Thread Depth Calculation and Constants

[eliot15]

Hello,

I'm studying the parameters of the G76 lathe thread cutting cycle today.

In the two line format, the P address indicates the total depth (or height) of thread, as a radius value.

I picked up from Peter Smid's CNC Programming Handbook, that there are two different constants to use when calculating the depth of external threads vs. internal threads.

For external thread depth (UN and ISO metric, 60 degree), one uses 0.61343/TPI.

For internal thread depth (UN and ISO metric, 60 degree), one use 0.54127/TPI.

I'm trying to locate some documentation on this 0.61343 figure. When I look at the thread form diagram's in Machinery's Handbook (p.1713 - 1714, Large Print), for example, they seem to suggest that the thread depth for both internal and external threads is 5/8ths of triangular height.

So if Pitch = 1, then triangular height from theoretical sharp point to sharp point = .5 / tan30 = .866025.

5/8 x .866025 = .541266.

However, 17/24 x .866025 = 0.61343, the constant for calculating external thread depths.

Where does this 17/24ths come from????? Does Machinery's Handbook, or some other documentation address it somewhere???

[eliot15]

This is essentially the same thread form diagram found on p.1714 of Machinery's Handbook. Its from the Wikipedia article on the Unified Thread Standard. Both internal and external thread height seem to be given as 5/8ths of "theoretical triangle" height (5H/8 in the diagram). No indication of a 17/24ths constant anywhere????



Thanks

[eliot15]

OK, its growing a little less murky...

I guess the diagrams I've been looking at are generally referred to as something like the BASIC PROFILE, which is generally shared by BOTH internal and external threads.

The ACTUAL PROFILES of internal and external threads factor in standardized tolerances and allowances that enable the internal and external threads to fit together correctly.

The fractional dimension of the standard for external threads just happens to be 17/24, which is 5/8H + H/12, or the fractional dimension of the standard for internal threads (5/8) + an additional 1/12 of the theoretical triangular height.

This snippet off the web seems to clarify the situation pretty well:

Usually nut (internal) threads have a tolerance applied to the basic profile so that it is theoretically possible for the nut thread profile to be equal to the theoretical profile. Bolt (external) threads usually have a gap between the basic and actual thread profiles. This gap is called the allowance with inch-based threads and the fundamental deviation with metric threads.