Problem with 4th axis toolpath

[Greolt]

As a new user I am reluctant to call this a bug.  More likely user error.

When cutting a 50 tooth 2.5 module spur gear with a 2mm ballnose cutter, the tool moves 28mm each side in the Y, as it cuts the final pass on the involute face.

However the tool never goes lower than the depth of the tooth at top dead centre.  This means it is cutting air on that last pass.  It needs to go lower in the Z.

I made a diagram to hopefully show this more clearly.

Can someone set me straight?

Greg

EDIT:  Forgot to say 20 degree pressure angle.

[ArtF]

Hi Greg:

  I think I know what you mean. As the blank rotates, the Y moves to the tangental position of
the top of the tip of the involute for that tooth. Since earlier passes have already cut that area, it cuts nothing but air.

   Im not sure this is true 100% of the time, which is why it does it. Its just a matter of the algorithm knowing that IS a point that needs cutting, and not knowing if it indeed was cut
earlier. Seems to me on some gears, with very sharp involutes that pass may actually cut some small amount. Ill keep this in mind though, and we'll see how that goes over time with various gears..

Thx
Art

[Greolt]

Just to demonstra te this point further I tried with a 100 tooth, module 3, 20 degree, spur gear.

4th axis toolpath requires that the Y axis travels 59mm each way as it cuts the involute curve.

However it only partially cut because the tool never goes below the depth of the tooth at top dead centre.

It needs to go about 7mm lower to make the last cut.  So the the last few cuts are not done, leaving the involute surface incomplet e.

The gear will not mesh with its partner.

Greg

[ArtF]

Greg:

   Hmm, I need to think about this one. I wasnt understan ding you before, I think I am now.
In theory, the tool should never have to go deeper, ater all, its simulatin g a hob basically . Since the hob can never go deeper, the mill shouldnt have to either.
  I cant see this happening mathmatic ally unless the blank was too small for the cut. But as Ive said many times, I can easily be wrong. But on first glance I cant see where its possible to
need more depth for the tool than max depth at top dead center. Ill have to cruch some numbers to see where a problem may lie. Since the actual portion of the involute thats  being cut is getting higher each pass, the target surface shouldnt be able to get lower than the bottom of the tool
during the rotation, just as the hob cannot go deeper as it cuts the involute. Perhaps Im missing something though, so Ill give it some carefull study.

Art

[ArtF]

Greg:

  Hmm, OK, Ive had some time to think about it. I checked it carefully because you mention a situation I hadnt considere d, one where the base diamter is less than the root which occurs after 50 teeth or so in mod 3.
     For what you describe to be happening it seems to be one of two or three things must be happening . Either the tool isnt set to correct diamter of the actual tool, the blank isnt the right size so zero is wrong, or my Y offsets must be wrong. I dont think dpeth can be an issue.

  Im thinking of it this way to prove that in my head. Consider you have a gear in the 4th axis, the space between teeth is at the top dead center and the tool is all the way down to the root.

   Consider the tool is on a pushable lateral axis, ( y is loose and pushable). You begin to rotate the 4th axis. The tool as you start is cutting the bottom of the tooths involute, As the axis rotates, the tool gets pushed sideways continuou sly cutting higher up the tooth. At some point the tip will contact the tool and push it sideways to its extreme. The positions of the Y during this mental excersize should be the same as where I send it during a cut.  I cant picture where the tip can miss the tool unless Im sending too far out. So I need to think a bit more about this in your base/root circle inversion example, its possibel my numbers go wrong at that point. I suspect maybe my lateral should then be based on the root diamter, not the base when inversion occurs.

[ArtF]

Greg:

  Yup, finally puzzled it the rest of the way. When the base gets smaller than the root, the tool must drop each rotation till it gets to the base diamters depth. The involute is always based on the base diamter, so the tangental position must be to base depth at all times of cut.
 Ive added this to the current fix list for next release, so I will hopefully have it fixed soon.

Thanks for the detailed report, it really helped me get my head around the issue.

Art

[Greolt]

When the base gets smaller than the root, the tool must drop each rotation till it gets to the base diameters depth.

