Machining Bevels.

[John S]

Art,
I think Dan has done all the replies necessary, I see no reason why an end mill can't be used, in fact because the DP changes as the tooth approaches the centre it's probably the only way to generate a tooth that requires no finishing.

Just to make it clear take a sample gear and say this gear is 10 DP measured on the outer diameter, pitch circle etc.
This gear has a face width of say 5/8" and because it's a genuine bevel it tapers on pitch and root to the cone point which is zero.

So at the inner face diameter this gear has a DP of probably 12 DP.

This is the problem milling, do you use a 10 DP cutter or a 12 DP ?

Your method will allow the profile to change. Using an involute cutter on the side it won't, it's back to milling.
Using a slitting saw probably won't work either as the the saw will interfere as it passes thu.

In the case of spur and helicals its on the cards ? to allow Gearotic to generate it's own involute cutter shaped like an end mill / D bit to allow very small profiles to be done that can't be done with convention end mills because of risk of tool breakage.

This feature won't be possible with bevels because of the differing DP / MOD.
One way round this may be to allow the user to define a tapered cutter similar to an engraving tool where the user specifies an included angle and tip width. The advantages of this are a stronger tool for a given size.
These are quite easy to make in HSS or even carbide given a couple of simple jigs.

Now back to mounting and cutting the gear.

If we have 45 degree bevels then cutting from the flat or horizontal is exactly the same as regards axis travels.
The Z axis is probably the most important as it will have to raise from the inner DP to the outer DP.

The problem I can see is the differing angles.



Take this 45 tooth wheel and the 10 tooth pinion, using a 4th axis the 10 tooth pinion will be easy as the cone angle is quite low. However the 45 tooth wheel is a different matter in that the cone angle is nearly vertical and an end mill will not be cutting perpendicular to the pitch line, in fact it will be hard put to form the tooth depth.

I know not everyone will have access to a tilting dividing head but there are simple ways of doing the same, this is one



My take on this is that anyone wanting to do bevels will either be geared up or be prepared to gear up so if the president is set that the blank HAS to be on the pitch angle it will make the maths a lot easier.

John S.

[John S]

Can't see a problem and if it works for you then why not go this way.

At the moment we have no way to cut bevels easily - period, so anything is going to be better and Chucks idea of locking the angle to 45 is very good as if you need a tilting devise for say a rotary table then you only need the one fixed option, far easier to make / modify / setup.

Art,
Can I request that you keep the tapered cutter option on the table for small pitches, they are easy to make in HSS or carbide and very strong.
I have just run the figures thru for a pair of 20 DP bevels and they require a 1/16" max cutter, any DP finer than this will need even finer cutters.
If a tapered cutter was used with a defined angle, your call, then the tip would need to be 1/16" but the body could slope up to 1/4" or whatever in metric.
At 1/2 PA angle it would cut most of the gear on it's 'blocking out' operation.

John S.

[John S]

Doing spur gears using a tapered cutter of the same PA is simple to understand as it's just one tooth space as generated by the Sunderland process which uses a short length of rack to do the same thing.

At the moment Gearotic uses  a normal endmill / slot drill to block the space out and then it alters the A,Y and Z values so that the sides of the cutter form the involute in multiple passes.



The Sunderland process drops the cutter to full depth and then rolls the blank as it moves the cutter along.

Transposed into GM terms this means it only has to drop to depth and then use just A and Y with Z staying constant at full depth.

When cutting bevels and I need to draw this out or at least think about it some more [ hard to do tonight - just got back from the pub ] but bevels have a varying DP depending on where on the line from the OD to the 0,0 centre point you measure.

So lets say for round figures the small end of the teeth measure 12 DP the larger end will perhaps be 10 DP [ rough figures ] so if we select a cutter with a 20 degree PA that matches up to the small end and the blank lies on horizontal on the root angle by the time it's got to the large end due to the rolling of the larger diameter it will be up to 10DP and deeper as the face is steeper than the root angle.

If Z is left at this depth and A is rolled as Y is stepped over it seems to me that it will follow an increasing involute.

Does this make sense ?

[EDIT]
It would be easy to test because if a program was written for a spur gear say 20 teeth 12 DP and instead of cutting a spur you cut onto a blank that was tilted at the root angle it should cut some form of bevel.
Perhaps the one tooth hob program in the Third Party folder would do this.

http://gearotic.com/ESW/FavIcons/index.php?topic=131.0

?? I need to get some kip, it's half past dark here.

