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Incremental forming of nonuniform sheet metal: Possibility of cold recycling process of sheet metal waste
ARTICLE IN PRESS
International Journal of Machine Tools & Manufacture 48 (2008) 477–482 www.elsevier.com/locate/ijmactool
Short Communication
Incremental forming of nonuniform sheet metal: Possibility of cold recycling process of sheet metal waste Hiroki Takano, Kimiyoshi Kitazawa, Teruyuki Goto Department of Environmental Science and Technology, Faculty of Engineering, Shinishu University, 4-17-1 Wakasato, Nagano-shi 380-8553, Japan Received 12 August 2007; received in revised form 12 October 2007; accepted 13 October 2007 Available online 23 October 2007
Abstract The objective of this study is to determine the feasibility of cold recycling of sheet metal wastes. The authors focused on deformation behavior in incremental forming of nonuniform sheet metals flattened from sheet metal wastes. These flattened sheet metals were shaped into conical shells with various half-apex angles by incremental forming. The forming limit of the flattened sheet metals was compared with that of a sheet metal of uniform thickness. It was found that the forming limit of the flattened sheet metals is similar to that of the sheet metal of uniform thickness. Experimental results showed that strain localization can be approximately inhibited in the flattened sheet metals by incremental forming. These results suggest that the cold recycling of sheet metal wastes can be accomplished by incremental forming. r 2007 Elsevier Ltd. All rights reserved. Keywords: Sheet metal forming; Incremental forming; Cold recycling process; Flattened sheet metal; Nonuniform sheet metal; Forming limit
1. Introduction Conventionally, sheet metal wastes are recycled by melting, during which an enormous amount of energy is consumed, increasing the amount of CO2 emission. If these wastes are recycled by a cold process, i.e., nonmelting process, the amount of CO2 emission can be reduced. The cold recycling of sheet metal wastes involves two processes. The first process is flattening of sheet metal wastes. The second process is forming of flattened sheet metals. In the first process, it is important to restore sheet thickness to its original volume. As in the study of Marciniak and Kuczyn´ski [1], the limit strain of sheet metals is determined by the initial inhomogeneity of sheet metals. Namoco Jr. et al. [2] have investigated the restoration behavior of sheet metals subjected to bulging deformation. On the other hand, Takano et al. [3] have presented an incremental flattening process in which thinned bent corners of metal cases can be thickened by flattening. In this process, as shown in Fig. 1, a nonuniform sheet metal having a Corresponding author. Tel.: +81 26 269 5522; fax: +81 26 269 5550.
E-mail address: [email protected] (H. Takano). 0890-6955/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2007.10.009
thickened region is obtained because the volume of the sides of a triangular residual corner is moved to the base of the corner. In this study, the authors focused on the forming of this flattened sheet metal with the thickened region. In the forming of the flattened sheet metal, it is important to employ a forming method in which strain localization can be inhibited at the boundary between the thickened and nonthickened regions. Incremental forming enables us to form sheet metals into products of various shapes without using dies [4–11]. The main characteristic of this process is that its forming limit is greater than that of press forming because of strain localization inhibition. Also, when uniform sheet metal is shaped into conical shells by incremental forming employing a single tool-pass schedule, plane strain conditions are assumed. The strain components in the shell wall agree with values calculated from the sine law [12]. From the sine law, the strain components in the shell wall are expressed as f ¼ lnðsin bÞ,
(1)
0 ¼ 0,
(2)
t ¼ f ,
(3)
ARTICLE IN PRESS H. Takano et al. / International Journal of Machine Tools & Manufacture 48 (2008) 477–482
478
where b is the half-apex angle of the conical shell, ef is the meridian component of strain in the conical shell wall, ey is the circumferential component of strain in the conical shell
b Thinning a Metal case a
Dismantling a Conical shell Incremental stretch forming
wall, and et is the thickness strain in the conical shell wall. When strain localization is inhibited, the strain in the conical shell wall is equal to that calculated from the sine law. Hirt et al. [13] presented the incremental forming of nonuniform sheet metal. Such nonuniform sheet metal, known as tailor rolled blanks (TRBs), has been developed for cost-saving lightweight production [14,15]. Here, to determine the feasibility of cold recycling, the authors experimentally investigated the forming limit of the flattened sheet metal with the thickened region by
b
A bent sheet
Cold recycling processes
Blank holder Tool
Unbending Residual corner
b
Incremental flattening
b
a
a
Thinning
Thickening
t
t R
t > t0
t0
Blank holder t0
Tool
V
=90°
β
D
t0
Sheet metal
Unbent sheet with residual corner
Flattened sheet
t < t0
h
N Fig. 1. Recycling of sheet metal wastes by cold process.
