Lathe threading math
Lathe threading math
what is the math formulas for figuring out the depth and amount of infeed for "Sharp V Groove" threads? I'm planning on using 16TPI..and the book has me all mixed up. I tried what I thought was the formula on some 4.5"OD AL pipe and the thread tops were flat..so the way I figured it out was wrong...mostly I'm trying to figure out how much "infeed"..and this is fairly new to me so please keep it simple..if possible.
Tony
Tony
Re: Lathe threadiing math
Assuming you're cutting 60 degree threads, the depth will be the reciprocal of the pitch, divided by two multiplied by the square root of three. So, for 16tpi:
Reciprocal: 1/16=0.0625
Divide by 2: 0.0625/2=0.03125
Multiply by square root of 3: 0.03125*sqrt(3)=0.054126587, which I would round off to 0.054 (or whatever number of significant digits you need.)
The amount of infeed depends on how you're feeding. If you feed straight in you just use the depth calculated above. If you're feeding at a 30 degree angle you use the reciprocal of the pitch (0.0625 for the 16tpi example). If you're feeding at 29.5 degrees, you could probably get away with the reciprocal of the pitch unless you're making a really precise piece of scientific equipment. If you're feeding at some other angle (for some strange reason) divide the depth by the cosine of the angle to get the feed distance. If you're feeding at an angle greater than 30 degrees, you're confused and your threads will not work.
Note that the above works only for 60 degree sharp V threads.
Reciprocal: 1/16=0.0625
Divide by 2: 0.0625/2=0.03125
Multiply by square root of 3: 0.03125*sqrt(3)=0.054126587, which I would round off to 0.054 (or whatever number of significant digits you need.)
The amount of infeed depends on how you're feeding. If you feed straight in you just use the depth calculated above. If you're feeding at a 30 degree angle you use the reciprocal of the pitch (0.0625 for the 16tpi example). If you're feeding at 29.5 degrees, you could probably get away with the reciprocal of the pitch unless you're making a really precise piece of scientific equipment. If you're feeding at some other angle (for some strange reason) divide the depth by the cosine of the angle to get the feed distance. If you're feeding at an angle greater than 30 degrees, you're confused and your threads will not work.
Note that the above works only for 60 degree sharp V threads.
Re: Lathe threadiing math
There's a simpler algorithm for the thread depth of a 60-degree Sharp-V thread: Depth = Pitch x Cosine 30.
Re: Lathe threadiing math
Get ahold of a copy of an old Atlas "Manual of Lathe Operations" book. Page 110 has the chart that gives the depth of compound feed when set at 29 degrees for 4 TPI thru 96 TPI, for both a NF Thread and a 60 degree "V" Form Thread.
Al Messer
"One nation, under God"
"One nation, under God"
Re: Lathe threadiing math
"...16 TPI sharp "V" threads..." Set the compound rest to 29 degrees and set the compound feed dial to Zero. Advance the tool with the Crossfeed until it just kisses the workpiece. Do your in-feeding with the compound feed only and when the dial on the compound reads .054, you are there.
Al Messer
"One nation, under God"
"One nation, under God"
Here's the easy method...
Oh, my god all the math's in those other posts looks scary!
This is the method I've always used and it's served me just fine.
For standard V threads here's the method I use:
Here's the magic numbers, for:
- Cross slide infeed use: 0.64952
- Compound feed use: 0.75
To work out the depth of infeed simply divide the magic number by the TPI.
Exaple 1:
16 TPI thread. Infeed using cross slide:
0.64952/16 = 0.040595 inch measured on the cross slide dial.
Example 2:
16 TPI thread. Infeed using compound (set at 29.5 degrees)
0.75/16 = 0.046875 inch measured on the compound dial.
If you've got a small machine, in both cases advance forward at .005 per pass.
Hope this helps.
Mike
This is the method I've always used and it's served me just fine.
For standard V threads here's the method I use:
Here's the magic numbers, for:
- Cross slide infeed use: 0.64952
- Compound feed use: 0.75
To work out the depth of infeed simply divide the magic number by the TPI.
Exaple 1:
16 TPI thread. Infeed using cross slide:
0.64952/16 = 0.040595 inch measured on the cross slide dial.
Example 2:
16 TPI thread. Infeed using compound (set at 29.5 degrees)
0.75/16 = 0.046875 inch measured on the compound dial.
If you've got a small machine, in both cases advance forward at .005 per pass.
Hope this helps.
Mike
Re: Lathe threadiing math
If I interpreted the description of a sharp V thread as a thread with no flats at the crest or the root, wouldn’t the depth of cut (by the compound) be equal to the pitch if the compound was set at exactly 30 degrees? For 16tpi this would be .0625”. With a 29 degree setting the depth of cut would be just slightly different.
