Question

A brass billet is to be extruded from its initial diameter of 100mm to a final diameter of 50 mm. The working temperature of ${700}^{\circ }C$ and the extrusion constant is 250 MPa. The force required for extrusion is

• A. 5.44 MN
• B. 2.72 MN
• C. 1.36 MN
• D. 0.36 MN

Answer 1

The correct option is B 2.72 MN

Force required for extrusion

= $K{A}_{i}ln\left(\frac{A_i}{A_f}\right)$

where K = extrusion constant

$K=250\times {10}^{6}N/m^2$

$A_i=\text{initial area}$

$=\frac{\pi }{4}\times (0.1{)}^2=7.854\times {10}^{-3}{m}^2$

$A_f=\text{final area}=\frac{\pi }{4}\times (0.05{)}^2$

$=1.96\times {10}^{-3}{m}^2$

Extrusion force,
$P=250\times {10}^6\times \frac{\pi }{4}\times (0.1{)}^2\times ln\left(\frac{7.854\times {10}^{-3}}{1.96\times {10}^{-3}}\right)$

= 2.72 $\times$ ${10}^{6}N$

= 2.72 MN