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Need help with a trigonometry question

MushCreek

Aluminum
Joined
Jan 7, 2018
I'm usually pretty good with trig, but I guess I'm getting too old to figure this stuff out. I need to cut a slot with a .098 radius on the bottom, blending into a 15 degree (vertical) angle. In the past, I would have either ground a form cutter (not an option where I work) or just used CAD/CAM software (also not an option). So, it's back to old-school trig.

The only cutter I have is a 5/32 (.156) carbide ball end mill. Obviously, a 5 mm BEM would make it easier, but not an option. I can figure out the offsets for the part that is 15 degrees. It is cutting the radius that baffles me. I was going to drop down in small steps, moving the cutter over the right amount to approximate the radius. Cutting an .098 radius with a .078 R cutter will minimize the steps. I started by plotting the points along the radius. So far so good. But I just can't wrap my head around the offsets for the ball end mill I have so I can hit those points. Can anyone enlighten me?
 
The two radii are tangent of course

Select a number of steps like 5 for the positions

divide the 75 degrees by 5 and get 15 degrees apart

Calculate the various positions using the .098 radius swing point and the center of the .078 radius

As can be imagined, we are talking small differences
 
Years ago, an old machinist said, draw it, or make a picture. if I just calculate, I always make a mistakes. I drew the slot I think you want, 1/2 deep, ball bottom 15 degree sides in white.

drew up a bunch of construction lines in red.

Capture.JPG

found the tool path in blue.

Capture2.JPG

used a 0.050 step over, way to ruff, just trying to show how.

Capture 3.JPG

dimensioned the depths in green


Just my way to avoid trig mistakes
 
It looks like Karl and I interpreted the same.

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Same idea applied to lathe - smaller radius tool generating fairly good representation of larger radius that incidentally is chatter free
 

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So I assume you are going to cut the entire groove with the ball end mill? Generating the numbers with a CAD program should be quite easy. I would need two numbers: the total depth of the groove at the center and the maximum amount of error that you can tolerate in the surface. The surface errors will be greater on the straight sides, so think about them. Stepping on those straight sides will produce a series of peaks there, between those steps.

If you can provide those two numbers then I can generate a table of step locations.

It would also be good to know the resolution of your DRO or handwheels so that can be considered in the step size.
 
If I had CAD, it would be easy to work out. We have a program, but the license expired, and they won't spend the money to re-up. I'm cutting this on a CNC bed mill. What I finally came up with was to bring in a 3/16 carbide ball end mill FROM HOME. The radius is so close it's hard to figure out any reasonable compensation. The part is going to be sent out for heat treat, and then finish ground. I'm going to make a few electrodes (in the grinder) and give them a quick EDM to eliminate any error.

The reason I emphasized 'from home' is that I have better tooling in my home hobby shop than I'm provided with at work. They won't spend any money on anything, so I have to come up with work-arounds to get the job done. Oddly enough, they think labor is free, so it doesn't matter how long it takes. I've posted other threads about this, such as cutting off stock with multiple passes of an end mill, because the cut-off saw is usually unusable due to dull, cheap blades.

At any rate, thanks for the pointers, and I'm going to play around with the info to see if I can actually work out the math. I was losing my patience with it as it's a hot job.
 
Thanks- I'll give that a try. I have SketchUp, but the radii aren't accurate enough at this level.
 








 
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