
05112013 #1
Hello,
I am trying to calculate the required plunge depth for a v cutter needed to produce a given diameter of hole.
Can someone explain the formula I need?
Thanks!

EDIT:
Answer:
Z = Depth of cut
d = Required diameter of cut
a = Cutter tip angle in degrees*
f = Flat spot
r = Tip radius
V Groove type cutter with no flat spot.
Z=d/(2*tan(a/2))
V Groove type cutter with flat spot.
Z=(df)/(2*tan(a/2))
VGroove type cutter with a radius tip.
Z=r(r^2d^2/4)^0.5, for Z<=2r
Z=r+(d2r)/(2*tan(a/2)), for Z>2r
Ballnose type cutter.
Z=r(r^2d^2/4)^0.5, for Z<=2r
* The TAN() function in some applications (such as Excel) require the angle to be expressed in radians, Not degrees. Convert degrees to radians  Radians = angleInDegrees x (PI/180)
So in excel the first formula above would become:
Z=d/(2*tan((a*(PI()/180)/2))Last edited by cncJim; 06112013 at 12:58 PM.

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05112013 #2
I might be wrong, but you should be able to use an online calculator similar to this.....
Right Triangle Angle And Side Calculator
Just assume your cutter is lying on its side, therefore.....
In the 'side b' box (this is your experimental 'cut depth')
In the angle box (enter your V cutter angle divided by two)
the cut width will be the 'a' result multiplied by two.
Example....
say you have a 60 degree V cutter & you want to know the diameter of a hole if you go 2mm deep
enter '2' in the side b box
enter 30 in the angle box
Click calculate.
the hole will be side 'a' multiplied by 2...therefore 1.15 x 2 = 3.3mm
I realsie it's not exactly what you seek (fwiw, I suck at trig), but if nobody else chimes in, te above method should get you there! There may well be a dedicated calculator out there, but that was just a quick search/kludge! (kludge is my friend...we know each other so well)Last edited by HankMcSpank; 05112013 at 01:18 PM.

05112013 #3
best I can do
width of cut/2 x tan (cutter angle)
tan 30 = 0.577
Tan 45 = 1
Tan 60 = 1.732
Such that for a 60 degree cutter wanting a 3.. wide cut then 3/(2*1.732) = 0.866 ( in whatever units yo are using)
peter

05112013 #4
Try the attached, just enter cutter angle and hole diameter required.
Last edited by EddyCurrent; 05112013 at 02:30 PM.

05112013 #5
Thank you everyone for your input! I think I am slowly understanding :)
Depth of cut = (requiredDiameter/2) X TAN(cutterAngle X (PI/180))
So..
requiredDiameter = 10
cutterAngle = 60
(10/2) X TAN(60 X (3.141593/180)) = 8.66 plungeLast edited by cncJim; 05112013 at 03:31 PM.

05112013 #6

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05112013 #7
Ah I see, thanks for that eddy, good to know!
I am using the formula with PHP for a web application and the TAN() function uses radians so I am sorted!

05112013 #8
Just spotted your diagram with the angles, I think i had the wrong angle in mind...
So...if my cutter has a 45 degree angle at the cutting head (top of your diagram) that would mean the angle I need to use with the formula would be 67.5?
(18045)/2 = 67.5
Is that correct?

05112013 #9
Vcutters are generally specified by the included angle, i.e. the angle at the tip. In that case the formula is:
Z=d/(2*tan(a/2))
Where:
Z=depth of cut
d=diameter cut
alpha=tip angle, as above.
So for example, lets say you have this cutter:
4x40Â°x0, 1mm Vtype Solid Carbide Engraving Tool Cutter f. CNC Engraving Machine  eBay
The angle is 40 degrees, so suppose you want to cut 1mm wide:
Z=1/(2*tan(40°/2))=1.37mm
However, there's an error since we've assumed the cutter has a sharp point when in reality it's got a flat, which makes things marginally more interesting, hence why I decided to make this post.
The formula you now need is as follows:
Z=(df)/(2*tan(a/2))
Using the same example, the tip flat is 0.1mm so:
Z=(10.1)/(2*tan(40/2))=1.24mm
There's also the chance that you're using Vcutters with a radiused tip.
Now the formula you'd need is:
Z=r(r^2d^2/4)^0.5, for Z<=2r [Note this is also valid for ballnose cutter]
Z=r+(d2r)/(2*tan(a/2)), for Z>2r
Where r=tip radius.
e.g. suppose this tool:
3x20Â°x1mm Vtype with radius Engraving Cutter graver HM for CNC engraver machine  eBay
It's 20°, and 1mm tip radius so a=20, r=1. Lets say you want to cut 2.5mm wide:
2.5>2*1, therefore:
Z=1+(2.52*1)/(2*tan(20/2))=2.42mm
Suppose you want to cut 1mm wide:
1<2*1, therefore:
Z=1(1^21^2/4)^0.5=0.13mm
Edit: If you don't have a calculator to hand, then using google is a quick way to evaluate it, e.g.
http://lmgtfy.com/?q=1%2B(2.52*1)%2...20%2F2+degrees))
You could of course just draw it in a CAD program, but where's the fun in that?Last edited by Jonathan; 05112013 at 07:30 PM.

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06112013 #10
Touch the tool off at the required Dia that you can measure on the part  and program machine to cut to the Face no trig needed but approach move should include room for the tip very common practice on combo tools
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