GearHeads Corner

General Category => Bevel Machining Discussions => Topic started by: ArtF on December 18, 2010, 08:53:47 PM



Title: Machining Bevels.
Post by: ArtF on December 18, 2010, 08:53:47 PM
Hi Guys:

 Here we will discuss Ideas for implement ations of Bevel Machining techiques
or possible ways to make Bevel gears under GM..

Ill post some thoughts over the next couple days as to how I intend to proceed.

Art


Title: Re: Machining Bevels.
Post by: ArtF on December 18, 2010, 09:11:57 PM
Notes on Bevels:

  Ive implement ed 3 types as a start, Zerol, straight and Helical.

Zerol is like a knuckle gear, its halfway between a straight and a helix. Bevel Helix's are not generated the same as any other type of helix, its a more complex helical proceedur e, but Im pretty sure mathmatic ally its correct. Whiel some specs call for the curvature of radius to be used for the helix tangental circle, Ive used the conedista nce as the radius of the helical cutter, this means less to consider when creating a helical. Ive tried to keep the settings very low, almost everythin g is automatic . For example the helical angle is always 35 degrees.. until someone who knows more than I explains why we need other angles... .then Ill likely add them. :)

 
  The facewidth of a bevel is set to a max of 25% of the cone distance. BUT its overridde n at
the width of the GearWidth setting. That is to say if you set a gear width of 10mm, the face will be clipped to 10mm.. thats the face, not the actual gear width. The gear width will be the facewidth times the sine of the pitchcone angle... which is computed from the wheel pinion relations hips.

 Remember, no two bevels will mesh properly unless they are generated for each other.. Always design bevels as a pair..

Shaft angles are allowed from about 1 degree to 90 degrees , so you can have shafts flying about everywher e.

 So the question for the next developme nt period is "How exactly will we make these in the shop".

 This , I think, requires some discussio n. We can do 2.5D, rotary on horizonta l axis, or rotary on the flat ( though Im not convinced this gives us any true advantage on a well working system. )

   There are many ways to do this, each with their own problems in terms of coding it. I dont think any one proceedur e will machine all bevel types or sizes.. but I do think we can solve this one together to make bevels easier than ever before. So give it some thought, and lets break new ground together.


   Im very proud of the helicals Ive seen cut, I think they have worked fantastic ally.. so Im determine d to make bevels work just as well, maybe easier.


  Lets use this topic board for all things bevel. If you have a question on bevels, ask it here. A comment.. same thing. An Idea.. Go for it. Lets see what makes sense and what doesnt.


Thanks
ARt

 

 


Title: Re: Machining Bevels.
Post by: tweakie on December 19, 2010, 12:01:01 PM
Art,

Expanding on what I was trying to say in another thread - If the rotary axis is mounted verticall y but tilted and fixed at the angle of the bevel then the tooth being cut would be plane with the table X - Y and the rotary is just indexed to the next tooth and so on in a similar way as a spur gear would be cut one tooth at a time.

Tweakie.


Title: Re: Machining Bevels.
Post by: ArtF on December 19, 2010, 03:27:44 PM
Hi Tweaky:

   This is one method we can consider. I fear that many hobbiests lack the capabilit y to tilt
without a hassle, but I could be wrong.. It woudl require an accurate tilting capabilit y. The cone angle
can easily be reported to the user, and posted in the Gcode. The machingin fo them at that point gets pretty
easy from my perspecti ve.

  Anyone else got feelings on this, is tilting easy enough to consider most can do it, or should I go the
way of tilting the code and find out if this limits the gear too much?

Art


Title: Re: Machining Bevels.
Post by: Greolt on December 19, 2010, 04:46:32 PM
In Tweakie's diagram, I am assuming that it is using X and Z axis with A being just an indexer.

Would that mean we can not machine the involute shape of the tooth without an involute shaped cutter.

Or would Y axis come into play as well to achieve the involute with a straight end mill, as it does now with a spur gear.

Greg


Title: Re: Machining Bevels.
Post by: ArtF on December 19, 2010, 04:55:57 PM
Greg:

 We should be able to use the shaving technique same as a spur oir helical to get the involutes ..

Involute cutters will be an option..

Art


Title: Re: Machining Bevels.
Post by: Jeff on December 19, 2010, 05:49:58 PM
Hi Tweaky:

   This is one method we can consider. I fear that many hobbiests lack the capabilit y to tilt
without a hassle, but I could be wrong.. It woudl require an accurate tilting capabilit y. The cone angle
can easily be reported to the user, and posted in the Gcode. The machingin fo them at that point gets pretty
easy from my perspecti ve.

  Anyone else got feelings on this, is tilting easy enough to consider most can do it, or should I go the
way of tilting the code and find out if this limits the gear too much?

Art



 If you can cut the gears with out tilting that would be the way to go for me. I don't have a forth axis capable tilting (with out major additions) - Just my 2 cents.

Jeff


Title: Re: Machining Bevels.
Post by: ArtF on December 19, 2010, 06:02:02 PM
Jeff:

  Even Im reticent about tilting my axis.. not that it cant be done,
but cone angles can vary quite a bit so there'd be no standard to the
tilt amount, so the only way to quick-setup such a system is to have a good variable tilt mechanism of some sort made up.. easy to do I supose.. but Im suspectin g most hobbiests would rather cut without the tilt.. assuming its possible. A lot of us arent machinist s but hackers who know from experienc e the fewer setup's we need to worry about the better the end result..

Art


Title: Re: Machining Bevels.
Post by: John S on December 19, 2010, 06:31:34 PM
To machine with an involute cutter would require the cutter to cut on the side of the gear in which case you can use a normal 4th axis and slew the axis on the bed in relation to the X axis.

Problem I can see here is that the interfere nce with an involute cutter will not allow the true profile.
Normally when using an involute cutter to cut bevels you do a centre pass, second pass with the cutter raised and dividing head rotated in the ++ then a last pass with the cutter lowered and the head rotated in the --

Even then you get a section of the tooth that has to be filed to get a proper fit.

(http://www.stevenson-engineers.co.uk/files/bevelshape.jpg)

One work round may be to still cut on the side and use a slitting saw instead of an end mill to plane the shape on?
Advantage s are saws are cheap and strong given they can go down far thinner than end mills.

I think for end mills then work on top and tilt the table. Anyone serious about bevels will have to have something very similar already.

John S.


Title: Re: Machining Bevels.
Post by: ArtF on December 19, 2010, 09:40:51 PM
John:

   I "Think" I understan d what you mean. Am I right in assuming the tooth must be filed because the involute is actually wrong? While you can design an involute cutter to match the profile at the start of outside of the bevel, since the bevel tooth shrinks as it goes to center, the correct involute is actually the involute of an ever shrinking base circle?

   I was thinking this was the problem with using a inv. cutter.. there is no way to dynamical ly match the involute curve..

   Provided the end mill can fit in the small end of the root, can you see any reason I cant do the same technique as a helical, only with simultane ous Z motion during the cut? To my mind if we control the facewidth as a function of the end mill max diamter we want, we should be able to do most bevels, perhaps with facewidth restricti ons due to bit size...

   I was thinking if all Z cutting passes started closest to lowest root, and cut upwards and inwards to gear radius, we shouldnt have any real plunge problems. Im suspectin g the tough problem is an algorithm to see the tooth
profile as an angled primitive for the clearance s during cutting..



Art



 Just want to be sure Im understan ding..

ASrt


Title: Re: Machining Bevels.
Post by: Dan on December 20, 2010, 03:51:19 AM
   Provided the end mill can fit in the small end of the root, can you see any reason I cant do the same technique as a helical, only with simultane ous Z motion during the cut?

If possible, this would be best. The biggest problem I can see is with helical bevels, where the end mill would have to be very small to fit in the tooth root close to the centre.

  To my mind if we control the facewidth as a function of the end mill max diamter we want, we should be able to do most bevels, perhaps with facewidth restricti ons due to bit size...

Exactly! The smaller the face width the bigger the end mill that can be used, but in the same time the tooth is weaker. May be give the user the control over it...?

   I was thinking if all Z cutting passes started closest to lowest root, and cut upwards and inwards to gear radius, we shouldnt have any real plunge problems.

Yes, mentioned it in some other thread. If we choose the normal 4th axis mounting, then this is the way to go. You can go full feed this way.

I think tilting the 4th axis has its advantage s and this is the most logical thing to do, but it has its difficult ies. For me, I would prefer not to have to do this. Besides, Gearotic doesn't follow common logic in how it cuts gears ;)

Dan


Title: Re: Machining Bevels.
Post by: John S on December 20, 2010, 04:48:05 AM
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 approache s 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 conventio n 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 advantage s 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 horizonta l 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.

(http://www.stevenson-engineers.co.uk/files/45_10helical.jpg)

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 perpendic ular 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

(http://www.stevenson-engineers.co.uk/files/tilttable.jpg)

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.


Title: Re: Machining Bevels.
Post by: ArtF on December 20, 2010, 09:16:37 AM
John:

   Yes, I think we're starting on the same page. ( Isnt that a nice picture of a bevel :-) ), the pinion in your case is faily easy I think, while the wheel is hard.  IF we dont tilt, then the wheel IS an example ( I think ) where machining would be very difficult . ( Though I suspect that I may be able to compute the milling bits vertical interfera nce in steps to even do that provided wheel.. but if you add a helix to it , it becomes near impossibl e to do the wheel.. )


 I suspect some experimen ts are in order.. For lower ratio's it all seems possibel without tilting, its the higher ratio's such as you show that worry me without tilting..

Art




Title: Re: Machining Bevels.
Post by: Dan on December 20, 2010, 01:57:38 PM
Art,

If we want to stay away from the need of tilting the 4th axis, I think we are back to the option where we would have a selection between: horizonta l 4th axis or vertical rotary table. Given you can do any bevel up to 45 degrees cone angle (still not sure 45 degrees helical bevels are doable when face width gets large - tried to visualize it with Gearotic, but just can't see it), the two variation s of the 4th axis mounting should cover whole the range.

Dan


Title: Re: Machining Bevels.
Post by: Maxmachine on December 20, 2010, 03:09:36 PM

If I may venture an opinion here (many of you are far superior to me in knowledge of gear making) the tilt/not tilt issue seems to be not very significa nt compared to  the ease of machining derived from the use of it.  It is easy to build a tilting table, and it is even easier to use a sine bar to get the proper angle to the required accuracy. Many low cost tilting tables are out there, some even come with worm drives to allow close adjustmen t.

Mark
Max Machine


Title: Re: Machining Bevels.
Post by: ArtF on December 22, 2010, 10:38:12 AM
Hi Guys:

  One question we havent dealt with is blanking. .

