How to calculate size of gear required.

[Ernest Jane 1Participant @ernestjane1]

Hi Chaps/esses, I have a gear set up where I know the number of and teeth pitch of teeth of a existing gear.

What I want to work out is the matching gears.

The outer gear is 88 teeth pitch of 3mm on an annular gear, I need to work out the remainimg two from the centre, I know there is two as there is space for a motor and an in between idler gear.

From the space I have I have worked out I need the idler at 40mm (ish) 40 teeth and the gear on the motor 20mm at 20 teeth.

I have dragged the depths of my memory from 40 years ago using Diameter X Pi (3.142) to come up with the above.

Is this the correct way to do it, I seemed to have mislaid my Technical notes from that era

Many thanks

John

BTW I used 'Blu Tack' to get the pitch of gear, we used to use 'Plastiguage?) all those years ago for similar tasks.

[Ernest Jane 1Participant @ernestjane1]

[Jeff DaymanParticipant @jeffdayman43397]

It sounds like you are trying to lay out a planetary gear set with a motor driving the centre gear.

Since you are not using the usual nomenclature and clear descriptions of pitch dia vs outside diameter for gearing design, a diagram of the gear layout you are attempting, with the known dimensions marked on, would help to understand what you need. It sounds like you are doing a metric design, do you mean you have a 3 mm module, or 3 mm circular tooth thickness or 3 mm circular pitch?

If you google metric gear design guide you will find a huge amount of detailed gear design data as well.

Gearing is usually not too complicated but there are a few fundamentals you need to get right to obtain a good result. The more info provided up front, the better, in diagram form especially.

JD

[Ernest Jane 1Participant @ernestjane1]

Thanks JD, I will explain further with a pic of what I have.

The gearing is for a Corgi Gallopers model, there is a facility to motorize it with the motor in the centre, the Diameter of the outer gear is approx 4 1/4 or 110mm, there is a indent for the 'planet' or idler gear about 20mm in.

My estimate is from trial and error with meccano gears and using Blu Tack.

I'll check my measurements on Monday when I get home.

As I said before I did gearing as part of an apprenticeship in 1970, I can remember some basics but have not used them in real life for years.

Many thanks for your reply.

John

[Ernest Jane 1Participant @ernestjane1]

Thanks to JD, Worked out what I needed and looked on Google for correct nomenclature.

I was confusing the dimension between teeth and pitch.

The 3mm I quoted was Circular Pitch, (CP), I used this to work out how many teeth I required on the 40mm gear 3.1416/P

Or in my case, 40mm X Pi = 125 divided by 3mm = approx 40 teeth (which seems to be a standard).

OK I know I was using the Outside Diameter and the Pitch Circle is probably in the region of 38mm.

But I knew in the darkest depths of my brain box I had to use Pi, was just lucky I guess, that I knew the actual gear size required for the Planet Gear, after further measurements I have calculated that the gear required for the motor at the centre has to be 30mm diameter.

Given that the Pitch Circle of the annular outer gear is 110mm, diivide by 2 gives 55mm (Diameter), less 40mm for planet gear gives me 15mm radius ie 30mm gear.

I hope this make sense to you all.

If there is an easier way let me know, but I don't think I'll be needing to calculate gears for a long time.

To think it's 40 odd years ago since I did my Royal Navy Apprenticeship, and I never thought I'd need the basics, especially as I was an Electrical Artificer and Hydraulics.

Thanks John

[Sub MandrelParticipant @submandrel]

Hi John,

Let's look at what happens assuming you have a metric gear. Module (which characterises the size of the teeth) is given by Pitch Circle Diameter/number of teeth. A caveat is that the PCD is roughly half way between teh tips and the roots of the teeth (actuially slightly nearer the tips) somake sure that is where you are measuring.

110/88=1.25. which is a standard metric size, so that looks good.

The sun and planet gears need to be dimensioned so the PCD of the planet gear plus HALF the PCD of the central sun gear add up to 110/2 or 55. As you have already calculated 40mm for the planet gear and 120mm for the sun gear work.

As we now know the module we can do the reverse calculation N=PCD/module

Planet 40/1.25=26.667

Sun 30/1.25=24

OK so a 26.666 gear doean't work but we can play with nearby combinations

Planet 38.75/1.25 = 31 teeth

Sun 32.5/1.2 5= 26 teeth

May well be the right combination.

Neil

[Ernest Jane 1Participant @ernestjane1]

Neil, Thanks, I have looked at various web pages and refreshed my memory banks, amazing what comes back to you.

