Question

A hollow shaft $d_0=2d_i$ (where $d_0$ and $d_i$ are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, $d_0$ is

• A. 11.29 mm
• B. 22.58 mm
• C. 33.87 mm
• D. 45.16 mm

Answer 1

The correct option is B 22.58 mm

Given data:

$d_0=2d_i$ ;

$k=\frac{d_i}{d_0}=0.5$

P = 20 kW
N = 3000 RPM

$\frac{2\pi NT}{60}=P$

$orT=\frac{60\times 20\times {10}^3}{2\pi \times 3000}=63.66197Nm$

$\tau =\frac{16T}{\pi d_0^3[1-{\left(\frac{d_i}{d_0}\right)}^4]}$

$\Rightarrow {\tau }_{max}=\frac{16T}{\pi d_0^3(1-k^4)}30=\frac{16\times 63.66197\times {10}^3}{\pi \times d_0^3(1-{0.5}^4)}$

$or{d}_0=22.59mm$