Cold Rolling vs Hot Rolling

How rolling reduces thickness

A slab, plate, or sheet of metal enters a stand with two work rolls that rotate in opposite directions. The roll surface speed exceeds the entry strip speed; friction grabs the strip and drags it into the bite. Between the rolls the metal is squeezed: thickness drops from h_in to h_out, length grows in proportion (volume is conserved), and width spreads only slightly because the rolls are wide compared with the strip thickness. Plane-strain compression is the textbook idealisation. The strip leaves the bite faster than it entered, climbing in speed exactly as it thins.

That single mechanical picture covers every rolling operation on Earth. The variable that decides whether the operation is hot rolling or cold rolling is the absolute temperature of the strip relative to the alloy's recrystallization temperature. Above it, the metal is soft and continually anneals itself as it deforms. Below it, the metal work-hardens with every pass.

                  ┌──────────────┐
            ───►  │   work roll  │  ◄── rotates clockwise
                  └──────┬───────┘
   slab  ████████████████│████████░░░░░░░░░░░  strip (faster, thinner)
   h_in                  │                     h_out
        ░░░░░░░░░░░░░░░░░│░░░░░░░░████████████
                  ┌──────┴───────┐
            ───►  │   work roll  │  ◄── rotates counter-clockwise
                  └──────────────┘
        ◄────── bite ──────►
        Δh = h_in − h_out  =  draft

The recrystallization line

Plastic deformation pumps dislocations into the metal at densities up to 10^16 m^-2. Each dislocation stores about 1 eV of energy in the lattice. If the temperature is high enough that atoms have enough thermal vibration to migrate — roughly 0.4 to 0.6 of the absolute melting point — the stored energy drives the nucleation and growth of new, strain-free grains. This is recrystallization.

Alloy            T_melt      T_recryst (~0.6 T_m)     Practice
─────────────    ──────      ───────────────────      ──────────
Plain-C steel    1538 °C     ~700 °C absolute         hot roll 1050–1250 °C
Aluminum         660 °C      ~150 °C absolute         hot roll 350–500 °C
Copper           1084 °C     ~200 °C absolute         hot roll 700–900 °C
Brass (70/30)    955 °C      ~370 °C absolute         hot roll 750–850 °C
Titanium         1668 °C     ~880 °C absolute         hot roll 950–1100 °C

Industrial hot rolling is always done well above T_recryst — hot enough that recrystallization completes between passes (and often during the bite itself, "dynamic recrystallization"). The metal stays soft no matter how many passes have already happened, so the same equipment can take a 250 mm thick slab down to a 1.6 mm hot band in seventeen passes without any intermediate anneal. Cold rolling is everything done below T_recryst, almost always at or near room temperature.

Hot rolling — big drafts, fine grain, scaled surface

A continuous slab caster pours molten steel into a 250 mm × 1500 mm × 12 m slab at a stand of rolls just beyond the mould. The slab is then reheated to 1200 to 1250 °C in a walking-beam furnace and fed into the hot strip mill: typically a five- or six-stand roughing line that brings it to 25 mm transfer-bar thickness, then a six- or seven-stand finishing line that takes it down to 1.6 to 25 mm hot-band thickness at strip speeds reaching 25 m/s on the exit stand. Total time from slab to coiled hot band is two to three minutes.

Hot rolling has three distinctive features. First, the flow stress is low — about 100 MPa for steel at 1100 °C, versus 500 to 1000 MPa at room temperature — so per-pass reductions of 30 to 50 percent are routine. Second, dynamic and metadynamic recrystallization between stands refines the grain on every pass; a typical hot band has 10 to 20 μm equiaxed ferrite grains, finer than the as-cast 100 to 500 μm columnar dendrites. Third, the strip oxidises continuously: oxygen reacts with the hot iron surface to form a multi-layer mill scale (FeO inside, Fe₃O₄ middle, Fe₂O₃ outside) that cracks and flakes off but leaves a coarse blue-grey finish. Tolerances on hot band are loose — about ±0.5 mm thickness, ±1 percent width — limited by mill stretch, scale variation, and thermal contraction during cooling on the runout table.

Cold rolling — work hardening, mirror surface, tight tolerance

Cold rolling starts where hot rolling ends. A hot band coil is pickled in hydrochloric acid to dissolve the scale, then fed into a five-stand tandem cold mill where it is reduced in one pass from 2 to 6 mm hot band thickness to 0.15 to 2 mm cold strip — a total reduction of 60 to 90 percent. The strip exits the last stand at speeds approaching 25 m/s; modern automotive lines run at 1500 m/min sustained.