  What do you think about the proceedur e of making the blanks for a bevel, how much
should be left to the maker.. Shoudl GM put out code to create the bevel of the blank, or should it assume the blank is properly sized and beveled for the process? Makeing the bevel can be time consuming on the 4th axis.. there is no real fast way for me to do that. Shoudl I worry about it all all? Or should the program assume you have a beveled blank available of the correct face  width?

  How about zeroing? Some get a bit tiffed that I zero Helicals to the top of the blank front for example.
The reason I do this , rather than zeroing the Z to center of axis, is to reduce the number of bad collision s due to improper centering or blank size. Running into the blank is much harder when one is zeroed to the blank rather than the arbitrary Z zero of axis center. While somewhat non-standard it seems to work as Ive
heard of very few ""oops" remarks as to collision s. If the blank isnt proper size you simply get a gear thats wrong, but didnt hurt anything mechanica l...

   Your call really, codewise it doesnt matter. SO what do you think about blanking. .and zeroing..?

Im about to do the output.. :)

Art


Title: Re: Machining Bevels.
Post by: tweakie on December 22, 2010, 10:47:55 AM
I would be happy to turn the blank to the correct size / shape.
Not fussy about Z zero position but as you say there is less risk with it at the top of the blank. (why is it that the expensive cutter breaks in a heartbeat and the old dull cheapo lasts forever ?).

Tweakie.


Title: Re: Machining Bevels.
Post by: Dan on December 22, 2010, 02:02:09 PM
Art,

I agree with Tweakie. If you output the blank dimension s, it would be very easy to make it on a lathe. May be consider even outputtin g a DXF of the blank in addition - isn't really necessary as Mach Turn has the required tapper wizard, but just as an option.

I agree with the point you made on zeroing.

Dan


Title: Re: Machining Bevels.
Post by: John S on December 22, 2010, 02:31:23 PM
Same as Dan.
2D drawing of blank would be nice.

Zero from wherever suits you. We as operators will adapt.


Title: Re: Machining Bevels.
Post by: John S on December 22, 2010, 05:44:12 PM
Just an add on.

Talking of blanks, just had a look at the on screen informati on for bevels.
It gives the pitch cone angle and root angle but no face angle which is nessesary for turning the blank up.

It's also necessary to define what the angle is to, a 45 degree mitre gear will probably have a 47 - to 49 degree face angle depending on size but it gets quite confusing when turning the blank whether the 47 degrees is from the X axis or Z axis.

Large ratio's won't suffer from this but mitre gears have such a small differenc e it's easy to get the wrong angle.

John S.


Title: Re: Machining Bevels.
Post by: ArtF on December 23, 2010, 12:26:41 PM
John:
 Noted.. Ill put out the face angle as well. ( which is basically the pitch angle with the addendum angle added to it. The reason I hadnt till now was if we decided to use parallel cutting, the angles woudl stay the same as the pitch cone angle.

  Looking at the math of all this, Ive decided that it doesnt make sense NOT to tilt the table. A tilted 4th can do pretty much any bevel while any other method will fail on large angles and likely on all helical bevels or zerols.

  This being the case Im thinking zeroing IS difficult as we need a point readily identifia ble on the blank. Zeroing to center of a tilted table can be difficult with the mounted blank.  Any thought on an easily definable zero point?  Perhaps inside top edge of the mounted blank? ( Thats assuming a bevel is already applied? )

  Gone to take a good look at my 4th to see what I can do to make it easily set to an angle..

Art


   


Title: Re: Machining Bevels.
Post by: Dan on December 23, 2010, 03:20:37 PM
Art,

When we tilt the 4th axis, we want the bevel face to be parallel to the XY plane (at its top end), right? Then why not zero the tool on top of the face there and on the OD... Does it makes sense...?

Dan


Title: Re: Machining Bevels.
Post by: John S on December 23, 2010, 05:03:04 PM
OK so tilt is agreed.
Following on to what Dan says and it makes perfect sense, we need a point that you can define easily.

Y is easy as you can touch off on both sides of the blank and take half the measureme nt to get on the centre line.

Z is also easy, touch off on the top outer edge as this is the highest point, rememberi ng that the pitch angle will be the one you set up on.

X, again easy as it the outer edge.

All points easily dome with wiggler and / or cigarette paper.


Title: Re: Machining Bevels.
Post by: Chuck on December 24, 2010, 01:50:33 AM
Art,

I expect you will be forced to come up with several machining options.  While setting the 4th axis to the pitch angle will help a bunch I think you should consider other setups.

Using standard endmills and 4 axis should be the first option for larger pitch.

If you create a Gcode generator and a simple setup you can make formed cutters  that will allow just about anything.   Don't get stuck on only using endmills.

You can do most strait cut gears on a 2.5D/3D if you create a cosine stretched formed endmill.  This would allow most users to make a cutter with one easy setup and the gear with another easy setup.

A non stretched involute form will do most of your gears with the 4th axis set at the pitch angle.  This can be a fly cutter for strait teeth or a formed endmill.

I do have a question for you Art,  is the involute curve the same at the small pitch end of a tooth as it is at the large end?  By this I am asking if one profile form can make the correct shape for the entire tooth with varying pitch?

If a form cutter can be made to cut the small pitch end and the angle of the gear set to cut the widening tooth any pitch strait tooth could be made with a formed fly cutter or a formed endmill.  The spiral teeth would require a formed endmill.

Soft material (soft compared to the machine rigidity) can be quickly done with a non rotating formed shaper tool with a 4 axis setup.

As for tool zero, if you specify points on the gear blank appropria te for the tool used I think it is up to the machinist to set up the machine and blank correctly or adjust his zero points as needed to put the zero where you want it. With 4 axis at any angle a Y centering touch on each side of the gear using a fixed X and Z then a point at the top of the gear blank for X and Z makes the most sense.

Chuck in Wyoming


Title: Re: Machining Bevels.
Post by: ArtF on December 24, 2010, 08:48:39 AM
Hi Chuck:


>>If you create a Gcode generator and a simple setup you can make formed cutters  that will allow >>just about anything.   Don't get stuck on only using endmills.


   We wont be, I plan on using tilted 4th axis at first, as it will cut most any bevel angle..
I then plan to put out code for cutters for normal spurs and helicals. . The tilted 4th axis is just the first step to prove the concept and get bevels cutting..


>>You can do most strait cut gears on a 2.5D/3D if you create a cosine stretched formed endmill.  This would allow most users to make a cutter with one easy setup and the gear with another easy setup.


   Im not sure what a cos stretched endmill is usefull for.. can you explain that one. If I stretch an endmill by cos, the involute would be lost woudlnt it? At least on spurs it would..


>>A non stretched involute form will do most of your gears with the 4th axis set at the pitch     angle.  This can be a fly cutter for strait teeth or a formed endmill.

    YOu mean bevels? I think the invcoltes woudl be lost.. (I think.. :) )


>>I do have a question for you Art,  is the involute curve the same at the small pitch end of a tooth as it is at the large end?  By this I am asking if one profile form can make the correct shape for the entire tooth with varying pitch?

   No. Thats the problem, since the diamter of the pitch changes, ( and the base circle), a proper involute changes over the length of the face. Unless I use a parrallel machined bevel.. which is possible but weakens the teeth..


>>If a form cutter can be made to cut the small pitch end and the angle of the gear set to cut the widening tooth any pitch strait tooth could be made with a formed fly cutter or a formed endmill.  The spiral teeth would require a formed endmill.

      A formed cutter doesnt help much with a proper bevel.. as far as I can see.. The involutes would be deformed across the length of the face..

 
    Zeroing and such I sont think will be a problem.. its more of a question of intuitive ness to ensure peopel can zero simply and easily.. I guess thats one that can be worked on when we're cutting to make sure people are happy.. pretty easily changed anyway I think..


 Thx

ARt



Title: Re: Machining Bevels.
Post by: BobL on December 24, 2010, 08:51:07 AM
Hi Guy's;

 So is this the new standard method we will be using?

Y - touch off on both sides of the blank and take half the measureme nt to get on the centre line.

Z - touch off on the top outer edge as this is the highest point, rememberi ng that the pitch angle will be the one you set up on.

X, - touch off on outer edge


Cheers
Bob


Title: Re: Machining Bevels.
Post by: Chuck on December 24, 2010, 01:20:55 PM
Art,

Sorry but I am thinking in terms of the non generatin g bevel gear shappers.  But if the involute curve changes from small pitch to large pitch then ALL my formed cutter ideas are crap.  As I knew, bevels are a whole different beast than strait spurs.... .with endless variation s!

How about a tapered endmill and 4 axis? or do we call it 4.5 axis setup for the pitch angel.  I have a nice Gcode program to make tapered endmills with a specific angle and tip width.


While trying to educate myself I found a few links to industry standard processes and equipment:

Straight Tooth Bevel Gears
Google books:
http://books.google.com/books?id=6PE0jZZ-nr0C&pg=PA445&dq=bevel+gear+shaper&hl=en&ei=OOIUTeKhNcOB8gay6cSyDg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCkQ6AEwADge#v=onepage&q=bevel%20gear%20shaper&f=false

http://books.google.com/books?id=U7ZKAAAAMAAJ&pg=PA328&dq=bevel+gear+shaper&hl=en&ei=6d8UTYqFE8P88Aa434T7DA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC8Q6AEwADgU#v=onepage&q=bevel%20gear%20shaper&f=false

http://www.youtube.com/watch?v=Adi0GgUc2Z4
http://www.youtube.com/watch?v=hvDO7t8h_sI
http://www.youtube.com/watch?v=LEvpy66AqWA
http://www.youtube.com/watch?v=8H-FDtDMfMg
http://www.youtube.com/watch?v=ul9wCexWlXM

Spirals
http://www.youtube.com/watch?v=0whwtairKOI

And nothing to do with gears but still cool: (state of the art 1860)
http://www.youtube.com/watch?v=SW1JFaFWtKI
http://www.youtube.com/watch?v=VLZHV3v_FIo


Title: Re: Machining Bevels.
Post by: ArtF on December 24, 2010, 02:00:40 PM
Hi Chuck:

    Thx fer the links, I'll browse them over the holidays.

 Im not sure a taper adds much capabilit y, sounds like it'd perhaps make the math worse..
but Ill dwell on it. I think an endmill should suffice for the first iteration s.. we'll see how they look
and go from there, there are several ways to skin this cat I think, obviously though its a complex
thing, you dont see homemade bevels very often..un less their basically engraved, and thats pretty slow. :)

Have a good XMas..

Art


Title: Re: Machining Bevels.
Post by: Chuck on December 25, 2010, 12:32:58 AM
Art,

The tapered endmill would allow you to cut the small pitch teeth.  It would let you get to the tooth root without undercutt ing the sides.  The taper makes the mill MUCH stronger for the size of cut.  I don't think the math will get much worse.  You wouldn't be able to use G42/43 offsets, but for computed paths would you use G42/43 anyway.

