Transmission of Power by Circular Shafts

power transmitted by a circular shaft, P

depends upon the magnitude of the torque and the speed of rotation, ω.  Power is the rate at which work is done.

P = Tω

power units:		ft-lb/s watts = Nm/s = J/s hp = 6600 in-lb/s = 746 watts
angular speed units:		rpm = rev/min rad/s

see M6.9 and M6.13

 

gear statics ΣM1 = T1 = r1F ΣM2 = T2 = r2F therefore,  r2T1 = r1T2 gear dynamics s = r1θ1 = r2θ2 v = r1ω1 = r2ω2 a = r1α1 = r2α2 where r can be replaced with d or N

Photo courtesy of Emerson Power Transmission Corp.

 

work done by a constant torque, W

the product of the torque and the angle through which it rotates, Ψ.  

W = TΨ

work units: ft-lb, Nm

 

frequency of rotation, f

the number of revolutions per unit of time

ω = 2πf

frequency units: Hz = rev/s