At first I thought the other side of the cutter may cut into the root of the next tooth but in this example it does not.

Greg

[ArtF]

Hi Greg:

   I do worry that in some instances the tool edge may cause a troichoid al
root to occur when none should in the inverted root situtatio n, but if it does
occur it should be minimal and not truly affect meshing.. the numbers seem to show that it shouldnt hit, but Im not sure of that in all situation s.

  I do see the error possabili ty and Ill keep an eye on that. I have the library code working and am now shifting to this problem, and Ill release
as soon as I have it cracked. TO my mind its simply a matter of dropping
on each pass to the base radius OR the root radius when rotated , whichever is higher. In truth I should be able to drop to base radius on first pass as the initial rotation is to bring the root portion to tangency, which should mean the depth of the root has now been rotated to the depth of the base radius.
  Anyway, shouldnt be too long before I have a release that fixes this one. All our testing never got large enough in # of teeth  to see this.. goes to show how one can be fooled by testing the obvious..

Thx
Art

[ArtF]

Greg:

  Fix posted. I havent tested as yet with large size gear, but the system now reports the min length tool youll need, skips unnecessa ry angualr changes where no cutting will take place, and drops the tool to proper
depth for tangental cuts to be done. Please lety me know result if you try it before I post that I have.

Thx for the report,

Art

[Greolt]

Art

It looks to be not right yet.  Just reading the gcode.

The tool goes to the depth of tooth at top dead centre while it clears out the bulk between teeth.  (in the above example 5.3925mm)

Then it immediate ly goes to the max depth for cutting the evolute sides.  (10.0383mm)

This of course will be too deep for the first of the side cuts.

It should go progressi vely deeper as the Y moves further from TDC.

Greg

[Greolt]

Here is the gcode for the first tooth only.

You can see the first cut to tooth depth in red.

And then subsequen t cuts are all in blue.   These should be getting progressi vely deeper.


              ( Tooth #1 )
  G0 Z2.0000
  G0 A0.0000
  G1 Y 0.0000 
  G1 Z-5.3925 F1000.000 0 'Initial cut to the depth of tooth
  F1000.000 0
  G1  A -0.0056   
  G1 X -4.5000  A -0.0056
  G1  A 0.0056   
  G1 X 0.0000  A 0.0056
  G1  A 0.0000   
  G1 Y -33.6215 A 16.3944 
  G1 Z-10.0383               'depth of all subsequen t cuts
  G1 X -4.5000  A 16.3944
  G1 Y -35.1796 A 17.1544 
  G1 Z-10.0383
  G1 X 0.0000  A 17.1544
  G1 Y -36.7376 A 17.9144 
  G1 Z-10.0383
  G1 X -4.5000  A 17.9144
  G1 Y -38.2957 A 18.6744 
  G1 Z-10.0383
  G1 X 0.0000  A 18.6744
  G1 Y -39.8538 A 19.4344 
  G1 Z-10.0383
  G1 X -4.5000  A 19.4344
  G1 Y -41.4118 A 20.1944 
  G1 Z-10.0383
  G1 X 0.0000  A 20.1944
  G1 Y -42.9699 A 20.9544 
  G1 Z-10.0383
  G1 X -4.5000  A 20.9544
  G1 Y -44.5280 A 21.7144 
  G1 Z-10.0383
  G1 X 0.0000  A 21.7144
  G1 Y -46.0861 A 22.4744 
  G1 Z-10.0383
  G1 X -4.5000  A 22.4744
  G1 Y -47.6441 A 23.2344 
  G1 Z-10.0383
  G1 X 0.0000  A 23.2344
  G1 Y -49.2022 A 23.9944 
  G1 Z-10.0383
  G1 X -4.5000  A 23.9944
  G0 Z2.0000
  G1 Y 0.0000  A 0.0000
  G1 Z-5.3925 F1000.000 0 'another cut at tooth depth before starting on next tooth flank
  F1000.000 0
  G1 Y 33.6215 A -16.3944 
  G1 Z-10.0383
  G1 X 0.0000  A -16.3944
  G1 Y 35.1796 A -17.1544 
  G1 Z-10.0383
  G1 X -4.5000  A -17.1544
  G1 Y 36.7376 A -17.9144 
  G1 Z-10.0383
  G1 X 0.0000  A -17.9144
  G1 Y 38.2957 A -18.6744 
  G1 Z-10.0383
  G1 X -4.5000  A -18.6744
  G1 Y 39.8538 A -19.4344 
  G1 Z-10.0383
  G1 X 0.0000  A -19.4344
  G1 Y 41.4118 A -20.1944 
  G1 Z-10.0383
  G1 X -4.5000  A -20.1944
  G1 Y 42.9699 A -20.9544 
  G1 Z-10.0383
  G1 X 0.0000  A -20.9544
  G1 Y 44.5280 A -21.7144 
  G1 Z-10.0383
  G1 X -4.5000  A -21.7144
  G1 Y 46.0861 A -22.4744 
  G1 Z-10.0383
  G1 X 0.0000  A -22.4744
  G1 Y 47.6441 A -23.2344 
  G1 Z-10.0383
  G1 X -4.5000  A -23.2344
  G1 Y 49.2022 A -23.9944 
  G1 Z-10.0383
  G1 X 0.0000  A -23.9944
  G0 Z2.0000
  G1 Y 0.0000  A 0.0000

