Deep drawing calculation: a worked example
A 40 mm diameter, 30 mm deep cup in 1.0 mm DC04 — the blank, the draw ratio, the draw force, the press and the die clearance, all the way through, with every assumption written down so you can check it.
1. The part
| Parameter | Value |
|---|---|
| Outer diameter d | 40 mm |
| Height h | 30 mm |
| Wall thickness t | 1.0 mm |
| Material | DC04 deep drawing steel |
| Tensile strength σB (assumed) | 300 N/mm² |
2. The blank
For a cylindrical cup the blank is sized on surface area, which for a flat bottom and straight wall reduces to:
D ≈ √(d² + 4·d·h)With d = 40 and h = 30:
D ≈ √(1600 + 4800) = √6400 = 80 mmSo an 80 mm blank. That already tells you something useful: the part needs a blank twice its own diameter, which means a lot of material has to flow inward from the flange, and that is what decides everything after this.
3. The draw ratio, and how many draws
β = D ÷ d = 80 ÷ 40 = 2.0A draw ratio of 2.0 is right at the edge for DC04, whose first-draw limit is around 1.8–2.0. Rather than gamble on a single operation, the part is planned as two draws:
| Stage | Diameter | Ratio for that stage | Within limit? |
|---|---|---|---|
| Blank | 80 mm | — | — |
| First draw | 55 mm | 80 ÷ 55 = 1.45 | yes |
| Second draw | 40 mm | 55 ÷ 40 = 1.38 | yes |
Splitting a 2.0 ratio into 1.45 and 1.38 keeps both stages comfortably inside what the material will take. It also costs a second tooling station — the trade every deep drawing quotation is really about.
4. The draw force
F = π · dp · t · σB · kwith dp the punch diameter of that stage and k an empirical factor that accounts for friction, bending over the die radius and the actual strain distribution. For a first draw of this shape, k around 0.6 is a reasonable starting point. Using the punch of the first stage, 55 mm:
F = 3.1416 · 55 · 1.0 · 300 · 0.6 ≈ 31,100 N ≈ 31 kNRoughly 3.2 tonnes of draw force. Add the blank holder, which for a first draw typically runs 20–30 % of the draw force:
FNH ≈ 0.25 · 31 kN ≈ 8 kN → total ≈ 39 kN5. The press
39 kN is under 4 tonnes, so on force alone almost any press would do. In practice the press is chosen on three other things:
| Factor | Why it decides the press |
|---|---|
| Bed and stroke | the blank is 80 mm and the part 30 mm deep, so the tool needs daylight and a stroke to match |
| Margin | a press run near its rating loses parallelism and the wall thickness drifts; shops plan 30–50 % headroom |
| Stages | two draws in one tool needs the bed length for two stations, or two separate presses |
This is why a part with a small calculated force can still need a disproportionately large press: the number in the formula is the force, not the machine.
6. The die clearance
Clearance per side is set as a multiple of sheet thickness. For DC04 at 1.0 mm, 1.2–1.4 × t is the usual starting range, so about 1.2–1.4 mm per side here. Too tight and the wall is shaved and the tool wears; too loose and the wall wrinkles instead of being ironed straight.
7. The whole plan in one table
| Quantity | Value | Set by |
|---|---|---|
| Blank diameter | 80 mm | surface area of the finished cup |
| Overall draw ratio | 2.0 | blank ÷ finished diameter |
| Draws | 2 | material limit for DC04 |
| Intermediate diameter | 55 mm | splitting the ratio evenly |
| Draw force, first stage | ≈ 31 kN | punch diameter, thickness, tensile strength, factor |
| Blank holder force | ≈ 8 kN | 25 % of draw force |
| Die clearance per side | 1.2–1.4 mm | 1.2–1.4 × thickness |
8. Run it with your own numbers
The example above is the arithmetic behind the deep draw force calculator: put in a blank diameter, a punch diameter, a thickness and a tensile strength and it returns the draw force, the draw ratio and a press tonnage. The wider method is in the complete technical guide, including what happens when the ratio will not fit in one draw.