Design of Deep Drawing Dies

1 Introduction 2 Theoretical Aspects 3 Blank size, shape, and trimming allowance for: i Cylindrical cups with and without flange, ii Progressive drawing, iii Short quadratic and rectangular sections drawn in single step, iv Quadratic section drawn in several steps, v Long rectangular section drawn in several steps.

4 Drawing ratios and steps for the same blue items. 5 Height of drawn parts in each step. 6 Forces for deep drawing and blankholder. 7 Deep drawing with and without blankholder. 8 Punch and die radii. 9 Clearance between die and punch.

10 Tolerances for the punch and die for accurate inside and outside dimensions.

11 Strain-hardening in deep drawing. 12 Special methods of deep drawing. 13 Air-Vent, Drawing speed, Lubrications

Blank size, shape, and trimming allowance

Fig. 94 Drawing ranges for quadratic and rectangular

parts

Above the curve 1, in the area Ia, Ib and Ic:

Such a part can be produced only by several drawings. Below the curve 2, as in IIa, IIb and IIc: The drawing part, however, can be decided to produced in only one step, with different values of H/B and r/B.

In Zone IIa In zones IIa can short parts with relatively small radii of curvature are produced in the corners. In this case, from the corner cuts only a small proportion of the material displaced into the side walls without losing their height is influenced. The blank shape is carried out for this case by settling of the side walls in a plane; actual drawing takes place only in the side walls are only bent.

1. The part height H, can be calculated from following equation taking into

consideration the bottom radius:

4257.0 b

bbrrHrHl π

+−=+=

2. To determine the blank radius R, the bottom diameter of the cylindrical cup ( d ) should be taken into consideration:

dHR =

Are the corners (ry) and bottom radius (rb) are different, then R is calculated according to equation:

( )bybyy rrrHrrR 16.086.022 +−+=

3. The blank shape takes place with step-like transitions from the rounded portions to the straight sides.

4. The distance ab are divided into two equal halves, a tangent is drawn from the midpoints to the circle of radius R.

5. The intersection between the tangent and straight sidewall is rounded with a radius R.

With such blank shape, a blank allowance in most cases isn't necessary because sufficient excess (+ f) of material is displaced into the side walls, the corrected value is (- f) portions is compensated.

Fig. 95 Determination of blank shape and size for rectangular

parts produced in one step (area IIa, Figure 94)

In Zone IIb Short drawing parts with relatively large radii of curvature can be produced in zone IIb. In this case, a significant proportion of the material from rounding the corners displaced into the side walls and influences their height. The blank shape can be known by unwind the part to a flat plane, and a correction factor is applied to the height of the side walls.

Figure 96 Determination of short cut rectangular drawn parts with large radii a) square drawn part; b) rectangular drawing part (area IIb. Figure 94)

With the notation in Figure 96, you will probably apply the Konstruction as follows:

1. The dimension l for the straight side walls and the corner radius R are calculated using the pre-mentioned formulas.

2. The blank is constructed so that a step-like transition between the straight walls and the

rounded portions is maintained.

3. The corrected corner radius is calculated as

R1 = x R.

Through it, the material that is pushed into the side wall compensate the height. According to AWF1) the coefficient of x can be calculated from the formula

x = 0.074 (R / d)2 + 0.982

The coefficient x can be taken from the following table

4 The width hb and ha are cut off from the determined cut. They are necessary for the

compensation of the material that is pushed out of the corner rounding. In calculating these values, the surface area of a quarter-circular area equal to the area to be extracted hb (B - 2r) and ha (A - 2r) are to be added. The formulas are:

,2

2

rBRyhb −

=

rARyha 2

2

−=

The correction value y can either be extracted from the Nomogram that is specified in AWF 5791, or taken from table 64:

Relative Draw Depth H/B Relativer Abrundungsradi

us r/B 0.3 0,4 0,5 0,6 0,10 — 0,15 0,20 0,27 0,15 0.08 0,11 0.17 0,20 0,20 0,06 0,10 0,12 0,17 0,25 0.05 0,08 0,10 0,12 0,30 0,04 0,06 0.08 —

5. A correction of the blank by the sense that the radius is increased up to R1 and the

values of the heights hb and ha is decreased. 6. After the width, length, and the corner radius have been calculated, the cut is recorded,

radii Rb and Ra are used for this construction (Figure 96).

This cut design is valid for the having the ratio A:B = 1.5 • • • 2.0. For draw parts, which can be trimmed, it is allowed to simplify the cut. In this case, each value be somewhat enlarged.

.

In Zone IIc In zone IIc, all parts with large radius of curvature in the corners can be produce. Here, a large proportion of material from the corner cuts displaced into the side walls and leads to a significant increase in the height. In this zone can almost all quadratic parts are manufactured, being used as the blank comprises a circular blank use. When pulling rectangular objects on the other hand, an oval blank is required, wherein two opposite outlines rounded and the other two opposite parallel. For square drawn parts with the side length B and height H is the diameter discs using the following formula [88] (Fig. 97):

r) 0,33 (Hr 1.72 r) 0,43 - 4B(H B13.1 2 ++=oD

H height of the drawn part with trim, r corner radius r and arc radius. Much easier is the cutting diameter of such parts of the formula are calculated.

Do = 2 b N = 2N (B – 2 r) The value N is found here from a diagram listed in the literature [244]. Are corners and bottom radii calculated differently, the cutting diameter as follows:

)0.11r (1.8r4r - )1.78r - (0.43H4r - )r 0.57 r -4B(H B bybyyby2 −++=oD

Drawn parts with the dimensions A x B (Fig. 98) can be considered as a part which is composed of two square parts of side B, which by an intermediate piece with the length A - B are connected. For this case the blank is an oval, which is formed by two semi-circles of radius R and two parallel sides (Fig. 98). This blank is sufficiently accurate and can be cut with a relatively simple editing tools

Figure 97 Determination of blank for square parts with large radii of curvature (zone IIc, Figure 94)

For this cutting of the center of the circle of radius Rb at a distance of B/2 on the narrow side-drawn part. The entire length of the oval is:

L = Do + (A - B). Do = 2Rb blank diameter of the corresponding square-drawing part with dimensions BxB, A - B distance between the two circle centers.

The width of the oval blank is calculated using the following formula Do(B - 2r) + [B + 2(H - 0,43r)] (A - B)K = A - 2 r

In most cases, K < L will be, and the shape of the blank corresponds to an oval. For K ~ L of the blank is the circular area.

Fig. 98 Cutting patterns for very large parts with square radii of curvature (section IIc, Fig. 94)

Fig. 99 Blank size and shape of a flat rectangular drawn part

Radius R, which connects the two radii of curvature of the oval with the two straight sides, is calculated from the formula.

R = 0.5 K With little difference between A and B (A < 1.3 W) and if H < 0.8 W, the measure can be equated to K = 2Rb. The production of a shallow drawn part made of galvanized steel sheet with a thickness of 0.7 mm (Fig. 99), whose radii of curvature are large (range IIc), may be cited as an example. The Forming of rectangular drawn part is done on a double-action press. The characteristics of the deep drawn part are:

H / B = 0.38, r / B = 0.33, r / (B - H) = 0.54. The limit drawing ratio for short rectangular parts is comparable to the drawing ratio of the part from the corners to the cylindrical drawn part.

In Zones Ia, Ib, and Ic Blank Calculation for Square and Rectangular drawn part

that will be produced in several draws Includes the left of the Figure 94 shown a range of redrawing the area and is divided into sections Ia, Ib, Ic. Ih the sections Ia and Ic are the elements whose ratios of height to radius of curvature different and therefore are for the shape and nature of the cutting shapes of importance. Region Ib represents a transition region between Ia and Ic. In the area covered parts of Ia, the square or rectangular in shape and not too high. Their radii of curvature are so small that the part can impossible be drawn in a single step. The task of the second draw is to reduce the corners and bottom curves (sizing). Only the radii of curvature can be reduced. For this reason, it is also possible to perform the blank shapes on geometric paths. The procedure described in the sections that fall within the range IIa (Fig. 94). The sequence of computation and the partial settlement have already been described. If such parts are manufactured in two moves, a certain amount of material displacement must be considered by the corner cuts in the sidewalls. Accordingly, it is advisable to increase the radius R for the blank construction by 10…..20%. Linter the condition that corner and bottom radius are the same, we calculate R according to the formula:

R = (1,1 ... 1,2). rH2 The corner radii for the 1st draw and redraw have different centers (Fig. 100).

