Version 3.47 online.

[Chuck]

Art,

I was looking for a diversion from a rather tricky embedded processor project.

The intersecting rack rotates as the bevel rotates, this complicates the rack generating method but it should still work.  Rotate the gear to the next involute shaving angle and calculate the end points. The changing pitch complicates the calculation of the tool path end points!  The Z must be moved with the changing pitch and must follow the pitch cone.  Also as the gear rotates the pressure angle generating has a 3 way compound angle with the cutter.

After some thinking, the only way I can visualize the spiral bevel is to do a 4 axis move cut with the tapered endmills. I don't see any way to do a simple linear move.  It looks like you will have to do short line segments along the tooth and do 4 axis move for each segment to maintain the involute contact with the cutter.

If you place an imaginary zero thickness crown  gear scaled for 2 diameters on the tooth cone and connect the dots for a given involute angle.  The X, Y, Z and A will have to move to keep the contact angle of the cutter at the involute angle.  The error in angle is controlled by how far apart the crowns are in the calculation.  Using the rolling rack idea at each end of the cut and rotating the gear to adjust the involute angle then compute the X,Y and Z to connect the endpoints.  With the angle change and the X,Y,Z change you can generate the G1 X.. Y.. Z.. A.. move.

instead of the crown gear it may be easier to use an imaginary flat spur gear tooth normal to the bevel cone, scaled to the changing pitch for each point and connect the dots.

This is much like strait endmills but at least it still has the advantage of fewer passes for the same generating step angle on the involute.  Spiral tooth bevels are just another level of complexity with the same setup.

Chuck