Question

In a multi-pass operation, a round bar of 10mm diameter and 100 mm length is reduced in cross-section by drawing it successively through a series of seven dies of decreasing exit diameter. During each of these drawing operations, the reduction in cross-section area is 35%. The yield strength of the material is 200 MPa. Ignore strain hardening.

Neglecting friction and redundant work, the force (in kN) required for drawing the bar through the first die, is

• A. 15.71
• B. 10.21
• C. 6.77
• D. 4.39

Answer 1

The correct option is D 4.39

Drawing force, $F_d=200\times \frac{\pi }{4}\times d_{f_1}^2\times ln{\left(\frac{d_i}{d_f}\right)}^2$

$A_{f_1}=0.65\times A_i=0.65\times \frac{\pi }{4}\times (10{)}^2$

$\frac{\pi }{4}\times d_{f_1}^2=0.65\times \frac{\pi }{4}\times (10{)}^2$

$d_{f_1}=8.06225mm$

$=200\times \frac{\pi }{4}\times (8.06225{)}^2\times 2ln(\frac{10}{8.06225})$

= 4.39 kN