Sheet metal
Before flattening
C A A’
After flattening
B C’
Thickened area
B’
1.4 After flattening
Type A
Type B
Thickness t (mm)
1.3 Fig. 3. Incremental stretch forming of flattened sheet metal using CNC incremental forming machine. (a) CNC incremental forming machine, (b) conical shell geometry and tool-pass speed and (c) array conditions of thickened regions.
1.2 C’
1.1 A’
B’
1.0 A
0.9
P Y0
B C
Before flattening
0.8 -15
-10
-5 0 5 Distance S (mm)
10
15
Fig. 2. Thickness distribution of sheet metal before and after flattening. The direction of bending is parallel to that of rolling.
S
P X Q
X0 Q
Y R
1mm
S
R 1mm
Fig. 4. Grid method used for strain measurement. (a) Before forming and (b) after forming.
ARTICLE IN PRESS H. Takano et al. / International Journal of Machine Tools & Manufacture 48 (2008) 477–482
479
incremental forming and the effect of strain localization inhibition by comparing measured strain components with those calculated from the sine law. 2. Experimental procedure Aluminum sheets A1050-H24 with a thickness t0 of 1.0 mm were used. The work hardening exponent of these sheets was 0.08. From these sheets, square blanks (230 mm 230 mm) were cut out using a shearing machine. These blanks were bent to form a residual corner using a press brake under the following conditions: bending angle a of 901, bending radius R of 0.01 mm, and triangular side length l of 10 mm. The direction of bending was parallel, perpendicular or diagonal to that of rolling. Then, these blanks with the residual corner were flattened using an incremental flattening machine [3]. Fig. 2 shows the thickness distribution of a flattened sheet metal, i.e., nonuniform sheet metal. The direction of bending is parallel to that of rolling. The thickness distributions are the same regardless of the bending direction. The flattened sheet metal was shaped into a conical shell using an incremental forming machine, as shown in Fig. 3(a). In this machine, the diameter of the cylindrical tool was 10 mm. The contact side of this tool was the noncontact side of the flattening tool. As shown in Fig. 3(b), a single tool-pass schedule was employed. In the pass schedule, V was 13.2 mm/min. The rotation speed of the flattened sheet metal N was 85 rpm. As a lubricant, press oil (viscosity; 734 cSt) was coated onto both the tool and the flattened sheet metal. The diameter D of the conical shell was 170 mm. The height h of the conical shell was 90 mm. The b values of the conical shell were 201, 251 301, 351, 401, and 451. In this study, as shown in Fig. 3(c), two types of conical shell were formed. In the case of type A, the thickened region is located at the center of the shell. In the case of type B, the thickened region is located on the side of the shell. To measure the strains in the conical shell wall, the authors employed the grid method. Straight lines were drawn on the surface using a 1-mm-thick oil-based black pen. The line pitch was 1 mm. The widths of the line before and after forming were measured using a toolmaker’s microscope. The meridian component of strain ef and the circumferential component of strain ey were calculated from Y f ¼ ln , (4) Y0 X y ¼ ln , (5) X0 where X0 and Y0 are the measured widths of lines before forming along the circumferential and meridian directions, respectively. X and Y are the corresponding measured widths after forming. The authors have confirmed that over the measured strain range, the difference between the
(a1) Crack: Type A, =20° , =107%
(a2) Success: Type A, =25° , =86%
(a3) Crack: Type B, =25° , =86%
(a4) Success: Type B, =30° , =69% Parallel
(b1) Crack: Type A, =20° , =107%
(b3) Crack: Type B, =25° , =86%
(b2) Success: Type A, (b4) Success: Type B, =30° , =69% =25° , =86% Diagonal
(c1) Crack: Type A, =20° , =107%
(c3) Crack: Type B, =30° , =69%
(c2) Success: Type A, =25° , =86%
(c4) Success: Type B, =35° , =56%
Perpendicular Fig. 5. Effect of location of thickened region on forming limit of flattened sheet metal. Arrows indicate cracks. (a) parallel, (b) diagonal and (c) perpendicular.
