Gear Cutting - Pressure angle.

Hello,

I've been looking at the Helicron site (don't know how to link) and his method of semi-hobbing gears.

My question is this- if I was to cut the grooves in the hob using a VCMT insert, I would end up with a pressure angle of 17.5 degrees.

I know that this is not a conventional angle but is there any reason that it wouldn't work when mated with similar gears?

Also, what is the smallest amount of teeth practical in an involute gear of this type?

Thanks,

Steve

The pressure angle is the angle of the teeth in a matching rack. If you had the means of rotating the gear blank and traversing the cutter at the correct rate you could cut gears with a pressure angle determined by the cutter angle. Doable on a CNC mill with a fourth (A) axis but a lot of messing about compared to just using a suitable involute cutter.

Martin C

There should be no problem with a 17.5 degree pressure angle as long as all the meshing gears are the same.

Not sure about the minimum number of teeth, but I would not go below 20 teeth as I have had some nasties when trying for much less. Not sure if the problem was an inherent one or just poor execution on my part.

Andrew.

As Andrew says you can use any pressure angle you like as long as they are all the same.

The minimum pinion count for involute is determined by the fact that the teeth get undercut which means they are hard to shape. I have a spreadsheet (based on an original from Mike Cox) to turn the G code to make involute cutters for any tooth count and pressure angle based on the usual circular approximation. This includes a flag to warn when the tooth count for a given pressure angle is too low to avoid undercutting. For a pressure angle of 17.5 degrees this tells me that the minimum tooth count is 20.

My goto online reference for all things gearing, at KHK Gears says z=2/sin^2(a) where is tooth count and a is pressure angle is what determines minimum teeth for no undercut when using a rack-type cutter.

https://khkgears.net/new/gear_knowledge/the-first-step-of-mechanism-design-using-gears/know-about-parameters-that-determine-gear-shapes.html (Section 3)

From what I can see on helicron this method creates an approximation to the involute curve by cutting a number of facets on each tooth. The more teeth of the gear blank that engage with the cutter, the more facets and hence better approximation. A small gear would only have two or three facets, hence the running noise he mentions.

You could probably improve small gears. If at the end of the full gear rotation, with the cutter engaged with the gear, unlock the indexer and move the cutter height. 1/2 tooth up, re -ut all teeth, 1/2 tooth down, re-cut teeth. That way you would cut more facets.

Probably easier to make a set of involute cutters.

I guess the edges of the facets would wear quickly so it may run OK after a while. I guess they would be ok for light duty and low speed gears.

How few teeth? Well, as the gear gets smaller the shape of each tooth changes - the outside looks much the same but the sloping flanks become closer together. This weakens the tooth - there is simnply less metal there. Smaller still and the teeth can 'interlock' as the gear rotates, making a smooth drive impossible and promoting rapid wear.

It is the same with sprockets for roller chain - anything less than about 20 and you will suffer. Yes, chainsaws do it and that is why the chain and sprocket both need replacing about every tree (well, nearly).

Cheers, Tim

The method is one well-recognised in industry and is by no means an approximation. It is a method of _generating_ gear teeth, the same as hobbing or gear shaping. Have a look for Sunderland gear planer. There are a few posts on this forum by John Stevenson that have discussed the method. There are numerous books available on the internet archive that discuss generation methods.

I haven't bothered to read the helicon method but hobbing and planing are approximations. They 'generate' the tooth form in the sense of a creating a series of straight lines rather than relying upon the cutter profile.

For many applications the tooth form as hobbed is fine. But for precision and/or high speed gears (as in a lathe headstock) the gears are often shaved and ground after hobbing to refine the profile.

Andrew

My reference book, Gear Engineering by H.E.Merritt, gives the same formula for the minimum number of teeth without undercutting and with zero addendum modification as DC31k has quoted. It works out as a theoretical 22.1 teeth for 17.5 degree pressure angle.

