1. Introduction
Constant height spiral bevel gears are widely used in various precision mechanical systems due to their advantages of stable transmission, high load capacity, and low noise. The milling cutter head for such gears is a critical component, and its manufacturing process significantly impacts the gear’s quality. Welding is a common method for fabricating the milling cutter head, but welding deformation remains a major challenge. This paper presents a comprehensive study on the numerical simulation and experimental verification of multi-layer welding deformation of the constant height spiral bevel gear milling cutter head, focusing on the effects of different welding groove gaps.
2. Literature Review
- Gleason and Klingelnberg Companies: These companies have been leading the development of spiral bevel gear manufacturing technologies. They have introduced various types of milling cutter heads, including integral and insert types, and have continuously improved gear processing accuracy.
- Laser Welding Research: Studies by researchers like D. Dittrich and T. Jokinen have explored laser multi-layer welding of thick plates, demonstrating the potential of laser technology in reducing welding deformation and improving weld quality.
- Domestic Research Institutions: Universities and research institutes such as Harbin Institute of Technology and Tsinghua University have conducted extensive research on laser welding technologies, including narrow gap welding and heat input control.
- Key Contributions: Chinese scholars have made significant progress in understanding the thermal elastoplastic deformation mechanisms during welding and have developed advanced numerical simulation models.
2.2 Research Gaps
Previous studies have primarily focused on single-layer welding or simple groove designs. There is a lack of comprehensive research on the effects of multi-layer welding and different groove gaps on the deformation of milling cutter heads. This study aims to fill this gap by investigating the thermal and mechanical responses during multi-layer welding using numerical simulation and experimental validation.
3. Research Methodology
3.1 Numerical Simulation Setup
3.1.1 Finite Element Model
The milling cutter head was modeled using UG software, considering both the main body and the outer ring. The model was simplified to focus on the welding region, and mesh generation was performed using HyperMesh, resulting in 110,472 nodes and 96,236 elements for the cutter head and 1,248 nodes and 816 elements for the welds.
3.1.2 Material Properties
The material used for the milling cutter head was 20CrMo alloy steel. Table 1 summarizes the key material properties, including thermal conductivity, specific heat capacity, density, elastic modulus, Poisson’s ratio, linear expansion coefficient, and yield strength at different temperatures.
| Property | Value at 20°C | Value at 200°C | Value at 500°C | Value at 700°C | Value at 900°C | Value at 1100°C | Value at 1300°C | Value at 1500°C | Value at 1800°C |
|---|---|---|---|---|---|---|---|---|---|
| Thermal Conductivity (W/(m·K)) | 46.1 | 43.5 | 38.2 | 32.7 | 27.3 | 22.1 | 17.8 | 14.2 | 11.5 |
| Specific Heat Capacity (J/(kg·K)) | 461 | 498 | 540 | 896 | 664 | 763 | 775 | 780 | 770 |
| Density (kg/m³) | 7850 | 7830 | 7780 | 7720 | 7650 | 7580 | 7500 | 7420 | 7350 |
| Elastic Modulus (GPa) | 212 | 195 | 170 | 145 | 120 | 95 | 70 | 45 | 20 |
| Poisson’s Ratio | 0.28 | 0.28 | 0.30 | 0.30 | 0.31 | 0.30 | 0.29 | 0.30 | 0.30 |
| Linear Expansion Coefficient (1/°C) | 11.1×10⁻⁶ | 12.3×10⁻⁶ | 13.9×10⁻⁶ | 14.0×10⁻⁶ | 14.1×10⁻⁶ | 13.9×10⁻⁶ | 14.1×10⁻⁶ | 14.0×10⁻⁶ | 14.1×10⁻⁶ |
| Yield Strength (MPa) | 720 | 680 | 600 | 500 | 400 | 300 | 200 | 100 | 50 |
3.1.3 Welding
A combined Gaussian-conical heat source model was employed to simulate the laser welding process. The Gaussian component represented the surface heat distribution, while the conical component accounted for the volumetric heat input. The parameters of the heat source model are listed in Table 2.
