View Full Version : Calculate 'length of engagement' for Thread Pitch Diameter Tolerance ???

05-10-2015, 03:06 PM
How ????

Ive looked at a ASME B1.1-2003 (https://www.google.com/search?q=ASME+B1.1-2003+pdf) pdf with the tables, but can not understand how to get the 'length of engagement' mathematically.

Im trying to create the tolerances for thread pitch dia.
Class 2A = ((0.0015 * 3√D) + (0.0015 * √LE) + (0.015 * 3√P^2))
If the 'length of engagement' is the same as the OD of the thread, im good, everything works out fine, but when the 'length of engagement' differs, like with a 7/16-24 all hell breaks loose.

There is a note in the pdf which read's:
For example: LE p 0.5000 is equivalent to one diameter for the 1⁄2 in. size, 9 pitches for 18 threads per inch, or 20 pitches for 40 threads per inch.

But that does not seam to be true, if you check a 5/8-18 (LOE = .625):

Any help would be great.


05-10-2015, 04:34 PM
Length of engagement is how far you screwed the screw into the threads! :)

Or how thick the tapped section is, if the screw goes right through.

See, if you only have 1 thread of engagement, the TPI can be WAYY off and it will still work fine, because error on 1 thread does not move much. You could likely have say 5% error and it would still work fine.

If you have a 40 thread of engagement, lets say a 1/4-40tpi thread through a 1" thick block (1" of thread engagement at 40tpi = 40 threads of engagement), then the error must be very small, because after 40 threads, 1/40 = 2.5% of error results in the last thread being 1 thread off from the first and the entire thing guaranteed to jam as some threads will be crest on crest.

Even at 1.25% error, you end up with one thread mated on one side, and on the other side the threads are 180 degrees out of phase.
Meaning your going to want a small fraction of 1.25% error as your max allowable error, if you have 40 threads of engagement. Say, 0.125% error will result in you only being 1/10th of a thread off at the end.

Try playing with metric and imperial thread gauges. you can see how very close thread pitches mate up fine if its only a couple threads engaged, but once you use the entire 1/2" long thread gauge, the tiniest of error results in the gauge not fitting correctly any more, because the error makes the threads misaligned worse and worse the more threads that are engaged.

Also, Note how many times you can get a metric nut onto an imperial bolt.. for a turn or two, but almost never more then that.

05-10-2015, 05:22 PM
Thanks, Black_Moons.

What im doing is creating a vbscript for thread info (i know theres a ton of them online, but thats another story).

By no means am i a thread expert and have learned alot over the last day.
To generate a threads pitch dia tolerance (along with class "tolerance/allowance" ), the formula requires a 'length of engagement' variable, which is where im stuck.

I search around and found formulas for dealing with engagement for tinsel strength (for designing), but have not found the standard used for the PD tolerance tables in the machinery handbook (and could not find it there ether :confused: ). Only thing i found where charts, which dont help me.

Im creating this for myself but see the use for it at work, if i bring it to work, it needs to be %100

As of now, im multiplying the pitch (1/TPI) by 10 and for the threads its off, its only off by 2-3 tenths which for me at home is fine, but for work it needs to be correct.



Paul Alciatore
05-10-2015, 09:29 PM
I am far, far from an expert, but I think the "length of engagement" is a user supplied variable that comes from the application. It could be very short for a lock nut and very long for some parts where a long, tapped hole with full thread engagement would be needed, like the nut that engages a lead screw.

Anyway, that's my guess.