Question

The thickness of a plate is reduced from 30 mm to 10 mm by successive cold rolling passes using identical rolls of diameter 600mm. Assume that there is no change in width. If the coefficient of friction between the rolls and the workpiece is 0.1, the minimum number of passes required is

• A. 3
• B. 4
• C. 6
• D. 7

Answer 1

The correct option is D 7

Given data:
$h_i=30mm$

$h_f=10mm$

$(\Delta h{)}_{actual}=30-10=20mm$

$(\Delta h{)}_{max}={\mu }^{2}R$

$=(0.1{)}^2\times 300$
$=3$ mm

Minimum number of passes required

$=\frac{(\Delta h{)}_{actual}}{(\Delta h{)}_{max}}=\frac{20}{3}=6.66\simeq 7$