Sheet Metal Drawing

Calculate the drawing ratio and punch force for sheet metal deep drawing operations

Inputs

D

Blank Diameter

d

Product Diameter

Formula Interpretation

Drawing Ratio

m = \dfrac{d}{D}

The drawing ratio $m$ is the ratio of product diameter $d$ to blank diameter $D$ . Metal drawing ratios are typically 0.50–0.62. A smaller $m$ means a more severe draw and higher risk of cracking. Check whether the ratio falls within the acceptable range for the material before proceeding.

Punch Force

F = \pi C_1 d t \sigma_s \quad (\text{N})

The punch force $F$ depends on the coefficient $C_1$ (from Table 1), product diameter $d$ , sheet thickness $t$ , and tensile strength $\sigma_s$ . The factor π accounts for the circumferential contact area. Units: N (newtons).

C₁ Coefficient Table

$m\,(=d/D)$	$C_1$
0.8	0.4
0.7	0.6
0.6	0.9
0.55	1.1

Table 1 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 in the table.

Knowledge Points

What Is Drawing?

Drawing (deep drawing) is a sheet-metal forming process that uses a punch and die to transform flat circular blanks into hollow cylindrical or box-shaped containers. It is the standard process for beverage cans and other thin-walled vessels. Because metal tooling is expensive, drawing is economical only for large production volumes.

Drawing Ratio and Feasibility

The drawing ratio m = d/D indicates how severe the deformation is. For the first draw, typical metal ratios range from 0.50 to 0.62. If m is too small, the blank will crack (tensile failure) at the punch radius. If m is too large, flange wrinkling may occur without a blank holder. A blank holder suppresses wrinkling and is essential for m < 0.65.

Wrinkling and Blank Holder

When drawing without a blank holder, the free flange of the blank is compressed circumferentially and tends to buckle, producing wrinkles on the rim of the product (see Fig 2). Applying a blank holder with controlled hold-down force prevents this defect. The hold-down force should be just enough to prevent wrinkling — excessive force increases punch load and risks tearing.

Worked Example

A blank of diameter $D = 100\,\text{mm}$ and thickness $t = 1.2\,\text{mm}$ is drawn into a cylindrical container of diameter $d = 70\,\text{mm}$ . The tensile strength of the sheet is $\sigma_s = 400\,\text{MPa}$ . Find the required punch force.

Given: D = 100 mm, t = 1.2 mm, d = 70 mm, σₛ = 400 MPa

Step 1 — Drawing ratio and C₁ (Formula ①)

m = \dfrac{70}{100} = 0.7 \quad \Rightarrow \quad C_1 = 0.6

Step 2 — Punch force (Formula ②)

F = \pi \times 0.6 \times 70 \times 1.2 \times 400 \approx 63{,}300\,\text{N} = 63.3\,\text{kN}

Result: F ≈ 63.3 kN. Note: without a blank holder the product rim will typically show 4 ears (earing defect). Using a blank holder eliminates wrinkling but may increase punch load slightly.

Extended Knowledge

•When blank diameter D is fixed, decreasing sheet thickness t reduces the punch load proportionally. However, a thinner sheet is more prone to wrinkling and fracture, so the process becomes harder to control.
•Multiple draws: if the required m is smaller than the single-draw limit (≈ 0.55 for steel), the part must be drawn in several stages. First draw: D → d₁ with m₁ = d₁/D typically 55–60%. Second draw: d₁ → d₂ with m₂ = d₂/d₁ at 75–85% (with holder) or 85–90% (without holder). Third and subsequent draws follow the same method as the second draw.
•Table 2 — Practical limiting drawing ratios for common materials (first draw / multi-draw): Deep-draw steel 0.55–0.60 / 0.75–0.80; Stainless steel 0.50–0.55 / 0.80–0.85; Copper 0.55–0.60 / 0.88; Brass 0.50–0.55 / 0.85; Zinc 0.65–0.70 / 0.85–0.90; Aluminium 0.53–0.60 / 0.80; Hard aluminium 0.55–0.60 / 0.90.

m\,(=d/D)

C_1

0.8

0.4

0.7

0.6

0.9

0.55

1.1