View Full Version : Diametral Pitch - confused...

lakeside53

03-06-2012, 11:16 PM

My lathe as a fancy qc gearbox that let's me select a zillion thread pitches. It separates "threading TPI" from DP (diametral pitch); lists DP from 4 to 184 with a symbol that indicates "pitch" and threads from 1 1/2 to 168 tpi.

Most of the thread "numbers" (Column group B and C below) are the same "numbers" listed under DP (Column group A below)

I see plenty of definitions where it relates to "gears", but this question is relating to a threading (or worm) type function.

Someone explain to me the difference between say 20 DP and 20 tpi, or 112 tpi and 112dp, or...... My lathe "manual" assumes I know the difference; I know otherwise.

http://i238.photobucket.com/albums/ff150/lakeside53/polamco/DSC_9036Medium.jpg

oldtiffie

03-06-2012, 11:27 PM

"DP" refers to cutting a thread that can be a worm etc. that has a pitch equal to the circular pitch of the mating worm-wheel. That pitch when inverted to get teeth per inch (TPI) will probably get an odd number of TPI.

Circular pitch is the circumference of the worm pitch circle divided by the number of teeth on the worm.

This may help.

http://i200.photobucket.com/albums/aa294/oldtiffie/Black_book/BB_50-51A.jpg

lakeside53

03-06-2012, 11:39 PM

Some of that I understand.

If I was to load a threading tool and select 20tpi or 20dp will I get the same result? I doubt it - it has a separate control selection. There must be more to this... I think ;)

Is there a simple relationship beteen tpi and DP numbers?

Paul Alciatore

03-07-2012, 12:45 AM

OK, Oldtiffie gave it a start. TPI does refer to Threads Per Inch. So, using your example of 20 TPI, if you put an inch ruler next to a 20 TPI thread, there will be exactly 20 complete threads in a one inch distance. For 16 TPI there are 16 complete threads in one inch. Etc. That should be simple.

DP stands for Diametrical Pitch. Diametrical Pitch refers to gear teeth and is defined as the number of teeth on a gear that has a one inch Pitch diameter. So, a gear with 20 teeth that has a pitch diameter of one inch would be a 20 DP gear. A gear with 16 teeth and a one inch Pitch diameter would be a 16 DP gear. Thus, the smaller the DP, the larger the gear teeth. Notice it is not the OD or outside diameter of the gear that is used, but the Pitch diameter which is somewhat smaller.

Now to compare them: since the teeth of a gear are strung around a circle (a circle with the Pitch diameter to be precise) the one inch Pitch diameter gears I spoke of above will have those teeth strung along a distance of 1 X pi or 1 X 3.141 because the circumference of a circle is equal to the diameter (the Pitch diameter) times pi. For our one inch circle, that distance is 3.141 inches. So the number of gear teeth per inch is equal to the total number of teeth divided by the length of the circumference or using your example of 20 DP, that is 20 / 3.141 which equals 6.366... TPI. The "..." after the number indicates that it is not an exact value, but an infinite decimal just as pi is not exactly 3.141, but an infinite decimal. This is also the pitch of a worm or a rack that will mesh with a 20 DP gear. Notice that I did put the correct unit of measure after that figure, "TPI" or threads per inch. Or in the case of a rack it would be Teeth Per Inch.

So a 20 TPI thread is 20 TPI while a 20 DP rack or worm is 6.366... TPI. They are very different.

Now for some real math. The fainthearted can stop reading now. Since Pi is an irrational number (infinite decimal), and it is a factor in the calculation of DP, there is no actual gear ratio that can exactly convert a lead screw that is a whole number of TPIs into an exact DP. So, the conversion on any real lathe from TPI to DP is never exact. It can only be an approximation. There WILL be some error beyond the inherent accuracy of the lead screw. Generally speaking, there are methods for calculating very close approximations: these approximations generally use two or more pairs or compound gears. The overall ratio is the product of the individual ratios of these pairs of gears. Machining texts show the way these calculations are made to the level of accuracy desired for a given application. "Screw Cutting in the Lathe" by Martin Cleeve is one such text.

http://ebookee.org/Screw-Cutting-in-the-Lathe-by-Martin-Cleeve_344912.html

Paul Alciatore

03-07-2012, 12:48 AM

Oh, the simple relationship between TPI and DP is:

TPI = Pi X DP

or

TPI = 3.141... X DP

lakeside53

03-07-2012, 12:51 AM

Thank you Paul (both posts)! I get it now.

