Abstract
In helicopter transmission systems, high contact ratio (HCR) spur gear is commonly lubricated and cooled via oil injection. Their thermal characteristics critically influence operational lifespan. This study establishes a numerical model for analyzing the temperature field of HCR spur gear under oil-jet lubrication using computational fluid dynamics (CFD). The Volume of Fluid (VOF) method and Multiple Reference Frame (MRF) approach were employed to simulate temperature distribution and convective heat transfer coefficients (HTC) on gear surfaces. A control variable method was applied to investigate the effects of lubricant parameters, operational conditions, and gear geometry on thermal behavior. Experimental validation was conducted using a CL-100 gear testing rig. Results indicate that gear temperature increases with load, aligning with CFD predictions. Notably, HCR gears exhibit higher temperatures than standard spur gear, with the disparity amplifying under elevated loads.
1. Introduction
High contact ratio spur gear, defined as spur gear with a contact ratio exceeding 2, maintain at least two pairs of meshing teeth during operation. This design reduces average load per unit contact length, enhancing transmission safety. However, power losses during operation manifest as heat, which, if inadequately dissipated, leads to thermal failures such as scuffing. In aerospace applications, HCR spur gear often operate under high-speed and heavy-load conditions, making thermal management imperative.
Oil-jet lubrication is widely adopted for cooling these gears. Understanding temperature distribution and convective heat transfer mechanisms is essential for optimizing cooling performance and reliability. While prior studies have explored gear temperature fields using CFD, this work uniquely focuses on HCR spur gear, combining advanced numerical simulations with experimental validation.
2. CFD Theory and Numerical Model
2.1 Governing Equations
The fluid dynamics within the gearbox are governed by the Navier-Stokes equations:
- Mass Conservation:∂ρ∂t+∇⋅(ρu)=0∂t∂ρ+∇⋅(ρu)=0
- Momentum Conservation:∂(ρu)∂t+∇⋅(ρuu)=∇⋅(μ∇u)−∇p+S∂t∂(ρu)+∇⋅(ρuu)=∇⋅(μ∇u)−∇p+S
- Energy Conservation:∂(ρT)∂t+∇⋅(ρuT)=∇⋅(kCp∇T)+ST∂t∂(ρT)+∇⋅(ρuT)=∇⋅(Cpk∇T)+ST
2.2 Multiphase Flow Modeling
The VOF method was used to track the oil-air interface:αoil+αair=1αoil+αair=1
where αα represents the volume fraction of each phase.
2.3 Heat Generation Model
Gear power losses include rolling, sliding, and windage losses:
- Rolling Power Loss (PrPr):Pr=90,000⋅Vˉt⋅h⋅b⋅ep1,000Pr=90,000⋅1,000Vˉt⋅h⋅b⋅ep
- Sliding Power Loss (PsPs):Ps=f⋅Fn⋅Vˉs1,000Ps=f⋅1,000Fn⋅Vˉs
- Windage Power Loss (PwPw):Pw=C(1+2.3bR)ρeq0.8n2.8R4.6μeq0.2Pw=C(1+2.3Rb)ρeq0.8n2.8R4.6μeq0.2
Total heat generation (QQ) is distributed between driving and driven gears based on thermal properties.
3. CFD Model Setup
3.1 Gear and Lubricant Parameters
Table 1: Geometric and Operational Parameters of HCR Spur Gear
| Parameter | Driving Gear | Driven Gear |
|---|---|---|
| Normal Module (mm) | 3.25 | 3.25 |
| Number of Teeth | 32 | 25 |
| Face Width (mm) | 16 | 16.5 |
| Pressure Angle (°) | 20 | 20 |
| Rotational Speed (r/min) | 1,500 | 1,920 |
| Load Level | 9 | 9 |
Table 2: Material Properties of Spur Gear
| Material | Thermal Conductivity (W/m·K) | Specific Heat (J/kg·K) | Density (kg/m³) |
|---|---|---|---|
| 20CrMnMoA | 46 | 470 | 7,850 |
Table 3: Lubricant Properties
| Lubricant Type | Density at 15.6°C (kg/m³) | Viscosity at 37.8°C (mm²/s) | Viscosity at 98.9°C (mm²/s) |
|---|---|---|---|
| Shell 555 | 993 | 29 | 5.4 |
3.2 Mesh and Boundary Conditions
The MRF method was applied to simulate rotating gears. Key boundary conditions included:
- Oil Inlet: Velocity = 40 m/s
- Outlet: Pressure = 1 atm
- Walls: Natural convection (HTC = 50 W/m²·K)
4. Simulation Results and Analysis
4.1 Temperature Distribution
- Driving Gear: Peak temperature (110°C) occurred near the tooth tip due to sliding friction.
