Compute the diameter of a solid shaft:

Compute the diameter of a solid shaft transmitting 150 kW at 25 rpm, if the maximum shear stress in the shaft is not to exceed 70 MPa. Compare it with the shaft delivering similar power at 25000 rpm.

Solution

Power transmitted, P = 150 kW = 150 × 10³  W

Number of revolutions, N = 25 rpm

Since, 1 Pa = 1 N/m² and 1 Mega Pascal = 10⁶ N/m² = 1 N/mm²

Then, maximum shear stress, τ_m = 70 MPa = 70 N/mm²

Let T be the torque transmitted in N m.

P = 2πNT /60

150 ×10³  = (2π × 25/60 ) × T

T = 57.28 × 10³ N m

T = 57.28 × 10⁶ N mm

T/  J= τ_m /(d/2)

d = 160.9 mm

If          N = 25000 rpm, then P = 2πNT /60   

150 ×10³  = (2π × 25000 × T )/60

T = 57.28 N m = 57.28 ×10³ N mm

T/ J= τ_m/(d/2)

57.28 × 10³ / (π/32) d ⁴     =   70/(d/2)

d = 16.09 mm

It is seen from this example that the size of the shaft is decreased very much if the power is transmitted at high speed. That is the cause for the modern tendency to utilize high speed machines, those results in considerable saving in the material cost.