Would you mesh with this?

[Sam StonesParticipant @samstones42903]

Some thoughts on cycloidal clock teeth

[Sam StonesParticipant @samstones42903]

As you will gather, I no longer make swarf and, although I considered if this should be entered into ‘What did you do today?’ I chose to give it its own title.

Perhaps it would interest first-time clock makers who know about depthing. Or perhaps do not.

I didn’t either, but as Basil Fawlty once said “I think I got away with it!”

Nevertheless, I have been enticed by my own curiosity into the inner sanctum of cycloidal gear teeth and how they mesh or don’t.

According to BS 978:Part 2, found via the good services of Meadows & Passmore **LINK**

Thornton **LINK**

(and others.), cycloidal wheel and pinion teeth look like this …

The trace line in yellow (via my CAD package) required that I rotated the 8 leaf pinion through fifteen x3° steps, and follow the pinion leaf (tooth) with a wheel tooth.

Using the same laborious process, I chose to decrease the depth of mesh from the ‘PCD coincidence’ by 0.1mm; 0.25mm; 0.5mm; and 1.0mm.

If this interests anyone, I’m prepared to add more results, including the Excel graphs of the corresponding pressure angles. The latter revealed some odd and (to me at least) somethings rather unexpected.

Sam

[John HaineParticipant @johnhaine32865]

Sam, please don't keep us in suspense! What direction was the pinion rotating?

[Brian OldfordParticipant @brianoldford70365]

As a complete aside, please can someone tell me why most horologists seem to use the cycloidal tooth form yet mechanical engineers mainly use the involute form? There's bound to be a simple reason.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Brian Oldford on 10/04/2019 08:05:12:

As a complete aside, please can someone tell me why most horologists seem to use the cycloidal tooth form yet mechanical engineers mainly use the involute form? There's bound to be a simple reason.

.

[quoting myself from this previous thread] 

https://www.model-engineer.co.uk/forums/postings.asp?th=116147&p=1

.

There is some very interesting reading on [and linked from] this page.

https://www.csparks.com/watchmaking/CycloidalGears/index.jxl

MichaelG.

.

Edited By Michael Gilligan on 10/04/2019 08:59:28

[John HaineParticipant @johnhaine32865]

In a word, tradition. Actually cycloidal gear teeth are not cycloidal but made up of arc segments because the ideal tooth form is very hard to generate (or was, today one would use CNC). Supposedly cycloidal gears don't have "action before the line of centres" which reduces friction, but this may be a myth. I believe that Sinclair Harding, one of the few makers left of high end mechanical clocks, use involute gears in their products. Somewhere I have a link to an article by a production engineer involved in making millions of fuse mechanisms in WW2 that thoroughly shows that the involute was better for precision timing mechanisms. I'll try to dig it out.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 10/04/2019 08:59:03:

… I'll try to dig it out.

.

See my post, above. … I've saved you the trouble

MichaelG.

[John HaineParticipant @johnhaine32865]

Aha, found it, thanks for the links Michael.

**LINK**

[Sam StonesParticipant @samstones42903]

Apologies John,

The big brass thingy (large wheel) pushes the little steel thingy (pinion) to the right.

As can be seen here, and when I get around to it, you'll see how the points of contact trace unexpected(?) paths.

Thanks for your support Michael.

I'll be back.

Sam

[Oily RagParticipant @oilyrag]

Looks like this would be the ideal tool to check the depthing and run-out?

[John HaineParticipant @johnhaine32865]

Sam, if you mean that the velocity ratio changes through the contact cycle, well, that's what cycloidal gear approximations do I think. As noted in the article in Sparks that Michael linked to, that's why the automotive industry started using cycloidal but very quickly switched to involute when they found them noisy running at speed.

[Bill Davies 2Participant @billdavies2]

The gear rolling tester takes me back a bit … Sorry to see inspection equipment so rusty (or any equipment, for that matter). You would require a master gear (or a very good one that's accurately concentric with its bore) to gave readings that you could interpret.

Making up a probe (a ball or a rack tooth) and test around the circumference of the gear would give you similar information. The clearance of the gear's bore with the central shaft would have an effect. Might not be useful for horological gears, though!

[Oily RagParticipant @oilyrag]

The gear rolling tester takes me back a bit … Sorry to see inspection equipment so rusty (or any equipment, for that matter)

Sorry about the state of the tester Bill – but that was how I received it. It was in the scrap bin at an old engineering firm that had closed down and was given to me by one of the 'old boys', that knew I would appreciate it and look after it. It did receive some TLC and looks a lot better now!