- Driven Gear: Slightly lower peak temperature (105°C) despite higher rotational speed, attributed to superior convective cooling.
Table 4: Temperature Distribution Comparison
| Parameter | Driving Gear (°C) | Driven Gear (°C) |
|---|---|---|
| Maximum Temperature | 110 | 105 |
| Minimum Temperature | 80 | 78 |
4.2 Effects of Lubricant Parameters
Table 5: Influence of Oil Temperature on Gear Temperature
| Oil Temperature (°C) | Driving Gear (°C) | Driven Gear (°C) |
|---|---|---|
| 40 | 85 | 82 |
| 60 | 95 | 92 |
| 90 | 110 | 105 |
Higher oil temperatures increased gear temperatures linearly due to reduced viscosity and elevated heat generation.
Table 6: Influence of Oil Flow Rate on Gear Temperature
| Flow Rate (L/min) | Driving Gear (°C) | Driven Gear (°C) |
|---|---|---|
| 0.44 | 120 | 115 |
| 1.76 | 95 | 90 |
| 2.64 | 100 | 95 |
Optimal cooling occurred at 1.76 L/min; excessive flow induced parasitic losses.
4.3 Effects of Operational Parameters
Table 7: Influence of Rotational Speed on Gear Temperature
| Speed (r/min) | Driving Gear (°C) | Driven Gear (°C) |
|---|---|---|
| 1,000 | 85 | 80 |
| 2,500 | 100 | 95 |
| 3,500 | 105 | 100 |
Temperature rose with speed but stabilized due to enhanced convective cooling at higher velocities.
Table 8: Influence of Load on Gear Temperature
| Load Level | Driving Gear (°C) | Driven Gear (°C) |
|---|---|---|
| 5 | 90 | 85 |
| 9 | 110 | 105 |
| 12 | 125 | 120 |
Higher loads intensified frictional heating, outweighing cooling effects.
5. Experimental Validation
5.1 Test Setup
- Equipment: CL-100 gear testing rig with torque sensors and wireless thermocouples.
- Conditions: Oil temperature = 60°C, flow rate = 1.76 L/min.
Table 9: Comparison of Simulated and Experimental Temperatures
| Parameter | Simulation (°C) | Experiment (°C) | Error (%) |
|---|---|---|---|
| Driving Gear (60°C) | 95 | 97 | 2.1 |
| Driven Gear (60°C) | 92 | 94 | 2.2 |
| Driving Gear (90°C) | 110 | 113 | 2.7 |
Results validated the CFD model’s accuracy, with errors below 3%.
5.2 HCR vs. Standard Spur Gear
Table 10: Temperature Comparison Under Varying Contact Ratios
| Contact Ratio | Driving Gear (°C) | Driven Gear (°C) |
|---|---|---|
| 1.73 | 90 | 85 |
| 2.21 | 110 | 105 |
HCR gears exhibited higher temperatures due to prolonged sliding contact and increased heat generation.
6. Conclusions
- Temperature Distribution: Maximum temperatures occurred near the tooth tip, with gradients along the face width.
- Convective Cooling: Driven gears exhibited superior cooling due to higher rotational speeds.
- Parameter Sensitivity:
- Temperature increased with load, speed, oil temperature, and contact ratio.
- Temperature decreased with oil flow rate, face width, and pressure angle.
- Validation: Experimental results confirmed the CFD model’s reliability. HCR spur gear require tailored cooling strategies for high-load applications.
This study provides critical insights into the thermal management of HCR spur gear, essential for advancing aerospace and heavy machinery transmissions.