[ArtF]

Hi Greg:

>>Then it immediate ly goes to the max depth for cutting the evolute sides.  (10.0383mm)
>>This of course will be too deep for the first of the side cuts.
It should go progressi vely deeper as the Y moves further from TDC.

   Normally, youd be correct. BUT, I also made a change to stop useless
motions to speed things up. In actual fact the fist rotation and the lateral motion is several steps in to the point where a full drop will work.

   The intermedi ate steps wouldnt have cut properly as they werent tangent. The idea here is that the first cut on the tool is tangent to the curve. This means the curve MUST rotate to the point at which the bottom
of the root is cut at the level of the base circle. This means the roation turns quite a bit ..to the point that the root bootom has rotated to the base circle, ( which means the tool on the first actual cut must be at base circle depth. ).  The Gcode looks right to me, we're having a few days of heavy rain here so I may not get to my workshop to test this, but the math tells me that what you see as an error, is in fact the correct positioni ng.

    To do tangental cutting, the tool should always be at a set depth of the base circle, and the recent change does that. Root clearing is a separate thing and cannot , of course, go deeper than the root, but when you rotate to tangency, that root depth becomes equal to base circle depth, and the tool then goes there and never  moves again during the involute cutting.

Thx
Art

[ArtF]

Greg:

 As a followup, notice the first cut to the involute. .

>> G1 Y -33.6215 A 16.3944 
      G1 Z-10.0383

 As you can see the first cut is already 16 degrees and 33mm's away from top center. If you take a root depth of -5 and rotate it 16 degree, youll find that its now located at -10 in the Z and 33 in the Y( or lateral direction). Cuttign prior to this point would not cut proper involutes, ( if it cut anything at all), only cuts made after the initial 16 degrees should have any involutio n to them, which is why I eliminate d them in this case.)

Art
       

[Greolt]

Ahh yes....I see now.  

Missed the fact that the first cut is at 16 degrees.

So I gather that the earlier cuts (at less degrees) are not necessary .

OK I will go ahead and cut one of these tomorrow.

Greg

EDIT:  I plotted it out and can see why the cuts at less than 16 degrees are not doing anything effective .

And I guess that 16 degrees will vary with pressure angle and number of teeth.

[ArtF]

Greg:

  Exactly, I saw as I fixed the "Inverted root" problem, that all the cuts up
to the time when the root actually became tangent to the tool ( which occurs exaclty when the root hits the base radius ) where useless. In essence they were attemptin g to involute the portion of the tooth between the root radius and the base radius ( which doesnt exist in root inversion ), so I eliminate d them to save time.
   So the first cut actually occurs when the root portion hit tangency, about 16 degrees in your example. From that time forward, the tool can stay at
the depth of the actual base circle, -20 in your example.
 By doing it this way, we dont need to worry about moving Z to cut the tooth.
   I did have to add a min tool length display so youd know just how far that plunge is .. is basicaly always to the base circle radius..