Gear cutting calculation – 73 teeth

[BazyleParticipant @bazyle]

Ok, this is not question of how to divide by 73 but "what do you think of this guy's method"

There is a home made 73 tooth drummond/myford gear (for metric threads with help of 46 tooth too) on ebay. Since the add will timeout and make the link meaningless in far future reading I will copy the maker's explanation of method:
"Outside Diameter was turned on our lathe where we also drilled the centre hole – the blank was then secured to an arbor & fitted into our 40:1 dividing head – teeth were then individually cut using the correct Number 2 Involute Gear Cutter using an 18 hole Division Plate – zero turns – & 10 holes between cuts on our vertical milling machine.

For those of you in the know….

……ok – so we 'mathematically' cheated 'a little bit' but we are momentarilly restricted to a BS 40:1 Non Universal Dividing Head – it was a 'trial & error' Find out process – & our blank being of 1 tooth larger outside diameter left EXACTLY the right amount of space for the extra tooth – we cut the first cut 'again' just to 'make sure' & its cock on

Happy Days

Dont know if this will work 'everytime' ???

Our next mission is to use formula 16 – 0 – 5 on a 'lesser' outside diameter normally required for this setting – of – 190.3mm using 1.5 mod cutter – hoping the finished gear will be 1 tooth short !!!!

Has anyone else out there tried this ?

Did it work ?"

The "next mission" is 127 tooth if you don't realise.
So what do you think – pure luck? I think impossible as described. Stepping round with dividers can get an extra tooth on an oversize blank but winding the handle on a dviding head set for 72 divisions gives 72 teeth at the wrong DP in my view.

[BazyleParticipant @bazyle]

How to cut a 73 tooth prime

[JasonBModerator @jasonb]

Using the head to give 72 divisions will give 72 divisions on any diameter blank so can't see how he did it

[Ed DuffnerParticipant @edduffner79357]

It would be interesting to see the maths and formulae to see how the 72T and then the 73T were arrived at. One extra tooth might be ok, but could this be one of those situations where mathematically error could creep in as the process progresses? similar to that on some threading (not that it matters in the case of one extra tooth).

[Les Jones 1Participant @lesjones1]

I agree with the 72 tooth calculation. I counted the teeth on the gear in the picture and counted 72. I only did it once so I could have miss counted. Has anyone else counted the teeth in the picture.

Les.

[Anonymous]

Yes, I counted them 3 times, and each time I got 72.

Andrew

Edit: His OD result is wrong too, for both 72 and 73 teeth…………..

Edited By Andrew Johnston on 24/07/2015 21:39:50

[Les Jones 1Participant @lesjones1]

Hi Andrew,
I did not even look at the diameters as the number of teeth will be the same regardless of the diameter. I was interested in the explanation of the "mathematical cheat" but it was not explained other than they did not calculate the result but used trial and error. (The error bit worked !)

Les.

[John HaineParticipant @johnhaine32865]

The seller obviously read this thread as it now says listing ended because there was an error in the listing!

[Les Jones 1Participant @lesjones1]

Hi John,
Did you scroll down to the questions section ? Here is the question and answer.

"Q: Have you, em, counted how many teeth there actually are? Specsavers?
A: ….thanks for your input muzzerboy – much appreciated"

Les

[John Stevenson 1Participant @johnstevenson1]

Interesting though and going off at a tangent but some years ago I made a cock up in counting holes and finished up with 41 1/2 splines instead of possibly 42 ? Long while ago, can't remember but it was my fault, did the cooon trick of counting the first hole as 1

But the tables only give you results that are exact but what if you chose a wrong circle of holes and wrong spacing, how close can you get ?

As I say, interesting.

[BazyleParticipant @bazyle]

mmmm well if you've gone and made the 72 one you could use it as the index plate and do alternate 39 and 40 counts (72*40/73 = 39.45)

 But I think more likely the plate set has 49 as the highest so have to count 27 and every fifth hole back off to 26. not quite so good.

But there again in this csse you have obviously got a Drummond so have a 65 and perhaps 100 tooth gear to use.

If only somebody made nice add on plates and sold them on ebay ……………………….

Edited By Bazyle on 24/07/2015 23:24:11

Edited By Bazyle on 24/07/2015 23:27:52

[MuzzerParticipant @muzzer]

Believe me, I've made a much bigger 4rse of myself in the past and I'm sure I'm by no means alone. Not into casting the first stone or sniggering at honest mistakes…

Interesting challenge how you'd do it though and I'm not about to argue with Bazyle. Although I possess a set of dividing plates for my rotary table I've never used them. Being a idle techno nerd, I'd obviously look for an opportunity to develop a CNC / stepper / rotary solution.

Muzzer

[DMBParticipant @dmb]

I am puzzled about 72/73 ?40 when
63/64 ? 40 = 39.375 exactly.

[John Stevenson 1Participant @johnstevenson1]

Posted by Bazyle on 24/07/2015 23:17:23:

If only somebody made nice add on plates and sold them on ebay ……………………….

