A question of beat

As a one-clock ‘expert’, I have often wondered why the late Mr John Stevens, in designing his skeleton clock with English lever escapement, chose wheels and pinions that produced a beat of 0.893 seconds instead of a very handy 1.0 beat per second.

In a simple spreadsheet for determining the ratios of the existing wheels and pinions while leaving the number of pinion teeth alone, I tested the feasibility.

With little more than intuition I changed three of the wheels from 84, 72, and 56 teeth down to 80, 70, and 54. I was amazed that it took so little effort.

Apart from shifting the arbor centres, slightly increasing the mass of the balance wheel, and/or using a slightly ‘softer’ balance spring, I can see no other obstacle.

Unless I’m off the beam for some reason I could (just for fun) make new wheels and even grab parts from my CAD file.

Any thoughts?

Sam

Edited By Sam Stones on 28/01/2020 02:45:45

Perhaps he found the 0.893 seconds per beat was more pleasing, to his ear, than only once per second? Certainly can’t so easily count ticks for a minute period!

As a matter of interest, do all other clock designs have a beat of 1.0 seconds?

Mathematically, the 0.893s is to one more significant figure, so should be more accurate than one only to two significant figures - or did you mean 1.00s?🙂

As this makes absolutely no difference to the time-keeping, does it really matter that much? A design simply needs to accurately mirror the true time of day.

Do these tooth counts require fewer set-ups or cutters than other tooth counts?

I would particularly frown on the use of smaller pinions being sized as a factor of the larger wheel it contacts. Any comment on this?

As only a clock repair ‘bodger’, I’m not particularly qualified to make too many meaningful comments (just to make it clear to those that are ‘funny’ about replies). Last comment is that it does show that a one second beat is not the ‘be all and end all’ of clock making.🙂

Unlike a pendulum I guess making a balance for a specific period is rather hard unless you have a lot of data on the spring material etc. So maybe he started with the balance and designed the train to suit?

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Yes, one comment: ... Sam wrote:

“ In a simple spreadsheet for determining the ratios of the existing wheels and pinions while leaving the number of pinion teeth alone, I tested the feasibility. “

[my emboldening, for emphasis]

MichaelG.

Well, they are always going to be a "factor" surely, since both have integer numbers of teeth? Was the point to try to make sure that they are relatively prime (if possible) to distribute wear evenly, or something like that? In any case you have to have specific ratios between hour and minute, and minute and seconds hand, if it has one.

For anything reasonably approximating accurate time-of-day-keeping we need many more orders of magnitude better than either of those representations. [so, of course, they are both very rough approximations]

MichaelG.

Just a suggestion as I've only made two clocks, both out of Meccano and one didn't work!

However the principle of all mechanical clocks is the same: an accurate oscillator, such as a pendulum, counts out steps allowing a gear train to translate a power source (spring or dropping weight) into a spindle turning at a known rate useful to humans, such as one rotation per hour.

Getting the required human rate is achieved by altering the period of the oscillator and the ratios of the gear train to get the required result. Designing the gear train is a little tough: clocks call for big ratios, ie small pinions engaging big wheels, and this is a challenge because there's a mechanical limit. Pinions with less than, say, 12 teeth are in the danger zone, and 6 teeth is probably the practical minimum. Friction rises and pinion teeth have to be undercut. Then, because gears only do integer division, there are limits to the number of gear combinations that achieve the desired ratios.

Sam's picture of Mr Steven's gear train shows a sensible combination of gears, in particular he avoids small pinions. But I think the reason for the 0.893s period lies in the Balance Wheel, which isn't shown.

Not mechanically difficult to make a pendulum oscillate at any reasonable period. The disadvantage is they take up a lot of space, and dislike vibration. Balance wheels can be made much smaller, and they don't mind if the clock is moved. But they're much more complicated to design. They also have mechanical limits: small and light is best for timing accuracy and low friction but they have to store enough energy to work the escapement. A big, heavy balance wheel will happily drive the escapement, but it will hammer the bearings, and need more effort to maintain oscillation which will spoil the time-keeping.

Sam said 'I have often wondered why the late Mr John Stevens, in designing his skeleton clock with English lever escapement, chose wheels and pinions that produced a beat of 0.893 seconds instead of a very handy 1.0 beat per second.' More the other way round I think. 0.893s is in the the zone that allows a sensible balance wheel and there's a sensible integer gear train to bring it to 1 revolution per hour. I think Mr Steven's clock brings together a practically sized balance wheel with an equally practical gear train. Not necessary for him to start with a neat round number oscillator, or even desirable to do so. Once the maths are understood, it's possible to design clocks so the mechanical details are optimised as a whole to improve timing, reduce wear, and simplify the movement.

