Producing Concave Surfaces With A Vertical Mill

Randy,
your right....I was thinking 2D again instead of 3D. If the tipped cutter was just passed along a part without the part turning it would then be the bottom of a parabola.
 
Randy,
your right....I was thinking 2D again instead of 3D. If the tipped cutter was just passed along a part without the part turning it would then be the bottom of a parabola.

Bill, are you sure ?

Seems to me that it would still be elliptical since the path of the tool would be similar to your example of examining a disc that is slowly rotated.

As the angle of the spindle axis is changed from 90 degrees (with respect to a non-rotating workpiece), the cutting path would gradually evolve from a circular arc to an ellipse to a straight line segment. Or so it seems to me.

Cheers -

edited to add: Not that this is really of importance to most of the forum, right :)
 
I am sure....it's how it was all explained to me by an engineer 50 yrs ago when I first started using the formula. In fact he used the same sketch I used to show it. The tool would be running as an elliptical but the cut if made straight through the part would be a parabola. As far as cutting a turning a piece while tipping the cutter I think it would appear more as an elliptical than a parabola. But then what do I know I only stayed at a Holiday Inn once.
 
Hi Bill,

I definitely agree with your first statement but I think that the second one is incorrect. But who knows, I’ve never even stayed in a Holiday Inn, LOL, so my education is incomplete :)

Tilting the axis of a cutter that rotates in a circular path will always produce an elliptical contour in my opinion. I can’t even think of a way to create a parabola with manual machinery except maybe with a tracer mill or some kind of pantograph. Anyway, this is the way that I see it:

ellipse_zpsabh7jsqi.jpg

On the right is a cutting tool whose axis is vertical. It rotates in a circular path that is indicated by the grey dashed line. The green object represents a stationary workpiece that has been machined by the cutting tool as it passed through the work.

On the left, the axis of rotation has been adjusted to about thirty degrees, producing a thirty degree ellipse, according to my CAD program. The grey dashed line is the path of the cutting tool and the green object again is the stationary workpiece that has been machined by passing the cutting tool through the workpiece. The contour of the resulting cut must follow the path of the cutting tool as shown, right?

Cheers,
randyc
 
Bill, I got confused, what I meant to say was: I disagree with the FIRST statement and agree with the SECOND.
 
I'm going to throw this out there for the sake of clarity. I can see how a parabola could be cut but I think it would require a more sophisticated setup.

180px-Conic_Sections.svg.png

-Ron
 
All I know is it was explained that way to me by someone with a much higher IQ than me and was a wiz in all kinds of math disaplines. He had even corrected college physics books when he was in high school. So I trust what he says about things like this.
But either way it worked for cutting a 32" rad in a part with a 6" cutter almost 50yrs ago.
 
I was just looking at scrapmetals post and think I can explain it better. looking at the picture he posted. An ellipse is a closed figure with no open ends where as a parabola and a hylerbola have open ends.
 
Bill: but the concave surface we're discussing is only part of a geometric shape - an ellipsoid segment to be nerdy about it - so it doesn't make any difference whether the configuration is open or closed.

It's only logical that the contour of the part being milled has to be identical to the path of the tool milling it. A circle tilted at an angle (which is the tool path) cannot be any other shape except an ellipse.

(You've mentioned your engineer friend a couple of times and he might be way smarter than me but FWIW, I have a BSME and a BSEE along with five decades of experience. I'm not claiming that this makes me right, just sayin'.)

ScrapMetal, that's the classic example I was taught with in high school drafting except that you can't obtain a hyperbola from a conic. A hyperbola is two curves that are mirror images.

Also I can't visualize how a concave surface can be obtained from a cone, help me out :)
 
you know what...we can debate this forever...I give up
 
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