Gear cutting calculation - 73 teeth

Been there, done that.

Russell.

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.

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.

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

Andrew

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Wow, that's clever

Patent

MichaelG.

The originator of the design posts regularly on the 'practicalmachinist' forum. There was a discussion of the design process some while ago, but I can't find it at the moment. If I recall correctly the key to the design was using partial sets of teeth on some rings.

Andrew

I think the use of the Drummond 46/73 combo for metric threads is all a bit academic and certainly not worth the bother of making the gears. It is at best an approximation ratio that does not give the perfect equivalent pitch. Then add to that the error in the lathe's 75-year-old leadscrew.

You can turn metric threads with the standard M-type gear set of 20-75 in fives, plus the standard 38T used for 19tpi, by using double compound gearing. The margin of error is 1 in 1000 or less - one thou per inch - close enough for anything I do. Certainly never anything that uses a nut more than an inch thick.

For example: 1mm pitch uses the gear train, starting from mandrel: 35 -- 50/45 -- 40/30 -- 75. (error 1 in 8,000)

0.5mm pitch = 30 - 60/45 - 55/25 - 65 (error 1 in 1144).

No, I am not a mathematical genius. All cribbed from an ancient paper chart that came with my lathe, Xeroxed from an old book on screwcutting by Martin Cleeves, I believe. I have played around with it and it seems to work. But I work exclusively on ancient British and American machinery so rarely have need to turn metric threads. (My Honda never breaks down!)

I haven't tried to do a 106 although I don't see why it should be any harder than anything else. My setup uses standard Myford change wheels so would not include an 86 but then if I needed one I would setup to make one. But so far none of the setups I have calculated have needed anything other than the standard dividing plates and the standard changewheels. I must dig out the table I did...I wrote the whole thing up and submitted it to ME, but the editor at the time appears to have discarded it, along with several others.

The basic approach is that you set up for something easy to divide with 1 or a few more teeth more (or less) then the one you want, then you work out a train that advances (or retards) the dividing wheel by just the right amount. So for instance if you want 71 you might set up for 72, then the differential train has to advance the dividing wheel by enough that it is back to the starting position after you have done your 71 teeth. It would of course be quite easy to produce non integer numbers of teeth too! I've also done that in a very non reproduceable manner, since the BS0 has a screw arrangement for the chuck and a taper which does not come with a drawbar in the body...both can easily move under milling loads. I drilled and tapped the taper in mine for a drawbar.

John

I can't see the point of 'super-universal' dividing arrangements.

Once the resolution of the placing of the divisions is less than the accuracy of the machining process, you may as well use a degree scale and a vernier. If you have to use that double tooth (or looking at the picture two sets of double tooth) wheel the convenience aspect of using a holed plate is lost.

Gear and screw makers (me included) seem to have an obsession with pursuing accuracy beyond either the needs of the final application and the capabilities of the generating cutter/machine combination.

Neil

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Maintain that obsession, Neil

Errors and approximations have a nasty way of compounding.

If you aim for perfection, and only achieve 90% then you get 90%

... But if you aim for 90% you might get 90% of 90%

etc.

MichaelG.

Fully agree Neil.

For a while years ago I worked at Raglan lathes which for their day were a decent lathe and well made. A lot of skill went into them.

The leadscrews were made on a special threading machine that was made by them. It was basically an old lathe with two leadscrews, one set for 8 tpi and the other geared to give 1tpi.

In operation it moved forward and cut the first cut, at the end of it's stroke a cam removed the cut, engaged the second drive and returned the carriage to the start and a new cut was applied and this went on until the thread was cut. It also carried a bearing type travelling steady to keep it straight when cutting.

This operation was fully automatic and no one ran the machine. Once it stopped anyone passing would take the new screw off and replace it with a blank and press go.

Because of internal stresses these screws came off bent like a banana. The shop fitter would collect them up, bung them on an arbour press and straighten them between two vee blocks by eye but in all fairness he's been doing this for so long he was very good at it.

Point I'm making is, that in no point of the process was a screw checked for errors. From also going round Myford's they had roughly the same quality control as Raglans. I even asked the guy responsible at the pre sale if they were checked and told no, they relied on the machinery.

So if no checking is done on these 'budget' lathes what is the point of trying to work to microns ?

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Did anyone notice the unfortunate error in the 'brief description of the drawing" ?

The " mark [meaning seconds of arc] has been 'corrected' to the word inch [or inches, according to context]. ... Which doesn't really help comprehension.

I don't know if it was an enthusiastic typist, or an autocorrection by a word-processor; but at least we can be grateful it did not come out as a 'Smiley'.

MichaelG.

Well astronomomy tends to be one application where higher accuracy is appreciated. So perhaps don't make telescope guiding systems using a crappy Myford dividing head?
Newbould used super precision rotary tables at great cost to make his instruments but one wonders if there are Chinese knock-offs bashed out on a CNC where they think that because the computer says it is such and such dimension it really is.

On the other hand you can overdo it. One of our club members tells how at Mercers (the instrument makers) he made taps in the smaller BA sizes using a lathe with a correcting apparatus for the leadscrew. The taps then made holes in watch plates just for fixing screws.

John Stevenson:

I seem to remember seeing somewhere that Myford lead screws were made by a "thread whirling" process - I assume this meant some kind of rolling process.

