Shear stress of a gear mounted on a shaft 1

[uh60rascal]

I'm a bit confused here. Trying to determine if we can mount a gear to a shaft and if it will be able to withstand the torque load or if it will slip. I need to find the shear stress.

Two ways I can think about doing this:

1. F = T/r. Then calculate shear as F/contact area. Thus shear = T/(2*pi*r^2*l) where r is the shaft radius and l is the length of the shaft that is in contact with the gear hub.

The other way:

2. Max shear at shaft = T*r/J. This gives me a much larger value than the previous calculation, and it doesn't account for the actual contact area between the gear and the shaft.

It seems like such a simple problem and yet despite my gut instinct, I cannot justify why one way is correct and the other would be wrong.

Thanks.

 

[desertfox]

Hi uh60rascal

If you're calculating the shear stress on the shaft then method 2 looks like the method.
Your first method is the shear stress if you're shearing across the diameter.
Method 2 is applying the torque from the gear wheel to the OD of the shaft and twisting the shaft about its central axis.

desertfox

 

[uh60rascal]

I do want to calculate the shear stress on the shaft at the area of contact between the shaft and the gear. The problem with method 2 is that it seems to be independent of the contact area. My intuition tells me that the shear stress would decrease with a larger contact area, but method 2 does not take the surface area into account at all.

 

[uh60rascal]

Also, what do you mean by shearing across the diameter? If anything, I thought that would be shearing around the circumference (or maybe it is just semantics).

F = T/r
Surface area = 2*pi*r*l

F/A = T/(2*pi*r^2*l)

 

[CoryPad]

You need to search for "press fit", both at this site and on the Internet in general.

 

[desertfox]

hi uh60rascal

If your looking at transmitting a torque between gear and shaft with a press fit use this calculator.

http://www.tribology-abc.com/calculators/e6_2.htm

or this site for formula:-

http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm#Press_fits

now going back to your method 1 the shearing stress your calculating is very similar to the single bolt in single shear at this site although the length of bolt engagement isn't included unlike your formula.
Method 2 is calculating shear stress on the shaft due to torsion see this site:-

http://emweb.unl.edu/negahban/em325/06-Torsion/torsion.htm

desertfox

 

[desertfox]

Sorry see this site for method 1

http://www.roymech.co.uk/Useful_Tables/Screws/Bolted_Joint.html

desertfox

 

[uh60rascal]

Thanks for the replies, guys.

I'm still confused, so let me pose the question in a slightly different manner. Suppose I wanted a close (but not press) fit between the shaft and gear and I used Loctite to fix it together. The Loctite says it's good to 3000 PSI.

Now I want to know from my anticipated torque load and geometries if I will exceed that rating. So method 1 or 2?

 

[tbuelna]

uh60rascal,

It sounds like what you want to know is the torque capacity of slip fit shaft joint secured only with a loctite adhesive bond, right? If so, it's simply P/A at the bondline. Of course you won't likely get anything close to that published 3Ksi shear strength from your loctite, except under laboratory conditions.

If you want to calculate the torque capacity of an interference fit shaft joint, that gets much more complicated. And the actual vs. calculated result can vary widely due to variables such coeff. of friction.

Hope that helps.
Terry

 

[desertfox]

Hi uhrascal60

Look at this site its gives you the torque capacity of a press fitted shaft and hub:-

http://www.faculty.fairfield.edu/wdornfeld/ME311/PressCylinderHam.pdf

desertfox

 

[hydtools]

Your calculation 1 is the one to use. Force over the contact area.

Ted

 

[hydtools]

Here is a Loctite reference:

http://loctite.fast.de/wwdh/us/i132ch07.htm

Ted

 

[uh60rascal]

Thanks, tbuelna, desertfox and hydtools! That Loctite reference is great.

I appreciate all of your hope, although I think this is a sign that I've been away from the books for too long...