Gear cutters

[Matt Stevens 1Participant @mattstevens1]

So i fancy having a go at gear cutting at some point yet there is alot of different cutters out there and they are not the cheapest so figure i would ask a few questions….

Lets assume that i am not trying to match to an existing gear and therefore we are a blank sheet of paper.

Module or DP? Since model engineering is typically imperial, is DP the way to go?

How do you select the correct DP range? Do i get a set of DP16, DP20, something else? You know the typical sizes of gears for models, what do people have?

Pressure Angle – Am i correct in think DP is typically 14.5 deg whereas module is 20 deg? If so, there is no question to ask once my one above is answered.

Thanks

[Matt Stevens 1Participant @mattstevens1]

[Thor 🇳🇴Participant @thor]

Hi Matt,

All the modern gears I have come across are 20 deg. PA. DP or module is up to you, the gears I have made are all module based. The DP (or module) size depends on what the gears will do. I have made extra change gears for my small lathe – module 1 (DP 25.4), a clock would use a smaller size. You can make your own gear cutters if you want to save money.

Thor

[JasonBModerator @jasonb]

There really is not a typical size gear fort Model engineering, A 1/3rd scale traction engine may have 6DP gears on the final drive, a small IC engine or stationary engine could easily get down to 48 or 64DP.

I mostly work in metric these days so tend to design my model engines with Module gears at 20deg pa as that's what's available for cutters as well as off the shelf gears. Older designs or those from the US will more likely be DP

[Martin KyteParticipant @martinkyte99762]

There is no reason why you cannot have 14.5 PA in module cutters. You can specify the same cutter in DP or module just as you would measure a dimension in inches or mm. That said Module is the more modern way of defining a gear and these days it is, I think, more normal to find 20 deg PA so Module and 20PA cutters are perhaps more common rather than there being a fixed association. In fact if you make your own cutters then you can have whatever you like.

However I would suggest that you aim for something useful in terms of cutters. For instance if you have a Myford with change wheels opting for 20DP and 14.5PA gives you a cutter which will generate change wheels should you wish to do so in the future.

RDG seem to have a fair range of cutters at the moment.

regards Martin

[HOWARDTParticipant @howardt]

This can get very scientific. In all my years of design I used DP at 14 1/2 deg then module at 20. The DP was because that is what the company had used for sixty years, and had their own gear shop. Moving to metric involved making the gear shop redundant and out sourcing from local gear manufacturers. In design we calculated gear strength to ascertain the tooth size, although we normally used EN24 induction hardened sometimes for strength we had to move upto EN36 or 42. The minimum number of teeth was 18, below that the teeth would be weakened by unercutting. So in answer as far as tooth size matters it is based on centres required and minimum number of teeth. I doubt for most models there is any need for transmission power calculations. There will be lots more answers to come, but that is m simple take. I am sure you know cutters come in a range with a single cutter working over a small variation of teeth able to be cut.

[DC31kParticipant @dc31k]

Think of DP or module as the size or scale of the gears. You might draw an analogy with socket sets: they are available in 1/4", 3/8", 1/2". 3/4" etc. drive. You choose a DP or module based on the power you need to transmit and the space available.

For DP gears, the lower the number, the 'bigger' the gear. For module, it is the inverse: the higher the number, the 'bigger' the gear.

A 32DP gear with '2x' teeth will be the same physical diameter as a 16DP gear with 'x' teeth, hence the teeth on the 16DP one are a lot coarser.

[Nigel Graham 2Participant @nigelgraham2]

It would help you gain more specific advice if you tell us what you building, and with what equipment; but I can offer some general points:

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Yes, model-engineering is predominantly Imperial at least for scale-model designs, but it is not universal, and if as you hint you are designing your own project you can decide metric or Imperial throughout; and choose the gears accordingly.

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You select the wheel sizes by the torque they need transmit and the space available for the ratios needed; but I would go for the coarse rather than fine for the given diameters, with the proviso that you try to avoid needing make pinions with very small teeth-counts. They seem to start getting awkward below about 15 teeth.

