Abstract
In order to analyze and control the surface residual stress during the processing of spiral bevel gear, DEFORM and ABAQUS software were used to establish a heat treatment and grinding simulation model. This study focused on the extraction and superposition method of residual stress during the heat treatment and grinding process, and analyzed the influence of grinding speed, grinding cutting depth, and feed rate on residual stress. Through grinding experiments, the credibility of the finite element simulation was verified, providing theoretical guidance for determining the heat treatment and grinding process parameters of gears.
Keywords: Spiral bevel gear, heat treatment, grinding, residual stress, analysis
1. Introduction
Spiral bevel gear is crucial components in mechanical equipment, widely used in the transmission systems of helicopters, automobiles, etc. The quality of spiral bevel gear directly affects the service life of mechanical equipment. Heat treatment and grinding processes are essential steps in the manufacturing of spiral bevel gear, and these processes can significantly impact the surface integrity of the gears, such as the residual stress on the tooth surface. During production, the detection of residual stress after heat treatment and grinding of gears is labor-intensive and costly. The application of finite element simulation analysis can greatly shorten the detection cycle and save costs. Therefore, it is practically significant to establish a mathematical analysis model for the heat treatment and grinding processes of gears through computer simulation methods.
In terms of numerical simulation of gear heat treatment, previous studies have explored various aspects. Sugianto et al. investigated the residual stress and microstructure distribution of SCr420H steel helical gears after carburizing and quenching. Lee Geunan applied numerical simulation to study the deformation of gears during the carburizing and quenching process. Sun Yonggang et al. studied the influence of temperature, stress, and carbon diffusion on the heat treatment of large internal gear rings using the finite element method. Du Guojun et al. conducted numerical simulations on the quenching process of 20CrMnTi steel gears, analyzing the effect of different carburized layer thicknesses on the distribution of residual stress. Zhu Jingchuan et al. used ABAQUS software to calculate the temperature and stress fields of bevel gear workpieces.
For metal grinding, Wang Haining et al. established a grinding model for single-particle cubic boron nitride (CBN) grains and studied the influence of grinding parameters on residual stress using DEFORM-3D software. Qu Wei used ANSYS software to simulate the residual stress in the grinding of cemented carbide with diamond wheels. Huang Xinchun et al. studied the mechanism of residual stress generation during the grinding of superalloys and discussed the impact of residual stress on fatigue life. Li Wan et al. established a thermal-mechanical coupling and residual stress calculation model 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. investigated the parameters affecting residual stress during the grinding process of EA4T steel.
However, previous studies have not conducted coupled analyses of heat treatment and grinding processes. In this study, DEFORM and ABAQUS software were used to establish a three-dimensional finite element analysis model for the carburizing, quenching, and grinding processes of spiral bevel gear. The changes and patterns of residual stress in spiral bevel gear after coupling heat treatment and grinding processes were obtained, and the influence of different grinding parameters on the residual stress of spiral bevel gear was analyzed. This provides guidance for controlling stress and deformation during actual gear processing, improving the performance of spiral bevel gear, and extending their service life.
2. Simulation of Heat Treatment for Spiral Bevel Gear
2.1 Heat Treatment Process Route
The material used for the spiral bevel gear in this study was 12Cr2Ni4A steel, with its chemical composition shown in Table 1 and mechanical properties in Table 2.
Table 1: Chemical Composition of 12Cr2Ni4A Steel
| 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% |
Table 2: Mechanical Properties of 12Cr2Ni4A Steel
| Property | Value |
|---|---|
| Yield Strength | 1080 MPa |
| Tensile Strength | 1175 MPa |
| Elongation | 12% |
| Reduction of Area | 55% |
| Impact Toughness | 80 J/cm² |
The heat treatment process for 12Cr2Ni4A steel spiral bevel gear included normalizing, quenching, tempering, carburizing, deep cold treatment, and low-temperature tempering.
2.2 Application of DEFORM Software
DEFORM software features a dedicated heat treatment module suitable for heat treatment finite element analysis. The finite element analysis process for heat treatment in DEFORM generally involves three steps:
- Mesh Generation: DEFORM software only supports tetrahedral meshing. The resulting mesh model.
- Medium Definition: In heat treatment simulation analysis, each heat treatment step involves different media, including heating, carburizing, oil cooling, air cooling, and nitrogen cooling. Different media have distinct heat transfer coefficients and surface deformation coefficients. The interface for defining air cooling.
- Heat Treatment Scheme Definition: Define the heat treatment scheme according to the heat treatment process route of the spiral bevel gear, requiring the input of time and temperature for each step. The overall heat treatment scheme definition interface.
2.3 Extraction Method of Heat Treatment Residual Stress
To more accurately define the initial residual stress field for grinding finite element analysis, it is necessary to extract the residual stress state after heat treatment. The extraction method for heat treatment residual stress is as follows:
- Section the spiral bevel gear heat treatment results perpendicular to the tooth length direction.