Not sure if I'lll ever use DP for worms, but I could cut some really wacky "custom" threads with it... the type where you're sure if it isn't inch it must be metric. Wrong! :-)

oldtiffie

03-07-2012, 01:15 AM

Its no so bad really.

Circular Pitch = (pi x Diametral Pitch)/number of teeth in the gear.

That is the lead required of the worm.

Note the "pi" factor ~ 22/7 which will be incorporated in your gear-box "DP" settings.

I will try to give a worked example later.

Carld

03-07-2012, 08:48 AM

lakeside53, is that a Tarnow lathe? If so what size is it?

lakeside53

03-07-2012, 11:27 AM

Close. In the USA it's a Polamco TUM35 - 14x40 - and at 3000lb+ built like a tank.

dfw5914

03-07-2012, 01:04 PM

Excellent post Paul.

oldtiffie

03-07-2012, 08:39 PM

http://i200.photobucket.com/albums/aa294/oldtiffie/Black_book/BB_50-51A.jpg

I think that the "DP" setting on the lathe will cause the thread lead to be equal to the linea oitch of the "worm" which is also equal to the circular pitch of the worm-wheel.

Circular Pitch is a function of the gear DP which is a function of the gear diameter and number of teeth and is (PCD x pi)/number of teeth.

DP = pi/circular pitch.

Circular pitch = pi/DP

Setting the lathe to the required DP together with the "pi" gears (22/7) will produce the screw pitch which is equal to the worm wheel circular pitch which is equal the the worm lineal pitch.

"Teeth per Inch" (TPI) is the inverse of the screw lead/pitch and is:

TPI = 1/worm pitch = 1/(pi/DP) = 1/(3.1416 x DP)

I am reasonably sure my maths are OK - but not dead sure.

Zahnrad Kopf

03-07-2012, 09:22 PM

OK, Oldtiffie gave it a start. TPI does refer to Threads Per Inch. So, using your example of 20 TPI, if you put an inch ruler next to a 20 TPI thread, there will be exactly 20 complete threads in a one inch distance. For 16 TPI there are 16 complete threads in one inch. Etc. That should be simple.

DP stands for Diametrical Pitch. Diametrical Pitch refers to gear teeth and is defined as the number of teeth on a gear that has a one inch Pitch diameter. So, a gear with 20 teeth that has a pitch diameter of one inch would be a 20 DP gear. A gear with 16 teeth and a one inch Pitch diameter would be a 16 DP gear. Thus, the smaller the DP, the larger the gear teeth. Notice it is not the OD or outside diameter of the gear that is used, but the Pitch diameter which is somewhat smaller.

Now to compare them: since the teeth of a gear are strung around a circle (a circle with the Pitch diameter to be precise) the one inch Pitch diameter gears I spoke of above will have those teeth strung along a distance of 1 X pi or 1 X 3.141 because the circumference of a circle is equal to the diameter (the Pitch diameter) times pi. For our one inch circle, that distance is 3.141 inches. So the number of gear teeth per inch is equal to the total number of teeth divided by the length of the circumference or using your example of 20 DP, that is 20 / 3.141 which equals 6.366... TPI. The "..." after the number indicates that it is not an exact value, but an infinite decimal just as pi is not exactly 3.141, but an infinite decimal. This is also the pitch of a worm or a rack that will mesh with a 20 DP gear. Notice that I did put the correct unit of measure after that figure, "TPI" or threads per inch. Or in the case of a rack it would be Teeth Per Inch.

