Calculating Epicyclic/Planetary gear ratio

[RainbowsParticipant @rainbows]

Want a backgear for my lathe project. Plan is to use a planetary by having the sun gear attached to the pulley, the planetary holder keyed to the spindle and the ring gear free to rotate except when pined to either the headstock casting or the planetary carrier (for either 5:1 or 1:1 gearing). Preferable the diameter of the assembly wouldn't be greater than 100mm so I could embed it in the pulleys.

Does anyone have a technique to work out the best gears to use for this? Wikipedia wasn't overly helpful with ratios for a dummy and the added factor of keeping a fairly close size requiremnt doesn't help. (25mm shaft and a limit of 100mm). Atleast I managed to work out the 285 N/m torque on the sun gear when backgeared to the lowest speed. Gears would probably be made on a lathe using a slotting attachment.

[RainbowsParticipant @rainbows]

[Keith LongParticipant @keithlong89920]

Rainbows, see if you can locate a copy of Model Engineer 1st April 1915. In there is a design for a epicyclic back gear, originally meant for a Drummond round bed, but applicable to any lathe with room in the inside of the main pulley, or could be adapted into a separate cassette fitted to the pulley. The article is by Bower-Lowe, and includes the formulae for calculating the gear ratios. The design works, I've got a version of it ready to fit to a round bed of about the same vintage as the design.

[RainbowsParticipant @rainbows]

I don't imagine its too easy to find 100 year old magasines. Good to know its been done on a lathe though. I was basing my idea of a US army instructional video.

 

edit: Upon further thinking I will probably increase the pulley size which will allow 150-200mm ring gear. 

Edited By Rainbows on 15/05/2016 00:46:13

[Keith LongParticipant @keithlong89920]

PM me your e mail address and I'll send you a pdf of the article. The other good news is that all the gears in it are normal spur gears, no internal ring gears involved at all.

[HopperParticipant @hopper]

An old copy of Machinery's Handbook – available cheap enough on the net – is probably a better reference than wikipedia for specialized engineering stuff.

[mahgniaParticipant @mahgnia]

Rainbows,

20T sun gear, 30T planetary gears and 80T ring gear gives 5:1 reduction with input to sun gear and output through the planetary carrier. ( 80/20 + 1 = 5 ). 1, 2 or 4 planetary gears will be required due to tooth numbers for even planetary spacing. (20 + 80 =100, which is divisible by factors 1, 2 or 4, or 5 etc)

MOD1 gear tooth profile gives a diameter of 82mm for the ring gear teeth, and allowing some meat for the mounting and dog clutch mechanism you should be able to keep it all at less than 100mm diameter. The only problem will be the input gear is much smaller than your 25mm shaft.

Alternatively, to give a larger sun gear diameter – 25T sun gear, 25T planetary gears and 75T ring gear gives 4:1 reduction with input to sun gear and output through the planetary carrier. ( 75/25 + 1 = 4 ). 1, 2 or 4 planetary gears will be required due to tooth numbers for even planetary spacing. (25 + 75 =100, which is divisible by factors 1, 2 or 4, or 5 etc)

Andrew

Edited By mahgnia on 15/05/2016 01:44:09

[Brian WoodParticipant @brianwood45127]

Keith,

I have also sent you a PM for a copy if it is not too much trouble.

Kind regards

Brian

[RainbowsParticipant @rainbows]

Thanks mahgnia. Sent a PM to keith though. Having no ring gear sounds interesting and would make life a lot easier.

[AjohnwParticipant @ajohnw51620]

There is another form of epicyclic gearing that doesn't involve internal gears.

I've never worked though the possibilities but have a part made ME Myford screw cutting gearbox that uses one to obtain feeds. Most parts made but I sold the lathe so the teeth never got cut. My dore westbury miller has one in the pulley on the main spindle as well for low speeds.

The image came of the royal mech eng site but I can't access the actual page. It may be possible during the week or might be members only.

John

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Edited By Ajohnw on 15/05/2016 10:25:38

[Keith LongParticipant @keithlong89920]

Info sent to those members who requested it – don't forget to check your "trash" "spam" or "junk" folders if it doesn't appear in your "inboxes"

Keith

Edited By Keith Long on 15/05/2016 10:31:16

[Brian WoodParticipant @brianwood45127]

Hello Keith,

Info received thank you very much and remarkably promptly

Regards Brian

[RainbowsParticipant @rainbows]

Got mine too. Still reading through it all but looks like good stuff. Thanks dude

[Thor 🇳🇴Participant @thor]

Hi Keith,

Info received, much appreciated.