The final draw will be made without blankholder. It is recommended therefore, provide a relatively small clearance [b = (4 ... 5)s]. When b = 0.43 (rb1 - rb2) changes the drawn part height between 1 and 2 draw, because the increase in height ∆H is calculated using the formula:

∆H = b - 0,43(rb1 - rb2); rbl and rb2 radii of curvature at the bottom of the 1 and 2 draw.

The redrawing of the square and rectangular drawn parts with large drawing depth (H / B ≥ 0.65....0.7) in the area Ic (Fig. 94). The blank is then either a circle or an ellipse. The blank determination is carried out as for parts corresponding to the range IIc. For square drawn parts, where the corners and bottom radii are equal and the blank area of a circle, the diameter is calculated from the relationship:

( ) ( )rHrrHBBDo 33.072.143.0413.1 2 +−−+=

H = h + ∆H part height after drawing, h finished part height according to working drawings, ∆H = (0.05 .... 0.1) h Trimming allowance.

Fig.100 Deep drawing steps and tool form for short parts Fig.101 Determination of blank shape

for high rectangular parts

If high rectangular parts manufactured by redrawing, you look at the blank shape with the corresponding corner transitions each of the narrow sides of the part than half a square drawn part, connected by a transition piece. The blank form is an ellipse. Their narrow sides correspond to the arcs of radius Rb, the broad sides of the arcs of radius Ra. A blank form can also be formed of two circular arcs (R = K / 2) and two parallel sides (Fig. 101). This form is for the practice so far the cheapest, because the cutting tool is simple. The calculation of the length L and width K of this blank is subject to the previously specified formulas. The radius of the great arc of the ellipse is given by

( )b

ba RK

LRKLR2

25.0 22

−−+

=

In many cases, the oval blank form to be replaced by a circle, namely, when a small difference exists between the dimensions A and B, only or when the finished parts are very high.

Draw ratio and calculation of the Deep drawing steps K = D/d = 1 / m ; m = d / D = l / K ;

D = Blank diameter [mm] d = Punch diameter [mm], m = drawing ratio, K = diameter ratio.

The curve I applies to small drawing ring curves, while curve 2 is applied for large rounding of the drawing ring. Figure 104 Dependence of the deep-drawing ratio on the relative material thickness when cupping (C10) steel material.

Table 68 contains the optimal values of the draw ratios for cylindrical parts without flange (drawing with blankholder) in dependence on the relative thickness of the material. The smaller values of the draw ratios in this table are valid of large tool radii of curvature in cupping [r = (8….15) s], while the larger values of smaller radii of curvature correspond to [r = (4…..8) s], and refer on deep drawable steel sheets as well as soft brass. Less deformable materials, e.g. C 20 - C 25, St 2, St 3, pickled sheets low-grade hard aluminum and brass plates must be drawn with larger draw ratios, well deformable materials, such as deep drawing sheets, aluminum sheets, and others are drawn with smaller values in comparison to the values in Table 68.

Table 68. Optimal drawing ratios when drawing parts without flange

Relative Material Thickness s/D [%] Drawing Ratio 2... 1,5 1,5... 1,0 1,0...0,6 0,6... 0,3 0,3... 0,10

m1 0,48...0,50 0,50...0,53 0,53...0,55 0,55...0,58 0,58...0,60

m2 0,73...0,75 0,75...0,76 0,76...0,78 0,78...0,79 0,79...0,80

m3 0,76...0,78 0,78...0,79 0,79...0,80 0,80...0,81 0,81...0,82

m4 0,78...0,80 0,80...0,81 0,81...0,82 0,82...0,83 0,83...0,85

ms 0,80...0,82 0,82...0,84 0,84...0,85 0,85...0,86 0,86...0,87

Determination of Deep drawing steps In Table 69 the number of draws for the deep drawing of cylindrical parts depends on the desired drawing h/d draw depth, the relative material thickness s/D*100 and the relative die radius rM / s.

Table 69 Maximum values for h / d when drawing parts without flange

Relative Material Thickness s/D [%] Number of draws 2...1,5 1.5... 1.0 1.0...0.6 0.6...0.3 0.3...0.1

1 0.94...0.77 0.84...0.65 0.7...0.57 0.62...0.5 0.52...0.45

2 1.88...1.54 1.60...1.32 1.36...1.1 1.13...0.94 0.96...0.83

3 3.5...2.7 2.8...2.2 2.3...1.8 1.9...1.5 1.6...1.3

4 5.6...4.3 4.3...3.5 3.6...2.9 2.9...2.4 2.4...2.0

5 8.9...6.6 6.6...5.1 5.2...4.1 4.1...3.3 3.3...2.7 The larger values of h / d are for the larger radii of the first draw From r = 8 s for s/D = 2…1.5 % to r = 15 s for s/D = 0.1 %

The smaller values of h / d valid for small radius (r = 4…8 s)

Fig. 105 Drawing and Redrawing

Deep Drawing Parts with Wide Flange

In deep drawing of parts with a wide flange (Fig. 109), are the draw ratio m = d / D no real idea about the size of the general order form degree, because the value of m are the same for each drawing step. Fig. 109 shows that the punch and die radii are have the same value r, in this case the blank diameter can be calculated from the following equation: Fig. 109 Cylindrical part with

wide flange

drdhdD Fl 44.342 −+=

The drawing ratio K can be calculated from the following equation:

dD

dr

dh

dd

mK Fl =−+⎟

⎠⎞

⎜⎝⎛==

44.341 2

Where: dFl/d relative flange diameter, h/d relative drawing height r/d relative radius of the punch and die

Table 70 Relative depth of draw h/d for cylindrical parts with flange (Cupping) for C10 Relative Material Thickness

S / D [%] Relative Flange

diameter

DFl/d 2.....1,5 1,5.....1,0 1.0.....0,6 0,6.....0,3 0,3.....0,10

bis 1,1 0,90.....0,75 0,82.....0,65 0,70.....0,57 0,62.....0,50 0,52.....0,45

1,3 0,80.....0,65 0,72.....0,56 0,60.....0,50 0,53.....0,45 0,47.....0,40

1,5 0,70.....0,58 0,63.....0,50 0,53.....0,45 0,48.....0,40 0,42.....0,35

1,8 0,58.....0,48 0,53.....0,42 0,44.....0,37 0,39.....0,34 0,35.....0,29

2,0 0,51.....0,42 0,46.....0,36 0,38.....0,32 0,34.....0,29 0,30.....0,25

2,2 0,45.....0,35 0,40.....0,31 0,33.....0,27 0,29.....0,25 0,26.....0,22

2,5 0,35.....0,28 0,32.....0,25 0,27.....0,22 0,23.....0.20 0,21.....0,17

2,8 0,27.....0,22 0,24.....0,19 0,21.....0,17 0,18.....0,15 0,16.....0,13

3,0 0,22.....0,18 0,20.....0,16 0,17.....0,14 0,15.....0,12 0,13.....0,10

The larger values relative depth of draw correspond to larger radii of curvature [r = (10 - 12) s for s / D = 2 - 1.5% and r = (20 - 25) s for s / D = 0.3, - 0.10%]

By gradual decreasing the relative depth h/d up to the value h=2r, the flange diameter increase. The lower values of h/d in table 70 is valid for small rounding radii [ r ≈ (4….8)s].

