Abstract: This paper experimentally studies the plastic forming method of the driving spiral bevel gear in automotive differentials. An experimental mold was designed and manufactured, and plastic forming experiments were conducted on a universal tensile testing machine. A grid experiment was used to study the metal flow on the cross-section of the plastically formed gear and the tooth filling process, revealing the orientation and distribution of metal fibers. The stroke-pressure curve of the plastically formed spiral bevel gear lead specimen was plotted, providing experimental basis for optimizing the design of the preform, forming mold structure, and calculating force and energy parameters. Keywords: Spiral bevel gear; Plastic forming; Metal flow; Forming force; Experiment I. Introduction Currently, in China, the driving and driven spiral bevel gears in automotive and tractor differentials are manufactured by machining the tooth profile of forged blanks using a Greenson gear cutting machine. While gear cutting is a mature and stable process, it has lower productivity and material utilization compared to plastic forming. Furthermore, machining the tooth profile of the forged blank cuts off the metal fibers, resulting in lower root bending fatigue strength, tooth surface contact fatigue strength, and tooth surface wear resistance, thus leading to a shorter gear service life. As the transmitter of vehicle motion power, gears operate under complex conditions and heavy loads. Shortening the vehicle's overhaul cycle not only results in significant economic losses but also raises concerns about vehicle safety. Practice has proven that plastic forming of gears not only offers high productivity and material utilization but also ensures that the metal fiber orientation adapts to the tooth profile, maintaining continuity. Compared to gears with machined teeth made from the same material, this significantly improves various strength indicators. If such gears are used to assemble automobile and tractor axles, it will undoubtedly extend the overhaul cycle and improve overall vehicle quality and operational safety. However, due to the complex tooth profile of the axle's driving spiral bevel gear (Figure 1), with its small cone apex angle and large helix angle, the metal's movement path to fill the cavity during plastic forming is long and winding, resulting in high flow resistance, difficulty in filling the cavity, and difficulty in demolding. Therefore, this study investigates and develops its precision forging production process and mold structure design through plastic forming simulation experiments. [align=center] Figure 1 Miniature vehicle axle active spiral bevel gear[/align] Z＝7 α＝22.5° Total tooth height h＝7.995 Helix angle β＝48° Tooth surface roughness 3.2μm, helix direction left II. Experimental mold 1. Simplification of specimen shape This experiment studies the plastic forming method of spiral bevel gear teeth. The shape of the gear shaft does not affect the plastic forming of the tooth shape. In order to simplify the structure of the experimental mold and facilitate processing and manufacturing, the experimental specimen of the spiral bevel gear in Figure 1 is designed with a simple cone shaft (Figure 2). [align=center] Figure 2 Experimental specimen[/align] 2. Experimental mold The tooth surface angle and tooth root angle of the die tooth of the active spiral bevel gear are the tooth root angle and tooth surface angle of the gear tooth, respectively. Both are acute angles less than 45° (Figure 1), and the node helix angle β＝48°. The interference of the geometric shape formed by this hinders the metal from entering the tooth cavity axially to form the tooth shape. The metal that can only enter the cavity axially through point A or point B (Figure 2) squeezes the corresponding part radially into the tooth cavity. This limits the preform part entering the die tooth cavity section to be contained within the tooth surface cone (i.e., the gear tooth root cone). The size and shape of the preform and the design of the experimental mold must adapt to this characteristic of the plastic forming of the active spiral bevel gear. (1) Closed die forging mold The mold structure of the closed die forging is shown in Figure 3. The characteristic of this mold is that before pressing the preform, screw 3 is tightened, thereby rigidly connecting the die 1 and the lower die 5 through the positioning connecting sleeve 4, forming a fixed cavity. Then, the press is started to press down the punch 2 until the punch 2 reaches the position shown in Figure 3. At this point, the press slide stops advancing and returns, screw 3 is removed, and the workpiece 6, together with the die, is ejected from the lower die 5 from the bottom. Then, the punch 2 ejects the workpiece 6 from the die, completing one work cycle. The pressed workpiece is shown in Figure 4. Because this mold requires a process of fixing and then opening the mold cavity during use, complex mold structures or double-action presses are required for production applications. [align=center] Figure 3 Closed die forging axle active spiral bevel gear test mold 1. Die 2. Punch 3. Screw 4. Connecting sleeve 5. Lower die 6. Workpiece 7. Pad 8. Ejector rod[/align] [align=center] Figure 4 Photograph of lead specimen of axle active spiral bevel gear plastic forming[/align] (2) Floating die Based on the operating experience of pressing active spiral bevel gear with closed die, we developed the floating die shown in Figure 5. The die 6 is located at the upper end of the screw 7 under the action of the spring 5. After the preform of workpiece 9 is loaded into the floating die 6, the press slide is started to drive the upper pad 11, guide sleeve 8 and upper die 10 downward. When the preform shaft is completely entered into the upper die cavity, the upper die 10 touches the floating die 6 and pushes it to compress the spring 5. During the compression of the spring 5, the punch 4 squeezes the preform to deform. The workpiece deformation ends when the floating die 6 contacts the limiting block 3 and the press slide returns. The workpiece remains in the floating die 6. A pad block (not shown in the figure) is placed at point C of the floating die 6, and then the press slide presses down a second