# Internal thread cutting on the lathe

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#### ajcgkm

##### Member
Hi I am attempting my first male - female thread cutting procedure on the lathe. Granted working out the external thread's are easier than the internal, being the major is basically the finished size of the bolt. So not much chance of making the bolt to small.

But and there is always a but I do have one big problem on the internal threading.
How the hell do I work out the minor dimension of the thread.

For example if I was cutting a unf 3/4 x 28 tpi then I would not want to bore a hole 3/4 otherwise It's a big boo boo. To big a hole leaves a problem I cant put the material back.

I got a video clip of the 3/4 x 28 example and it states that the minor diameter should be .715 but it does not explain how he came to this number. Granted the major is 3/4 or .750 in decimal.

Surely there has to be a formula for this procedure but I can't find one that an idiot like me can undersatnd, I mean the major dia - 5 * the sqaure root of 3 divided by 8 divided by the pitch was quite sickening for a non mathy like me. so any help would be really helpful

bear in mind that I am not a mathmatician so laymans terms please. Also I come from a metric background and slowly learring the imperial way and the numerous types of threads available so be gentle please :bow:

#### rklopp

##### Well-Known Member
I am going to assume you are talking about a standard 60-degree thread form. In that case, start by calculating the height H of a theoretically sharp thread. It will be the height of an equilateral (60-degree) triangle whose base is equal to the thread pitch (1/28" = 0.0357 in the case of your 3/4-28 thread). Sketch it. The height of this triangle is 0.5*SQRT(3) times the base = Cosine(30 degrees) times the base = 0.8660 times the base. So H=0.8660*0.0357=0.0346" in your example. For the female thread, the distance from major (outer) diameter to the minor (inner diameter) is H*5/8 = H*0.625. In your example, this is 0.0217". The nominal minor diameter is therefore the outer diameter minus twice this amount (there are thread crests on both sides of the hole). So the nominal minor diamer is 0.7500"-2*0.0217" = 0.7067".

Using the same idea with a 1/4-20 thread, we get a pitch of 1/20" = 0.05",
H=0.0500" * 0.866=0.0433". H*5/8=0.0271". The nominal minor diameter is
0.2500"-2*(0.0271")=0.1959". That's spot on what Machinery's Handbook tabulates for this size thread. The customary tap drill size for 1/4-20 is a #7, which is 0.201", and probably makes a hole 0.001" or so oversized, so customary tap drills give a little bigger minor diameter than nominal theoretical. That's a necessary tradeoff between thread strength and risk of broken taps. Nevertheless, a standard male thread should fit in a female thread with the theoretical minor diameter, assuming all the other geometry, such as major diameter and pitch diameter, are correct.

#### mklotz

##### Well-Known Member
In essence, the question you're asking is:

What is the tap drill size for a 3/4-28 thread?

The fact that you're cutting this thread on the lathe rather than with a tap is irrelevant; the computation remains the same.

The formula for computing tap drill size is:

TD = MD - 0.013*DOT/TPI

where:

TD = tap drill size
MD = major diameter of thread
DOT = depth of thread expressed as a percentage

MD = 3/4
TPI = 28
DOT = unspecified but we'll use the typical value of 75%

Then,

TD = 0.75 - 0.013*75/28 = 0.75 - 0.035 = 0.715

If applying this formula to your job is beyond your arithmetical abilities, you can download DRILL from my site. It has a tap drill calculation option which will do the arithmetic for you.

#### jonesie

##### Well-Known Member
do yourself a favor and buy a machinist handbook. it will give you all the info. you will need to cut any thread. jonesie

#### rklopp

##### Well-Known Member
Note that the 0.013 in Marv's formula is simply 2 x 5/8 x 1/100 rounded. See my post above.

#### ajcgkm

##### Member
Thanks for the quick responses people,

except jonesie, bit rude I think, I asked for help that's why this post is here.

I have got a few books pardon me if I have difficulty understanding them we can't all be clever can we.

On the other hand the people who were willing to help a newbie who may be a bit thick thank you very much.

#### steamer

##### Well-Known Member
ajcgkm said:
Thanks for the quick responses people,

except jonesie, bit rude I think, I asked for help that's why this post is here.

I have got a few books pardon me if I have difficulty understanding them we can't all be clever can we.

On the other hand the people who were willing to help a newbie who may be a bit thick thank you very much.

I would tend to agree with the assessment, but remember, it can be very hard to convey intent in posts....lets all just keep it polite OK?

