A Z-map update method for linearly moving tools

In numerically controlled (NC) machining simulation, a 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, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when automatically programmed tool-type tools move along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these properties, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. 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, making it possible to verify the tool path more accurately and reliably.