Spiral bevel gears are mainly used for transmission between intersecting or offset shafts, offering advantages such as smooth transmission, low noise, and high load-bearing capacity. They are key components in mechanical products such as automobiles, tractors, and construction machinery. Current research on spiral bevel gear machining simulation is mostly based on secondary development of AutoCAD, constructing 3D solid models within the AutoCAD environment. However, due to the limited surface functionality of AutoCAD, it is difficult to construct complex curved surface parts. Mainstream CAE software (such as ABAQUS, MSC, and ANSYS) rarely develops interface programs for data exchange with AutoCAD, relying instead on data conversion files (such as SAT and STL), which are prone to data loss and surface defects, causing inconvenience for tooth surface machining errors and finite element analysis of the solid model. There are also studies that construct solid models of spiral bevel gears by deriving the equations of the tooth profile surface. However, for some machining methods of spiral bevel gears (such as the modification method) or when tooth surface parameter corrections are required during machining, it is difficult to obtain the analytical expression of the corrected tooth profile equation. Furthermore, the transition surface at the tooth root varies greatly due to different cutting tools, and the connection between the tooth surface and the transition surface is also difficult. Therefore, this method struggles to construct an accurate three-dimensional solid model of the spiral bevel gear, leaving unfavorable factors for the digital design and manufacturing of spiral bevel gears. Neither of these two studies addressed the specific manufacturing methods of spiral bevel gears, and currently, there is no research on spiral bevel gear machining simulation based on CATIA V5. This paper studies the implementation process of computer simulation machining of spiral bevel gears using the double-sided method. Using CATIA V5 as the platform, a double-sided machining simulation system based on the domestic YH603 spiral bevel gear CNC milling machine was developed. The system's development method is universal and can realize the machining simulation of any spiral bevel gear, providing a convenient and fast modeling platform for various analyses of spiral bevel gears. 1. Double-sided Machining of Spiral Bevel Gears 1.1 Cutting Principle of Arc-shaped Bevel Gears Spiral bevel gear machining uses a rocking table mechanism on a machine tool to simulate an imaginary gear. The cutting surface of the cutter head mounted on the rocking table is a tooth of the imaginary gear. When the gear being machined and the imaginary gear rotate around their respective axes at a certain transmission ratio, the cutter head cuts a tooth groove on the gear blank, as shown in Figure 1. When adjusting the cutting machine tool, the pitch cone surface of the gear being cut must be tangent to the pitch cone surface of the imaginary flat-topped gear and roll purely, while the cutting tip rotation plane must be tangent to the root cone of the gear being cut, as shown in Figure 2. Therefore, the milling cutter head axis is inclined to the pitch cone surface of the gear being cut by an angle equal to the root angle y of the gear being cut. This creates the problem of tool number correction. Consequently, the machining and adjustment of the gear being cut is relatively complex, and there are many specifications of cutting tools. This cutting principle is used when machining tapered arc-shaped bevel gears. [img=484,308]http://www.c-cnc.com/news/file/2008-6/2008610154211.jpg[/img] 1.2 Double-sided machining Double-sided machining refers to a machining process in which a gear is cut simultaneously on both sides of a tooth groove using a milling cutter disc with alternating internal and external cutting teeth. The width of the tooth groove is controlled by the cutter tip distance (i.e., the distance between the two concentric cutter tips). This is the most common gear cutting method used for the large gear in spiral bevel gears and hypoid gear pairs. In the double-sided machining method, both the large and small gears are machined using double-sided machining. The large gear can be machined using the generating method or not, while the small gear must be machined using the generating method. The double-sided method is suitable for gears with small modules (m≤2.5mm) and narrow tooth grooves. It is difficult to process the concave and convex surfaces of the small gear teeth separately using the hobbing method. Therefore, it is required that both the large and small gears be precisely cut with a double precision cutter in one operation to produce both the concave and convex surfaces. This method is suitable for mass production of small-sized gears. 