Posted by Henri on .
Find the Inside diameter(d) and outside diameter(D) of a hollow shaft given:
Power transmitted by shaft=1400kW
Shaft speed=45 RPM
Angle of twist on shaft=1 degree
Shaft lenght(L)=25D
Assume d=0.6D
Modulus of Rigidity(G)=81.75GPa
My answer:
Shaft ang. vel.=45*2pi/60s
A.V.=4.71rads/s
Torque transmitted by shaft=Power/A.V.
Torque=1400000W/4.71
T=297240Nm
Then using the Torsion equation:
T=297240
J=pi/32*(D^4d^4)
G=81.75X10^9
Angle of twist=1*pi/360=0.01745
L=25D
Using the general torsion equation:
T/J=G*Twist ang./L
287240Nm/J=(81.75X10^9)*0.01745/25D
J=297240X25D/(81.75X10^9)*0.01745
J=0.005209D
Since J=pi/32*(D^4d^4)
Then:
0.005209D=pi/32*(D^40.6D^4)
(0.005209D*32)/pi=1D^40.1296D^4
0.05307D=0.8704D^4
D^3=0.05307D/0.8704D
D^3=0.06097
D=39.35cm(ans.)
d=39.35*0.6=23.61cm(ans.)
Hope this is correct!
Thank you for checking it out.

Is my math correct? 
drwls,
The angular velocity is correct.
The torque (T) is correct
The angle of twist in radians is pi/180, not pi/360, but the 0.01745 rad is correct.
The annulus polar moment of inertia (J) formula is correct.
The stress/strain formula is correct.
D has been calculated properly and cnverted to centimeters. I did not check all of the numbers, but all steps seem to have been followed correctly. 
Is my math correct? 
Henri,
Thank you so much