Shaft Torsion Calculation 1

[ChuckOU812]

I am looking for a formula to calculate shaft diameter needed.

The shaft is 20 feet long with one end stationary with no load and the other end has a 6500 in/lb load @90deg. I am looking for the angular deflection at the loaded end to determine the proper shaft diameter needed.

Thanks for your help.
Fred

 

[unclesyd]

You didn't give very much information in you post, but you may wasn't to look over this site.

Dr Lemaster's Lecture at UT.

http://www.utm.edu/departments/engin/lemaster/Machine Design/Lecture 18.pdf

 

[CoryPad]

Elastic deflection of a shaft:

[θ] = TL/GJ

where

[θ] = shaft angular deflection in radians
T = applied torque in N[·]m
L = shaft length in m
G = shear modulus in N/m[sup]2[/sup] (steel is 80[·]10[sup]9[/sup]
J = polar moment in m[sup]4[/sup] (J = [π][·]r[sup]4[/sup]/2 for a solid cylinder)

If you solve for radius r, you get about 12 mm; thus, your shaft diameter should be about 24 mm, or about 1 inch.

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[dvd]

1" diameter shafting for those loads does not seem realistic. Size your shaft to safely transmit the torque with appropriate shock loading factor if needed. How is your load attached to the shaft? Are there keys and keyways, welds, etc? I came up with a much larger shaft. Do you really want the 20 foot long shaft to deflect 90 degrees?

 

[ChuckOU812]

Thanks for your help everyone. Here is some more information. The shaft is supported as varoius points along its length with bearings. One end of the shaft is fixed/mounted to a gearbox. The other end has a sprocket welded on it with a load hanging on the chain of 6500in/lbs. My goal is to determine the proper shaft size so there is little to no rotational (torsional) deflection at the end with the load. I would like to use a 2-7/16" shaft if possible.

 

[CoryPad]

Your original post was unclear, but it seems you have clarified. You don't want 90 degrees of elastic torsion in your shaft, rather, you want something close to zero.

The equation I provided is correct. If T, L, and G are fixed, then you must increase J (which really is only r multiplied by a constant) to result in the smallest deflection. Your choice of shaft (2-7/16 in) results in an angle much smaller than one degree.

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[dvd]

It is a somewhat dangerous practice to size a shaft based on the torsionsal deflection equation only. The equation does not account for bending stresses in the shaft. Without knowledge of the bending moment applied to the shaft the 2 7/16 diameter may not be enough. Also depending on the rpm of the shaft and bearing locations there may be shaft whip, or vibrations.

 

[satchmo]

Designing based on torsional deflection also doesn't take into account any shaft fatigue. I'm not sure if I understand your application completely. In my experience, if you design against fatigue, the shaft will be plenty stiff.

 

[ChuckOU812]

Thanks again everyone.
My application requires me to turn the shaft at one end (very low, 18 rpm) with a gearbox to turn a sprocket at the other end to lift 6500 in/lbs. The shaft is anchored along its length with 5 pillow block bearings to support it. Two of the pillow blocks will be mounted very close to the ends. Under a static load, I am looking for as little shaft "twist" as possible. The shaft will see little to no shock load and the gearbox will be driven with a drive to start/stop it slowly.

 

[PeterCharles]

"The shaft is anchored along its length with 5 pillow block bearings to support it."

You'll have to be a bit careful lining up all these bearings.