Thread: cutting a 73 tooth gear

HELLO TO ALL,
i have a dividing head, with the
three standard plates. ratio,40/1
i want to cut a 73 tooth gear.
my book says 12 holes, on a 21 hole
circle, but it also says what gear
i should have on the head. my divider
only has capabilities for simple
indexing.
will i be able to do this with the setup
i have? comments please, and thanks.
wlbrown

What do you mean by simple indexing?

Do you have a pin plate with a 21 hole pattern?

You already know the gear you have.. the 40:1 gear.

That being the case, you are looking at differential gearing. You can also get an extremely close approximation by using the compound method but this is very tedious. The compound method for 73 teeth requires 6 whole turns plus 28 holes on a 47 hole circle. You then clamp the spindle and roll the hole plate backward 1 hole on the 49 hole circle. This is repeated until the workpiece has rotated through fully 12 revolutions but you can tell when your done because all the teeth have been cut, haha. This will be accurate, if you take proper care of the backlash, to about .0001 of a division.

73 is prime so, unless you have a 73 hole plate, simple indexing isn't
possible.

There are numerous compound indexing solutions depending on the final accuracy
you require. Here are just the first few from my program:

Number of divisions = 73
Allowable approximation accuracy = 0.005000 %
Required increment = 40/73 = 0.54794521

PLATE #1
1 & 10/17 +1 * ( 1/18) = 1.64379085 [ 3] (-2.7233E-003 %) **
2 & 10/17 -1 * (17/18) = 1.64379085 [ 3] (-2.7233E-003 %) **
1 & 1/18 +1 * (10/17) = 1.64379085 [ 3] (-2.7233E-003 %)
2 & 1/18 -1 * ( 7/17) = 1.64379085 [ 3] (-2.7233E-003 %)
2 & 1/18 +1 * (13/19) = 2.73976608 [ 5] (+1.4620E-003 %) **
3 & 1/18 -1 * ( 6/19) = 2.73976608 [ 5] (+1.4620E-003 %) **
2 & 13/19 +1 * ( 1/18) = 2.73976608 [ 5] (+1.4620E-003 %) **
3 & 13/19 -1 * (17/18) = 2.73976608 [ 5] (+1.4620E-003 %) **
...

Differential dividing is another possibility. If you want to pursue that,
there's a program (DDH) on my page for sorting out the math and gearing.

Regards, Marv

Home Shop Freeware - Tools for People Who Build Things
http://www.geocities.com/mklotz.geo

A possibility is to buy a 16DP, 73T gear from Boston Gear (change gears) and use a sliding index pin to just pick off their gear.

Mount and key your blank and the gear above to a common shaft and away you go, having expended $20 in the process.

My suggestion is more of a 'get R done' strategy than about pure precision or base principles.

- Matt

If your indexer only does simple indexing, then you won't have the capability to do differential via the gear train method.

What I would suggest, is that you make up a graduated dial to fit in place of your index hole plate, graduated so that the circumference is broken into 9 degrees.

Then, sit down with pen and paper and make yourself a list of "stops" to make on the degree dial for each tooth of your 73 tooth gear.
First position 0 degrees.
Second position 4.931 degrees or 4 degrees 56 minutes
Third position 9.863 degrees, less the 9 would be .863 degrees or 0°52'
etc.

Make yourself a nice legible chart that you can work your way down, and check off each completed movement.

While not super convenient, its good for a one shot use.

wl,

I hope you have a good buddie with a wire edm. This would cost you a couple of 6 packs.

TMD

I think you may have read the wrong line in the table. 12 holes on a 21 hole circle with a 40:1 head will give you a 70 tooth gear. And it will be exact. But exactly 70 teeth, not 73.

More later.

Paul A.

RJ, and EPA, he's referring to the standard B&S tables as in Machinery's and elsewhere, for differential indexing. His dividing head is a simple index, but to use the chart, a head that can gear the dividing plate to the crank so it turns differentially, is needed. Referring to the chart, the gear train is simple gearing (as opposed to compound), gear on worm, 28; gear on spindle, 48; and 2 idlers, one of 24T and one of 44T (so apparently the dividing plate rotates opposite the crank, which makes sense).

Anyway, the answer is that the simple ("Plain")dividing ad can't be used with the plate and set up described, for reasons already pointed out. I beleive a Vertex universal dividing head is a direct copy of the B & S universal, and should be able to be used if set up with the gear train described.

smt

This kind of difficulty in indexing is one of the things that led to my inventing the "Newbould Indexer".

It consists of 4 face gears with 3 different pitches:
1 degree
1 degree one minute
1 degree 1 minute, 1 second.
Patent # 3,846,912 direct link to patent in the patent office It increments every one arc second, and is direct reading.

Since 73 teeth = a pitch of approx. 4d 55' 53" you could make a list of each position and set the indexer, at random if you like, at each position to do the work. A handheld calculator could be used to calculate each position and round it off to the nearest second. I do it the easy way with an excel spreadsheet.

This makes simple work of any number of indexes you want.

