Abstract
This paper presents a numerical simulation study on the welding temperature field of the multi-layer V-groove welding process of a spiral bevel gear cutter disk using the SYSWELD solver integrated within the Visual-Environment welding simulation software. The simulation results are visualized through temperature field distribution maps, and temperature cycle curves at the weld center, weld toe, and 5 mm away from the weld center of each layer are analyzed and compared. Furthermore, a three-layer welding temperature field formula is derived for verification. The findings reveal that the highest temperature occurs at the center of the weld pool, and the temperature gradient varies significantly as the distance from the weld center decreases.
1. Introduction
With the rapid development of the automotive and aerospace industries, spiral bevel gears are increasingly used due to their advantages such as high contact ratio, smooth meshing, high load-bearing capacity, and low energy loss. The spiral bevel gear cutter disk, as a specialized tool for machining spiral bevel gears, is commonly manufactured through either monolithic or welded construction. The welded construction, specifically multi-layer V-groove welding, requires precise control of the welding process to ensure optimal mechanical properties and dimensional accuracy.
During the welding process, heat input and thermal conduction significantly impact metallurgical transformations, microstructural changes, mechanical properties, residual stresses, and deformations. Thus, numerical simulation of the welding temperature field is crucial for understanding the welding process, predicting weld quality, and optimizing welding parameters. This study focuses on the numerical simulation of the multi-layer welding temperature field of a spiral bevel gear cutter disk using SYSWELD.
2. Model Establishment and Mesh Generation
2.1 Geometry and Material Properties
The spiral bevel gear cutter disk analyzed in this study is made of 20CrMo low-alloy structural steel, with an outer diameter of 287 mm, an inner diameter of 225 mm, and a thickness of 32 mm. A three-dimensional model of the cutter disk was created using SolidWorks and simplified to exclude non-critical features such as holes and milling slots.
2.2 Mesh Generation
Mesh generation is crucial for accurate and efficient numerical simulations. A finer mesh was employed in the weld region to capture the steep temperature gradients, while a coarser mesh was used in other areas to reduce computation time. The entire model was meshed using hexahedral elements, resulting in 43,248 3D elements for the base model and 51,810 3D elements for the weld region.
3. Heat Source Model and Temperature Field Calculation
3.1 Heat Source Model
For laser welding, the double-ellipsoid heat source model was selected due to its higher accuracy compared to the Gaussian heat source model. The double-ellipsoid heat source is divided into two parts: the front and rear ellipsoids, with different energy distributions. The heat flux distribution within each ellipsoid is given by:
q(x,y,z,t)=abc1ππe63ffQe−a23x2e−b23y2e−c123z2 (Front ellipsoid)
q(x,y,z,t)=abc2ππe63frQe−a23x2e−b23y2e−c223z2 (Rear ellipsoid)
where ff and fr are the energy fractions of the front and rear ellipsoids, respectively (ff+fr=2); a, b, c1, and c2 are the ellipsoid shape parameters; and Q is the actual heat input.
3.2 Temperature Field Calculation
The non-linear three-dimensional heat conduction equation governs the temperature field calculation:
ρc∂t∂T=k(∂x2∂2T+∂y2∂2T+∂z2∂2T)+F(x,y,z,t)
where ρ is the material density, c is the specific heat capacity, T is the temperature distribution function, k is the thermal conductivity, and F(x,y,z,t) represents internal heat sources.
The temperature field at any point within the workpiece is calculated by superimposing the contributions from both the front and rear ellipsoids of the double-ellipsoid heat source:
T−T0=T1(x,y,z,t)+T2(x,y,z,t)
where T0 is the initial temperature, T1 and T2 are the temperature contributions from the front and rear ellipsoids, respectively.
4. Numerical Simulation and Results
4.1 Simulation Setup
The welding simulation was performed using SYSWELD, with the following parameters:
- Welding speed: 4 mm/s
- Laser power: 2900 W
- Efficiency: 0.8
- Material properties (Table 1): Thermal conductivity, specific heat capacity, density, elastic modulus, Poisson’s ratio, and coefficient of thermal expansion at various temperatures.
| Temperature (°C) | Thermal Conductivity (W/m·K) | Specific Heat Capacity (J/kg·K) | Density (kg/m³) | Elastic Modulus (GPa) | Poisson’s Ratio | CTE (10⁻⁶/°C) |
|---|---|---|---|---|---|---|
| 20 | 43.2 | 461 | 7800 | 212 | 0.28 | 11.1 |
| 200 | 43.1 | 498 | 7750 | 203 | 0.28 | 12.3 |
| … | … | … | … | … | … | … |
| 1500 | 36.3 | 780 | 7400 | 170 | 0.30 | 14.0 |
The simulation included heat exchange between the cutter disk surface and ambient air, with an ambient temperature of 20°C. The cutter disk was preheated to 200°C before welding, and a 5-second cooling period was allowed after each welding layer.
4.2 Simulation Results
The welding temperature field distribution was visualized using temperature contour plots for each welding layer.
The highest temperature was observed at the center of the weld pool, with a gradual decrease in temperature towards the weld periphery. The peak temperatures for the first, second, and third welding layers were 2782°C, 2025°C, and 1666°C, respectively.
Temperature cycle curves were plotted for key points at the weld center, weld toe, and 5 mm away from the weld center for each layer.
The temperature cycle curves indicate that the weld center experienced the highest temperatures, followed by the weld toe and the point 5 mm away from the weld center. The temperature gradients were steeper near the weld center, with gradual temperature changes further away.
5. Discussion
The numerical simulation results provide valuable insights into the welding process of the spiral bevel gear cutter disk. The highest temperatures occurred at the weld pool center, confirming the importance of precise temperature control during welding to prevent overheating and associated metallurgical issues.
The temperature gradients were significant near the weld center, highlighting the need for refined meshing in this region. The temperature cycle curves indicated that the welding process was well-controlled, with consistent temperature profiles across the different welding layers.
The derived three-layer welding temperature field formula can be used for further validation and optimization of the welding process. The temperature field simulation is a crucial step in predicting residual stresses and deformations, which will be addressed in future studies.
6. Conclusion
This study presents a comprehensive numerical simulation of the multi-layer V-groove welding process for a spiral bevel gear cutter disk using SYSWELD. The simulation results reveal detailed temperature field distributions and temperature cycle curves for different welding layers. The findings demonstrate that the highest temperatures occur at the weld pool center, with significant temperature gradients near the weld periphery. The derived welding temperature field formula provides a valuable tool for validating and optimizing the welding process.