1. Introduction
Spiral bevel gear plays crucial role in many mechanical transmission systems. The quenching process is an important heat treatment method to improve the mechanical properties of spiral bevel gear. However, the quenching process is complex, involving heat transfer, phase transformation, and stress generation. Numerical simulation has become an effective tool to study the quenching process of spiral bevel gear. In this article, we will focus on the numerical simulation of the spiral bevel gear quenching process based on a thermo-fluid-solid coupling model.
1.1 Importance of Spiral Bevel Gear
Spiral bevel gear is widely used in various industries such as automotive, aerospace, and machinery due to their ability to transmit power at different angles and high load-carrying capacity. The performance of spiral bevel gear directly affects the efficiency and reliability of the entire transmission system.
1.2 Quenching Process and Its Significance
Quenching is a heat treatment process that rapidly cools the workpiece from a high temperature to room temperature or below. This process can significantly improve the hardness, strength, and wear resistance of the workpiece. For spiral bevel gear, proper quenching can enhance their mechanical properties and service life.
1.3 Numerical Simulation in Quenching Process
Numerical simulation can predict the temperature distribution, phase transformation, and stress generation during the quenching process. It can help engineers optimize the quenching process parameters, reduce the distortion of the workpiece, and improve the quality of the heat treatment.
2. Thermo-Fluid-Solid Coupling Model
2.1 Flow-Solid Coupling Model
The flow-solid coupling model is an important part of the thermo-fluid-solid coupling model. It describes the heat transfer between the fluid and the solid during the quenching process.
- Wall Function Method: The wall function method is used to establish the heat transfer model on the flow-solid coupling surface. The dimensionless distance and dimensionless temperature are introduced to calculate the heat flux and the equivalent thermal conductivity .
- Interpolation and Data Exchange: Due to the differences in physical field characteristics and discretization methods, the flow-solid boundary grids may not match completely. Interpolation methods are used to couple the physical quantities of the two regions and complete the data exchange on the coupling surface.
2.2 Fluid Flow and Heat Transfer Model
The fluid flow and heat transfer model describes the boiling heat transfer of the quenching medium during the quenching process.
- Euler Multiphase Flow Model: The Euler multiphase flow model is used to describe the behavior of the quenching medium. It assumes that the fluid obeys the compatibility principle and each phase of the fluid still obeys the conservation law.
- RPI Wall Surface Heat Transfer Model: The RPI wall surface heat transfer model is used to describe the heat flow on the wall surface. It includes three types of heat transfer: single-phase convection heat transfer , phase change heat transfer , and intense transient heat transfer after the bubble escapes.
2.3 Solid Temperature-Stress-Organization Coupling Model
The solid temperature-stress-organization coupling model describes the temperature change, phase transformation, and stress generation in the solid during the quenching process.
- Heat Transfer Model: The heat transfer model is based on Fourier’s law. It assumes that the material is isotropic and solves the heat conduction equation for non-steady-state heat transfer problems.
- Phase Transformation Model: The phase transformation model combines the Johnson-Mehl-Avrami (J-M-A) equation with the Scheil superposition rule to describe the diffusion transformation of ferrite, pearlite, and other tissues in a non-isothermal environment. The martensitic phase transformation is described by the K-M (Koistinen-Marburger) equation.
- Stress-Strain Model: The stress-strain model is based on the decomposition of the deformation tensor and the assumption of thermoelastic-plastic materials. The total strain includes elastic strain, plastic strain, thermal strain, phase transformation strain, and phase transformation plastic strain.
3. Experimental Setup and Methods
3.1 Experimental Workpiece
The experimental workpiece is a 45 steel spiral bevel gear. The parameters of the spiral bevel gear are shown in Table 1.
| Parameter | Value |
|---|---|
| Number of teeth | 20 |
| Module | 4mm |
| Tooth face width | 23 mm |
| Helix direction | Right |
| Average pressure angle | 20° |
| Step diameter | d65 mm |
| Inner hole diameter | 18 mm |
| Step height | 22 mm |
3.2 Experimental Methods
- Thermocouple Installation: Glass fiber thermocouples are spot-welded at five characteristic points on the spiral bevel gear, including the middle part of the tooth tip (A), the middle part of the tooth middle (B), the middle part of the tooth root (C), the inner hole surface (D), and the step outer surface (E).
- Heating and Quenching: The spiral bevel gear is heated uniformly in a heating furnace to 850°C and held for 32 min. Then, it is quenched in water at 20°C. The temperature changes of the thermocouples at the five positions are automatically collected and recorded by a multi-channel thermometer.
