Rolling a cutter around a corner.

[TXFred]

I'd love some help with the math here.

This is a lathe operation. The tool has a tip radius of 0.0625". It is moving at a 45 degree angle, and then comes to a corner that has a 0.010" radius. It rolls around that corner, and then makes a linear move to X=0 to face the part.

What I want to learn is, how does the tool radius interact with the radius on the part, and the angle on the part, to determine how the toolpath is offset?

I can fire up a CAD program and work it out graphically. And MasterCAM will calculate it in less than a second. I would like to learn how to get the same result with a calculator.

I've attached an image of the example problem. In the image, the blue line is the part profile. The green circles are the nose of the tool, with the green lines converging at the tool's virtual tip. The red line is the resulting toolpath.

To hand program this toolpath, I would need to calculate the two tool locations shown, as well as the radius of the red arc.

Does anyone know the formula to accomplish this?

Sincerely,
Frederic

[angelw]

Originally Posted by TXFred I'd love some help with the math here. This is a lathe operation. The tool has a tip radius of 0.0625". It is moving at a 45 degree angle, and then comes to a corner that has a 0.010" radius. It rolls around that corner, and then makes a linear move to X=0 to face the part. What I want to learn is, how does the tool radius interact with the radius on the part, and the angle on the part, to determine how the toolpath is offset? I can fire up a CAD program and work it out graphically. And MasterCAM will calculate it in less than a second. I would like to learn how to get the same result with a calculator. I've attached an image of the example problem. In the image, the blue line is the part profile. The green circles are the nose of the tool, with the green lines converging at the tool's virtual tip. The red line is the resulting toolpath. To hand program this toolpath, I would need to calculate the two tool locations shown, as well as the radius of the red arc. Does anyone know the formula to accomplish this? Sincerely, Frederic

The coordinates for a circular interpolation move is not difficult to obtain using a calculator.

If Tool Nose Radius compensation is NOT used, and I'm not a fan of its use on a lathe, then the path of the arc generated by the center of the Tool Radius is what you must focus on. I'm not an advocate of the use of cutter radius compensation on a lathe for the following reasons:
1. Unlike a machining center, generally, cutter radius compensation is not required to adjust the size of the feature being machined; size is controlled by the Tool Wear/Geometry offsets. Cutter radius compensation is very useful and important with a machining center, but not so necessary with a lathe.
2. The true position of the tool is easily obtained, even manually with a calculator.

With all math calculations, some information must be known to obtain the required unknowns. In the attached picture, it will be fairly normal for either the intersection point of the chamfer line and vertical line representing the end of the work to be given, or the center coordinates of the corner radius.

1. If the corner intersection coordinates are known, then the corner radius center can be calculated using trigonometry applied to the Yellow triangle T2. Angle A2 will be the compliment of half the included corner angle.
2. Once the corner radius center coordinates are known, the center coordinates of C1 can be calculated using trigonometry applied to the Red triangle T1. As can be seen, the hypotenuse of T1 is the sum of the corner radius and the tool radius.
3. The center coordinates of C2 are obtained in a similar manner.
4. The coordinates obtained for C1 and C2 centers are the coordinates of the start and end of ARC1 described by the center of the Tool Radius.
5. Once the center coordinates of C1 and C2 are known, the true tool location at P1,P2 and P3,P4 are obtained by applying the Tool radius to the center of C1 and C2 respectively.
6. The length of the X and Z sides of T1 will be the I and K values used in the circular interpolation code.

Regards,

Bill

[TXFred]

Thanks, Bill. I've printed out your post and will read over it this weekend.

Frederic

[CNCRim]

very well reprentation. +1