Three things change versus hot rolling. First, flow stress is high. Roll-separating forces are two to four times what they would be at the same draft hot — the work rolls deflect, mill stretch grows, and the strip flattens its own profile rather than the rolls profiling the strip. Mills compensate with hydraulic roll bending, roll crown grinding, and CVC shifting. Second, because there is no recrystallization, dislocations accumulate and the metal work-hardens: yield and tensile strength climb by 30 to 50 percent at the cost of ductility, which drops from 30 to under 10 percent elongation. Cold mills install batch (bell-furnace, 16-hour) or continuous (radiant-tube, 5-minute) anneals at 600 to 720 °C between passes when ductility has run out. Third, the surface is whatever the rolls give it: ground-to-mirror rolls produce bright finish, electric-discharge-textured (EDT) rolls produce a controlled microscopic roughness that car-paint adhesion and stamping lubricant retention both depend on.

Roll-separating force — Schey's formula

The simplest engineering estimate of roll force uses a slab-method balance and gives, for plane-strain rolling without friction or front/back tension:

P = w · k_f · √(R · Δh)

  P    = roll-separating force (N)
  w    = strip width (mm)
  k_f  = mean flow stress in the bite (MPa)
  R    = work-roll radius (mm)
  Δh   = h_in − h_out = draft (mm)

The square root captures something physical: the arc of contact between the roll and the strip is √(R·Δh) long, and the integrated pressure scales with it. With friction, k_f is augmented by a factor (1 + μL/2h̄) where L = √(R·Δh) is the contact arc length, h̄ the mean thickness, and μ the friction coefficient — typically 0.04 to 0.10 for lubricated cold rolling and 0.20 to 0.40 for hot. With strip tension, k_f is reduced.

Worked example. A 1500 mm wide cold mill takes 6 mm hot-band steel down to 4 mm on R = 350 mm work rolls. The strip flow stress is k_f ≈ 250 MPa (mid-bite mean for low-carbon steel after 30 percent prior reduction):

P = 1500 × 250 × √(350 × 2)
  = 375,000 × √700
  = 375,000 × 26.46
  ≈ 9.9 MN  ≈ 1000 tonnes per stand

Multiplied across five stands of a tandem mill, total mill force exceeds 4500 tonnes. The same draft hot — with k_f ≈ 100 MPa — would need only about 400 tonnes per stand. The factor-of-2.5 force premium is one half of the cost premium of cold-rolled sheet versus hot-rolled coil.

Head-to-head comparison

Attribute	Hot rolling	Cold rolling
Temperature	Above T_recryst (~1100 °C for steel)	Below T_recryst (room temp)
Flow stress	~100 MPa (steel)	~500–1000 MPa (steel, after work hardening)
Draft per pass	30 to 50 percent	20 to 35 percent
Mechanism	Continuous recrystallization keeps grain fine	Dislocation accumulation — work hardens
Yield strength change	~unchanged after each pass	+30 to 50 percent over starting hot band
Ductility	High (recovery in pass)	Drops sharply; needs intermediate anneal
Surface	Oxide scale (mill finish, blue-grey, rough)	Bright/EDT/mirror — controlled texture
Thickness tolerance	±0.5 mm typical	±0.05 mm typical
Width tolerance	±1 percent	±0.2 percent
Lubrication	Mostly water (descales + cools); some emulsions	Forced oil-in-water emulsion or neat oil
Anneals required	None — recrystallization in-line	Batch (bell) or continuous (CAL) between passes
Roll force (same draft)	1× baseline	2 to 4× baseline
End products	Plate, beam, rebar, hot band, pipe, rail	Auto sheet, can stock, lamination steel, cable sheath
Cost premium	Reference	+30 to +60 percent per tonne

The tandem mill — five stands in series

A modern cold strip mill is a tandem mill: five (or sometimes six) four-high rolling stands in a line, with the strip threaded continuously through all of them. Each stand has a pair of small-diameter work rolls (350 to 600 mm) backed up by much larger back-up rolls (1200 to 1500 mm) that resist deflection. The strip enters stand 1, passes through 2, 3, 4, 5 without rewinding, and is coiled at the exit. Strip speed multiplies down the line: a 6 mm entry at 5 m/s becomes a 0.7 mm exit at 43 m/s, because volume is conserved.

PICKLING ──► STAND 1 ──► STAND 2 ──► STAND 3 ──► STAND 4 ──► STAND 5 ──► COILER
  scale       6.00 mm     4.20 mm     2.95 mm     2.07 mm     1.45 mm     0.70 mm
   off       (30% red)   (30% red)   (30% red)   (30% red)   (52% red)
              5 m/s       7.1         10.2        14.5        20.7        43.0 m/s

Three computer loops run constantly: an automatic gauge control (AGC) loop that adjusts hydraulic screw-down to hold exit thickness, a shape-control loop that adjusts roll bending and CVC shifting to flatten the strip profile, and a tension loop that adjusts inter-stand strip tension to keep the strip straight without breaking it. A tandem cold mill running flat-out produces a 25-tonne coil of body-panel sheet every 90 seconds — about 12,000 tonnes per day on a busy line. A reversing mill — one stand the strip passes through repeatedly — is the older alternative, used for stainless, silicon steel, and special low-volume grades.

