NC simulation using Z-map cutting curves

Abstract

In Numerically controlled(NC) machining, the verification process for tool paths is usually required; in particular, graphical simulation plays an important role in this process. For large dies and molds such as parts of an automobile, the Z-map has been frequently used for representing the workpiece. Since the Z-map is usually represented by a set of z-axis aligned vectors on the xy-plane, the machining process can be simulated through calculating the intersection points between the Z-map vectors and the surface swept by a machining tool. In this thesis, we present a method to calculate those intersection points for both linear and circular paths, commonly used in 3-axis NC machining. For linear paths, each of the intersection points can be expressed as the solution of a system of non-linear equations. For fast and accurate computation, we transform this system of equations into a single-variable non-linear function, called the Z-map cutting curve, whose zero gives an intersection point. We also calculate the candidate interval in which the unique solution exists. We prove the existence of a solution in this interval and its uniqueness. Then, we numerically calculate the solution of the Z-map cutting curve within a given precision. To generalize the results for circular paths, we restrict the radii of tools to be smaller than those of circular paths. Under such a condition, the tool swept surfaces for both linear and circular paths have a similar structure. Thus, we can extend our approach to circular paths although we prove the existence of the unique solution in a different way. The whole process of NC simulation is achieved by updating the Z-map properly. Our method can improve accuracy greatly while increasing processing time negligibly in comparison with previous Z-map update methods.