Thor

[duncan webster 1Participant @duncanwebster1]

Many moons ago I worked on the design of epicyclic gearboxes for gas turbines. We used to drive the sun, take the output from the planet and lock the ring, but we'd arrange for one of planet carrier, sun or ring to be able to float radially. This was because no matter how careful you are you'll never get equal loading through all planets otherwise. For the same reason we used 3 planets, as three points define a circle. If you then make the sun and ring gear tooth numbers divisible by 3 it must go together, although I think this might have been over restrictive.

This is all getting a bit heavy for a lathe back gear. Have you considered gutting an old fashioned car automatic gearbox? I think they used epicyclic

[Michael GilliganParticipant @michaelgilligan61133]

For general info.

A useful crib-sheet from Davall

**LINK**

MichaelG.

.

P.S. … Neil is vindicated: Astronomy is relevant.

Edited By Michael Gilligan on 16/05/2016 08:32:52

[RainbowsParticipant @rainbows]

Im seeing gears b, h, j, d on the diagram but the equation mentions k, h, j, d. Am I just getting confused by the font?

[Keith LongParticipant @keithlong89920]

Hi Rainbows – no it's not you, looks like there is a mistake in the text (what a mistake in an old copy of ME – never!!). I think the formula should read j/d : j/d – h/b

Not sure where that leaves the calcs in the spread sheet as I can't remember what I put in there – it was quite a time ago.

The fancy fonts and the rather strange section line through the main pulley do take a bit of getting used to.

Edited By Keith Long on 16/05/2016 12:04:23

[Michael GilliganParticipant @michaelgilligan61133]

Thanks for replying so promptly, Keith

… I thought Rainbows was responding to my post.

You've saved me the effort of reviewing the Davall information.

MichaelG.

[RainbowsParticipant @rainbows]

Woops, should have specified that

Can anyone recommend some gear suppliers? Keith recommended a RC site but the variety of teeth there was too small to get a 5:1 ratio. Best I found so far is that Aliexpress can give me 6 4MOD gears (3 20 tooth, 3 18 tooth) for £60. From Accuscrew it costs £25 per gear Shame about the £35 postage from china. In future it might be an idea to get people to club together to buy in bulk to reduce unit cost for shipping.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Rainbows on 16/05/2016 22:18:54:

Woops, should have specified that

.

No problem

MichaelG.

[john carruthersParticipant @johncarruthers46255]

I've seen a couple of old lathes that use a Sturmey Archer 3 speed hub as a back gear ?

[AjohnwParticipant @ajohnw51620]

Posted by Rainbows on 16/05/2016 22:18:54:

Woops, should have specified that

Can anyone recommend some gear suppliers? Keith recommended a RC site but the variety of teeth there was too small to get a 5:1 ratio. Best I found so far is that Aliexpress can give me 6 4MOD gears (3 20 tooth, 3 18 tooth) for £60. From Accuscrew it costs £25 per gear Shame about the £35 postage from china. In future it might be an idea to get people to club together to buy in bulk to reduce unit cost for shipping.

Have you checked HPC prices ? They are probably the biggest UK on line etc gear retailer.

John

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[Keith LongParticipant @keithlong89920]

Rainbows – why are you looking to use 4MOD gears – those are enormous for the back gearing on a lathe. Drummond back gears are 14 dp – about 1.5 MOD and those are OTT. Myford back gears from what I read on here are typically 20 dp or approx 1.25 MOD. Forget the 285 Nm theoretical max. torque. If you succeed in getting that then assuming that you're still looking at a 30mm dia spindle, then you'll probably be be looking for a new spindle because the one you're using will have snapped or something else will have done. Step back from the design and do a reality check and look to see what other lathes of a similar size use.

Edit

I've just re-read your original post, and seen that your talking about a 25mm dia spindle at 285 Nm that certainly will snap or the tread that hold the chuck will! The Drummond lathes are 1 inch spindles so the same size to all intents and purposes. When folk break back gears on the Drummonds it's because they try and use the back gears to lock the spindle while they change the chuck, certainly not through cutting forces. On a lathe with a 25mm spindle I doubt that the tool post and tool would be able to generate that torque without failing or tearing out of the top or cross slide.

Edited By Keith Long on 18/05/2016 16:39:56

[RainbowsParticipant @rainbows]

4 mod gears were the first I found for a decent price, I then went to the other gear sizes from the same seller and found they were higher. Later when I decided to sketch it in a model I realised I was about to get a 300mm dia pulley and downgraded to 2 mod. Now fits in a 150mm radius and seeing the comparisons to Drummonds sounds much more sensible. Took a while longer to find good prices for them for some reason (maybe the mod4 were surplus stock).

And yeah the bearing mounts are 35mm but to preload the bearings needs a m30 threaded section then to be able to thread that portion I need a 25mm section after that. 285 Nm is just a number to me though, no real appreciation as to what cut needs that.

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