Length of Standard Flat Key to Prevent Failure

[cmmcnamara]

Homework Statement

Hi all, I have a question about a standard flat key being specified to prevent failure. I'm just quickly giving a problem description because once I understand what's going on I can easily run calculations but I'm missing something fundamental.

Essentially the problem I am struggling with is given an allowable shearing stress and an allowable bearing stress, determine the required length of a standard flat key to prevent failure while allowing a certain power and speed transmission as well as a specific diameter. It's simple enough I think, use diameter, HP, and speed to determine the force acting on the key, then solve the resulting stress equations and pick the length which prevents failure. Since the key is standard, it's dimensions should be specified by the shaft diameter. I think my logic on the stresses may be wrong though. Correct me if I am wrong but there should exist 3 stresses acting on the key. If you view the key in a way such that the face lies in XY and the length goes along Z then you should have a shear in xy (stress parallel to the face), a shear in xz (stress parallel to the length face) and a normal stress in the x direction. My problem is that although XY stress doesn't depend on the key length, for my particular problem, it exceeds the allowable shear stress, meaning that I'd have to specify a larger diameter shaft to increase key dimensions. I asked my professor about this but he said we couldn't change the shaft diameter and said the problem was able to be solved. He was in a general bad mood so I couldn't really get him to elaborate any further despite the reasoning I presented him.

Additionally, I've looked around on the web for more info and found a derivation I've seen before here: http://engineering.union.edu/~tchakoa/mer419/MER419_keys-and_couplings.pdf

But this analysis also neglects the shear I am talking about. Am I forgetting something fundamental about strengths? Please guide me!

Homework Equations

σ=F/A
τ=F/A
P=Tω
T=Fd

The Attempt at a Solution

Already stated above, my bad.

 

[cmmcnamara]

Does anyone have any suggestions regarding this?

 

[SteamKing]

Check out this file for a basic analysis:

http://engineering.union.edu/~tchakoa/mer419/MER419_keys-and_couplings.pdf