What is wrong with my Nut (K) factor calculation?

[cbrf23]

I'm trying to calculate K factor, following the guidelines of the Machinery's handbook (I have 29th edition paper copy, and 27th edition electronic copy) but I'm not real confident in the results I'm getting.
The machinery's handbook lists the CoF for stainless steel/stainless steel as .14 - so that is what I've input.
However I'm getting a calculated K factor of -.02 for un-lubricated stainless steel fasteners, which just can't be right.

I've tried other CoF's from the chart on engineer's edge, but none of them seem to yield a resulting K factor that makes sense to me.
I think there has to be some mistake in the equations I'm using, but I don't know where. Hoping some more experienced eyes can help me out here.

Also, I'm open to different equations or methods of calculating the K factor. Preferably with source cited so I can justify in my reports.
Attached is my excel spreadsheet and below are screenshots in case you don't feel like downloading it.

Thanks for any assistance.

Inputs/outputs:

Formulas:

Machinery's handbook references.
CoF's:

K factor equations:

 

[desertfox]

Hi

I think the formulae part in brackets after the 2*d is dividing into the number 1, try it this way round:-
(p/*****)*1/(2*d) and i think you will get the right answer.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[ehbadger]

Change your alpha prime and Beta to radians instead of degrees. Row 21 and 23

Doing that, your nut factor comes out to 0.1672

 

[cbrf23]

@desertfox - I tried playing with order of operations - getting no difference using additional parentheses or changing placement.

@ehbadger - I'm getting a different result than you just changing those to radians. Was there another change you made possibly that I missed? With just that change I get a nut factor of .5432.

 

[ehbadger]

Here is a screenshot with the formula shown and then the results. I attached the file I updated as well.

 

[desertfox]

Hi cbrf23

Oh sorry that it didn't work I'll try and work through the calculation and see what result I get.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[cbrf23]

@Ehbadger - I see what you did.
However, those results would be incorrect I believe.
Excel returns Radians by default for all the trig functions (AFAIK)
including ATAN.

So using the RADIANS function is unnecessary and is actually taking the ATAN result (already in radians) and multiplying by π/180.


Using radians, I get a nut factor of around .54, which seems really high to me.

 

[ehbadger]

Ah right.

Ok looking closer, your alpha you use (B22) is in degrees. Change that to radians. Doing that and removing the =RADIANS from alpha prime and beta, and you get 0.1778 nut factor.

 

[desertfox]

Hi again

Calculating the nut factor by hand I get the value to be 0.177796 which agrees with the post ehbadger, so modify the spreadsheet to the one ehbadger used.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[cbrf23]

Excellent!!
Than you gentlemen, I really appreciate the help!