Skin pass — the last 0.5 percent

Cold-rolled and annealed sheet is too soft for direct stamping: the moment a customer's press starts to deform it, the metal develops localised yield lines (Lüders bands) that print visible stretch marks on the finished part. The remedy is a final skin-pass or temper pass — a very light reduction of 0.3 to 1.5 percent — that pre-strains the strip just past the yield point, eliminating the discontinuous-yield plateau. As a bonus, the skin-pass rolls transfer their surface texture to the strip: mirror-ground rolls give a bright finish, EDT rolls give a uniform random texture that paint adheres to, shot-blasted rolls give a coarser stamping-lubricant-retention finish. Skin-pass mills are single-stand or two-stand and run far slower than the tandem mill upstream — they are about finish, not throughput.

Where each ends up in the real world

• Hot-rolled structural beams. I-beams, H-beams, channel, angle, and rebar are all hot-rolled out of bloom or beam-blank slabs through profiled stands. Surface finish is irrelevant — the steel will be painted or fireproofed once in place — and section thickness is too high for cold work to be economic.
• Hot-rolled plate. Shipbuilding plate, pressure-vessel plate, and pipeline plate are produced on heavy plate mills as 5 to 200 mm hot-rolled product. Ultra-large reversing two-high or four-high stands roll a single slab through dozens of reciprocating passes to reach the final thickness.
• Cold-rolled automotive body sheet. A modern body-in-white is built almost entirely from 0.6 to 1.2 mm cold-rolled steel sheet: dual-phase, TRIP, martensitic, and press-hardenable grades. The surface texture and tolerance are why door inner panels, hoods, and fenders can be drawn, painted, and welded together without visible defects.
• Beverage cans. A modern aluminum two-piece can is drawn from a cold-rolled 0.28 mm 3104-H19 blank, ironed (squeezed between concentric rings) down to 0.10 mm walls. Without cold rolling and ironing, no can plant would run at 2400 cans per minute per line.
• Cable sheath and conduit. Cold-rolled and welded steel tube — armoured cable jackets, electrical conduit, hydraulic line — relies on the dimensional consistency of cold strip slit to width.
• Electrical steel. Transformer cores and motor laminations are stamped from cold-rolled grain-oriented silicon steel (3 percent Si), which depends critically on the cold reduction schedule and final anneal to develop the Goss texture that lowers core loss.

Defects, and what causes them

• Chatter (cold mill). Vertical-mode resonance between the work-roll stack and the strip, typically at 100 to 600 Hz. Imprints periodic thickness variations and a "tiger-stripe" surface. Triggered by inadequate damping, worn back-up roll bearings, or running too fast with too much friction reduction.
• Edge cracking (both). Lateral spread at the strip edge creates a free surface in tension. Hot strip with surface chill or cold strip with work-hardened brittleness cracks at the edge, propagating inward. Mitigated by edge heaters (hot) and edge trimming (cold).
• Alligatoring (hot). A slab whose centre is colder than the surface — typical when the surface picks up scale and emissively cools — splits along the rolling plane during the pass, producing two diverging plates with an open jaw. Avoided by adequate reheat soak and lower reduction on the first pass.
• Shape defects (cold). Centre buckle, wavy edge, quarter buckle: longitudinal length differences between strip zones that exceed about 30 microns over the strip width buckle into visible waves. Controlled by hydraulic roll bending, work-roll CVC shifting, and selective roll cooling.
• Rolled-in scale (hot). Mill scale that does not fully descale gets pressed into the surface as a hard pit. Carried through into the cold rolling stage and cannot be removed without surface grinding.
• Coil set and crossbow (both). Residual curvature from uneven through-thickness deformation. Skin-pass with strip-flattener rolls is the standard fix.

Common pitfalls

• Confusing "warm rolling" with cold rolling. Warm rolling at 200 to 500 °C for steel — between recovery and recrystallization — partly relaxes the dislocation network without full annealing. It produces intermediate strength and surface finish; some stainless and silicon steel mills run warm passes between cold passes.
• Assuming hot-rolled means weak. Hot-rolled microalloyed steels (HSLA grades) reach 500 to 700 MPa yield through controlled precipitation of niobium, vanadium, or titanium carbides during cooling on the runout table — without any cold work. Strength does not have to come from a cold mill.
• Skipping the pickle line. A hot band fed into a cold mill with residual scale will tear up the work rolls in seconds. Pickling is non-negotiable.
• Underestimating springback. Cold-rolled high-strength steel has high yield and modest modulus, so a bent part springs back more — up to 10 degrees on dual-phase grades. Die designers overbend to compensate.
• Confusing temper rolling with thermal tempering. Temper rolling (skin pass) is a mechanical operation that flattens and textures finished strip. Thermal tempering is a heat treatment that softens quenched martensite. They share no physics.