Metric Thread Engagement Length

[nds88]

I know this question may have been asked in some form at some time but I can't seem to find an answer.

I am wondering what the typical method for thread engagement length is for metric bolts of differing materials? I do have Bickford as a reference and also Machinery's but both have essentially the same content with different notation. The issue is that the term for "n" (cited in both texts as 'number of threads per inch') leaves you with mixed units (per inch) if you use metric dimensions for your threads. If I were to convert TPI to Pitch in inches, then I feel like maybe I have violated the relationship. I suppose you could alternatively convert everything to inches but that seems like a stretch as well.

I have tried to find a readable copy of VDI2230 as some have suggested, but I couldn't, its all ink-blobs to me.

Thanks for your help.

 

[desertfox]

Hi nds88

To obtain n in metric I just divide 25.4 mm by the metric pitch of the thread, at the end of the day its just a ratio

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[nds88]

I think the reason I don't really agree here is if we consider an M8x1.25, where KnMax = 6.912mm, EsMin = 7.042mm,

'n' can then either equal [pitch of 1.25 mm/thread = 20.32 thread/inch ] or [ pitch of 1.25 mm/thread = 0.8 thread/mm]

and the result would be if n = 20.32, Le = 1.6645 and if n = 0.8, Le = 6.019, and again im not sure of what units I now have but I obviously have different results...

 

[desertfox]

The formula is looking for number of threads per inch or 25.4mm, I can’t see why you would put 0.8 of a thread per mm ?

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[nds88]

Not to beat a dead horse about this but I would say that my first instinct might be to maintain the dimensional analysis, and if I had, I would arrive at a different result. Both references specifically cite "threads per inch" but neither actually mention or include a metric example or conversion option. I thought this was curious and basically wondering what others do in this case.

 

[Settingsun]

You use threads per inch, or you convert the entire formula to metric so that you get the same answer aside from it being in metric.

 

[nds88]

Heres a citation from RoyMech, which i've seen other users here mention as well. Here, the unit is "threads per unit." I think it's inherently confusing to assign a native unit to a variable...

https://roymech.org/Useful_Tables/Screws/Thread_Calcs.html

 

[Settingsun]

Actually, maybe it does work. Run metric and imperial to check. I thought 0.57735 might be related to threads/inch but it's actually 1/sqrt(3).

 

[nds88]

I will run it back both ways and compare.

0.57735 is tan30 degrees. Ive seen it written either way some places. Im not sure but it may be related to the threads in some way.

 

[nds88]

Well I'm glad I took some time to chop it up. It appears that I was right, the units have to match. If you substitute n as 'threads per inch' into your metric values, the result is an under-sizing of minimum engagement length against thread shear. Here is the breakdown if anyone is interested. Feel free to verify it as you see fit.

Note:
I got tired of writing threads and kind of substituted that with 't' randomly.
I also recognize that there is an unreconciled 'threads' unit no matter how you sort the units, but im assuming this could be considered 'unitless' which leaves Le as 'mm' or 'inches'

In retrospect, I see that Bickford references Machinery's and Blake references Bickford, and they all kind of mention n as 'threads per inch.' Shouldn't it read 'threads per unit' as RoyMech writes?

 

[desertfox]

Hi nds88

yes you are correct, it only works predominately for Imperial threads and not metric ones, you can of course convert the metric thread dimensions to inches and get a correct result but only relating the threads per inch with metric dimensions gives the wrong figures,

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein