Sheet metal operations: blanking, bending and deep drawing

Shearing mechanics, clearance and die sizing for blanking and piercing, bending allowance, force and springback, and deep drawing blank size, drawing ratio and force.

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Why it matters

A car body-in-white is several hundred pressed steel and aluminium panels, and brackets, oil sumps, fuel tanks, wheel discs and filter housings are all blanked, bent or drawn. Press tonnage, die dimensions, blank sizes and the number of draws are decided by the calculations in this topic, and getting clearance or springback wrong shows up as burrs, cracked flanges and parts that do not fit.

Key ideas

Shearing operations (cutting). A punch pushes the sheet into a die. The sheet first deforms plastically, then the punch penetrates part of the thickness (the burnished zone), and finally cracks run from punch and die edges and meet (the fracture zone), leaving a burr.

  • Blanking – the piece punched out is the part. Piercing/punching – the hole is wanted and the slug is scrap. Others: notching, lancing, slitting, trimming, shaving, fine blanking, nibbling.
  • Clearance is the gap between punch and die, per side. Correct clearance lets the two cracks meet cleanly. Too small: secondary shearing, higher force and tool wear. Too large: big burr, rollover and a rough edge. Clearance rises with sheet thickness and strength; take the allowance factor from a handbook (commonly about 4–8 % of thickness per side for steel).
  • Which tool gets the clearance? In blanking the die is made to the blank size and the punch is smaller by 2c. In piercing the punch is made to the hole size and the die is larger by 2c. Reason: the blank takes the size of the die opening and the hole takes the size of the punch.
  • Reducing press force: give shear (an inclined face) to the punch for piercing or to the die for blanking, so the part stays flat; or stagger punches in a progressive die.
  • Die types: progressive (several stations, strip advanced each stroke), compound (blanking and piercing at one station, one stroke) and combination dies (cutting plus forming).

Bending. The outer fibres stretch, the inner fibres compress, and the neutral axis shifts towards the inside for tight bends. The developed length is found with the bend allowance measured along the neutral axis.

  • Springback: elastic recovery after unloading opens the bend. It grows with yield strength/E and with R/t. Counter it by over-bending, bottoming or coining the bend, or stretch-bending.
  • Minimum bend radius: below it the outer fibres crack; it depends on ductility (reduction in area) and on bending across rather than along the rolling direction.
  • Operations: V-bending, edge (wiping) bending, flanging, hemming, roll forming, tube bending.

Deep drawing. A punch pulls a flat blank, held under a blank holder, into a die to make a cup or box.

  • The flange is under radial tension and circumferential compression – too little blank-holder force gives wrinkling; too much causes tearing at the punch radius, where the wall is thinnest.
  • Limiting drawing ratio (LDR = D/d) is about 2 for most steels; it improves with high normal anisotropy (r̄), which resists thinning. Earing is caused by planar anisotropy (Δr).
  • Cups too deep for one draw are redrawn (successive reductions smaller, e.g. about 40–45 % first, 25–30 % second, then lower; take values from a handbook), with intermediate annealing if needed. Ironing thins the wall to make tall cans.
  • Related: stretch forming, spinning, bulging, hydroforming, embossing.

Formulas

F_s = τ·L·t (≈ 0.7·σ_u·L·t if only UTS is known) Shearing force (N); τ = shear strength (Pa), L = cut perimeter (m), t = sheet thickness (m).

F_shear = F_s·(p·t) / s (when s ≥ p·t) Force with shear on the punch or die; p = fractional penetration at fracture (about 0.3–0.6), s = amount of shear (m). The work done, F_s·p·t, is unchanged.

D_die = D_blank D_punch = D_blank − 2c (blanking) D_punch = D_hole D_die = D_hole + 2c (piercing) c = clearance per side (m).

BA = α·(R + K·t) Bend allowance (m); α = bend angle (rad), R = inside bend radius (m), K = neutral-axis factor (about 0.33 for R < 2t and 0.5 for R ≥ 2t in a common textbook rule; other books use slightly different values).

