Help cutting a gear

[old mart]

I will be engraving 50 lines on an aluminium nut some time, and have yet to look at the dividing plates to see if there is a suitable one. Then I would have to re read the instructions, because I have completely forgotton how. Otherwise it will be the 7.2 degrees (7.12.0) increments.

[Baz]

I want to make a gear with 74 teeth. I mentioned this to a friend with a 3 D printer. The next time I visited he gave me a 6 inch diameter disc with 74 neatly cut triangular notches, ready to take a positioning pin and a 3/4in diameter centre hole. As far as I can tell it is true within 3 or 4 thous., plenty good enough for my needs. Just got to make the gear now. Regards David Powell

There is an entry in Thingiverse for generating index plates to 3D print using Open SCAD to make it any number of holes and control diameter of plate, centre hole, even PCD of fixing holes. I did a test one seen here look at my picture not the site referenced in the title.

[BCRider]

If you want simple direct indexing using a 50 hole or 50 notch circle that's doable as well. CAD is your friend. Or someone with CAD is your friend....

I did a second circle but this time it's an 8" diameter with 50 hack lines around the perimeter. The lines are 0.500" apart. So even if you only printed the circle and lined up on the lines you'd have pretty good accuracy.

If I had the size for the center hole and screw hole pattern you need to make up an index plate it would be pretty easy work to make up a PDF for you that gave you a 25 hole pattern along with a few other circle patterns that you could use to make a plate that expands your options for the future in addition to being able to index your gears.

[Randy]

An orrery should be a very cool project! Please give a occasional progress report. Someday I'll take up clock making, and I'm sure there's a lot of overlap.

[lugnut]

An orrery should be a very cool project! Please give an didoccasional progress report. Someday I'll take up clock making, and I'm sure there's a lot of overlap.

I was able to capture a screen shot photo of the ornery the largest gear near the top ia 4"diameter. the next 2 down are sprockets with a ladder chain between them. the planet with the slanted shaft is the Earth with the moon rotating around it. I could br in way over my head and capability

[RSG]

Cool lugnut!

Looking forward to watching this evolve.

I just finished a scale tourbillon I designed/built which required a lot of gear cutting as well that you may be interested in seeing. I posted the results here a while back in two threads titled "4:1 scale watch Tourbillon build" and " Flying tourbillon finished".

[Mcgyver]

I was able to capture a screen shot photo of the ornery

Cool project, I hope you post photos of the build. Did your mean an orrey, or is that actually an image of what makes Doozer tick?

[lugnut]

Cool project, I hope you post photos of the build. Did your mean an orrey, or is that actually an image of what makes Doozer tick?

Damn auto spelling corrector, Yes I meant to spell Orrey. WAY back in 1950 when I was in the 4th grade at school we had some sort of a Orrey in our classroom. it always caught my attention.

[RMinMN]

That answers one of the questions. The gear is intended to set a proper ratio. The original was probably brass gears. Will that be what you will use or will a plastic gear be OK. A 3D printed 50 tooth gear will get the ratio but will not have the aesthetics of a brass gear.

Next question is whether the goal is to make a gear or is the goal to finish the project?

[BCRider]

As far as making machine "models" for entertainment and artful content goes an orrery would be pretty high class stuff. I hope you do post as you go.

If you want the PDF for a direct "glue and drill" plan for the disc let me know if you want the 25 hole idea and what the outer diameter needs to be. And include a few other hole numbers you don't have and I can put those in as well.

[lugnut]

As far as making machine "models" for entertainment and artful content goes an orrery would be pretty high class stuff. I hope you do post as you go.

If you want the PDF for a direct "glue and drill" plan for the disc let me know if you want the 25 hole idea and what the outer diameter needs to be. And include a few other hole numbers you don't have and I can put those in as well.

