# How do you calculate cnc bit width by angle/depth?



## LittleRain (Jun 15, 2018)

I'm using an Eagle plugin to make G-Code commands called pcb-to-gcode, for those who don't know what eagle is, its a program to design circuit boards.

In the program,  of course are able to set your tool diameter and cutting depth, but it does not take into account the angle of the bit, so it can take off more material than you want.

What calculation can I use to find the width of the bit at a certain depth?
In my case the bit diameter is 0.1mm, and the angle is 30°, and I'm cutting 0.127mm.

Thanks

Edit: I found another forum post, so maybe someone could double check my math.


He basically starts with saying "Assuming the bit ends in a point, A is the angle, and D is the depth, do this."
W = tan(A/2)*D*2

Then he says "Since bit tips have a width, we do this"
W = tan(A/2)*D*2 + Tw

But then he says "In your case (the OP) for 60° do this"
W = 1.1547*D + Tw


But tan(60/2) is 0.577.... not 1.1547?

I tried it anyways, and for my case I got 0.134..., so is this right?

tan(30/2) * 0.127 + 0.1?


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## derf (Jun 15, 2018)

If your cutter has a 60 degree included angle, the depth will be 75% of the width. The cutter diameter only limits you to the width.


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## LittleRain (Jun 15, 2018)

I understand that the deeper the cut, the more material being cut, width wise.

So what would the width of a 30° bit be at 0.127mm?


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## T Bredehoft (Jun 15, 2018)

Are we talking about drill bits? a 1 mm drill bit will cut a 1mm hole  (plus a tiny bit) Or are  you asking how deep do  we need to drill to get a full hole depth (plus the tip)?

Sorry,
CNC bits are beyond my knowledge base.


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## LittleRain (Jun 15, 2018)

Oh sorry, my bad. CNC bits.


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## P. Waller (Jun 16, 2018)

What exactly is a "CNC" bit?


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## RJSakowski (Jun 16, 2018)

LittleRain said:


> I'm using an Eagle plugin to make G-Code commands called pcb-to-gcode, for those who don't know what eagle is, its a program to design circuit boards.
> 
> In the program,  of course are able to set your tool diameter and cutting depth, but it does not take into account the angle of the bit, so it can take off more material than you want.
> 
> ...



The tangent gives you the radius at your selected height  x2 gives you the diameter.  Then add the tip width.
For a 30º tool with a tip width of .1mm and a cutting depth of .127mm, tan(30/2)*.127 =.034mm.  x2 = .068mm.  +.1mm =.168mm.


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## LittleRain (Jun 16, 2018)

Thank you RJ. Thats wierd how I originally got 0.134, I swear I did the exact same thing in the calculator but I'm getting .168 now.

P.Waller, I think I'm using the correct terminology, but its the bit used in CNC machines, an engraving bit in my case.


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## P. Waller (Jun 17, 2018)

I see, engraving tools are also used in non NC machines such as pantograph engravers.

The tangent of 30 degrees is .577
Since it is a rotary tool the angle is 60 Deg. included or 1.154
In order to achieve a 1 mm groove width the tool must be moved 1 / 1.154 = .866 mm deep into the part. This assumes a theoretical sharp point which the tool does not have, At such small dimensions any flat or radius on the point will effect the groove width when it is plunged into the work after touching off the tool point to find zero in Z.

.127 / 1.154 = .110 or .127 X .866 = .1099

A graphical representation would look like so. Any error in the Z axis will result in multiplied error in groove width as will any runout in the machine spindle, how one would go about setting a tool for your required 3 decimal MM accuracy may require a setting gauge and very accurate tooling indeed.


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## RJSakowski (Jun 17, 2018)

LittleRain said:


> Thank you RJ. Thats wierd how I originally got 0.134, I swear I did the exact same thing in the calculator but I'm getting .168 now.
> 
> P.Waller, I think I'm using the correct terminology, but its the bit used in CNC machines, an engraving bit in my case.


I suspect that you forgot to multiply the .034mm by 2 your first time through.  That would give you the .134mm.


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