time. The ejector rod (not shown in the figure) pushes the workpiece out of the floating die. The press slide returns, removes the pad block and the workpiece, and completes one work cycle. The gear specimen formed by this die is shown in Figure 4. [align=center] Figure 5 Floating die for forming spiral bevel gear 1. Lower pad plate 2. Die base 3. Limiting block 4. Punch 5. Spring 6. Floating die 7. Screw 8. Guide sleeve 9. Workpiece 10. Upper die 11. Upper pad plate[/align] III. Mesh test and pressure test 1. Mesh test The lead specimen blank is split along the plane at a predetermined position. After grinding and smoothing, straight mesh is engraved. Then, the split blocks are glued together with a low melting point alloy and processed into a preform of a predetermined shape. After die forging, the low melting point alloy is heated and melted to separate the specimen from the original split surface. Figure 6 shows a photograph of the mesh on the cross-section of the specimen after deformation. The strain at various points on the cross-section of the specimen was calculated based on the dimensions of the mesh before and after deformation, as shown in Figures 7 and 8. [align=center] (a) (b) Figure 6 Deformation of the grid on the split surface of the lead specimen (a) Cross section, grid prototype: circumferential division 5°40, radial 3mm (b) Longitudinal section, grid prototype is 3mm×3mm 1. Deformed grid with axial compression of 10mm 2. Deformed grid with axial compression of 20mm 3. Deformed grid with axial compression of 30mm 4. Deformed grid with axial compression of 40mm[/align] [align=center] Figure 7 Radial strain distribution on the cross section of the large end of the tooth (Δr0, Δr are the radial lengths of the grid before and after deformation) a. Grid on the cross section after deformation b. εr—r curve[/align] [align=center] Figure 8 Distribution of axial strain at the gear shaft center (Δz0, Δz are the axial heights of the grid before and after deformation) a. Gear cross section bz—εz curve[/align] 2. Pressure test The stroke-pressure curve of the lead specimen of the active spiral bevel gear of the axle plastic forming on the universal tensile testing machine is shown in Figure 9. [align=center] Figure 9 Stroke-pressure curves of lead specimens for plastic forming of active spiral bevel gears of micro automobile axles a—S-P curve of closed mold forming b—S-P curve of floating mold forming c—S-P curve of unloading d—S-P curve of lead specimen (φ34.6mm×h40mm) for free upsetting[/align] Substituting the axial projected area F of the gear formed in the test and the flow limit σs＝20N／mm2 of lead ε=-0.8 into equation (1), the coefficient k＝1.11～1.39 can be calculated. Therefore, the empirical formula for calculating the forming force of bevel gear teeth is: P＝（1.11～1.39）Fσ＊s（2） When forming with a closed mold with a locked die cavity, k＝1.39; when forming with a floating die cavity, k＝1.11. IV. Discussion The following conclusions were drawn from the experimental study: (1) It is feasible to use a die with a locking die cavity (Fig. 3) or a floating die cavity (Fig. 4) to upsetting the tooth profile of the axle drive spiral bevel gear with a punch. When forming in the locking die cavity, the punch needs to transmit a larger pressure (Fig. 9a), so the punch needs to have higher strength. Moreover, the opening, closing and locking of the upper and lower dies of this die requires additional power, or the use of a double-acting press, which also increases the complexity of the die structure. In comparison, the floating die cavity is better. (2) During upsetting, axial compression (εz < 0), radial and tangential extension (εr = εθ > 0) deformation occurs. Starting from the small diameter end, the small end tooth profile is formed and filled first. As the pressure continues to increase, the upsetting force increases, and the tooth profile is formed and filled sequentially from the small end to the large end. The preform shape required by this method is contained within the curved surface of the tooth root cone and the cylindrical surface formed by the axial translation of the tooth root circles at the large and small ends. Furthermore, the volume of the small end cylinder must be greater than half of the total tooth volume. If this part of the metal is placed at the large end, the upper and lower dies must be able to rotate relative to each other during the upsetting process. In severe cases, the pressure rises sharply, and although the tooth shape at the large end is full, the remaining tooth shapes are missing material. This deformation characteristic of the plastic forming tooth shape of the spiral bevel gear becomes the design criterion for the preform shape. (3) Since the grid lines are engraved on the cross section of the specimen according to the rolling direction of the bar, the deformation of the grid lines caused by the plastic deformation of the specimen also represents the deformation of the metal rolling fibers. The grid on the cross section of the specimen after deformation (Figure 6) shows that: the metal fibers remain continuous without any cutting marks; their distribution corresponds to the strain distribution; the direction of the fibers is related to the shape of the workpiece, and the shape of the fibers gradually becomes consistent with the shape of the workpiece from the inside to the outside, and the fiber linear density at the tooth root increases. The internal structure of the gear improves its quality, enhances its fatigue strength and wear resistance, and extends its service life. (4) Plastic forming of spiral bevel gear teeth has a higher productivity than cutting, lower equipment and tooling investment, and increases material utilization by more than 15%, reducing product cost by 10%. (5) The measured S-P curves of lead specimens (Figures 9a and 9b) show that the process force of upsetting spiral bevel gear teeth is relatively large, and it is all applied to the punch. However, the punch diameter is less than or equal to the root circle diameter of the small end of the gear, so its rigidity and strength cannot be increased, which limits its ability to withstand process force. The only way to achieve warm and hot plastic forming is to heat the steel parts to reduce the process force.