That would be great. As you can see, I'm in way over my head.🤔

[Paul Alciatore]

The first "secret" in dividing a circle into N equal parts is prime numbers. All numbers are either prime themselves or they have a UNIQUE set of prime factors. Thus, 3, 5, 7, 11, etc. are prime numbers. They have no factors except 1 and themselves. And 10 is not prime. The unique prime factors of 10 are 2 and 5. 2 x 5 = 10. No other factors for 10 exist and this is generalized by my statement above citing a "UNIQUE set of prime factors" for every number that is not a prime number. This has been strictly proven for all possible numbers (integers, actually).

When you are "dividing" a circle into an integral number of divisions you are actually looking for a way to have ALL of the prime factors of that integral number in your apparatus. In the case of a rotary table, that apparatus consists of the worm gear and the hole circle plate. All of the prime numbers in your desired number of divisions must be in either the worm or the hole circle. A 72::1 worm has the prime factors of 2, 2, 2, 3, and 3. That is the unique list of primes for 72.

And your 50 tooth gear has 2, 5, and 5. So your worm only provides the 2. It actually has three 2s, but the extra ones do not help for this division. You still need two 5s and 5 x 5 = 25 so a 25 hole circle is the smallest one that will let you cut your 50 tooth gear. Of course, whole number multiples of 25 will also work: 50, 75, 100, 125, 150, etc. because all of these contain two 5s in their list of prime factors.

A "LITTLE SLOP":

The problem with a "little slop" when using indexing to cut a gear is that it may be OK for a tooth or a few teeth or even all but the last tooth. All of them, up to that point, will probably mesh almost perfectly. You may have to space the center lines of the shafts just a bit wider, but the gear teeth will mesh with no problems.

BUT, that "little slop" on each tooth (actually the space between the teeth) is cumulative. I used a big word, but "cumulative" means that it ADDS to the error for the previous space for each space that you cut. So if you are off by 0.001" for the second space then the third space will be off by 0.002". And then 0.003" and then 0.004", etc. By the time you are cutting the 49th space it will be off by 0.048". So for your 1.625" diameter, 50 tooth gear will have about 0.102" on the OD space between teeth. 0.048" is almost half that and the 50th gap will be cut half way into the first tooth. That is not going to be acceptable and you would be a lot better off just 3D printing that gear or, going old school, and marking off 50 divisions by hand and using a file to cut the teeth.

If you are going to have "a little slop" in gear cutting, you must be careful how you define that term. Is a single tooth to tooth error of 0.005" acceptable? Probably not, but if that were your largest acceptable error then you need to divide that by your 50 teeth (0.005 / 50 = 0.0001") to get the allowable slop per tooth. Yes, that is 0.0001". NO ERROR in the math there. That is what "a little slop" looks like if you are going to use indexing for cutting your gear.

Now, there are methods where the error is not cumulative. 3D printing is one of them. Using a divider to hand mark the 50 divisions with trial and error is another.

Of course, making a CAD drawing of 50 divisions is also another way and, while there may be errors in the individual positions, those errors will not be cumulative. There is another reason why this is a good way to do this. The worm gear, in your RT will reduce the errors by a factor of the inverse of it's gear ratio. You say it is a 72 tooth worm so the errors in a shop made circle, using a printed CAD pattern would be 1/72nd as great in the gear you cut as they are on that printed CAD pattern. A 0.005" error in a hole plate made this way would result in only a 0.005 / 72 = 0.000069" error in each space between teeth of your gear. Now, that is just a "little slop" for real.

I would:
1. Make a blank hole circle plate for your RT.
2. Use a CAD program to generate a 20 hole circle sized for your blank plate. Be sure to include the center hole because alignment is important.
3. Print that CAD drawing 1::1 on adhesive backed paper.
4. Paste the printed drawing on your blank plate.
5. Carefully center punch and drill (and ream to final size) the 25 holes.

That gives you the hole circle plate that you need. And the gear you cut with it should be quite accurate.

PS: If you don't have a CAD program there are a number of free 2D ones on the web. Or PM me with your e-mail address and I will send you one along with a link to a free companion program that allows you to print it.

I don't think there 9s a positive answer, just wanting a close answer... I'm not planning to the moon and back, just wanting to make the rest of gears mesh. A little slop would suffice.