You can go lower if you apply addendum modification, this increases the diameter of the blank that the teeth are cut on, but there is a limit to how much you can apply before the teeth become pointed and you start to lose the top part of the profile.

With regard to the method used by Helicron, you may start to see more facets as the number of teeth reduces. I seem to remember that the Sunderland gear planer rotates the gear blank and moves it sideways relative to the cutter for a number of strokes before resetting for the next tooth, reducing the number of facets. Someone may correct me on this, it has been a while since I watched a Sunderland in action.This would be much the same action as a Maag or Niles gear grinder if I'm correct.

Perhaps someone else has made some gears in this manner and can share their experience.

Neil

Thank you for your replies.

I'm interested in this method as I'm looking at making gears with a mod going down to 0.2

Making single point cutters of that size sounds tricky and I don't have access to a grinder. This seems a relatively simple way to make a cutter.

Has anybody tried this method?

I thought that the minimum teeth for involute gears was 12?

Good point about roller chain sockets - I didn't know that the minimum tooth count was so high.

Steve

That's what happens when formulae are quoted without understanding how they are derived. The formula given relates to undercutting when a gear is hobbed. The undercutting is a consequence of the hobbing, not a neccessity for the resulting gears to mate.

I have made 13 tooth 5DP pinions with an involute cutter that mesh properly without needing undercutting. On the other hand these 6DP bevel gears are 10 teeth, and do need an undercut:

In both cases the gears were 20 degrees PA.

Andrew

I've shown these before, all made with a straight hob*.

The more teeth, the more facets, up to the length of the hob.

With three passes per tooth the maximum error is about the same as with the circular approximation. Facets should wear in reasonably well.

Main advantage is the ease of cutting working gears at larger or smaller PCDs than typical to allow for non-standard centre distances (you do get skinny teeth)

*Except the constant depth bevels.

Edited By Neil Wyatt on 03/04/2020 19:10:48

The other good thing about a generating method as opposed to a form cutting method is that you can profile shift the gears if necessary. Again, lots of info. at a digestible level on khkgears' site.

I do not know if you have or want CNC facilities, but if you do, a look at Gearotic might give you some options.

I've just got round to looking at the KHK site. Very useful indeed, the best gear resource I've seen.

I don't have CNC apart from my rotary table but Gearotic looks interesting anyway as a design tool.

Thanks for the tips.

Steve

Neil's not alone, here's my crude version for making Meccano compatible gears,

The rack cutter cuts an involute because the cutting teeth either side of centre shave off material from adjacent flanks whilst metal is being crudely removed by the centre cut. The amount and placement of adjacent shaving depends on the angle of the gear blank, which changes as the blank is rotated. The shaving effect progressively improves tooth shape towards a perfect involute. It's not like a form tool or gear-cutter where the tooth shape depends directly on the tool and can be cut in one go.

Dave

If one can make a gear with this method, however many facets it end up with, one must be able to make the 'inverse' an involute cutter by the same principle. But how?

There is some difficulty in your request. The method shown cuts the gaps between the teeth. The cutter you want is the shape of the gaps between the teeth. The bit you want to save is the bit that is ending up as swarf.

If you have a look at Fellows gear shapers, the cutters resemble a spur gear, so you might be able to make something like one of those, but the machine to drive that style of cutter is somewhat specialised.

It is just an intellectual challenge for a Sunday afternoon. The method we have been discussing is rather 'neat', using a cutter with straight edges to make teeth with curved faces. The involute cutter has curved faces but concave so can anyone come up with a neat trick to generate them?

Bazyle,

I think it’s fair to say that Shortt showed us the general principle, when he devised the profile of the gravity impulse pallet on Frank Hope Jones’ Synchronome.

See pp 179-180 of ‘Electric Clocks’ by FHJ

MichaelG.

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Link : https://clockdoc.org/gs/handler/getmedia.ashx?moid=23813&dt=3&g=1

Edited By Michael Gilligan on 05/04/2020 14:41:15