Temperature Field Analysis and Experimental Validation of High Contact Ratio Spur Gears Under Oil Jet Lubrication

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This study investigates the thermal characteristics of high contact ratio (HCR) spur gears under oil jet lubrication conditions through computational fluid dynamics (CFD) simulations and experimental validation. The analysis focuses on temperature distribution patterns, convective heat transfer mechanisms, and parametric influences on gear thermal performance.

1. Fundamental Equations and Numerical Modeling

The governing equations for fluid-thermal coupling analysis include:

Continuity Equation:
$$
\frac{\partial \rho_f}{\partial t} + \nabla (\rho_f \mathbf{u}) = 0
$$

Momentum Conservation:
$$
\frac{\partial (\rho_f u_i)}{\partial t} + \nabla (\rho_f u_i \mathbf{u}) = \nabla (\mu \nabla u_i) – \frac{\partial p}{\partial x_i} + S_i
$$

Energy Conservation:
$$
\frac{\partial (\rho_f T)}{\partial t} + \nabla (\rho_f \mathbf{u} T) = \nabla \left( \frac{k_f}{C_p} \nabla T \right) + S_T
$$

The VOF model tracks oil-air interfaces using:
$$
\alpha_{air} + \alpha_{oil} = 1
$$

2. Heat Generation Mechanism

Power losses in spur gear systems comprise three components:

Rolling Power Loss:
$$
P_r = 90{,}000 \cdot \overline{V}_t \cdot h \cdot b \cdot e_p
$$

Sliding Power Loss:
$$
P_s = f \cdot F_n \cdot \overline{V}_s / 1{,}000
$$

Windage Loss:
$$
P_w = C \left(1 + 2.3 \frac{b}{R}\right) \rho_{eq}^{0.8} n^{2.8} R^{4.6} \mu_{eq}^{0.2}
$$

Table 1: Key Parameters of Spur Gear System
Parameter Driver Gear Driven Gear
Module (mm) 3.25 3.25
Teeth Count 32 25
Face Width (mm) 16 16.5
Contact Ratio 2.2

3. Thermal Boundary Conditions

Critical thermal parameters for spur gear analysis:

Table 2: Material Properties
Property Value
Density (kg/m³) 7,850
Thermal Conductivity (W/m·K) 46
Specific Heat (J/kg·K) 470
Table 3: Lubricant Properties
Parameter Value
Density @15.6°C (kg/m³) 993
Viscosity @37.8°C (cSt) 29
Viscosity @98.9°C (cSt) 5.4

4. Parametric Sensitivity Analysis

The thermal behavior of spur gears demonstrates significant dependence on operational and geometric parameters:

4.1 Lubrication Parameters
$$
\Delta T_{gear} = 0.78(\Delta T_{oil})^{1.02} \quad (R^2=0.96)
$$
$$
h_{conv} = 1250 \cdot Q_{oil}^{0.33} \quad (20^{\circ}\text{C} \leq T_{oil} \leq 90^{\circ}\text{C})
$$

Table 4: Temperature Variation with Oil Flow Rate
Flow Rate (L/min) Driver Temp (°C) Driven Temp (°C)
0.44 142 138
1.76 118 114
2.64 112 109

4.2 Operational Parameters
$$
T_{max} = 85 + 0.12n + 0.25F_n \quad (n\ \text{in rpm}, F_n\ \text{in kN})
$$

Table 5: Speed-Temperature Correlation
Speed (rpm) Temperature Rise (°C)
1,000 28
2,000 43
3,000 57

5. Experimental Validation

The CL-100 gear test rig measurements confirm CFD predictions with <5% deviation. Key findings include:

Table 6: Experimental vs Simulated Temperatures
Condition Experimental (°C) CFD (°C)
60°C Oil, 9级 Load 121 118
90°C Oil, 9级 Load 135 131

The thermal behavior of spur gears exhibits distinct characteristics compared to standard gears:

$$
\Delta T_{HCR} = 1.15\Delta T_{Standard} \quad (F_n > 5\ \text{kN})
$$

6. Conclusion

This comprehensive analysis establishes that high contact ratio spur gears under oil jet lubrication exhibit:

  1. Maximum temperatures at tooth tip regions (15-20% higher than root zones)
  2. Convective coefficients 18-22% greater on driven gears versus drivers
  3. Non-linear thermal sensitivity to lubricant flow rates beyond 1.76 L/min

The developed CFD methodology demonstrates strong correlation (R²=0.93) with experimental measurements, validating its effectiveness for spur gear thermal analysis.

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