2 Simulation of CNC Milling Machining of Spiral Bevel Gears 2.1 Structural Model of CNC Milling Machine for Spiral Bevel Gears The fully CNC machining machine tool for spiral bevel gears uses three orthogonal translational motion axes (X, Y, Z) and two orthogonal rotary motion axes (A, B) to replace the complex rocking table drum and tool tilting mechanism, realizing the generating machining of spiral bevel gears. Its structure is shown in Figure 3. O-XYZ is the machine tool coordinate system. The rotation of the rocker seat around the Y-axis, the rotation of the workpiece gear around its own axis A, the translation of the cutter head along the X and Y axes, and the translation of the workpiece head box along the Z-axis represent the five linkage axes B, A, X, Y, and Z of the CNC machine tool, respectively. It condenses the machining principle, control method, and motion of spiral bevel gears into a minimum of three linear shift axes and three rotary axes. Since the five-axis CNC machine tool can achieve any position of the tool relative to the workpiece in the machining space, it can fully meet the CNC machining requirements of spiral bevel gears. The machine tool adjustment parameters mainly determine parameters such as tool position, bed position, gear position, and rolling ratio. Based on these parameters, the relative position between the cutter head and the gear blank at any given time can be determined when the cutter head is cutting the gear blank. The machine tool adjustment parameters are given in multiple coordinate systems, but CNC machining must be performed in a unified coordinate system. That is, first, the coordinate position and posture of the tool relative to the workpiece are determined in the workpiece coordinate system, and then the coordinate values ​​of each axis in the CNC machine tool coordinate system are transformed to obtain the coordinate values. This ensures the relative motion relationship between the tool and the workpiece. Through the continuous change of the coordinates of each axis of the CNC machine tool, the generating motion of the spiral bevel gear can be simulated by CNC. 2.2 Machine Tool Parameters According to the meshing machining principle of spiral bevel gears, the cutting gear and the gear being machined can be regarded as a pair of meshing gears. The geometric and cutting parameters of the spiral bevel gear can be calculated, thus obtaining the machine tool adjustment parameters. With the machine tool adjustment parameters, the relationships between various coordinate systems, as well as the positions and orientations of the tool and workpiece within these coordinate systems, can be established. Figure 4 shows the coordinate relationship between the machine tool and the tool, and Figure 5 shows the coordinate relationship between the machine tool and the workpiece. [img=587,284]http://www.c-cnc.com/news/file/2008-6/2008610154319.jpg[/img] First, establish the coordinate systems. S[sub]o[/sub]={O[sub]o[/sub]；x[sub]o[/sub]，y[sub]o[/sub]，z[sub]o[/sub]}、S[sub]q[/sub]={O[sub]q[/sub]；x[sub]q[/sub]，y[sub]q[/sub]，z[sub]q[/sub]} are the coordinate systems of the machine tool and the workpiece, and are fixedly connected to the bed. S[sub]c[/sub]={O[sub]c[/sub]；x[sub]c[/sub]，y[sub]c[/sub]，z[sub]c[/sub]}、S[sub]p[/sub]={O[sub]p[/sub]；x[sub]p[/sub]，y[sub]p[/sub]，z[sub]p[/sub]} is a movable coordinate system fixed to the rocking table and bevel gear. S[sub]t[/sub]=｛O[sub]t[/sub]；x[sub]t[/sub]，y[sub]t[/sub]，z[sub]t[/sub]｝ is the coordinate system fixed to the tool, S[sub]b[/sub]=｛O[sub]b[/sub]；x[sub]b[/sub]，y[sub]b[/sub]，z[sub]b[/sub]｝ is the coordinate system fixed to the rocker table before the tool tilts and rotates, and S[sub]n[/sub]=｛O[sub]n[/sub]；x[sub]n[/sub]，y[sub]n[/sub]，z[sub]n[/sub]｝ is the transition coordinate system and fixed to the machine tool. The figure shows all the initial conditions and symbols that determine the relative positional relationship between the cutter head and the workpiece: O[sub]c[/sub] is the center of the rocker table, O[sub]t[/sub] is the center of the cutter head, i is the total tool tilt angle, j is the tool rotation angle, δm is the blank mounting angle, E is the machining offset distance, O[sub]p[/sub] is the intersection point of the gear axis, q is the angular tool position (i.e., the production wheel rotation angle), S is the radial tool position, x[sub]b[/sub] is the bed position, x is the axial wheel position, and φ[/font] is the rotation angle of the gear around its axis. 3 Computer simulation system for double double-sided machining of spiral bevel gears based on CATIA V5 platform 3.1 Machining simulation principle In order for the tool to remove part of the metal from the gear blank to obtain the gear part, there needs to be an instantaneous overlap area between the tool and the gear blank during the cutting process. This overlap area is the metal to be cut off. From a geometric perspective, let the geometry of the gear blank be A and the geometry of the cutting tool be B. Discretizing the motion of the gear blank and the cutting tool, the cutting process can be divided into n cutting time periods. During these time periods, the cutting tool geometry and the blank geometry are relatively stationary and have a certain overlapping area. Then, the cutting in this time period can be regarded as subtracting the area overlapping between the gear blank geometry A and the cutting tool geometry B from the gear blank geometry A. By subtracting in each time period, the result left on the workpiece blank is the envelope of the cutting tool surface, which gives us the surface of the machined gear. The spatial topological relationship of this process can be represented as A_i+1 = A_i - (A_i ∩ B)ⁱ = (0, 1, 2, ..., n). The cutting tool trace is the "mark" left by the cutting edge of the cutting tool on the gear blank during the gear generating process. The simulation of the tool trace formation process aims to reproduce the process of the tool trace forming successively on the gear blank, and vividly describe the relationship between the tool tooth profile curve and the gear tooth shape. To this end, a coordinate system is fixed to the gear blank and rotates with it according to its rotational speed. In this coordinate system, the gear blank is "stationary," while the tool moves spatially according to certain rules. On the one hand, it rotates around the gear blank axis, constituting the tool's entanglement motion; on the other hand, it rotates relative to the machine tool's rocker table. The tool's motion is a synthesis of these two motions. Machine tool cutting is a continuous process, while simulation can only provide a finite number of relative positions between the tool and the workpiece. Therefore, we must discretize the motion relationship to obtain data corresponding to a finite number of relative positions. Discretization means taking one variable in the motion relationship as the independent variable, giving it some values ​​during the machining process, and then calculating the corresponding values ​​of other variables at these points based on the motion relationship. 3.2 Method for Simulating Spiral Bevel Gear Machining using CATIA V5 3.2.1 Introduction to CATIA V5 CATIA V5 is a high-end CAD/CAM software system developed by IBM/DS based on the Windows core. CATIA has evolved into an integrated CAD/CAE/CAM system with a unified user interface, data management, and compatible databases and application programming interfaces, comprising over 20 independent modules. CATIA V5, with its powerful surface design capabilities, is widely used in mechanical, aerospace, automotive, and shipbuilding design fields. CATIA's surface modeling capabilities are reflected in its rich set of modeling tools to support users' modeling needs. For example, its unique high-order Bezier curve and surface function, with a degree of up to 15, can meet the stringent requirements of special industries for surface smoothness. CATIA V5 also has interface programs with CAE software (such as MSC.simDesigner), allowing for easy import of models into software such as Nastran, ad-ams, ANSYS, and ABAQUS for various linear or nonlinear analyses and simulations. For the study of complex surface parts such as spiral bevel gears, it facilitates model construction and data conversion. 3.2.2 Method for Simulating Spiral Bevel Gear Machining in CATIA V5 For CNC milling machine tool machining, the adjustment process and the entire machining process are achieved by the movement of CNC axes. Therefore, simulating the movement of this machine tool is actually simulating the movement of the five CNC axes of the machine tool. To simulate the machining process of spiral bevel gears in CATIA V5, firstly, the simulation system can be set to the same coordinate system as the machine tool; then, the rotation of the disc milling cutter geometric model around the axis of the rocker table can be used to represent the two translations of the machine tool in the X and Y directions; finally, the rotation of the cutter head geometric model around the gear blank geometric model can be used to represent the A-axis movement. The complete simulation system implementation process is as follows: First, generate the gear blank entity and disc milling cutter entity based on the workpiece gear parameters and disc milling cutter parameters; then, adjust the position of the gear blank entity and the disc milling cutter position according to a set of CNC axis linkage parameters, while performing a Boolean subtraction operation between the two entities, and continue reading the linkage data until one tooth groove is machined; the gear blank indexes around its own axis to machine the next tooth groove, until all tooth grooves are machined. Because the simulation process discretizes the machining process, manual operation would be too labor-intensive and could not dynamically demonstrate the machining process. In CATIA V5, its convenient secondary development functions allow for the development of corresponding machining simulation systems, enabling the machining process to be controlled by a program. 3.2.3 Composition of the Virtual Machining System The machining simulation system mainly consists of two parts: a tool database and a machine tool database. The tool database records the shape and size of the tools, while the machine tool database records the adjustment parameters of the machine tools during machining. As shown in Figure 6, after the gear blank model enters the manufacturing system, by selecting the corresponding tool type and size from the tool database, and adjusting the position parameters of the gear blank on the machine tool and the machining stroke of the tool, a virtual machining model of the gear part can be generated. 3.2.4 System Program Flow The above functions can be implemented through the program flow shown in Figure 7. After starting the program, the parameters of the gear part, tool parameters, and machine tool parameters are input in the corresponding virtual machining system interface, and the machining command is executed. The program then checks whether CATIA V5 is started. If CATIA V5 is already started, it directly enters the part module; if CATIA V5 is not started, it starts CATIA V5 before entering the part module. After entering the part module, create a new gear blank model, then create a tool model, and simultaneously adjust the tool position. Then, perform Boolean operations on the tool geometry and gear blank geometry to cut off the position occupied by the tool on the gear blank, and determine whether a tooth groove has been cut. If not, repeat the above steps and adjust the tool to the next cutting position. After completing one tooth groove, process the next tooth groove to complete the entire manufacturing simulation modeling process. 3.3 Steps for CATIA V5 secondary development There are already many articles that introduce the principles of CATIA V5 secondary development in detail. This article only introduces the steps for CATIA V5 secondary development using VB6.0: (1) Initialize the COM library and import the type library file. VB6.0 can import it from the IDE. The type library file is a binary file, but after compilation, it generates a type library header file (extension TLH) and a type library implementation file (extension TLI). The type library header file is a language format file in the corresponding environment, containing object definitions, globally unique identifiers, definitions of structures, methods and properties used in the object, smart pointer (SmartPoint-er) definitions, cross-references to type libraries, etc. If it is a cross-referenced type library, it should be imported in the order of reference, otherwise a compilation error will occur. The type library implementation file is the implementation code of the object and its interface. (2) Open or create a global object Application, which starts CATIA. (3) Add Document objects to Application to realize data management, such as PartDocument used for part drawing design, ProductDocument used for product drawing, and DrawingDocument used for three-view drawing. (4) Declare the object to be used, set the reference plane and viewpoint, and draw the geometry. (5) Update the Document object or Viewer object so that the geometry is displayed correctly. (6) Close Document and release COM library resources. 4 Application example 4.1 Simulation system development Take the YH603 series spiral bevel gear CNC milling machine as the simulation system development object. Since the YH1603 series spiral bevel gear CNC milling machine is a four-axis linkage machine tool, the simulation program can realize a five-axis linkage machine tool. The simulation system can realize the simulation of a four-axis linkage machine tool by fixing the rotation of the C-axis during the machining simulation. 4.1.1 Interface Development Based on the machining parameter types of the YH603 series spiral bevel gear CNC milling machine, the simulation program interface was developed as shown in Figure 8. The interface consists of three parts: (1) Parameter comparison area. There are many machining parameters for spiral bevel gears. Each parameter is represented in the form of a diagram to facilitate parameter input and prevent parameter input errors; (2) Parameter input area; (3) Program operation area. 4.1.2 Simulation System Development Based on the simulation program development flowchart, and following the steps of CATIA V5 secondary development, a corresponding VB program was developed to control the modeling process of CATIA V5. The machining process is controlled by the "clock control" to control the time interval of each Boolean operation, which allows the cutting process of the gear blank to be seen during the modeling process, as well as the speed of machining. Due to space limitations, the development process of the simulation program will not be described in detail. 4.2 Application of the Simulation System [img=634,186]http://www.c-cnc.com/news/file/2008-6/2008610154749.jpg[/img] Select a pair of spiral bevel gears, and their machining parameters are shown in Table 1. Input the parameters into the simulation program, and after running the program, the machining process can be seen in the CATIA V5 window. Figure 9 is a momentary image of the simulated machining process. After machining is completed, other features are added to the model to obtain the final model image, as shown in Figure 10. Figure 11 is a photograph of a pair of meshing spiral bevel gears actually machined on a YH603 gear milling machine using the same data as the machining simulation software. As can be seen from the figure, the tooth profile and tooth direction of the machining simulation image and the actual image are consistent. After actual verification, the simulation results are also consistent with the actual results. This shows that the CNC machining simulation system can very accurately simulate the actual machining process of the CNC gear milling machine, and the simulation results are accurate and reliable. [img=496,223]http://www.c-cnc.com/news/file/2008-6/2008610154826.jpg[/img] 5 Conclusion Based on CATIA V5 as the platform and the principle of conjugate tooth envelope as the theoretical foundation, this study uses a method of simulating the machining process of real gears to construct a spiral bevel gear model. By utilizing the secondary development technology of CATIA V5 to automate the machining process, it is possible to simulate the machining of complex parts such as gears and construct a solid model consistent with the actual machined parts. This provides an accurate three-dimensional geometric model for spiral bevel gear tooth surface contact analysis (TCA) and finite element stress analysis (FEA).