Screw Threads: Mean Diameter versus Pitch Diameter 1

[MCRodg]

This is a very basic question but still a source of confusion for me at least.
More annoying than it is critical to know, but here it is:

Shigley & Mitchell Mechanical Engineering Design 4th ed. P339 refers the dm = "Mean Diameter" of a screw thread.

What's not clear in my old 4th edition is if Mean Diameter = Pitch Diameter or even how "Mean diameter" is defined. Average of Major and Minor diameters ???

I know that the Pitch diameter is the diameter of an imaginary cylinder that intersects each flank of the screw thread, such that the distance between these intersections is twice the pitch. Pitch being the distance between crest, etc. That's got nothing to do with averaging anything so I don't believe "Mean dia"=Pitch dia.

I've also seen the pitch diameter referred to as the "Effective Diameter", so I'm confident Effective Diameter = Pitch Diameter

So what is the "mean diameter" that Shigley & Mitchell uses ?

I know it's semantics but when certain formulas use a variable, it generally good to be clear on what that variable is exactly.

If you know the answer, please try to site a reference somewhere. I might believe you but that doesn't help me convince others.

Doing a keyword search on ASME B1.1-2003 I did not get any hits for the word "mean" at all.

 

[pylfrm]

MCRodg,

What's the context?

Stress calculation? It may refer to the diameter of a cylinder having cross-sectional area equal to that of the thread.

Friction calculation? It may refer to the mean diameter of flank contact between mating internal and external threads.

It may refer to the radius, averaged over 360 degrees at any one cross-section, and multiplied by 2.

It may refer to the average of the minor diameter and major diameter.

It may simply refer to the pitch diameter.

For a standard UN or M thread form, the difference between these options should be pretty small. I'll leave it to you to work out exactly how small.


pylfrm

 

[MCRodg]

PylFrm.

It is used by Shigley & Mitchell in their equation for thread stress. As=pi*dm*Le/2 As=shear area of the thread

I think I may have an answered to my own question.

In the footnotes of Table (8-1) and (8-2) it says: "the pitch diameter dm=d - 0.649 519p" Where d=major dia and p=pitch=1/N, N=number of threads per inch.

So dm=pitch diameter as far as Shigley & Mitchell are concerned. Hidden in a footnote, and dp is what I would have called it, and certainly, would not have labeled it "mean diameter". But who am I. :-D

 

[drawoh]

MCRodg,

According to the Handbook of Bolts and Bolted Joints, by Bickford andd Nasser, the stress are is as follows...

English: A[sub]s[/sub] = [π]/4 [×] (D - 0.9743/n)[sup]2[/sup] where n is TPI.

Metric: A[sub]s[/sub] = [π]/4 [×] (D - 0.9382p)[sup]2[/sup] where p is the pitch.

There were slightly different equations for UNJ and MJ series threads.

--
JHG