Fig. 110 Determining the draw dept for wide Flange

The max. draw depth for the finished draw parts is calculated from the formula:

n

nnnnn

n

nn d

rdrdhd

dh −−= −−

−− 11

11 86.0

Table 71 Lowest drawing ratios for cylindrical parts with flange (Cupping) for C10

Relative Materials Thickness s/D [%] Relativer Flange durchmesser dFlld 2- 1,5 1,5-1,0 1,0-0,6 0,6-0,3 0,3 -0,10

bis 1,1 1,3 1,5 1,8 2,0 2,2 2,5 2,8 3,0

0,51 0,49 0,47 0,45 0,42 0,40 0,37 0,34 0,32

0,53 0,51 0,49 0,46 0,43 0,41 0,38 0,35 0,33

0,55 0,53 0,50 0,47 0,44 0,42 0,38 0,35 0,33

0,57 0,54 0,51 0,48 0,45 0,42 0,38 0,35 0,33

0,59 0,55 0,52 0,48 0,45 0,42 0,38 0,35 0,33

 

Table 72 shows the drawing ratios for each drawing step and these values will be increased by 5…8 % after annealing process. Parts with narrow flange (dFl/d = 1.1….1.4 and h/d = 1) can be drawn in one step.

Table. 72 Drawing ratios of the various stages in drawing of cylindrical parts with flange  

Retative Material Thickness S / D [%] Drawing Ratio

2,0.....1,5 1,5.....1,0 1,0.....0,6 0,6.....0,3 0,3.....0,10

m2 0,73 0,75 0,76 0,78 0,80

m3 0,75 0,78 0,79 0,80 0,82

m4 0,78 0,80 0,82 0,83 0,84

m5 0.80 0,82 0,84 0,85 0,86  

Deep Drawing Steps for Wide Flange Part

Deep Drawing Steps for Wide Flange Part (St 08; s = 1.2)

Deep Drawing from Strips

Deep drawing of the band is a manufacturing method for manufacturing parts smaller in size in large numbers, especially for the precision engineering. Man with separator between two technological options: a) deep-drawing from strips without preparing the strips, i.e. slitting in accordance with Fig. 114a, b) drawing from the strip after preparing the strips by slitting and blanking between the parts as shown in Figure 114b.

The draw ratios and the achievable draw depth in cupping are selected according to experience and are not suitable for deformation conditions for deep drawing of strips without slitting between parts (tables 73 and 74). Deep drawing of strips using slitting and blanking between the gaps is identical to drawing of parts with flange. The draw ratios for this purpose are shown in the tables 71 and 72.

Table 73 Permissible draw depth ( h/d ) for cupping strips Drawing ratio for cupping Relative Thickness s/D [%]

dFl/d1 >2,0 2,0-1,0 1,0-0,6 1.3 0.45 0.40 0.35 1.5 0.40 0.36 0.32 2.0 0.35 0.32 0.30

Table 74 Drawing ratio ( m ) for redrawing in strips Drawing

rations for redrawing

Relative Thickness s/D [%]

m1 >2,0 2,0 1,0 1,0-0 ,6 m2 0,80 0.82 0,85 m3 0.82 0.84 0,87 m4 0,85 0.87 0,90 m5 0,87 0.89 0,92

Deep drawing of SHORT Quadratic and Rectangular Sections IN SINGLE STEP

Table 75 Relative draw depth h/r1 for the 1st draw (cupping) from C10 Quadratic Draw Part Rectangular Draw Part

Relative Material Thickness s/D [%) Ratio r/B

0,3 ... 0,6 0,6 ... 1,0 1,0 ... 2,0 0,3 ... 0,6 0,6 ... 1,0 1,0 ... 2,0 0,4 2,2 2,5 2,8 2,5 2,8 3,1 0,3 2,8 3,2 3,5 3,2 3,5 3,8 0,2 3,5 3,8 4.2 3,8 4,2 4,6 0,1 4,5 5,0 5,5 4,5 5,0 5,5

0,05 5,0 5.5 6.0 5,0 5,5 6,0

The values in table can be increased or decreased by 5 … 7% for more or

less ductile materials, respectively.

Draw ratios m1 for Quadratic and Rectangular Parts from C10

Relative Material Thickness s/D [%] Ratio r/B 2,0 ... 1,0 1,0 ... 0,6 0,6 ... 0,3

0,40 0,40 ... 0,42 0,42 ... 0,45 0,44 ... 0,48

0,30 0,36 ... 0,38 0,38 ... 0,40 0,40 ... 0,42

0,20 0,33 0,34 0,34 ... 0,36 0,36 ... 0,38

0,10 0,30 0,32 0,33

0,05 0,29 0,30 0,32 D = blank width; the highest value valid for quadratic- while the lowest value for

rectangular-parts.

Deep Drawing QUADRATIC Parts IN SEVERAL STEPS

Fig. 118 Drawing steps for Quadratic draw Parts

Table 77 Calculation of the drawing steps for long quadratic parts

Values to be determined 1. Method 2. Method 3. Method

Material thickness 2100. ≥Bs

1100. >Bs

1100. ≤Bs

Blank diameter (at r = ry = rb ) ( ) ( )rHrrHBBDz 33.072.143.0413.1 2 +−−+=

Corner radius sBy 50≈ ----

Value bn sbn 10≤ sbn 10≤ sbn 8≈

Tool dimension of last drawing nb bBR

n+=

−5.0

1 nyy bBRn

+=−

5.01 28

2

1

n

nb

bb

BRn

+=−

rRny 5.2

1≈

−

Width of the last draw ---- nn bBB 21 +=− nn bBB 21 +=−

Value x Brbx n 207.041.0 −+= Brbx n 207.041.0 −+= r

mm

xn

n−=

1 ;

7.065.0 −=nm

Corner radius of (n - 2) draw 12

2

5.01

2mD

mR

R n

n

bb == −

−

1

1

2−

−

−=

n

yy m

RR n

n

112 −+=−− nbb bRR

nn

1

1

1−

−

−=

n

yy m

RR n

n

6.055.01 −=−nm

Value bn-1 ---- 121 −−

−=− nn yyn RRb =−1nb 9 … 10 Width of (n - 2) draw (at n = 4 ) ---- Bn-2 = Bn-1 + 2 bn-1 Bn-2 = Bn-1 + 2 bn-1

Diameter of (n - 2) draw (at n = 3 ) ---- ( )⎥

⎦

⎤⎢⎣

⎡−+=

−−

−

yn

yn BB

mR

D n 707.021

21 ----

Tool dimension of (n - 3) draw

---- ----

2

1

12

5.0

5.03

mbb

mDR

nn

bn

−++=

=−

Part height H =1.05 … 1.10 Ho ( Ho = from the graph) Part height of before the last draw HH n 88.01 ≈− HH n 88.01 ≈− HH n 88.01 ≈−

Part height of cupping (n - 2) or (n - 3) draw

( )rddr

dmDHH n 32.043.025.0 1

1

11

121 ++⎟⎟

⎠

⎞⎜⎜⎝

⎛−== −

Part height of (n - 2) draw (Hn-3 = H1) ---- ----

11

21 5.0

1

−−

−− += −

nn

bnn bB

RHH n

The drawn parts have in most cases cylindrical shapes until the penultimate draws. Only in the last two draws the desired square shape is formed.

Fig. 119 Dependence of bn, r/B and drawing steps. Fig. 120 Shapes of the bottom radii

The calculation of the dimensions for the penultimate drawing step is affected, therefore, with the aid of the mediator draw ratio, which is determined as follows

This is determined by the radius of curvature of the penultimate draw

With the aid of the drawing ratio can the value bn calculated as follows:

To reduce the generated residual stresses and make the last step at a suitable drawing ratio, the penultimate draw the bottom radius has to take a slope of 45˚, provided the bottom flat as indicated in (Figure 120).

Deep drawing of long rectangular parts For drawing long rectangular parts in several steps, two methods are used: 1. The blank is an elliptic shape. Cupping and redrawing have also elliptic cross-section and at the final drawing step the draw part take the rectangular shape. 2. The blank is a circle. Cupping has a cylindrical shape while redrawing steps are elliptic. The final shape has the rectangular shape. The first rule is for parts with an aspect ratio of A:B ≥ 1.2, and the second one applies to A:B < 1.15 or very large relative heights H / B, which require more than three consecutive drawing steps. The first method, the blank and intermediate forms have an oval shape with radii Ra and Rb each with parallel sides. For very long parts or small difference in the lateral dimensions, A and B, the blank is a circle. This example of drawing steps can be used only at a relative material thickness s / B ≥ 2% and low bn (bn ≤ 10s). If large corner radii [r = (0.2 .. 0.4) B] are required, can the part be produced by this method even with a low relative material thickness. The condition bn ≤ 10 s, must be fulfilled in each case. The second method is applied to relative material thicknesses of s/b ≥1%. It brings easier conditions for the last draw, as even the penultimate and under the last but two step, showed a rectangular form with great radii. The value bn is taken from Fig. 119. The value of an is determined with the help of the

coefficient . This method is simple and the tools are cheap. The third method applies to parts with relatively small thickness of the material (s / B <1%). It differs primarily in the form of the individual drawing stages from the other methods. The value bn here should be about 8s, which facilitates the drawing conditions in the two last steps significantly. The tooling for this is complicated and expensive.

