Free Engineering Tool

Deep Drawing Force Calculator

Calculate the drawing ratio (drawing coefficient) m = d/D and the punch (drawing) force for cylindrical deep drawn parts — plus the recommended die and punch radius (r-angle) and the blank-holder force. Enter the blank diameter, product diameter, sheet thickness and tensile strength; the calculator returns the force in kN, N and ton-force, the C₁ coefficient, and radius guidance for the drawing die.

This is the calculation our tooling engineers run when designing a deep drawing die: the setting of the r-angle and the drawing coefficient of the drawing die, as well as the calculation of the punch pressure. Getting the ratio and the radii right decides whether the first draw succeeds, how much press tonnage you need, and whether a redraw is required.

1 · Units
2 · Blank & Product Dimensions
Drawing ratio m = d / D  ·  Punch force F = π·C₁·d·t·σs
mm
Diameter of the flat circular blank
mm
Inside or mean diameter of the drawn cup
mm
MPa
Ultimate tensile strength of the sheet material
3 · Die & Punch Radius (r-angle)
mm
Optional — if blank, the recommended range is shown in the result
mm
Optional — typical 0.6–1.0 × r_die
The die radius controls material flow over the die edge — too small a radius tears the blank (fracture at the die shoulder), too large a radius allows wrinkling and reduces dimensional control. Punch radius mainly affects the stress at the punch nose.
Material Quick Reference
σs is the tensile strength (not shear strength) for deep drawing. Select a material to auto-fill.

Enter the blank diameter D, product diameter d, sheet thickness t and tensile strength σs above — the drawing ratio and punch force update automatically.

How it works: the drawing ratio m = d/D measures how severe the draw is. For a first draw, metals usually stay between 0.50 and 0.62. The punch force F = π·C₁·d·t·σs uses the C₁ coefficient from the standard table (interpolated), the product diameter, sheet thickness and tensile strength. The blank-holder force is estimated at ≈ 25% of the punch force. Add 10–20% safety margin for production conditions.

How the Calculation Works

Deep drawing transforms a flat circular blank into a hollow cup with a punch and die. The blank is clamped by the blank holder, the punch pushes the sheet into the die cavity, and the flange is drawn inward as the wall forms.

C₁ Coefficient Table (first draw)

m (= d / D)C₁
0.800.40
0.700.60
0.600.90
0.551.10

Table values apply to the first draw operation only. C₁ increases as the drawing ratio m decreases, reflecting the greater deformation required. Use linear interpolation for values not listed.

Material Tensile Strength & Radius Reference

Materialσs (MPa)Recommended r_die
Deep drawing steel (DC01/SPCC)280–3406–10% of D
Stainless steel 304580–7008–12% of D
Brass (H62)300–3806–10% of D
Copper (soft)200–2606–10% of D
Aluminium 5052190–2605–8% of D
Aluminium 1100 (soft)90–1305–8% of D

σs is the ultimate tensile strength. Deep drawing uses tensile strength (unlike blanking, which uses shear strength). The recommended die radius is expressed as a percentage of the blank diameter D.

Knowledge Points

Worked Example

A blank of diameter D = 100 mm and thickness t = 1.2 mm is drawn into a cylindrical cup of diameter d = 70 mm. The tensile strength of the sheet is σs = 400 MPa.

Step 1 — Drawing ratio and C₁: m = 70 / 100 = 0.70 ⇒ C₁ = 0.60.

Step 2 — Punch force: F = π × 0.60 × 70 × 1.2 × 400 ≈ 63,300 N = 63.3 kN.

Step 3 — Die radius: r_die ≈ 6–10% × 100 = 6–10 mm; punch radius ≈ 0.6–1.0 × r_die = 3.6–10 mm. Result: F ≈ 63.3 kN. Without a blank holder the rim will typically show four ears (earing); with a blank holder, wrinkling is suppressed but the punch load rises slightly.

Frequently Asked Questions

The drawing ratio m = d/D is the ratio of the drawn product diameter d to the flat blank diameter D. It measures how severe the deformation is. For a first draw, typical metal ratios are 0.50–0.62. A smaller m means a more severe draw and a higher risk of cracking at the punch radius; a larger m is a shallow draw where flange wrinkling becomes the main concern.

Punch force F = π·C₁·d·t·σs, where C₁ is a coefficient taken from the standard first-draw table (0.40 at m = 0.80 up to 1.10 at m = 0.55, linearly interpolated), d is the product diameter, t the sheet thickness and σs the tensile strength. The π factor accounts for the circumferential contact area. For a typical cup of 70 mm from a 100 mm blank, 1.2 mm steel at 400 MPa, F ≈ 63 kN.

The die radius r_die is normally 6–10% of the blank diameter D for steels (8–12% for stainless, 5–8% for aluminium). Too small a radius increases the bending stress at the die shoulder and can tear the blank; too large a radius lets the flange wrinkle and reduces control of the drawn wall. The punch radius r_punch is typically 0.6–1.0 times r_die.

A lower drawing ratio m means the blank must be drawn down much further relative to its size — the deformation work per part increases, so the coefficient C₁ (and therefore the punch force) rises. This is why deep cups need more press tonnage than shallow ones even at the same diameter and thickness.

A blank holder (pressure plate) is essential when m is below about 0.65, otherwise the free flange buckles and produces wrinkles on the product rim. The hold-down force should be just enough to prevent wrinkling — typically around 20–30% of the punch force. Too much hold-down force raises the punch load and risks tearing the part.

If the required m for a single operation would fall below the material's first-draw limit (about 0.50 for most steels), the part must be drawn in two or more steps. Each redraw uses a larger C₁ if applicable or the redraw coefficient, and intermediate annealing may be required for hard materials such as stainless steel.

Need a deep drawing die design or a quotation?

Send your drawing to shawn@balford.net — our tooling engineers will confirm the drawing ratio, r-angle setting, punch force and pricing within 24 hours.