Abstract:
This article focuses on the power loss simulation and analysis of helical gear in an electric vehicle’s reducer system. Using Amesim simulation software, the possible energy losses during helical gear transmission are thoroughly investigated. A simulation model of a pair of helical gear and a mathematical model for energy loss based on varying gear parameters are established. Calculation methods for energy loss are provided, and the new SKF equation is applied to determine the friction torque generated by the bearings on both sides of the helical gear. A PID speed control method ensures the required rotational speed. The simulation results demonstrate the model’s effectiveness in simulating various types of energy loss and total loss during helical gear rotation. By adjusting different gear parameters, the set of data with the lowest total loss is identified, providing valuable insights for optimizing gear parameters and design.
1. Introduction
In recent years, with the rapid development of electric vehicles and intense competition in the automotive industry, there has been a growing demand for improved vehicle performance, including higher transmission efficiency. Helical gear play a crucial role in transmitting power in vehicles, and understanding their power loss is essential for enhancing overall vehicle efficiency. The primary sources of power loss in helical gear include gear mesh power loss, churning loss, and windage loss. While prior studies have focused primarily on theoretical calculations, this article adopts a simulation-based approach using Amesim to provide a more comprehensive analysis.
2. Theoretical Calculation of Helical Gear Power Loss
2.1 Friction Power Loss in Helical Gear Mesh (P_F)
The friction power loss in helical gear mesh can be divided into sliding friction power loss (P_f) and rolling friction power loss (P_n).
Sliding Friction Power Loss (P_f):
The sliding friction power loss occurs due to the relative motion between the mating tooth surfaces during meshing. The formula for calculating P_f is:
Pf=1000fs⋅Fn⋅vs
Where:
- fs is the sliding friction coefficient,
- Fn is the normal force acting on the mating tooth surfaces,
- vs is the sliding velocity between the tooth surfaces.
Rolling Friction Power Loss (P_n):
The rolling friction power loss arises from the elastic fluid dynamic lubrication conditions during gear meshing. The formula for calculating P_n is:
Pn=c0.09hc⋅vt⋅b⋅εα⋅cosβ
Where:
- hc is the average elastohydrodynamic film thickness,
- vt is the tangential velocity,
- b is the face width of the gear,
- εα is the transverse contact ratio,
- β is the helix angle,
- c is a constant factor.
The total friction power loss in the helical gear mesh (P_F) is the sum of P_f and P_n:
PF=Pf+Pn
2.2 Churning Power Loss in Helical Gear (P_G)
Churning power loss occurs due to the resistance imparted by the lubricating oil as the gear rotates. It comprises smooth outer diameter churning loss (P_C1), smooth disk churning loss (P_C2), and tooth surface churning loss (P_C3):
PG=PC1+PC2+PC3
The formulas for calculating each component are:
PC1=7.37fgμ0n3D4.7LAg10−26
PC2=1.474fgμ0n3D5.7Ag10−26
PC3=10267.37fgμ0n3D4.7bRftanβAg
Where:
- fg is the gear immersion factor,
- μ0 is the dynamic viscosity of the lubricant,
- n is the rotational speed,
- D is the outer diameter of the rotating component,
- L is the length of the rotating component,
- b is the face width of the gear,
- Rf is the roughness factor,
- β is the helix angle,
- Ag is a proportionality constant.
2.3 Power Loss in Bearings (P_z)
The power loss in bearings includes friction power loss, churning and windage losses, and sealing element losses. The new SKF equation is used to calculate the friction torque, which comprises rolling friction torque (M_r), sliding friction torque (M_s), drag torque due to lubricant (M_d), and seal drag torque (M_e):
Pz=9549(Mr+Ms+Md+Me)⋅n
The formulas for calculating M_r and M_s are:
Mr=Gr⋅v0.6
Ms=f1⋅Gs
Where:
- Gr and Gs are rolling and sliding friction variables, respectively,
- v is the dynamic viscosity of the lubricant,
- f1 is the bearing friction coefficient.