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measured strain and the principal strain calculated from the measured strain including the shear strain is less than 3.6%. In this study, the authors neglected the shear strain. The thickness strain et was calculated from t t ¼ ln , (6) t0 where t0 is the sheet thickness before forming and t is the sheet thickness after forming. The sheet thickness was Table 1 Forming limits of flattened sheet metal Bending direction
Type
Half-apex angle b (1) 45
40
35
30
25
20
Strain ef (%) 35
44
56
69
86
107
Uniform sheet metal
–
J
J
J
J
J
K
Parallel
A B
J
J
J
J
J
J
J
J
J
K
K K
A B
J
J
J
J
J
J
J
J
J
K
A B
J
J
J
J
J
J
J
J
K
K
Diagonal Perpendicular
K, crack;
J,
K K K K
success.
measured at P in Fig. 4(a) and (b) using a point micrometer. 3. Results and discussion Fig. 5 shows the effect of the location of the thickened region on the forming limit of the flattened sheet metal. In the case of the type A shell formed from flattened sheet metal for which the bending direction is parallel, diagonal or perpendicular to the rolling direction, as shown in Fig. 5(a1), (b1), and (c1), a crack occurs at the nonthickened region and propagates along the circumferential direction when b is smaller than 201. In this case, the crack stops at the boundary between the thickened and nonthickened regions. The uniform sheet cracks when b is smaller than 201. These results show that the forming limit of type A is equal to that of the uniform sheet and is not affected by the bending direction. In the case of the type B shell formed from flattened sheet metal for which the bending direction is parallel or diagonal to the rolling direction, as shown in Fig. 5(a3) and (b3), a crack occurs at the boundary between the thickened and nonthickened regions when b is smaller than 251. On the other hand, in the case of the type B shell formed from flattened sheet metal for which the bending direction is perpendicular to the rolling direction, as shown in Fig. 5(c3), a crack occurs at the center of the thickened region when b is smaller than 301. These results show that the forming limit of type B is
b a
a’
b’
1.2
1.2
Thickened region
0.4
Thickened region
0.8 : Sine law
Strain t
Strain t
0.8
0 -0.4
: Sine law
t
-0.8 a -1.2 -15
-10
10
15
: Sine law
0 : Sine law
-0.4 -0.8
t: Sine law a’ 5 -5 0 Distance S (mm)
0.4
-1.2 -30
t
b -20
t: Sine law b’ -10 0 10 Distance S (mm)
20
30
Fig. 6. Comparison of measured strain components with calculated strain components, b ¼ 301. The direction of bending is parallel to that of rolling. Positions a and a0 in the type A shell, and positions b and b0 in the type B shell denote the boundaries between the thickened and original regions ( : measured strain components, J K: sine law). (a) type A and (b) type B.
