1. Introduction
Spiral bevel gears are crucial components in mechanical equipment, widely used in the transmission systems of helicopters, automobiles, etc. The quality of spiral bevel gears directly affects the service life of mechanical equipment. Heat treatment and grinding processes are important steps in the manufacturing of spiral bevel gears, which can have an impact on the surface integrity of the gears, such as the presence of residual stresses on the tooth surface. Detecting the residual stresses after heat treatment and grinding of gears is time-consuming and resource-intensive in the production process. The application of finite element simulation analysis methods can significantly shorten the detection cycle and reduce costs. Therefore, it is of practical significance to establish a mathematical analysis model of the gear heat treatment and grinding process through computer simulation methods.
2. Literature Review
In the field of gear heat treatment numerical simulation, many researchers have made contributions. Sugianto et al. studied the residual stress and microstructure distribution of SCr420H steel helical gear after carburizing and quenching. Lee Geunan applied numerical simulation methods to study the deformation problem of gears during the carburizing and quenching process. Sun Yonggang et al. studied the influence of temperature, stress, and carbon element diffusion on the heat treatment of large internal gear rings through the finite element method. Du Guojun et al. numerically simulated the quenching process of 20CrMnTi steel gears and studied the influence of different carburized layer thicknesses on the residual stress distribution. Zhu Jingchuan et al. calculated the temperature field and stress field of bevel gear workpieces using ABAQUS software.
Regarding metal grinding problems, Wang Haining et al. established a grinding model of a single cubic boron nitride abrasive grain and studied the influence of grinding parameters on residual stress using Deform – 3D software. Qu Wei used ANSYS software to simulate the residual stress of diamond wheel grinding cemented carbide. Huang Xinchun et al. studied the mechanism of residual stress generation during the grinding of superalloys and discussed the influence of residual stress on fatigue life. Li Wan et al. established a calculation model of tooth surface force – heat coupling and residual stress for the forming process of face gears. Zhang Yinxia et al. studied the influence of diamond roller dressing parameters on the grinding residual stress of high – strength steel. Wang Chuanyang et al. studied the influencing parameters of residual stress during the grinding process of EA4T steel.
However, previous studies have not conducted a coupled analysis of heat treatment and grinding processes. In this study, DEFORM and ABAQUS software are used to establish a three – dimensional finite element analysis model of the carburizing and quenching and grinding processes of spiral bevel gears, to obtain the change process and law of the residual stress of spiral bevel gears after the coupling of heat treatment and grinding processes, and to analyze the influence of different grinding parameters on the residual stress of spiral bevel gears, so as to guide the control of stress and deformation in the actual production process of gear machining and improve the performance and service life of spiral bevel gears.
3. Spiral Bevel Gear Heat Treatment Simulation
3.1 Heat Treatment Process Route
The material of the spiral bevel gear is 12Cr2Ni4A steel. The chemical composition and mechanical properties are shown in Table 1 and Table 2 respectively. The heat treatment process of the 12Cr2Ni4A steel spiral bevel gear includes normalizing, quenching, tempering, carburizing, deep – cold treatment, and low – temperature tempering. The process route is as follows: 930°C + 14K, 807°C, 927°C carburizing with a carbon potential of 0.9%, 815°C, 600°C, 621°C, air cooling, hot oil cooling, 500°C air cooling, air cooling, hot oil cooling, deep – cold treatment at – 80°C for 1.5h, air cooling at – 140°C for 1.5h, and low – temperature tempering at 140°C for 3h.
| Element | Mass Fraction |
|---|---|
| C | 0.10% – 0.150% |
| Mn | 0.30% – 0.60% |
| Si | 0.17% – 0.37% |
| Cr | 1.25% – 1.75% |
| Ni | 3.25% – 3.75% |
| P | <0.025% |
| S | <0.015% |
| Project | Numerical Value |
|---|---|
| Yield Strength / MPa | 1080 |
| Tensile Strength / MPa | 1175 |
| Elongation | 12% |
| Section Shrinkage Rate | 55% |
| Impact Toughness / (J·cm) | 80 |
3.2 Application of DEFORM Software
DEFORM software has a dedicated heat treatment module and can be used as a tool for heat treatment finite element analysis. The finite element analysis process of DEFORM software for heat treatment generally has three steps:
- Mesh Division: The mesh division of DEFORM software only has tetrahedral meshes, and the obtained mesh model is shown in Figure 2.
- Medium Definition: In heat treatment simulation analysis, the medium of each heat treatment process is different, including heating, carburizing, oil cooling, air cooling, and nitrogen cooling. Different media have different heat transfer coefficients and surface deformation coefficients. The air cooling definition interface is shown in Figure 3.
- Heat Treatment Scheme Definition: According to the heat treatment process route of the spiral bevel gear, the heat treatment scheme is defined, and the time and temperature of each process need to be input. The total heat treatment scheme definition interface is shown in Figure 4.
3.3 Heat Treatment Residual Stress Extraction Method
- The spiral bevel gear heat treatment result is sectioned in a direction perpendicular to the tooth length direction, and the section is shown in Figure 6.