I) II)

III)

Fig. 121 Drawing steps for rectangular parts for:

I for s/B ≥ 2% II for s/B ≥ 1% III for s/B ≤ 1%

Table 78 Calculating the drawing steps for LONG RECTANGULAR parts

Table 78 Translation from German to English for the 1st column in the last two paged  

Values to be determined    Values to be determined 

Relative material thickness 

  Tool dimensions for last but two steps 

Blank diameter (at r = ry = rb) 

  Distance between draws 

Blank length    Tool dimensions for last but two steps 

Blank width    Measure x 

Blank rounding off    Tool dimensions for last but two and three steps 

Proportionality coefficient 

  Tool dimensions for last but three steps 

Value bn    Distance between draws 

Tool dimension of next to last draw. 

  Tool dimensions (graphical) 

Measure x    Part to drawn height 

Tool dimension of next to last draw  

  Height of intermediate draw 

 

Deep Drawing Oval Parts in several Steps The blank is either circle or wide oval and can be drawn according to long rectangular parts.

Fig. 122 Drawing steps for oval parts Fig.123 Draw defect through wrong draw step.

Deep Drawing Complex Parts The tendency to form wrinkles in deep drawing the above mentioned parts depends on how big the unconfined area of the blank, i.e. the value of f depends on the radius of both punch and die. In Fig.124 the dependence of the drawing depth is illustrated by the blank surface. The figure shows that the most favorable drawing conditions exist for parts with cylindrical shape (curve I). The curve IV applies to conical parts and represents the worst case.

Fig. 124 Hold and free areas for parts during drawing Drawing stepped parts: If in doubt, the following approximate solution can be applied:: First, the ratio of the draw depth to the smallest diameter of the part h/d should be determined and then with the help of table 69 the number of draw steps. Thus, e.g. the part after Figure 125 can be produced in one draw if the relative material thickness is s/D > 0.6%.

Table 69 Largest h/d values for drawing parts without flange

Bigger values of h/d is valid for larger radii of the 1st draw. From r = 8s for s/D = 2 ... 1.5% to r = 15s for s/D = 0.10% Lower values of h/d is valid for lower radii ( r = 4 … 8s )

Fig. 125 Stepped part

If it is necessary to produce deep drawing parts with several steps, the number of draw has to be determined according to Tables 68, 72.

Table 68 Optimal drawing ratios when drawing parts without flange

Relative Material Thickness s/D [%] Drawing Ratio 2... 1,5 1,5... 1,0 1,0...0,6 0,6... 0,3 0,3... 0,10

m1 0,48...0,50 0,50...0,53 0,53...0,55 0,55...0,58 0,58...0,60 m2 0,73...0,75 0,75...0,76 0,76...0,78 0,78...0,79 0,79...0,80 m3 0,76...0,78 0,78...0,79 0,79...0,80 0,80...0,81 0,81...0,82 m4 0,78...0,80 0,80...0,81 0,81...0,82 0,82...0,83 0,83...0,85 ms 0,80...0,82 0,82...0,84 0,84...0,85 0,85...0,86 0,86...0,87

Table. 72 Drawing ratios of the various stages in drawing of cylindrical parts with flange  

Retative Material Thickness S / D [%] Drawing Ratio

2,0.....1,5 1,5.....1,0 1,0.....0,6 0,6.....0,3 0,3.....0,10 m2 0,73 0,75 0,76 0,78 0,80 m3 0,75 0,78 0,79 0,80 0,82 m4 0,78 0,80 0,82 0,83 0,84 m5 0.80 0,82 0,84 0,85 0,86

 

Fig. 126 Sequence of deep drawing stepped parts. Arbeitsgang 6

The following rules must be considered: 1. The part is drawn from the blank over cupping and the necessary draws out the inner sections and from there stepwise the outer diameter. A possible flange is thus formed in the final step (Figure 126). 2. At each step so much material is drawn into the drawing die, as is required for the next step. In order to avoid waste of material, 5 … 8% more material has to be drawn than the calculated. As the rules are applied in practice, figure 127 illustrates the examples.

Drawing spherical (hemispheres) and parabolic parts

Fig. 128 Wrinkling due to weak blankholding forces and big clearance between draw die and blankholder

Fig. 129 Bead

The draw ratio is constant for hemispheres and equal in any case m = 0.71. After that, one might speculate that they may be produced more easily than cylindrical parts. This is not the case. Hemispheres are preparing for the big production difficulties, because the blank is pressed partly with the blankholder and initiate the hemispherical draw punch at the beginning of the drawing a small area in the center. These two disadvantages are favored for the formation of wrinkles (Fig. 128) and on the other hand, the material is considerably stretched.

To suppress the tendency to form wrinkles, prepare the tools either with beads or make the blankholder to force the blank securely. Studies of stress distribution during the deep drawing of part with spherical or irregular shape with brakes or beads show that between a normal deep drawing for cylindrical parts and the present work, basic differences. 1. The greatest difficulty in drawing such complicated part is that the wrinkles should be prevented. 2. The bead reduces the tangential stress and affects against the tangential deformation and at the same time increases the radial stresses.

Usually, in deep drawing, a material of low strength value and higher ductility is used. For drawing complicated parts, a material of low strength but sufficient, as it would no longer satisfies the condition of the strength depending on shape or design on critical sections BG σσ 1.1≤ . The increased ductility values, on the other hand, are not fully utilized and are only in that part of the drawing material required that the punch from the beginning of drawing touch the material. The drawing tools with beads require higher strength and lower ductility than in normal drawing. At s/D > 3%, the hemisphere can be drawn without a blank holder. At s/D > 0.5%, the hemisphere can be produced either with blankholder or cupping and after that reverse drawing.

At s/D < 0.5%, hemisphere can be produced either by reverse drawing or the drawing ring stepped as bead rounding (Fig. 129). Large thin-walled parts with a hemispherical bottom can be drawn without blankholder when the tool is designed so that the material is bent during the forming process in addition to a radius (Fig. 130). Production of dishes can be drawn, for a long time, in multilayer of blanks (2-3 blanks simultaneously). Parts of non-cylindrical shape made of thin material (0.4 - 0.45 mm) were used (Fig. 131).

Deep drawing of conical parts For drawing conical part there are various possibilities, the relative height, the conical form and the relative material thickness are dependent on each other. Technologically, the conical parts are divided into four types: 1. Parts with low relative height (h/d = 0.1 … 0.25) and a large cone angle, the half cone angle lies within the limits of 50 … 80° (d larger diameter of the conical part), 2. Parts with a relative height of h/d = 0.3 … 0.7 and a half cone angle of 15 … 45 °, 3. Parts with a relative height h/d > 0.8 and a half angle of up to 10 °, 4. Cone with a large height and a half angle of up to 40 °. Drawing of hemispheres and tapered parts prepares many difficulties in manufacturing. The first difficulty is that at the beginning of drawing, the punch touches the blank at a very small area that leads to local material strain and can causes tearing in the center of the blank. Furthermore, the blank at the beginning of drawing will not be fully grasped by the blankholder, so that may form wrinkling between application point of the punch and draw die. For tall and slender conical drawn parts, the drawing ratio is calculated for each stage as follows:

\1

\

−

=n

nn d

dm

2arg\ smallel dd

d+

=

Calculating the drawing stages of the compact parts related to the mean diameters has no practical significant. Small conical parts are difficult to draw due to the small deformation in the walls. The parts are spring open after forming and thus lose the desired shape.

