Gear cutting basics help needed.

[Anonymous]

Posted by ian voller on 02/04/2022 10:02:37:

…books just don't do it for me

Ah, that explains quite a lot.

Andrew

[ian vollerParticipant @ianvoller79273]

Suffolk born and bred, strong in the arm thick in the head.

[SillyOldDufferModerator @sillyoldduffer]

Posted by ian voller on 02/04/2022 11:27:28:

Suffolk born and bred, strong in the arm thick in the head.

Gear design is difficult. The designer not only has to cut the right number of teeth, but the teeth have to mesh with another gear without jambing, and, especially in a clock, with low friction. The other problem with poorly shaped gears is they wear rapidly.

Low friction and wear requires the flanks and valleys have to be curved in a particular way, the idea being the teeth roll over each other rather than bump and grind.

In days of yore, the gear wheels used in mills, were shaped approximately and they ground themselves to a moderately efficient shape. On first fit, the mill would be stiff and underpowered. After running for a while, the teeth would wear closer to the right shape and the mill would run free at full power. Unfortunately, the teeth rarely settle into the exact shape needed, so they wear rapidly. For that reason the teeth in traditional mills were usually replaceable.

Clockmakers were first to put effort into finding an optimum curve. Mathematically, it's a hypocycloid, and understanding what that is allows really good gears to be made. The maths are difficult and were cracked in the 16th Century by the Italian genius Gerolamo Cardano. Still a steep learning curve for non-mathematicians.

Later, it was realised that the Hypocycloid curve is inferior for most purposes to the Involute, described by another genius (Huygens), a century later. Apart from clocks, almost all modern gears are of Involute form. Clockmakers firmly believe hypocycloids are best for gearing up light mechanisms that don't transfer power. In contrast, involutes have several advantages: including being best for transmitting power and easier to make accurately. Unfortunately another steep learning curve.

Controversial view: I think satisfactory clocks can be made with involute gears. (SoD puts Tin Hat on and retreats to bunker.)

Ideally, a clock design would provide an exact recipe!

• Hold a disc of diameter x in a rotary table,
• set the dividing plate and clock-hands up to count the required number of gears
• Put a module cutter of given size in the milling spindle
• Cut n teeth

This is OK as long as the tools are affordable. ( Just because a child needs shoes 'She Who Must be Obeyed' often makes a silly fuss about 'Man in Shed' spending another few hundred quid on more toys!) However, most of the theory can be avoided unless you have to roll your own using one of the other, cheaper, methods.

I think most of us have to mix book learning with hands-on before machining makes sense.

Dave

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 02/04/2022 13:10:23:

.

Controversial view: I think satisfactory clocks can be made with involute gears. (SoD puts Tin Hat on and retreats to bunker.)

 

.

Not particularly controversial, Dave … that view has been exercised several times on this forum.

BUT __ Involute gears don’t play very nicely with Lantern Pinions

MichaelG.

Edited By Michael Gilligan on 02/04/2022 13:18:36

[roy entwistleParticipant @royentwistle24699]

Don't forget that in a clock the wheel is driving the pinion. Not an ideal situation.

Roy

Note to Ian. If using Thorntons or Bergeons cutters, the bore of the cutter is 7mm.

Edited By roy entwistle on 02/04/2022 13:55:39

[Simon Williams 3Participant @simonwilliams3]

Am I right in thinking that the reason involute gears aren't used by and large in clocks is that the very small pinions (6 and 8 teeth) beloved of compact clock designs need undercut teeth to follow the correct involute shape. Undercut teeth are weak and impossible to cut with a rotary milling cutter, they have to be planed.

Fact or fiction?

By the by, I built a clock using 20 DP involute gears – that was the set of cutters I had available. To be strictly accurate I was building the 12:1 gear train from the minute hand to the hour hand on the local church clock, so space wasn't an issue. The minute hand is driven by a synchronous motor rotating once per hour, and obviously the hour hand is coaxial. Thus the 12:1 reduction driving the hour hand is equivalent to the back ear on a lathe headstock a la Myford etc. As I say, space was not a consideration but longevity is a point of honour!

[Michael GilliganParticipant @michaelgilligan61133]

Have a look at this thread, Simon : **LINK**

https://www.model-engineer.co.uk/forums/postings.asp?th=141778

It’s one of several that include a link to an excellent essay on the subject.

MichaelG.

.

Ref. http://www.csparks.com/watchmaking/CycloidalGears/index.jxl

… and be sure to follow the link from there to Richard Thoen

http://www.csparks.com/watchmaking/CycloidalGears/RichardThoen.xhtml

Edited By Michael Gilligan on 02/04/2022 17:48:22

[Martin KyteParticipant @martinkyte99762]

Posted by Simon Williams 3 on 02/04/2022 16:55:14:

By the by, I built a clock using 20 DP involute gears – that was the set of cutters I had available. To be strictly accurate I was building the 12:1 gear train from the minute hand to the hour hand on the local church clock, so space wasn't an issue. The minute hand is driven by a synchronous motor rotating once per hour, and obviously the hour hand is coaxial. Thus the 12:1 reduction driving the hour hand is equivalent to the back ear on a lathe headstock a la Myford etc. As I say, space was not a consideration but longevity is a point of honour!

What you describe is a gearbox rather than a clock. I would say the use of involute gears for your application is totally appropriate. In a clock the train from the power source to the escapement is geared up not down which is where the issues of friction arise. Tower clocks in general have lots of spare power and space and have the luxury of massive frames. Involutes could be usefully employed on the lower end of tower clocks as can steel or cast iron gearing.

regards Martin

[Simon Williams 3Participant @simonwilliams3]

My thanks as ever to Michael Gilligan, whose recommendations for further research by the student proved to be fascinating and educational.