So a 20 TPI thread is 20 TPI while a 20 DP rack or worm is 6.366... TPI. They are very different.

Now for some real math. The fainthearted can stop reading now. Since Pi is an irrational number (infinite decimal), and it is a factor in the calculation of DP, there is no actual gear ratio that can exactly convert a lead screw that is a whole number of TPIs into an exact DP. So, the conversion on any real lathe from TPI to DP is never exact. It can only be an approximation. There WILL be some error beyond the inherent accuracy of the lead screw. Generally speaking, there are methods for calculating very close approximations: these approximations generally use two or more pairs or compound gears. The overall ratio is the product of the individual ratios of these pairs of gears. Machining texts show the way these calculations are made to the level of accuracy desired for a given application. "Screw Cutting in the Lathe" by Martin Cleeve is one such text.

http://ebookee.org/Screw-Cutting-in-the-Lathe-by-Martin-Cleeve_344912.html

Paul, this is part of what I do for a living and you've put it well, plainly, and it deserves reading again. Well done.

metalmagpie

03-08-2012, 11:15 AM

Hey, Lakeside -- I have that Martin Cleeve book on screwcutting if you want to borrow it or (gasp) acquire it permanently for your library.

MM

Carld

03-08-2012, 08:08 PM

A Palamco is a Tarnow sold by Palamco. That was the lathe I used the last place I worked and it is fact built like a tank. It's the best lathe I have ever ran and I wish I had one now. It was a 22x80 and did extremely accurate work even as big as it was. I treated that lathe like it was one of my children, it got the best care possible.

oldtiffie

03-08-2012, 09:19 PM

My lathe as a fancy qc gearbox that let's me select a zillion thread pitches. It separates "threading TPI" from DP (diametral pitch); lists DP from 4 to 184 with a symbol that indicates "pitch" and threads from 1 1/2 to 168 tpi.

Most of the thread "numbers" (Column group B and C below) are the same "numbers" listed under DP (Column group A below)

I see plenty of definitions where it relates to "gears", but this question is relating to a threading (or worm) type function.

Someone explain to me the difference between say 20 DP and 20 tpi, or 112 tpi and 112dp, or...... My lathe "manual" assumes I know the difference; I know otherwise.

http://i238.photobucket.com/albums/ff150/lakeside53/polamco/DSC_9036Medium.jpg

The direct and short answer to the OP's question is that in the"DP" section of your setting up guide/plate you put in the DP of the worm, the lead of the screw/worm-wheel will equal the circular pitch of the worm-wheel.

If the worm-wheel has 60 teeth and a DP of 15 the Pitch Circle Diametr will be 60/15= 4"

The Pitch Circle Circumference will be pi x 4 = 22/7 x 4 = 12.571"

Circular Pitch = 12.571/60 = 0.210"

That will be the lead of the worm being cut on the lathe.

As always, Threads per Inch (TPI) = 1/lead = 1/0.210 = 4.77 TPI

Paul Alciatore

03-09-2012, 12:37 AM

Paul, this is part of what I do for a living and you've put it well, plainly, and it deserves reading again. Well done.

Wow, praise from a pro. Thanks. Only thing I forgot to say was, "And now let me step down off this soapbox before it breaks." I do enjoy explaining things when I can. And I enjoy learning about things when I don't know enough to explain them.

toyjeep73

03-13-2012, 09:10 AM

So after reading this a few times and scratching my head even more, I have come to the conclusion that diametral (and module) pitch is primarily used on a lathe to cut the "worm" gear and you would then need to cut the "worm-wheel" on a mill.

Primarily I have seen people on this site using some acme rod to hob the worm-wheel to the pitch of the acme, but this would allow one to pick their own ratios?

