Homework Help: Is my math correct?

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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