Bulk forming: forging, rolling, extrusion and drawing

Hot and cold working, flow stress, and the mechanics of forging, rolling, extrusion and drawing with force, torque and power calculations.

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Why it matters

Crankshafts, connecting rods, steering knuckles and gear blanks are forged; body sheet and chassis sections start as rolled strip; window frames, bumper beams and radiator tubes are extruded; valve springs and wire harness conductors are drawn. Bulk forming gives continuous grain flow and work-hardened strength that machining from bar cannot, and estimating the force or power a process needs is the core numerical skill in this topic.

Key ideas

Hot, warm and cold working. The dividing line is the recrystallisation temperature, roughly 0.4–0.5 of the absolute melting temperature.

  • Hot working (above recrystallisation): low flow stress, large strains possible, no strain hardening, but oxide scale, poorer tolerances and finish.
  • Cold working (room temperature): higher forces, strain hardening raises strength and lowers ductility, excellent finish and accuracy; anneal between stages if more reduction is needed.
  • Warm working sits between them (for steel, typically a few hundred °C below the hot-working range).

Flow stress. In cold working the material strain-hardens, σ_f = K·εⁿ, so force calculations use an average flow stress Ȳ over the strain range. In hot working the flow stress depends mainly on strain rate and is taken as nearly constant.

Forging – compressive shaping between dies.

  • Open-die forging (flat dies, upsetting, cogging) for large simple shapes; impression-die forging with flash for most automotive forgings (the flash cools quickly and builds pressure that fills the cavity); closed-die (flashless) forging needs exact billet volume.
  • Friction at the die faces causes barrelling in upsetting and makes the average pressure rise with diameter-to-height ratio.
  • Hammers apply energy (impact); presses apply force (mechanical presses are stroke-limited, hydraulic presses load-limited). Related processes: upset forging (bolt heads), swaging, coining, ring rolling.

Rolling – the strip is drawn into the gap between rotating rolls by friction.

  • Draft Δh = h₀ − h_f. The strip enters slower than the roll surface and leaves faster; the neutral (no-slip) point lies between, and forward slip is the exit speed excess over roll speed.
  • The bite needs μ ≥ tan α, which gives the maximum draft Δh_max = μ²·R.
  • Roll force rises with contact length, so smaller rolls (and back/front tension) reduce force; cluster mills use small work rolls backed by larger rolls.
  • Defects: wavy edges and zipper cracks from roll bending, edge cracks, alligatoring.
  • Shape (profile) rolling, ring rolling, thread rolling and gear rolling are variants.

Extrusion – a billet is pushed through a die.

  • Direct (forward): ram and product move the same way; billet–container friction adds to force. Indirect (backward): die on a hollow ram, no billet–container sliding, lower force. Impact extrusion (thin-walled cans, cups), hydrostatic extrusion (fluid pressure, very low friction).
  • The extrusion ratio R = A₀/A_f defines the strain. Typical defects: centre-burst (chevron) cracks at low reduction and large die angles, piping, surface cracking (speed or temperature too high).

Drawing – the product is pulled through a die, so the drawing stress must stay below the flow stress of the exiting material. That caps the reduction per pass (ideal limit 63 %); wire is drawn through several dies in series. Tube drawing uses fixed or floating plugs or a mandrel.

Formulas

ε = ln(A₀ / A_f) = ln(h₀ / h_f) (true strain) A = area (m²), h = thickness (m); dimensionless.

Ȳ = K·εⁿ / (1 + n) Average flow stress (MPa) for a material obeying σ_f = K·εⁿ from zero strain to ε; K = strength coefficient (MPa), n = strain-hardening exponent.

F = K_f·Y_f·A Impression-die forging force (N); Y_f = flow stress at the end of forging (Pa), A = projected area including flash (m²), K_f = shape factor (about 1.2 for simple upsetting up to about 6–10 for complex parts with flash; take from tables).

p_avg = Y_f·(1 + μ·d / (3·h)) Average pressure for upsetting a cylinder with sliding friction (slab method); d = diameter, h = height (same units), μ = coefficient of friction.

L = √(R·Δh) Δh_max = μ²·R Roll contact length (m) and maximum draft (m); R = roll radius (m), Δh = draft (m).

F = Ȳ·w·L Roll separating force (N), ignoring friction-hill effects; w = strip width (m).