The tapered endmill would allow CNC to replicate  the generated octoical tooth form of bevel gear machines for strait and spiral bevels.

Have you looked at octoical bevel tooth forms?  This is the common tooth for for generated bevel gear shaper machines like Fellows and Bilgram.  This form should be much easier to generate than involute for bevels.

More REALLY GOOD light reading ( a few thousand pages) from Google scanned machine shop books:

The last 1/2 of this book is really good.
http://books.google.com/books?id=icxKAAAAMAAJ

Good theory and descripti on of octoical bevel tooth forms
"AMERICAN MACHINIST GEAR BOOK"
http://books.google.com/books?id=339syGI6JW0C&pg=PA9

http://books.google.com/books?id=O7dKAAAAMAAJ

http://books.google.com/books?id=Y1ZJAAAAMAAJ

http://books.google.com/books?id=U7ZKAAAAMAAJ

Lots of theory and math:
http://books.google.com/books?id=0KVBAAAAIAAJ

http://books.google.com/books?id=aLVKAAAAMAAJ

There are more but these are all I have looked through and selected as relevant over the last 2 days of speed reading.

Chuck


Title: Re: Machining Bevels.
Post by: ArtF on December 26, 2010, 12:49:51 PM
Hi Guys:

  Chuck just had a great idea offlist.. How about we agree to machine bevels with the 4th axis tilted only to 45 degrees. This effective ly splits the differenc e of troubleso me angles bringing them to a level where we can probably do them all.. and its a much easier thing to arrange.

   This means one could find a setup or adjustmen t that puts their tabel to 45 degrees and know the code is OK for that gear. Otherwise we'll be trying to angle to things liek 23.1254 degrees ..the numbers will rarely be integer..

   By tilting to 45, the worst bevels at 89.99 degrees become 45 degree to the code, much easier to cut.. and lower bevels like 45 degrees, become straight cuts..  lower become upward cuts.. downside being a probable
code modificat ion to cut from the other direction to eliminate plunge problems with an endmill..

  This is handy because statistic ally most bevels will fall between 20 and 70 degrees meaning the normal cut angle will range from upcutting at 25 degrees to downcutti ng at 25 degrees. Its very likley we can do all types with that small a variation in angle... at least in my head at the moment, Im still visualizi ng.... .. :)

    It DOES also mean that I can do the fractiona l angling internall y so youd only have to worry about making your 4th angle to exactly 45 degrees for any bevel gear.

  Anyone see a probalem with this compromis e solution?  John? Anyone? :-)

  I think Ill start to do the code on this .. so yell if you see a pitfall..

Art


Title: Re: Machining Bevels.
Post by: John S on December 26, 2010, 01:33:03 PM
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.


Title: Re: Machining Bevels.
Post by: Dan on December 26, 2010, 02:53:32 PM
Good idea! If it is doable code-wise and you can do any bevel angle this way - go for it!

Dan


Title: Re: Machining Bevels.
Post by: Dan on December 26, 2010, 02:55:43 PM
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.


Hi John,

Would be nice if you could share your experienc e in making these. They are not cheap to buy.

Dan


Title: Re: Machining Bevels.
Post by: Chuck on December 26, 2010, 03:52:23 PM
Dan,

The small engraving carbide cutters are about $2US each on ebay.

For larger pitch a strait endmill will probably be best but won't do the gears down to 80DP I want.

look on ebay the taper endmills and engraving bits are sold by taper and tip diameter. ...the stock angles we are likely to use are 20, 30, 45 and 60 degrees included angle.  A 20 (or maybe 22.5) degree pressure angle should work well with the 45 cutters but 30 should do any pressure angel we see on bevels.

If Art gets the bevels working with taper cutters maybe he can go back and work on spur gears with taper endmills. Then the 4 axis spurs can also be cut down to 80DP..... ..Art??

http://cgi.ebay.com/10-PCS-CNC-Router-Carbide-PCB-Engraving-Bits-30-0-5mm-/180604601886?pt=LH_DefaultDomain_0&hash=item2a0cdf861e

Chuck in Wyoming


Title: Re: Machining Bevels.
Post by: ArtF on December 26, 2010, 04:29:43 PM
Chuck:


  Other than the Z suface modifcati ons the bevel Gcode source will be very close to the spur gear source. (In fact Im starting from an exact copy and mofiying it to do bevels. So while Im doing that, I will find a tapering hook and see if I can add tool taper to the mix. If it works, Ill port it back to spurs.

Art


Title: Re: Machining Bevels.
Post by: Dan on December 27, 2010, 02:45:30 AM
Hi Chuck,

Actually engraving bits never came to mind. When I thought about tapered end mills I was meaning these: http://www.menlo-usa.com/catalog/ProductDetail.aspx?pid=242

Thanks for another good idea. However, they are good for very fine gears, but not for something more substanti al like a 1.5 module gear. The tip radius is too small and they are too weak to take any real cut - compared to the real tapered end mills. But still probably better than using a plain tiny end mill....

Dan


Title: Re: Machining Bevels.
Post by: Chuck on December 27, 2010, 01:18:15 PM
Dan,

I will make you a deal,  when Art gets the taper end mills working I will write and post a program to generate Gcode to make any 1, 2 or 4 flute taper mills.  What I have now is code to make strait flutes but can add code to do spirals too.  Strait cut flutes have a much higher cutting load than spirals.

I use a setup on my 4 axis mill with a Dremel grinder and diamond wheel to make carbide taper endmills.  You could use hardening stock and an endmill, or hard drill rod or carbide and a grinding wheel.

The first gears I made this way was back in 1974 with an early Fortran version of the "one tooth hobbing" program I posted in 3rd party programs on this forum.

Chuck


Title: Re: Machining Bevels.
Post by: Dan on December 27, 2010, 01:38:44 PM
Very interesti ng, Chuck!!! Would be nice to be able to grind taper end mills from carbide stock.

Dan


Title: Re: Machining Bevels.
Post by: ArtF on January 08, 2011, 02:46:05 PM
Hi Guys:

  Just a status report..

 Ive learned quite a bit about the math of making a bevel with involute shaving, but still havent managed to complete the algorithm s to cut them. I can see trouble though..

   When we create a helical or spur on the 4th axis, we do it by tangental shaving. This means we take a point on the involute curve of the tooth, and rotate it till its tangent to the Z axis ( the tool). Since its tangent to the tool we're OK to make a pass which will shave only points above that involute tangent point..
( Hard to visualize I know..).

   Our problem with bevels is that tilted gears do not change tangent at the same rate as a spur.They rotate their tangent at a ratio of 180 - 2*PitchCone angle / 180 . This means some bevels never hit a tangent point
during their rotation, others have to be rotated to a involute angle times the ratio above.

   What this all means is the amount of involute angle for a tooth is limited by the above ratio ,
so as the gear increases its pitchcone angle, the amount of rotation of the toolpath necessary
 to get to a shaving point increases . When it hits 90 degrees your ususally hosed.

 The best way to picture this is to picture a 90 degree bevel pitchcone gear.
 This is a gear laying totally flat. It has no angle. Its teeth go straight in to center. Obviously,
there is no rotationa l position that will make those teeth go tangent to the Z axis. The involute tangents
 point the same direction in any rotationa l angle of the gear.   The other extreme
is the 0 degree bevel, ( a normal spur gear ), where we'd have no trouble as the tangent rotationa l angle is equal to the
involute angle for the point in question. Since the involute angle on  a gear never goes as high as 90, the rotation that
has to be done is always less than 90 degrees. But in a 20 degree pitchcone angle, for example, you need to rotate the gear almost 180 degrees. ( cutting the gear on its back face).

   The numbers tell me that 90 degree pitchcone angles are impossibl e, while 0 degrees are easily done. Basically
all bevels fall within the two extremes. Whether a bevel is possible or impossibl e then, falls to a certain amount
of variables that affect the end max involute angle.. Tooth count is important as the lower the tooth count the
higher the involute angles are, thus limiting the amount of pitchcone that can be cut. The higher the tooth count the
more easily it CAN be cut, but the larger the gear. ( A limitatio n for most of us based on rotary table size. )

 John Stevenson, who is annoying correct almost always, was also correct in his assumptio n that tilting to the pitchcone
angle ( thus making the tooth pitchline flat at the top of the table ), would make the calculati ons easier. In fact tilting to
an arbitrary degree such as 45 degree's, makes the calculati ons near impossibl e. By tilting to a straight pitchline Ive managed to
create several routines that check the numbers for me that prove out the above statement s on limitatio n of tangental angles
based on toothcoun t , gear diameter, and pitchcone angle.


  Sooo.. Im starting a third iteration of the code. ( Not unusual for me to go through several iteration s on complex algorithm s as each
try teaches a valuable lesson in getting your mind in the right frame of 3d referance . :) Im still convinced its possible, but with limitatio ns
as to what gears can and cannot be cut. Ill need to implement some calculato r to auto figure out if we can cut this on a 4th axis or not.
If nothing else it explains to me why no-one else does this in the context of a 4 axis mill. ( That 5th axis would certainly come in handy here. :)


Just a status update as to why Ive been pretty quiet.

Art


Title: Re: Machining Bevels.
Post by: John S on January 08, 2011, 07:09:41 PM
Art, Gert says annoying yes, always correct no....... ......... .

John S.


Title: Re: Machining Bevels.
Post by: tweakie on January 09, 2011, 04:08:04 AM
Hi Art,

Looks like you have been doing an awful lot of work on this over the holidays when you should have been enjoying the break.

Totally impractic al I know but wouldn't it be nice to have a rotary mounted on a rotary ?    ;D ;D

Tweakie.


Title: Re: Machining Bevels.
Post by: ArtF on January 09, 2011, 09:40:37 AM
Ive thought o the same thing.. :) I kinda doubt it'd fit on my table. :)

 Also, the math would be horrendou s I suspect. lol

Art


Title: Re: Machining Bevels.
Post by: Chuck on January 10, 2011, 09:33:10 PM
Art,

Thanks for all your hard work...

For the gears with teeth near 90 degrees you always have 3D ball milling to fall back on.  Much easier to calculate too but take longer to machine with lots of fussy little passes.

I tried some graphic 3D modeling to try to visualize the problem with gear on 45 rotated A axis and while I know I can do it, my first attempt failed.  A bit like your first 2 efforts at 4 axis tool path generatio n.

But you are totally correct on the limitatio ns of 4 axis bevels near 90!  Tapered endmills will get you farther but even they have a limit.

Solving this with trigonome try may not be the best solution. Even if it looks like the most direct path.

