Find out the power - hollow shaft, Mechanical Engineering

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Find out the power - hollow shaft:

A hollow shaft of internal diameter 400 mm & external diameter 450 mm is needed to transmit power at 120 rpm. Find out the power it may transmit, if the shear stress is not to exceed 50 N/mm2 & the maximum torque exceeds the mean by 30%.

Solution

do = 450 mm,  di = 400 mm,   N = 120 rpm

τmax = 50 N/mm2 = 50 × 106 N/m2

Tmax  = τmax  × Z P

625_Find out the power.png

=  (π /32 )(4504  - 4004 ) = 1.51 × 109 mm4

R = do /2 = 450 = 225 mm

Z P        = J/ R = 1.51 × 109 /225 mm3 = 6.7 × 10- 3  m3

τmax  = (50 × 10 ) (6.7 × 10) = 335 × 10  N-m

τmax  = 1.3 × T

⇒         335 × 103  = 1.3 T

∴          T = 258 × 103 N-m

∴          Power, P = 2π NT/60 = 2π × 120 × 258 × 103 /60

                         = 3242 × 103 watts = 3242 kW


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