Dave

Edited By SillyOldDuffer on 28/01/2020 10:50:25

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I’m not sure if that ^^^ was intended as a comment on my response to ndiy, John

If so, I must emphasise that Sam computed his new train for the existing pinions.

If not ... please ignore this interjection

MichaelG.

Factors are whole numbers which will divide into the other number by a whole number. All primes, other than two, have only two factors.

Using factors is bad practice with gear sets, as the same teeth will be engaging every revolution. Far better for even wear is to have the gears wearing with any of the teeth wearing against all the teeth on the other gear.

You never had an exact 4.00 differential in your car - it would wear much better and evenly if the ratio were the pinion teeth multiplied by an integer, then plus (or minus) one for the crown wheel. A much higher rotational speed and power, but the same physical principles still apply - but clearly ignored in the clock movement exampled.

Yes I do know what a factor is, thanks. It was just the expression that puzzled me. Quite common I think to see a 60:1 ratio as an 8:60 x 8x64 teeth = 7.5 x 8 = 60.

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Apologies ... I evidently misinterpreted your usage of the word ‘factor’ in your first response.

I wrongly thought that you were saying that the number of of teeth on the pinions would be a relevant factor [rather than a mathematical one].

MichaelG.

Let me put it another way.

It is bad practice to make gears pairs with whole number ratios.

Is that more clearly understood? I don’t design gear boxes or anything like that and maybe clock makers ignore the principle (that gears pairs should not run on the same teeth for the whole life of the machine). Comments? I’d like to know if they do (and if they do, why?).

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Agreed ...

MichaelG.

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https://www.mobiusinstitute.com/site2/item.asp?LinkID=8062&iVibe=1&sTitle=Gearbox

Edited By Michael Gilligan on 28/01/2020 16:08:03

Yes they do in the motion work. Getting that 12:1 ratio is not easy in two stages when limited to pinions probably of 8, 9, 10, 11, 12 so tend to use 3:1 x 4:1.
There are combinations with factors of, 2.2 or 3.3 that work with 2.4, 2.5, and 3.2 as runners up.

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Which is, of course, one of the reasons why clocks in the ‘Regulator’ class typically omit motion work.

MichaelG.

Well a pair of gears is bound to have a whole number ratio surely!

In the motion work as opposed to the going train the gears carry very little load.

Maybe he made a balance wheel, tested it, then mcame up with a train that worked for its practical range of adjustment.

Neil

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So ... What are the various whole number ratios between the wheels and pinions in Sam’s first picture ?

Ratio being, by convention, expressed as N to 1

[ tried to use a colon, but that generated a stupid smiley thing ]

MichaelG.

Edited By Michael Gilligan on 28/01/2020 23:40:43

What a wealth of responses and information. Where do I start?

I think it might be easier (for me at least), to address some of these in separate postings.

I'll be back!

Sam

NDIY – I enjoyed your replies, so here are my thoughts.

Q. Pleasing to his ear? Perhaps it was. Maybe he didn’t have a preference for the pace of a military beat 120bpm (shades of square-bashing). Personally, I enjoy a good brass or military band.

The ratios the designer selected were 8.4:1, 8:1, and 4:1. The calculated beat (per ‘scape wheel tooth) is 0.892666(recurring) seconds. Whatever reason crossed my mind, I resisted the temptation to quote #1 followed by a string of zeros.

Unintentionally, the three ratios emerging from my choice of wheel teeth were …

8:1, 7.777778:1, and 3.857143:1. Not bad for little effort

Q. Do ALL other clock designs beat at 1.0s?

My guesses …, in not knowing much about clocks would be …

Antique clocks? … not many … apart from longcase (pendulums close to 1 metre).

Electric clocks? … Hummm? … locked into mains frequency at 50 or 60cps.

Quartz clocks? … most of them that I’ve heard ticking ... [sourced from a 2^{^15} crystal.]

I agree that none of it (i.e. the ratios) really matters other than that the clock keeps accurate time which, as I found out while building and setting up the clock, is another story altogether.

I chose to refrain from ‘messing’ with the pinion count. Other than a 6-leaf pinion onto a 72 tooth (motion work) wheel, the drive train for the Stevens clock uses lantern pinions.

It seems I've overrun the number of characters ... I'll be back.