F_b = K_bf·σ_u·w·t² / D Bending force (N); K_bf ≈ 1.33 for V-bending and 0.33 for edge bending, w = bend length (m), D = die opening (m), σ_u = UTS (Pa).

D = √(d² + 4·d·h) Blank diameter for a cylindrical cup with sharp corners (constant area, thickness unchanged); d = cup diameter, h = cup height (m).

DR = D / d r = (D − d) / D Drawing ratio and reduction; first draw typically DR ≤ about 2 (r ≤ about 0.5).

F_d = π·d·t·σ_u·(D / d − 0.7) Empirical maximum drawing force (N); d = punch diameter (m).

Worked examples

Example 1 (standard) – washer die sizes and force. A washer of 50 mm OD with a 25 mm hole is made from 2 mm steel (τ = 300 MPa). Clearance per side c = 0.12 mm.

  1. Blanking (OD 50 mm): die = 50.00 mm, punch = 50.00 − 2 × 0.12 = 49.76 mm.
  2. Piercing (hole 25 mm): punch = 25.00 mm, die = 25.00 + 0.24 = 25.24 mm.
  3. Forces: blanking F = τ·L·t = 300 × π × 50 × 2 = 94.2 kN; piercing = 300 × π × 25 × 2 = 47.1 kN.
  4. In a compound die both act together: 141.4 kN.
  5. If penetration p = 0.4 and the tools are given 1 mm shear, the peak force falls to 141.4 × (0.4 × 2)/1 = 113 kN.

Example 2 (GATE level) – cup drawing. A cup d = 60 mm, h = 40 mm is drawn from 1 mm steel with σ_u = 350 MPa.

  1. D = √(d² + 4dh) = √(3600 + 9600) = √13 200 = 114.9 mm.
  2. DR = 114.9/60 = 1.915 (below about 2, so one draw is possible); reduction r = (114.9 − 60)/114.9 = 47.8 %.
  3. t/D = 1/114.9 = 0.87 % – a thin blank, so a blank holder is needed against wrinkling.
  4. F_d = π·d·t·σ_u·(D/d − 0.7) = π × 60 × 1 × 350 × (1.915 − 0.7) = 80.1 kN.

Example 3 – bend allowance. 90° bend, R = 5 mm, t = 2 mm. Since R ≥ 2t, K = 0.5: BA = (π/2) × (5 + 0.5 × 2) = 9.42 mm.

Common mistakes

  • Applying clearance to the wrong tool (blanking die vs piercing punch).
  • Using the blank diameter instead of the punch diameter in the drawing-force formula, or the cup height instead of the blank diameter in the drawing ratio.
  • Mixing MPa with N/m² and getting forces off by 10⁶.
  • Thinking more blank-holder force always helps – it prevents wrinkles but causes tearing.
  • Treating springback as larger for softer, lower-strength material – it is larger for high Y/E and large R/t.
  • Putting shear on the punch in blanking (it distorts the blank); for blanking the shear goes on the die.

For GATE ME

Very common numericals: blanking/piercing force, punch and die dimensions with clearance, force reduction by shear, work done in punching, blank diameter for cups, drawing ratio and number of draws, bend allowance and bending force. Conceptual questions cover clearance effects, springback, progressive vs compound dies, wrinkling vs tearing, and anisotropy. Practise keeping track of which tool carries the clearance.

Quick check

  1. In piercing a 20 mm hole with 0.1 mm clearance per side, what is the die diameter?
  2. Blank diameter for a cup d = 40 mm, h = 30 mm (sharp corners)?
  3. Force to punch a 10 mm hole in 3 mm sheet with τ = 400 MPa?
  4. What defect is caused by too little blank-holder force?
  5. Does springback increase or decrease with higher yield strength?

Answers: 1. 20.2 mm; 2. √(1600 + 4800) = 80 mm; 3. 37.7 kN; 4. Wrinkling of the flange; 5. Increase.

Interview questions

All Engineering Materials and Manufacturing Processes interview questions

Try answering each one aloud before you open it.