[masheenest]

I would make another set of holes (25) on the existing plate which now has "14 and 28" hole circles. Grid co-ordinates for drilling a 25 hole circle can be found in Machinery's
Handbook, sometimes referred to as "Jig Bore co-ordinates".

[Paul Alciatore]

Bare Bones Method:

OK, now for how this was done, with the best possible accuracy and back in the days before CAD, before 3D printing, and even before computers. How did a company/a machinist make the hole circle plates for a dividing head or rotary table back before the 1940s or even earlier? How was it done by hand? They needed a technique that generated greater accuracy than they started with. Here's my take on how it was probably done. And how it can be done in our home shops today.

The first step was to make an accurate worm gear. There are methods for that, but I will skip over them here and just talk about making the hole circles plates that will be used with them to provide the prime numbers that are not included in the worm gear itself. The following will work with any worm mechanism or other gear mechanism that provides an integral division of a circle (360 degrees).

You can generate a hole circle to the same degree of accuracy as your primary (worm) gear using nothing other than the indexing head or rotary table itself and making three generations of each hole circle. So the first step is to make three hole circle plate blanks that fit your indexing head or rotary table.

The first generation can be very crudely divided as by using a hand layout with a dime store protractor and pencil or pen marks. The only tolerance I would place on the process at this point would be +/- 1 degree and even that is tighter then it really needs to be. You can use the lines on that dime store protractor. Center punch and drill the holes. Reaming is a total waste of time at this point.

Mount that first generation plate on your indexing head or rotary table and make a second generation plate by drilling each hole as carefully as possible. And here comes the secret of this process. That second generation plate will have a maximum error that is, only a small fraction of the original error in the first generation plate. This fraction is the reduction ratio of the worm gear in the indexing head or rotary table. So with a 90::1 worm, the error is reduced by a factor of 90. Or with a 40::1 worm, the error is reduced by a factor of 40. This is due to the reducing nature of the worm gear. If a hole is off by one full degree on the first generation circle, then it will be off by only 1/90th or 1/40th of that degree on the second generation hole circle. Or, as I like to say it, the worm gear acts like an accuracy amplifier. The result is more accurate than the crude circle used to generate that result. Of course, since this action comes from the worm, you can never get more accuracy than the worm itself possesses unless you use more advanced, error canceling techniques. But the real beauty of this method is that those more advanced methods are not needed and only normal shop "best practices" are employed.

Finally a third generation plate, made from the second generation one, will then have a double reduction of the original error plus, of course whatever error is in your "worm" gear. That works out to 1/8100 with a 90::1 worm or 1/1600 for a 40::1 worm. A one degree error in the original would wind up as only a 0.44 arc second error plus the worm error with a 90::1 worm or 2.25 arc second error plus the worm error with a 40::1 worm. Both of these numbers are far better than the accuracy of my 10" rotary table so there is no point in going any further. When making this third generation plate, the time has come for using the best techniques possible. I would use a spotting drill to locate each hole. Then a TC, screw machine length drill bit, and finally a reamer. All of this aimed at keeping that hole at the exact location the indexing head or RT is set to.

This works for any number of holes in the circle so you can easily generate divisions of any number that you need and use that to generate any number of teeth on a gear. That includes strange prime numbers like 53 or 91 or 127 or whatever you need as long as you can fit the required number of holes in the circle. And it is the accuracy of the worm gearing in your device that is the limiting factor. Well, that and your technique in performing the work.

[lugnut]

I would make another set of holes (25) on the existing plate which now has "14 and 28" hole circles. Grid co-ordinates for drilling a 25 hole circle can be found in Machinery's
Handbook, sometimes referred to as "Jig Bore co-ordinates".

I have a DRO that could get me a set of 25 holes, but what next would I use to get me the correct spacing for the teeth, You have to remember your dealing with a 82 year old HMS. I suppose that some where there is a guide for using a 25 hole dividing plate, but I don't know where, any help for that would help.
Thanks
Mel