Compute the outside diameter of the shaft:

A hollow shaft of diameter ratio is 0.4 is needed to transit 600 kW at 120 rpm. The maximum torque being 20% greater than the mean torque. The shear stress is restricted to 60 N/mm² and the lowest of 0.01 radians per unit length. Compute the outside diameter of the shaft. Take G = 0.8 × 105 N/mm².

Solution

d_i / d_o   = 0.4

di  = 0.4 d_o

R = d_o/ 2

P = 600 kN, N = 120 rpm,  P = 2π NT  /60

600 × 10³  =( 2π× 120T )/60

∴          T = 47.7 × 10³ N-m

T_max  = 1.2 T = 1.2 × 47.7 × 10³  = 57.3 × 10³  N-m

τ_max  = 60 N/mm²  = 60 × 106  N/m²

 T_max  = τ_max  × Z P

⇒         57.3 × 10³  = 60 × 10⁶  × 0.19

∴          do  = 0.17 m

T_max / J = G θ/ l

∴          do = 0.165 m

∴          do = 0.17 m = 170 mm