Consequently there is no "typical" size for model gears, any more than there is a "typical" size for them in any machinery, such as your car. They are sized, and the material chosen, for the application.

If your project is a scale model of some fairly common type you could try examining representative examples to see what they use. As a rough guide to power, consider what might be in your machine-tools or powered DIY equipment; but square-laws on scales tend to work in the favour of strength for force.

How big is a gear?

– The DP pitch circle diameter is [Tooth-count / DP number] in inches.

So an 80T 20DP wheel is of 4" PCD.

– Metric module pitches: PCD = [Tooth-count X Module].

So an 80T 1.5 Mod wheel is of 120mm PCD.

– Plus twice the addendum in each case.

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The Pressure-angle on modern gears is usually 20º whether mm or inch sizes: module or circular pitch. The only rule really is that you must not try to mix wheels of different pressure-angles because though they might apparently mesh they will not do so correctly, leading to rapid wear.

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The cutters, at least in DP sizes, are made in tooth-count ranges; and the geometry dictates the fewer the teeth on a gear, the small the count-range a given cutter can produce; so if you need a large variety of low-count wheels you end up with lots of cutters.

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Before you start buying costly gear-cutters, study gears and basic gear-cutting! I think you have started that, so please forgive me if I am stating the obvious.

A professional engineers' book on the subject will swamp you in Very Advanced Trigonometry and PhD-level stress-calculations from Page One, not tell you how to make them.

All the theoretical and practical information you or I are likely to need for model-engineering is condensed into books such as:

Law, Ivan; Gears and Gear Cutting; 'Workshop Practice Series no.17', pub. Special Interest Model Books, latest 2003.

Marshall, A.W.; Gear Wheels and Gear Cutting; first pub. 1947; facsimile reprint, TEE publishing, 1994.

Look first in the TEE Publishing's catalogue: TEEpublishing.co.uk.

I happen to own both, hence able to give the formal references, but Law's is the more up-to-date. He also tells you how to make single-tooth (per side) cutters that generate involute-arc teeth. Although I'm not sure I'd make a habit of cutting hefty steel gears with those or any other fly-cutter type tools, thanks to their hammering action on the poor machine-tool.

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Hope that lot helps!

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Finally, if you decide for the project as a whole you might be safer buying the gears, they won't earn you Brownie Points but it is common manufacturing-trade practice to purchase stock gears. These have pilot-bored centres and optionally, bosses, amenable to modifying to suit the applications – with very careful machining for concentricity.

[SillyOldDufferModerator @sillyoldduffer]

Are you metric or imperial? If you can, choose one and stick to it. I'm metric, but DP is a better choice for anyone building to old UK plans, modern US, or renovating older UK machines.

DP and Module are both ways of relating the number of teeth to the diameter of the wheel. DP is more obvious because a 2" diameter gear with 40 teeth is 40/2=20DP. A 20 DP cutter is needed to cut teeth of the correct size to fit that diameter. Sums have to be done in order for teeth to mesh with different diameters or different cutters.

I recommend a book, wet-towel and Paracetamol. Ivan Law's "Gears and Gear Cutting", No 17 in the Workshop Practice Series is good except it skimps over Module. Not a big problem, but it's annoying for a metric fan to learn Module via DP. The book covers theory and practice, including how to make them in a slim volume. Different book needed if the gears are for a clock rather than power transmission.

Wet-towel and Paracetamol suggested because gears are more mathematical than most Model Engineering jobs and there's a lot to it.

Dave

[DC31kParticipant @dc31k]

Posted by SillyOldDuffer on 22/08/2022 18:53:28:

…a 2" diameter gear with 40 teeth is 40/2=20DP.

Would you please advise how we might measure that diameter to make that calculation?

If you edit your post so it says 'pitch' before diameter, it will be factually correct, otherwise it is highly misleading.

[Pete RimmerParticipant @peterimmer30576]

Yes that's correct for pitch diameter but not outside diameter.

