Cylindrical gears serve as critical components in automotive transmissions, where their performance directly determines system reliability and operational efficiency. This study investigates the carburizing-quenching process optimization through numerical simulation and experimental validation, focusing on 20CrMnTi steel cylindrical gears. The multi-physics coupling mechanism involving carbon diffusion, temperature evolution, phase transformation, and residual stress generation is systematically analyzed using finite element modeling.
1. Fundamental Theories and Numerical Modeling
The carburizing process follows Fick’s second law of diffusion, mathematically expressed as:
$$ \frac{\partial C}{\partial t} = \frac{\partial}{\partial x}\left(D(C)\frac{\partial C}{\partial x}\right) $$
where $D(C)$ represents the carbon concentration-dependent diffusion coefficient calculated by:
$$ D(T,C) = D_{0.4}\exp\left(-\frac{Q}{RT}\right)\exp[-B(C-0.4)] $$
Thermal evolution during quenching is governed by the heat conduction equation:
$$ \rho C_p\frac{\partial T}{\partial t} = \nabla\cdot(\lambda\nabla T) + Q_{phase} $$
The phase transformation kinetics consider both diffusive and martensitic transformations:
$$ \xi_M = 1 – \exp[\phi_1(T) + \phi_2(C) + \phi_{31}(\sigma_m) + \phi_{32}(\sigma_{eq})] $$
Mechanical properties are evaluated through mixed-phase calculations:
$$ P = \sum x_iP_i + \sum\sum x_ix_j\Omega_{ij} $$
2. Material Characterization and Process Parameters
The chemical composition of 20CrMnTi steel is detailed in Table 1.
| C | Si | Mn | Cr | Ti | Fe |
|---|---|---|---|---|---|
| 0.19 | 0.28 | 0.93 | 1.12 | 0.065 | Bal. |
3. Process Parameter Effects
The influence of key parameters on carburizing effectiveness was investigated through orthogonal experiments (L9(34)) as shown in Table 2.
| Factor | Level | ||
|---|---|---|---|
| 1 | 2 | 3 | |
| Strong carburizing time (min) | 60 | 80 | 100 |
| Diffusion time (min) | 40 | 50 | 60 |
| Strong carburizing potential (%) | 0.85 | 0.90 | 0.95 |
| Diffusion potential (%) | 0.80 | 0.85 | 0.90 |
The optimized parameters were determined through range analysis:
$$ R_j = \max(\bar{K}_{ji}) – \min(\bar{K}_{ji}) $$
Key findings from parameter optimization include:
- Diffusion potential shows the strongest influence on surface carbon concentration (R=0.061)
- Strong carburizing time dominates carburizing depth (R=0.1787)
- Optimal parameter combination: 80min strong carburizing, 40min diffusion, 0.9% strong potential, 0.9% diffusion potential
4. Intelligent Prediction Model
A PSO-BP neural network was developed for performance prediction:
$$ \text{Input layer: } [t_s, t_d, C_s, C_d] $$
$$ \text{Output layer: } [C_{surf}, D_{case}] $$
The network structure with 4-9-2 nodes demonstrated superior prediction accuracy (MAPE <4%) compared to conventional BP networks, as shown in Table 3.
| Model | Surface C (%) MAE | Case Depth (mm) MAE |
|---|---|---|
| BP | 0.023 | 0.041 |
| PSO-BP | 0.008 | 0.016 |
5. Experimental Validation
Microstructural analysis revealed:
- Surface: Acicular martensite + retained austenite (61.3 HRC)
- Sub-surface: Mixed acicular/lath martensite (58-61 HRC)
- Core: Lath martensite + bainite (48-52 HRC)
The simulation-experimental correlation shows excellent agreement with maximum errors of 2.1% in carbon concentration and 3.8% in hardness distribution.
6. Conclusion
This study establishes a comprehensive numerical framework for cylindrical gear carburizing process optimization. The developed PSO-BP prediction model enables efficient parameter selection for desired case depth (0.9±0.03mm) and surface carbon concentration (0.8±0.04%). The methodology provides significant guidance for improving gear manufacturing quality while reducing experimental costs.