T = F·L / 2 (per roll) P = 2·π·N·F·L / 60 (both rolls) Torque (N·m) and total power (W); N = roll speed (rpm).

p = Ȳ·ln R F = p·A₀ Ideal (frictionless) extrusion pressure (Pa) and ram force (N); R = A₀/A_f, A₀ = billet area. Real pressures are higher: an empirical form p = Ȳ·(a + b·ln R) is used, with a and b from a data book.

σ_d = Ȳ·ln(A₀ / A_f) F_d = σ_d·A_f Ideal drawing stress (Pa) and drawing force (N). Real stresses are higher by a friction and redundant-work factor. Limit for a non-hardening material: σ_d = Y ⇒ ln(A₀/A_f) = 1 ⇒ maximum reduction = 1 − 1/e = 63.2 %.

Worked examples

Example 1 (standard) – flat rolling. Strip 300 mm wide is rolled from 25 mm to 20 mm with rolls of R = 250 mm at 50 rpm; Ȳ = 180 MPa; μ = 0.15.

  1. Check bite: Δh_max = μ²R = 0.0225 × 250 = 5.63 mm ≥ 5 mm ✓.
  2. L = √(R·Δh) = √(250 × 5) = 35.36 mm.
  3. F = Ȳ·w·L = 180 × 300 × 35.36 = 1.909 × 10⁶ N = 1.91 MN.
  4. Torque per roll T = F·L/2 = 1.909 × 10⁶ × 0.03536/2 = 33.75 kN·m.
  5. P = 2·π·N·F·L/60 = 2π × 50 × 1.909 × 10⁶ × 0.03536/60 = 353 kW (both rolls).

Example 2 (GATE level) – wire drawing with strain hardening. Wire is drawn from 10 mm to 8 mm diameter; the material follows σ_f = 500·ε^0.2 MPa. Ideal conditions.

  1. ε = ln(A₀/A_f) = ln(10²/8²) = ln 1.5625 = 0.4463.
  2. Ȳ = K·εⁿ/(1 + n) = 500 × 0.4463^0.2/1.2 = 500 × 0.8510/1.2 = 354.6 MPa.
  3. σ_d = Ȳ·ε = 354.6 × 0.4463 = 158.2 MPa.
  4. A_f = π × 8²/4 = 50.27 mm²; F_d = 158.2 × 50.27 = 7.95 kN.
  5. Check: σ_d (158 MPa) is below the exit flow stress 500 × 0.4463^0.2 = 425 MPa, so the pass is feasible.

Example 3 – direct extrusion, ideal. A 100 mm aluminium billet is extruded to 50 mm with Ȳ = 150 MPa. R = (100/50)² = 4; p = 150 × ln 4 = 207.9 MPa; F = 207.9 × (π/4)(100²) = 1.63 MN. Friction and redundant work raise the real force.

Common mistakes

  • Multiplying extrusion pressure by the die (product) area instead of the billet area for ram force.
  • Using engineering strain (or diameter ratio instead of area ratio) in ln terms.
  • Using the final flow stress instead of the average flow stress Ȳ for drawing, rolling and extrusion energy.
  • Forgetting the factor 2 for two rolls when computing power, or using diameter instead of radius in L = √(R·Δh).
  • Assuming any draft is possible – check Δh ≤ μ²R.
  • Calling forging "grain refining" by default; its main advantage is continuous grain flow following the part contour (hot forging does refine grains through recrystallisation).

For GATE ME

Expect numericals on rolling (contact length, maximum draft, roll force, torque, power, neutral point concepts), drawing (ideal stress, force, maximum reduction per pass), extrusion (ratio, ideal pressure, force), and forging (upsetting pressure with friction, force with shape factor, volume constancy). Conceptual questions cover hot vs cold working, direct vs indirect extrusion, and matching processes to products and defects. Practise volume constancy and true strain until they are automatic.

Quick check

  1. What is the maximum draft for μ = 0.1 and R = 300 mm?
  2. Why can't drawing exceed about 63 % reduction per pass under ideal conditions?
  3. Which extrusion has no billet–container friction?
  4. What is the contact length for R = 200 mm and Δh = 2 mm?
  5. Is hot working done above or below the recrystallisation temperature?

Answers: 1. 3 mm; 2. Drawing stress would exceed the flow stress of the drawn material; 3. Indirect (backward) extrusion; 4. 20 mm; 5. Above.