  1. 1.What is blanking in sheet metal operations?Concept

    Blanking is a sheet metal cutting process where a punch and die are used to cut out a piece of metal from a larger sheet. The piece that is cut out is called a blank and is typically the desired part, while the remaining material is scrap. This process is commonly used in manufacturing to produce parts that will be further processed or assembled.

  2. 2.Explain the bending process in sheet metal operations.Concept

    Bending is a sheet metal forming process where a force is applied to a piece of sheet metal, causing it to bend at an angle and form the desired shape. This process is typically performed using a press brake and can create simple bends or complex shapes. Bending is used to create parts like brackets, enclosures, and frames.

  3. 3.What is deep drawing in sheet metal operations?Concept

    Deep drawing is a sheet metal forming process where a sheet metal blank is radially drawn into a forming die by the mechanical action of a punch. It is used to produce cup-shaped, box-shaped, or other complex-curved, hollow-shaped parts. This process is commonly used in the manufacturing of automotive components, kitchen sinks, and beverage cans.

  4. 4.Why is blanking preferred over other cutting processes for mass production?Application

    Blanking is preferred for mass production because it is a highly efficient and cost-effective process. It allows for the rapid production of large quantities of parts with consistent quality and precision. The use of a punch and die setup ensures that each blank is identical, reducing material waste and minimizing the need for secondary operations.

  5. 5.What happens if the punch–die clearance is too small during blanking?Application

    With too little clearance the cracks starting at the punch and die edges miss each other, so a second shearing (secondary burnish) occurs and the edge shows two shiny bands. The blanking force and energy rise and punch and die edges wear and chip faster. Too large a clearance gives the opposite problem: large rollover, a big burr and a rough, tapered edge. Clearance is chosen as a percentage of sheet thickness that rises with material strength.

  6. 6.How does the material's ductility affect the deep drawing process?Application

    The ductility of the material is crucial in the deep drawing process because it determines how well the material can be stretched into the desired shape without cracking. Materials with high ductility can undergo significant deformation, allowing for deeper draws and more complex shapes. If the material is not ductile enough, it may crack or tear during the process.

  7. 7.What are the common defects in the bending process, and how can they be minimised?Application

    The main defects are springback, cracking on the outer surface and thinning or distortion at the bend. Springback is countered by over-bending, bottoming or coining the bend, or stretch-bending; it is worse for high yield-strength-to-modulus materials and large R/t. Outer-fibre cracking is avoided by keeping the radius above the material's minimum bend radius, bending across the rolling direction and keeping burrs on the inside of the bend. Wrinkling is mainly a risk on the compressed inner side of flanges and in tube bending, controlled with proper tooling support.

  8. 8.Calculate the blank diameter required for a deep drawing operation to produce a cylindrical cup with a diameter of 100 mm and a height of 150 mm. Assume no material thinning.Numerical

    To calculate the blank diameter, use the formula: Blank Diameter = √(D² + 4DH), where D is the cup diameter and H is the height. Substituting the given values: Blank Diameter = √(100² + 4 × 100 × 150) = √(10000 + 60000) = √70000 ≈ 264.58 mm.

  9. 9.A sheet metal part requires a bend angle of 90 degrees. If the material thickness is 2 mm and the inside bend radius is 5 mm, calculate the bend allowance.Numerical

    Bend allowance BA = α(R + K·t), where α is the bend angle in radians and K locates the neutral axis. In the common textbook rule K ≈ 0.33 when R < 2t and 0.5 when R ≥ 2t; here R = 5 mm ≥ 2t = 4 mm, so K = 0.5. BA = (π/2)(5 + 0.5 × 2) = 1.571 × 6 ≈ 9.42 mm. Using K = 0.33 would give 8.89 mm, so state the K value assumed.

  10. 10.Explain why springback occurs in the bending process and how it can be compensated for.Application

    Springback occurs in the bending process due to the elastic recovery of the material after the bending force is removed. This causes the material to partially return to its original shape, resulting in a bend angle that is less than intended. To compensate for springback, over-bending the material slightly or using materials with lower yield strength can help achieve the desired final angle.

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