The gear in the photo (on the tester) is marked up as the 'master' (stamped "RR PV12 S/C MS" – which I interpreted as 'Rolls Royce Private Venture 12 [the in house code for the Merlin] Supercharger Medium Speed&quot and it was used, I believe, as a Merlin supercharger drive gear tester. The 'Old Boy' told me that the company did Government contract work for Rolls during the war and this was one of the tools that had lain about for years under a bench. It works beautifully still – the clock is graduated in 1/10000ths – I have a video of it with a couple of close ratio motorcycle gears on it being checked for 'depth' and 'run out'. Now I know why they were so harsh! I haven't mastered how to post video's yet! There are some more photo's of the tool in my album. The plant reference paint markings are pure artistry. You will also see it is a Parkson make, from memory Parkson took over the Sunderland Gear business in the 1930's which ties in with the quoted history.

[Sam StonesParticipant @samstones42903]

It was rather rude of me to refer to the wheel and pinion as thingies. My apologies to anyone I've offended.

Thanks John, the term velocity ratio struck a note in the depths of my memory.

More explanation is required with regards to the direction I was taking. For a start, I'm no expert in gearing or clocks. It just so happened from an earlier post and my choice to respond, that I began pondering how the teeth of John Wilding's large wheel skeleton clock would actually mesh at different depths. Like Topsy, 'It just growed'.

Before grasping the significance, I had generated the wheels and pinions for the clock. In particular, the large wheel with 290 teeth, and its corresponding pinion with 8 teeth (leaves). Similarly, the 198 tooth wheel, and the 7 tooth pinion joined the gathering collection.

Here is my rendering of the gear train in position …

I’m still preparing additional diagrams, so watch this space.

Sam

[Sam StonesParticipant @samstones42903]

Continuing with meshing about with cycloidal(?) teeth, here are two more images and their respective contact traces.

Shown close up, they indicate how the teeth mesh while reducing the depth.

My guess is that at the 1.0mm offset, the teeth are likely to jam or at least wear quickly.

In this next image, I have superimposed all five traces for comparison.

The relatively straight-line section of the ‘On C-line’ trace occurs where the flanks (sides) of the teeth and leaves make contact with the opposing tooth radii.

At this level of magnification, the CAD package presents large arcs as polylines. It was rather confusing at first while trying to determine why the PCD’s failed to coincide. They are touching in the original working file.

Some of the data I gathered makes it quite clear that the velocity ratio (thanks John) varies thus giving rise to varying torque.

This may seem insignificant, but at the slow speeds of the large and centre wheels, the torque variation could have a noticeable effect on sensitive escapements, e.g. John Stevens’ English lever mechanism. I suspect that this will not be so noticeable with Mr Wilding’s large wheeler.

More to come.

Sam

[John HaineParticipant @johnhaine32865]

Torque variation will affect any escapement. At the least it will vary the impulse, hence the amplitude and circular deviation. If the escapement isn't giving a central impulse it will also cause varying escapement error.

But this is far from the only problem. One tends to think of a clock train as if smoothly moving, but of course it moves in jerks as released by the escapement. Some research has shown that when the escapement releases, the gears only start moving as the sticktion between the mating gear faces releases, so the drive torque gets rather noisy and "chaotic". Interesting paper on this here.

So clocks like Harrison's and "Clock B" at Greenwich have remontoires driving the escapement wheels to try to isolate them from these torque variations. Even then I've seen results from Clock B that show cyclic variations in rate as the escapement wheel rotates due to small inaccuracies in its manufacture.

[Sam StonesParticipant @samstones42903]

Thanks for your ongoing support John, especially the link.

Your mention of torque variation and its effect on the behaviour of (any) escapement, is most valid. I’d always presumed that the time period of a pendulum (and spring/balance wheel) was a constant. This anomaly became obvious while I watched mine as it came close to running out of puff. With less torque, it was running faster, but that also seemed to relate to the mark/space ratio.

Against the drift of too many Senior’s Moments, and a similarly elderly CAD package, which still grabs my attention, I’ll try to get to grips with the contents of that link John.

To be perfectly honest, as my ailing friend in a nursing home still asserts, this level of investigation has come as something of an unexpected challenge. None of which, I had a clue about while building my one and only clock back in the 70’s. The teeth on the wheels of my version of John Stevens’ skeleton clock are vaguely similar to an involute. In contrast, and though I say it myself, my lantern pinions look quite respectable.

Having, over the past few weeks completed the (depthing) exercise including the other pair of (198/7) wheel/pinion ‘gears’, I still feel the urge to offer it here. It just needs to be in a presentable form.

What I wasn’t expecting was this rather odd set of pressure-angle curves.

It was surprising to see straight lines and a comparatively sudden change of direction, not to mention the cross-overs. So, I laboriously repeated the complete exercise with greater accuracy. This time, any errors I had made were likely to be ‘accurate’ to several decimal places.

