Simulation of NC machining based on the dexel model: A critical analysis

Simulation systems for NC machining that also provide an analysis and verification component are a powerful tool to detect errors in NC codes off-line, i.e. before the NC program is put onto the machine and before damage can happen. The modelling scheme used to represent the workpiece and its development during machining has a great influence on the behaviour and the efficiency of the whole system. Without a well-chosen modelling scheme a realistic simulation and, especially, analysis and verification of NC programs are not possible. Recently, at RISC-Linz, an NC simulation system, NC-SAVE, has been developed that is based on the dexel model. The dexel model is an instance of spatial enumeration techniques, so it is an approximation technique, which allows the user to specify the accuracy he needs. Practical experience with the system has shown that the dexel model allows an efficient dynamic update of the workpiece and provides many facilities for analysis operations. In this paper, we study the accuracy of this modelling scheme. More precisely, we give formulae that state, depending on the curvature of the objects to be modelled, which resolution to take for the model to achieve a certain (pre-specified) accuracy. We also consider the influence of Boolean operations on the accuracy of models. The question of the interdependence between accuracy and resolution of the model, and also the influence of various operations on the model is quite important, in order to choose the resolution of the model in such a way that tolerances are kept. It turns out that the encoding of an object has to be done quite carefully in order to guarantee a certain accuracy of the model and to ensure that analysis operations and comparisons of models work properly. The insights from the theoretical analysis of the dexel model are interpreted in terms of their influence on practical applications of the system NC-SAVE. A much better understanding of the importance of good choices for the resolution of the model and the number and the positions of the viewpoints is provided. It is not the intention of this paper to demonstrate the usefulness and the advantages of the system NC-SAVE. It is rather the goal of this paper to give a careful analysis of the accuracy of the modelling scheme used within NC-SAVE. Such an analysis, together with recommendations for the use of the system, improve the results of the simulation.