John S.

[Damo]

Hi all, I'm new to this forum but was really excited to join and have been reading quite a bit of what's going on with the bevel gears.

I think there is quite a cross section of people here with lots of different ideas and probably trying to find the best solution that suits their needs. The way I understand it is that the bevel gears don't use an involute tooth form, probably for the reason that we've been commenting on and that the tooth form changes as it moves in toward the centre. If yo were to have an involute toothe form you could do it only by machining it from a cad model, and therefore the octoidal tooth for was invented so as to solve this problem. One thing in the past that determined any standard for producing a gear was 1. it had to function and 2. it had to be easy to produce. Involute tooth forms may have been able to be used for bevel gears but really would have been awkward and expensive to produce due to having to use either a 5 axis machine or to do waterline passes over the whole tooth, and in the case of spiral bevel, where it couldn't be done from just xy & z movements because of undercutting. So they came up with the octoidal tooth form, and then when they found that the spiral gears can be made with a face mill type cutter, they then evolved to zero gears. Mainly because the machinery used to face mill a spiral bevel, couldn't do it straight.

My idea about how to machine them in GM.
It would be nice to see it with a few different options, (more work for Art) but to satisfy different levels of peoples needs. First would be straight bevel gears from moving in xy&z movements only, with a ball nose cutter. Very time consuming but some people like watching cutters.  Next for the more adventurous to tilt the table to the root cone angle. This way they could be cut with an octiodal shaped D bit, or use side cuts and flank passes. Also with this set-up we could use a face mill type fly cutter and make either zerol or spiral gears. It would be nice if GM could output a tool form that we can then try to produce on a D bit grinder. My idea was to get a projector and made a tool for a single tooth face mill type cutter from a 10 to 1 profile image. GM could also output the diameter that the cutter need to be set at to follow the spiral.

Cheers Damo

[ArtF]

Damo:
 
    Well, I have ot start by saying Im no expert. BUT, heres what I think I know so far. :)
   
      In GT ( or GM) the tooth of a bevel IS an involute. It is modified as to profile shift, but other than that its a standard
involute.The originating tooth form is a spur gears involute tooth. This is true at least of "straight bevel" gears of both standard and
gleason type calculations. ( This is basically what GT does for bevels.). ( Lets Ignore GM's bevels, they are
not corect by any measure, but GT's are industry standard "straight type) , both in gleason and standard nomenclature.

    I do see where Octoids are the prefered tooth form in making bevels due to ease of manufacture, BUT the data seems very hard to come
    by so far. Can you point me to some source for more info on their shape and creation. I think I understand it as being the conjugate
    to a stright sided pinion done on a sphere, meaning the rack for them is bascially a square wave I think.. but that makes it hard to picture
    the math involved in making them, at least digitally. Ive commmitted to making the toolpath generator make them once the non-circluar
    gears are added to GT, but as of yet, Im not sure exactly how.. so the discussion is well worthwhile..
   
    Art
   

[Damo]

Hi Art, I agree it's hard to find a definate understanding of the octoidal tooth form but it is what I have been trying to understand from reading various papers on the web, but am not exactly sure. Maybe I am not understanding it correctly, most papers do seem a bit vague but talk about the form being close to an involute. 

[ArtF]

Damo:

    Noone seems to specify a formula for such a shape, it seems its formed by using a circular shaped rack in essence..instead of an involute being the result
of a linear rack shape on a gear, a circular rack shape on a bevel gives you an octoid..  This will be easy to implemenbt as a cutting routine, we just need to figure
out a formula for the cutter. The GCode will be easy, its just cut to depth in a single spot on a tilter ( or not ) 4th axis.. That I can do pretty easily, the results form there would simply be seen from various cutter shapes.. Ill give this some thought till I finish non-circluars which is when I intend to add bevel machining..

Art

[Damo]

It's a very interesting subject. I have a need to produces some spiral bevel so will continue investigating. What is also worth noting is that in literature describing setting up spiral bevels correctly, the tooth contact area should be checked and made sure that it is in the middle of the tooth, and not toward either the heel or toe of the tooth. That in itself suggests that maybe contact is not that uniform along the tooth flank. If it were a spur or helical gear contact would occur along the whole tooth flank. Also, maybe industry adopts a certain geometry that is close to an involute that becomes proportionally smaller as it approaches the centre axis, to accommodate ease of manufacture?

