Spiral bevel gears are crucial components in mechanical equipment, widely applied in transmission systems of helicopters, automobiles, and other machinery. 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 have a certain impact on the surface integrity of the gears, such as the presence of residual stresses on the tooth surface. In the production process, the detection of residual stresses after heat treatment and grinding of gears is rather labor- and material-intensive. However, the application of the finite element simulation analysis method can significantly shorten the detection cycle and save costs. Therefore, establishing a mathematical analysis model of the gear heat treatment and grinding process through computer simulation has certain practical application significance.
1. Research Background
Spiral bevel gears play a vital role in the transmission system of mechanical equipment, and their quality directly relates to the lifespan of the machinery. The heat treatment and grinding processes are significant for these gears, which can affect the surface integrity, such as generating tooth surface residual stresses. In the production, the detection of residual stresses after heat treatment and grinding of gears is quite laborious and resource-consuming. However, the utilization of the finite element simulation analysis approach can greatly reduce the detection period and cost. Hence, establishing a mathematical analysis model of the gear heat treatment and grinding process through computer simulation holds definite practical application significance.
In the aspect of numerical simulation of gear heat treatment, Sugianto et al. studied the distribution of residual stresses and microstructure in the teeth of SCr420H steel helical gears after carburizing and quenching; Lee Geunan investigated the deformation problem of gears during the carburizing and quenching process using the numerical simulation method; Sun Yonggang et al. studied the influence of temperature, stress, carbon element diffusion, etc. on the heat treatment of large internal gear rings through the finite element method; Du Guojun et al. conducted a numerical simulation of the quenching process of 20CrMnTi steel gears to research the influence of different carburizing layer thicknesses on the distribution of residual stresses; Zhu Jingchuan et al. calculated the temperature field and stress field of bevel gear workpieces by applying the ABAQUS software. Regarding the issue of metal grinding, Wang Haining et al. established a grinding model of a single particle of cubic boron nitride abrasive grains and studied the influence of grinding parameters on residual stresses using the Deform-3D software; Qu Wei conducted a residual stress simulation of diamond grinding wheels grinding hard alloys by applying the ANSYS software; Huang Xinchun et al. studied the mechanism of the generation of residual stresses during the grinding process of high-temperature alloys and discussed the impact of residual stresses on fatigue life; Li Wan et al. established a calculation model of tooth surface force-thermal coupling and residual stresses for the forming process of face gears; Zhang Yinxia et al. investigated the influence of diamond roller dressing parameters on the residual stresses of high-strength steel grinding; Wang Chuanyang et al. studied the parameters influencing the residual stresses in the grinding process of EA4T steel.
Comprehensively, previous studies have not conducted a coupled analysis of the heat treatment and grinding processes. In this study, the DEFORM and ABAQUS software were applied to establish a three-dimensional finite element analysis model of the carburizing, quenching, and grinding processes of spiral bevel gears, obtaining the change process and rules of residual stresses after the coupling of the heat treatment and grinding processes, and analyzing the influence of different grinding parameters on the residual stresses of spiral bevel gears, so as to guide the control of stress and deformation in the actual gear processing, improve the performance of spiral bevel gears, and extend their service life.
2. Heat Treatment Simulation of Spiral Bevel Gears
2.1 Heat Treatment Process Route
The material of the spiral bevel gear is 12Cr2Ni4A steel, and its chemical composition is shown in Table 1, while its mechanical properties are presented in Table 2. The heat treatment process of 12Cr2Ni4A steel spiral bevel gears includes normalizing, quenching, tempering, carburizing, cryogenic treatment, and low-temperature tempering, and the process route is as shown in Figure 1.
| 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 | Value |
|---|---|
| Yield Strength / MPa | 1080 |
| Tensile Strength / MPa | 1175 |
| Elongation | 12% |
| Section Shrinkage | 55% |
| Impact Toughness / (J·cm) | 80 |
2.2 Application of DEFORM Software
The DEFORM software has a dedicated heat treatment module and can be used as a tool for heat treatment finite element analysis. The general process of finite element analysis with the DEFORM software for heat treatment includes three steps:
- Mesh Division: The mesh division of the DEFORM software is only tetrahedral mesh, and the obtained mesh model is as shown in Figure 2.