I have gone with a gear of 40mm 40 teeth, for the planet gear, as there is an indent for this size and a 30mm 30 tooth, for the sun gear.

These sizes are available in my local model shop, with a 4mm spindle hole whiich suits my requirements.

After perusing the web I remember words like 'involute gears' PCD etc, maybe I did listen all those years ago, when I was thinking " I'm in the Electrical Department what do I need to listen to this rubbish for".

Thanks to all who responded.

John

[Sub MandrelParticipant @submandrel]

Hi John – I must admit I'm confused.

Those must be 1DP gears to be those sizes – if your outer internal gear has 88 teeth (1.25DP) then they won't mesh properly – the teeth will be too small. They would suit an outer 1DP internal gear with 110 teeth on the 110mm PCD.

Neil

[AndyfParticipant @andyf]

I think you may have meant Mod 1 and Mod 1.25, Neil. 1 DP and 1.25 DP might be a bit on the big side.

I'm confused by the dimensions. A Mod 1 gear will have a pitch of 3.1416mm around the pitch circle, and from John's initial measurement of 3mm I thought his ring gear might be Mod 1. But with 88 teeth, a Mod 1 gear has a PCD of 88mm (Mod 1 gears are easy!), whereas he reported a diameter of 110mm. However, his 40mm, 40T gear sounds like Mod 1 again.

Anyway, if he can put the 40T and the 30T inside his ring gear, and the bore of the 30T is in the right place for the motor shaft when all thrre are meshed, it sounds like mission accomplished!

Andy

[Sub MandrelParticipant @submandrel]

Oops! Trying to generate clarity I have sown the seeds of confusion again. Yes I did mean 1 mod and 1.25 mod.

John's first post said 88 teeth, his second says 110mm, which would be 1.25 mod. This would give a tooth pitch of just under 4mm, but if he is measuring the width of a tooth near the root the 3mm would be a reasonable approximation.

1 mod and 1.25 mod might be forced to run together, but it will be rough and wear rapidly.

Neil

[Ernest Jane 1Participant @ernestjane1]

Hi Chaps, Just to clear things up, I counted 88 teeth on the outer annular gear which is 110mm diameter as close as I could measure.

I used blutack to get an impression of the teeth and the distance from tooth to tooth is 3mm and actually formed a gear using blutack with a pivot in the pivot point on the model. Careful 'trimming gave me a template to compare.

My local model shop (if you call 15 miles local) had the 41.5mm, 40 tooth gear in stock and this meshes well, when I get the 31.5mm 30 tooth will let you know how it goes, especially when the motor turns up.

All the gears are plastic and seem to be 'stock sizes' with a 4mm shaft hole. I am quite happy now I've found these gears as it gives me more ratios to 'play' with on meccano builds. They have all sizes of gears including combination gears. Just no 31.5mm in stock today. When I talked to them they were very helpful. I think I was talking 40mm etc when the outside diameter is actually 41.5

I never thought that at 66, I would be having fun playing with toys I had in the 1950's.

I also have satiafied a boyhood dream and purchased 2 Mamod steam engines, one static one traction engine.

I am currently building a Showmans caravan to pull behind the Mamod Traction.

I know this is probably blasphemous to members of this forum working in wood!

Thanks for your help, I might indulge my curiosity further by delving deeper into this subject on the 'tinternet'.

Many thanks

John

[Jeff DaymanParticipant @jeffdayman43397]

Just FYI it is never wise to run gears of different module together, generally speaking. Neil is right, mesh will not be efficient and there may be severe wear or tooth breakage. You might get away with it in plastic toy gearing but really it should be avoided.

Efficient gear mesh is not just intermingled teeth, it is two involute curved surfaces sliding past one another at a controlled pitch diameter.

JD

[MICHAEL WILLIAMSParticipant @michaelwilliams41215]

Hi ,

PCD(annulus) = PCD(sun) + 2 x PCD(planet)

N Teeth(annulus) = N Teeth(sun) + 2 x N Teeth(planet)

Know or decide upon any two and third one drops out of the calc .

Use trial and error to get practical numbers of teeth on gears .

Worth noting a couple of cases for easier working sometimes :

(1) Decide on sun and planet gear tooth count first then annulus always has a whole number of teeth .

(2) If sun and planet are the same then annulus gear has three times number of teeth on sun .

There is a math method using computer for optimising gears for specific ratios .

Michael Williams .

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