Best rgds Simon

[ian vollerParticipant @ianvoller79273]

PP Thorntons site askes you to select module and leaves? Putting "Gear leaves" into google just shows green leaves is "leaves" the tooth count? The site also doesn't show bore size, anyone know what it is?

[SillyOldDufferModerator @sillyoldduffer]

Posted by ian voller on 03/04/2022 18:28:51:

PP Thorntons site askes you to select module and leaves? Putting "Gear leaves" into google just shows green leaves is "leaves" the tooth count? The site also doesn't show bore size, anyone know what it is?

Not a clockmaker myself, so not expert on their jargon. However pretty sure a leaf is what an engineer would call a tooth.

I dimly recall the term comes from the petal shape gear teeth become on small diameter gearwheels, what clockmakers call pinions.

My memory is terrible, I should have mentioned before that another book worth buying is Stan Bray's "Making Clocks".

Dave

[roy entwistleParticipant @royentwistle24699]

As stated earlier bore size is 7mm. ( 02/04/2022 ) You only need leaf count for pinions, all wheels use one cutter

Roy

[ian vollerParticipant @ianvoller79273]

thanks so I need an R8 arbour that will take a 7mm bore cutter, more expense.

[ian vollerParticipant @ianvoller79273]

thanks so I need an R8 arbour that will take a 7mm bore cutter, more expense.

Sorry double post for some reason

Edited By ian voller on 03/04/2022 20:19:39

[John HaineParticipant @johnhaine32865]

As you mention R8 I assume you have R8 collets. No need to buy an arbor (note spelling), you can make your own. Start with say 12mm steel, turn down a length to 10mm, stepping down to 7mm for the cutter, either with an M6 threaded portion for a clamp nut or an M6 threaded hole for a clamp bolt. Make sure the 10mm and 7mm parts are to accurate size and turned without removing from the chuck. Part off from the parent stock, mount in an R8 10mm collet. I'm sure you can work out the lengths.

[John HaineParticipant @johnhaine32865]

Oh, and you'll need to make some arbors to mount the gear blanks on too.

[brickyParticipant @bricky]

I have made two regulators in the past and I made my own fly cutters from broken centre drills and mounted in a cutter bar made from stock.This cutter bar can be mounted in the mill.In my case I had two revolving centres with the cutterbar mounted between centres with a pulley attached driven from a motor at the rear, as the lathe is not fast enough for a fly cutter.The Myford dividing head was set at an angle on a adjustable milling slide and driven over the cutter.I never bought any cutters for either clock.

Frank

[ian vollerParticipant @ianvoller79273]

Thanks John yes I have ER32 imperial and metric collets, 6mm bolt it will be, my old Acorn lathe doesn't do metric threads.

[ChrisLHParticipant @chrislh]

In response to Simon Williams 3, for involute gears using standard hobs (20 PA) the minimum number of teeth for satisfactory meshing is 10. However as for all gears with less than 20 teeth, the gear diameter would need to be increased above the usual (T+2)/DP.

I was told by an ex Smiths employee that, at one time, they made clocks using involute gears.

To accomodate the limitation on tooth numbers imposed by the involute system most clock gear trains would of course need to be redesigned.

As an aside, gear pumps have been made using gears with only 8 teeth but these were made using special involute hobs of 25 PA (?) with non-standard cutting depths.

Although clock and watch gears are referred to as Cycloidal, I believe they are only approximately so. For example, it seems unlikely to me that the inner part of the contact faces of 6 leaf pinions (the hypocycloids), which are straight in practice, are theoretically so.

But I'm no expert so please feel free to put me right.

[John HaineParticipant @johnhaine32865]

Actually, the straight dedenda of both pinions and wheels are the only part of the so-called cycloidal tooth forms that actually are parts of hypocycloids! The addenda curves are circles or segments of circles.

If you use Mike Cox's spreadsheet for designing button cutters it's relatively easy to find non standard pressure angles that permit small tooth counts without undercut.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 04/04/2022 07:31:13:

Actually, the straight dedenda of both pinions and wheels are the only part of the so-called cycloidal tooth forms that actually are parts of hypocycloids! The addenda curves are circles or segments of circles.

.

True

… as noted in Mr Sparks’ essay, to which I referred earlier.

MichaelG.

[Martin KyteParticipant @martinkyte99762]

Posted by ian voller on 03/04/2022 18:28:51:

PP Thorntons site askes you to select module and leaves? Putting "Gear leaves" into google just shows green leaves is "leaves" the tooth count? The site also doesn't show bore size, anyone know what it is?

Hi Ian

In horology a leaf is a tooth.

If you click on Wheel Cutters instead of pinion cutters you will be able to select what you need. Pinion cutters vary in shape according to the number of leaves (teeth) on the pinion. Wheel cutters will cut any number of teeth. As you are making latern pinons you do not require any pinion cutters. I've put a link to wheel cutters below if that helps.

I know there is a trend to advocate involute tooth shape for clocks but as you will deduce from the above there are practical advantages in using cycloidal not least that you only require ONE cutter for all wheel counts from 17 to infinity. Another is that fly cutters are simple to make.

**LINK**

regards Martin

[Michael GilliganParticipant @michaelgilligan61133]

For those curious about the Lantern Pinion: **LINK**

Lantern pinion as a special case of cycloidal gear

MichaelG.

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Edit: __ I’ve just found this : https://youtu.be/dCeBCR0-lr0

Part 4 is about making the lantern pinion

Edited By Michael Gilligan on 04/04/2022 09:20:40

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