- Taking the extraction of X-direction stress as an example, use the SV Distribution between Two Points function in the DEFORM software post-processing. Select two points, 0.25 mm apart, in the vertical direction of the tooth length, i.e., the tooth depth direction, as the starting and ending points. Divide the space between the two points into 25 equal parts to obtain stress results at each point with 0.01 mm intervals, and save the stress results to a text document. The X-direction stress variation curve with depth.
- Follow the steps in (2) to save the stress results in the other five directions to text documents. The extraction results of heat treatment residual stress are shown in Table 3.
Table 3: Extraction Results of Heat Treatment Residual Stress
| Depth (mm) | X-Direction (MPa) | Y-Direction (MPa) | Z-Direction (MPa) | XY-Direction (MPa) | XZ-Direction (MPa) | YZ-Direction (MPa) |
|---|---|---|---|---|---|---|
| 0 | -4.05143 | -1.07973 | -6.60093 | 12.5401 | -13.4972 | -11.2482 |
| 0.01 | -3.86176 | -1.11938 | -6.74462 | 12.27085 | -13.2886 | -11.1906 |
| 0.02 | -3.66828 | -1.16167 | -6.88946 | 11.99188 | -13.0745 | -11.1306 |
| … | … | … | … | … | … | … |
| 0.19 | -0.37916 | -1.88052 | -9.35182 | 7.249412 | -9.43457 | -10.1102 |
| 0.20 | -0.18568 | -1.92281 | -9.49667 | 6.970443 | -9.22046 | -10.0502 |
| 0.21 | 0.007796 | -1.9651 | -9.64151 | 6.691474 | -9.00635 | -9.99014 |
- Follow the steps in (1) to (3) to extract the stress distribution at four other points on the tooth surface of the spiral bevel gear and then calculate the average stress of the five points to obtain the distribution state of heat treatment residual stress.
3. Simulation of Grinding for Spiral Bevel Gear
3.1 Simulation Model
- Grinding Particle Determination: The process of grinding a workpiece with abrasive particles involves the material undergoing elastic deformation, plastic deformation, and eventually fracture under the action of the abrasive particles. During this process, the workpiece material is subjected to high temperature, large strain, and high strain rate, resulting in thermo-elastic-plastic deformation until ductile fracture occurs. In this study, the abrasive particles were assumed to be cones with a height of 180 μm, and the tips of the abrasive particles were partially worn. Since the time for grinding to reach a steady state is relatively short, and the grinding heat does not affect the entire workpiece, only a portion of the workpiece was modeled and meshed. According to relevant literature, the residual stress trend below 200 μm from the tooth surface is not significant; therefore, a small area of 300 μm below the tooth surface was selected as the workpiece model.
- Mesh Generation: Mesh the abrasive particles and the workpiece. Since the primary focus of the study is the residual stress analysis of the workpiece, tetrahedral meshing was used for the abrasive particles, which were modeled as rigid bodies. The workpiece was modeled as an elastoplastic body, and hexahedral meshing was selected for computational accuracy. To simulate the actual grinding process, a virtual wheel model based on the random distribution of multiple abrasive particles was established. The abrasive particles were randomly distributed on the wheel surface according to the wheel grit size. The overall assembly model of the wheel and workpiece.
- Definition of Contact Friction Relationship: During grinding, the grinding heat primarily originates from the plastic deformation of the removed material and the friction between the material and the tool. The abrasive particles were defined as the active part, and the spiral bevel gear was defined as the driven part. The friction between the abrasive particles and the tooth surface was defined as Coulomb friction with a friction coefficient of 0.2.
- Material Parameter Setting: Depending on the properties of the abrasive, grinding wheels can be classified into carbide series wheels, oxide series wheels, and superabrasive wheels. In this analysis, cubic boron nitride (CBN) was used as the abrasive material, with its main performance parameters shown in Table 4. After defining the material parameters, they were assigned to the model.
Table 4: Performance Parameters of Cubic Boron Nitride
| Property | Value at 20°C | Value at 1000°C |
|---|---|---|
| Thermal Expansion Coefficient (μm/m·K) | 2.1 | 2.3 |
| Density (kg/m³) | 34800 | – |
| Poisson’s Ratio | 0.16 | – |
| Elastic Modulus (GPa) | 720 | – |
| Thermal Conductivity (W/m·K) | 1300 | – |
| Specific Heat Capacity (J/kg·K) | 612.5 | – |
- Strain and Failure Model Setting: To obtain the gear deformation and stress-strain state considering thermal-stress-strain coupling during the simulation, a constitutive model describing the mechanical behavior of the material under large strain, wide strain rate range, and wide temperature range is required. The Johnson-Cook model used in this study satisfies these working conditions for metallic materials. In the Johnson-Cook model, the relationship between deformation parameters and temperature is given by:
sigma=[A+B(εpl)n][1+Cln(ε˙0ε˙pl)](1−θm)
where:
- σ is the stress applied to the material;
- εpl is the equivalent plastic strain;
- ε˙pl is the equivalent plastic strain rate;
- ε˙0 is the reference plastic strain rate;
- A is the initial yield stress of the material;
- B is the strain hardening modulus of the material;
- C is the strain rate strengthening parameter of the material;
- n is the hardening exponent of the material;
- θ is the dimensionless temperature parameter.
