Abstract:

One of the most common problems in CAD/CAM is to find an optimal tool path for milling a pocket (defined by a planar shape on the x-y plane). Traditional approaches employ zigzag or contour-parallel paths. Unfortunately, these approaches typically provide paths with high curvature segments. Motions along such paths increase forces on the tool leading to increased wear and a consequent decrease in tool life. Another objective for tool path planning is to minimize the machining time. Thus for a given pocket shape we want to find the tool path such that this exact shape is machined and the tool path is good with respect to some metric. This optimization problem is very hard, so we restrict the class of admissible paths to spiral curves that wind around the initial engagement point and eventually "track" the boundary of the pocket. Our idea is to find a function f(x,y) that is positive over the given pocket shape S and consider this function as a kind of "energy" of a one-degree-of-freedom oscillator. We make the correspondence between the position x and velocity x of the oscillator and the spatial coordinates(x,y). If the oscillator is conservative, the trajectories are (in general) closed curves corresponding to constant energy and are level sets of f(x,x). One way to make a transition between these curves is to introduce negative damping into the equation of motion of the oscillator. A fast milling simulator based on composite adaptively sampled distance fields is discussed. We describe an algorithm that couples the oscillator-based path planner and this milling simulator to evaluate paths.