Dave

##### Project of the Month Winner!!!
Project of the Month Winner
Hi all
I doubt jonesie ment to be rude and his advice is solid,a machinist handbook is a good buy !!
Pete

#### TroyO

##### Well-Known Member
Yeah, I read it more as real advice... Machinery's will have a chart with all reasonable thread sizes and all you will have to do is look it up. No math involved.. (Well, minimal math... I guess you would need to look up the page number, LOL.)

#### Paulsv

##### Well-Known Member
I'm sure jonesie didn't mean to be rude. The Machinist's Handbook has handy charts that lay out all this information, for those of us, like me, who failed to pay attention in trigonometry classes oh so many years ago.

#### mklotz

##### Well-Known Member
The problem with handbooks and such is that they may not include oddball threads that one might encounter (can you find the tapdrill size for 3/4-28 in MB?). Even if they do, finding that information in a book with a thousand pages can be a test of patience.

A formula is good for any size and is small enough to be jotted in the flyleaf of the shop notebook or scratched into the top of the workbench or, better yet, memorized.

#### ajcgkm

##### Member
Ok I didn't want to start a war :-[ lol just wanted a constant which was that 75%. When explained that I can use the tap formula then it makes it easier to understand. I happen to be a person that learns from watching and asking questions. Books can only teach you so much and they don't answer questions.

Granted Jonsie was not being rude I put the wrong word in there but if someone asked for my help I would if I could and if I couldn't then I wouldn't. I am a member of a few motorcycle forums where my knowledge is put to use (yeah I am quite good with electrical problems on motorbikes) but even there you will have someone come along and post straight after you simply saying yes I agree with what he just said to bump his karma rating.

So lets forgive and forget and learn. Also remember that we can become quite complacent when we know things and we forget that we once started at the bottom. For me my journey is only two months in I got a long long way to go and then I will probably still only know a small amount.

All the best AJ

#### jonesie

##### Well-Known Member
sorry my reply was short. i did not intend to be rude , the handbook is a good bible to have, just tying to give some good advice, been doing this for almost 40 yrs for a living. the handbook will answer almost any machining question. jonesie

#### ajcgkm

##### Member
sorry my reply was short. i did not intend to be rude , the handbook is a good bible to have, just tying to give some good advice, been doing this for almost 40 yrs for a living. the handbook will answer almost any machining question. jonesie

I appreciate what your saying and as you stated you been doing this for 40 years :bow: (you machine god) so it's second nature to you, I got Tubal Cain's Model engineer's handbook and as I said it's like russian to me ;D I am slowly working things out and I mean slowly so no worrys lets all start over. The last thing I want is to offend the people with the experience.

All the best AJ

#### jonesie

##### Well-Known Member
not a machine god i still learn every day, called open mimded. the end jonesie

#### FIXIT

##### Well-Known Member
Just a thought but the machinery's hand book in this country retails for over 100 pounds which is very expensive for something you might not understand in the early stages.

( i have one !)

Steve

#### tel

##### Well-Known Member
I bought my copy years ago for \$5. OK, it's an old edition, but in excellent condition and the info contained therein is still relevant. 25 odd years on it is still in excellent condition, despite almost daily use.

They come up on ebay pretty regularly.

#### Ken I

##### Project of the Month Winner!!!
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I still have my Father's (wartime edition) handbook - guess what - not much has changed in the nuts and bolts department.

In fact some of the sections are more usefull than the newer vesions. My old book shows how to make a worm gear on a lathe - my new one tells me to use a hobbing machine.

So keep your eyes peeled for a bargain at a bookstore / sale and don't worry (much) about its age.

Ken

#### mklotz

##### Well-Known Member
Haunt the used book sales at your local library. Every time an engineer dies his technical books get donated to the library.

Over the years I've picked up at least seven copies of MH of various vintages, none for more than \$5, some for as little as \$2.

#### ajcgkm

##### Member
yep been looking on ebay, found the zeus precision data charts booklet but amazon do it cheeper.

I find the bit I have to get my head around is my lathe is rigged up for imperial cutting. Most of the plans I have are imperial. However I live in the uk am under 45 so my method of machining is metric. So my first build I converted the imperial to metric and improvised when it came to fitting the screws. I used a M2 x 6 instead of the UNC # 56 that the drawing asked for.

It is this bridge between imperial and metric that I am crossing at the moment, I am learning the imperial way.

Rome was not built in a day they say, well if it was left to me it would still be in the planning stage.

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