[Matt Stevens 1Participant @mattstevens1]

Wow….thanks for the rapid responses everyone, this is clearly a topic of interest to many!

I have purchased the mentioned book "Gears and Gear Cutting" but am only part way through reading it and hence some of my questions may get answered, i am not sure. However much of what i have read to date on the internet centers around how to match to an existing gear rather than where to start if you are cutting your own and can choose any range.

I am based in Canada (dictates either module or DP i guess) but i tend to make Stuart type engines and will be lining up the Reeves ME Beam at some point that has a couple of gears….that gives you an idea of the physical size and application i have in mind. I certainly can't see me making any true power transmission type applications and so that i guess rules out the low number DP (or high Module?).

I run a Myford Super 7B and a fairly small mill since someone asked on equipment.

The comment about module gears off the shelf being more readily available is interesting – that might point me this way if only because there is a higher chance of being able to make a gear for something thats broke on 'whatever' compared with DP…..

I guess i was hoping to to get down to buying the set of 8 of DPxx or Module xx which would cover 90% of needs. perhaps more thinking is required!

[Roderick JenkinsParticipant @roderickjenkins93242]

A few comments if I may:

In the model engineering world pressure angle is immaterial provided both meshing gears are the same. Modern gears are 20 degrees.

Module and DP gears are both involute and are the same form. For example: 32DP gears are identical to 0.794 (25.4/32) Module and 0.8 Module gears are identical 31.75 DP ( 25.4/0.8). Just use the correct number in your calculations

The important numbers for the design are the gear ratio and the distance between the centres of the gears.

The cheapest sets of gears are 20PA Module gears from China and that it what I use even though all the designs I have made are in Imperial units. I adjust the numbers of teeth of my chosen gears to give the ratio required that results in gears that are a similar diameter to the gears specified in the design and then adjust the centre distance accordingly.

Lets take the example of a design that calls for 48DP gears giving a 2:1 ratio with 32 and 16 teeth

PD= 32/48 and 16/48 which is 0.667" and 0.333" therefore a centre to centre distance of 0.500"

Instead of 48 DP we will use 0.5 Module which are the same as 50.8DP

Because the 50.8DP gears will be a little smaller diameter than 48 DP we can add some teeth to give the same ratio and a similar diameter. We can try 34 and 17.

PD= 34/50.8 and 17/50.8 which is 0.669" and 0.334" therefore a centre to centre distance of 0.501"

On the Hoglet I am building at the moment the design of the cam drive calls for 40 and 20 tooth 32DP gears. I shall use 0.8 Module (31.75 DP) but keep the tooth numbers the same. Using the DP gears the centre distance is 0.938" but using the Module gears the centre distance needs to be changed slightly to 0.945".

I hope this helps, the math(s) really isn't that complicated. I used the 0.8M gears for the Farm Boy, the Hoglet and, indeed, for the helical gears for the Wyvern. 0.8M is good size if you are into i.c. engines that are made on a Myford.

Rod

[Dave HalfordParticipant @davehalford22513]

20dp 20pa gears are used on Minnie, which is a 1" to the foot model, now they don't have to be 20pa, the pa was chosen due to the availability of gears off the shelf. It would however look wrong if 16dp had been used.

Don't forget that what ever your chosen dividing system is there will be various numbers of teeth which cannot be derived. There are tables on the web that show the gaps check with more than one table and dry run the teeth with a felt tip before cutting to spot any errors. It's tedious and slow, but avoids later disappointment.

If a model needs a 2:1 ratio for timing etc you can't change the ratio, if it's to a winding drum or wheels etc then it doesn't really matter and 2 and bit :1 will be OK.

[Howard LewisParticipant @howardlewis46836]

Normally, we are dealing with spur gears, where the cutter / blank movement is parallel to the axis of the gear and the shaft on which it will be mounted.

Helical gears obviously need the teeth to be cut at an angle to the axis of the gear.

