Length-optimal tool path planning for freeform surfaces with preferred feed directions

TL;DR

This paper introduces a globally optimal, efficient method for planning tool paths on freeform surfaces that balances preferred feed directions and scallop height, avoiding topological issues of previous approaches.

Contribution

It formulates tool path planning as a Poisson problem, providing a globally optimal solution that is computationally efficient and avoids path singularities.

Findings

Achieves minimized path length while respecting feed direction preferences.

Provides a globally optimal solution via solving a sparse linear system.

Successfully validated with multiple examples and comparisons.

Abstract

This paper presents a new method to generate tool paths for machining freeform surfaces represented either as parametric surfaces or as triangular meshes. This method allows for the optimal tradeoff between the preferred feed direction field and the constant scallop height, and yields a minimized overall path length. The optimality is achieved by formulating tool path planning as a Poisson problem that minimizes a simple, quadratic energy. This Poisson formulation considers all tool paths at once, without resorting to any heuristic sampling or initial tool path choosing as in existing methods, and is thus a globally optimal solution. Finding the optimal tool paths amounts to solving a well-conditioned sparse linear system, which is computationally convenient and efficient. Tool paths are represented with an implicit scheme that can completely avoid the challenging topological issues of path singularities and self-intersections seen in previous methods. The presented method has been validated with a series of examples and comparisons.