1. Introduction
Spiral bevel gears are crucial components in mechanical transmission systems, widely used in various industries such as automotive, aerospace, and machinery manufacturing. The traditional machining methods of spiral bevel gears have certain limitations, and with the development of numerical control technology, CNC milling machines have become an important means for machining spiral bevel gears. However, in the actual machining process, due to the influence of factors such as the size and installation conditions of the CNC milling machine, the machining specifications and precision of spiral bevel gears cannot be significantly improved. Therefore, it is of great significance to study the automatic programming processing technology of spiral bevel gears on CNC milling machines to improve the machining quality and efficiency of spiral bevel gears.
2. Design of Cutting Parameters for Spiral Bevel Gear CNC Milling Machine
2.1 Controllable Parameters
- Cutting Speed: The cutting speed of the CNC milling machine is the rotary motion of the hob around its own axis. The formula is (v = \frac{n}{d_{0}}), where (n) is the rotational speed of the hob of the CNC milling machine, and (d_{0}) is the outer diameter of the hob of the CNC milling machine. Different machining modules of spiral bevel gears correspond to different cutting speeds. As shown in Table 1, for different machining modules, the cutting speed of the CNC milling machine should be set within the required range. When the number of hob heads and the manufacturing precision of the hob change, the cutting speed of the milling machine should be adjusted accordingly.Machining ModuleCutting Speed Range(m_1)(v_1) – (v_2)(m_2)(v_3) – (v_4)……
- Number of Feeds: The number of feeds of the CNC milling machine should be set according to the machining efficiency requirements of spiral bevel gears. If there are no special requirements for machining efficiency, a single feed method can be used for machining.
2.2 Uncontrollable Parameters
In addition to the above controllable parameters, there are also some uncontrollable parameters in the machining process of spiral bevel gears on CNC milling machines, such as the material properties of the workpiece, the wear of the cutting tool, and the machining environment. These uncontrollable parameters will also affect the machining quality of spiral bevel gears, so it is necessary to pay attention to and control these factors as much as possible in the actual machining process.
3. Trajectory Planning of Spiral Bevel Gear CNC Milling Machine Tool
3.1 Selection of Cutting Method
After the design of the cutting parameters of the spiral bevel gear CNC milling machine is completed, a cutting method with a high degree of adaptability should be selected. Different cutting methods have different characteristics and适用范围, and the appropriate cutting method should be selected according to the specific machining requirements and characteristics of spiral bevel gears.
3.2 Determination of Tool Trajectory Route
- Setting of Coordinate Positions: The starting point coordinate position of the milling machine tool is set as ((x_{0}, z_{0})), and the coordinate of the contact point between the milling machine tool and the spiral bevel gear workpiece is set as ((x_{2}, z_{2})). The installation deflection angle of the milling machine tool is set as (\theta).
- Derivation of Ellipse Section Curve Equation: According to the relationship between the installation deflection angle of the milling machine tool and the size of the long axis of the ellipse, the ellipse section curve equation of the CNC milling machine tool is obtained as (\frac{(x_{0}-x_{2})}{R^{2}}+\frac{(z_{0}-z_{2})\cos^{2}\theta}{R^{2}} = 1), where (R) represents the ellipse tooth tip curve of the CNC milling machine tool.
- Determination of Cutting Depth and Tool Trajectory: According to the ellipse section curve equation of the tool, the cutting depth of the CNC milling machine is determined. A set of cutting planes is used to intercept the machined surface of the spiral bevel gear based on the principle of automatic programming, forming a series of intersection lines. The tool is controlled to move along the intersection lines of the surface. Based on the automatic programming processing technology, the width change of each cutting layer in the tooth groove of the CNC milling machine is analyzed in real time, and the section angle line of the tooth surface is offset according to the travel times of the cutting layer. Combined with the width change of the tooth groove, the cutting depth of the milling machine tool is adjusted, and then the next machining trajectory of the milling machine tool is determined to ensure that the machining trajectory of the tool covers the entire tooth groove.
4. Automatic Programming Design of CNC Milling Machine
4.1 Design of Tool Setting and Preparation Program
- Tool Setting: Due to different machining requirements of spiral bevel gears, there are certain differences between the machine origin in the CNC milling machine coordinate system and the tool position origin in the tool coordinate system. Therefore, tool setting should be carried out before each machining of the CNC milling machine. The program origin in the workpiece coordinate system is determined, and the machining tool reference point is determined by using MATLAB analysis software according to the relative position of the program origin. The tool setting point is controlled to coincide with the reference point, and the tool tip plane is perpendicular to the root cone plane of the gear blank to complete tool setting.
- Preparation Work: After tool setting, preparation work is carried out, including setting the spindle rotation speed of the milling machine tool, the tool feed speed, and the flow rate of the milling machine cutting fluid. If there are no special machining requirements, the default values can be set according to the default values.
4.2 Design of Machining Main Program and Auxiliary Program
- Machining Main Program: The machining main program is mainly responsible for controlling the milling of the tooth profile of the CNC milling machine to ensure that the tooth profile is evenly distributed in a ring shape. The linkage relationship between the motion axis and the rotation axis of the CNC milling machine is set. After machining one gear, the rotation axis begins to perform the indexing motion.
- Auxiliary Program: The auxiliary program for indexing and cutting teeth is nested in the machining main program. The main program is used when machining the two sides of the large gear of the spiral bevel gear, and the auxiliary program is used when machining the two side surfaces of the spiral bevel gear. In this CNC program, design statements are used to perform corresponding actions, as shown in Table 2.Program StatementCorresponding Action(S1)Action 1(S2)Action 2……
5. Experimental Analysis
- Modeling and Coordinate Calculation: The geometric parameters of the spiral bevel gear blank, such as the number of teeth and the module, are input into the automatic programming processing software, and the geometric model of the spiral bevel gear blank is generated through software geometric modeling. According to the machining parameters of the CNC milling machine, such as the vertical wheel position and the horizontal wheel position, the coordinates of the tooth points of the spiral bevel gear are calculated, including the position, path, and cutting direction of the tool during the machining process.
- Generation of Theoretical Tooth Surface: The coordinate data of the tooth points is saved in a file format and read by the automatic programming software. The software automatically fits and generates the theoretical tooth surface of the spiral bevel gear according to these tooth point coordinates.
- Tool Trajectory Planning and Machining: On the generated spiral bevel gear model, the tool trajectory of the CNC milling machine is planned by using the automatic programming software.