ARTICLE IN PRESS H. Takano et al. / International Journal of Machine Tools & Manufacture 48 (2008) 477–482
smaller than that of the uniform sheet and is affected by the bending direction. These experimental results are summarized in Table 1. It is found that the forming limit of the flattened sheet metal is similar to that of the uniform sheet metal, although the location of the thickened region and the bending direction affect the forming limit of the flattened sheet metal. Fig. 6 shows the strain components (ef, ey, et) in the conical shell wall with b ¼ 301 when the direction of bending is parallel to that of rolling. In this figure, a–a0 and b–b0 are thickened regions, and solid lines show strain components calculated from the sine law. In the type A shell, S is the distance in the circumferential direction from the center of the thickened region. In the type B shell, S is the distance in the meridian direction from the center of the thickened region. In the case of type A, as shown in Fig. 6(a), the strain components in the conical shell wall approximately agree with those calculated from the sine law, although ey values disagree with those calculated from the sine law at a and a0 . In the case of type B, as shown in Fig. 6(b), the strain components in the conical shell wall approximately agree with those obtained from the sine law, although ef values are larger than those calculated from the sine law at b and b0 . ef has a maximum at b. As shown in Fig. 5(a3), the crack occurs at b. These results suggest that strain localization can be inhibited in the shell wall except for at the boundary between the thickened and nonthickened regions. Fig. 7 shows the strain components (ef, ey, et)
c c* c’
1.2
Strain t
0.8 0.4
Thickened region
: Sine law
-0.8
: Sine law
-1.2 -18
t
in the conical shell wall of the type B shell with b ¼ 351 when the direction of bending is perpendicular to that of rolling. In this figure, c–c0 is the thickened region, and c is the center of the thickened region. The strain components in the conical shell wall approximately agree with those calculated from the sine law, although ef values are larger than those calculated from the sine law at c, c0 , and c. ef has a maximum at c. As shown in Fig. 5(c3), the crack occurs at c. As shown in Fig. 2, the sheet thickness of the center of the thickened region is thin. The reason why the crack occurred at the boundary between the thickened and nonthickened regions may be attributed to the difference in sheet thickness between the two regions. To clarify this reason, the thickened region in the flattened sheet metal for which the bending direction is parallel to the rolling direction was machined to uniform thickness. This sheet metal was shaped into a conical shell by incremental forming. Experimental result shows that this sheet metal can be formed when b is larger than 251. It was found that the forming limit of this sheet metal is equal to that of the uniform sheet metal. Therefore, the crack initiation is caused by the difference in sheet thickness between the thickened and nonthickened regions. 4. Conclusions The aim of this study is to determine the feasibility of the cold recycling of sheet metal waste. The authors focused on the forming limit in the incremental forming of nonuniform sheet metal flattened from sheet metal waste. It was found that the forming limit of flattened sheet metal was similar to that of uniform sheet metal because the strain localization can be approximately inhibited by incremental forming. These results suggest that the cold recycling of sheet metal waste can be accomplished by incremental forming. References
0 -0.4
481
t: Sine law c
c*
c’
-12
-6 0 6 Distance S (mm)
12
18
Fig. 7. Strain distributions of type B shell, b ¼ 351. The direction of bending is perpendicular to that of rolling. Positions c and c0 denote the boundaries between the thickened and original regions, and c denotes the center of the thickened region ( : measured strain components, J K: sine law).
[1] Z. Marciniak, K. Kuczyn´ski, Limit strains in the processes of stretched-forming sheet metal, International Journal of Mechanical Science 9 (9) (1967) 609–620. [2] C.S. Namoco Jr., T. Iizuka, R.C. Sagrado, N. Takakura, K. Yamaguchi, Experimental and numerical investigation of restoration behavior of sheet metals subjected to bulging deformation, Journal of Materials Processing Technology 177 (2006) 368–372. [3] H. Takano, K. Kitazawa, H. Yamamoto, N. Marutani, Recycling method of sheet metal wastes by non-smelting process for CO2 emission reduction, in: Proceedings of the 22nd International Conference on Solid Waste Management, Philadelphia, March 2007, pp. 831–842. [4] E. Leszak, Apparatus and process for incremental dieless forming, Patent US3342051, 1967. [5] H. Iseki, K. Kato, S. Sakamoto, Forming limit of flexible and incremental sheet metal bulging with a spherical roller, in: Proceedings of the 4th International Conference on Technology and Plasticity, Beijing, September 1993, pp. 1635–1640. [6] S. Matsubara, Incremental backward bulge forming of a sheet metal with a hemispherical head tool—a study of a numerical control
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[7]
[8]
[9]
[10]
H. Takano et al. / International Journal of Machine Tools & Manufacture 48 (2008) 477–482 forming system II, Journal of JSTP 35 (406) (1994) 1311–1316 (in Japanese). T.J. Kim, D.Y. Yang, Improvement of formability for the incremental sheet metal forming process, International Journal of Mechanical Science 42 (2000) 1271–1286. K. Dai, Z.R. Wang, Y. Fang, CNC incremental sheet forming of an axially symmetric specimen and the locus of optimization, Journal of Materials Processing Technology 102 (2000) 164–167. M.S. Shim, J.J. Park, The formability of aluminum sheet in incremental forming, Journal of Materials Processing Technology 113 (2001) 654–658. J. Jeswiet, Incremental single point forming, Transactions of the North American Manufacturing Research Institution of SME 29 (2001) 75–79.