If such parts are made correctly, the radial strain in the blank with increased blankholding pressure or by means of appropriate design of drawing edges (e.g. beads) increased (Fig. 133). Another possibility is the production using hydroforming process. • The production of conical parts of medium depth is usually in one stage. • Only at low relative material thickness or drawing with flange, two or three drawing stages is required. • Parts with a relative thickness of the material s/D > 2.5% will be drawn without blank holder as the cylindrical parts (Fig. 135). • Conical parts with flange (Fig. 136) may be drawn in one stage with blankholder when the relative material thickness amounts s/D = 1,5 … 2%.

Fig. 133 Tool with bead for conical parts.

Fig. 135 Drawing of thick conical parts

Fig. 136 Drawing of conical parts with flange

• Thin-walled parts with large difference between the diameters dbig and dsmall, as in Fig. 137, are usually drawn in several stages. • The preparation of a conical tube flange is not easy. Figure 138 shows the required operations. • deep conical parts are manufactured in several drawing stages. By the penultimate step gives the part a stepped cone shape. By stamping the final step, the final cone is formed. Because of the large number of drawing stages can not be guaranteed smooth surface (Figure 139a). • Smooth surfaces can be achieved with the method given in Figure 139b. This is drawn from an early stage to stage bowl of a cone with a blunt tip without heels. The last step is simply to form the top. • The draw ratios for the methods indicated in Figure 139 are calculated using the mean diameter and are shown in Table 79. High conical parts with a large difference between the two diameters are prepared by the method shown in Fig. 140. Slender conical parts are made of a cylindrical bowl with a curved bottom. In one stage can slender truncated cone be drawn (Fig. 141).

Table 79 Drawing ratios for conical Parts

Relative material thickness s/dn-1 [%] 0.5 1.0 1.5 2.0

Drawing ratio mn = dn/dn-1 0.85 0.8 0.75 0.7

dn = Diameter of the following draw; dn-1 = diameter of the carried out stage

Fig. 137 Drawing conical parts with great difference in diameter

Fig. 138 Manufacturing of conical flange tube

Fig. 139 Drawing stages of conical parts a. less favorable b. cleaner surfaces c. example

Fig. 140 Sequence of drawing conical shapes Fig. 141 Purposeful tool design of deep drawing slender truncated cone

• For thick materials, the conventional deep drawing (Fig. 141a) is applied, while parts made of thin material better to draw by the reverse drawing (Figure 141b) for a slender truncated cone. The drawability is calculated from the ratio of both diameters and is also dependent on the relative thickness of the material; their value can be taken from table 80.

Table 80 Ability to draw conical parts

Relative material thickness s/dN [%] 0.25 0.5 1.0 2.0

Drawability \\\ / KK dd 0.9 0.85 0.80 0.75

dN = Pan (cup) diameter, d'K, d"K = diameters of truncated cone

• Another example for the production of a stepped conical portion is shown in Figure 143.

Fig. 143 Sequence of drawing stages for parts with pulled in cone

Ironing Cylindrical Thick wall Cups

Ironing grade

1

1

1

1

−

−

−

− −≈

−=

n

nn

n

nn

sss

AAA

E

Where sn-1 , sn Cup thickness before and after ironing, An-1 , An Cross-sectional area before and after ironing. Ironing Ratio

11

−−

== nnnn

nn smsor

ssm

Number of ironing operations

E

ssn

−

−=

100100log

loglog 21

Table 81 Average ironing grade E % for ironing First stage Following stages

Sheet material E mn E mn

Weicher Stahl Mittelharter Stahl Ms Al

55 … 60 35 … 40 60 … 70 60 … 65

45 … 40 65 … 60 30 … 40 40 … 35

35 … 45 25 … 30 50 … 60 40 … 50

65 … 55 75 … 70 50 … 40 60 … 50

Determination of the draw depth in subsequent stages In calculating the depth of draw to Table 82 following assumptions are noticed: 1. for cylindrical parts with low bottom rounding r = 0, 2. for cylindrical parts with large rounded bottom to determine the radius:

2232

221

1ddrddr −

=−

=

3. for cylindrical drawn parts with conical bottom (α = 45 °) are the heights of the truncated cones:

2232

221

1dddd −

=−

= αα

4. for cylindrical drawn parts with wide flange accepted the radii of curvature at the bottom and flanged as equal, 5. for all draw shapes (except the last but one in Table 82) the change in thickness is not taken into account during the forming process, so that in most cases the actual drawing depth with respect to the calculation fails.

Table 83 A. Draw depth of cylindrical parts (cupping) with small bottom radius

Draw depth h1 in mm in cupping for draw ratio ml Blank Diameter

0.60 0.58 0.55 0.53 0.50 0.48 0.45 [mm]

—

9 12 15 18

9,5 13 16 19

10 14 17 20

11 15 19 22

12 16 20 24

13 18 22 26

30 40 50 60

19 22 24 27

20 23 26 29

22 24 29 32

24 27 30 34

26 30 34 37

28 32 36 40

31 35 40 44

70 80 90 100

32 40 50 55

35 44 52 58

38 48 58 64

40 50 60 68

45 55 67 75

48 60 72 80

—

120 150 180 200

Table 83 B. Draw depth cylindrical parts (2nd draw) with small bottom radius

Draw depth h2.in mm in 2nd draw for draw ratio m1 . m2 Blank Diameter

0,6 • 0,80,58 • 0,790,55 • 0,78 |0.53 • 0,760,5 • 0,750,48 • 0,730,45 • 0,72[mm]

—

13 17 22 26

14,5 19 24 29

16 21 26 31

17 23 28 34

19 25 31 33

20 27 34 40

30 40 50 60

28 32 36 40

30 35 39 43

34 39 43 41

36 42 47 52

40 46 51 57

44 50 57 63

47 54 60 67

70 80 90 100

48 60 72 80

52 65 78 86

58 72 87 96

63 78 95 105

68 85 100 115

76 95 115 125

—

120 150 180. 200

  

Table 85 A. Draw depth cylindrical parts (cupping) with conical bottom

 

Draw depth h1 in mm in Cupping for drawing ratio m1 Blank diameter

[mm] 0,48 0,50 0,53 0,55 0,58 0,60 0,62 120 53 50 45 43 40 37 — 150 66 61 56 52 50 46 — 180 79 74 67 65 59 57 — 200 88 83 76 72 66 63 58 250 110 103 95 - 90 83 78 73 300 132 122 114 108 98 92 86 350 154 144 134 126 116 108 102 400 176 166 152 144 132 123 115 450 198 184 172 162 148 140 130 500 220 205 190 180 165 155 145 550 242 226 210 198 182 172 160 600 264 244 228 216 200 185 173

Tafel 85 B. Draw depth for cylindrical parts (2nd draw) mit conical bottom

Blank Diameter Draw depth h2 in mm in 2nd draw for draw ratio m1 • m2

[mm] 0,48-0,73 0,5-0.75 0,53-0.76 0,55-0,78 0,58-0,79 0,6-0,8 0,62-0,82 120 81 73 68 63 57 53 — 150 102 92 85 79 72 67 — 180 123 108 103 95 86 80 — 200 134 124 114 105 95 89 83 250 170 154 141 131 118 111 104 300 203 184 169 157 143 133 123 350 235 215 197 183 165 155 145 400 270 245 225 210 190 177 165 450 303 275 253 235 212 200 185 500 336 306 281 261 236 221 206 550 370 337 309 287 260 243 227 600 405 367 337 315 285 265 247

Table 84A. Draw depth of cylindrical parts (Cupping) mit great bottom radius

Blank diameter Draw depth h1 in mm in Cupping for draw ratio m1

[mm] 0,45 0,48 0,50 0,53 0,55 0,58 0,60 30 14 13 12 11 10,5 10 — 40 19 17 16 15 14 13 — 50 23,5 21,5 20,5 17,5 16,5 15,5 — 60 28 26 24 22 21 20 — 70 33 30 28 26 24 22 21 80 37 34 32 29 28 25 24 90 42,5 38,5 36,5 32,5 32 29 27