Chuck


Title: Re: Machining Bevels.
Post by: ArtF on January 10, 2011, 11:19:38 PM
Chuck:

 Actually, Ive managed to reduce the trig to a few simple equations . I think this next try will work. It isnt bad once I got past a few bad assumptio ns. I suspect the limitatio n will mean as the bevel angle falls towards zero the involute will degrade to a gleason gear type of pressure angle side. At least the math seems to indicate it will. Thats not necessari ly a bad thing, and low degree bevels that have a pressure angled side will likely roll fine on the pinions conjugate s.. at least thats what Im hoping. This is one of those ones that only testing will tell. Ive made it so the hooks are in place for me to more easily add the zerol and helical aspects once the straight flutes prove out one way or the other. Only testing will tell me more. As soon as Ive cut one wheel and one pinion that mesh, Ill release a version with that code and begin to add the helicals while more testing gets done. I dont dare release a code version till I see physicall y what the results are.. Testing is a pain due to blanking requireme nts, but Im using styrofoam, so its much less painfull when I screw up. :)   ( pink styro insulatio n makes an easy blank that shows the path well.. )

  I figure a few more days and Ill know how it will all work, the tangent angles I can now compute with some certainty, its all a matter of IF its physicall y possible now.. :)

   Your right that we could fall back to ball milling, but I dont like that solution at all, way too slow...an d nasty to clean up..

Art




Title: Re: Machining Bevels.
Post by: Archie on May 23, 2011, 06:35:16 PM
Art et al,

I am new to this forum, but am intereste d in gear making. If this discussio n has continued in a different topic, please let me know.

I have a long-lead-time (almost a year) project restoring a 99-year-old Lucas horizonta l boring mill -- I hope to have it running in time for its 100th birthday. One aspect of this is replaceme nt of a pair of 25-tooth miter gears, 5" pitch diameter, with a 5 diametral pitch at the big end of the teeth -- straight teeth. A young student volunteer ed to cut these gears using 3-axis contourin g (ball end mill) and is working on generatin g the tool paths. I was referred to this forum and find it to be very interesti ng. At risk of being out of touch with the current state of the bevel gear cutting project, I would like to "join the party".

I am impressed after an initial study of your approach, that cutting gears with 4-axis contourin g, cutting with the side of an end mill tangent to the involute is a good approach -- far better than using a ball end mill. I also am keen on the idea of using a tapered end mill, noting that this has already been discussed . The one thing I can add is the idea of using a ball end tapered end mill, which would allow cutting a full-radius root in one setup. I would not minimize the gain of rigidity (allowing greater chip loads) gained with a tapered end mill -- when it comes to cutting real gears in steel, the time saved would be a major gain.

 I would like to help address the stated problem of accessing all possible pitch cone varieties . I think I understan d it right that you are rolling the gear to accomplis h keeping the cutter edge tangent to the involute. I am glad to hear that this works well with spur & helical gears because I have thought that it might be a good approach. I see how it can become a problem with the size of the involute varying along the length of the tooth of a bevel gear. I do not think I have a clear answer to this problem, but I am intereste d in being a part of seeking one if that is appropria te. I have been thinking about a set tool paths implied by the antique machines developed for bevel gear planing -- the "nut" of this is that all the lines along the pitch cone (as well as the addendum & dedendum cones) all intersect at the same point. It seems to me that a set of tool paths based on a single common point and the involute form at the "big end" of the tooth might be a starting point for generatin g the 4-axis tool paths.

Pardon me if this does not make sense -- it definitel y is a "half-baked" concept.

Archie


Title: Re: Machining Bevels.
Post by: ArtF on May 23, 2011, 07:59:01 PM
Archie:

   Thats basically how the current flawed bevel code works. I say its flawed because it needs more work. I have sucessful ly cut mating gears with it, BUT, others havent. Some of that is due to blank variation s between us, and zeroign differenc es. The current code is close, but not absolute. I neglected to bend the vitual gears tooth properly around the blanks angles, but that having been said, the gears I cut look pretty good. I used exactly as you described . I find a point rotated so that its tangent on the virtual face, then sweep it toward the apex of the blank, with the theory that all paths converge.

   I havent found anything wrong with that theory.  I do know though that on the last pass or two of the involute, the tool just misses the edge, tellign me the math isnt quite right. Also I feel the root clearing is wrong due to using the wrong root diameter during the calcs.. ( the root diamter of the vurtual rather than the rotating blank..).

   I hope to revisit this soon, its a rarely done thing mainly due to the complexit y of setup..

     Also, Id like to analyse just how far off the involutes woudl be if I tilted the blank to the root angle, ( allowing for a straigth sweep ) and used a tool which is involute to the outer tooth to sweep to apex. Since the cutter woudl be using a lower and lower spot on the involute bit to do the forward tooths path, its quite possible the involute would be close to spot on along the tooths path.. Thought experimen ts show me the involute would get shallower as the tooth goes to center.. and I suspect the effect is very close or exactly what a shrinking base circle would call for... 

    So my thinking is that contrary to intuitive thinking. .a single involute bit on a straight path on a blank tilted to root angle, woudl give a good bevel gear.

 As to tapered bits, Im conflicte d. TO use one properly you have to compute a tangental derivativ e to make sure the tangental shave is ( and can be ) done at the tapered angle.. Im not sure how much of a pandora's box that implies in the math..



Art


Title: Re: Machining Bevels.
Post by: John S on May 24, 2011, 02:49:33 AM
Art,
On the tapered bits what about sticking to the PA for the gear in question?

Instead of the punter telling you what bit they have and making you jump thru hoops to use it then they have to use the PA of the gear.
Long short is they have a choice, source or make the cutter or use a normal end mill with the size limitatio ns.

John S.



Title: Re: Machining Bevels.
Post by: ArtF on May 24, 2011, 07:11:14 AM
John:

   You know, I havent done any of the math involved .. I suppose its intuitive that if a taper is the PA
then the shaving would always work... BUT.. Im not 100% sure of that. While the PA is the differenc e between
the tangent of a point on the tooth and a radial tangent.. .Im not sure that means that a taper of the PA would
always work in those terms. Id think the length of the tooths involute may be an important considera tion..
...
...
   quickly drawing it out on paper seems to work ..the Y offset simply needs to be adjusted to the angle of the taper
creating a tilted view of the tangental plane.. ( I say simply.. not sure how that translate s.. :) )

   Hmm.. Requires more thought. When you do tangental shaving, the bottom of the endmill ( a straight flute) matches the
bottom of the involute on first shave.. the point of contact then shifts upwards on the tool as you shave higher in the involute. .
BUT in tapered endmills, the first contact point would by ncessity be higher on the tool.. looks linked ot the taper angle as to how high
up the bit.. this makes issues with possible root contamina tion.. 

Lets remember that the initial portion of an involute is almost straight up.. as it goes up it tilts more and more ( involutes ) outwards. . So while the PA affects the involutes point by point tilt, theres no guarantee that even a PA taper woudl fit
on the initital portion of an involute. . unless Im missing something ..

   Again, quickly analysing it on paper. ( perhaps too quickly ), a PA taper may or may not cut off higher area's of the involute. Im not 100% sure of this but it certainly has that feel to it..

 Ill give it some thought. Im separatin g the tooth data now in an effort to see if perhaps I can generate a tool form for involutes, timing pulleys and perhaps.. bevels.

  For bevels Im of the opinion that perhaps a thinned involute bit that has a thin width of just the involute may be able to be swathed back and forth in its path to create the bevel.. For the others, a full tooth form would allow a quick cut of the tooth. 


   Ill let you know as I get there what problems remain.


If you figure Im wrong on the above, let me know. Draw it out and see what it looks like to you, Im going almost solely on intuition here..


Art


  This is hard to explain..
   


Title: Re: Machining Bevels.
Post by: Archie on May 24, 2011, 05:45:21 PM
Art,

I need to get up to speed and catch up with all that has been discussed already, but there are a few things I could not find that were not discussed, or at least not resolved. I hope my "learning curve" does not cause too much of a distracti on -- I would restrict myself to "lurking" if I did not think I had something to contribut e to the discussio n. I will limit myself to one item per post so as to not get things confused.

One issue I am still consideri ng is the form of the prototype involute takes when spur gear theory is transform ed into the realm of bevel gears. In spur gears, one starts with a base circle and unwraps the "string" with the string, and hence the involute generated, lying in the same plane as the base circle. This is not necessari ly the case with a bevel gear where there are at least three possibili ties (this planar case and two others):

o The involute lies on a plane perpendic ular to one of the many lines through the common point of the cones. It seems that a good choice would be the line intersect ing the pitch circle and the involute. This is the simplest but the choice of which perpendic ular line to use still seems arbitrary to me.

o The involute lies on the "back cone" of the bevel gear. This cone is defined by straight lines are all perpendic ular to the pitch circle lines mentioned above. The back cone is a convenien ce for fabricati ng the blank, but there is one more option;

o Sometimes gear blanks are fabricate d with a "back sphere" that is centered on the common point of the cones, using a radius defined by the intersect ion of the pitch circle with the involute. This one seems most logical to me.

I did not originate this line of thought -- it was in one of the ancient gear theory books on google.bo oks. The bottom line is to determine if there is enough differenc e to need to worry about this and both the original thinker and my own thinking comes out that this becomes unimporta nt for most practical gears. The more teeth on the gear, the less the differenc e between these ways to construct the master involute is. I ran the numbers for my 25-tooth gears and the differenc es were negligibl e.

The bottom line of all this is that one should be able to use an involute construct ed on a plane when working with a bevel gear, but I am still not certain if there is a better choice than making the plane perpendic ular to a line through the pitch circle's intersect ion with the involute. The extreme choices of the base circle, addendum circle, or dedendum circle all would tend to distort the involute more.

If this is what you are referring to when you stated: " . . . bend the vitual gears tooth properly around the blanks angles . . . ", then I think you are making a reasonabl e approxima tion, unless the number of teeth gets very small.

Archie


Title: Re: Machining Bevels.
Post by: John S on May 24, 2011, 06:24:05 PM
Doing spur gears using a tapered cutter of the same PA is simple to understan d as it's just one tooth space as generated by the Sunderlan d 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.

(http://www.stevenson-engineers.co.uk/files/sunderland1.jpg)

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

Transpose d 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 horizonta l 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 increasin g 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 (http://gearotic.com/ESW/FavIcons/index.php?topic=131.0)

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

John S.


Title: Re: Machining Bevels.
Post by: ArtF on May 24, 2011, 09:07:05 PM
>>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.


  Actually, it stays at a Z = the base circle depth at 0 degrees. Since the blank is rolling, this depth allows the involute to shave on the end mill, always from the bottom of the mill upwards.. No Z is done anymore, though originall y it did, and that was found to be in error.

  In bevels I have to move Z as the rotation of the blank drops the tangental point that we shave at..

  As to the bevels, the tooth is a tooth from a virtual gear on the back plane of the tooth on the bevel. When I spoke of rounding that tooth it was to form it to the bevel blank. ( not really necessary I think..).