Sure enough, the (sudden?) shift from a smooth curve to a straight line matched where the point of contact changed from the pinion radius contacting the wheel flank to wheel radius contacting the pinion flank.

Sam

[John HaineParticipant @johnhaine32865]

Sam, while your work is of not much practical relevance these days, it is extremely interesting to clock nuts like me. Quite a few years ago I spent many hours trying to analyse "cycloidal" gears by a series of spreadsheets to get a handle on their performance, because as far as I could tell though there were standard profiles there wasn't any data on just how well they worked (or didn't). I was looking at how well simple circular profiles might work, which are easy to make. Also, all clock gears are made with symmetrical profiles but only one side of each tooth ever engages, at least in the power train. I could see that an article on your results would be very appropriate in Horological Journal or Horological Science News.

[Sam StonesParticipant @samstones42903]

Back in 2010 when I set about finishing my skeleton clock that had stood for more than thirty years, I received an enormous amount of help from this forum. In many respects, that is why I like to plough back some of my ‘discoveries’, and will continue to do so.

As the forum records show John, you were amongst many who helped me.

As an aside, I’m sending you a PM.

Sam

[Sam StonesParticipant @samstones42903]

This is the next pair of gears in the large wheel skeleton clock designed by John Wilding.

They comprise a 198-tooth wheel, and a 7-tooth (leaf) pinion. Again I constructed their profile according to BS 978:Part 2 supported by notes from other places, e.g.

Meadows & Passmore … http://www.m-p.co.uk/muk/acrobat/tech/cutters.pdf

and Thornton’s … https://watchmaking.weebly.com/uploads/1/1/7/9/1179986/pp_thornton_information.pdf

As before, a result of a previous forum post, I investigated the interaction between corresponding teeth at varying depths. Choosing to rotate the pinion one whole tooth (about 51° in steps of 3° ‘pushed’ along by a wheel tooth, I traced the respective points of contact. With one less pinion tooth (i.e. 7 versus the previous 8), 17 steps of the pinion were required for a full trace.

The depth of meshing from where the two PCD’s made contact was scanned at decreasing depths. They were … the ‘correct’ (on Centre-line as designed) condition followed by 0.1mm, 0.25mm, 0.5mm, and 1.0mm; i.e. five conditions in total.

At the worst condition (shallow by 1.0mm) the entering pinion tooth can be seen to clash while the exiting tooth is still engaged. Clearly, although the trace is incomplete, this condition is irrelevant.

To continue with this thread, here are the five traces similar to those for the 290/8 wheel/pinion combination. To avoid an unwieldy post, I aim to add the final image(s) shortly.

Sam

Edited By Sam Stones on 13/04/2019 00:58:33

[Sam StonesParticipant @samstones42903]

To bring this thread to a close, here is the last graphic …

Once again, the appearance of straight lines and cross-overs (seen in the previous 290 tooth 8 leaf wheel/pinion combination), confirm that the scans were relatively accurate. The pale blue line ends abruptly, the result of the entering pinion tooth colliding with the next wheel tooth.

That is where I should sign off.

Sam

[HncladParticipant @hnclad]

Sam.

Great CAD dwgs. Up front I'll say I know nothing about gear design or theory and my clock making knowledge is not much better. I have made 2 clocks Allan Timmins 8 day long case and Wildings Elegant Skeleton clock and at the moment I am again constructing Timmins long case clock.

Looking at Sam's charts on "pressure angles" I am surprised at how quickly that the angle of the power component is not acting directly in line the tangent of the pitch circle dia. i.e. theta is not zero! in other words there are reaction forces so that only part of the power force is actually driving the gear train, the other reaction force would be acting on the pivots, creating friction and wear. This gets worse as the tooth completes one cycle.

It is making me wonder how accurate do I have to be with my depthing since the pc will not line up for long anyway.

It was always my assumption that cycloidal gears were used because there was a rolling action keeping the pc.in contact for most of the cycle.

Help me out here, and tell me what I am doing wrong.

Thanks David,

[Sam StonesParticipant @samstones42903]

Thank you David.

This business of teeth making rolling contact has been discussed here. **LINK**

I felt the need pose the question because I couldn't accept that two contact points on the faces of gear teeth through travelling along their own vector lines could not be rolling but sliding (skidding). As was mentioned, true rolling only takes place where the PCD's converge. Unless I didn't understand the explanation.

Does this help David?

Sam

 

Edited By Sam Stones on 15/04/2019 04:58:14

[Michael GilliganParticipant @michaelgilligan61133]

Sam,

As an interesting diversion [and maybe of value in that it simplifies the model] you might try modelling the behaviour of a lantern pinion with your cycloidal wheel.

MichaelG.

[BazyleParticipant @bazyle]

Am I right in thinking the pressure angle graph would be flat if the gears are the same size?

[Author]

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