[11] J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, J. Allwood, Asymmetric single point incremental forming of sheet metal, Annals of the CIRP 54 (2005) 623–649. [12] K. Kitazawa, H. Okaku, Possibility of CNC incremental stretchexpanding of sheet metal by single-tool-pass process, Transactions of JSME 62 (597) (1996) 2012–2017 (in Japanese). [13] G. Hirt, J. Ames, M. Bambach, R. Kopp, Forming strategies and process modeling for CNC incremental sheet forming, CIRP Annals—Manufacturing Technology 53 (1) (2004) 203–206. [14] R. Kopp, P. Bo¨hlke, A new rolling process for strips with a defined cross section, CIRP Annals—Manufacturing Technology 52 (1) (2003) 197–200. [15] R. Kopp, C. Wiedner, A. Meyer, Flexibly rolled sheet metal and its use in sheet metal forming, Advanced Materials Research 6–8 (2005) 81–92.
International Journal of Machine Tools & Manufacture 48 (2008) 477–482 www.elsevier.com/locate/ijmactool
Short Communication
Incremental forming of nonuniform sheet metal: Possibility of cold recycling process of sheet metal waste Hiroki Takano, Kimiyoshi Kitazawa, Teruyuki Goto Department of Environmental Science and Technology, Faculty of Engineering, Shinishu University, 4-17-1 Wakasato, Nagano-shi 380-8553, Japan Received 12 August 2007; received in revised form 12 October 2007; accepted 13 October 2007 Available online 23 October 2007
Abstract The objective of this study is to determine the feasibility of cold recycling of sheet metal wastes. The authors focused on deformation behavior in incremental forming of nonuniform sheet metals flattened from sheet metal wastes. These flattened sheet metals were shaped into conical shells with various half-apex angles by incremental forming. The forming limit of the flattened sheet metals was compared with that of a sheet metal of uniform thickness. It was found that the forming limit of the flattened sheet metals is similar to that of the sheet metal of uniform thickness. Experimental results showed that strain localization can be approximately inhibited in the flattened sheet metals by incremental forming. These results suggest that the cold recycling of sheet metal wastes can be accomplished by incremental forming. r 2007 Elsevier Ltd. All rights reserved. Keywords: Sheet metal forming; Incremental forming; Cold recycling process; Flattened sheet metal; Nonuniform sheet metal; Forming limit
1. Introduction Conventionally, sheet metal wastes are recycled by melting, during which an enormous amount of energy is consumed, increasing the amount of CO2 emission. If these wastes are recycled by a cold process, i.e., nonmelting process, the amount of CO2 emission can be reduced. The cold recycling of sheet metal wastes involves two processes. The first process is flattening of sheet metal wastes. The second process is forming of flattened sheet metals. In the first process, it is important to restore sheet thickness to its original volume. As in the study of Marciniak and Kuczyn´ski [1], the limit strain of sheet metals is determined by the initial inhomogeneity of sheet metals. Namoco Jr. et al. [2] have investigated the restoration behavior of sheet metals subjected to bulging deformation. On the other hand, Takano et al. [3] have presented an incremental flattening process in which thinned bent corners of metal cases can be thickened by flattening. In this process, as shown in Fig. 1, a nonuniform sheet metal having a Corresponding author. Tel.: +81 26 269 5522; fax: +81 26 269 5550.