   In normal spur, the depth is set to base circle because if dropped deeper, it will cut into the opposing face depending on the gear.. At base circle it will not. For a bevel its a case of the involute changing as John said.. but since the base circle drops in proportio n to the DP increase, I suspect the same involute curve will cut the proper form front to back..

 ( this is all hard to explain without drawings I guess..bu t its damn hard to draw as well.:) )

Art


   


Title: Re: Machining Bevels.
Post by: John S on May 25, 2011, 03:15:55 AM

   In normal spur, the depth is set to base circle because if dropped deeper, it will cut into the opposing face depending on the gear.. At base circle it will not. For a bevel its a case of the involute changing as John said.. but since the base circle drops in proportio n to the DP increase, I suspect the same involute curve will cut the proper form front to back..

 ( this is all hard to explain without drawings I guess..bu t its damn hard to draw as well.:) )

Art
   

So if the bevel blank is tilted to the base angle this makes the base circle horizonta l and no further Z movement is needed ?

I really need this scan of the bevel I sent into the universit y - let me make a phone call.

Anybody got an accurate 3D of a bevel ?

John S.


Title: Re: Machining Bevels.
Post by: ArtF on May 25, 2011, 07:04:54 AM
John:

  No. In a bevel , the base circle changes over the run of the X axis.. AND the blank is rotating on an angle, so the two condition s impose
a Z motion no matter what..

   My thought on tilt of a bevel is that it should be tilted to the dedendum angle. The only real advanatag e to that is that no
Z motion is required for the centerlin e pass.

 
Art


Title: Re: Machining Bevels.
Post by: ArtF on May 25, 2011, 07:06:53 AM
If you do get a 3d scan of a real bevel,,send it to me, Id love to see the true proportio ns of angle they use.
Specs dont really show me.. all I read mostly is process and your left to deduce the reality from the process,
something that sometimes makes you miss it in reality.. .

Art


Title: Re: Machining Bevels.
Post by: John S on May 25, 2011, 07:23:57 AM
Rang them up and bollocked them, they had forgotten to do it.
Hopefully they will get time later today to get it on the 3D scanner.

John S.


Title: Re: Machining Bevels.
Post by: ArtF on May 30, 2011, 06:26:47 AM
Hi Guys:

 Just for clarity on the bevel issue, I thought Id post a couple notes..

 First.. I did get a 3d scan of a bevel from John for compariso n, and as I had planned in GM, a bevel tooths involute as it travels towards the cone is a scaling
of the original tooth. In other words you start with a normal involute tooth, and as it approache s the cones apex, it scales to zero. If the tooth travels 50% of the way towards the apex, the tooth is exactly 50% in proportio n to the original tooth.

   This makes sense in the math involved and is intuitive in nature as well. This is just to clarify exactly what happens to a bevels involute over the facewidth .

Sometimes, when we talk about tapers, we are speaking cross purposes. John sent me some video links to variosu bevel gear machines doign their thing. The tools often are tapered in such operation s..BUT its a different process.

 I include two photos to try to illustrat e the differenc e. The first photo is showing how I do a normal 4th axis gear. This is also currently done for bevels.

 The second photo shows how a gleason is using a tyapered tool to do its bevel tooth.
It does use a taper.. seemingly at 1/2 PA to do its cut. This is done ( I think) because the gleason is maching many more points than GM over the tooth. In the forst photo Ive cut the sequence to 3 examples, GM actually does about 8-10 normally.

  The gleason does many more depending on the tooth size, but probably every .05 inches or so through the length of the tooth. It uses a taper both for strength and also to "round off" the errors involved in moving from point to point by angling the cut to meet the next point.

  The two methods are not the same in terms of what they are trying to do. Using a taper in GM's methods woudl help in that the strength of the tool woudl be better,
but the math would be a bit more involved as youd have to rotate the tooth more to connect to the tapered tool on a shaving tangent.

   It would be possible to do a bevel the same way as photo #2, but the number of passes would be MUCH higher and take MUCH longer than current methods.


  John: This is only a clarifica tion of my understan ding of the processes . Correct me if Im wrong.. There is of course a dual cutter in some videos, but that appears to simply cut both sides of a tooth for faster end result.




Title: Re: Machining Bevels.
Post by: John S on May 30, 2011, 01:53:25 PM
Nearly Oh Master.

What I was proposing is halfway between what you have come up with, still do the shaving but with the tapered cutter for strength.

Excuse the bad pic, I had to scan yours and alter it by rotating the blank 1/2 the PA

(http://www.stevenson-engineers.co.uk/files/bevel%20taper.BMP)

Does this make sense ?

John S.


Title: Re: Machining Bevels.
Post by: Archie on May 30, 2011, 02:38:33 PM
Art & John,

I agree with Art's descripti on of how the involutes of bevel gears change along the length of the tooth, I am puzzled by the statement: " . . . seemingly at 1/2 PA . . . ". In one of my reference s, the orientati on of the Gleason tool is stated to be: " . . . so that its cutting edge coincides with the plane of one of the teeth of the crown gear . . ." (When generatin g bevel gears, the crown gear replaces the rack used in generatin g spur gears.) This agrees with my understan ding that the cutting edge of generatin g process is set at the pressure angle of the gear to be cut.

Regarding how the tool moves along the tooth, in most, if not all, of the generatin g processes, the rack-shaped cutting edge "rolls" along the face of the tooth being cut, distribut ing wear along the tool's edge. (I put "rolls" in quotes, because there actually is a small amount of slip in the meshing of involutes, but rolling is the majority of the action.) I understan d that the approach in GM is not bound to the motions used in mechanica l generatio n of involutes, but in practice it is very nice to distribut e the cutting action in more than a small area of the tool.

Archie


Title: Re: Machining Bevels.
Post by: Chuck on May 30, 2011, 07:42:11 PM
Art, John and Archie,

Art's lifting pass is NOT the generatin g method used.  John and Archie are on track, I would add that a shaper cut  tooth is formed by a cutter on each side of the rack tooth that is split and mounted on a tapered slide.  The tapered slide forms the cone of the bevel and the gear is rotated and moved by the shaper as if it was a thin rack tooth.  The machine then takes care of the involute generatio n.

Art, just keep the pitch cone center point aligned with the tool path offset at tool edge and move the rack tooth past it to generate the gear.   By keeping a point on the pitch diameter of an imaginary crown gear in constant synchroni zed motion with an imaginary rack tooth. Then rotate and adjust the path to keep the offset surface of the cutter on a line to the gear pitch center point.  If the cutter is rack tooth form of the desired involute the generatio n is automatic, you just have to rotate and align the gear with the cutter.

Look at this gear shaper video:

http://www.youtube.com/watch?v=Adi0GgUc2Z4&feature=related

Chuck


Title: Re: Machining Bevels.
Post by: ArtF on May 30, 2011, 08:02:39 PM
Hi Guys:

  I suspect in some instances we're talking the same thing..in others Ive been off track from what your speaking of..

 In essence, the current bevel code does a shaving..

     That last video is a bit confusing to me.. ignoring that there are two cutters.. just consideri ng one..

 The taper appears to be straight to apex as I's expect.. the gear can't rotate while that tooth is cut.. so I assume the tapered slide moves outwards to create the involute? I mean is has to have the cutters further apart duing root as opposed to tip right? Id love to see that machien myself to see exactly what moves..

  I think I understan d the process, but the machine confuses me on that point. Doesnt clearly show it..

 John:
     Yes, I think what your describin g is possible. . an adjustmen t to the math is required of course for the taper.. But if the taper is set at the PA.. then if I simply act as if its a rack... and roll it along the tooth each pass it should work fine. The current spur gear is bascially doing that by rolling the gear till its equal to the pressure angle on a straight flute bit. Id roll it different ly to match the taper..
( in your drawing ..the taper shoudl be at the same depth on each pass..sim ulating a rolling rack? )

Archie: Current spur cutting involute keeps the depth static, so a differing part of the tool IS used during form cutting..)

Might be possible to simply compute the diference in roll angle to match any taper bit..

Art


Title: Re: Machining Bevels.
Post by: Archie on May 30, 2011, 08:51:42 PM
Art,

Gleason's use of a double cutter is a very inexpensi ve way to double productio n. It cuts two tooth faces for the price of one and since the tool shape is simple, the cost is low. In the case of a rotating cutter, a double spindle machine would be necessary and, because the two spindles would have to be very close together, this would be difficult or expensive to accomplis h. Just ignore the second cutter for your purposes.

When you mention the "root angle", are you perhaps thinking of the base circle of the involute? At the point where the involute intersect s the baser circle of the involute, the involute is radial and then, as it moves out, the involute "bends over". One issue is how GM defines the tooth profile in cases where the working depth of the tooth profile exists inside the base circle. Form cutters "cheat" and use a cycloid form in the tips and roots, while using an involute for most of the working tooth in between. Generated gears with small numbers of teeth have an undercut generated by the interfere nce of the tips of the teeth when they operate below the base circle. I suggest that for most gears with PA's of 20 or more and larger numbers of teeth this is not an issue, although it will have to be addressed for 14-1/2 PA gears and pinions of any PA.

In order to understan d the generatio n of a straight-toothed bevel gear, the key is to see that a crown gear replaces the rack as the generatin g form. The crown gear has planar teeth(!) -- just as a rack is a degenerat e involute form that has planar tooth profiles, so is the crown gear. You may wonder how a crown gear can have lines that intersect at the common point of the cone, just observe that the lines that meet at the common point all lie on the surface of a cone that has degenerat ed into a plane. The tapered involute gear teeth of the gear being generated rolls its form on the planar surface of the crown gear. I'll see if I can find a decent graphic that shows this clearly -- if I have to make it myself, there may be a slight delay. (If someone beats me to it, my feelings will not be hurt . . .)

Archie


Title: Re: Machining Bevels.
Post by: John S on May 30, 2011, 08:57:46 PM
When we say root angle and base angle i think we are talking the same, quite a few post back I said cut on the base angle so no Z movement was needed.

John S.


Title: Re: Machining Bevels.
Post by: Archie on May 30, 2011, 09:05:34 PM
One more thing:

The Gleason cutters and any approach that is similarly applied to bevel gears must use a tapered form that has a small end that will pass through the small end of the root of the bevel gear. So long as this is the case, the tool, which could be a tapered end mill, will be able to generate the tapered involute tooth form in the same manner as the Gleason (& other) gear planers that is to move a straight-edged cutter in a set of straight line motions as the gear blank is rolled with the involute tooth surface tangent to the plane establish ed by the linear cutting edge and its feed motion.