100 47 43 40 37 35 32 30 120 — 52 49 44 42 39 36 150 — 65 60 55 53 49 45 180 — 77 72 65 63 57 55 200 — 86 81 74 70 64 61

Tafel 84B. Draw depth cylindrical parts (2nd. draw) with great bottom radius

Blank diameter Draw depth h2 in mm im 2nd. draw for draw ratio m1 • m2

[mm] 0,45 … 0,72 0,48 … 0,73 0,5 … 0,75 0,53 … 0,76 0,55 … 0,78 0,58 … 0,79 0,6 … 0,8

30 21 20 18 16 15,5 14 — 40 28 26 24 22 20 18 — 50 36 33 30 28 j 26 24 — 60 42 40 36 33 31 28 | — 70 49 46 42 38 36 32 30 80 57 53 49 45 41 38 35 90 63 60 54 50 46 41 39

100 70 66 60 55 51 46 43 120 — 80 72 67 62 56 52 150 — 100 90 83 77 70 65 180 — 120 106 100 93 84 78 200 — 132 122 112 102 92 86

Table 86. Practical Formulae to determine the Drawing Forces

Part shape Drawing stage Formula Coefficient from Table

Cupping P = π d1 s σu K1 87 Cylindrical without flange

Redrawing P = π d2 s σu K2 88

Cylindrical with wide flange Cupping P = π d1 s σu KFl 89

Conical and spherical form with flange Redrawing P == π dK s σu KFl 89

cupping P = π dFl-1 s σu K1 87 Qval

Redrawing P = π dFl-2 s σu K2 88

Rectangle, short — P = (2A + 2B – 1.72 r) s σu Ka 90

Ist and 2nd draw As for cylindrical parts 87; 88 Quadratic, high

Final stage P = (4 B – 1.72 r) s σu Kb 91

Ist and 2nd draw As for oval parts 87; 88 Rectangle, high

Final stage P = (2 A+ 2 B – 1.72 r) s σu Kb 91

Cylindrical with stretched walls Redrawing P = π dn (sn-1 – sn) σu Ky —

 

Where: P Drawing Force [N], d1, d2 Internal and external diameter after 1st and 2nd draw, respectively. [mm], dK smaller diameter of conical and hemispherical draw parts, respectively. [mm]. dFl-1, dFl-2 Average diameter of oval parts after the 1st and 2nd draw [mm]. dn External diameter of part after n-draw [mm], A,B Length and width of rectangular parts [mm], r Corner radius [mm], s Material thickness [mm], Sn-1, sn Wall thickness of the penultimate and last draw [mm], σu Ultimate tensile strength [N/mm2]. Ky Coefficient, for Brass = 1,6 • 1,8; for Steel = 1,8 - 2,25.

Teble 87. Coefficient K1 for cupping czlindrical parts from St TZ A3 ••• C15

Relative Material

Thickness, (s/D)

Relative part

diameter (D/s)

Drawing Ratio m1 for Cupping

[%] 0,45 0,48 0,50 0,52 0,55 0,60 0,65 0,70 0,75 0,80 5,0 20 0,95 0,85 0,75 0,65 0,60 0,50 0,43 0,35 0,28 0,20 2,0 50 1,10 1,00 0,90 0,30 0,75 0,60 0,50 0,42 0,35 0,25

1,2 83 1,10 1,00 0,90 0,80 0,68 0.56 0,47 0,37 0,30

0,8 125 1.10 1,00 0,90 0,75 0,60 0,50 0,40 0,33

0,5 200

1,10 1,00 0,82 0,67 0,55 0,45 0,36

0,2 500 1,10 0,90 0,75 0.60 0,50 0,40

0,1 1000

Material Separation

1,10 0,90 0,75 0,60 i 0,50

For small bottom radius [r = (4 … 6) s], K will increase by 5%

Table 88. Koefficient Kz for redrawing cylindrical draw parts from St TZ A3 ••• C15

Relative material thickness (s/D)

Relative ratio

(s/D1) Drawing Ratio m- for Redrawing

[%] [%] 0,70 0,72 0,75 0,78 0,80 0,82 0,85 0,88 0,90 0,92 5,0 11 0.85 0,70 0,60 0,50 0,42 0,32 0,28 0,20 0,15 0,12 2,0 4 1,10 0,90 0,75 0,60 0,52 0,42 0,32 0,25 0,20 0,14

1,2 2,5 1,10 0,90 0,75 0,62 0,52 0,42 0,30 0.25 0,16

0,8 1,5 1,00 0,82 0,70 0,57 0,46 0,35 0,27 0,18 0,5 0,9

1.10 0,90 0,76 0,63 0,50 0,40 0,30 0.20

0,2 0,3 1,00 0,85 0,70 0,56 0,44 0,33 0,23

0.1 0,15

Material separation 1,10 1,00 0,82 0,68 0,55 0.40 0.3

For small bottom radii, K2 is chosen 5% larger. The coefficients for redrawing (3, 4, 5 stages) will also be taken from this table, but the draw ratios must and the s / D values are taken into consideration. The following applies: a) In deep drawing without intermediate annealing, the next higher value of K2 is chosen which corresponds to the relative thickness of the material. b) In deep drawing with intermediate annealing is the reverse. The first stage is less than the maximum achievable (i.e, it will be drawn with the best possible draw ratio), then with the same s / D, the relative proportions s/D1 smaller than indicated in the table.

Tafel 89. Kotffizimi Kmfir zylindrische Teile mit breitem Flansch aus St TZ A3 — C15 (s/D = 0,6 - 2.0%)

Drawing Ratio for cupping m1 = d1 /D Relative Flange

diameter dFl/d 0.35 0.38 0,40 0.42 0.45 0.50 0.55 0,60 0.65 0,70 0.75

3,0 1,0 0,9 0,83 0.75 0.68 0.56 0.45 0,37 0,30 0,23 0,18

2,8 1.1 1,0 0,90 0,83 0.75 0.62 0,50 0.42 0,34 0,26 0.20

2,5 — 1.1 1,0 0.9 0.82 0,70 0,56 0,46 0,37 0,30 0,22

2.2 1.1 1.0 0.90 0.77 0,64 0,52 0,42 0,33 0,25

2,0 1.1 1.0 0,85 0,70 0,58 0,47 0,37 0,28

1,8 Material separation 1.1 0.95 0,80 0,65 0,53 0,43 0.33

1,5 1.10 0,90 0,75 0,62 0,50 0.40

1.3

— 1.0 0,85 0.70 0.56 0.45 These coefficients are also valid for conical and hemispherical drawn parts with flange, when a toolis used without draw bead. The coefficient increases from 10 to 20 % if the drawing tools have beads. 

Table 90. Coefficient Kmfor short rectangular draw parts

Relative height h/B for relative material thickness s/D [%] Kn for relative corner Radius r/B

2 … 1,5 1,5 … 1,0 1,0 … 0,6 0,6 … 0,3 0.3 0,2 0,15 0,10 0,05 1,0 0,95 0,9 0,85 0,7

0,90 0,85 0,76 0,70 0,6 0,7 0,75 0,70 0,65 0,60 0.5 0,6 0,7 0,60 0,55 0,50 0,45 0,4 0,5 0,6 0,7 0,40 0,35 0,30 0,25 0,3 0,4 0,5 0,6 0,7

After the relative height of h / B or the relative material thickness s / D and by the known relative radius r / B is on the right side of the Table 90 found the coefficient Kn. The relative amount of h / B is valid for St TZ A3 and C15. For other materials, the values should be corrected accordance to the material ductility.

Table 91 Coefficient Kb for the finished high quadratic and rectangular Parts from cylindrical and oval first draw (St TZ A3 - C15)

Relative Kb

Material Thickness [%] For relative Radius der Corner Radius r/B s/D s/d1 s/d2 0,30 0,20 0,15 0,10 0,05 2,0 4.0 3.5 0,40 0,50 0,60 0,70 0,80 1,2 2.5 3,0 0.50 0,60 0,75 0,80 1,0 0,8 1.5 2,0 0.55 0,65 0,80 0,90 1,1 0.4 0.9 1.1 0,60 0.75 0,90 1,00 -

For rectangular parts, the values of dl and d2 that are the smallest oval diameters are taken from the first and second draws. If the values are smaller than the maximum possible values, then the first stage is less than the maximum allowed, then, the values will be smaller than s/d1 and s/d2 given in the table. For other materials, as St ZT A3 and C15, appropriate corrections must be made.

