Pitch circle diameter calculations

[gbritnell]

Gentlemen, could someone tell me what I'm overlooking in the calcuation of a screw pitch diameter. First the definition of pitch diameter taken from several sources:

PITCH CYLINDER: The pitch cylinder is an imaginary cylinder of such diameter and location of its axis that its surface would pass through a straight thread in such a manner as to make the widths of the thread ridge and groove equal. It is, therefor, located equidistantly between the sharp major and minor cylinders of a given thread form. On a theoretically perfect thread these widths are equal to one-half the basic pitch. (See also Axis of Thread and Pitch Diameter.)

From this I created an AutoCad drawing with the information I was given.
That was a 2.3125 Dia. with 40 tpi. Something for a telescope cover. After drawing it up and dimensioning it I came up with a pitch diameter of 2.2908.

Now the poverbial "fly in the ointment". There is a formula for calculating the pitch diameter and it is:

dp = (D - 0.64952.p )

And on the chart for my 3 wire measuring wires it says:

Note: Basic P.D. equals basic major diameter plus the decimal in the "ADD" column (.01611) minus the decimal in the "CONST" column (.03235)

Now, both of these formulas give me a number of 2.2962

Why the difference of .005?

gbritnell

[TGTool]

My first thought would be the difference between the theoretical thread with a line to line fit between male and female thread forms, versus a real world thread with clearance and tolerance for mating parts.

I'd tend to trust the numbers from the thread wire documentation and Machinery's Handbook since those are used for actual thread making. I've often machined a thread to size from Machinery's numbers and had it fit a mate that I didn't have on hand to try and that's the basis for standardization.

[bobw53]

I just did a quick draw and got the same #s you did.

The reason why is that threads are not calculated based on a sharp V. Measure a tap someday, you will see that it is actually bigger than its nominal size.

It goes back to the standards thing. Some people many years ago got together and decided this is the way we are going to do it.

[John Garner]

I sounds to me like bobw53 has diagnosed your mistake correctly, you probably drew the 60 degree Sharp V screwthreads. The basic Pitch Diameter of a 60 degree Sharp V screwthread is calculated as the Major Diameter minus Pitch times Cosine 30 degree, and 2.3125 inch - 0.025 inch x Cosine 30 degree = 2.2908 inch.

But the Sharp V threadform has been obsolete for nearly 150 years now, being replaced in the US first by the Sellers threadform, which was itself replaced by the Unified threadform 50 years ago. Both the Sellers and Unified threadforms are modifications of the 60 degree Sharp V, but using flats at both the Major and Minor Diameters of the screwthread instead of the damage-prone and hard to manufacture sharp edges.

The Sellers threadform has 1/8 x Pitch flats at both the Major and Minor Diameters, which means that the Single Depth a Sellers thread is less than the Single Depth of a same-pitch Sharp V thread. The Unified threadform has the same 1/8 x Pitch flat at its Major Diameter, but has a broader, 1/4 x Pitch flat at its Minor Diameter.

The Single Depth of a Sellers screwthread is 3/4 x Pitch x Cosine 30 degree;

The Single Depth of a Unified screwthread is 5/8 x Pitch x Cosine 30 degree.

Because both the Sellers and Unified threadforms have the same-size flat at the Major Diameter and the same 60 degree flank angle, their Pitch Diameters are calculated in the same way.

Pitch Diameter = Major Diameter - 3/4 x Pitch x Cosine 30 degree.

Working your example: 2.3125 inch - 0.75 x 0.025 inch x Cosine 30 degree = 2.29626 inch, which misses the handbook value by 0.00006 inch.

John

[gbritnell]

I want to thank you for your quick and accurate response. I would have taken those factors into account if it had not been for the wording of the first paragraph which stated: "between the sharp major and minor cylinders of a given threadform". This coming from my Machinery's Handbook.
gbritnell