Abstract
This article presents an in-depth analysis and optimization of the windage power loss in an aeronautical spiral bevel gear pair. Utilizing Computational Fluid Dynamics (CFD) theory, the study leverages Fluent software and the parallel computing power of supercomputers to simulate and calculate the windage power loss. The three-dimensional model of the spiral bevel gear pair is constructed through the local synthesis method, and the RNG k-ε turbulence model is employed to account for swirling flows in the average flow field. Gear boundary motion is driven by User-Defined Functions (UDFs), and dynamic mesh technology simulates the time-varying fluid domain due to boundary motion. The simulation results under different shroud configurations are compared, identifying the optimal shroud design that minimizes windage power loss. This study provides valuable insights for the practical design of shrouds in high-speed gearbox systems.
Introduction
In aeronautical transmission systems, spiral bevel gears are widely used due to their superior load-bearing capacity, smooth transmission, and excellent lubrication characteristics. However, at high rotational speeds, these gears can generate significant windage power loss, impacting overall system efficiency. Windage power loss, also known as spin power loss, is a type of load-independent power loss that arises from interactions between rotating components and the surrounding fluid medium. This loss can be substantial, especially in high-speed applications, necessitating careful analysis and optimization.
Background and Literature Review
Previous studies on windage power loss have primarily focused on individual non-meshing gears, with limited research on meshing spiral bevel gear pairs. Experimental and computational fluid dynamics (CFD) methods have been used extensively to investigate windage power loss in gears. Dawson [4] conducted experiments on rotating spur and helical gears and derived empirical formulas to describe windage power loss. Diab and Ville [5] performed windage tests on disks and gears of various shapes and sizes, proposing a quasi-analytical model. Winfree [6] analyzed the windage power loss of a shrouded spiral bevel gear and optimized shroud design.
CFD has emerged as a powerful tool for fluid analysis, allowing for rapid and non-experimental solutions. Al-Shibl and Simmons [8] used Fluent software to study windage power loss in an enclosed spur gear, while Rapley and Eastwick [9] analyzed the effects of rotation direction and shroud configuration on spiral bevel gears. Jia [10] developed a CFD model for spur gears, investigating windage power loss under oil-air two-phase flow conditions. Domestic studies have also focused on spiral bevel gears, such as the work by Liang et al. [11] and Bao et al. [12], who optimized shroud and baffle designs to reduce windage loss.
Methodology
Modeling and Simulation Approach
This study adopts a comprehensive approach to model and simulate the windage power loss in an aeronautical spiral bevel gear pair. The modeling and simulation process involve several key steps, including gear pair modeling, shroud design, fluid domain creation, mesh generation, boundary condition settings, and simulation execution.
Gear Pair Modeling
The spiral bevel gear pair’s basic dimensions are detailed in Table 1. Using the local synthesis method [16], the gear pair’s three-dimensional model is constructed in Unigraphics NX (UG) software. The model includes the active and driven gears, with specific tooth numbers, module, pressure angle, helix angle, and face width. To simplify the simulation and improve computational efficiency, the gear shafts are modeled as solid shafts, and intricate details such as bearings, fasteners, and lubricant are omitted.
Table 1: Basic Parameters of Spiral Bevel Gear Pair
| Parameter | Active Gear | Driven Gear |
|---|---|---|
| Number of Teeth (z) | 30 | 76 |
| Rotational Speed (rpm) | 20,900 | 7,626 |
| Module (m<sub>t</sub>) | 3.85 mm | 3.85 mm |
| Pressure Angle (α<sub>n</sub>) | 20° | 20° |
| Helix Angle (β) | 30° | 30° |
| Face Width (B) | 38.5 mm | 38.5 mm |
| Shaft Angle (σ) | 69.77° | 69.77° |
| Pitch Circle Diameter (D) | 103.95 mm | 284.9 mm |
Shroud Design
The shroud is designed to cover the driven gear, attached to the gearbox housing via bolts. The shroud’s material is 45 steel, and its configuration parameters include the small-end gap, large-end gap, tooth-face gap, and meshing opening angle.
Fluid Domain and Mesh Generation
The fluid domain encompasses the space between the gear pair and the housing, with or without the shroud. ICEM CFD is used to generate an unstructured mesh with a maximum element size of 4 mm and a boundary layer of 6 layers (maximum size of 1 mm) on the gear surfaces. The total mesh count is approximately 13 million elements, with around 2 million nodes.
Simulation Settings
The Fluent solver is employed for the simulations, considering air as an incompressible fluid. The transient analysis is conducted using a pressure-based solver with a coupled algorithm. The RNG k-ε turbulence model is selected to account for swirling flows and high strain rates. Dynamic mesh technology is activated to simulate the fluid domain’s shape changes due to gear rotation. UDFs define the rotational speeds of the gears, and the time step is set to 2e-6 seconds with 6000 iterations.
Results and Discussion
Windage Power Loss Analysis
The simulation results are analyzed under different shroud configurations, including no shroud and various gap and opening angle combinations. The windage power loss for each configuration is summarized in Table 2.
Table 2: Windage Power Loss in Different Configurations
| Test No. | Gap (mm) | Opening Angle (°) | Total Windage Power Loss (W) |
|---|---|---|---|
| 1 | No shroud | – | 2,704.39 |
| 2 | 7 | 45 | 2,164.09 |
| 3 | 7 | 60 | 2,019.47 |
| 4 | 5 | 45 | 2,010.95 |
| 5 | 5 | 60 | 2,045.85 |
| 6 | 1 | 45 | 1,665.05 |
| 7 | 1 | 60 | 1,795.34 |
The results indicate that installing a shroud significantly reduces windage power loss, with smaller gaps leading to greater reductions. The optimal configuration (Test No. 6) reduces windage power loss by 55.3%.
Component-wise Windage Power Loss
Table 3 details the windage power loss contribution from the tooth faces, end faces, and shafts of the gears.
Table 3: Component-wise Windage Power Loss
| Test No. | Tooth Face (W) | End Face (W) | Shaft (W) | Total (W) |
|---|---|---|---|---|
| 1 | 2,650.03 | 54.36 | – | 2,704.39 |
| … | … | … | … | … |
| 7 | 1,477.68 | 271.66 | 46.00 | 1,795.34 |
The tooth faces contribute the most to the total windage power loss, highlighting their critical role in reducing overall loss.
Conclusion
This study comprehensively analyzed and optimized the windage power loss in an aeronautical spiral bevel gear pair using CFD simulations. Key findings include:
- Shroud Effectiveness: Installing a shroud significantly reduces windage power loss, with smaller gaps providing greater reductions. The optimal shroud configuration reduced loss by 55.3%.
- Pressure and Velocity Distributions: Pressure contours show higher pressures on entering teeth and lower pressures on exiting teeth. Velocity contours indicate that shrouds effectively reduce air velocities between the shroud and housing.
- Turbulent Kinetic Energy: Smaller shroud gaps lead to lower turbulent kinetic energy, contributing to lower windage power loss.
- Component-wise Contributions: Tooth faces contribute the most to overall windage power loss, emphasizing the importance of optimizing these surfaces.
This study provides valuable insights for the design and optimization of shrouds in high-speed gearbox systems, ultimately leading to improved system efficiency and reliability. Future work could explore the effects of lubricant properties and gearbox sealing on windage power loss.