Bob
Bob
Re: Lathe threadiing math
SIR,
first of all, i would like to know why everybody is not
getting the same answer. my chart shows the double
depth of 16tpi as .07668. single depth .03834. if you
want to set the compound on 29.5 degrees. the secant
of 29.5 is 1.1489 x .03834 = .04404. this is the amount of
feed in on the compound for 16 tpi. this is what my
figures say, and this is the way i was taught to do it.
comments!
wlbrown
wright city, mo.
first of all, i would like to know why everybody is not
getting the same answer. my chart shows the double
depth of 16tpi as .07668. single depth .03834. if you
want to set the compound on 29.5 degrees. the secant
of 29.5 is 1.1489 x .03834 = .04404. this is the amount of
feed in on the compound for 16 tpi. this is what my
figures say, and this is the way i was taught to do it.
comments!
wlbrown
wright city, mo.
Back to Bob W
Bob W --
Your understanding of the geometry of the 60 degree Sharp V threadform is exactly right, and you're also right that if thread is cut by feeding the toolbit along the flank of the thread (using the compound slide) the infeed would be equal to the Pitch of the thread. But the Depth of the Thread is essentially the distance that the toolbit would be fed into the workpiece using the lathe cross slide.
Picture an eqilateral triangle with sides as long as the Pitch of the thread. Now label the base of that triangle as the Pitch of the thread, and the other sides as the flanks of the thread. Since by definition the three sides of an equilateral triangle are of equal length, the length of the flank -- which is equal to the infeed if the toolbit is fed along the flank -- is equal to the Pitch. The Depth of the Thread is the height of the triangle measured along a line perpendicular to the base.
Analytically, this height of the triangle (aka Depth of Thread) is Pitch x Cosine 30 degree.
I'll add that there are three common-in-North-America threadforms that are derivatives of the 60 degree Sharp V threadform: 1. the obsolescent U S Standard threadform, 2. the Unified threadform, and the ISO Metric threadform. These threadforms in their most basic configuration feature flats at both the Minor and Major Diameters, making their Depths less than the Depth of a same-Pitch Sharp-V thread.
For the U S Standard threadform, the flank length is 0.75 x Pitch and the Depth of Thread is 0.75 x Pitch x Cosine 30 degree.
For both the Unified and ISO Metric threadforms, flank length is 0.625 x Pitch and the Depth of Thread is 0.625 x Pitch x Cosine 30 degree.
It should go without saying, but for both the U S Standard and Unified threadforms the Pitch is specified in inches and the flank length and Depth of Thread calculated using these formulae are in inches. For the ISO Metric threadform the Pitch is specified in millimeters and the flank length and Depth of Thread calculated from the Pitch will be in millimeters.
John
Your understanding of the geometry of the 60 degree Sharp V threadform is exactly right, and you're also right that if thread is cut by feeding the toolbit along the flank of the thread (using the compound slide) the infeed would be equal to the Pitch of the thread. But the Depth of the Thread is essentially the distance that the toolbit would be fed into the workpiece using the lathe cross slide.
Picture an eqilateral triangle with sides as long as the Pitch of the thread. Now label the base of that triangle as the Pitch of the thread, and the other sides as the flanks of the thread. Since by definition the three sides of an equilateral triangle are of equal length, the length of the flank -- which is equal to the infeed if the toolbit is fed along the flank -- is equal to the Pitch. The Depth of the Thread is the height of the triangle measured along a line perpendicular to the base.
Analytically, this height of the triangle (aka Depth of Thread) is Pitch x Cosine 30 degree.
I'll add that there are three common-in-North-America threadforms that are derivatives of the 60 degree Sharp V threadform: 1. the obsolescent U S Standard threadform, 2. the Unified threadform, and the ISO Metric threadform. These threadforms in their most basic configuration feature flats at both the Minor and Major Diameters, making their Depths less than the Depth of a same-Pitch Sharp-V thread.
For the U S Standard threadform, the flank length is 0.75 x Pitch and the Depth of Thread is 0.75 x Pitch x Cosine 30 degree.
For both the Unified and ISO Metric threadforms, flank length is 0.625 x Pitch and the Depth of Thread is 0.625 x Pitch x Cosine 30 degree.
It should go without saying, but for both the U S Standard and Unified threadforms the Pitch is specified in inches and the flank length and Depth of Thread calculated using these formulae are in inches. For the ISO Metric threadform the Pitch is specified in millimeters and the flank length and Depth of Thread calculated from the Pitch will be in millimeters.
John
Re: Back to Bob W
Thanks John. Ahhhhh, I wasn't thinking about the term 'thread depth' as a part of the thread geometry description but as the cutting feed on the compound. I figured I must be doing something wrong there.
