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Parabolic End - How to Program for Turning?

Hoppy

Cast Iron
Joined
Feb 21, 2005
Location
Millington, NJ
I have to turn a round bar whose end is parabolic. There is a mathematical formula that defines the X values in terms of the Z values. How can I program this in G code?
 
If all you have is the mathematical formula, you could just plug numbers in your formula.

Z0 X0
Z-.0005 = X.002
Z-.001 = X.004
etc

Up to you how many points you plot.

You could probably make this way way easier by plugging the formula in an excel spreadsheet and let it do all the math for you. Just need to populate a column of Z values (or X values, if you want) at some interval that suits you, such as 5 tenths in my example above.
 
If you have the formula there is a draw function in solid works for equation of a line.
then you most likely plug it into a CAM package to do the tool path.
then write g code and put that in the machine program where required.

Yet to do this particular thing but did have a problem similar to this where i know the equation of the line....so took notice of the solid works line draw option...
 
Did something a long time ago with a simple arc, but I had to turn the rotary axis at the same time as the arc was created. I used a while/do loop with the formula in the program. Indexed the X value by .0001" every time thru the loop.
 
I'm obviously misunderstanding, please feel free to explain better.

A Parabola is a plane that crosses over the Axis of rotation. It is no ALONG the Axis of rotation. So the answer is-you can't "Turn" that feature. The plane is a cross section of a cone. You either get the cone or not. Obviously you could use live tools to do it on a Lathe, but that ain't Turning.

R
 
I'm obviously misunderstanding, please feel free to explain better.

A Parabola is a plane that crosses over the Axis of rotation. It is no ALONG the Axis of rotation. So the answer is-you can't "Turn" that feature. The plane is a cross section of a cone. You either get the cone or not. Obviously you could use live tools to do it on a Lathe, but that ain't Turning.

R

I'm pretty sure he is talking about turning the end of rod into a half sphere, but a bit
more complicated than just rounding the end.


You can program point to point, but that can be a pain in the butt if your control
gets a little cranky processing a million tiny little moves.

First thing I would do is to get it drawn out. Then I would look at the tolerance.
Then based on the form tolerance, I would see if I could approximate it with a few
arcs, that would make it a much shorter program, and easier for the machine to
process.

I've done ovals like that, approximate them with 4 arcs, and they look pretty decent.
 
In addition to the above, lots of CAD software can create a curve from a formula, then you can analyse it or run it through CAM.
Or if you want to get fancy you could write a macro program that evaluates the formula as it goes.
 
Section 8.4 of my book will give you an idea of how to do it, though it explains the method for internal parabolic turning (for a reflector, for example).
PM me your mail ID. I will send you the pdf.
 
Macro?...
CAD/CAM generate, Excell generate lots of points.
Any arc in a cnc is always just a bunch of short lines. Block processing time and memory gets in the way on occasion.
Too tight or small and the system mechanical and electrical responses can't follow it anyways so there is a limit on how many points at how fast before the control is overwhelmed and sort of studders leaving marks.
Some controls can handle input of a spline or such a curve directly but that not very common.
Bob
 
What diameter, tolerences and material are you working with?
If its small enough a form tool might get it done and hijack the need for the code-busting. Some high-school maths, a grinder and an optical comparator would get your tool.

I don't have any insight otherwise. I'm watching this thread to see what shakes out. I'm curious mostly about some of the limits of the gcode language in a basic machine.
Its an interesting question.
 
The question is how accurate we want the parabola to be. If it must be 100% mathematically accurate, then there is no way other than generating it as a sequence of small line segments. If the segments are large then smoothness will not be there, and if segments are too small then the motion will be sluggish.
On the other hand, if only an approximate parabola is required then it can be approximated by circular segments of finite lengths.
In manual isometric drawings, an ellipse is approximated by just four arcs, and it looks too good!
(Can see the details in any engineering drawing book, under the heading 4-center method of making ellipse)
 
The question is how accurate we want the parabola to be. If it must be 100% mathematically accurate, then there is no way other than generating it as a sequence of small line segments.
Or you could buy a Tera control, which featured parabolic interpolation .... but when you come right down to it, even arcs are "straight line segments" if you subdivide them far enough.
 








 
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