Sheet metal: shearing, blanking force and die clearance

Why it matters

Car body panels, appliance housings, electrical laminations and washers all start as blanks sheared from coil. Press selection depends on the cutting force, part quality depends on the punch–die clearance, and whether the clearance goes on the punch or the die decides whether the part comes out to size. These are routine calculations in a press shop and a regular GATE item.

Key ideas

Shearing mechanics. As the punch descends, the sheet first bends and is pushed into the die (forming a rounded rollover edge), then is cut cleanly for part of the thickness (the shiny burnished zone, roughly a third of the thickness for soft metals), and finally cracks run in from the punch and die edges and meet, leaving a rough fracture zone and a burr on the side away from the punch. The fraction of thickness the punch travels before fracture is the penetration (p); it is larger for soft, ductile metals.

Operations.

• Shearing / cutting off — straight cuts across a sheet.
• Blanking — cutting a closed outline; the piece removed (the blank) is the product.
• Punching (piercing) — cutting a closed outline; the piece removed (the slug) is scrap and the hole is the product.
• Notching, slitting, lancing, perforating, trimming, nibbling, fine blanking — variants. Fine blanking uses very small clearance, a V-ring holder and counter-pressure to give a fully burnished edge.

Clearance. The gap between punch and die, per side, usually expressed as a fraction of thickness, c = a·t. Typical values range from about 2–10% of t per side depending on the metal (take from your data book or the question).

• Too small — the cracks from punch and die miss each other, giving a double burnish (secondary shear), higher force and fast tool wear.
• Too large — large rollover and burr, sheet pulled into the gap, poor edge.
• Correct — the cracks meet cleanly; minimum force and good edge.

Where to put the clearance. The die opening sizes the blank; the punch sizes the hole. So:

• Blanking: die size = blank size; punch size = blank size − 2c.
• Punching: punch size = hole size; die size = hole size + 2c. Tool wear enlarges the die and shrinks the punch, so new tools are made toward the tight end of tolerance.

Cutting force. The punch shears the metal around its whole perimeter at once, so force = perimeter × thickness × shear strength. Shear strength of sheet metal is roughly 0.7–0.8 of its ultimate tensile strength. The press also needs a stripping force (to pull the punch out of the sheet, often 10–20% of the cutting force) — take its value from the question or data book.

Reducing peak force. Shear (bevel) on the punch or die makes the cut progress gradually like scissors. The total work stays roughly the same, but it is spread over a longer stroke, so the peak force falls. Shear goes on the die for blanking (the blank stays flat) and on the punch for punching (the sheet stays flat). Stepped punches in multi-punch tools have the same effect.

Die types. Simple (one operation per stroke), progressive (several stations along the strip, one operation each, a part completed every stroke), compound (blanking and punching at one station in one stroke — accurate, flat parts such as washers), and combination (cutting and forming at one station).

Formulas

F = L × t × τ — cutting force (N); L = cut perimeter (mm), t = sheet thickness (mm), τ = shear strength (MPa = N/mm²).

c = a × t — clearance per side (mm); a = clearance allowance (fraction).

Blanking: D_die = D_blank, D_punch = D_blank − 2c.

Punching: D_punch = D_hole, D_die = D_hole + 2c.

W = F × p × t — work (energy) per cut (J with F in N and t in m); p = penetration fraction.

F_shear ≈ (F × p × t) / (p × t + s) — peak force with shear s (mm) on the punch or die, from equal work spread over the longer travel (p·t + s). Some textbooks use the approximation F·p·t / s; follow the form the question gives.

τ ≈ 0.7 to 0.8 × σ_UTS — when only tensile strength is given (use the factor the question states).

Worked examples

Example 1 (standard — washer). A washer of 50 mm outside diameter and 25 mm hole is made from 2 mm sheet with τ = 350 MPa. Clearance is 6% of thickness per side. Find the blanking and punching forces and the punch and die diameters.

1. Blanking force: F_b = π × 50 × 2 × 350 = 1.100 × 10⁵ N = 110 kN.
2. Punching force: F_p = π × 25 × 2 × 350 = 5.50 × 10⁴ N = 55 kN.
3. Clearance: c = 0.06 × 2 = 0.12 mm.
4. Blanking: die = 50.00 mm, punch = 50 − 0.24 = 49.76 mm.
5. Punching: punch = 25.00 mm, die = 25 + 0.24 = 25.24 mm.

Answer: 110 kN and 55 kN (165 kN in a compound die doing both at once); blanking die 50.00 / punch 49.76 mm; piercing punch 25.00 / die 25.24 mm.

Example 2 (GATE level — shear on punch). A 100 mm diameter hole is punched in 5 mm steel sheet, τ = 400 MPa, penetration 40%. Find the peak force without shear, the work done, and the peak force with 3 mm shear on the punch.

1. F = π × 100 × 5 × 400 = 6.283 × 10⁵ N = 628 kN.
2. W = F × p × t = 6.283 × 10⁵ × 0.4 × 0.005 = 1257 J.
3. With shear: F_shear = W / (p·t + s) = 1257 / (0.002 + 0.003) = 2.51 × 10⁵ N.

Answer: 628 kN without shear; 1.26 kJ per stroke; about 251 kN with 3 mm shear (the F·p·t/s approximation would give 419 kN).

Example 3 (non-circular). A 100 × 50 mm rectangular blank from 4 mm sheet, τ = 300 MPa: F = 2(100 + 50) × 4 × 300 = 3.6 × 10⁵ N = 360 kN. (Using the blank's area instead of its perimeter is the classic error.)

Common mistakes

• Multiplying shear strength by the area of the blank instead of perimeter × thickness.
• Putting the clearance on the wrong tool: in blanking the punch is made smaller; in punching the die is made larger.
• Forgetting that clearance is per side, so diameters change by 2c.
• Using tensile strength directly as shear strength.
• Converting thickness to metres for force but not for work, or vice versa — check units.
• Placing shear on the punch in blanking, which distorts the blank.

For GATE PI

Very common: blanking and punching force for round, square and rectangular shapes; punch and die sizes with clearance; work done and peak force with shear on the punch; press tonnage for compound or progressive dies with several cuts per stroke. One-mark items ask which tool gets the clearance, which zone is burnished, and what fine blanking and progressive dies do. Practise each sizing rule until you can write it without thinking.

Quick check

1. A 20 mm hole is punched with 0.1 mm clearance per side. Punch and die diameters?
2. Which is scrap in punching: the slug or the strip?
3. Force to blank a 40 mm square from 3 mm sheet, τ = 320 MPa?
4. Why does shear on a punch reduce peak force?
5. What happens if clearance is too large?

Answers: 1. Punch 20.0 mm, die 20.2 mm. 2. The slug. 3. 4 × 40 × 3 × 320 = 153.6 kN. 4. The cut progresses gradually, spreading roughly the same work over a longer stroke. 5. Large burr and rollover, poor edge quality.