Archie


Title: Re: Machining Bevels.
Post by: ArtF on May 30, 2011, 09:23:43 PM
Hi Guys:

   Chuck explained this well to me offlist. I hadnt considere d properly a crown gear.. makes perfect sense when Chuck finally beat that into me. :) , I think I understan d what needs to be done now to make it work on a PA tapered bit. Im in the middle of some cutter creation routines, but I may switch to a new bevel Gcode maker using this theory as discussed here. Takes a bit to get your head around it all properly. But I think I have it firmly in head enough to code it. It will mean that cutting a bevel MUST be done with a PA taper as the code ( at least initially ) will be written with that in mind.

>>When you mention the "root angle", are you perhaps thinking of the base circle of the involute?

  No, I meant as opposed to the pitchcone angle vs the tip angle vs the rooth angle. Sometimes called dedendum angle. If tilted to pitchcode, the initial passes are at changing Z.. if tilted to the root angle, the initial passes have no Z motion.

>> At the point where the involute intersect s the baser circle of the involute, the involute is radial and then, as it moves out, the >>involute "bends over". One issue is how GM defines the tooth profile in cases where the working depth of the tooth profile exists inside >>the base circle. Form cutters "cheat" and use a cycloid form in the tips and roots


   The proper method is a trochoida l cut.The trochoid is the shape the edge of a rack will make when rolled under the base .. GM has a dual trochoid generator for low PA's with few teeth. Always best to eliminate undercut, but if it senses one is needed , it generates a trochoid for the root curve. Isnt perfect but does a pretty good job.


Thx
Art



Title: Re: Machining Bevels.
Post by: Archie on May 31, 2011, 05:18:39 AM
Art,

Thanks for your patience regarding the clarifica tions of the cone angles and how tooth profiles inside the base cone are handled. I am glad to see the latter seems to be well under control. Undercut is a problem if significa nt power is being transmitt ed, but there are a lot of cases where this is not an issue and proper undercuts are satisfact ory. In my own primitive investiga tions into using a ball end mill & 3-axis contourin g I avoided undercuts by using a high PA because I thought that this was a necessary simplific ation because that the undercuts could not be machined. I am glad to see that your 4-axis approach handles them.

I realize a crown gear approach will require some re-think, but I think the end result will be well worth the trouble. Not only will the generatio n work properly, but tool life should be higher and total cutting time should be much lower due to the advantage s of the tapered end mill.

Thanks,

Archie


Title: Re: Machining Bevels.
Post by: ArtF on May 31, 2011, 07:01:01 AM
Archie:

   Actually, it's you guys that are owed a thank you. I started this forum for that very reason. As with Mach3 when I began, I was not very knowledga ble in CNC,
the CNC group taught me what I needed to know. Same is happening here.

  Not being an expert on gears, its invaluabl e to have it explained at times. For Spur and bevel, I was generatin g an involute and matching the tool to the curve.. I can see now thats inefficen t , more so in bevels than spurs. I suspect Spur code could be sped up by tapers around 20% or so as the Y motion is the predomina nt saving. Less Y and a bit less rotation will be necessary .

  On bevels, a much larger saving shoudl be able to be done. Not huge in time, but vastly better in complexit y. As an example, my bevels cut so far, ( which do look and run nicely together, are very complex to calculate . An involute is generated, selected point by point, and then rotated on a pitch cone plane increment ally to find a point where the next involute point is above the current one, this indicated a tangental sweet spot and confirms the pass as a proper shaving pass. Very inefficen t, but the only way I could think of at the time. I hadnt considere d crowns at all.. my mistake. :)

   My thanks to all of you..codi ng continues .. :)

Art


Title: Re: Machining Bevels.
Post by: ArtF on June 02, 2011, 10:05:05 AM
OK, I have a quick question. .

  TO use a taper to generate or simulate the Crown gear, is the taper actually double the PA?
Ive never used a tapered bit, but it appears to me the included angle of the PA must be used, that woudl imply
a taper of 40 degrees for a 20 degree gear.. the PA is always at right angles to one side of the rack, so while the
racks sides angle is for example 20 degrees, a taper that makes that rack wouidl be a 40 degree taper would it not?

  This is more a question about the specs of a taper bit, is a 40degree taper , 20 degrees on each side, or is a 20 degree
taper 20 degree's on each side.. Makes a bit of a differenc e in the calculati ons. :)

   I also see that with this method, to be done properly, a double sweep must be performed, that is that the tapered bit must be swept
coming into the tooth from base to root ( if undercut exists ), in order to create a proper trochoid. ( I suspected this ). In all cases it must be swepth from base to tip on the other side.

 see http://www.brockeng.com/mechanism/RackNPinion.htm for an example, watch carefully and you can see the necessity of the sweep below base circle on the opposing side as the rack comes into the tooth. ( again, only necessary if the base diamter is larger than the root diamter.

   I figure you guys know the taper question quicker than I can find the damn spec ..

Art

 

Art


Title: Re: Machining Bevels.
Post by: Archie on June 02, 2011, 11:26:34 AM
Art,

Whether a taper is the angle from the axis or the whole (included) angle can be a source of confusion and different folks prefer one or the other. A direct analog is radius vs diameter: one can measure a diameter directly if the part is round, while a radius is a distance to an imaginary center. If one is working with an arc, then a radius would seem to be the correct term. I recommend not making assumptio ns, but always stating what you are using and asking what the other person is using.

In our case, the tapered tool is replacing the tapered crown gear tooth, so it would be the same half-angle (the pressure angle) and would also be the same included angle. I would expect that most tapered cutters you buy from stock would be specified at the included (whole) angle because it can be measured directly. (When one uses such a tool, it actually only generates a bevel at the half-angle.) If the cutter was expensive I would always confirm that the seller was using the same reference as I was before laying down $$$.

I am not certain that you need to separate the cuts below and above the base circle, but it seems that this is the way you attacked spur and helical gears, so as long as the two paths are stitched together so that the whole working surface of the tooth is cut without lost motion, it should work fine.

(On the other hand . . .) Machines that cut gears by the generatin g process always have some sort of gear train that couples the motion of the tool to the motion of the gear blank. In the case of bevel gear generatio n one can think of this gear train as two cones with infinitel y fine teeth that represent the meshing of an ideal model of the gear to be cut and the crown gear that would mesh with that gear. Because of the high number of teeth, these gears would mesh and rotate with no undercut or interfere nce. If the real gear being cut had a base circle that was above the bottom of the working surface of the gear's teeth, the undercut would automatic ally be cut by the cutting tool edge (near its tip) -- the tool edge would always lie in the extended plane of a tooth face on the crown gear. The end (tip) of the tool edge would always lie on a line which would be an extension of the tip of the same crown gear tooth that the cutter edge was coplanar with. In the case of a tapered end mill, the edge we are discussin g is a line that lies on the cone of the cutter's taper and is where the cutting occurs. I think you could dispense with calculati ng the trochoid, but I am not telling you that this is necessary -- you have already done the work and the computer can handle the work.


Archie


Title: Re: Machining Bevels.
Post by: ArtF on June 02, 2011, 11:43:42 AM
Archie:

  So then to cut a PA 20 gear, the taper would bne a whole angle of 40 degree's if Im correct. ( Just to make sure we're on the same page ).

 As to computing the trochoid, its not a computati on, its actually just what happens when the tip of the rack is under the base circle. BUT, it means in our case, if the base circle IS larger than the root, the cutter must rotate into thew tooth as well as rotate out.

 By that I mean we have always used a mill in spurs to basically go to the edge of a tooth and rotate out.. we then move to the other edge and rotate out in the other direction . In the case where the base circle is larger than the rooth, we have to both rotate the tool into the tooth as well as rotate it out. The rotation in only needs to be done from base circle inwards, as opposed to the rotation out which occurs from base circle outwards.

 
   Anyway.. thats not difficult, its the angle I questione d, I just wanted to make sure.. A taper normally speced at 40 degrees' ( whole ) woudl be necessary to cut a 20PA gear...

Art
 


Title: Re: Machining Bevels.
Post by: Archie on June 02, 2011, 01:57:01 PM
Art,

I think we are on the same page . . . You have control over the model of the tool inside your software -- it is only in the real world that someone might try to cut a 20 PA gear with a 20 included angle cutter. I recommend you call the cutter angle out as: "20-degree angle from tool axis, 40-degree total included angle."

I am glad to hear that you are letting the tool calculate the trochoid. A mechanica l  gear generator does the whole operation by rolling the tool in from the tip of the gear to the root on one side and then rolling out root to tip on the other. This action seems normal to me, but none of my projects requires such motion or much focus on efficienc y. All tool-paths take the tool off the work, so dwell marks should not be a problem.

Archie

P.S.: I am working on getting Windows 7 on my Mac so I can get your software running locally and hence be more aware of what is going on. Thanks for your patience.


Title: Re: Machining Bevels.
Post by: John S on June 02, 2011, 05:29:55 PM
Yup, 40 degrees included, imagine you are using one rack tooth but its rotating as a cutter.

John S.


Title: Re: Machining Bevels.
Post by: ArtF on June 02, 2011, 07:15:49 PM
Good, thats what I figured.. .just wanted to make sure.. I couldnt seem to find any suplliers of 40degree tapered mills.. didnt look hard though..

Art


Title: Re: Machining Bevels.
Post by: Chuck on June 02, 2011, 07:34:10 PM
Art,

You are on track,  I wonder if you will be back to point to point calculati ons on spiral bevels?  The compound angle may mess up the "simple" rack generatio n method when you start rotating the gear. I have been thinking about it and can't get my head screwed up enough to visualize it!  Oh well get the strait cut bevels working and then we can discuss spirals.  I can see how the helical spur gears will work but that is a much simpler setup.


And yes 40 degrees included or 20 per side,  here is a catalog link:
3-Flute 15 deg. Per Side End Cutting Tapered End Mills
http://www.wttool.com/index/page/category/category_id/13820/

Chuck


Title: Re: Machining Bevels.
Post by: Chuck on June 02, 2011, 08:13:37 PM
Looking for 20 degree stock taper endmills.  not much out there!
I have been grinding single flute taper endmills,  I will put together a program to generate the Gcode.

I did find an interesti ng link:
http://www.homemodelenginemachinist.com/index.php?topic=9759.0

Side not I am building a 1/4 scale Shay Loco.

Chuck


Title: Re: Machining Bevels.
Post by: ArtF on June 02, 2011, 09:06:50 PM
Thats kinda what I was concerned about, I didnt see any 40 degree tapers out there.. Though I guess its easy enough to make one..

  However, 30 degree woudl give a 15PA..not too bad I guess..

 As to zerol and spiral bevels, I already made the code to compute the offset angles involved. . ( Helical bevels are quite a bitch to calculate really.. at least the way I do it.. We'll see.

  Im into the code for Bevel2 so we'll see how that works for straight, then Ill hook in the helical generator to see hwo that works, in theory, it shoudl work alraight under all the assumptio ns we discussed .

