If the maximum allowable shear stress is 70 MPa, find the shaft diameter needed to transmit 40 kW when the shaft speed is 250 rpm.

The diameter is 50mm

Explanation:

The answer is in two stages. At first the torque (or twisting moment) acting on the shaft and needed to transmit the power needs to be calculated. Then the diameter of the shaft can be obtained using another equation that involves the torque obtained above.

T = (P*60) / (2*pi*N)

T is the Torque

P is the the power to be transmitted by the shaft; 40kW or 40*10³W

pi=3.142

N is the speed of the shaft; 250rpm

T = (40*10³*60) / (2*3.142*250)

T=1527.689Nm

Diameter of a shaft can be obtained from the formula

T = (pi * SS * d³) / 16

Where

SS is the allowable shear stress; 70MPa or 70*10⁶Pa

d is the diameter of the shaft

Making d the subject of the formula

d = cubroot[ (T*16) / (pi*SS) ]

d=cubroot[ (1527.689*16) / (3.142*70*10⁶) ]

d=0.04808m or 48.1mm approx 50mm