Abstract
This study investigates the temperature field distribution during multi-layer V-groove welding of a spiral bevel gear milling cutter disc using SYSWELD as the solver within the Visual-Environment platform. A three-dimensional finite element model of the cutter disc was developed, incorporating a double-ellipsoid heat source to simulate the laser welding process. The temperature cycles at the weld center, weld toe, and 5 mm from the weld center were analyzed for each layer. Results indicate that the weld pool center exhibits the highest temperature, with temperature gradients intensifying near the weld center. A validated three-layer temperature field formula was derived, demonstrating the feasibility of predicting thermal behavior in complex spiral bevel gear welding applications.
Introduction
Spiral bevel gears are critical components in automotive and aerospace industries due to their high load-bearing capacity and smooth transmission characteristics. The manufacturing of spiral bevel gear milling cutter discs often involves welding processes to couple inner and outer rings. Multi-layer welding with V-grooves is commonly employed to ensure structural integrity. However, the intense thermal gradients during welding induce residual stresses and distortions, necessitating precise control of the temperature field.
This work focuses on simulating the transient thermal behavior of a spiral bevel gear milling cutter disc using SYSWELD. The study emphasizes the interplay between heat input, material properties, and temperature distribution, providing insights for optimizing welding parameters in high-precision gear fabrication.
Model Development and Meshing
Geometry Simplification
The spiral bevel gear milling cutter disc, made of 20CrMo low-alloy steel, has an outer diameter of 287 mm, inner diameter of 225 mm, and thickness of 32 mm. Non-welded regions (e.g., upper sections and holes) were omitted to reduce computational complexity. A simplified model with 34 V-grooves was created, each with the following dimensions:
- Groove width: 4 mm
- Groove angle: 37°
- Depth: 8 mm
- Length: 10 mm
Meshing Strategy
Hexahedral elements were prioritized for their superior deformation characteristics and computational efficiency. Mesh refinement was applied to the weld zone to capture steep thermal gradients, while coarser grids were used elsewhere. Key meshing parameters include:
- Base mesh size: 5 mm
- Weld zone mesh size: 0.5–1 mm
- Number of layers along thickness: 16 (base) / 32 (weld zone)
- Total elements: 43,248 (base) / 51,810 (weld zone)
Heat Source Model
The double-ellipsoid heat source model was selected to replicate laser welding dynamics. Its mathematical formulation comprises two ellipsoidal regions:
- Front Ellipsoid (Steep Gradient):
qf(x,y,z,t)=63f1Qπabc1e−3×2/a2e−3y2/b2e−3z2/c12qf(x,y,z,t)=πabc163f1Qe−3x2/a2e−3y2/b2e−3z2/c12
- Rear Ellipsoid (Gradual Gradient):
qr(x,y,z,t)=63f2Qπabc2e−3×2/a2e−3y2/b2e−3z2/c22qr(x,y,z,t)=πabc263f2Qe−3x2/a2e−3y2/b2e−3z2/c22
where:
- f1+f2=2f1+f2=2 (energy distribution factors)
- a,b,c1,c2a,b,c1,c2: ellipsoid dimensions
- QQ: total heat input
Temperature Field Calculation
The nonlinear transient heat conduction equation governs the temperature distribution:ρc∂T∂t=k(∂2T∂x2+∂2T∂y2+∂2T∂z2)+F(x,y,z,t)ρc∂t∂T=k(∂x2∂2T+∂y2∂2T+∂z2∂2T)+F(x,y,z,t)
where ρρ, cc, and kk denote material density, specific heat, and thermal conductivity, respectively.
For multi-layer welding, the temperature field of each layer was superposed:Ttotal=∑i=1n(T1,i(x,y,z,t)+T2,i(x,y,z,t))+TinitialTtotal=i=1∑n(T1,i(x,y,z,t)+T2,i(x,y,z,t))+Tinitial
where T1,iT1,i and T2,iT2,i represent contributions from the front and rear ellipsoids of the ii-th weld pass.
Material Properties
The temperature-dependent properties of 20CrMo steel are summarized in Table 1.
Table 1: Thermophysical properties of 20CrMo steel
| Temperature (°C) | Thermal Conductivity (W/m·°C) | Specific Heat (J/kg·°C) | Density (kg/m³) | Elastic Modulus (GPa) | Poisson’s Ratio | Expansion Coefficient (×10⁻⁶/°C) |
|---|---|---|---|---|---|---|
| 20 | 43.2 | 461 | 7780 | 212 | 0.28 | 11.1 |
| 200 | 43.1 | 498 | 7750 | 203 | 0.28 | 12.3 |
| 500 | 36.8 | 540 | 7693 | 178 | 0.30 | 13.9 |
| 700 | 30.2 | 896 | 7648 | 131 | 0.30 | 14.0 |
| 900 | 29.7 | 664 | 7574 | 188 | 0.31 | 14.1 |
| 1100 | 32.2 | 763 | 7480 | 178 | 0.30 | 13.9 |
| 1300 | 35.3 | 775 | 7436 | 175 | 0.29 | 14.1 |
| 1500 | 36.3 | 780 | 7400 | 170 | 0.30 | 14.0 |
Boundary Conditions and Welding Parameters
- Welding speed: 4 mm/s
- Laser power: 2900 W
- Thermal efficiency: 0.8
- Preheating temperature: 200°C
- Ambient temperature: 20°C
- Interpass cooling time: 5 s
Convective heat transfer was applied to exposed surfaces, and mechanical constraints were imposed on four nodes to prevent displacement.
Results and Discussion
Temperature Distribution
- First Layer: Peak temperature at the weld center reached 2782°C, cooling to 290°C after 10 s.
- Second Layer: Maximum temperature decreased to 2025°C, stabilizing at 434°C after 20 s.
- Third Layer: Further reduction to 1666°C, cooling to 366°C at 30 s.
Temperature gradients were most pronounced near the weld center, diminishing with distance.
Thermal Cycle Analysis
Nodes at the weld center (Node 1, 4, 7), weld toe (Node 2, 5, 8), and 5 mm from the center (Node 3, 6, 9) exhibited distinct thermal profiles:
- Weld Center: Rapid heating to melting temperatures (>1500°C), followed by exponential cooling.
- Weld Toe: Lower peak temperatures (1200–1400°C) with delayed cooling.
- 5 mm from Center: Moderate temperature rise (~500°C) and gradual cooling.
The thermal cycles confirmed the efficacy of the double-ellipsoid model in capturing transient heat transfer dynamics.
Conclusion
This study successfully simulated the multi-layer welding temperature field of a spiral bevel gear milling cutter disc using SYSWELD. Key findings include:
- The weld pool center attains the highest temperature, with gradients intensifying proximally.
- Layer-wise superposition of the double-ellipsoid heat source accurately replicates thermal cycles.
- Temperature-dependent material properties significantly influence heat dissipation and residual stress formation.
The derived temperature field formulas and simulation framework provide a robust foundation for optimizing welding processes in spiral bevel gear manufacturing, ensuring enhanced structural performance and longevity.