Answer:
The roll force is 1.59 MN
The power required in this operation is 644.96 kW
Explanation:
Given;
width of the annealed copper, w = 228 m
thickness of the copper, h₀ = 25 mm
final thickness, hf = 20 mm
roll radius, R = 300 mm
The roll force is given by;
[tex]F = LwY_{avg}[/tex]
where;
w is the width of the annealed copper
[tex]Y_{avg}[/tex] is average true stress of the strip in the roll gap
L is length of arc in contact, and for frictionless situation it is given as;
[tex]L = \sqrt{R(h_o-h_f)} \\\\L = \sqrt{300(25-20)}\\\\L = 38.73 \ mm[/tex]
Now, determine the average true stress, [tex]Y_{avg}[/tex], for the annealed copper;
The absolute value of the true strain, ε = ln(25/20)
ε = 0.223
from true stress vs true strain graph; at true strain of 0.223, the true stress is 280 MPa.
Then, the average true stress = ¹/₂(280 MPa.) = 180 MPa
Finally determine the roll force;
[tex]F = LwY_{avg}[/tex]
[tex]F = (\frac{38.73 }{1000})(\frac{228}{1000})*180 \ MPa\\\\F = 1.59 \ MN[/tex]
The power required in this operation is given by;
[tex]P = \frac{2\pi FLN}{60}\\\\P = \frac{2\pi (1.59*10^6)(0.03873)(100)}{60}\\\\P = 644955.2 \ W\\\\P = 644.96 \ kW[/tex]
