Respuesta :
Answer:
13.9357 horse power
Explanation:
Annealed copper
Given :
Width, b = 9 inches
Thickness, [tex]$h_0=2.2$[/tex] inches
K= 90,000 Psi
μ = 0.2, R = 14 inches, N = 150 rpm
For the maximum possible draft in one pass,
[tex]$\Delta h = H_0-h_f=\mu^2R$[/tex]
[tex]$=0.2^2 \times 14 = 0.56$[/tex] inches
[tex]$h_f = 2.2 - 0.56$[/tex]
= 1.64 inches
Roll strip contact length (L) = [tex]$\sqrt{R(h_0-h_f)}$[/tex]
[tex]$=\sqrt{14 \times 0.56}$[/tex]
= 2.8 inches
Absolute value of true strain, [tex]$\epsilon_T$[/tex]
[tex]$\epsilon_T=\ln \left(\frac{2.2}{1.64}\right) = 0.2937$[/tex]
Average true stress, [tex]$\overline{\gamma}=\frac{K\sum_f}{1+n}= 31305.56$[/tex] Psi
Roll force, [tex]$L \times b \times \overline{\gamma} = 2.8 \times 9 \times 31305.56$[/tex]
= 788,900 lb
For SI units,
Power = [tex]$\frac{2 \pi FLN}{60}$[/tex]
[tex]$=\frac{2 \pi 788900\times 2.8\times 150}{60\times 44.25\times 12}$[/tex]
= 10399.81168 W
Horse power = 13.9357
