Question

A solid cylindrical stainless steel work piece of 200 mm diameter and 150 mm height. This component is reduced by 50% in height with flat die in open die forging. Assuming the flow stress of the material as 1000 MPa and the coefficient of friction to be 0.2, the estimated forging force at the end of the stroke is

• A. 20.8 kN
• B. 31 kN
• C. 78.6 kN
• D. 82.11 MN

Answer 1

The correct option is D 82.11 MN

Given : $D_1=200mm,h_1=150mm,h_2=\frac{1}{2}{h}_1,$

$h_2=75mm,{\sigma }_0=1000MPa,\mu =0.2$

$\Rightarrow r_1^2{h}_1=r_2^2{h}_2$

$\Rightarrow r_2=\sqrt{\frac{{100}^2\times 150}{75}}$

= 141.421 mm

$R_s=141.421-\frac{75}{2\times 0.2}In\left(\frac{1}{\sqrt{3}\left(0.2\right)}\right)$

= -52.35

$\Rightarrow Load={\int }_0^R{P}_{r1}2\pi rdr$

= ${\int }_0^R{\sigma }_0{e}^{\frac{2\mu }{h_2}(R-r)}2\pi rdr$

$={\int }_0^{141.421}\left(1000\right)\times e^{\frac{2\times 0.2}{75}(141.421-r)}2\pi r.dr$

= 82119524.32 N= 82.119 MN