Deflection & stresses of steel support base for cantilever shaft

[John2004]

Hi everyone,

I have a round steel bearing shaft that is cantilever mounted. One end of the shaft is pressed into a rectangular steel support.

The shaft has to be pressed close to one corner of the support so that the amount of material surrounding the shaft is not the same on all sides of the support.

I need to know how far the end of the shaft will deflect under the cantilever-load strictly due to the deformation of the steel support. I can then add this to the deflection or bending of the shaft itself to get the actual deflection of the shaft due to shaft bending and support deformation.

I also need to determine the stresses in the support base so I can be sure the stress does not go past the steel yield point and cause the support to become Permanently deformed.

Can anyone please tell me the formulas I need ? I am hoping there is a formula based on shaft diameter, the distance of the shaft-quadrant or shaft-center from the rectangular support base edges, thickness of the support base, and load, that will tell me what I need to know. I've been searching for an online calculator that might help but have not found one yet.

Thanks
John

 

[40818]

I'm not totally clear with your explanation, but is this correct:

You have a round shaft which is set into a rectangular support?? Does the shaft interface with both sides of the rectangualr support?

If i'm visualising correctly, I suppose a quick and dirty estimate could be obtained by taking the applied cantilever load and directly compressing the support structure and working out the deflection of that item, ahich would be added to the standard cantilever deflection.
Castiglianos theorum would do it for you.
Have a read of roark or other usual suspects.
But i'm still not sure if i have read your post right!!

 

[hacksaw]

John,

A common issue. Do a search under "support compliance". There are several on-line references. That said, the configuration you've described is 3D and you'll need a proper finite element code to solve.

The simple formula apply only to a few idealized cases.

 

[John2004]

Thanks for your replies guys,

40818, I've uploaded a zip file with a Top and Right Side-view sketch to Rapidshare to clarify the problem...

http://rapidshare.com/files/52347881/Cantilever_Shaft_Support.zip.html

I will keep searching under "support compliance" my first try on google did not seem to produce relevant results, but I will add other search terms and keep at it.

If I had more space I would just beef up the design and not worry about it. Is there an easy to use freeware or shareware FEA program I could download that would shed some light on this ?

Regarding my drawings, the support is shown in blue and the shaft is shown in green. Regarding the right side view, I could add more support material to the left side of the 1/2" OD shaft, (this would increase the.785" dimension) but the other dimensions must stay the same. I have no choice but to locate the shaft close to one side of the rectangular support.

I'm not sure if I will go with a 3/8" or 1/2" OD shaft.

Thanks again guys,
John

 

[Heckler]

Buy a copy of Roarks Formulas for Stress & Strain.

Heckler
Sr. Mechanical Engineer
SWx 2007 SP 4.0 & Pro/E 2001
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"Avoid the base hypocrisy of condemning in one man what you pass over in silence when committed by another." -- Theodore Roosevelt