Abstract: The dense grid pattern method is introduced into the study of gear precision forging. Based on the grid pattern image of the flow distribution surface of the forging at the final stage of spur gear stamping precision forging, the displacement-velocity field is derived, and the corresponding deformation law is obtained, providing a basis for further research on strain distribution. Keywords: Spur gear; Stamping precision forging; Dense grid pattern method I. Introduction For three-dimensional unsteady nonlinear large deformation problems such as spur gear precision forging, it is difficult to obtain the displacement and strain fields of the metal flow throughout the entire deformation process using theoretical methods. The dense grid pattern method, as an experimental analytical method, can realistically record the full-field displacement of the deformed body using the grid pattern image. Through analysis, strain information can be obtained, thus identifying the macroscopic plastic flow law of the deformed body. Therefore, introducing the dense grid pattern method into the study of gear precision forging is appropriate. This paper takes a certain type of tractor reduction pinion [1] (15 teeth, 3.5 module, height displacement coefficient 0.395, gear thickness 26.5mm, Figure 1) as the research object. The principle of "displacement increment differential method" [2] of the in-plane dense grid pattern cloud pattern method is used to obtain the cloud pattern image of the deformation of the flow surface of the forged part of the extruded precision forging of the gear, and then solve the displacement velocity field to analyze the deformation law of the metal. [align=center] Figure 1 Reduction pinion part[/align] II. Cloud Pattern Experiment The extrusion precision forging simulation experiment was carried out in the special mold [1] shown in Figure 2 using industrial pure lead solid cylindrical blanks. The mold is separable and uses a combined floating die to ensure that the lower corner of the tooth tip is filled. The upper die is equipped with a flow punch and flash groove to ensure that the upper corner of the tooth tip is filled. The punch radius is 10mm and has a draft angle. The die is equipped with a push rod to ensure that the forging is ejected from the die. The experimental forming equipment is a YE-1000 hydraulic pressure testing machine. According to the displacement increment differential method, when the billet is stamped and forged to the final stage of deformation, the billet is taken out and split along the splitting surface (since the number of gear teeth is odd, one side of the splitting surface has teeth and the other side does not), a cloud-patterned grid is attached, and then it is put back into the mold for incremental deformation, and the corresponding cloud-patterned image is photographed (Figure 3). The deformation situation is shown in Table 1. The grid line density of the reference grid and the test piece grid is 12l/mm. [align=center] Figure 2 Simplified diagram of the splittable mold for stamping and forging of spur cylindrical gear[/align] [align=center] Table 1 Cloud-patterned experimental situation[/align] [align=center] Figure 3 Cloud-patterned image of the final stage of stamping and forging of spur cylindrical gear with industrial pure lead simulated hot steel (a) Field cloud-pattern (b) Field cloud-pattern[/align] III. Determination of displacement velocity field The above cloud-patterned image is essentially a displacement velocity field of a certain proportion. With the central axis of the forging as the z-axis, its direction is upward, and a rθz cylindrical rectangular coordinate system is established. Based on the mottled image, the center line of the mottled black band was drawn, the mottled order was determined, and a scanning grid was divided along the r and z directions (Figure 4). The grid spacing was 2-5 mm. In areas with denser mottled patterns, the strain gradient was larger, so the grid should be denser, and vice versa. After the grid was divided, the field of the center line of the mottled black band was scanned along the grid section in the z direction and along the grid section in the r direction, thus obtaining the relationship data between the coordinate position (r, z) of the center of the mottled black band and the displacement velocity components (s). In order to eliminate scanning errors, the data were fitted according to the relevant numerical method [3], and then the displacement velocity field curves of the split surface -r, -z, -r and -z were plotted based on the fitted data (Figures 5-12). [align=center] Figure 4 Center line and scanning grid division of black bands in field (a) and field (b)[/align] [align=center] Figure 5 Left half of the flow splitter