- Medium Definition: In the 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 Analysis Results: The heat treatment analysis results are as shown in Figure 5.
2.3 Heat Treatment Residual Stress Extraction Method
In order to more accurately define the initial residual stress field for grinding finite element analysis, it is necessary to extract the residual stress state of heat treatment. The heat treatment residual stress extraction method is as follows:
- Sectioning the Heat Treated Spiral Bevel Gear: Cut the heat treated result of the spiral bevel gear along the direction perpendicular to the tooth length direction, and the cross-section is as shown in Figure 6.
- Selecting the Starting and Ending Points: Take two points spaced 0.25mm apart in the vertical direction of the tooth length direction, that is, the tooth depth direction, as the starting and ending points, as shown in Figure 7. Evenly divide the points between the two points into 25 parts to obtain the stress results at intervals of 0.01mm, and save the stress results in a text document. The stress variation curve in the X direction with the depth is shown in Figure 8.
- Saving the Stress Results of the Other Five Directions: Save the stress results of the other five directions in the text document respectively according to the content of step 2. The extraction results of heat treatment residual stresses are shown in Table 3.
- Extracting the Stress Distribution States of the Other Four Points on the Tooth Surface of the Spiral Bevel Gear: Extract the stress distribution states of the other four points on the tooth surface of the spiral bevel gear according to the content of steps 1 to 3, and then calculate the average value of the stresses of the five points 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 |
3. Grinding Simulation of Spiral Bevel Gears
3.1 Simulation Model
- Abrasive Grain Determination: The process of abrasive grains grinding the workpiece is that the workpiece material forms elastic deformation to plastic deformation and even fracture under the action of abrasive grains. In this process, the workpiece material is in a situation of high temperature, large strain, and large strain rate, generating thermoelastic-plastic deformation until ductile fracture failure occurs. In the study, it is assumed that the abrasive grain is a cone with a height of 180 μm, and the top part of the abrasive grain is worn. Due to the relatively short time for grinding to reach a steady state, the grinding heat does not affect the entire workpiece, so only a small part of the workpiece is modeled and meshed. According to relevant literature, the change trend of the residual stress of the workpiece is not obvious below 200 μm of the tooth surface, so a small part of the area 300 μm below the tooth surface is selected as the workpiece model, and the selection of the workpiece model is as shown in Figure 9.
- Mesh Division: Mesh the abrasive grains and the workpiece. Since the main focus of the research process is the residual stress analysis of the workpiece, the abrasive grains are divided by tetrahedral mesh, which is a rigid body model. The workpiece is an elastoplastic body, and in order to ensure the accuracy of the calculation, a hexahedral mesh is selected. To simulate the actual grinding process, a virtual grinding wheel model based on the random distribution of multiple abrasive grains is established, and the abrasive grains are randomly distributed on the surface of the grinding wheel according to the grain size of the grinding wheel. The overall assembly model of the grinding wheel and the workpiece is as shown in Figure 10.
- Contact Friction Relationship Definition: During grinding, the grinding heat mainly comes from the plastic deformation of the removed material and the friction between the material and the tool. The abrasive grain is defined as the active part, and the spiral bevel gear is the passive part, and the Coulomb friction is between the abrasive grain and the tooth surface, with a friction coefficient of 0.2.
- Material Parameter Setting: According to the properties of the abrasive, the grinding wheel can be divided into carbide grinding wheels, oxide grinding wheels, and super-hard abrasive grinding wheels. In the analysis, the abrasive grain material adopts cubic boron nitride, and its main performance parameters are shown in Table 4. After defining the material parameters, it is necessary to assign the material parameters to the model.
- Strain and Failure Model Setting: In order to obtain the gear deformation and stress-strain state of the thermal, stress-strain coupling in the simulation process, it is necessary to describe the constitutive model of the mechanical behavior of the material in the range of large strains, wide strain rates, and wide temperature ranges. The Johnson-Cook model adopted by the author can meet the above working environment conditions of metal materials.
