Section: Forming
Forming

Rolling

Quick Cheat Sheet

Summary

Rolling reduces stock thickness by passing it between two counter-rotating rolls. Roll force depends on flow stress, contact length and friction (the friction hill).

Key Points

  • Flat rolling vs shape rolling (rails, I-beams)
  • Draft Δh = h₀ − hf; reduction r = Δh/h₀
  • Contact length L = √(R·Δh); contact arc small angle approx
  • Friction hill: pressure peaks at the neutral point, falls toward entry & exit
  • Maximum draft Δhmax = μ²·R — friction-limited
  • Defects: wavy edges, alligatoring, edge cracks, centre split

Remember This

  • 1L = √(R · Δh) and F = Yf · L · w
  • 2Δhmax = μ² · R — increase μ or R to take a heavier reduction
  • 3Hot rolling: scaled surface, high reduction; Cold rolling: tight tolerance, work-hardened
  • 4Roll torque T ≈ 0.5 · F · L (per roll); Power P = 2π·F·L·N / 60
  • 5Width spread is negligible in flat rolling (plane strain assumption)

Quick Formulas

Contact length

L = √(R · Δh)

Roll force

F = Yf · L · w

Max draft

Δhmax = μ² · R

Rolling power

P = 2π · F · L · N / 60

Introduction to Rolling

Rolling is a metal forming process where metal is passed between two rotating rolls to reduce thickness and increase length.

Key Features

  • Most widely used metal forming process
  • ~90% of all metals produced undergo rolling
  • High production rates
  • Good surface finish
  • Economical for large quantities

Rolling Process Mechanics

Basic Principle

  • Metal stock passes between two rotating cylindrical rolls
  • Rolls rotate in opposite directions
  • Friction pulls metal into the roll gap
  • Compressive forces reduce thickness
  • Length increases (volume constant)

Roll Gap Geometry

Draft (Δh) = h₀ - hf

  • h₀ = Initial thickness
  • hf = Final thickness

Reduction (r) = (h₀ - hf)/h₀ × 100%

Roll Radius (R) = Radius of the rolls

Contact Length (L) = √(R × Δh)

  • Approximate length of contact between roll and workpiece

Neutral Point/No-slip Point:

  • Point where roll surface velocity = workpiece velocity
  • Before this point: workpiece slower than roll (pulled in)
  • After this point: workpiece faster than roll (pushed out)

Types of Rolling Mills

1. Two-High Rolling Mill

  • Two rolls rotating in opposite directions
  • Simplest configuration
  • Non-reversing: material passes in one direction only
  • Reversing: rolls can reverse direction, material passes back and forth

2. Three-High Rolling Mill

  • Three rolls stacked vertically
  • Material passes forward through bottom gap
  • Returns backward through top gap
  • No need to reverse roll direction
  • Higher productivity than two-high

3. Four-High Rolling Mill

  • Two small work rolls (contact with workpiece)
  • Two large backup rolls (support work rolls)
  • Prevents deflection of work rolls
  • Allows smaller diameter work rolls → less force required
  • Better for thin sheets

4. Cluster Rolling Mill

  • Multiple backup rolls supporting small work rolls
  • Used for very thin sheets
  • Sendzimir mill (20-high) - for stainless steel and other hard materials

5. Tandem Rolling Mill

  • Series of rolling stands in sequence
  • Continuous rolling operation
  • High production rate
  • Used in hot strip mills

Hot Rolling vs Cold Rolling

Hot Rolling

  • Performed above recrystallization temperature (typically 1000-1300°C for steel)
  • Large reductions possible (up to 99%)
  • Lower forces required
  • Poor surface finish (scale formation)
  • Less dimensional accuracy
  • Products: slabs, blooms, billets, plates, structural shapes

Cold Rolling

  • Performed at room temperature
  • Limited reduction per pass (typically 50% max)
  • Higher forces required
  • Excellent surface finish
  • Better dimensional accuracy
  • Strain hardening occurs
  • Products: sheets, strips, foils

Rolling Force and Power

Rolling Force (F)

Simplified Formula: F = Yf × L × w

Where:

  • Yf = Average flow stress of material
  • L = Contact length = √(R × Δh)
  • w = Width of workpiece

More Accurate Formula: F = Yf × L × w × Qp

Where Qp is a factor accounting for friction and geometry

Rolling Torque (T)

T = F × a

Where:

  • a = Moment arm ≈ 0.5 × L

Rolling Power (P)

P = 2πNT/60

Where:

  • N = Roll speed (rpm)
  • T = Torque per roll

Maximum Draft

Maximum Possible Draft: Limited by friction

Condition for Rolling: μ ≥ tan α

Where:

  • μ = Coefficient of friction
  • α = Angle of contact (bite angle)

Maximum Draft: Δh(max) = μ² × R

Implications:

  • Higher friction → larger draft possible
  • Larger roll radius → larger draft possible
  • For cold rolling: μ ≈ 0.1, limited draft
  • For hot rolling: μ ≈ 0.4, larger draft possible

Rolling Defects

1. Surface Defects

  • Scale: Oxide layer on hot-rolled surface
  • Scratches: From roll surface defects
  • Pits: From scale particles pressed into surface

2. Structural Defects

  • Edge cracks: Due to tensile stresses at edges
  • Alligatoring: Horizontal splitting due to non-uniform deformation
  • Wavy edges: Edges longer than center

3. Shape Defects

  • Camber: Curvature along length (banana shape)
  • Warping: Twisting or bending
  • Roll deflection effects: Thicker at edges than center

Rolling Products

Primary Rolling (Hot)

  • IngotsBlooms (square cross-section, >150mm)
  • IngotsSlabs (rectangular, width > 2× thickness)
  • IngotsBillets (square, <150mm)

Secondary Rolling

  • Blooms → Structural shapes (I-beams, rails, channels)
  • Slabs → Plates, sheets, strips
  • Billets → Bars, rods, wire (after wire drawing)

Specialized Products

  • Seamless tubes: Piercing and rolling
  • Thread rolling: For screws and bolts
  • Ring rolling: For large rings and bearings
  • Shape rolling: Rails, I-beams, channels

Advantages of Rolling

  1. High production rates
  2. Good mechanical properties (grain refinement)
  3. Economical for large quantities
  4. Wide range of products
  5. Good dimensional control (especially cold rolling)
  6. Continuous operation possible

Limitations of Rolling

  1. High capital cost (expensive equipment)
  2. Limited to simple cross-sections
  3. Residual stresses in cold rolling
  4. Surface defects in hot rolling
  5. Roll wear and maintenance costs