I only ask because I to have found a chart for the DP, although my gear box is not as fancy and requires change gears. My chart is on the inside of the cover that the change gears are located behind.

http://i284.photobucket.com/albums/ll21/toyjeep1/Tools/IMGP1873.jpg

http://i284.photobucket.com/albums/ll21/toyjeep1/Tools/IMGP1872.jpg

Just trying to get a feel for the use of these options.

Thanks

oldtiffie

03-13-2012, 10:12 PM

I've thought about this a bit more and while the "spur Gear" tables are correct it should be pointed out that the circular pitch of a worm or helical or spriral gear is measured at right angles to the face of the worm/gear which is "skewed" an angular amount equal to the spiral helix angle of the "worm" (or mating gears in the case of helical and spiral gears).

The effect of the "skew" is mininal if the helix angle is not more than about 5 degrees.

For what its worth, a spur geear is a helical/spiral gear with a zero helix angle.

Pi is used as 22/7 (3.1429) instead of 3.1416 as the error is minimal (3.1429 - 3.1416)/3.1429 x 100/1 = 0.00414 % (when inverted) = 1 in 2,418

The reason pi = 22/7 is used is that 22 and 7 ratio gears are available:

22/7 = 110/35 = 220/70 etc.

Barrington

03-14-2012, 06:05 AM

the circular pitch of a worm or helical or spriral gear is measured at right angles to the face of the worm/gear

Yes, that is a definition of the 'Normal Circular Pitch" - however standards are I think usually written in terms of the 'Axial Circular Pitch'.

From Machinery's Handbook section on Worm Gearing:

American Standard Design for Fine-pitch Worm Gearing (ANSI B6.9-1977).

...

Pitches: Eight standard axial pitches have been established to provide adequate coverage of the pitch range normally required: 0.030, 0.040, 0.050, 0.065, 0.080, 0.100, 0.130, and 0.160 inch.

Axial pitch is used as a basis for this design standard because: 1) Axial pitch establishes lead which is a basic dimension in the production and inspection of worms; 2) the axial pitch of the worm is equal to the circular pitch of the gear in the central plane; and 3) only one set of change gears or one master lead cam is required for a given lead, regardless of lead angle, on commonly-used worm-producing equipment.

...

Cheers

.

vincemulhollon

03-14-2012, 12:02 PM

Note the "pi" factor ~ 22/7 which will be incorporated in your gear-box "DP" settings.

No one wants to cut a 9-tooth and a 22-tooth so it always ends up something like 27T and 66T.

However, a bored machinist can go to

http://en.wikipedia.org/wiki/Approximations_of_%CF%80#Miscellaneous_approximati ons

and scroll down to "continued fraction" and find the fraction, and the set of gears, that means you have to buy the fewest tooth cutters. See you can't cut a 27T and a 66T with the same cutter... you need to buy a #2 cutter and a #4 cutter. However... you can cut a pair of 54/132 tooth gears using just a single number 1 cutter because that covers 55-134 and technically the 54 is too few (err one few) teeth but "it'll work mostly".

On the other hand, if you're gonna cut "about 200 teeth", you're better off with the more accurate fraction 179/57 although that means buying two cutters or kinda stretching the limits and using #2 to cut whats darn close to a rack.

So cutting 132/54 is less accurate but better tooth quality, whereas 179/57 is more accurate but worse tooth quality. Decisions decisions...

I've done these calculations before... I was going to make a "slide rule" thing for kids with two resetable turn counters and the gears between them so you turn the "diameter" crank 10 times or whatever and the diameter reads 10 and the "circumference" counter reads whatever. One of those "in my infinite spare time I will" jobs.

oldtiffie

03-14-2012, 06:36 PM

Vince.

If the 22/7 value is used in the equation then the 22/7 ratio gears will cancel out any errors that may arise from not using the true value of "pi" (3.1416) in what is a truly/completely all-mechanical set-up.

If a computer/CNC solution is used the value for "pi" may perhaps be set at any value and the accuracy of the "worm" lead/pitch will be wholly determing by the "stepping" or "servo" values that are imparted to the lead-screw.