Modern high-end transmission systems, such as next-generation aero-engine gearboxes, face extreme operational challenges including high-speed rotation, elevated temperatures, and heavy loads. These conditions significantly increase the risk of scuffing failure in cylindrical gears, which critically impacts system reliability and service life. This paper conducts a comprehensive comparison of three predominant Chinese standards for scuffing capacity evaluation: GB/Z 6413.1-2003 (flash temperature method), GB/Z 6413.2-2003 (integral temperature method), and HB/Z 84.4-1984 (aviation-specific adaptation). Through theoretical analysis, parametric comparisons, and case studies using FZG A-type gears, we reveal critical differences in computational methodologies and application scopes.
1. Theoretical Framework Comparison
The scuffing resistance of cylindrical gears primarily depends on the maximum contact temperature at the tooth interface, comprising bulk temperature (\(\Theta_{M}\)) and flash temperature (\(\Theta_{fl}\)). Table 1 summarizes the fundamental differences between the analyzed standards.
| Standard | Methodology | Applicability |
|---|---|---|
| GB/Z 6413.1 | Flash temperature method | Band-shaped Hertzian contacts with high Péclet numbers |
| GB/Z 6413.2 | Integral temperature method | General applications excluding localized hot spots |
| HB/Z 84.4 | Simplified integral method | Aviation-grade hardened steel gears |
The flash temperature method calculates instantaneous peak temperatures along the path of contact:
$$\Theta_{Bmax} = \Theta_M + \Theta_{fl}^{\text{max}}$$
whereas the integral temperature method employs weighted averaging:
$$\Theta_{\text{int}} = \Theta_M + C_2 \cdot \Theta_{fl}^{\text{avg}}$$
with \(C_{2}\) = 1.5 for cylindrical gears per GB/Z 6413.2.
2. Critical Formula Comparison
Table 2 contrasts the core equations for bulk temperature calculation across standards, demonstrating how lubrication and material factors are differently incorporated.
| Standard | Bulk Temperature Formula |
|---|---|
| GB/Z 6413.1 | $$\Theta_M = \Theta_{\text{oil}} + 0.47X_sX_{mp} \int_{\Gamma_A}^{\Gamma_E} \frac{\Theta_{fl}\,d\Gamma_y}{\Gamma_E – \Gamma_A}$$ |
| GB/Z 6413.2 | $$\Theta_M = \Theta_{\text{oil}} + 0.7\Theta_{fl}^{\text{avg}}$$ |
| HB/Z 84.4 | $$\Theta_M = (\Theta_{\text{oil}} + 0.7\Theta_{fl}^{\text{avg}})X_s$$ |
Key parameter differences emerge in friction coefficient estimation. For FZG A-type gears (m = 4.5 mm, \(z_{1}\)/\(z_{2}\) = 16/24), HB/Z 84.4 computes 49.1% higher average friction coefficients than GB/Z 6413.2:
$$\mu_{m}^{\text{HB}} = 0.114 \quad \text{vs.} \quad \mu_{m}^{\text{GB}} = 0.058$$
3. Parametric Case Studies
Using FZG A-type gears (Table 3), we systematically compared temperature predictions under varying operational conditions.
| Parameter | Value |
|---|---|
| Module (mm) | 4.5 |
| Pressure angle | 20° |
| Face width (mm) | 20 |
| Pinion teeth | 16 |
| Gear teeth | 24 |
| Material | 18CrNiMo7-6 |
3.1 Torque Dependency
Figure 1 illustrates significant divergence in scuffing temperature predictions across standards under increasing torque (FZG Load Stages 3-12). HB/Z 84.4 yields 30-50% higher values due to omitted roughness/lubricant factors.
| Torque (Nm) | GB/Z 6413.1 (℃) | GB/Z 6413.2 (℃) | HB/Z 84.4 (℃) |
|---|---|---|---|
| 35.3 | 81.37 | 76.78 | 106.58 |
| 534.5 | 267.16 | 268.68 | 474.46 |
3.2 Module Sensitivity
Prediction discrepancies amplify with decreasing module size (Figure 2). At m = 2 mm, HB/Z 84.4 overestimates by 42.2% compared to GB/Z 6413.2.
| Module (mm) | GB/Z 6413.1 (℃) | GB/Z 6413.2 (℃) |
|---|---|---|
| 2.0 | 557.66 | 685.09 |
| 7.0 | 190.56 | 176.83 |
4. Operational Limits and Recommendations
For cylindrical gears operating within 4-7 mm modules, GB/Z 6413.1 and GB/Z 6413.2 demonstrate ≤5% prediction variance. However, HB/Z 84.4 remains conservative due to:
- Omission of surface roughness coefficient \(X_{R}\)
- Simplified lubrication factor \(X_{s}\)
- Overestimated friction coefficients
The critical temperature escalation factors are quantified as:
$$\Delta\Theta_{\text{Torque}} = 249.9\% \quad (\text{Load Stage }3\!\rightarrow\!12)$$
$$\Delta\Theta_{\text{Speed}} = 95.9\% \quad (1,\!000\!\rightarrow\!10,\!000 \text{ rpm})$$
$$\Delta\Theta_{\text{OilTemp}} = 41.8\% \quad (40℃\!\rightarrow\!120℃)$$
5. Conclusion
This systematic comparison reveals that HB/Z 84.4’s conservative nature stems from incomplete parameter consideration, while GB/Z standards show strong consistency except for small-module gears. Engineers should select standards based on module size and application criticality, with GB/Z 6413.2 preferred for precision components and HB/Z 84.4 suitable for aviation safety margins.