Question

A fully recrystallized sheet of metal with a thickness of 11 mm is to be cold worked by 40% in rolling. Estimate the necessary roll force if the sheet was 0.5 m wide and there was no lateral spreading during rolling. The strength coefficient is 200 MPa, the work hardening exponent of 0.1 and the roll contact length is 40 mm. Assume no friction.

Answer 1

Roll force, F = 5.6 MN

Step-by-step explanation:

Sheet width, b = 0.5 m

Roll contact length,
`l_(p) = 40 mm`

Strength coefficient,
`\sigma_(0) = 200 MPa`

Thickness, h = 11 mm

Since the sheet of metal is cold worked by 40%, the reduction in thickness will be:

Δh = 40% * 11 = 0.4 * 11 = 4.4 mm

Strain, e = (Δh)/h

e = 4.4/11 = 0.4

The roll force is calculated by the formula:

`F = \sigma_(f) l_(p) b`

`\sigma_(f) = \sigma_(0) (e+1)\\\sigma_(f) = 200 (0.4+1)\\\sigma_(f) = 200 *1.4\\\sigma_(f) = 280 MPa`

Substituting the value of
`\sigma_(f)`,
`l_(p)`, and b into the formula for the roll force:

`F = \sigma_(f) l_(p) b\\F = 280 * 0.04 * 0.5\\F = 5.6 MN`