Sheet metal operations: blanking, bending and deep drawing

Why it matters

Car body panels, appliance cabinets, electrical enclosures, brackets, washers and beverage cans are all pressed from sheet. Press work is fast and cheap per part once the tooling exists, so engineers must size punches and dies correctly, choose a press of the right tonnage and develop blanks that bend or draw without cracking or wrinkling.

Key ideas

Shearing operations separate material along a closed or open contour between a punch and a die.

• Blanking: the piece pushed out (the blank) is the product; the strip left behind is scrap.
• Piercing (punching): the hole is wanted; the slug punched out is scrap.
• Others: notching, lancing, slitting, trimming, shaving, fine blanking.

Mechanics of the cut. As the punch descends, the sheet first deforms elastically and plastically (rollover), then is sheared over part of its thickness (the bright burnished band), and finally cracks run from the punch and die edges and meet (the rough fracture zone and a burr). The punch penetration before fracture is a fraction of thickness, smaller for harder materials.

Clearance is the gap between punch and die, quoted per side as c = a·t, where the allowance a depends on the material (roughly 0.045 for soft aluminium to 0.075 for stainless and hard steels; take it from your data book).

• Correct clearance makes the cracks from both edges meet cleanly.
• Too small: secondary shear, a double burnished band, higher force and faster tool wear.
• Too large: large rollover and burr, rough edge, the sheet is pulled into the gap.
• Where to put the clearance: in blanking the die is made to the blank size and the punch smaller by 2c; in piercing the punch is made to the hole size and the die larger by 2c. The reason: the blank takes the die's size, the hole takes the punch's size.

Reducing press force. Giving the punch or die a shear (angled face) makes the cut progressive, lowering the peak force without changing the total work. Stepped punches in multi-punch dies do the same. Press types: progressive dies do several operations at successive stations as the strip advances; compound dies do several operations at one station in one stroke.

Bending strains the sheet about a straight axis. Fibres outside the neutral axis stretch, those inside compress, and the neutral axis shifts towards the inside of the bend.

• Bend allowance is the arc length of the neutral axis, used to find the flat blank length.
• Minimum bend radius is limited by cracking on the tension side and is a multiple of thickness that depends on ductility.
• Springback: when the load is removed the elastic part of the strain recovers and the bend opens slightly. It increases with yield strength and bend radius and decreases with elastic modulus and thickness. It is compensated by overbending, bottoming (coining the bend) or stretch bending.

Deep drawing forms a flat blank into a cup by pushing it through a die with a punch while a blank holder prevents the flange from wrinkling.

• The flange is in radial tension and circumferential compression (hence wrinkling); the cup wall carries the drawing force in tension, and failure usually occurs as tearing near the punch-nose radius.
• Limiting drawing ratio (LDR) – the largest D/d that can be drawn in one stage, about 2 for most sheet steels (depends on the material's normal anisotropy; see your data book). Deeper cups need redrawing.
• Too little blank-holder force → flange wrinkles; too much → tearing. Ironing thins the wall deliberately to make taller cups such as cans; earing at the rim comes from planar anisotropy.

Formulas

F_s = L·t·τ

• F_s = maximum shearing (blanking or piercing) force (N), L = length of cut perimeter (m), t = sheet thickness (m), τ = shear strength of the sheet (Pa); τ ≈ 0.7 × ultimate tensile strength if only UTS is known.

c = a·t

• c = clearance per side (m), a = clearance allowance from data book (dimensionless).

BA = α·(R + K·t)

• BA = bend allowance (m), α = bend angle (rad), R = inside bend radius (m), t = thickness (m), K = neutral-axis position factor (about 0.33 when R < 2t, 0.5 when R ≥ 2t).

F_b = K_b·σ_u·w·t² / D

• F_b = bending force (N), K_b = die factor (1.33 for V-bending, 0.33 for wiping/edge bending), σ_u = ultimate tensile strength (Pa), w = bend length (m), D = die opening (m).

D = √(d² + 4·d·h)

• D = blank diameter (m) for a cylindrical cup of mean diameter d and height h (m), thin sheet, sharp corners, no trimming allowance.

