Helical Gears

[jadge]

I was saving up all my queries until the 10th when I get my fondle 

They were packed up ready for the 10th last night. Beforehand the gears washed, dressed and cleaned their teeth ready for handling.

Andrew

[jadge]

Hi Andrew,
I went back through my helical gear information to double check what I had stated and it is as I said. The reason being is that for helical gears you have normal pitch and real pitch. The normal pitch would be a measurement take at right angles to the teeth and the real pitch is taken at right angles to the axis. By using the same pitch (24, 32, 48) and the same tooth count we can change the pitch diameter by changing the helical angle. That's because the tooth shape for a set pitch will have the same numbers as a spur gear ( normal pitch) but as the teeth are angled (helix angle) the real pitch gets larger because of the secant of the angle.

I think we're saying pretty much the same thing. I tend to use the terms normal and transverse pitch; probably because I'm an electronics engineer, so 'real' has a different meaning to me.

I concur that changing the helix angle changes the PCD, and hence the OD and centre to centre distance, which allows considerable flexibility in the design process.

Just to clarify, the ratio of two, or more, helical gears depends only on the ratio of the numbers of teeth, not on the helix angle. That certainly seems to be the case with the 30° helix gears I made for parallel axes. Both LH and RH gears have the same number of teeth so the ratio is 1:1. I've mounted both gears on spigots and marks on both gears line up once per revolution, ie, a ratio of 1:1.

A more interesting question is the precise shape of the tooth in terms of the normal pitch. Convention specifies a plane normal to the helix angle at the PCD. However, the helix angle varies across the depth of the tooth, getting smaller towards the root and larger towards the OD. Mathematically I think that the normal to a helicoid is another helicoid. So the normal tooth shape should be defined on the normal helicoid, not on a normal plane. From a practical viewpoint I suspect that the differences are very small, and most home workshops would have no way of taking the differences into account anyway, without some sort of CNC.

It's been a while since I read the Cincinnatti book, and the one by Brown and Sharpe; I'll have to revisit them.

Ah, I see that links have been posted to documentation. I don't know why I didn't see them before; thanks for posting.

Andrew

[Craig DeShong]

As good a place as any to ask a question. 

I'm starting a new model that will use helical gears and I've cut them before using Chuck Fellow's fixture.   believe I have all the math correct but the one question I'm a little dubious about is the formula for calculating the "virtual" teeth of a helical gear (in other words, the number of teeth you'd use in selection of the proper involute gear cutter)

I'm using:
N= number of teeth on the gear
A= angle in degrees of helical angle

virtual teeth on gear= N/(cos(A)*cos(A)*sin(A))

Is this a good formula?  what do you use?

[Jo]

Maths  I cheat and use this 

Jo

[nj111]

Oh that's a useful chart! Thank you, Nick

[Craig DeShong]

Maths  I cheat and use this 

Jo

Thanks Jo, that certainly answers the question.   But it takes all the "fun" out of it 

[gbritnell]

Hi Craig,
The cutter selection (involute cutter) is based on a standard involute cutter. By that I mean if you used a cutter for X amount of teeth, as per a spur gear, when it was moved to the proper depth of cut for a helical gear the teeth would be too narrow so you use a cutter with a profile that will give the proper involute shape to the teeth. Don had made a spread sheet for cutting helical gears but I don't remember if it specified what number cutter to use.
gbritnell

[jadge]

The formula is:

N' =  N/cosł(A)

It arises from looking at the teeth in the normal plane. In this plane the teeth are not on a circle, but on an ellipse, and it is the radius of this ellipse that determines the number of equivalent teeth, and hence the number of the cutter to be used. The derivation is simple (high school trig) like this:



None of the methods using an involute cutter produce perfect teeth as the whole of the cutter is at a fixed angle, whereas the helix angle across the depth of the tooth varies slightly from top to bottom. From a practical viewpoint gears made by such methods are often fine.

Andrew

[Craig DeShong]

Thanks Andrew.  Actually that was the formula I was using before I found another.