Module is the Metric equivalent of Diametral Pitch

The formula for both, as you will, see from "Gears and Gear Cutting", is O D = (Tooth Count + 2 ) / D P ( Or Module )

So for if working with D P, you measure and work in Imperial units, if Module in Metric units.

Your Myford uses 20 DP gears gears, so a 20T gear will have a PCD of 1" and an OD of 1.1"

But these will be 14.5 degrees Presssure Angle.

A 1 Module 20T gear will have an OD of 22 mm.

These are most likely to be 20 Degrees Pressure Angle.

Cutters for Involute gears are numbered from 1 to 8, with each cutter being suitable (Not necessarily theoretically perfect, but quite acceptable ) for a limited number of teeth.

For DP gears, Cutter No. 1 will cut gears with a tooth count from 135 upwards, to a Rack. A No. 8 cutter is suitable to cut gears with 12 or 13 teeth..

I believe that cutters for Module gears are numbered in the reverse order!

The cutters normally are engraved with the P A and a number , usually shown as "D+f" which is the Depth of Cut

This is the Depth of the cut + clearance.. ((Between the peak of one gear and the root of the mating gear )

It is usual to cut each tooth space at full depth, with a very fine feed, rather than repeated passes with an increasing depth of cut.. In this way any differences caused by any backlash or vibration are minimised.

Because the cutting loads are high, it is advisable to to provide support for the shaft / mandrel carrying the gear blank, with a Tailstock, if possible..

Gears should not be run without backlash, since this will cause noise and wear.

For the same reason, excess backlash should be avoided, since the teeth will no longer be making contact on their correct PCD,

One method of setting backlash, such as when setting up a train of changegears on the banjo on a lathe, is to run a sheet of paper through the mesh (This should give a backlash of about 0.0015 to 0.003" )

The centre distance of the shafts carrying the gear gear.s is the sum of the Pitch Circle Diameters

(Thus two 20 DP 20T gears would be mounted at 1" centres )

Howard

[John HaineParticipant @johnhaine32865]

Posted by Howard Lewis on 23/08/2022 10:20:11:

….

The formula for both, as you will, see from "Gears and Gear Cutting", is O D = (Tooth Count + 2 ) / D P ( Or Module )

….

Um, no. OD = (N+2)*mod for metric gears.

[Howard LewisParticipant @howardlewis46836]

Thank You John, Clutch slip between brain and hand!

Howard

[JasonBModerator @jasonb]

Posted by Dave Halford on 23/08/2022 09:39:56:

20dp 20pa gears are used on Minnie, which is a 1" to the foot model, now they don't have to be 20pa, the pa was chosen due to the availability of gears off the shelf. It would however look wrong if 16dp had been used.

Depends on how you look at it, many full size traction engines used different DP or circular pitch for each pair of mating gears so would not have the same DP.

Take the 2" Fowler as an example as that is a scale model not a freelance and you have 12DP on the crank and 2nd shaft, 10DP 2nd shaft to 3rd shaft and 8DP on 3rd Shaft to final drive all with the correct number of teeth and PCD spacing.

So the Minnie with all the same DP ends up with far too many teeth on the final drive. I also had a feeling that it was originally 14.5pa as that allowed Myford gears to be modified or assumed builders would have 20DP 14.5PA from cutting stuff to use with the Myford.

14.5pa also better matches the profile of the older gears as well as sliding better if you have a sprung back axle on say a road loco or tractor.

[SillyOldDufferModerator @sillyoldduffer]

Posted by DC31k on 22/08/2022 19:39:31:

Posted by SillyOldDuffer on 22/08/2022 18:53:28:

…a 2" diameter gear with 40 teeth is 40/2=20DP.

Would you please advise how we might measure that diameter to make that calculation?

If you edit your post so it says 'pitch' before diameter, it will be factually correct, otherwise it is highly misleading.

I plead guilty to misleading by trying to keep my reply simple. DP is explained properly in gear books.

For completeness, the 2" refers to PCD or Reference Diameter shown on the diagram below. It's not the outer diameter of the gear blank:

Dave

[Matt Stevens 1Participant @mattstevens1]

Whilst on topic….. how does one calculate the blank size? So as an example, if you know your PCD is say 2", what size do you make the blank to?