Myford leadscrews were indeed rolled threads, I saw this done on a visit in around 1977. It used a very powerful press. ISTR the rationale was that the forming in this way led to a very strong product. The leadscrews for power crossfeed warped considerably when the keyway was cut and had to be straightened in Vee blocks.

Regards

Tony

It curious that people just think about lead screw in regard to screw cutting and discount any errors in the gears used to drive the gear train. In practice just like the lead screw they wont be exact. Even the nuts and bolts we buy aren't. That's one of the factors that sets the thickness of nuts and the lengths that fixing screws are allowed to engage.

73T could probably be cut via compound dividing or with the universal dividing head type arrangement but really it would be better to find conversion gears that are easier to cut.Maybe 80 - 63. There are lots listed in screw cutting in the lathe if I remember correctly.

People often go for 100 - 127 as it has to be exact etc and arguing that errors will be less and etc. Some lathes just use a 127 and the 100 isn't needed. One I am thinking about just fits a 127 to the lead screw and can cut metric and BA.

There are a couple of little programs on lathe co uk that will accept a list of gears and a pitch and work through to the closest approximation that can be obtained with them.

A spread sheet can also be used to produce things like this - for a boxford with a gearbox. Boxford supply one of the gears needed as packing on the screw.

All in all though I'd guess many worry about not being able to cut metric threads than actually needing to. I do. The problem only really comes up when something has to be made to fit or replace an existing metric part. I see up to M10 at least being related to taps and dies. When metric designs are being made using 25mm x 16 tpi rather than a 1.5mm pitch isn't going to upset anything. If measuring threads are required careful finishing with a hand chaser might lead to a more accurate result even on a metric lathe - especially on lathes where the lead screw also provides the power feed. Metric measuring threads are a pain but thanks to certain styles of small board camera lenses there are some reasonably priced 0.5mm pitch taps about in suitable sizes.

John

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Funnily enough I've been bashing my head against this for a while. In the absence of a 'proper' polarscope the best I can get is 30 seconds of exposure without star trailing, and then only about 50% of the time.

The typical errors are about 5 arc-seconds in 30 (time) seconds.

Now in 1/2 a minute stars move 0.125 of a degree or 450 arc seconds, so my error is 1 part in 15 which seems quite high. But when you think of it as a misalignment of about a thou over the length of the scope in the context of three gears followed by a worm and gear with all that potential for backlash, or a mispositioning of the worm gear by less than one wavelength of visible light...

It's been recommended to me that I give up chasing these little errors and just go for active guiding - some people use this to take pictures with exposures of an hour or more and it is usual to achieve a sub-pixel level of error.

Neil

You mean it's dark enough where you are to take 30 sec exposures Neil ? I'm envious.

On your problem I strongly suspect that the ancient rule that the worm wheel should be the same or larger diameter of the scope being driven is probably correct but would still need correction. I think Becon Hill will still supply some large ones.

When Astrophysics rebadged and changed Meade mounts I'm told one of the things they did was to lap the worm and wheel against each other to improve the mesh.

All in all autoguiding makes most sense but a lot of the problems seem to be solved in many cases by the size of the images shown and the processing. I have also seen photo's that show resolutions several times greater than the scope can possibly have plus planet shots especially from smaller scopes where some one has actually painted the detail in.

John

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The 1" x 40tpi screw thread that drives the declination of the 28" at Greenwich was hand chased in gunmetal. Parts of the drive date to the 1893 clockwork (which replaced the earlier water driven system) with recent modifications in 1970 when the scope was relocated from Herstmonceaux. The main source of periodic error comes from the pitch circle and bore of the gears being slightly eccentric. Most errors are now corrected via the recent AWR drive box and a guide scope.

Last time I was there the whole thing had ground to a halt because one 1" tapered pin had dropped out

(note to self: don't get fingers in the clutch when the solenoid fires up )

I did hear that Barrie Watts (Beacon Hill) was packing up making worms/wheels?  might be an opportunity for someone?

Edited By john carruthers on 31/07/2015 18:20:38

If we were really serious about accuracy, we would not only want to use the best method we had available to us, but would also want some independent means of checking the accuracy of the result afterwards. Mostly as amateurs we lack the latter. If I make a leadscrew, what am I going to use to check it, other than the leadscrew that I used to do the screwcutting? think it is this general lack of some means of checking the result that makes people try to use theoretically perfect methods rather than just good enough. Although I have managed to resit the temptation as far as cutting metric threads with a Myford leadscrew goes. Although I do have a 127 tooth wheel, I have never bothered to use it. I have always just used the 63 tooth wheel...partly because that is good enough for all practical purposes, and partly because the 127 tooth wheel is so big that fitting it is a pain. It does look good hanging on the wall. If I really needed a long accurate leadscrew I would probably just buy one, since they are readily available to specified standards of accuracy. Sometimes as amateurs we should accept that we simply don't have the gear to do a particular job. For instance I will cheerfully make my own gears for changewheels, or for that matter for a traction engine, but would never bother to try to make gears for a car or motorcycle gearbox, where both high accuracy and correct material and finish are needed to provide a durable end product.

The accuracy of the differential dividing technique actually comes down pretty much to the accuracy of the worm and wheel in the dividing head, so the results will be of similar accuracy to those obtained from the same dividing head with conventional dividing. Errors in the dividing wheel will be divided by the worm ratio, and errors in the train driving the dividing wheel will also be divided by the worm ratio. So although there are are more sources of error and they will sometimes add, they are still going to be pretty small compared to the desired outcome.

John