Trigonometry help please, plunge depth for a v cutter!

[cncJim]

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!

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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=(d-f)/(2*tan(a/2))

V-Groove type cutter with a radius tip.
Z=r-(r^2-d^2/4)^0.5, for Z<=2r
Z=r+(d-2r)/(2*tan(a/2)), for Z>2r

Ballnose type cutter.
Z=r-(r^2-d^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))

[HankMcSpank]

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)

[ptjw7uk]

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

[EddyCurrent]

Try the attached, just enter cutter angle and hole diameter required.

[cncJim]

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 plunge

[EddyCurrent]

With Excel you have to remember that the TAN() function uses Radians for the angle so the PI()/180 is to change the angle into radians.
So if you use just a calculator it would be (requiredDiameter/2) X tan(angle in degrees)

These are the angles reffered to.