1. ## tangent point

Can anyone help me figure out the tangent point of a ball nose cutter? For example, if I wanted to machine an edge of a 2 inch thick plate with a 30 degree angle across the thickness of one edge with a 1.0 ball cutter taking passes at .05.I don't have any problem writing a program to step down and mill across the edge or doing any of the math. My problem is figuring out where the cutter is making contact.Do I have to use those values (.05 , .5 30 degrees)to find the tangent point? On a diagram of the ball of the cutter, where would I start to construct the triangle?.

2. I draw it in a CAD program to figure it out. I don't know the math off hand.

3. I assume you are talking about a 1" cutter and not a 1MM cutter....

I am putting together a quick DWG for you - if someone doesn't beat me to it - I will post it up in a few minutes (I am at work at the moment).

UPDATE -

The tangent point is 1/4" from center - or at 1/2" Diameter.

Scott

4. If I understand your question, what you want is the cord of a tangent?

The tangent point for the purposes of the calculation will be referenced from the cutter centerline. The actual tangent point depends on which plane the angle is taken from.

Here are 2 examples of your 1" cutter with a .5R ball nose.

DC

• Good point, One of Many - I assumed 30 from the horizontal. That may not be a good thing to assume, huh?

Good job.

Scott

• You don't really need to worry about tangent points, just use the ratio of the two perpendicular sides of the right angle triangle that includes your chamfer angle. A 60, 30, 90 triangle has sides in the ratio 1 as to 2 as to 1.732 as I have shown in the attached sketch. Your vertical and horizontal steps should just be in the same ratio; 1 as to 1.732 or 1.732 as to 1. For a 0.05" horizontal step your vertical will be either 0.866 or 0.0289.

For a 45degree chamfer the ratio is 1 as to 1.414, for any other chamfer angle (which could be applicable in weld prep) you can calculate the ratios using trignometry.

If you are doing weld prep which sometimes requires a double angle chamfer then you might need to get into tangent points on your cutter in order to calculate the transition between the two chamfers. Unless you do it my way which is to stick in a piece of scrap and just tweak the steps right on the machine.

• Thanks for the replies.The main reason I was asking is that I was doing basically the same type of thing at work the other day.It was just a large scrap chute and we usually use a regular roughing endmill and just do a xz or a yz ramp in incremental with no cutter comp.I decided to try stepping up and over using a ball cutter and running it across the width of the plate.The surface finish was a ton better and the resulting angle was right.I did notice that I had passed my scribed line by about .060 though.I also use a ball cutter to do tapered thru holes in a macro I wrote a while back and notice the same thing if I dont cheat the z axis a bit then I get some overcut.This is what got me thinking about tangent points and if I needed to calculate that and use the answer to adjust cutter comp values.

• "I did notice that I had passed my scribed line by about .060 though."

This is why I tweak; move about 0.1 further out for the first pass which would be in absolute then just measure and correct. Although considering that with 30/60 chamfers using a 1" the calculation for tangent point is mental arithmetic it is debatable which easier to do.

• Originally Posted by bob in windsor
I did notice that I had passed my scribed line by about .060 though.I also use a ball cutter to do tapered thru holes in a macro I wrote a while back and notice the same thing if I dont cheat the z axis a bit then I get some overcut.This is what got me thinking about tangent points and if I needed to calculate that and use the answer to adjust cutter comp values.
Yes you do need to calculate tangency points.

This drawing shows the tool path in green, you can set the cutter at each side of the chamfer, at the tangency point and it will cut to the mark:

Fred Smith - IMService

• Thanks Fred.If I'm reading that right, it looks like I could add .033 to the radius comp and still hit the line?

• No.

To cut the chamfer on the right:

You set the tip of the cutter at the top of the part. Z=0
Set the center of the cutter at the right vertical edge of the part X=0 ( The part has depth in the "Y" direction into the screen, we are looking at a front view)

The first cut will proceed along the left side of the chamfer, then later cuts will be towards the right side of the part.

Position the cutter above the left side of the chamfer. If you want a 1/4 wide chamfer, move to x-.25. Z is still above the part.

Now move to the first tangency point, move X+.050. The Z depth will be -.125* (.050/.217). That's your first cut, Z-.0288

Move to the next pass .050 more in X and Z again -.0288 more.

Repeat these moves stepping over and down until the chamfer is completed.

Fred Smith - IMService

• Got it.Thanks for drawing me a picture!