 3
4. Slab method analysis Because the energy method cannot give any information about the stress distribution, the slab method is also used. Fig. 3 shows the stresses acting on an element taken from the flange portion of the blank. Equilibrium of forces in the radial direction results in the following equation: dσr σθ − σr p(µ1 ± µ) = − dR R t
(5)
where the ± sign in the fourth term of the right-hand side correspond to (+); Ri ≤ R ≤ Rn and (−); Rn ≤ R ≤ Ro . Eq. (5) can be solved simultaneously with Eq. (3) by using the fourth order Runge–Kutta method under the following boundary conditions: at R =
Ri Ro
σr = σp σr = 0
Hill’s yield criterion for normal anisotropy was taken as a yield condition, and plane strain condition (no change in thickness) was assumed for simplicity. Thus σθ − σr =
2(r + 1) σ, ¯ 1 + 2r
σ¯ = F ε¯ n
M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
411
Table 1 Experimental conditions Blank
Material Radius, Ro (mm) Thickness, t (mm) Hardening law
Soft aluminum 60 0.3, 0.6 σ¯ = 173 ε¯ 0.24
Die
Outer radius, Ro (mm) Inner radius, Ri (mm) Profile radius, Rp (mm)
120 22, 32 3, 5
Blank-holder
Outer radius, Ro (mm) Inner radius (mm) Gap, W (mm)
62 24, 35 6
Punch
Radius (mm) Assistant load (kN)
10, 15 2.0, 3.0
Lubrication
Blank–blank-holder Die-blank
None Teflon film
Fig. 5. Schematic diagram of the divided blank-holder.
Also, the relation between the effective strain and radial strain is given as 2 2+r ε¯ = √ εr 3 1 + 2r 5. Experimental work The experimental conditions are listed in Table 1. In the experiments, soft aluminum sheets of 0.3 and 0.6 mm in thickness were used. The effects of blank holding force, punch force and blank-holder displacement on the cup height and wrinkling behavior were mainly investigated. Fig. 4 shows the appearance of the newly developed blank-holder divided into four segments. Each segment can be moved radially inwards to the die opening as shown in Fig. 5. Initially, the gap, W, between the segments is 6 mm, but after one deformation step this gap reduces to 3 mm. In this process, when a blank undergoes drawing deformation, wrinkles tend to occur at the gaps between the four segments of the divided blank-holder. From the volume constancy of the blank material and the geometrical relation, the height of the wrinkles which occur between the gaps is given
Fig. 6. Schematic diagram showing the experimental procedure used to eliminate wrinkles.
as follows: √ 1/2 S2 2 h= SW − 2 2
(6)
where h is the wrinkle height at the free surface, S the blank-holder displacement and W the gap between the blank-holder segments. This wrinkling is a serious problem to be overcome. The experimental procedure used to correct and eliminate such wrinkling is shown schematically in Fig. 6. The deformed blank with wrinkles was rotated by 45◦ after each deformation step and compressed to correct the local wrinkling.
6. Results and discussion 6.1. Calculated results
Fig. 4. Photograph of the developed blank-holder divided into four segments.
The effect of lubrication condition between the blank and the blank-holder on the position of the neutral point was calculated from Eq. (3). The calculated results are shown in Fig. 7. It is clear that as the friction coefficient increases, the neutral point moves radially toward the die opening. This means that the efficiency of the drawing process increases as the friction coefficient increases.
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M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
Fig. 7. Neutral radius versus friction coefficient.
Fig. 10. Effects of blank holding force and blank-holder displacement on occurrence of wrinkle.
displacement increases. For the blank holding force of 50 kN, the experimental results show good agreement with the theoretical curve calculated from Eq. (6), but for the blank holding force of 38 kN, Eq. (6) overestimates the wrinkle height. 6.2. Experimental results
Fig. 8. Radial stress distribution and variation of neutral point with number of drawing, N.
The radial stress distributions at the flange of deformed blank are shown in Fig. 8, which are calculated from Eq. (5). It is seen that the radial stress is almost compression or slightly tension; this means that any fracture does not occur at the flange portion unlike Maslennikov’s process. This is the superior point of the present new process over the Maslennikov process. It is also recognized that the neutral point moves inward as the current outer radius of the blank Ro decreases. The effects of the blank-holder displacement and blank-holder force on the height of wrinkle are shown in Fig. 9. The height of wrinkle increases as the blank-holder
Fig. 9. Wrinkle height versus radial displacement of blank-holder.
In the present drawing process, the occurrence of wrinkles means the onset of drawing deformation. Fig. 10 shows the effects of the blank holding force and the blank-holder displacement on the occurrence of wrinkles. It is seen that when the blank holding force is lower than about 40 kN no wrinkling occurs; in other words, the drawing deformation of blank does not proceed at all because the friction force induced at the interface between the blank and the blank-holder is not sufficient. Therefore, from the practical point of view, the blank-holding force over 50 kN is recommended to achieve the successful drawing. Fig. 11 shows the increase in cup height with the number of drawing operations, N, for different blank-holder displacements, S. Observations show that the cup height increases as the blank-holder displacement increases. Fig. 12 shows examples of cups produced by the present deep drawing method, which have drawing ratios β = 3.8 and 5.5, and cup heights 48 and 75 mm, respectively. In fact, many drawing operations are required to obtain these cups, but
Fig. 11. Effect of sliding distance, S, on cup height.
M.A. Hassan et al. / Journal of Materials Processing Technology 139 (2003) 408–413
413
respectively, which are calculated from Eq. (4). In Fig. 13, there are two limits; one is the limit due to flange fracture as an upper limit; the other is the onset of deformation as a lower limit. The region between those two limit curves gives the forming region. While, in Fig. 14, it is clear that the flange fracture limit disappears and the only one limit exists for the onset of deformation. Therefore, the forming region becomes wide compared with that for the Maslennikov process. This is another advantage of the new process using the metal blank-holder divided into four segments instead of the rubber ring used in the Maslennikov process. Fig. 12. Examples of cups produced by the new process: (a) β = 3.8, height = 48 mm; (b) β = 5.5, height = 75 mm.
Fig. 13. Forming region for Maslennikov’s process after Yamaguchi and coworkers [6].
the possibility of the present process has been confirmed. Since this drawing process can easily be automated, the time required for production will be reduced. 6.3. Comparison of forming regions between Maslennikov’s process and the present process The forming region for Maslennikov’s process and that for the present new process are shown in Figs. 13 and 14,
7. Conclusions A new friction aided deep drawing process has been developed to overcome the problems in Maslennikov’s process. This could be achieved by using the metal blank-holder divided into four segments instead of the rubber ring. The process parameters have been studied by the energy and slab methods to obtain the optimum drawing conditions. The possibility of the process has been confirmed by obtaining successful cups with drawing ratios of β = 3.8 and 5.5, and cup heights 48 and 75 mm, respectively. This process is still under developing to prevent the local wrinkling simultaneously with the drawing process. Also, further study should be done to increase the productivity of the process. In this process drawing deformation is achieved mainly by the friction force at the flange. Thus the application of this new technique to the drawing of low-grade sheets and thin sheets can be expected.
Acknowledgements The authors would like to thank Messrs. K. Hino and R. Suenaga, graduate students of Kyoto Institute of Technology, for their cooperation in the experiment. The authors also would like to thank the Japan Science Society for financial support to complete some parts of this work.
References
Fig. 14. Forming region for present new process using a blank-holder divided into four segments.
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