Question

A cylindrical billet of 100 mm diameter and 100 mm length is extruded by a direct extrusion process to produce a bar of L-section. The cross sectional dimensions of this L-section bar are shown in the figure. The total extrusion pressure (p) in MPa for the above process is related to extrusion ratio (r) as

p = K s σ m [ 0.8 + 1.5   l n ( r ) + 2 l d 0 ]

where σm, is the mean flow strength of the billet material in MPa, l is the portion of the billet length remaining to be extruded in mm, d0 is the initial diameter of the billet in mm, and Ks is the die shape factor.

If the mean flow strength of the billet material is 50 MPa and the die shape factor is 1.05, then the maximum force required at the start of extrusion is _______ kN (round off to one decimal place).

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Answer :

Correct answer is : 2429.78

σm = 50 MPa, Ks = 1.05

diameter do= 100 mm, length l = 100 mm

Area of the initial section

Ai = πd2/4 = π × 1002 / 4 = 7853.98 mm2

Area after extrusion, area of L- section

Af = 60 × 10 + 40 × 10 = 1000 mm2

Extrusion ratio, r = Ai / Af = 7.853

Total extrusion pressure :

p = K s σ m [ 0.8 + 1.5   l n ( r ) + 2 l d 0 ]

p = 1.05 × 50  [ 0.8 + 1.5   l n ( 7.853 ) + 2 × 100 100 ]

p = 1.05 × 50 × 5.89 = 309.296 MPa

The force required at the start of extrusion :

F = P × Ai = 309.296 × 7853.98 = 2429.78 kN

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