Bob
Bob
Re: Lathe threadiing math
Having machined threads for years on end that had to pass inspection to military standards, the only thing I have to offer is to forget using any of the formulas for achieving proper pitch diameters by measuring thread depths. The best thing to do is have the pitch diameters at hand (Machinery's Handbook has pretty much everything you need) and use wires for the measurements. That may sound like overkill for the home shop, but machining threads by dial is asking for more than your share of trouble. I agree that in principle it should work, but considering the variations in major diameter of the material and the considerable variations of the tool tip flat, you can easily miss the pitch diameter of a thread by a greater margin than the tolerance. We don't live in a perfect world.
Yeah, I know, it doesn't matter, this is just a hobby shop application, but learning to do anything properly will never be a mistake. Some day it may be a requirement and you'll already know how. The best thing is you don't have to remember a series of formulas that work only under ideal conditions.
Harold
Yeah, I know, it doesn't matter, this is just a hobby shop application, but learning to do anything properly will never be a mistake. Some day it may be a requirement and you'll already know how. The best thing is you don't have to remember a series of formulas that work only under ideal conditions.
Harold
Wise people talk because they have something to say. Fools talk because they have to say something.
Back to Harold V
Harold V --
I don't know if I should agree with you or argue with you.
Your point about cutting a screwthread based on Pitch Diameter is excellent, and you are absolutely right about the effect of the toolbit-tip flat on the infeed. But Major Diameter and Pitch Diameter control is not the whole of threading; that flat (or optional radius) needs to be correctly sized and the flank angle correct in addition to the Pitch Diameter correct for the thread to be acceptable.
I maintain that a machinist or engineer who understands the fundamental geometry of screwthreads has a big advantage over the machinist or engineer whose knowledge of screwthread dimensioning is restricted to the limits and formulae in a table. If anything, the advantage of understanding fundamental screwthread geometry is greater in the home shop and in remote locations where the threading toolbit is a product of the machinist's knowledge and skill with a bench grinder.
As an exercise, ask the next half-dozen machinists and mechanical engineers you encounter to describe the theoretical geometry of the Unified threadform, or if you're pinched for time, just ask them how wide/long the flat at the end of the toolbit should be theoretically.
In my 27 years of asking the latter question, I would guess that fewer than ten percent of the engineers and machinists I've asked -- all of them working in North America -- know the right answer. The correct answer is either another question: "For cutting an internal or external thread?" or is a conditional statement "For cutting an external thread the flat should be one-forth the Pitch, for an internal thread one-eighth the Pitch." (Incidentally, many current machine-shop textbooks don't answer this question correctly.)
Incidentally (Mk II version), I don't think I've ever seen a 60-degree center gage with Double Depth of Thread tables containing the correct Double Depth values for the Unified threadform (developed in 1949 and incorporated into the US Federal and Military standards shortly thereafter); every one that I've noticed has listed values for the obsolescent-for-fifty-years U S Standard threadform.
John
I don't know if I should agree with you or argue with you.
Your point about cutting a screwthread based on Pitch Diameter is excellent, and you are absolutely right about the effect of the toolbit-tip flat on the infeed. But Major Diameter and Pitch Diameter control is not the whole of threading; that flat (or optional radius) needs to be correctly sized and the flank angle correct in addition to the Pitch Diameter correct for the thread to be acceptable.
I maintain that a machinist or engineer who understands the fundamental geometry of screwthreads has a big advantage over the machinist or engineer whose knowledge of screwthread dimensioning is restricted to the limits and formulae in a table. If anything, the advantage of understanding fundamental screwthread geometry is greater in the home shop and in remote locations where the threading toolbit is a product of the machinist's knowledge and skill with a bench grinder.
As an exercise, ask the next half-dozen machinists and mechanical engineers you encounter to describe the theoretical geometry of the Unified threadform, or if you're pinched for time, just ask them how wide/long the flat at the end of the toolbit should be theoretically.
In my 27 years of asking the latter question, I would guess that fewer than ten percent of the engineers and machinists I've asked -- all of them working in North America -- know the right answer. The correct answer is either another question: "For cutting an internal or external thread?" or is a conditional statement "For cutting an external thread the flat should be one-forth the Pitch, for an internal thread one-eighth the Pitch." (Incidentally, many current machine-shop textbooks don't answer this question correctly.)
Incidentally (Mk II version), I don't think I've ever seen a 60-degree center gage with Double Depth of Thread tables containing the correct Double Depth values for the Unified threadform (developed in 1949 and incorporated into the US Federal and Military standards shortly thereafter); every one that I've noticed has listed values for the obsolescent-for-fifty-years U S Standard threadform.
John