Optimization and correction of the tool path of the five-axis milling machine: Part 1. Spatial optimization

We introduce three algorithms for optimization of a tool path of a numerically controlled five-axis milling machine. The unifying idea is a flexible geometric structure which adapts itself to a certain cost function defined on the required part surface. Algorithm 1 is based on the variational grid generation, Algorithm 2 is based on a new modification of the space filling curves techniques. Algorithm 3 is based on construction of vector fields composed of optimal cutting directions. The algorithms verified by numerical experiments as well as by practical machining display a priority with the reference to the standard methods.