- Taking the extraction of X – direction stress as an example, using the SV Distribution between Two Points function in the post – processing of DEFORM software, two points with a distance of 0.25mm are selected in the direction perpendicular to the tooth length direction (i.e., the tooth depth direction) as the starting point and the ending point, as shown in Figure 7. The points are evenly divided into 25 parts, and the stress results of each point with an interval of 0.01mm are obtained. The stress results are saved in a text document, and the X – direction stress variation curve with depth is shown in Figure 8.
- According to the above steps, the stress results in the other five directions are saved in text documents respectively, and the heat treatment residual stress extraction results are shown in Table 3.
- According to the above steps, the stress distribution states of the other four points on the tooth surface of the spiral bevel gear are extracted, and then the average value of the stresses of the five points is calculated to obtain the distribution state of the heat treatment residual stress.
| Depth | X – direction | Y – direction | Z – direction | XY – direction | XZ – direction | YZ – direction |
|---|---|---|---|---|---|---|
| 0 | – 4.05143 | – 1.07973 | – 6.60093 | 12.5401 | – 13.4972 | – 11.2482 |
| 0.010417 | – 3.86176 | – 1.11938 | – 6.74462 | 12.27085 | – 13.2886 | – 11.1906 |
| 0.020833 | – 3.66828 | – 1.16167 | – 6.88946 | 11.99188 | – 13.0745 | – 11.1306 |
| 0.03125 | – 3.4748 | – 1.20396 | – 7.03431 | 11.71291 | – 12.8604 | – 11.0706 |
| 0.041667 | – 3.28132 | – 1.24624 | – 7.17915 | 11.43394 | – 12.6463 | – 11.0105 |
| 0.052083 | – 3.08785 | – 1.28853 | – 7.324 | 11.15497 | – 12.4321 | – 10.9505 |
| 0.0625 | – 2.89437 | 1.33081 | – 7.46884 | 10.876 | – 12.218 | – 10.8905 |
| 0.072917 | – 2.70089 | – 1.3731 | – 7.61368 | 10.59704 | – 12.0039 | – 10.8305 |
| 0.083333 | – 2.50741 | – 1.41538 | – 7.75853 | 10.31807 | – 11.7898 | – 10.7705 |
| 0.09375 | – 2.31394 | – 1.45767 | – 7.90337 | 10.0391 | – 11.5757 | – 10.7104 |
| 0.104167 | – 2.12046 | – 1.49995 | – 8.04822 | 9.760129 | – 11.3616 | – 10.6504 |
| 0.114583 | – 1.92698 | – 1.54224 | – 8.19306 | 9.481161 | – 11.1475 | – 10.5904 |
| 0.125 | – 1.7335 | – 1.58453 | – 8.33791 | 9.202192 | – 10.9334 | – 10.5304 |
| 0.135417 | – 1.54003 | – 1.62681 | – 8.48275 | 8.923223 | – 10.7192 | – 10.4703 |
| 0.145833 | – 1.34655 | – 1.6691 | – 8.6276 | 8.644255 | – 10.5051 | – 10.4103 |
| 0.15625 | – 1.15307 | – 1.71138 | – 8.77244 | 8.365286 | – 10.291 | – 10.3503 |
| 0.166667 | – 0.95959 | – 1.75367 | – 8.91729 | 8.086318 | – 10.0769 | – 10.2903 |
| 0.177083 | – 0.76611 | – 1.79595 | – 9.06213 | 7.807349 | – 9.8628 | – 10.2302 |
| 0.1875 | – 0.57264 | – 1.83824 | – 9.20698 | 7.52838 | – 9.64869 | – 10.1702 |
| 0.197917 | – 0.37916 | – 1.88052 | – 9.35182 | 7.249412 | – 9.43457 | – 10.1102 |
| 0.208333 | – 0.18568 | – 1.92281 | – 9.49667 | 6.970443 | – 9.22046 | – 10.0502 |
| 0.21875 | 0.007796 | – 1.9651 | – 9.64151 | 6.691474 | – 9.00635 | – 9.99014 |
| 0.229167 | 0.304984 | – 2.02312 | – 9.86662 | 6.644376 | – 8.85951 | – 10.0834 |
| 0.239583 | 0.617178 | – 2.08343 | – 10.1033 | 6.630829 | – 8.72241 | – 10.1988 |
| 0.25 | 0.929371 | – 2.14373 | – 10.3401 | 6.617282 | – 8.58531 | – 10.3142 |
This method allows for a detailed understanding of the residual stress distribution after heat treatment of the spiral bevel gear. By analyzing the data in different directions and at different depths, we can better assess the impact of heat treatment on the gear’s surface integrity.
The extracted residual stress data can then be used as an initial condition for the subsequent grinding simulation. This coupling of heat treatment and grinding simulations provides a more comprehensive analysis of the overall manufacturing process of the spiral bevel gear and its resulting surface residual stress.
As shown in Figure 8, the X – direction stress shows a certain variation trend with depth. This trend can be further analyzed in combination with the mechanical properties of the gear material and the heat treatment process parameters. For example, the change in stress may be related to the cooling rate during heat treatment, the diffusion of alloying elements, or the formation of microstructure.
Similarly, the stress data in other directions also provide valuable information. The XY – direction and XZ – direction stresses, for instance, can reflect the shear stress components on the gear surface, which may affect the gear’s fatigue life and load – carrying capacity.