The specific parameters of the Johnson-Cook model are shown in Table 5.
Table 5: Parameters of the Johnson-Cook Model
| Property | Value |
|---|---|
| A (MPa) | 507 |
| B (MPa) | 320 |
| n | 0.28 |
| C | 0.064 |
| m | 1.06 |
During the actual grinding process, the material fractures due to the action of the tool, forming grinding chips. To more accurately describe this phenomenon in the simulation, a damage parameter ω was introduced to characterize the material failure mode. When the damage parameter reaches a certain value, the material fractures. The damage parameter is given by:
omega=εplfεpl0+∑Δεpl
where:
- εpl0 is the initial equivalent plastic strain;
- Δεpl is the incremental equivalent plastic strain;
- εplf is the equivalent failure plastic strain at the reference temperature and strain rate.
In ABAQUS software, material fracture is characterized by inputting failure parameters d1 to d5. The failure parameters are shown in Table 6.
Table 6: Failure Parameters
| Failure Parameter | Value |
|---|---|
| d1 | 0.1 |
| d2 | 0.76 |
| d3 | 1.57 |
| d4 | 0.005 |
| d5 | -1.84 |
- Assumptions: The following assumptions were made for the simulation of single abrasive particle grinding:
- The CBN abrasive particles were partially worn, with friction on the bottom surface.
- The workpiece material was defined as an ideal thermo-elastoplastic body.
- The friction coefficient between the abrasive particles and the workpiece remained constant and did not change with external conditions.
- The size of the abrasive particles was much smaller than that of the workpiece on a macroscopic scale, and the interaction time between the abrasive particles and the workpiece was very short. Under these conditions, the grinding process was considered as single-particle plane grinding.
- Coupling of Initial Stress Field from Heat Treatment: The residual stress state after heat treatment was added to the grinding finite element simulation as the initial stress field for grinding to improve the initial conditions of grinding. First, the stress distribution results along the depth direction were obtained according to the heat treatment residual stress extraction method. Then, in ABAQUS software, a 25-layer element set was established along the grinding depth direction. Finally, the stress states of the 25 points were sequentially input into the 25-layer element set through the predefined stress field variable settings.
3.2 Extraction of Simulation Results
After establishing the simulation model based on the aforementioned content, the job file was submitted, and the single abrasive particle grinding process was obtained through finite element analysis using ABAQUS software,.
The stress extracted for analysis was the S11 component stress, which is the stress component aligned with the grinding direction in the three-dimensional space. Utilizing the system’s Cartesian coordinate system, from the result file generated after the grinding simulation computation, regions with significant errors were disregarded, and a layer of 515 nodes along the grinding path was selected for stress extraction. The extraction of grinding residual stresses. By averaging the stresses at these 515 points, the mean stress value for the corresponding layer after grinding could be obtained.
3.3 Influence of Grinding Parameters on Residual Stress
To investigate the influence of grinding speed, grinding depth, and feed rate on grinding residual stress, a three-factor, five-level orthogonal experiment was conducted, comprising a total of 25 test cases. The maximum residual compressive stress was chosen as the evaluation criterion for the experimental results, as shown in Table 7, with the experimental analysis presented in Table 8.
Among the three factors, grinding depth had the most significant influence on the maximum residual compressive stress, followed by grinding speed, while feed rate had the least impact. In practical grinding processes, it is essential to select appropriate grinding depths and speeds based on actual conditions and research findings, followed by selecting a suitable feed rate to complete the grinding operation.
The following primarily analyzes the influence patterns of grinding depth and grinding speed on residual stress.
By setting the grinding speed at 15 m/s and the feed rate at 0.04 m/s, the distribution of residual stress along the depth direction on the grinding path was simulated for grinding depths of 0.01 mm, 0.015 mm, 0.02 mm, and 0.025 mm. The distribution of residual stress along the depth direction for different grinding depths.
The maximum residual compressive stress occurs in the subsurface layer, gradually transitioning to residual tensile stress in deeper layers. As the grinding depth increases, the maximum residual compressive stress increases, and the depth of its effect also increases slightly.
By setting the grinding depth at 0.02 mm and the feed rate at 0.04 m/s, the distribution of residual stress along the depth direction on the grinding path was simulated for grinding speeds of 17 m/s, 20 m/s, 22 m/s, and 25 m/s. The distribution of residual stress along the depth direction for different grinding speeds is illustrated
The maximum residual compressive stress occurs in the subsurface layer, gradually transitioning to residual tensile stress in deeper layers. As the grinding speed increases, the maximum residual compressive stress also increases, although the depth of its effect does not change significantly.