Interview questions

All Engineering Materials and Manufacturing Processes interview questions

Try answering each one aloud before you open it.

  1. 1.What is forging in the context of bulk forming processes?Concept

    Forging is a bulk forming process where metal is shaped by applying compressive forces using tools like hammers or presses. It is typically performed at high temperatures to make the metal more malleable, allowing it to be shaped without cracking. Forging improves the mechanical properties of the metal, such as strength and toughness, due to the refinement of its grain structure.

  2. 2.Explain the rolling process in manufacturing.Concept

    Rolling is a bulk forming process where metal stock is passed through one or more pairs of rolls to reduce thickness, increase length, and improve surface finish. It can be performed hot or cold, with hot rolling being used for large reductions and cold rolling for better surface finish and dimensional accuracy. Rolling is widely used for producing sheets, plates, and structural components.

  3. 3.Describe the extrusion process and its applications.Concept

    Extrusion is a bulk forming process where a billet is forced through a die to create objects with a fixed cross-sectional profile. It can be done hot or cold, with hot extrusion being more common for metals. This process is used to produce complex cross-sections and is widely used in manufacturing pipes, tubes, and structural components. Extrusion allows for high production rates and efficient material usage.

  4. 4.What is drawing in the context of bulk forming, and how does it differ from extrusion?Concept

    Drawing is a bulk forming process where metal is pulled through a die to reduce its diameter and increase its length. Unlike extrusion, where the material is pushed through a die, drawing involves pulling the material. Drawing is commonly used for producing wires, rods, and tubes. It is typically performed at room temperature, which enhances the strength of the material through work hardening.

  5. 5.Why is hot rolling preferred over cold rolling for large reductions in thickness?Application

    Hot rolling is preferred for large reductions in thickness because the metal is heated above its recrystallization temperature, making it more malleable and easier to shape. This reduces the force required for deformation and minimizes the risk of cracking. Additionally, hot rolling can handle larger initial thicknesses and produce significant reductions in a single pass, which is more efficient for large-scale production.

  6. 6.What happens if the temperature is too low during the forging process?Application

    If the temperature is too low during forging, the metal may not be sufficiently malleable, leading to increased resistance to deformation. This can result in higher forces being required, which may cause tool wear or failure. Additionally, the risk of cracking or fracturing the metal increases, as it is less ductile at lower temperatures. Proper temperature control is crucial to ensure the quality and integrity of the forged product.

  7. 7.Why is lubrication important in the extrusion process?Application

    Lubrication is important in the extrusion process because it reduces friction between the billet and the die, which decreases the force required for extrusion. This helps in achieving smoother surfaces and more precise dimensions. Lubrication also reduces wear on the die and extends its life, making the process more cost-effective. Additionally, it helps in controlling the temperature rise due to friction, preventing defects in the extruded product.

  8. 8.Calculate the ram force required to extrude an aluminium billet of diameter 0.1 m through a die of diameter 0.05 m, given that the extrusion pressure is 150 MPa.Numerical

    The extrusion pressure acts on the ram face, so the force uses the billet (container) area, not the die area. A₀ = π × 0.1²/4 = 7.854 × 10⁻³ m². F = p × A₀ = 150 × 10⁶ × 7.854 × 10⁻³ ≈ 1.18 × 10⁶ N, i.e. about 1.18 MN. For reference, the extrusion ratio here is (0.1/0.05)² = 4.

  9. 9.A steel rod is drawn from an initial diameter of 10 mm to a final diameter of 6 mm. Calculate the percentage reduction in area.Numerical

    The percentage reduction in area is calculated using the formula: % Reduction = [(A_initial - A_final) / A_initial] × 100. First, calculate the initial and final areas: A_initial = π × (10/2)^2 = 78.54 mm², A_final = π × (6/2)^2 = 28.27 mm². Then, % Reduction = [(78.54 - 28.27) / 78.54] × 100 = 64.02%.

  10. 10.What are the advantages of using the drawing process for wire production?Application

    The drawing process offers several advantages for wire production, including improved mechanical properties due to work hardening, precise control over dimensions, and a smooth surface finish. It is also a cost-effective method for producing long lengths of wire with consistent quality. Additionally, drawing can be performed at high speeds, making it suitable for large-scale production.

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