×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Shear stress of a gear mounted on a shaft

Shear stress of a gear mounted on a shaft

Shear stress of a gear mounted on a shaft

(OP)
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.

RE: Shear stress of a gear mounted on a shaft

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

RE: Shear stress of a gear mounted on a shaft

(OP)
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.   

RE: Shear stress of a gear mounted on a shaft

(OP)
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)

RE: Shear stress of a gear mounted on a shaft

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

RE: Shear stress of a gear mounted on a shaft

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

RE: Shear stress of a gear mounted on a shaft

(OP)
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?

 

RE: Shear stress of a gear mounted on a shaft

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

RE: Shear stress of a gear mounted on a shaft

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

Ted

RE: Shear stress of a gear mounted on a shaft

(OP)
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...

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources