Abstract: Several 3D modeling methods were comprehensively analyzed and applied, considering the external structure, actual machining characteristics, and simulation animation forms of CNC machine tools. Based on the Structural Solid Geometry (CSC) modeling concept, a hierarchical and structured modeling method was adopted to construct the machine tool body (including cutting tools) model. A discretization method based on triangular meshes was used to effectively solve the problem of blank deformation animation simulation, realizing dynamic simulation of turning and milling processes. A particle system-based modeling strategy was used to realize physical animation simulation of irregular objects (such as coolant). The CNC simulation system developed based on the above methods has good realism and real-time animation simulation. 0 Introduction CNC machining is becoming increasingly important in modern manufacturing, and CNC simulation has been widely used. Compared with traditional CNC program verification methods such as dry running, trial cutting, and two-dimensional trajectory display, CNC simulation is safer and more effective. Modeling and simulating geometry and behavior based on actual CNC machine tools and machining processes has always been a key focus of CNC simulation systems. Various methods exist for representing and modeling 3D objects based on different characteristics, such as polygonal meshes and surfaces, quadratic surfaces and spline surfaces, scan representation, Constructive Solid Geometry (CSG), octree representation, fractal geometry, and particle system representation. Therefore, this paper adopts different modeling methods for different parts of the CNC simulation system with different geometric and behavioral characteristics, comprehensively adopting various excellent modeling strategies to achieve visualized modeling and simulation of the system. 1 Modeling Ideas Taking actual CNC machine tools as the object, based on their geometric and behavioral characteristics, the modeling and simulation of the CNC simulation system mainly includes the following three parts: (1) CNC machine tool body modeling (including cutting tools) The existence of the CNC machine tool body model not only increases the realism of the machining scene but also allows for collision detection during the machining process through the movement of various machine tool components. The machine tool geometric model can be regarded as an assembly, composed of components such as bed and column, and the components can be further subdivided; the motion simulation of machine tool components (such as the rotational motion of the tool magazine and the up-down motion of the spindle box in a CNC vertical machining center) is also relatively regular. Therefore, the machine tool body in the CNC simulation system usually adopts the idea of ​​CSG modeling method, and constructs a complex model through simple Boolean operations such as intersection, union, and difference between voxels. This method can intuitively and efficiently describe the machine tool body, and it is also easy to realize the regular motion of each component. (2) Dynamic modeling and simulation of machining process During the machining process, as the NC code is executed, the tool continuously cuts the workpiece, and the shape of the workpiece changes continuously, which belongs to the deformation animation of the workpiece. This has always been a difficult point to realize in the CNC simulation system. There are currently two main types of simulation methods: solid-based simulation method provides complete geometric and topological information of three-dimensional shape, performs accurate process simulation and tool path verification, but for the machining simulation of complex parts with a large amount of CNC code, the amount of calculation is huge and quite time-consuming; discrete simulation avoids the complex solid model representation and Boolean operation in solid simulation, and the method is simple and has high computational efficiency. This paper adopts a widely used, simple and efficient object space discretization method based on surface triangular mesh. By controlling the properties of a series of mesh points on the workpiece surface, the problem of deformation animation simulation of blank is solved. This avoids the problems of poor graphic generation quality and unsuitability for viewing workpieces from arbitrary perspectives caused by image space discretization method. Moreover, it can be well extended to CNC machining verification and error analysis. (3) Modeling of other dynamic processes during machining (such as coolant and chips) The motion simulation of coolant and chips can ensure the integrity of system functions and increase the realism of the scene. Taking coolant as an example: a large amount of liquid moves continuously and dynamically according to a certain law. This is a kind of motion that is not easy to point out by artificial description. Moreover, the geometry of the liquid is not easy to express accurately. For the physical animation simulation of such irregular objects, the modeling idea of ​​particle system is usually adopted - a scene generation system that simulates irregular and blurry objects. 2. Modeling Process 2.1 Machine Tool Body Modeling The CSG modeling approach is adopted, using a hierarchical and structured approach to construct the machine tool body model. The complex modeling process of the machine tool body is transformed into a combination of simple shape modeling activities. Specific modeling methods include: using the actual machine tool as the object, ignoring internal transmission devices and servo devices; subdividing the machine tool's geometric structure layer by layer, simplifying the geometric shapes of components according to similarity rules; and finally constructing the main component models of the machine tool through intersection and union operations of a set of regular geometric entities (cubes, cylinders, tori, etc.) from the software's 3D modeling library, thus ultimately forming a complete 3D model of the machine tool body. In the specific development of the system, difference operations were not used; instead, they were converted into a combination of intersection and union operations. This is because the 3D modeling of this software is based on the OpenGL 3D graphics library, and the difference operation of basic voxels in OpenGL involves template caching, which is relatively complex. In addition, behavioral modeling of the machine tool body is also required, mainly referring to handling the motion characteristics and mutual motion relationships of the moving parts of the machine tool, mainly considering aspects such as coordinate system determination, motion mode, degrees of freedom, and motion stroke. The modeling of cutting tools, fixtures, etc., is similar to that of the machine tool. Figure 1 shows the modeling process based on the CSG strategy, using the geometric modeling of a twist drill as an example. It can be seen as a microcosm of the machine tool body modeling process. First, two helical grooves are constructed through Boolean operations on basic voxels, which form the guide part of the twist drill. The twist drill is ultimately composed of three parts: the shank, the guide part, and the cutting part. In addition, parametric design is an important idea in tool modeling. Various parameters (such as the tool shank length L in Figure 1) are extracted from the actual tool to control the geometric features of the tool's three-dimensional model. [align=center] Figure 1 Schematic diagram of twist drill modeling[/align] 2.2 Dynamic simulation modeling of the machining process The specific strategy of the object space discretization method based on surface triangular mesh is: the upper surface is discretized into a uniform lattice, and then these lattices are connected into a triangular patch matrix. During program execution, the properties of the upper surface lattice are continuously modified according to the tool path, and then realistic rendering is performed to achieve the effect of real-time display of the machining process. The entire algorithm is divided into three parts: blank discretization; judgment and calculation process; blank drawing. 2.2.1 Blank Discretization This paper mainly focuses on CNC turning and three-axis milling: turning blanks are mostly cylindrical and are often used to machine rotating surfaces; three-axis milling blanks are generally cuboid, and only the upper surface of the blank is machined. Therefore, the discretization process differs slightly between the two. Figure 2 shows the discretization principle diagram of turning and milling blanks. Taking the turning blank as an example, its rotating surface is subdivided along the axial and radial directions to form a uniform quadrilateral grid array; if there is hole machining, the inner surface of the blank hole is also discretized into a quadrilateral grid; the two end faces are discretized into triangular or quadrilateral grids depending on whether there is hole machining. In blank discretization, not all general triangular grids are used (according to the principle of three points being coplanar), sometimes quadrilateral grids are used as the basic unit. Taking any quadrilateral ABCD in Figure 2 as an example, it is part of the rotating surface of the turning blank. Obviously, the four points ABCD are coplanar, which has the same effect as using triangular grids ABD and BCD, but is just a special case of triangular grids. [align=center]Figure 2 Schematic diagram of blank discretization[/align] The blank discretization process also includes the definition of node data structure and the sequential storage of node data. The choice of blank discretization accuracy (mesh node density) is also very important in the discretization process. The higher the accuracy, the better the realism of the graphics; however, it will also affect the real-time performance of the simulation. 2.2.2 Judgment calculation process The judgment calculation process of simulation generally includes: calculating the tool scanning domain and tool scanning surface according to the tool movement trajectory and tool type; judging whether the blank node is located in the tool scanning domain and whether it intersects with the tool scanning surface (to determine whether the blank node is cut by the tool); modifying the data of the cut node (node ​​radius value or height value). The focus of the judgment calculation process is the calculation of the tool scanning surface. Taking milling as an example, the material removal process in milling is the process of blank node data changing according to the tool scanning surface. We mainly discuss milling simulation for three types of tools (ball end mill, flat end mill, and ring mill). First, based on the APT (Automatically Programmed Tools) tool model, we judge the three types of tools through tool parameters, and then calculate the tool cutting scanning surface by category. The calculation of the tool scanning surface is relatively complex. Currently, one method for calculating the tool scanning surface involves: after obtaining the shape of the tool scanning surface based on the tool type, dividing the complex tool scanning surface into several components according to certain rules (the relationship between the shape features or the tool movement direction vector and the normal vector of the tool surface points), and then solving the mathematical expression for each component separately. This system uses the above method, decomposing the calculation of the complex tool scanning surface into relatively simple calculations for each component (plane, sphere, cylinder, etc.) according to the shape features. 2.2.3 Blank Drawing The blank drawing is based on the discretized mesh nodes, ignoring the internal structure of the blank, and drawing the entire blank shape envelope. Each face is approximated by triangular or quadrangular facets. Considering the software's real-time performance and realism, attention should be paid to issues such as the graphic hidden surface removal algorithm, smooth animation implementation, and node normal vector calculation (affecting lighting) during the specific implementation. Figure 3 shows the blank surface effect after row cutting using a ball end mill according to the above algorithm. 2.3 The application of particle system modeling method In order to simulate the dynamic effect of coolant spraying in actual processing, according to the particle system modeling strategy, the flowing coolant is regarded as being formed by the continuous movement of many liquid particles. First, these liquid particles are abstracted into particles with certain geometric features and behavioral attributes (such as particle position, type, growth time, etc.), and a doubly linked list structure is used to ensure the continuity of particle system movement; then, a set of mathematical features (particle shape features, motion trajectory equation, motion constraint equation) are defined to control the particle attributes; finally, the following four tasks are repeated in the dynamic movement of the particle system: particle source generates new particles, calculates and updates particle attributes, deletes dead particles, and draws particles, ultimately forming a continuous flow of particles. However, the particle system modeling method occupies memory and slows down the real-time performance of the simulation. Considering the real-time requirements of the entire system simulation, the following simplifications and assumptions are made when drawing the coolant: (1) Shape simplification. The texture mapping method can realistically reproduce the particle shape, but when the number of particles is huge, this method will greatly weaken the real-time performance of the simulation. Therefore, this paper defines the geometric shape of the particles in the coolant particle system as a short line segment along the particle movement direction. (2) Assuming the initial position of the particle's motion is the origin of the local coordinate system, this avoids the complexity of the motion equation and constraint equation; at the same time, the position of the coolant in the world coordinate system is determined by calling the glTranslate and glRotate functions in OpenGL. (3) The motion trajectory of the particle is simplified to a straight line trajectory instead of a complex curve equation; and the motion range of the particle is constrained to a mathematically describable region, such as a cone. (4) Assuming that the motion direction of each particle is random, it remains unchanged throughout its entire life cycle once determined. Figure 4 shows the final coolant effect diagram, in which the color, particle size, motion range, and particle density of the coolant particles can be modified by parameters. [align=center] Figure 4 Coolant simulation effect diagram[/align] 3 Conclusion This paper comprehensively applies a variety of modeling techniques and utilizes the advantages of various modeling methods to complete the modeling of a complex CNC simulation system. On this basis, in the Windows environment, based on OpenGL, a CNC simulation system was developed using Visual C++ 6.0. Figure 5 shows the three-dimensional model diagram of the lathe and the simulation effect diagram of the turning process. The example shows that the three-dimensional graphics display has a certain sense of realism, and the real-time simulation of the machining process animation is good. [align=center]Figure 5. Simulation effect of turning[/align]