interface pressure and possible torque - LamT's equations

[kingnero]

I've found the formulas (see attached pdf-file) in thread 1090698.

However could someone confirm those, or can provide a source?
I've checked Roark's but it isn't mentiond (the section "thermal stresses" is rather limited).
Machinist's handbook also doesn't give the formule for two different materials.

Problem is that it differs 10^6 even with being consistent in N and mm and mm², and that the found value seems rather high (even when divided by 10^6).

Am I using the correct formula? all opinions are much appreciated...

The application is a brass knob (22-40 dia) which needs to be heated and fitted to a steel shaft (14-22 mm dia) with a total interference of about 0.03 mm (tolerance is 22R8 on the knob).

Thanks.

 

[kingnero]

editing made the attachment disappear (?), so here it is again:

 

[kingnero]

Also, what would an appropriate COF be for brass (CuZn40) hub and steel shaft, both machined to standard Rm ?

I found sources for 0.05-0.10 and other says around 0.35.
This is less critical, as even with 0.05 the torque would suffice for this application - I'm just being curious.

 

[kingnero]

My mistake about the 10^6 difference, I made a mistake in my Young's modulus.

Any comments on the correctness of the formula (although now I seem to have rather correct values)
and about the COF ?

 

[ione]

Thick walled cylinder theory.

COF (steel-brass): 0.35 (dry clean surfaces) - 0.19 (lubricated)

 

[kingnero]

The formula I found here gives other results than the one in this pdf (page 14)

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

That formula gives the exact same results as the tribology calculator

http://www.tribology-abc.com/calculators/e3_8.htm

so I believe it to be correct.

So I believe either I misinterpreted something, or the formula given in that thread contains an error (in the denominator, there are two "[" but only "]" ???
That formula can be found here:

http://www.eng-tips.com/viewthread.cfm?qid=109069&page=204

 

[ione]

The formula in the original thread is correct and it's the same as that reported in the link concerning thick walled cylinder. The formula in your OP is not correct: you've definitely misinterpreted it

 

[kingnero]

For any future reference or searches:

This would be the correct formula: see attached file.

 

[Cockroach]

These equations in the original thread are from Thick Wall Pressure Vessel Theory and are the classical ones for contact pressure. These are correct, as Icone has pointed out.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[kingnero]

The intention of the formula was correct, however if you check my last attached file (march 22 - 9:57) you'll see that there is a sign (plus/minus) and an index Vo/Vi) incorrect, as well as two brackets.

Hence my question, as there was a 20+ % difference with the on-line calculator (tribology website) I referred to above.