Re: Mr. PV teaches jb spread*** geometry (Re: Garlic's contouring article



"Proctologically Violated©®" wrote:


Take a triangular insert pocket, my latest project, on a boring bar.
What would be the very first thing you'd have to do?
Purely rhetorical Q, since I'm sure you don't know.
A: Find a suitable offset.

Turns out there are two on this tool, but the main one would be,
unsurprisingly, the center of the insert.
What is that center?
Well, centers of equilateral triangles can be described two ways, the center
relative to any vertex, or as a perpendicular line to any edge.
It turns out you will need both these values.

Placing the insert's edge length of .600 in A122, the vertex angle in I122,
and the radian-to-degree conversion factor (180/pi) in J122, you calc out
the following:
center to vertex: (A122/2)/cos(j122*I122/2), which is calc'd in C122. =
.3464
center to edge: C122*sin(j122*I122/2), in D122. = .1732

So the offset *rel. to the edge of the tool* is X-.1732,Y0--for now.

Now, to cut a 60 deg pocket, you need to know where the cutter must stop to
make the second line w/o gouging, etc.
IOW, you want the em to move *just as it would in cutter comp*.

So you drop a circle (= to the diam of the em) in a 60 deg V, and calculate
the coordinates of the center of the em.
It turns out that for a 60 deg angle, and only a 60 deg angle, this
value turns out to be exactly the diameter of the em in from the *vertex* of
the V.
In this case, C122-E122 or .3464-.218 = .1284, actually -.1284 from the
insert center.
The simple calc C122-E122 is actually the result of a lot of effing lines
and angles'n'***, again simplified bec of the 60 deg angle.
The general result is a bunch of sines/cosines.

Now,
we form three columns, labled R, X, and Y.

.1284 is placed under R, because if it is rotated, we then will need to
calculate new X's and Y's for the "stop coordinates" of the em, or if we
change the diameter of the cutter.
For a 1 deg. rotation, X and Y change from -.1284 and 0.0, to
-.1284xx and +.0022 (cw rotation), and where "1 deg" is in cell H122.
By putting various empirically-determined lengths in the R column, we
generate the *start/entry* motion of the em *along that line*, we end
at -.1284,+.0022, move the em along the next angle/pocket wall, and *exit*
at another distance from the -.1284,+.0022 point, at the prescribed angle,
with suitable exit clearance.

I didn't show the rotation calcs, but they are there.

NOW,
you gotta do this *all over again*, as a tapered em comes in to chamfer the
pocket ledge at 10 deg, and it's *effective* diameter is .1300, which
changes the whole tool path.
But the spread*** just pops out the numbers, cuz all you had to do was
copy the above cells, and preserve the relationships, and plug in .1300
instead of .218.
It turns out that the "vertex point" of a .130 diam em is not -.1284 as
above, but -.2164,+.0038, which makes qualitative sense, as it can go
"further" into the material.

Note what was absent from all of the above:

Nowhere on the spread*** do you see the actual coordinates of the vertices
of the triangular insert!
Why?
First, because when all is said and done, *two* of the vertices actually
hang off the tool.
Second, since you are essentially generating your own cutter comp/empirical
start/stop points, you don't need these coordinates anyway.

There is actually much more involved in this spread***, such as other
operations, AND the very interesting calc of how to generate the back
clearance for a sharp-cornered insert in a pocket made by a broad-ish .218
em.

Turns out there is a very elegant relationship, which is essentially taking
the circle dropped in the 60 deg V, and flipping it 180 deg around the chord
formed by the circle/V contact points.
This gives the *exact* clearance needed for that insert vertex, using the
same cutter that made the pocket, altho I buzz the em +/- .01 in X, "just to
make sure". The relationship can be proven, geometrically.
That coordinate happens to be -.237,+.0041 for a .218 em.

PV:

OK, I just drew it up to check your numbers. I didn't bother to check
the .130 Dia. ones. I got your .237 corner plunge relief number by
drawing a circle through the two tangency points of the corner radius of
your end mill. I got all your other numbers and it took about 10
minutes (estimate), and I didn't have to do ANY manual trig. at all.
IMO, .218 Dia. is WAAY too big a cutter diameter, as visually, it cuts
into the edge support radically. I've got three circles, the triangle,
dimensions all over the place, but rotating the whole mess takes 4 mouse
clicks and all the dimensions automatically adjust.
Not to belittle your spread*** efforts, since it obviously works
beautifully, but my suggestion would be to try that MasterCAM demo.
You'll be lovin' life after you get the hang of it. LOL

--
BottleBob
http://home.earthlink.net/~bottlbob
.