Re: [CAD_CAM_EDM_DRO] Re: 7 square holes --was,lost post

Sperical trig isn't really all that difficult, but is not neceesaary...as
you can see (I hope) from the sketch I posted.

Smoke


-----Original Message-----
From: Kevin P. Martin <kpmartin@...>
To: CAD_CAM_EDM_DRO@egroups.com <CAD_CAM_EDM_DRO@egroups.com>
Date: Thursday, December 14, 2000 9:16 AM
Subject: RE: [CAD_CAM_EDM_DRO] Re: 7 square holes --was,lost post

>The formula is a simple problem in spherical trigonometry (simple, that is,

once

>you can visualize all the angles).
>
>Imagine you've already cut part of the inside corner. The tip of the cutter

is

>at O, the origin for all the spherical angles.
>Now imagine the spherical triangle ABC defined by the directions:
>One corner of the spherical triangle A is back along the feed direction,

along

>the cut inside corner.
>One corner B is along the axis of the cutter spindle.
>The third corner C is in the direction of the point where the cutter is
>currently cutting the final surface. Because of the geometry of milling
>processes, the corner angle at C is 90 degrees so you have a right

spherical

>triangle.
>The angle at A is half of the inside corner angle you want to produce.
>
>The *sides* of the spherical triangle are:
>a (opposite corner A) is half the cutter's tip angle,
>c (opposite corner C) is the tilt angle of your milling spindle
>b doesn't mean much useful
>The solution for such a triangle is: sin a = sin A sin c.
>
>In your example, you want a 90 degree inside corner, so A is 45 degrees and

sin

>A is sqrt(1/2).
>If, for instance, you tilt your spindle 30 degrees, A is 30 degrees, sin A

is

>1/2, so sin a = sin A sin c = sqrt(1/8), and c = 20.7 degrees, and your

cutter

>must have a total tip angle twice this, or 41.4 degrees.
>If you tilt your spindle 45 degrees, sin a = 1/2 and a = 30 degrees, so you

need

>a 60 degree cutter, which you might actually be able to buy.
>As an extreme case, if you tilt your spindle 90 degrees, a = 45 degrees,

and you

>need a 90 degree cutter. This is just the usual geometry for using a 90

deg.

>cutter to cut a 90 degree vee groove.
>-Kevin Martin
>
>
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