Drawing without Blankholder

Table 92. Limits for drawing with or without blankholder

Cupping Redrawing

Process s/D m1 s/D m2

Drawing with blankholder < 0,015 ≤ 0,6 < 0,01 ≤ 0,8

Drawing without blankholder ≥ 0,017 ≥ 0,55 > 0,015 ≥ 0,78

Fig.150 Shapes of drawing dies for deep drawing without blankholder

Drag curve profiles at the drawing ring edge during deep drawing without a blank holder

Limit drawing ratio for drawing without blankholder Limitations of cupping without

blankholder

Table 93 Limit drawing ratios for deep drawing without blankholder and conical drawing die

s/D * 100 dM / dK 3.0 2.5 2.0 1.5 1.0 0.6 0.50 0.52 0.54 0.56 0.58 0.7 0.58 0.60 0.62 0.64 0.66 0.8 0.66 0.68 0.70 0.72 0.75

Conical draw die

Table 94 Formulae to calculate blankholding force Drawing stage Formula

Blankholding force to draw parts having any form (general calculations) Q = A * p Blankholding force for cupping cylindrical parts Q = (π/4) * [D2 - (d1 + 2rz)2] * p Blankholding force for redrawing of cylindrical parts Q = (π/4) * [D2

n-1 - (dn + 2rz)2] * p

A = Area covered by blankholder from the blank or the cup, p = specific blankholding pressure [N/mm2], d1 … d2 = drawing die diameter of the corresponding stage, rz = radius of curvature of the drawing die.

Material Specific blankholding pressure p [N/mm2]

Soft steel; s < 0,5 mm 0.25 … 0.30 Soft steel; s > 0.5 mm 0.20 … 0.25 brass 0.15 … 0.20 Copper 0.10 … 0.15 aluminum 0.08 … 0.12

Accurate calculation of the blankholding force can be deduced from the following empirical formula:

sD

dDp

1002.12.0 ⎟⎠⎞

⎜⎝⎛ −=

Radius of Curvature of the Punch and Die

Fig. 154 Dependence of drawing ratios on draw punch and -die radius (as brass)

Fig. 155 drawing tools for double-action press with extra blankholder; 1 punch, 2 draw die, 3 normal blankholder, 4 extra blankholder, 5 rubber cushion, 6 press ring

Table 97 Radius of curvature of the die edge

Relative Material Thickness s/D [%] Type of part 2.0 … 1.0 1.0 … 0.3 0.3 … 0.1 Without flange (6 … 8) s (8 … 10) s (10 … 15) s

With flange (10 … 15) s (15 … 20) s (20 … 30) s With bead (4 … 6) s (6 … 8) s (8 … 10) s

Table 98. Radius of curvature for deep drawing from the band s/D 100 Drawing

stage > 2,0 2,0 … 1.0 1.6 … 0.6 Cupping <2 … 4) s (3 … 5) s (4 … 6) s

Redrawing (0,6 … 0.7) rn-1 (0,65 … 0.7) rn-1 (0,7 … 0,8) rn-1 In deep drawing in several stages using a blankholder, the punch radius can be selected according to the following points of view: a) Cupping: s/D . 100 > 0.6 rp = rd s/D . 100 = 0.6 … 0.3 rp = 1.5 rd s/D . 100 < 0.3 rp = 2 rd b) Redrawing: either the punch radius equal to half the decrease in diameter of the respective previous stage selected or provided a chamfer of 45°. c) Calibration: punch radius is equal the radius of the final part. For parts that are drawn from the band, choose the punch rounding slightly larger than the drawing ring curvature, namely, (3 … 6) s. In Figure 156 are shown the dependencies described.

r = 0.05 d s0.5 Fig. 157 Dimensions of the bead

Table 99 Radius of curvature when drawing thick material without

blankholder

Material Thickness s Radius of curvature [mm] for cupping 4 … 6 (3 … 4) s

6 … 10 (1,8 … 2,5) s 10 … 15 (1.6 … 1,8) s 15 … 20 (1.3 … 1.5) s

Fig. 156

Fig. 158 Bead Table 100 Dimensions of bead

Fig. 159 Stepped arrangement of bead close to

draw edge

( )[ ] ood sddr 150035.0 −+=

Draw Clearance The drawing gives the gap in deep drawing in the draw ring metal flowing space. In his calculation, the wall thickening at the plate and cup edge tolerances are taken into account. If the drawing clearance is too small, then there is no pure Forming, but ironing. The drawn part wall can under this circumstance be weak to bottom tear. If the draw clearance is interpreted too large, the finished parts are inaccurate. Depending on the deep-drawing method and tool design drawing of the gap must be chosen (reverse drawing with and without blankholder, etc.). The drawing clearance has a significant influence on the accuracy of the finished part. Formulas for determining drawing clearance sizes are summarized in table 101.

Table 101. One side clearance for deep drawing cylindrical parts Achievable tolerances Working level 4. und 5. Classe 7.. 8. und 9. Classe

Cupping Redrawing Finished part

z = s + δ + a z = s + δ + 2 a z = s + δ

z = s + δ + (1.5 … 2.0) a z = s + δ + (2.5 … 3.0) a z = s + δ + 2 a

The small values within the parentheses are valid for relative thick materials, the larger for thin (s/D 100 = 1,0 … 0.3) Where: z One-side clearance [mm], s Material thickness [mm], δ thickness tolerance (higher value) [mm], a Allowance according to table 102.

Table 102. Allowance a [mm] Material thickness s [mm] 0.2 0.5 0.8 1.0 1.2 1.5 1,8 2,0 2.5 3.0 4,0 5.0 Allowance a [mm] 0,05 0,1 0.12 0,15 0,17 0,19 0,21 0,22 0,25 0,3 0,35 0,4 For parts whose conicity is low, the drawing clearance as a function of the cone angle are set.

Design rules for the drawing gap: 1 For all draw stages, except the last, it is immaterial whether the drawing clearance is formed at the expense of the draw ring or of the drawing punch. 2 For the finishing draw:

a) Should items be manufactured with a given outer diameter, so the drawing clearance is formed at the expense of the punch diameter.

dd = da; dp = dd - 2 z.

b) If required by specific drawing parts the inside diameter, the dimensions of the drawing clearance at the expense of draw die be determined.

dp = di; dd = dp + 2 z;

Where: da outer diameter of the part [mm]. di inner diameter of the part [mm], dd, dp draw ring- and drawing punch-diameter [mm] z one-side clearance between punch and die [mm].

TABLE 10-5. Draw Clearance

Blank thickneaa, in. First draws Redraws Sizing draw* Up to 0.015 1.07 t to 1.09 t 1.08 t to 1.10 t 1.04 t to 1.05 t

0.016 to 0.050 1.08 t to 1.01 t 1.09 t to 1.12 t 1.05 t to 1.06 t 0.051 to 0.125 1.10 t to 1.12 t 1.12 t to 1.14 t 1.07 t to 1.09 t 0.136 and up 1.12 t to 1.14 t 1.15 t to 1.20 t 1.08 t to 1.10 t

Used for straight-aided shells where diameter or wall thickness is important, or where it is necessary to improve the surface finish in order to reduce finishing costs

t = thickness of the original blank.

Oehler and Kaiser empirical equations are valid only for deep drawing of circular components without ironing:

ooD ssu 1007.0+= for steel sheet

ooD ssu 1002.0+= for aluminum sheet

ooD ssu 1004.0+= for other nonferrous metals

ooD ssu 1020.0+= for high-temperature alloys

Part, Punch and Die Tolerances

Tolerance on external Diameter Tolerance on internal Diameter

Table 227. Manufacturing size for the working items on Deep Drawing Tools  

Deep drawing parts Manufacturing size of drawing die Manufacturing size of drawing punch a) with tolerance on external

dimension ( D - ∆) Dd = ( D – ∆ )+δz Dst = ( D - ∆ - z )-δ

st

b) with tolerance on internal dimension ( d + ∆) dd = ( d + z ) +δ

z Dst = d-δst

Where: D nominal external diameter of the finished part, d nominal internal diameter of the finished part, ∆ Tolerance of finished part, Dz; Dst; dz; dst manufacturing size of deep drawing die and punch, respectively, z both sides deep drawing clearance ( z = Dz – Dst ).