surface (with teeth) -r curve[/align] [align=center] Figure 6 Right half of the flow splitter surface (without teeth) -r curve[/align] [align=center] Figure 7 Left half of the flow splitter surface (with teeth) -z curve[/align] [align=center] Figure 8 Right half of the flow splitter surface (without teeth) -z curve[/align] [align=center] Figure 9 Left half of the flow splitter surface (with teeth) -r curve[/align] [align=center] Figure 10 Right half of the flow splitter surface (without teeth) -r curve[/align] [align=center] Figure 11 Left half of the flow splitter surface (with teeth) -z curve[/align] [align=center] Figure 12 The right half of the flow splitting surface (toothless) - z curve[/align] IV. Results Analysis 1. Mottle Pattern Image As shown in Figures 3 and 4, the field and field mottle patterns are as follows: (1) The mottle patterns are very dense near the punch end face and the small protrusion at the tooth tip, indicating that the metal plastic deformation and strain in these areas are relatively large. The mottle patterns in other areas are relatively sparse, and the strain is relatively small. (2) There are no mottle patterns at the tooth bottom corner and the punch root, indicating that these areas may be rigid or viscous areas. (3) Due to the asymmetry of the left and right parts of the flow splitting surface, the mottle patterns are also asymmetrical overall. However, in some locally symmetrical areas, such as near the punch end face and the outer edge of the die ejector pin, the mottle patterns are relatively symmetrical, indicating that the displacement and strain of the deformed body in these areas are relatively symmetrical. (4) In the area near the punch, the field mottle patterns and field mottle patterns are basically parallel to the reference grid lines, indicating that there is mainly normal strain in these areas. The mottle patterns in other areas are basically oblique to the reference grid lines, indicating that both normal strain and shear strain have certain values. (5) The cloud patterns of each level converge at the outer edge of the top of the ejector pin (r≈15mm) to form radial cloud patterns, indicating that the metal deformation flow here is very intense and there is a strain concentration phenomenon. The strain source is concentrated in the center of the cloud pattern ray. In reality, this is because a small amount of metal is squeezed out from the joint gap between the die core and the ejector pin here. (6) The areas such as the rounded corner of the punch, the outer edge of the ejector pin and the small protrusion of the tooth are the "singularities" of the displacement velocity. Various different flow velocities converge here. 2. Displacement velocity field As can be seen from the displacement velocity field curves shown in Figures 5 to 12: (1) The radial displacement velocity of the deformed metal is distributed as follows: its direction is always the same as the r axis. Its value is zero at the center of the forging. Then it gradually increases along the positive direction of the r axis. After reaching the maximum at a certain point, it decreases again until it decreases to zero again at the die wall. The areas where the maximum value is obtained are distributed in the punch fillet (r=9～10mm, z≤4.35mm), between the punch sidewall and the die wall (r＝18～20mm, z≥4.35mm), etc. However, due to the blank being split and covered with grid plates, a small amount of metal is squeezed into the gap at the die wall, which is slightly greater than zero. (2) The axial displacement velocity is distributed as follows: Before the punch shoulder forges to the die, in the region of r＝0～7mm, the direction is opposite to the z-axis, and the magnitude gradually decreases from the punch end face along the z-axis to zero at the bottom of the die; in the region of r＝7～10mm, the half-conical surface is the flow splitting surface, the direction is reversed, and the magnitude is about zero; in the region of r＞10mm, the direction is the same as the z-axis, and the magnitude gradually increases along the positive z-axis. After forging to the rear, the direction is opposite to the z-axis, and the magnitude gradually decreases along the z-axis to zero at the bottom of the die. V. Conclusion This paper applies the dense grid pattern method to study the deformation of spur gears during stamping and precision forging. Based on the pattern images of the flow distribution surface of the forging obtained in the final stage of deformation, the corresponding displacement velocity field was derived, and the metal deformation was analyzed accordingly. This provides a basis for further application of the dense grid pattern method to study the strain distribution of spur gears during stamping and precision forging.