  Art


Title: Re: Machining Bevels.
Post by: Chuck on June 03, 2011, 09:44:36 AM
Art,

For small pitch we have the engraving tools.  These should work for about 20DP down to about 80DP

http://cgi.ebay.com/5-x-Carbide-PCB-Engraving-CNC-Bit-Router-40-Deg-0-2mm-/130528323178?pt=LH_DefaultDomain_0&hash=item1e6418266a

The stock sizes of 30° are close to 14.5° and the 40° are spot on for 20° pressure angles.

They are easy to make yourself and can be made for larger pitch from 1/8", 1/4", 3/8" or 1/2" drill rod.
With a Gcode generator program we can make any size we want with a 4 axis CNC!  I have made cutters in the lathe by turning them off center for clearance heat treating and grinding a cutting edge rack tooth endmill cutter for 6DP.

A basic spec for the cutter in sizes of 1/8" and 6mm:
http://www.arceurotrade.co.uk/Catalogue/Cutting-Tools/Engraving-Cutters

Chuck


Title: Re: Machining Bevels.
Post by: ArtF on June 07, 2011, 10:58:30 AM
Hi Guys:

    Just a note on the bevels, its taking a bit longer than I would have thought, this isnt because of the difficult y in theory or anything, the theory is working well so far, but Im verifying very carefully the numbers and code Im doing, so its slow going ( but I hate bevels so Im going slowly and accuratel y so I only have to do this once more. :) )

   It looks like I can allow for lower taper values as well, so Im hooking that in as well as I go.
I hope to be able to release some tests soon. ( Just so you know work is progessin g..)

Art


Title: Re: Machining Bevels.
Post by: ArtF on June 23, 2011, 06:21:19 AM
Hi Guys:

   I just completed a simulatio n of the bevel cutting. It seems Ill have to start the shaving rotations a bit earlier as the portion below the pitch is not getting fully shaped. Haveing no real root in the bevel makes it awfully close, but the root isnt being fully shaped by the current zone of rotations Im doing, so an update will come out for that problem.

Art


Title: Re: Machining Bevels.
Post by: DesertRunner on February 23, 2012, 03:48:20 PM
Hi All whats the latest did you get the bevel gears sort so thsy can now be miilled.

Do I understan d correctly that its a issue at 90 degree?
Tony


Title: Re: Machining Bevels.
Post by: ArtF on February 23, 2012, 08:37:45 PM
Tony:

   They are ready to be tested, but Im not setup to do so, so until Ive heard they work, I wont claim they do. Mathmatic ally, they work as best I can test them internall y. The process is to have a blank of proper size, tilt the 4th axis to the requested degree, and use a tapered bit, tapered at the pressure angle of the tooth form selected.
   You cant cut one at 90 degrees, the tangent of 90 degrees may cause math errors in the routines, though to be honest I havent tried one..may work.. Ill have to check. The tooth form on a 90 degree bevel is a rack form..so I dont think Ive allowed it..

Art
 


Title: Re: Machining Bevels.
Post by: Dan on February 24, 2012, 08:57:12 AM
The process is to have a blank of proper size, tilt the 4th axis to the requested degree, and use a tapered bit, tapered at the pressure angle of the tooth form selected.

Is it only restricte d to this kind of a cutter? A straight cutter won't work? And a one having a smaller taper than the pressure angle?

Dan


Title: Re: Machining Bevels.
Post by: ArtF on February 24, 2012, 09:41:53 AM
Dan:

   Lets put it this way.. No matter what pressure angle is selected when designing the bevel, the Code will produce a toothform with a pressure angle
equal to the cutters taper. The code attempts to reproduce a racks motion in cutting, but in bevel fashion, so if you use a straight flute, youll likely get a rack shaped
tooth. Give it a 14 degree taper, and the result should be a 14 degree pressure angled tooth form. So you can really use any tapered bit, closer to PA the better..

   I must admit, its been at least 8 months since I coded it, so while I was an expert on its operation as I wrote it, I'd have to study it now to refamilia rize myself.
Its the problem with bevel code, I cant test it myself properly as I like to do with other types, and its so complex to do that I rapidly forget the exact specifics of the
process. If someone attepts it and gets an error, or unexpecte d reult, Ill revisit the code as necessary to correct trouble.

Thx
Art


Title: Re: Machining Bevels.
Post by: Dan on February 24, 2012, 09:50:51 AM
Thanks, Art. Still not ready to test these either, but as soon as I will, I will let you know.

Dan


Title: Re: Machining Bevels.
Post by: JustinO on August 03, 2012, 03:43:46 AM
Wake up thread!

Did I hear someone say there was a video of a Gearotic bevel gear being machined?

What is the geometry of a machined Gearotic bevel gear?

I am of the opinion that there are two ways to make a bevel gear, the right way, and the possible way.

--Justin


Title: Re: Machining Bevels.
Post by: ArtF on August 03, 2012, 07:55:36 AM
Justin:

 I didnt video my bevels as I cut them. ( I cut mine from foam ), and to my knowledge none has made any on 4th axis, though I know some were 3d printed.
You have to cut the beveled blank at the right angles to actually machine one, and your 4th axis has to tilt to the rigth angle. On my system this severly limits
me as I hit my spindle if I tilt more than a few degree's, so Ive never actually built one with latest code for bevels, though a mathmatic al analysis was done
on the posted files to ensure they "should" work fine. :)

Art


Title: Re: Machining Bevels.
Post by: JustinO on August 03, 2012, 09:47:07 AM
Art,

I've read that the "octoidal" tooth form has been the modern epitome for a long time. I assume that the approxima tions you find in sources such as Ivan Law were trying to stay within error of octoidal while still being economica lly practical . But I don't know for sure. What are you're algorithm s aiming at? Were you shooting for a theoretic ally perfect form, or compatibi lity with what the industry has been approxima ting all these years?

I'm kind of liking the octoidal because the generativ e motions are simple. I don't know if octoidal gears can run with "Machinery's Handbook" bevel gears.

--Justin











Title: Re: Machining Bevels.
Post by: ArtF on August 03, 2012, 10:12:42 AM
Justin:

   The specs of the bevel are as close to proper specs as I can make them, the only thing I am attemptin g is to allow them to be machines with a "simple" 4 axis machine.
They are incredibl y difficult to make which is why few have tried..

Art


Title: Re: Machining Bevels.
Post by: JustinO on August 04, 2012, 12:47:09 AM
Art,
These gears are not correct. I tried to make them with only four axes -- two linear, and two rotary. They mesh nicely, but they're not theoretic al.

Machining bevel gears with only three linear and one rotary axis as you are is a really tough constrain t. The math and or tooling gets tough, it takes longer, etc.

I've got five axes now, three linear, and two rotary. This allows the math and tooling to remain simple and the run time short. But not everyone can be as obsessed and impractic al as I am.

--Justin


Title: Re: Machining Bevels.
Post by: ArtF on August 04, 2012, 07:48:59 AM
Justin:

  Well, they may not be standard, but the only real important thing for any set of gears is that they mesh and work
for the job you intend. Look pretty good for a clock or orery or something . (Looks like the tooth profile needs to be
divided down by the secant to get they tooth profile shorter like in helical gears..)

  They look pretty good though, so if they work, theyt are by deinfitio n perfect. :)

Art


Title: Re: Machining Bevels.
Post by: JustinO on August 04, 2012, 09:05:49 AM
Thanks Art,

They aren't as long-toothed as they look. The way the blanks were cut left the cross sections of the teeth on an angle that exaggerat es their length.

The really cool thing is that when you hold them together and roll them, they almost feel magnetic the way they align to each other - and they roll so smoothly!

There aren't many things as fun as making your own bevel gears.

--Justin


Title: Re: Machining Bevels.
Post by: Ken_Shea on August 04, 2012, 09:59:57 AM
Justin those look great, you by chance take a pic of the set up on your machine?

For some long overdue practice am trying to duplicate your gears in GM.
But am unable to duplicate the look of them when displayed .

What are the D pitch and P angle so I can duplicate them in GM and see what they look like displayed there.?

Thanks
Ken


Title: Re: Machining Bevels.
Post by: JustinO on August 04, 2012, 02:31:48 PM
Ken,

Sorry, no photo of the setup. I'm hoping to make some videos soon.

The gears are just simple miter gears -- 45 degree pitch cone angle. The pressure angle was probably 14.5 degrees but I'm not sure.

Because the setup and method was not correct, the "shift" varied from place to place within the gears, and because I was really just hacking, the shift was probably not correct overall. Also, because the cutter came to a point, it cut a trochoid between the teeth, and because the blank was over generous, the teeth have points. So the teeth may not be reproduci ble with GM. But aside from all that, they should be approachi ng good octoid/involute form.

--Justin


Title: Re: Machining Bevels.
Post by: Ken_Shea on August 04, 2012, 05:47:58 PM
I understan d, from your earlier post I suspected they may not be reproduci ble with in GM and made on the fly so to speak.

Thanks
Ken


Title: Re: Machining Bevels.
Post by: DECLAN MC CLOSKEY on November 18, 2012, 09:49:54 AM
Hi everyone I have newly installed the GM software and am fairly new to gearcutti ng. But I am totally amazed at what the software can do it is a huge credit to everyone involved in designing it!!

I have been looking at all the different gears and the gcodes for them but i cant get any codes for helical bevel or zerol bevel gears when I select the 4th axis option. I get the rapid Z axis codes and the red writing details about the gear.

Can anyone tell me what I am doing wrong? Many thanks in advance.

Regards Declan.


Title: Re: Machining Bevels.
Post by: bosr on November 18, 2012, 01:54:00 PM
Maybe now would be a good time to post a link to the setup procedure s for bevels on the main web site?

Also, when cutting bevels, where do we stand on angled cutters?

Randy


Title: Re: Machining Bevels.
Post by: ArtF on November 18, 2012, 02:37:55 PM
Hi:

    The reason the bevel gears arent fully documente d as to how to do them is they really are untested in many ways. The original code works and had been exemplifi ed, but the new bevel and zerol code isnt. It requires a tool taped to the pressure angle, a blank cut appropria te to the dxf shape thats put out , and the 4th axis tilted to the rigth angle as put out in the code.
( You may get a bad output with no motions if the tool diamter is too large by the way..).

   In the end its so complex to actually cut one that I suspect most wouldnt bothere. I think what I need to put in is a engrave bevel feature where it can be done in 2.5D machining, in raster form , which doesnt produce the best finish but may allow them to be doen much more easily. Thats on my list of todo's in the bevel category. I see them as most usefull as stl's for 3d printing at the moment rather than machining ..