DR = D / d, reduction r = (D − d) / D

• DR must not exceed the LDR (about 2); r is about 0.5 or less.

F_d = π·d·t·σ_u·(D/d − 0.7)

• F_d = maximum drawing force (N), empirical estimate.

Worked examples

Example 1 – washer: punch and die sizes and press force (standard). A steel washer, outer diameter 50 mm and hole 20 mm, is made from 2 mm sheet in a compound die. Shear strength τ = 300 MPa, clearance allowance a = 0.06.

1. Clearance per side: c = a·t = 0.06 × 2 = 0.12 mm.
2. Blanking (outer diameter): die = 50.00 mm; punch = 50 − 2 × 0.12 = 49.76 mm.
3. Piercing (hole): punch = 20.00 mm; die = 20 + 2 × 0.12 = 20.24 mm.
4. Both cuts happen in one stroke, so L = π × (50 + 20) = 219.9 mm.
5. F_s = L·t·τ = 219.9 × 2 × 300 = 1.319 × 10⁵ N. Blanking die 50.00 mm, punch 49.76 mm; piercing punch 20.00 mm, die 20.24 mm; F ≈ 132 kN

Example 2 – deep-drawn cup (GATE level). A cylindrical cup of mean diameter 60 mm and height 40 mm is drawn from 1 mm sheet with σ_u = 400 MPa. Take LDR = 2.0.

1. Blank diameter: D = √(d² + 4dh) = √(60² + 4 × 60 × 40) = √13 200 = 114.9 mm.
2. Drawing ratio: DR = 114.9 / 60 = 1.915 < 2.0, so one draw is enough (reduction r = (114.9 − 60)/114.9 = 47.8%).
3. Drawing force: F_d = π·d·t·σ_u·(D/d − 0.7) = π × 60 × 1 × 400 × (1.915 − 0.7) N.
4. F_d = 75 398 × 1.215 = 9.16 × 10⁴ N. D ≈ 115 mm, single draw, F_d ≈ 91.6 kN

Example 3 – bend allowance and V-bending force. A 2 mm steel sheet, 100 mm long along the bend, is bent to 90° with an inside radius of 6 mm in a V-die of opening 16 mm. σ_u = 400 MPa.

1. R/t = 3 ≥ 2, so K = 0.5.
2. BA = α·(R + K·t) = (π/2) × (6 + 0.5 × 2) = 1.5708 × 7 = 11.0 mm.
3. F_b = K_b·σ_u·w·t²/D = 1.33 × 400 × 100 × 2² / 16 = 13 300 N. BA ≈ 11.0 mm, F_b ≈ 13.3 kN

Common mistakes

• Applying clearance to the wrong tool: blank size goes on the die, hole size goes on the punch.
• Using area (π·d²/4) instead of perimeter × thickness for the sheared area.
• Forgetting to convert bend angle to radians in the bend allowance.
• Using the cup's height alone to judge drawability; the check is D/d against the LDR.
• Thinking a shear on the punch reduces the work done; it lowers peak force but the energy is the same.
• Expecting springback to fall with higher-strength steel; it rises.

For GATE ME

Frequent questions: punch and die dimensions for blanking and piercing with given clearance; shearing force and the effect of shear on the punch; blank diameter for a cup and whether redrawing is needed; drawing ratio and reduction; bend allowance and flat-blank length; and conceptual questions on springback, wrinkling, tearing and earing. Practise mixed problems where a washer or a cup needs both sizing and force.

Quick check

1. In piercing a 25 mm hole with 0.1 mm clearance per side, what is the die diameter?
2. What is the shearing force to blank a 40 mm disc from 1.5 mm sheet with τ = 250 MPa?
3. What is the blank diameter for a cup 50 mm in diameter and 25 mm high?
4. Does a larger bend radius increase or decrease springback?
5. What defect appears if the blank-holder force is too low?

Answers: 1. 25.2 mm. 2. ≈ 47.1 kN. 3. ≈ 86.6 mm. 4. Increases. 5. Wrinkling of the flange.