Posted by **Henri** on Monday, April 20, 2009 at 5:09am.

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^4-d^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^4-d^4)

Then:

0.005209D=pi/32*(D^4-0.6D^4)

(0.005209D*32)/pi=1D^4-0.1296D^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**, Monday, April 20, 2009 at 8:05am
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**, Monday, April 20, 2009 at 2:28pm
Thank you so much

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