.

Just done a bit of checking on dividing heads and this is not a complete list.

Most heads that follow the B&S standards won't do 73 divisions.

However the Ellis head with plate no 5 [ that have three extra plates 4 to 6 for such as these primes ] wll do 73.

The Cincinnati head with the high count plates, Side E will also do 73.

And the Myford head with plate no 3 will also do 73.

On the No 3 Myford COMPATIBLE plate I sell and at the moment it's by direct selling as well as the nornal row of 6 holes, my plate also has a 127 hole ring on the No 3 plate.

I will not be using Ebay as my wife did but later this year Debs and myself will be opening the old website to sell goods made by both of us.

Sorry for the dig.

[Anonymous]

Given that 73 is a prime number if you don't have a plate with 73 holes you'll need to use compound/differential indexing. I'd make a plate with 73 holes since I already have a custom plate I made for some other numbers.

Andrew

[BazyleParticipant @bazyle]

72/73 was to use the 72 tooth gear as an index on the advertiser's declared 40:1 dividing head. Just a dig at the fact that now he's made it he could use it for something.

Good find on the ratio but 63/64 would need a 64 tooth circle or gear. Most standard plate sets don't go above 50 and, again referring back to the advert being for a drummond/myford (early one) the gear set mostly go in multiples of 5 (though I have a 32 that would do it's not standard as it's not on the original lathe charts)

John, I was working along the line of approximations which benefit from a high hole count and as I have a set of your plates was making the oblique reference to the 127 circle you squeeze onto them which I figured many of the regulars on here would pick up on as my post directly followed yours.

Edited By Bazyle on 25/07/2015 00:17:29

[John OlsenParticipant @johnolsen79199]

I made myself a differential dividing attachment to go with my Vertex BS0 dividing head and used it to make a 71 tooth and a 113 tooth gear, mostly just for the interest of it. Used with a 5 to 1 ratio, this pair can give a good approximation for Pi (113/355) although so far I haven't actually found an application for this fact. However it was interesting to do, and it is nice to know that I can know cut pretty much any number of teeth on a gear that I might happen to want. The same attachment could with a little modification be used to cut helices on the mill, although again, that is something I have not actually found an excuse to do yet.

But there are ways to divide awkward numbers without the differential setup. The simplest is probably if you have CAD and a printer. Just draw a dividing wheel with the required number of holes, print it out, glue it on a suitable piece of plate, and centre pop and drill all the holes. Now use it as a dividing plate and make another one, which will have all the errors you made with the popping and drilling divided by the ratio of the worm in your dividing head.

John

[Anonymous]

Even easier if a DRO is available, only one go round the loop is required, like this:

Andrew

[BazyleParticipant @bazyle]

John, can you do 106? You may already know why this number is special.

[Neil WyattModerator @neilwyatt]

You lot think you're clever cutting prime numbers of teeth!

That's nothing,. I can cut gears with non-integer numbers of teeth

I'll fetch my coat…

Neil

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Neil Wyatt on 26/07/2015 14:55:09:

That's nothing,. I can cut gears with non-integer numbers of teeth

.

Just keep indexing and cutting, Neil

You should eventually reach zero teeth.

MichaelG.

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by Neil Wyatt on 26/07/2015 14:55:09:

That's nothing,. I can cut gears with non-integer numbers of teeth

Been there, done that.

Russell.

[John Stevenson 1Participant @johnstevenson1]

Posted by Bazyle on 26/07/2015 12:17:06:

John, can you do 106? You may already know why this number is special.

Yes, we make a set of what we call watchmakers plates, only a small set about 4" in diameter, 4 to a set with 8 rows of holes in them.

They are made to go on 40:1 or 60: 1 worm drives and not direct indexing.

The No 4 plate has 18, 22, 27, 33, 43, 53, 61 and 67 holes in it. So the 53 hole will do 106 as 20 holes on the 53 for a 40:1 reduction or 30 on the 53 circle for the 60:1 reduction.

Not sure if I have any in stock, would need to check.

Again the Myford No 4 plate also has 53 in it.

[BazyleParticipant @bazyle]

106 – the question was aimed at John and his differential gear cutting. The point was just that the tables show it needs an 86 tooth gear in the train which is supplied as part of the normal 11 gear set for differential indexing. So does he have the 86?

However 106 is the only time it is needed up until 212 so there must be hundreds of these gears made and sold that never got used, especially if the machine shop had an extension set of plates with 53 on it.

Non integer counts. What's the name of that gizmo, named after its American inventor, that uses non integer circles of holes as a vernier to create very wide range of angle settings? (instead of using a sine bar). An article on it might be interesting in MEW.

[Anonymous]

Posted by Bazyle on 26/07/2015 20:41:53:

Non integer counts. What's the name of that gizmo, named after its American inventor, that uses non integer circles of holes as a vernier to create very wide range of angle settings? (instead of using a sine bar). An article on it might be interesting in MEW.

The indexer invented by R J Newbould, the prototype of which is in the Smithsonian?

Andrew

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