3. Modeling and Simulation in Amesim
3.1 3D Model of Helical Gear
A 3D model of a pair of helical gear, two shafts, and two pairs of roller bearings was created. This model allowed for a detailed observation of the transmission structure and facilitated the simulation of power loss.
3.2 Amesim Simulation Model
The Amesim simulation model incorporates the 3D model of the helical gear and bearings, along with the PID speed controller. The gear and bearing parameters are defined as shown in Tables 1 and 2.
Table 1: Basic Gear Parameters
| Parameter | Small Gear | Large Gear |
|---|---|---|
| Number of Teeth | 18 | 79 |
| Module (mm) | 1.75 | 1.75 |
| Face Width (mm) | 30 | 30 |
| Pressure Angle (°) | 25 | 25 |
| Helix Angle (°) | 30 | 30 |
Table 2: Bearing Basic Parameters
| Parameter | Large Gear Bearings | Small Gear Bearings |
|---|---|---|
| Average Diameter (mm) | 40 | 40 |
| Friction Coefficient | 2.5e-4 | 2.5e-4 |
| Inertia (kg·m²) | 1 | 1 |
| Viscous Friction Coefficient [N·m/(r/min)] | 0.05 | 0.05 |
3.3 Simulation Results
The simulation results reveal various aspects of power loss during helical gear transmission.
The sliding friction power loss is significantly higher than the rolling friction power loss, indicating its dominance in total friction power loss.
Churning power loss varies with gear rotation, mainly influenced by lubricant properties and gear geometry.
The power loss in bearings includes friction, churning, windage, and seal drag losses, contributing significantly to the overall power loss.
3.4 Parametric Study
By varying gear parameters such as the number of teeth, face width, immersion depth, helix angle, and pressure angle, the impact on total power loss was investigated.
Table 3: Varied Gear Geometric Parameters
| Sequence | Number of Teeth | Face Width (mm) | Immersion Depth (mm) | Helix Angle (°) | Pressure Angle (°) |
|---|---|---|---|---|---|
| 1 | 79 | 35 | 55 | 40 | 35 |
| 2 | 58 | 30 | 50 | 30 | 30 |
| 3 | 50 | 25 | 40 | 23 | 25 |
| 4 | 42 | 20 | 35 | 15 | 20 |
| 5 | 36 | 15 | 30 | 5 | 15 |
The results indicate that increasing the number of teeth on the large gear reduces total power loss, while increasing face width, immersion depth, and helix angle leads to higher power loss. Conversely, increasing the pressure angle reduces total power loss.
4. Discussion
The simulation results provide valuable insights into the mechanisms of power loss in helical gear. The sliding friction power loss is the primary contributor to total friction power loss, emphasizing the importance of minimizing friction coefficients and optimizing lubricant properties. The churning power loss is influenced by gear geometry, lubricant properties, and immersion depth, suggesting a need for optimized gear designs and lubricant formulations.
The parametric study underscores the sensitivity of total power loss to gear parameters. Specifically, increasing the number of teeth on the large gear while maintaining other parameters constant leads to a reduction in total power loss. However, increasing face width, immersion depth, or helix angle exacerbates power loss, highlighting the need for a balanced approach in gear design.
5. Conclusion
This article presents a comprehensive simulation-based analysis of power loss in helical gear using Amesim software. By establishing a detailed simulation model and incorporating theoretical calculations, various types of power loss were investigated. The results demonstrate that the model effectively simulates total power loss during helical gear transmission and identifies optimal gear parameters for minimizing power loss. This work provides a valuable reference for helical gear design and optimization, contributing to the development of more efficient electric vehicle transmission systems.
6. Future Work
Future research can build upon this foundation by exploring additional factors that influence power loss, such as material properties, surface texturing, and thermal effects. Additionally, integrating machine learning and optimization algorithms into the simulation framework can facilitate the rapid identification of optimal gear designs across a broader parameter space.