| Parameter | Value |
|---|---|
| Gaussian Surface Radius (mm) | 2.5 |
| Gaussian Depth (mm) | 2 |
| Conical Upper Radius (mm) | 2.5 |
| Conical Lower Radius (mm) | 1.1 |
| Conical Depth (mm) | 3.2 |
| Volume Heat Fraction | 0.7 |
3.2 Experimental Setup
3.2.1 Laser Welding System
A diffusion-cooled RF-excited CO₂ laser system was used for the welding experiments. The welding parameters, including power, speed, defocusing distance, and wire feed rate, were set according to the numerical simulation results, as shown in Table 3.
| Parameter | Value |
|---|---|
| Laser Power (W) | 2900 |
| Welding Speed (mm/s) | 10 |
| Defocusing Distance (mm) | 0 |
| Wire Feed Rate (mm/s) | 10 |
3.2.2 Specimen Preparation
The milling cutter head specimens were prepared with double Y-shaped grooves and three different bottom gaps: 2 mm, 2.5 mm, and 3 mm. Prior to welding, the specimens were cleaned using acetone and preheated to 200°C to reduce residual stress.
4. Results and Discussion
4.1 Numerical Simulation Results
4.1.1 Temperature Distribution
The temperature distribution during welding was analyzed for each layer. Figure 1 shows the temperature profiles for different groove gaps. The maximum temperature was observed at the weld center, and the temperature gradient decreased with increasing distance from the weld. The cooling rate was faster for smaller groove gaps, leading to higher thermal stress.
4.1.2 Stress and Deformation Analysis
The equivalent stress and deformation results are presented in Figures 2 and 3. The maximum equivalent stress occurred in the weld region and decreased towards the base material. The deformation was most significant in the radial direction, with larger groove gaps resulting in greater deformation. Table 4 summarizes the maximum deformation values for each layer and groove gap.
| Layer | Groove Gap (mm) | Maximum Deformation (mm) |
|---|---|---|
| 1 | 2 | 0.023 |
| 1 | 2.5 | 0.028 |
| 1 | 3 | 0.032 |
| 2 | 2 | 0.025 |
| 2 | 2.5 | 0.031 |
| 2 | 3 | 0.035 |
| 3 | 2 | 0.027 |
| 3 | 2.5 | 0.033 |
| 3 | 3 | 0.038 |
4.2 Experimental Validation
4.2.1 Deformation Measurement
After welding, the deformation of the milling cutter head was measured using an electronic plug gauge. The results, shown in Table 5, indicated that the deformation increased with larger groove gaps. The experimental results were consistent with the numerical simulation findings, validating the accuracy of the simulation model.
| Groove Gap (mm) | Average Deformation (mm) | Maximum Deformation (mm) |
|---|---|---|
| 2 | 0.024 | 0.027 |
| 2.5 | 0.029 | 0.032 |
| 3 | 0.033 | 0.037 |
4.2.2 Weld Quality Evaluation
The weld quality was evaluated by visual inspection and mechanical testing. No significant defects such as cracks or porosity were observed. The tensile strength of the welded specimens met the requirements for 20CrMo alloy steel, confirming the reliability of the welding process.
5. Conclusion
This study investigated the multi-layer welding deformation of a constant height spiral bevel gear milling cutter head using numerical simulation and experimental validation. The key findings are as follows:
- The combined Gaussian-conical heat source model effectively simulated the laser welding process, providing accurate temperature, stress, and deformation predictions.
- Larger groove gaps resulted in greater welding deformation due to increased heat input and reduced constraint.
- A groove gap of 2 mm was found to be optimal, minimizing deformation while ensuring weld quality.
- The experimental results closely matched the numerical simulations, validating the proposed methodology.
Future research should explore the effects of different welding sequences and post-weld heat treatments on the residual stress and fatigue life of the milling cutter head.
