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Author Topic: Machining Bevels.  (Read 56766 times)
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ArtF
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« Reply #45 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
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John S
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« Reply #46 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.

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John S.
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« Reply #47 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.. Smiley )

   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..
   
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Archie
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« Reply #48 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
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Archie
John S
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« Reply #49 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.



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

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

John S.
« Last Edit: May 24, 2011, 06:32:54 PM by John S » Logged

John S.
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« Reply #50 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.Smiley )

Art


   
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John S
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« Reply #51 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.Smiley )

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.
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John S.
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« Reply #52 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
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ArtF
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« Reply #53 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
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John S
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« Reply #54 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.
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John S.
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« Reply #55 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.




* shaving.jpg (22.65 KB, 762x570 - viewed 435 times.)

* taper.jpg (15.13 KB, 276x461 - viewed 429 times.)
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John S
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« Reply #56 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



Does this make sense ?

John S.
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Archie
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« Reply #57 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
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« Reply #58 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
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ArtF
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« Reply #59 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
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