The paper presents an efficient realtime simulator for 3-axis milling processes. In this system, solid modeling is performed using isometric projection with a z-map structure. As a result, all the solid elements are either fully exposed or fully hidden, and they are well arranged and symmetrical. These characteristics make visible surface determination for the raster display more efficient, and they reduce the memory requirements considerably. As a result, this efficient and realtime voxel-based model can simulate NC milling processes satisfactorily even in personal computers, without the aid of extra hardware devices or coprocessors. This simulation system will be useful to NC programmers and machining operators for identifying programs and checking gross programming errors visually.
"This method is not usable for 04-axis and 05-axis machining since the tool axis is not vertical. Later, many researchers have used different approaches to improve the Z-map model     Proceedings of the World "
[Show abstract][Hide abstract] ABSTRACT: The simulation techniques development for multiaxis machining is key to the evolution of productivity and quality in the manufacture of mechanical parts with complex shapes (aerodynamic shapes, molds, etc.). The machining simulation representing accurately the cutting phenomenon is indispensable. However, this technique is penalized by the lack of knowledge of the cut. This field is wide and deals with various aspects. In this paper, the main machining simulation techniques are classified by category (geometrical and physical), by scale (multi-scale approach) and Part-ToolMachine (dynamic and geometric) system. In the end, particular attention is given to geometric simulation techniques at macroscale.
World Congress on Engineering 2014, London, U.K.; 07/2014
"Geometric simulation of the material removal process is an essential aspect in CNC machining simulation. Three groups of modelling methods have been applied, namely, the solid modelling and approximation methods    , the discrete vector intersection (DVI) methods  , and the spatial partitioning representation (SPR) methods using dexels   . "
[Show abstract][Hide abstract] ABSTRACT: CNC machining simulation has been developed to validate NC codes and optimize the machining process. Conventional simulation systems are usually performed in virtual environments, and this has the limitation that the operator needs to transfer the knowledge from the software environment to the real machining environment. The ARCNC system is proposed in this paper where the operator can observe in situ simulation between the real cutter and a virtual workpiece. The system design and the research problems addressed are discussed in this paper, including the tracking and registration methods and the physical simulation approach based on an enhanced dexel model.
"In the Z-map representation, an object is approximated as a set of z-axis aligned vectors, called Z-map vectors, passing through the grid points on the xy-plane  . This representation can be effectively used for the surface that is always visible from above in the direction parallel to the z-axes. "
[Show abstract][Hide abstract] ABSTRACT: 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.
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