BTW, the Newbould Indexer is considered the 28th basic mechanism in history and was put into the Smithsonian in 1974, even before the patent actually issued.

For a one off gear that cannot be accomodated by the normal index plates, simple indexing is easier than differential or compound indexing or other methods your shop may not be equipped for.

Using another gear to index will work well, but you will be hard pressed to find a 73 tooth gear. If you could buy one, you would not need to make one.

There are a couple of methods to produce an odd indexing wheel. One of the simplest is to use a length of bandsaw blade with the appropriate number of teeth plus enough to join it in a ring. Carefully solder it together so the teeth in the joint match, mount on a round blank and have at it.

Just make sure it is not a vari tooth blade.

Another post regarding exchanging skills (http://www.practicalmachinist.com/ub...c;f=1;t=014619) could suggest a fairly simple alternative:

How about shipping one of your indexing plates to a member with CNC or differential indexing capability and having the 73 index holes added to the existing plate ? Perhaps an exchange of services could be arranged ...

Mr. Newbould I'm interested by your device, but I can't figure out how it indexes to one arc second, I can see the face gear that allows 5 degree indexing where is the adjustment for the rest? Possibly if I had one in front of me this would be more obvious. Forgive me I'm still pretty green. The patent link doesn't work for me either I guess that doesn't help.

Also is there anywhere online that lists the basic mechanisms that are in the smithsonian? Sounds like interesting reading.

Sorry about the link not working. I got more than one message about that.

I guess the patent office stuff is not too friendly with some browsers. It works fine with my Netscape 7.2

I just made a PDF of the patent and posted it in my forum site. Patent PDF It is almost 3 meg but if you have high speed access it comes up pretty quickly, and I'm working on making a smaller set of jpg files.

The Smithsonian, so far, has not made a display of all the basic mechanisms that I know of. The Wall Street Journal published a story about the 27th based on a list made by engineers at Sandia Laboratories. I have a copy of that article and the list.

The story of my indexer has been published in print and put on TV several times.

I may compose something about the whole subject. It is interesting, to me at least.

I could make a deal with furnishing index plates somehow to members in here and in my forum.

I've sold them by the hundreds to the Timken company who uses them to check angles on their races. I even have a written endorsement from Timken which I'm allowed to publish.

rj www.newbould.com and www.newbould.info

hello
i had to make a 73 tooth internal gear several years ago and did not have a dividing head to do it. i drilled a 73 hole plate for my 5c spindex and used that. a cnc mill or manual mill with digital readout makes drilling custom plates easy.

Reckon you could sneak a 72 tooth gear in ??? 5 degrees per tooth... LOL

had to make a 73 tooth internal gear several years ago and did not have a dividing head to do it. i drilled a 73 hole plate for my 5c spindex and used that. a cnc mill or manual mill with digital readout makes drilling custom plates easy.

If you can get the jig boring coordinates for 73 teeth, drill a 73 tooth pattern in an index plate for your indexer. I had to do that for 41 teeth once.

smt,

I did understand that he has only simple indexing capability and only the three standard circles. My B&S table for a 40:1 indexer shows 12/21 (12 holes on a 21 hole circle) for 70 divisions.

If he had additional gearing inbetween the circle and the worm, then 12/21 might be used. But for an exact solution, one of those gears would have to have 73 teeth or an exact multiple of that number. In checking with all even numbered gears between 16 and 72, the closest, APPROXIMATE combination I found was 46/48. This produces a 0.06% error in the gear ratio. Or expressed in the same manner as the B&S tables, it will produce 73.0435 teeth. Of course that is assuming only one one pair of gears (one on the worm and one on the plate's shaft, if an intermediate compound was added on an additional shaft, it would be able to produce a far better approximation. If I am incorrect here, please let me know.

wlbrown,

If an exact solution is desired, a 73 hole plate could be easily (well fairly easily) made. The 40:1 gear reduction of the indexer is actually an accuracy amplifier. A circle made on the indexer will be 40 times as accurate as the circle it is made from. You can take advantage of this by using a two step procedure. First make an approximate circle with 73 divisions, layed out BY HAND or by a CAD print. This circle is only temporary so it can be just printed on paper and taped over one of the regular plates. Now make a blank plate and mount it for drilling. Use the temporary 73 hole/line plate to drill the real one. Use 40 holes or lines on the temporary plate for each hole.

The new, shop made plate will be 40 times as accurate as your temporary one so if the temporary one is accurate to +/-1/4 degree, the permanent one will be within +/-1/160 degree or +/-22.5 seconds. Now when you use the shop made plate to cut the gear, it will be 40 times as accurate as that or about +/-0.56 seconds. I really doubt that your indexer is that good or even anywhere close to it so any further refinement would be a totally wasted effort.

Paul A.

So far we've heard from a lot of people in here, but nothing back from wlbrown... Is he even watching this or are we just talking to each other?

RJ, I would like to know what kind of indexing you were doing and how it inspired you to creat the Newbound Indexer. How long did it take to solve the gearset? This seems like a tough nut to crack. [img]smile.gif[/img]