E-mail address: [email protected] (H. Takano). 0890-6955/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2007.10.009
thickened region is obtained because the volume of the sides of a triangular residual corner is moved to the base of the corner. In this study, the authors focused on the forming of this flattened sheet metal with the thickened region. In the forming of the flattened sheet metal, it is important to employ a forming method in which strain localization can be inhibited at the boundary between the thickened and nonthickened regions. Incremental forming enables us to form sheet metals into products of various shapes without using dies [4–11]. The main characteristic of this process is that its forming limit is greater than that of press forming because of strain localization inhibition. Also, when uniform sheet metal is shaped into conical shells by incremental forming employing a single tool-pass schedule, plane strain conditions are assumed. The strain components in the shell wall agree with values calculated from the sine law [12]. From the sine law, the strain components in the shell wall are expressed as f ¼ lnðsin bÞ,
(1)
0 ¼ 0,
(2)
t ¼ f ,
(3)
ARTICLE IN PRESS H. Takano et al. / International Journal of Machine Tools & Manufacture 48 (2008) 477–482
478
where b is the half-apex angle of the conical shell, ef is the meridian component of strain in the conical shell wall, ey is the circumferential component of strain in the conical shell
b Thinning a Metal case a
Dismantling a Conical shell Incremental stretch forming
wall, and et is the thickness strain in the conical shell wall. When strain localization is inhibited, the strain in the conical shell wall is equal to that calculated from the sine law. Hirt et al. [13] presented the incremental forming of nonuniform sheet metal. Such nonuniform sheet metal, known as tailor rolled blanks (TRBs), has been developed for cost-saving lightweight production [14,15]. Here, to determine the feasibility of cold recycling, the authors experimentally investigated the forming limit of the flattened sheet metal with the thickened region by
b
A bent sheet
Cold recycling processes
Blank holder Tool
Unbending Residual corner
b
Incremental flattening
b
a
a
Thinning
Thickening
t
t R
t > t0
t0
Blank holder t0
Tool
V
=90°
β
D
t0
Sheet metal
Unbent sheet with residual corner
Flattened sheet
t < t0
h
N Fig. 1. Recycling of sheet metal wastes by cold process.
Sheet metal
Before flattening
C A A’
After flattening
B C’
Thickened area
B’
1.4 After flattening
Type A
Type B
Thickness t (mm)
1.3 Fig. 3. Incremental stretch forming of flattened sheet metal using CNC incremental forming machine. (a) CNC incremental forming machine, (b) conical shell geometry and tool-pass speed and (c) array conditions of thickened regions.
1.2 C’
1.1 A’
B’
1.0 A
0.9
P Y0
B C
Before flattening
0.8 -15
-10
-5 0 5 Distance S (mm)
10
15
Fig. 2. Thickness distribution of sheet metal before and after flattening. The direction of bending is parallel to that of rolling.
S
P X Q
X0 Q
Y R
1mm
S
R 1mm
Fig. 4. Grid method used for strain measurement. (a) Before forming and (b) after forming.