Tafel 228. Manufacturing tolerance (mm] for drawing punch and die to draw thin steel sheet having different thickness

Nominal diameter of drawing parts [mm]

10 ... 50 50 ... 200 200 ... 500 Material thickness

[mm] + δz -δst + δz -δst + δz -δst 0,25 0,02 0,01 0,03 0,015 0,03 0,015 0,35 0,03 0,02 0,04 0,02 0,04 0,025 0,5 0,04 0,03 0,05 0,03 0,05 0,035 0,6 0,05 0,035 0,06 0,04 0,06 0,04 0,8 0,07 0,04 0,08 0,05 0,08 0,06 1,0 0,08 0,05 0,09 0,06 0,10 0,07 1,2 0,09 0,06 0,10 0,07 0,12 0,08 1,5 0,11 0,07 0,12 0,08 0,14 0,09 2,0 0,13 0,085 0,15 0,10 0,17 0,12 2,5 0,15 0,10 0,18 0,12 0,20 0,14

Table 176 Diameter tolerance of cylindrical part without Flange in % from Diameter

Cupping by s/D [%] Calibration by s/D [%] Draw Ratio m

2 ... 1 1 ... 0,3 0,3 ... 0,1 2 ... 1 1 ... 0,3 0,3 ... 0,10,8 0.3 0,4 0,5 0,12 0,16 0,20 0,7 0,4 0,5 0,6 0,16 0,20 0,25 0,6 0,5 0,6 0,7 0,20 0,25 0,30 0,5 0,6 0,7 — 0,25 0.30 - 0,4 0,7 — — 0,30 - -

Tafel 177. Height tolerance of cylindrical parts without flange [mm]

Material thickness Part height (mm)

[mm] <18 18 ... 30 30 ... 505 0 ... 8 0 80 ... 120 120 ... 180 180 ... 260< 1 ±0.5 ±0,6 ±0,8 ±1,0 ±1,2 ±1,5 ±1.8

1 ...2 ±0.6 ±0.8 ±1.0 ±1.2 ±1,5 ±1,8 ±2,0 2 ...4 ±0.8 ±1.0 ±L2 ±1.5 ±1,8 ±2,0 ±2,5 4 ...6 - ±1.2 ±1.5 ±1J ±2,0 ±2.5 ±3,0

Table 178. Height tolerance of cylindrical parts with flange [mm]

Material thickness Part height (mm)•

[mm] <18 18 ... 30 30 ... 50 5 0 ... 8 0 80 ... 120 120 ... 180 180 ... 260< 1 ±0,3 ±0,4 ±0,5 ±0,6 ±0,8 ±1,0 ±1,2

1 ...2 ±0.4 ±0,5 ±0,6 ±0,7 ±0,9 ±1,2 ±1,4 2 ...4 ±0,5 ±0,6 ±0,7 ±0,8 ±1,0 ±1,4 ±1,6 4 ...6 ±0,6 ±0,7 ±0,8 ±0,9 ±1.2 ±1,6 ±1,8

Trimming of Drawn Shells

There are several ways to trim a simple drawn shell, with or without a flange. The most often used pinch-trimming method was already shown in the Fig. 3-32. A newer method using a Brehm's Shimmy Diem, was shown previously in Figs. 3-33 through 3-36. In Fig. 9-47, the values to be used when designing the pinch-trimming station are given. Notice that the trim section is added to the assembly as a separate insert, which allows for sharpening of the cutting edge, or for its exchange. Another approach to pinch trimming of angular flanges is presented in Fig. 9-48. The two methods shown can trim the parts by placing the undercut either downward, m up.

Air Vents

No drawing operation can be successful if appropriate air vents are missing from the body of a punch, as a drawn part has a tendency to stick to the punch around which it is wrapped, and remain there, as retained by the force of vacuum thus created. Air vents serve a dual purpose in the drawing operation (Figs. 9-49 and 9-50). During the drawing cycle, they eliminate the air entrapped between the face of the punch and the bottom of the drawn shell. At the end of drawing, they permit the air to reenter the space between the punch and the part, to aid in the stripping of the latter. In the absence of vents, the drawn shell would either collapse or be impossible to strip off the punch.

 

 Air vents must be protected from any dirt and lubricants, which are so abundant in the drawing operation. For this reason, air vents should be placed where the least of contamination can be expected. With complex parts, vent openings should be planned in such a way, as to guide the air from the deepest areas of the drawn part. Preferably, vents should be placed on the opposite side of sections, which will be trimmed off later on. Practical air vent diameters for tooling with a single air vent opening are as shown in Table 9-1 1. For cylindrical shell, a single air vent will suffice most of the time. However, where noncircular shapes are drawn, more than one air vent should be considered.

 Drawing Speed

While other die processes are not overly affected by the actual speed, the drawing operation is speed-dependent with respect to the material drawn. Where zinc is included in the material buildup, a slower drawing rate should be chosen. Such speed is also beneficial for drawing of austenitic stainless steel. With aluminum- and copper-based materials, greater speeds are possible. Generally used drawing speeds for single-action and double-action dies fall within a range of values as shown in Table 9-6. Exceeding the limits of drawing speed can impair the quality of produced parts, as inadequate flow of material will be obtained. An approximate drawing speed (SpeedDR) can be calculated as follows:

SpeedDR = 2 LST (PS/min) where LST is the length of the press stroke and PS/min is the number of strokes per minute.

  

 Severity of Draw and Number of Drawing Passes

The severity of the drawing operation may be expressed by the relationship of the blank diameter to the cup diameter. This ratio, often called a cupping ratio, allows for an assessment of the amount of drawing passes needed to produce a particular shell. Where this ratio is exceeded, a fracture of the shell results, attributable to the exhaustion of drawing properties of the particular material. This means that from a blank of a certain size, only a certain cup diameter and its depth may be produced during a single drawing pass. The severity of draw Is calculated using Eq. (9-4):

where K is the severity of draw factor and M is the reverse value of severity of draw factor. Recommended values of M to be used for the first drawing pass are M = 0.48 to 0.60, with dependence on the drawn material properties. The CSN 22 7301 (Czech National Standard, similar to DIN) recommends a range from

Up to

The advantage of using the severity of draw calculations at the early stages of the drawn shell evaluation is the immediate assessment of the number of drawing passes needed. Subsequent drawing passes may use the CSN 22 7301 recommendations of the M-value range, starting at

 

And up to  

 The total of all M coefficients for the particular drawing sequence is dictated by the geometry of all drawn and redrawn shapes and by the subsequent geometry of the finished shell. It may be calculated by using Eq. (9-7a):

 and subsequently

 With a greater radius of the drawing die ranging between 8t and 15t, smaller values of the severity of the draw coefficient may be used. Subsequently, with smaller drawing die radii such as those ranging between 4t and 8t, larger coefficients are recommended. For metals low in ductility, such as brass and some harder grades of aluminum, the coefficient should be made purposely larger and lowered for more ductile materials. The height h of each step of drawing sequence (see Fig. 9-13) for various types of materials must be figured out, and perhaps even tested considering the material's properties.  Other guidelines are provided by the final part's dimensioning demands and restrictions. As already mentioned, sometimes annealing between the steps becomes necessary. 

 

Lubrication in Drawing

During deep drawing, different lubrication conditions exist, from hydrodynamic lubrication in the blank holder to boundary lubrication at the drawing radius, where breakdown of the film very often occurs. Lubrication in deep drawing is important in lowering forces, increasing drawability, reducing wear of the tool, and reducing defects in the workpiece. Lubricant selection is based on the difficulty of the operation, the type of drawing operation; and the material; recommendations are given in Table 6.5. In this table, a mild operation typically is a shallow draw on low-carbon steel, a medium operation is a deep draw on low carbon steel, and a severe operation is a cartridge-case draw or a seamless tube draw.