4. Results and Analysis
4.1 Cooling Curve Comparison when Quenching Medium is Static
- Temperature Trend: The temperature change trends predicted by the thermo-fluid-solid coupling numerical simulation and the experimental results are basically the same. The cooling speed of the tooth tip is the fastest, followed by the tooth middle, and finally the tooth root. The maximum temperature difference during the cooling process of the characteristic points does not exceed 40°C, indicating that the simulation prediction results are accurate.
- Relative Error: The relative errors between the predicted results of different simulation methods and the experimental results are compared. The maximum relative error of the thermo-fluid-solid coupling numerical simulation is 9.2% , and the maximum relative error of the traditional quenching numerical simulation is 7.4%. The higher relative error of the thermo-fluid-solid coupling numerical simulation is due to the fact that its accuracy largely depends on the heat transfer on the coupling surface, and the boiling heat transfer model on the coupling surface is still in the process of continuous improvement.
4.2 Differences in Numerical Simulation Methods when Quenching Medium is Flowing
- Velocity Difference at Different Positions: When the inlet flow rate of the quenching oil is 2.0m/s, the velocity near the spiral bevel gear varies due to the perturbation of the quenching tank device and the action of gravity. The minimum velocity is on the tooth top surface (0.1084m/s), and the maximum velocity is in the inner ring.
- Temperature Result Differences: The thermo-fluid-solid coupling numerical simulation and the traditional quenching numerical simulation are used to simulate the oil quenching of the spiral bevel gear. The temperature distributions predicted by the two methods are slightly different. The thermo-fluid-solid coupling numerical simulation can more accurately describe the temperature distribution on the spiral bevel gear because it considers the velocity difference on the tooth surface and the turbulence effect.
4.3 Analysis of Quenching Hardness and Stress under Different Quenching Oil Flow Rates
- Hardness and Stress Variation: The hardness and residual stress of the spiral bevel gear is analyzed under different inlet flow rates of the quenching oil. The hardness gradually increases along the path from point 1 to point 6, and the residual stress increases in the directions from point 3 to point 6 and from point 3 to point 1. The minimum residual stress occurs at point C.
- Optimal Flow Rate: The residual stress is mainly favorable compressive stress under different flow rates. When the inlet flow rate is 2m/s, the hardness reaches the maximum value of 52.0 HRC, and the residual stress is mainly favorable compressive stress. Therefore, 2m/s is the optimal quenching medium flow rate in this study.
5. Discussion
5.1 Accuracy of Thermo-Fluid-Solid Coupling Simulation
The thermo-fluid-solid coupling simulation method proposed in this article has certain accuracy. Although its relative error is slightly higher than that of the traditional simulation method, it can more accurately predict the temperature distribution when the quenching medium is flowing. This is because the thermo-fluid-solid coupling simulation considers the fluid flow and heat transfer process more comprehensively.
5.2 Convenience of Thermo-Fluid-Solid Coupling Simulation
The thermo-fluid-solid coupling simulation is more convenient than the traditional simulation method. In the traditional simulation method, it is necessary to divide the regions with different flow rates and select the corresponding heat transfer coefficients for simulation. In the thermo-fluid-solid coupling simulation, only the inlet flow rate needs to be set, and the flow rate at different positions on the coupling surface is calculated, not preset.
5.3 Influence of Quenching Medium Flow Rate on Quenching Results
The flow rate of the quenching medium has a significant impact on the quenching results of the spiral bevel gear. With the increase of the flow rate, the hardness and residual stress of the spiral bevel gear also increase. The optimal flow rate can make the hardness reach the maximum value and the residual stress be mainly favorable compressive stress.
6. Conclusion
- A thermo-fluid-solid coupling numerical simulation method for quenching is proposed, and the quenching experiment of 45 steel spiral bevel gear is carried out. The maximum relative errors between the cooling curves of the thermo-fluid-solid coupling simulation and the traditional simulation and the experimental measurement are 9.2% and 7.4% respectively, verifying the accuracy of the thermo-fluid-solid coupling numerical simulation.
- By comparing the temperature distributions of the thermo-fluid-solid coupling simulation and the traditional simulation when the quenching oil is flowing, it is found that the thermo-fluid-solid coupling simulation can more simply implement the quenching simulation and more accurately describe the temperature distribution on the spiral bevel gear, verifying the convenience of the thermo-fluid-solid coupling numerical simulation.
- The influence of different inlet flow rates on the quenching effect is studied. When the inlet flow rate is 2m/s , the residual stress is mainly favorable compressive stress and the maximum hardness of 52.0 HRC is reached, which is the optimal value in this study.
In future research, more attention can be paid to the improvement of the coupling surface heat transfer model and the optimization of the quenching process parameters to further improve the quality of the spiral bevel gear quenching.