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incremental forming and the effect of strain localization inhibition by comparing measured strain components with those calculated from the sine law. 2. Experimental procedure Aluminum sheets A1050-H24 with a thickness t0 of 1.0 mm were used. The work hardening exponent of these sheets was 0.08. From these sheets, square blanks (230 mm 230 mm) were cut out using a shearing machine. These blanks were bent to form a residual corner using a press brake under the following conditions: bending angle a of 901, bending radius R of 0.01 mm, and triangular side length l of 10 mm. The direction of bending was parallel, perpendicular or diagonal to that of rolling. Then, these blanks with the residual corner were flattened using an incremental flattening machine [3]. Fig. 2 shows the thickness distribution of a flattened sheet metal, i.e., nonuniform sheet metal. The direction of bending is parallel to that of rolling. The thickness distributions are the same regardless of the bending direction. The flattened sheet metal was shaped into a conical shell using an incremental forming machine, as shown in Fig. 3(a). In this machine, the diameter of the cylindrical tool was 10 mm. The contact side of this tool was the noncontact side of the flattening tool. As shown in Fig. 3(b), a single tool-pass schedule was employed. In the pass schedule, V was 13.2 mm/min. The rotation speed of the flattened sheet metal N was 85 rpm. As a lubricant, press oil (viscosity; 734 cSt) was coated onto both the tool and the flattened sheet metal. The diameter D of the conical shell was 170 mm. The height h of the conical shell was 90 mm. The b values of the conical shell were 201, 251 301, 351, 401, and 451. In this study, as shown in Fig. 3(c), two types of conical shell were formed. In the case of type A, the thickened region is located at the center of the shell. In the case of type B, the thickened region is located on the side of the shell. To measure the strains in the conical shell wall, the authors employed the grid method. Straight lines were drawn on the surface using a 1-mm-thick oil-based black pen. The line pitch was 1 mm. The widths of the line before and after forming were measured using a toolmaker’s microscope. The meridian component of strain ef and the circumferential component of strain ey were calculated from Y f ¼ ln , (4) Y0 X y ¼ ln , (5) X0 where X0 and Y0 are the measured widths of lines before forming along the circumferential and meridian directions, respectively. X and Y are the corresponding measured widths after forming. The authors have confirmed that over the measured strain range, the difference between the
(a1) Crack: Type A, =20° , =107%
(a2) Success: Type A, =25° , =86%
(a3) Crack: Type B, =25° , =86%
(a4) Success: Type B, =30° , =69% Parallel
(b1) Crack: Type A, =20° , =107%
(b3) Crack: Type B, =25° , =86%
(b2) Success: Type A, (b4) Success: Type B, =30° , =69% =25° , =86% Diagonal
(c1) Crack: Type A, =20° , =107%
(c3) Crack: Type B, =30° , =69%
(c2) Success: Type A, =25° , =86%
(c4) Success: Type B, =35° , =56%
Perpendicular Fig. 5. Effect of location of thickened region on forming limit of flattened sheet metal. Arrows indicate cracks. (a) parallel, (b) diagonal and (c) perpendicular.
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measured strain and the principal strain calculated from the measured strain including the shear strain is less than 3.6%. In this study, the authors neglected the shear strain. The thickness strain et was calculated from t t ¼ ln , (6) t0 where t0 is the sheet thickness before forming and t is the sheet thickness after forming. The sheet thickness was Table 1 Forming limits of flattened sheet metal Bending direction
Type
Half-apex angle b (1) 45
40
35
30
25
20
Strain ef (%) 35
44
56
69
86
107
Uniform sheet metal
–
J
J
J
J
J
K
Parallel
A B
J
J
J
J
J
J
J
J
J
K
K K
A B
J
J
J
J
J
J
J
J
J
K
A B
J
J
J
J
J
J
J
J
K
K
Diagonal Perpendicular
K, crack;
J,
K K K K
success.
measured at P in Fig. 4(a) and (b) using a point micrometer. 3. Results and discussion Fig. 5 shows the effect of the location of the thickened region on the forming limit of the flattened sheet metal. In the case of the type A shell formed from flattened sheet metal for which the bending direction is parallel, diagonal or perpendicular to the rolling direction, as shown in Fig. 5(a1), (b1), and (c1), a crack occurs at the nonthickened region and propagates along the circumferential direction when b is smaller than 201. In this case, the crack stops at the boundary between the thickened and nonthickened regions. The uniform sheet cracks when b is smaller than 201. These results show that the forming limit of type A is equal to that of the uniform sheet and is not affected by the bending direction. In the case of the type B shell formed from flattened sheet metal for which the bending direction is parallel or diagonal to the rolling direction, as shown in Fig. 5(a3) and (b3), a crack occurs at the boundary between the thickened and nonthickened regions when b is smaller than 251. On the other hand, in the case of the type B shell formed from flattened sheet metal for which the bending direction is perpendicular to the rolling direction, as shown in Fig. 5(c3), a crack occurs at the center of the thickened region when b is smaller than 301. These results show that the forming limit of type B is
b a
a’
b’
1.2
1.2
Thickened region
0.4
Thickened region
0.8 : Sine law
Strain t
Strain t
0.8
0 -0.4
: Sine law
t
-0.8 a -1.2 -15
-10
10
15
: Sine law
0 : Sine law
-0.4 -0.8
t: Sine law a’ 5 -5 0 Distance S (mm)
0.4
-1.2 -30
t
b -20
t: Sine law b’ -10 0 10 Distance S (mm)
20
30
Fig. 6. Comparison of measured strain components with calculated strain components, b ¼ 301. The direction of bending is parallel to that of rolling. Positions a and a0 in the type A shell, and positions b and b0 in the type B shell denote the boundaries between the thickened and original regions ( : measured strain components, J K: sine law). (a) type A and (b) type B.
