Concept:
The power transmitted by the shaft is given by,
\(P = T.\omega = \frac{{2\pi NT}}{{60}}\)
Torsion equation,
\(\frac{T}{{{J}}} = \frac{\tau }{{{r}}}=\frac{{Gθ }}{l}\;\)
Calculation:
Given:
P = 30 kW, N = 700 rpm, θ = 1° , G = 80 GPa and di = 0.7 do
from \(P = T.\omega = \frac{{2\pi NT}}{{60}}\)
\(30 \times 1000 = T \times \frac{{2π \times 700}}{{60}}\)
∴ T = 409.256 N – m
From Torsion equation,
\(\frac{T}{{{J}}} = \frac{{Gθ }}{l}\;\)
L = 1 m, θ = 1° = π/180 rad
\(\frac{{409.256}}{{\frac{π }{{32}}\left( {1 - {{0.7}^4}} \right)d_0^4}} = \frac{{80 \times {{10}^9}}}{1} \times \frac{π }{{180}}\)
on Solving, we get
d0 = 44.52 mm