A rolling mill is used to reduce the thickness of a plate from 50 mm to 25 mm. The roll diameter is 700 mm and the coefficient of friction at the roll work interface is 0.1. It is required that the draft in each pass must be the same. Assuming no front and back tensions, the minimum number of passes required in the rolling are:

Concept:

Draft in rolling (ΔH_max):

It is the maximum possible reduction in thickness in one pass of a rolling operation. It is given by 

ΔH_max = μ²R

where

μ = coefficient of friction at the roll work interface

R = radius of roller and

ΔH = H₁ – H₂ (in one pass of rolling)

Calculation:

Given:

Diameter of roll = 700 mm ⇒ radius R = 350 mm, μ = 0.1, H_initial = 50 mm, H_final = 25 mm.

∵ ΔH_max = μ²R ⇒ (0.1)² × 350 = 3.5 mm

∴ In one pass of rolling operation 3.5 mm of thickness is reduced.

Total reduction required = H_initial - H_final ⇒ 50 – 25 = 25 mm.

⇒ 8 passes required (rounded off to next integer)