A common problem in CAD/CAM is to find a suitable tool path for milling a pocket that is defined by a shape in the plane. CNC machines can be programmed to follow a path that consists of straight-line segments and circular arcs; recent NC controllers do also support (specific families of) spline curves. When using high-speed machining (HSM), the spindle rotation speed and the feedrate are higher than for conventional milling in order to minimize the manufacturing time without a decrease in the part quality. The high rotation speeds and feedrates of HSM impose new constraints on the tool path: Due to its kinematic characteristics, the spindle has to slow down and stop its movement in a sharp corner, change its direction and accelerate until the desired maximum speed is reached again. The reduction of the speed has also thermic effects on the tool and on the currently machined location of the workpiece: The temperature at the point of contact rises if the feedrate shrinks.

It is folklore that overheating might cause chipping of the tool and degradation in the part quality. Thus, in order to meet the kinematic constraints of HSM, it is essential that the path is smooth, i.e., at least G1-continuous.

In joint work with Christian Spielberger an alternative to conventional contour-parallel machining was proposed. Let R be an arbitrary point inside of (the machinable area of) the pocket, chosen by the user. We compute a spiral-out tool path that exhibits the following properties:

- The tool path starts at R and stops once the boundary of the pocket is reached.
- It has no self-intersections.
- It is G1-continuous. (Further smoothing yields G2-continuity.)
- The cutting width is strictly greater than zero and strictly less than a user-specified threshold along the entire tool path.

More recently, we introduced a geometric heuristic for decomposing an arbitrarily complex pocket with or without islands into simpler sub-pockets that are better suited for efficient spiral high-speed machining. Within every sub-pocket we apply a second heuristic for selecting a "good" start point of the spiral tool path. Several machining parameters such as the step-over distance and the engagement angle are considered as measures and indicators for a good tool path. Again, our heuristics are based on the Voronoi diagram of the pocket contours, and we can handle contours consisting of straight-line segments and circular arcs.

The resulting new algorithm for high-speed spiral pocket machining was implemented and tested successfully on real-world data. Our experiments provide strong evidence that our heuristics reduce the total length of the tool path, while also reducing the variation of the curvature and of the engagement angle over the entire tool path, and decreasing the ratio between the maximum and the minimum step-over distance.

This research was supported by the Austrian FWF Grant L43-N12.

M. Held,
C. Spielberger (2014):

"Improved Spiral High-Speed Machining of Multiply-Connected
Pockets".

Computer-Aided Design and Applications,
11(3):346--357, 2014.

M. Held,
C. Spielberger (2013):

"Improved Spiral High Speed Machining of Pockets With
Islands".

Proc. 10th Annual CAD Conference, p. 126-127,
Bergamo, Italy, June 2013.

M. Held,
C. Spielberger (2009):

"A Smooth Spiral Tool Path for High Speed Machining of 2D
Pockets".

Computer-Aided Design,
41(7):539--550, July 2009.

M. Held, C. Spielberger (2008):

"A Smooth Spiral-like Tool Path with Controlled Cutting Width for
Pocket Machining".

Proc. 5th Int. Symp. on Voronoi Diagrams, p. 88-100,
Kiev, Ukraine, Sep 2008.

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