Also, How do you know the depth of cut – take it from the cutter?

[Nigel Graham 2Participant @nigelgraham2]

I've not seen it called "Reference Diameter" before (US terminology?) but …

Outside diameter = Pitch Circle Diameter + 2S,

where S is the Addendum, and = 1/DP or 0.3183 X Circular Pitch

Working depth of tooth, called D for Dedendum, = 2/DP

Then there is a root clearance below that, called the "f" value on a gear-cutter; so the full depth milled out is D+f; and = 06866 X Circular Pitch.

(Law, p. 30)

So for a 40T 20DP gear, outside diameter = 2 + [2(1/20)] = 2.1" .

Cutting to the designated depth labelled "D+f" on the cutter itself, with a commercial cutter, from the correct blank diameter, will give the correct form. If you make your own gear-cutter you will need books such as Law's to calculate everything, but it is a good plan to go through all the sums anyway even with a commercially-made cutter, to understand what is actually happening and make sure your blank diameters and cut depth settings are correct.

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The text-books also tell us to cut to full-depth in one pass on a fine, steady feed, to minimise over-cutting errors.

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For our purposes it is usually sufficient that the finished gears mesh as they should and run smoothly together, with the tiny bit of clearance they need (the usual tip for setting up change-wheels on a lathe is to nip a piece of thin paper between them). The trade has special micrometers etc. for gear-tooth measuring to the sort of precision and accuracy demanded.

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Having written all this lot, I must get on and put that horizontal mill back into action so I can actually cut gears too!

[HopperParticipant @hopper]

Posted by Matt Stevens 1 on 22/08/2022 17:50:48:

….

Lets assume that i am not trying to match to an existing gear and therefore we are a blank sheet of paper.

Module or DP? Since model engineering is typically imperial, is DP the way to go?

In that case, go with Module cutters. Much cheaper to buy and more readily available these days from the usual cheep Chinese suppliers.

Cheap enough to buy by the set so then you can cut any sized gear of that module. Which module depends on what you are making.

[Pete RimmerParticipant @peterimmer30576]

Posted by Matt Stevens 1 on 23/08/2022 21:30:57:

Whilst on topic….. how does one calculate the blank size? So as an example, if you know your PCD is say 2", what size do you make the blank to?

Also, How do you know the depth of cut – take it from the cutter?

I have a chart that's laminated and stuck on my wall. It's tailored to my own hobbing machine and common pitches I might cut but it's a very good quick reference. You could easily knock up your own chart in excel/calc.

 

Depth of cut you should take from the cutter – if it's a hob you should certainly take the DOC from the cutter because there are different types. Brown and Sharp hobs have different DOC to others and there seems to be no fixed rule for the older ones at least.

Edited By Pete Rimmer on 24/08/2022 06:52:03

[not done it yetParticipant @notdoneityet]

My advice might be to stick to cutters specified by kits, if that is appropriate. At least until confident of calculating distances between centres, etc.

Too many, who don’t have a good understanding of the intricacies and maths, should proceed with care. Following specific instructions for DP/MOD, centre distances of gears, etc, to gain experience is the safer route for many.

[JasonBModerator @jasonb]

As Rod mentioned earlier 32DP is quite commonly used on stationary engines as well as small IC engines and I have just looked up what size the drive gears on the ME Beam are and they too are 32DP.

So that would seem to be a good general purpose size set for your likely usage. It is then really then a case of deciding to use 32DP or make the very small adjustments needed and go with 0.8MOD, myself I would go with the MOD option as cheap far eastern gears can be had as well as reasonably priced ones from better known suppliers in a larger range of tooth counts and you can often use gears from RC cars etc which are plentiful on ebay etc if you decide you don't want to make them all.

Cutters are also more readily available a low prices though I have found they don't last quite as long as know branded ones but probably still work out the most economic even if you have to replace worn ones they still won't add up to industrial prices

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