Art


Title: Re: Machining Bevels.
Post by: Damo on December 08, 2013, 02:53:34 AM
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 understan d it is that the bevel gears don't use an involute tooth form, probably for the reason that we've been commentin g 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 determine d 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 undercutt ing. 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 adventuro us 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


Title: Re: Machining Bevels.
Post by: ArtF on December 08, 2013, 08:49:48 AM
 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 originati ng tooth form is a spur gears involute tooth. This is true at least of "straight bevel" gears of both standard and
 gleason type calculati ons. ( 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 nomenclat ure.
 
    I do see where Octoids are the prefered tooth form in making bevels due to ease of manufactu re, 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 understan d 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 commmitte d 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 discussio n is well worthwhil e..
   
    Art
   


Title: Re: Machining Bevels.
Post by: Damo on December 09, 2013, 09:11:57 AM
Hi Art, I agree it's hard to find a definate understan ding of the octoidal tooth form but it is what I have been trying to understan d from reading various papers on the web, but am not exactly sure. Maybe I am not understan ding it correctly, most papers do seem a bit vague but talk about the form being close to an involute. 


Title: Re: Machining Bevels.
Post by: ArtF on December 09, 2013, 10:02:20 AM
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 implemenb t 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


Title: Re: Machining Bevels.
Post by: Damo on December 09, 2013, 05:55:59 PM
It's a very interesti ng subject. I have a need to produces some spiral bevel so will continue investiga ting. What is also worth noting is that in literatur e describin g 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 proportio nally smaller as it approache s the centre axis, to accommoda te ease of manufactu re?

Cheers Damo


Title: Re: Machining Bevels.
Post by: ArtF on December 09, 2013, 09:02:03 PM
>>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


Title: Re: Machining Bevels.
Post by: Damo on December 09, 2013, 10:12:44 PM
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 horizonta l, 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 geometric ally 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



Title: Re: Machining Bevels.
Post by: ArtF on December 09, 2013, 10:32:44 PM
It IS hard to explain.. .near impossibl e 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
..



Title: Re: Machining Bevels.
Post by: Damo on December 10, 2013, 12:19:48 AM
This link is about the best definitio n of an octoidal tooth form that sort of makes sense.

http://books.google.com.au/books?id=IAE5t4OD03YC&pg=PA253&lpg=PA253&dq=octoidal+vs+involute&source=bl&ots=mHykSDR8gO&sig=b28Mfj8V2WpXuIPwC3hmknkPoMM&hl=en&sa=X&ei=haOmUuL4E4WfkAXKk4CoCw&ved=0CEkQ6AEwBDgK#v=onepage&q=octoidal%20vs%20involute&f=false


Title: Re: Machining Bevels.
Post by: Damo on December 10, 2013, 12:36:29 AM
Actually, I like this book, goes into the cutting tool manufactu re in detail.

http://books.google.com.au/books?id=wZpaPKcQZxAC&pg=PT697&lpg=PT697&dq=octoidal+vs+involute&source=bl&ots=eN-tM7kbAd&sig=1eRWxY8froShIFqViarBfY6NmHQ&hl=en&sa=X&ei=haOmUuL4E4WfkAXKk4CoCw&ved=0CGUQ6AEwCTgK#v=onepage&q=octoidal%20vs%20involute&f=false


Title: Re: Machining Bevels.
Post by: ArtF on December 10, 2013, 08:37:21 AM
Damo:

  Heres a photo of an octoidal generatio n. 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 manifista tion 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 spherical ly now a proper octoid? I highly suspect the answer to this is yes. If we consider just the infinitel y 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 modificat ion into that tooth. I would submit its the same process as folding the rack and then generatig n 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 considera tion, 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
 



Title: Re: Machining Bevels.
Post by: Damo on December 10, 2013, 03:30:48 PM
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 microscop ically where the tooth flank is, so so miniscule ly, it's slightly "s" shaped. Would be nice to prove it mathemati cally. And remember this is just the crown gear, not yet bent around a smaller gear. What'd you think?


Title: Re: Machining Bevels.
Post by: Damo on December 10, 2013, 03:53:34 PM
I think all the calculati ons for a stanard involute are correct, just have to do one more function to them. Imagine a spur gear and the flat plane on the side of the spur gear, now all of a sudden that flat plane is spherical? Image the teeth. They are still an involute, just the world they live in is now a sphere. Now imagine 2 spur gears working together on parallel shafts, no imagine the flat plane on the side has become a sphere and the 2 shafts are now at right angles. Gives more meaning to me now of the work spherical involute. :-)


Title: Re: Machining Bevels.
Post by: ArtF on December 10, 2013, 03:59:51 PM
Damo:

   To the first question:   I cant imagine that piece of paper, though Im sure you can. Its the problem with such dicusions, their very hard
to describe in words. To the second comment.. exactly, I think when you take that spur tooth and fold it into a sphere you create a spherical
involute whos pattern of contact is then an octiod if its done correctly . Are mine? Christ only knows. I know they mesh very well, but if they pattern
on a figure 8... beats me.
   When I do finish the non-circ's in GT, I will visit the Gcode generator to add bevels. Since we're speaking only of using a ground cutter for these
the GCode will work fine no matter if we're rigth or wrong..th e entire issue will be the cutter shape.. so we'll see.. :)

  Ill have the Gcode put out so that the blank will have to be tilted to root angle..

Art


Title: Re: Machining Bevels.
Post by: Damo on December 10, 2013, 08:28:52 PM
Hi Art, I tried to draw what I meant. Sort of looks like a potato chip. The line passes through 2 sets of axes at the same angle. From the side it looks like a figure 8. Imagine the rack going around the circumfer ence and 2 opposite tooth flanks are on the surface.
Cheers Damo

Not sure if this will work, am attaching 2 images


Title: Re: Machining Bevels.
Post by: ArtF on December 10, 2013, 08:59:26 PM
I see what you mean, it is a figure 8 on profile..  Im just not sure how that helps me in terms of getting the rigth profile..

 Its interesti ng to note that the specifica tion for the calculati on of the bevel toothform produces a very bad looking curve in the
axial plane..it s only once you fold that to spherical that the curve looks correct as a semi-evolute..

Art


Title: Re: Machining Bevels.
Post by: ArtF on December 10, 2013, 09:08:49 PM
Damo:

 Just found this out there..

>>While gear manufactu ring is well developed, with precision gears cut under
tight tolerance s and producing smooth motions, the geometry of gear meshing
is not yet fully exploited in the industry. For example, bevel gears are
still designed using Tredgold’s approxima tion, under which the tooth profile
is designed so as to yield a projectio n onto the tangent plane of the back cone
that matches the profile of an equivalen t involute spur gear.


  This IS what Im doing. The tooth form IS created to be correct as a typical spur when viewed from the
tangent plane on the back face..

  This link explains how to make the correct  (if thats the correct word) method..
http://www.geometrie.tuwien.ac.at/stachel/Duisburg_Proc.pdf

 
  As you can see, its not something Ill jump into lightly. :)

Art


Title: Re: Machining Bevels.
Post by: Damo on December 12, 2013, 02:11:48 AM
Out of those 5 theorems, they lost me at the first.  :D
Cheers Damo



Title: Re: Machining Bevels.
Post by: Damo on December 12, 2013, 03:13:21 AM
Actually, i'm just happy i understan d the word "octoid" now.


Title: Re: Machining Bevels.
Post by: ArtF on December 12, 2013, 07:41:25 AM
Words just dont work..do they. :)

Art


Title: Re: Machining Bevels.
Post by: John S on December 26, 2013, 12:46:28 PM
Yes but will it cook the turkey on Gas MK 5 ?


Title: Re: Machining Bevels.
Post by: CMcDaniel on February 24, 2015, 10:17:10 AM
Hey Art, Anything new with the bevels or are You busy working on other things?


Title: Re: Machining Bevels.
Post by: ArtF on February 24, 2015, 02:26:25 PM
Hi:

  Bevels will be dealt with in a waterline engraving module, but probably not till next fall.

Art


Title: Re: Machining Bevels.
Post by: Chuck on May 09, 2015, 10:34:57 PM
Art,

Here is another paper on spiral bevel gear generatio n and inspectio n.

http://gear-net.com/report/rep-03.html

Also Klingelnb erg method is in a spread sheet with macros that create tooth form for Solid Works IGES inport.

https://www.youtube.com/watch?v=k-WdPTxinZk

Chuck in Wyoming



Title: Re: Machining Bevels.
Post by: Nate on May 11, 2015, 08:44:50 AM
Hi:

  Bevels will be dealt with in a waterline engraving module, but probably not till next fall.
...

Naively, it seems like the easiest way to cut bevel gears on a 3-axis CNC machine would be to generate a gear profile numerical ly, and then profile cut with a ball nose end mill, but I haven't seen any discussio n of that in the thread.  Is there some compellin g reason not to take that approach?


Title: Re: Machining Bevels.
Post by: ArtF on May 11, 2015, 08:50:52 AM
Nate:

 Thats the plan. Its not easy to cut bevels, but for beverls less than 45 degrees, the workbench shoudl be
able to profile them, for more than 45 degrees, he 4th axis shoudl eb able to profile them..

Art


Title: Re: Machining Bevels.
Post by: Nate on May 11, 2015, 01:53:28 PM
That's the plan. Its not easy to cut bevels, but for bevels less than 45 degrees, the workbench should be
able to profile them, for more than 45 degrees, he 4th axis should be able to profile them..

A bevel gear with lots of helicity, a small pressure angle, and large teeth can have both radial and axial overhangs .  (That is to say, require a 'tilt' or 5th axis set up.)  I'm not sure whether gears like that have any practical applicati on.

This is a section of a decorativ e bevel gear I  modeled.  If the pitch cone angle were larger, you can see that there would be a 'double undercut'.
(http://www.pedantic.org/~nate/imgs/section.png)


Title: Re: Machining Bevels.
Post by: ArtF on May 11, 2015, 02:32:01 PM
Nate:

 Couldnt agree more. Fact is, bevels are hard, Ill try to make it so some work, some dont, basically we'll just have ot
live with whatever we ifnd the limitatio ns are...unl ess we all want to buy 5th axis machines. . :)

Art


Title: Re: Machining Bevels.
Post by: Nate on May 11, 2015, 07:09:46 PM
Couldn't agree more. Fact is, bevels are hard, I'll try to make it so some work, some don't, basically we'll just have to
live with whatever we find the limitatio ns are...unl ess we all want to buy 5th axis machines. . :)

On second thought, it may be possible on that 4th axis after all, but it will require the cutting tool and the gear axis to be skew to each other.   (I'm not sure what the right term for that is.)

Just for fun, a 45 degree chevron bevel gear section - these really want to be 3-D printed, if anything.
(http://www.pedantic.org/~nate/imgs/chevrongear.png)


Title: Re: Machining Bevels.
Post by: ArtF on May 11, 2015, 07:33:38 PM
I must admit, bevels is one reason I like 3d printers. . :)

Art