Blank Calculation

Sheet metal forming and blanking

162

Calculation of the blank size Before starting drawing operations the size and form of the blank must be determined for the desired final part geometry and die layout. This should be shown using the example of a simple rotationally symmetrical body. In order to calculate the blank diameter, it is necessary to devide the entire axisymmetric part into various individual axisymmetric components, in accordance with Table 4.2.1 and then calculate the surface areas of these components. The total surface area as a sum of the individual areas enables the calculation of the diameter of blank D. This is shown in Table 4.2.1 for commonly used drawn shapes, starting from the desired inner diameter d. As the material will be somewhat stretched in the drawing process, there is more surplus material on the upper edge of the draw part, which cannot be precisely calculated. With high parts this can lead to distorted edges, because of the non-uniform deformation properties of the blank material (anisotropy). Therefore, in general the drawn parts must be trimmed accordingly on the edge, when produced via deep drawing. The selection of the blank size for non-symmetric and irregular parts is often carried out on a trial and error basis, as it is not possible to use simple formulas. Based on practical experience, the blank geometry is determined with experiments. Initially a sufficiently large blank size is selected for the drawing operation. After observing the actual material demand and flow, the blank size is reduced to satisfy the material requirements. More recently, computer programs are being increasingly used for the determination of the blank size (cf. Sect. 4.1.2).

Table 4.2.1: Formulas for the circular blank diameter D Container shape (cross-section) rotationally symmetrical shapes 1

Blank diameter D =

h

d

2

d2 + 4 ⋅ d ⋅ h *

d2

d1

d 2 2 + 4 ⋅ d1 ⋅ h *

* Containers with small (bottom) radii r < 10 mm

Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998

Deep drawing and stretch drawing

163

Container shape (cross-section) rotationally symmetrical shapes 3

h2

d2

d 2 2 + 4 ⋅ (d1 ⋅ h1 + d 2 ⋅ h 2 ) *

4

d3 d2

d 3 2 + 4 ⋅ (d1 ⋅ h1 + d 2 ⋅ h 2 ) *

h1

d1

h2

h1

d1

5

Blank diameter D =

d2

d 12 + 4 ⋅ d 1 ⋅ h + 2 ⋅ f ⋅ ( d 1 + d 2 ) *

d1 f

d3

h2

6

d2

7

d 2 2 + 4 ⋅ (d1 ⋅ h1 + d 2 ⋅ h 2 ) + 2 ⋅ f ⋅ (d 2 + d 3 ) *

h1

d1

d

2 ⋅ d 2 = 1.414 ⋅ d

8

d2 d1

d 12 + d 2 2

9

d2 d1

1.414 ⋅

d12 + f ⋅ (d1 + d 2 )

1.414 ⋅

d2 + 2 ⋅ d ⋅ h

f

10 d

h

* Containers with small (bottom) radii r < 10 mm

Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998

Sheet metal forming and blanking

164

Container shape (cross-section) rotationally symmetrical shapes 11

Blank diameter D =

d2 d1

h

12

d 12 + d 2 2 + 4 ⋅ d 1 ⋅ h

d2 d1

1.414 ⋅ d12 + 2 ⋅ d1 ⋅ h + f ⋅ (d1 + d 2 )

h

f

13

d

2

14

h

d2 + 4 ⋅ h2

h

d22 + 4 ⋅ h2

d2 d1

15

d2 d1

h2 h1

(

d 2 2 + 4 ⋅ h 12 + d 1 ⋅ h 2

16 d

h2 h1

17

(

d 2 + 4 ⋅ h 12 + d ⋅ h 2

)

)

d2 h

d 12 + 4 ⋅ h 2 + 2 ⋅ f ⋅ ( d 1 + d 2 )

h2 h1

d12 + 4 ⋅ h12 + d1 ⋅ h 2 + 0.5 ⋅ f ⋅ (d1 + d 2 )

d1 f

18

d2 d1 f

19

[

d2

d1 s

d 12 + 2 ⋅ s ⋅ ( d 1 + d 2 ) *

* Containers with small (bottom) radii r < 10 mm

Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998

]

Deep drawing and stretch drawing

165

Container shape (cross-section) rotationally symmetrical shapes 20

Blank diameter D =

d3 d2

d 12 + 2 ⋅ s ⋅ ( d 1 + d 2 ) + d 3 2 – d 2 2 *

d1 s

21

d2

[

h

d 12 + 2 ⋅ s ⋅ ( d 1 + d 2 ) + 2 ⋅ d 2 ⋅ h

d1 s

22

d2

d12 + 6.28 ⋅ r ⋅ d1 + 8 ⋅ r 2

d1

]

*

or

r

d 2 2 + 2.28 ⋅ r ⋅ d 2 – 0.56 ⋅ r 2

23

d3

d12 + 6.28 ⋅ r ⋅ d1 + 8 ⋅ r 2 + d 32 – d 2 2 or

d2

r

d1

24

d 32 + 2.28 ⋅ r ⋅ d 2 – 0.56 ⋅ r 2

d3 d2 d1

25

d12 + 6.28 ⋅ r ⋅ d1 + 8 ⋅ r 2 + 4 ⋅ d 2 ⋅ h + d 32 – d 2 2 or

h r

d 32 + 4 ⋅ d 2 ⋅ (0.57 ⋅ r + h ) – 0.56 ⋅ r 2

d3

d12 + 6.28 ⋅ r ⋅ d1 + 8 ⋅ r 2 + 2 ⋅ f ⋅ (d 2 + d 3 ) or

d2 r

d1

f

d 2 2 + 2.28 ⋅ r ⋅ d 2 + 2 ⋅ f ⋅ (d 2 + d 3 ) – 0.56 ⋅ r 2

26 d3

d2 f

r

d1

h

d12 + 6.28 ⋅ r ⋅ d1 + 8 ⋅ r 2 + 4 ⋅ d 2 ⋅ h + 2 ⋅ f ⋅ (d 2 + d 3 ) or d 2 2 + 4 ⋅ d 2 ⋅ (0.57 ⋅ r + h + 0.5 ⋅ f ) + 2 ⋅ d 3 ⋅ f – 0.56 ⋅ r 2

27 d2 d1

h

r

(

d12 + 4 1.57 ⋅ r ⋅ d1 + 2 ⋅ r 2 + d 2 ⋅ h

)

d 2 2 + 4 ⋅ d 2 ⋅ (0.57 ⋅ r + h ) – 0.56 ⋅ r 2

* Containers with small (bottom) radii r < 10 mm

Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998

or