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

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.

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.

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.

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

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

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.

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

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.

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