ARTICLE IN PRESS H. Takano et al. / International Journal of Machine Tools & Manufacture 48 (2008) 477–482
smaller than that of the uniform sheet and is affected by the bending direction. These experimental results are summarized in Table 1. It is found that the forming limit of the flattened sheet metal is similar to that of the uniform sheet metal, although the location of the thickened region and the bending direction affect the forming limit of the flattened sheet metal. Fig. 6 shows the strain components (ef, ey, et) in the conical shell wall with b ¼ 301 when the direction of bending is parallel to that of rolling. In this figure, a–a0 and b–b0 are thickened regions, and solid lines show strain components calculated from the sine law. In the type A shell, S is the distance in the circumferential direction from the center of the thickened region. In the type B shell, S is the distance in the meridian direction from the center of the thickened region. In the case of type A, as shown in Fig. 6(a), the strain components in the conical shell wall approximately agree with those calculated from the sine law, although ey values disagree with those calculated from the sine law at a and a0 . In the case of type B, as shown in Fig. 6(b), the strain components in the conical shell wall approximately agree with those obtained from the sine law, although ef values are larger than those calculated from the sine law at b and b0 . ef has a maximum at b. As shown in Fig. 5(a3), the crack occurs at b. These results suggest that strain localization can be inhibited in the shell wall except for at the boundary between the thickened and nonthickened regions. Fig. 7 shows the strain components (ef, ey, et)
c c* c’
1.2
Strain t
0.8 0.4
Thickened region
: Sine law
-0.8
: Sine law
-1.2 -18
t
in the conical shell wall of the type B shell with b ¼ 351 when the direction of bending is perpendicular to that of rolling. In this figure, c–c0 is the thickened region, and c is the center of the thickened region. The strain components in the conical shell wall approximately agree with those calculated from the sine law, although ef values are larger than those calculated from the sine law at c, c0 , and c. ef has a maximum at c. As shown in Fig. 5(c3), the crack occurs at c. As shown in Fig. 2, the sheet thickness of the center of the thickened region is thin. The reason why the crack occurred at the boundary between the thickened and nonthickened regions may be attributed to the difference in sheet thickness between the two regions. To clarify this reason, the thickened region in the flattened sheet metal for which the bending direction is parallel to the rolling direction was machined to uniform thickness. This sheet metal was shaped into a conical shell by incremental forming. Experimental result shows that this sheet metal can be formed when b is larger than 251. It was found that the forming limit of this sheet metal is equal to that of the uniform sheet metal. Therefore, the crack initiation is caused by the difference in sheet thickness between the thickened and nonthickened regions. 4. Conclusions The aim of this study is to determine the feasibility of the cold recycling of sheet metal waste. The authors focused on the forming limit in the incremental forming of nonuniform sheet metal flattened from sheet metal waste. It was found that the forming limit of flattened sheet metal was similar to that of uniform sheet metal because the strain localization can be approximately inhibited by incremental forming. These results suggest that the cold recycling of sheet metal waste can be accomplished by incremental forming. References
0 -0.4
481
t: Sine law c
c*
c’
-12
-6 0 6 Distance S (mm)
12
18
Fig. 7. Strain distributions of type B shell, b ¼ 351. The direction of bending is perpendicular to that of rolling. Positions c and c0 denote the boundaries between the thickened and original regions, and c denotes the center of the thickened region ( : measured strain components, J K: sine law).
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