Abstract
Power loss in cylindrical gears during operation significantly impacts transmission efficiency. This study investigates the power loss mechanisms of cylindrical gears with variable hyperboloid circular-arc-tooth trace (VH-CATT) under gas-liquid two-phase flow conditions. By combining fluid dynamics theory and the Smooth Particle Hydrodynamics (SPH) method, a 3D model based on the FZG gearbox was established to simulate lubrication flow fields and power loss characteristics. Key parameters such as rotational speed, lubricant viscosity, and oil immersion depth were analyzed. Experimental validation using the FZG test bench confirmed that higher rotational speeds, elevated lubricant viscosity, and increased oil immersion depth exacerbate power loss. Optimizing these parameters can enhance lubrication efficiency and reduce energy waste.
Keywords: cylindrical gear; power loss; SPH method; FZG test bench; lubrication
1. Introduction
Cylindrical gears are pivotal components in mechanical transmission systems, widely used in industries ranging from automotive to renewable energy. However, power loss due to churning and windage effects remains a critical challenge, diminishing overall efficiency. With growing emphasis on energy conservation and emission reduction, understanding and mitigating power loss in cylindrical gears has become imperative.
This study focuses on VH-CATT cylindrical gears, characterized by their unique tooth geometry that optimizes load distribution and reduces stress concentration. Despite these advantages, their complex interaction with lubricants under high-speed conditions necessitates a detailed analysis of power loss mechanisms. By integrating SPH-based simulations and experimental validation, this work provides actionable insights for optimizing gear design and lubrication strategies.
2. Literature Review
Prior research on gear power loss has predominantly focused on conventional spur and helical gears. Key contributions include:
| Study | Methodology | Key Findings |
|---|---|---|
| Li et al. [1] | Partitioned helical gears into thin spur gears | Quantified churning losses in helical gears |
| Zhu et al. [3] | Boundary layer theory for orthogonal face gears | Developed analytical models for churning losses |
| Changenet et al. [5] | Experimental validation of churning losses | Identified errors in summing individual gear losses |
| Ji et al. [13] | SPH simulations for oil flow | Validated SPH accuracy against experimental data |
While these studies advanced the field, gaps remain in analyzing cylindrical gears with non-standard tooth profiles like VH-CATT. This work addresses these gaps by incorporating multi-phase flow dynamics and advanced SPH simulations.
3. Theoretical Analysis
3.1 Churning Power Loss
Churning losses arise from viscous drag and turbulence as gears interact with lubricants. For VH-CATT cylindrical gears, total churning loss (PchurningPchurning) comprises three components:
- Circumferential loss (P1P1): Caused by viscous drag along gear teeth.
- End-face loss (P2P2): Due to oil agitation at gear end faces.
- Squeeze loss (P3P3): Generated by lubricant compression during meshing.
P1=7.37fsν1.5d0.5LAs×1026,P2=1.474fsν1.5d0.5As×1026,P3=7.37fsν1.5d0.5BRt/tanβAs×1026P1=As×10267.37fsν1.5d0.5L,P2=As×10261.474fsν1.5d0.5,P3=As×10267.37fsν1.5d0.5BRt/tanβPchurning=P1+P2+P3Pchurning=P1+P2+P3
Variables:
- fsfs: Immersion factor (h/dah/da)
- νν: Kinematic viscosity
- dd: Pitch diameter
- BB: Face width
3.2 Windage Power Loss
Windage losses stem from air-oil mixture friction. The Anderson model [19] was adapted:Pwindage=C(1+2.3BR)ρ0.8n3R4.6ν0.2Pwindage=C(1+2.3RB)ρ0.8n3R4.6ν0.2
Variables:
- C=2.4×10−8C=2.4×10−8
- ρρ: Air-oil mixture density
- RR: Pitch radius
4. Simulation Model
4.1 3D Modeling
The FZG gearbox geometry was replicated in UG NX. Key parameters of the VH-CATT cylindrical gear pair are summarized below:
| Parameter | Pinion | Gear |
|---|---|---|
| Teeth (zz) | 21 | 29 |
| Module (mm) | 4 mm | 4 mm |
| Face Width (BB) | 80 mm | 80 mm |
| Pressure Angle (αα) | 20° | 20° |
4.2 SPH Method
The SPH approach discretizes fluids into particles, avoiding mesh distortion issues. Governing equations include:dρdt=−ρ∇⋅u,dudt=1ρ∇⋅S+gdtdρ=−ρ∇⋅u,dtdu=ρ1∇⋅S+g
Stress tensor (SS):S=−pI+μ(∇u+∇uT)+(ξ−23μ)(∇⋅u)IS=−pI+μ(∇u+∇uT)+(ξ−32μ)(∇⋅u)I
Particle diameter was set to 1 mm to balance accuracy and computational cost.
5. Results and Discussion
5.1 Lubricant Flow Dynamics
5.2 Impact of Rotational Speed
| Speed (rpm) | Torque Loss (Nm) |
|---|---|
| 600 | 0.15 |
| 1200 | 0.28 |
| 1800 | 0.42 |
| 3000 | 0.75 |
5.3 Impact of Oil Immersion Depth
| Immersion Depth (mm) | Torque Loss (Nm) |
|---|---|
| -20 | 0.18 |
| 0 | 0.28 |
| +20 | 0.39 |
5.4 Impact of Lubricant Viscosity
| Viscosity (cSt) | Torque Loss (Nm) |
|---|---|
| 15.2 | 0.21 |
| 30.1 | 0.33 |
| 79.5 | 0.48 |
6. Experimental Validation
The FZG test bench measured torque loss under varying conditions. Key findings include:
- Speed Dependency: Experimental torque matched simulation trends but exceeded values due to auxiliary component losses.
- Immersion Depth: Higher immersion depths caused greater discrepancies between simulation and experiment.
7. Conclusion
- Churning Loss Dominance: VH-CATT cylindrical gears experience significant churning losses, exacerbated by high speeds and viscous lubricants.
- Optimal Lubrication: Adjusting oil immersion depth and viscosity can reduce power loss by up to 30%.
- SPH Validation: Simulations aligned with experimental data, confirming SPH’s efficacy for multi-phase flow analysis.
Future work will explore advanced lubricants and hybrid simulation methods to further optimize cylindrical gear performance.