Consider an open-die upsetting experiment. Iinitially, the cylindrical workpiece
ID: 1841856 • Letter: C
Question
Consider an open-die upsetting experiment. Iinitially, the cylindrical workpiece has a diameter of 20 mm and height of 50 mm. It is first hot forged to an intermediate height of 30 mm, and then cold forged to a final height of 20 mm. A constant velocity of 20 mm/sec was applied in both cold and hot forging processes. The friction coefficient at the die-workpiece interface was assumed to be 0.1 for both cases. For hot working condition, assume m = 1.16, C = 50 MPa. Determine the strain rate for the workpiece height of 40 mm. Evaluate the minimum power required to complete the hot forging process. For cold working condition, assume n = 0.16, K = 220 MPa. Determine the true strain for the workpiece height of 25 mm. Evaluate the minimum power required to complete the cold forging process.Explanation / Answer
a)
In hot forging, Strain rate e = v / h = 20 / 40 = 0.5 /sec
Flow stress = C*em = 50*(20 / 30)0.16 = 46.86 MPa
By volume constancy, Ao*ho = Ai*hi
3.14/4* 202 * 50 = Ai*30
Ai = 523.33 mm2
Final dia = sqrt(523.33*4/3.14) = 25.82 mm
Friction factor k = 1 + 0.4*u*D/h
k = 1 + 0.4*0.1*20 / 30
k = 1.026
Forging force = Flow stress * Final area * k
= 46.86 * 523.33 * 1.026
= 25177 N = 25.2 kN
Power required = Force*velocity
= 25.2 * 20
= 503.5 W
b)
In cold forging,
True strain = ln (horiginal / hfinal) = ln (30 / 25) = 0.182
Flow stress = K em = 220 * 0.1820.16 = 167.5 MPa
Force = stress * Ai * k
= 167.5 * 523.33 * 1.026
= 89936.9 N = 89.94 kN
Power = Force*velocity
= 89.94 * 20
= 1798.7 W