Conic sections with G02 & G03?

[JimmyJazz]

I usually find that G02 and G03 are defined as "circular interpolation", but I've found the odd literature that tantalisingly defines them as "parabolic interpolation", without really expanding on the idea. Are there tricks that one can pull with the I and J offsets in G02/03 to define conics? If not with G02/03, is anyone aware of a macro or canned cycle that will create ellipses, parabolas and/or hyperbolas in addition to circles? I'm working on Haas machines exclusively at the moment, if that has any bearing.

[tex]

I found an example of ellipse interpolation, but still can't figure it out...take a look:

http://216.239.59.104/search?q=cache...polation&hl=en


There's an "ELLIPSE EXAMPLE" at page7.

[CAMFUN]

I usually find that G02 and G03 are defined as "circular interpolation", but I've found the odd literature that tantalisingly defines them as "parabolic interpolation",


Jimmy, it´s possible using parametric programming. You must to create a equation that defines your shapes. For example, if you wanna mill a conic shape, you can set in a variable inside your program, the angle of your cone. After that, in another variable, you can set your step in Z, in another, your initial radius, for example: .01 mm, the final depth in Z. After have created all variables, you build a equation that uses this values and recalculate for you the positions in X/Y/Z axes.

It depends on of your control, due to this, I`ll put here an exemple in general language, OK. (The sample are in mm)

N10 R1= 0.005 ; (INITIAL RADIUS IN X AXIS)
N20 R2= -0.1 ; (STEP INCREMENT IN Z AXIS)
N30 R3= -20.0 ; (FINAL DEPTH IN Z AXIS)
N40 R4= 15 ; (ANGLE OF CONE)
N50 G1 G41 D1 X(R1) Y0 S3000 M3
N60 G1 Z-(R2) F1000
N70 G3 X(R1) Y0 I0 J0
N70 R1 = TAN (R4) * (R2)
N80 R2 = (R2)-(R2)
N90 G1 G40 X-10 Y0
N100 IF R2 < R3 RETURN N50, ELSE N110
N110 G0 G53 Z0 M30; END

This is a sample. I´m not sure if the values are correct. But it´s the main idea. The program will verify the coordinates in Z axis till the conditions established be pleased. After that, the program ends. Any type of mathematical geometries can be done. Everthing depends of your equation. A parabola for example, can be milling creating a equation and variables that defines it.


HTH

[JimmyJazz]

Thank you very much for your replies.

I'm not sure which part you don't understand in that tutorial, tex -- the geometry or the g-code -- but the geometry can be found in the Machinery's Handbook, if you have a copy of that laying around. It's an old practice to fake or approximate an ellipse by connecting 4 circular arcs, 2 long and 2 short. I was just reading that today, actually -- it's in the first section of the book, under the heading "Geometric Constructions." That's essentially all that this tutorial is doing, plus it seems to be dealing with some overhead related to the machine's very small memory footprint.

CAMFUN, that's beautiful. I'm a former software developer who's chosen to change careers into machining (had to satisfy a creative urge that wasn't being met), and I'm currently a student who's just started into g-code. For the moment, I'm actually just trying to work in 2 dimensions, throwing a felt marker into the chuck and writing on a pad in a mill. I can take this and get the math right. We simply hadn't got around to variables, conditional logic, subroutines or any other programming constructs in our class yet. Thanks a lot for the point in the right direction.

Incidentally, I found today in my Machinery's Handbook a reference to G06, which that book describes as "parabolic interpolation." I haven't Googled that yet, but I'll see what I find and report back here in the event that I answer my own question.

[tex]

Originally Posted by JimmyJazz I'm not sure which part you don't understand in that tutorial, tex -- the geometry or the g-code -- but the geometry can be found in the Machinery's Handbook, if you have a copy of that laying around. It's an old practice to fake or approximate an ellipse by connecting 4 circular arcs, 2 long and 2 short. I was just reading that today, actually -- it's in the first section of the book, under the heading "Geometric Constructions." That's essentially all that this tutorial is doing, plus it seems to be dealing with some overhead related to the machine's very small memory footprint.

Actually, the g-code looks kind of strange to me…I have some experience with HAAS CNC mill and lathe (as you do) and find this G-code unusual. I have also tried to backplot it, but it looks terrible…no ellipses, just circles.

I am aware that an ellipse could be approximated by two circles…however still can’t find a way to interpolate it in CATIA CNC modules.