Rolling ball method for 5-axis surface machining

Curvature matching for 5-axis surface machining has been plagued by the complexity of the task. As a result the current tool positioning strategies are likewise computationally complicated. Gouging the surface has been the main concern and has presented the greatest dif®culty in the algorithms. Some of the methods perform exhaustive searches of the surface to avoid gouging while others incrementally adjust the tool orientation until gouges are no longer detected. In this paper a new positioning strategy is presented that is simple to implement and is not dif®cult to compute. The rolling ball method rolls a variable radius ball along the tool path and positions the cutting tool to cut the rolling ball. A small region of the ball's surface is used to approximate a small region of the surface being machined. The radius of each ball is computed by checking a grid of points in the area of the surface that the tool casts a shadow for each tool position. A pseudo-radius is computed for each grid point and the most appropriate radius is selected to be the rolling ball's radius. The selection process follows a hierarchy of surface pro®les ranging from convex to concave. Convex, concave, and saddle (mixed) surface regions are all computed in a similar fashion and there are no special cases for which the positioning strategy must be changed to compute a tool position. Local gouge checking is automatically built-in to the positioning computations so that the typical iterative strategy of checking for gouging, then incrementally tilting the tool until no gouges are detected is eliminated. The method is robust and simple to implement and it only requires surface coordinates and surface normals. A simulation of the method and a cutting test were performed and are presented in this document.