Cheers Damo

[ArtF]

>>Also, maybe industry adopts a certain geometry that is close to an involute that becomes proportio nally smaller as it approache s the centre axis

  I suspect thats exactly what an octoid form is..

>> setting up spiral bevels correctly, the tooth contact area should be checked and made sure that it is in the middle of the tooth, and not toward either the heel or toe of the tooth

  I suspect too that this is a function of the proper centering of the spiral generator. In bevels, unlike helicals, the spiral generator is at 90 degrees to the center of the
spiral. This migth explain that referance..

Art

[Damo]

I'm not sure I get what you mean about the spiral generator Art.

At the moment, this is how I intent to make the spiral bevels; (My machine is horizontal, it has a rotary pallet and a rotary table on top of that)

1. In my CAD, draw the helix geometry on the root cone, the start of the helix is at the heel of the geometry, on the axis line.
2. Arc fit a radius to the helix in the root cone plane and find the centre of this arc, this is the start point of the cut.
3. Rotate the helix in the cad so that the end of the helix is at the toe of the geometry, on the axis line.
4. Arc fit another arc and find the centre point, this is the end point of the cut, not the angle between the start and end.
5. Set the rotary table to the root cone angle.
6. With a face type fly cutter (and the correct geometry on the tool), make a depth cut to the depth of the root cone.
7. Make a feed move by rotating the required amount as well as a linear move in the vertical axis.
8. Retract and then index to the next tooth, repeat until all the teeth are cut.

My theory is that when the cutter is cutting the spiral, the only part that is geometrically important, is when the cutter is normal to the cone surface (hard to explain). The rest of the cutters path is just clearance.

Cheers Damo

[ArtF]

It IS hard to explain...near impossible I think. Only pictures can really show it. By Spiral generator I meant the code
that generates the helix. In a helical gear you use a true helix, but in bevel's a spiral is really just an arc of a circle
of cutter diameter which is offset from center of toothface by the helical angle. Again, hard to explain in words. I believe
I use the pitch cone distance as the cutter diameter for the purpose of the spirals but Id have to check the code..


Art
..

[Damo]

This link is about the best definition of an octoidal tooth form that sort of makes sense.

http://books.google.com.au/books?id=IAE ... te&f=false

[Damo]

Actually, I like this book, goes into the cutting tool manufacture in detail.

http://books.google.com.au/books?id=wZp ... te&f=false

[ArtF]

Damo:

  Heres a photo of an octoidal generation. If the rack in this picture were not bent into a circle, the output
woudl be an involute tooth. BUT, as I suspected if you simply bend the rack into a circle, the result is an
octoidal tooth. Thats why no math formulas seem to exist. Its a physical manifistation of the bending of the rack to a circular form.
  Now..the golden question. I generate my bevel "Involutes" by formulas derived from standard involute teeth ( so a linear rack ), BUT then I bend those teeth into a spherical form in order that they taper
correctly in a bevel. If a octoidal is generated by a straight rack bend round, then is a tooth generated from a linear rack but then folded spherically now a proper octoid? I highly suspect the answer to this is yes. If we consider just the infinitely thin outside tooth of a spur for example, mentally its easy to see that if you take this tooth and fold it upwards in bevel form so it fits a spere, you have folded a modification into that tooth. I would submit its the same process as folding the rack and then generatign the tooth prefolded. I would have to do a great deal of math to prove that though, its simply my intuition that tells me this is so..
  I will give this more consideration, but I highly suspect an octoidal tooth is what we have. It cannot, after, all be called an involute tooth as the process of folding it into a bevel has changed its shape, so if it isnt an involute..what is it?... I suspect perhaps its an octoid. Since the term "Octoid" refers only to its contact pattern and not its shape, I can only surmise this as yet..

  SO perhaps just putting out this tooth shape for grinding will work..
Art

[Damo]

Hi Alf, yes i think you're right. If you get a straight rack and project onto a sphere you will get 2 crown gears. But what happens to the tooth form when you get closer to the centre? This is where the octoid comes in. If you take one tooth flank of that crown gear, and another flank on the opposite side and imagine a surface that runs through those 2 flanks. As if you were holding a circular disc of paper and on one side twist it to that flank angle, then on the other side twist it to the other tooth flank angle. If you look at this shape side on, it looks like a figure "8". So microscopically where the tooth flank is, so so minisculely, it's slightly "s" shaped. Would be nice to prove it mathematically. And remember this is just the crown gear, not yet bent around a smaller gear. What'd you think?