Abstract:
This paper delves into the power loss simulation and analysis of helical gears in electric vehicle reduction gears using Amesim software. The research focuses on establishing simulation models for a pair of helical gears and mathematical models to compute energy losses based on varying gear parameters. The New SKF equation is employed to calculate the friction torque generated by the bearings on both sides of the helical gears, while a PID speed control method maintains the desired rotational speed. The simulation results demonstrate the model’s efficacy in simulating various types of energy losses during helical gear rotation, identifying the optimal gear parameters for minimizing total power loss. This study provides a foundation for optimizing gear design and parameter selection.
1. Introduction
In recent years, the rapid development of new energy vehicles and intense competition within the automotive industry have necessitated a continuous improvement in vehicle technologies. Helical gears, as essential components in power transmission, play a crucial role in vehicle performance. Studying the power loss during helical gear rotation is instrumental in optimizing overall vehicle efficiency. This paper focuses on simulating and analyzing power loss in helical gears using Amesim software, aiming to provide insights into minimizing energy dissipation.
2. Theoretical Calculation of Helical Gear Power Loss
Helical gear power loss can be categorized into three primary types: friction power loss at the meshing interface, churning power loss, and windage power loss. This section details the theoretical calculations for each type of power loss.
2.1 Friction Power Loss at the Meshing Interface (P_F)
Friction power loss at the helical gear meshing interface can be further classified into sliding friction power loss (P_f) and rolling friction power loss (P_n).
2.1.1 Sliding Friction Power Loss (P_f)
Sliding friction power loss occurs due to the relative velocity difference between the meshing gear teeth. The formula for calculating P_f is:
P_f=f_n⋅F_n⋅v_s⋅10001
where:
- f_n is the average sliding friction coefficient,
- F_n is the average normal load at the meshing point,
- v_s is the average sliding velocity at the meshing point.
2.1.2 Rolling Friction Power Loss (P_n)
Rolling friction power loss arises under elastohydrodynamic lubrication conditions and can be calculated using:
P_n=0.09⋅h_c⋅v_t⋅b⋅ε_α⋅cosβ
where:
- h_c is the average elastohydrodynamic oil film thickness,
- v_t is the tangential velocity at the meshing point,
- b is the tooth width,
- ε_α is the transverse contact ratio,
- β is the helix angle.
Table 1: Key Variables and Their Formulas for Friction Power Loss Calculations
| Variable | Formula | Description |
|---|---|---|
| f_n | f_n=0.0127⋅lg(29660⋅F_n⋅cosβ⋅b⋅μ⋅v_s⋅v_t) | Average sliding friction coefficient |
| F_n | F_n=r_1⋅cosα⋅cosβT | Average normal load |
| v_s | v_s=0.02618⋅n⋅g⋅z_2z_1+z_2 | Average sliding velocity |
| v_t | v_t=0.2094⋅n⋅r_1⋅sinα−0.125⋅g⋅z_2z_1−z_2 | Tangential velocity |
| h_c | h_c=2.051⋅10−7⋅(μ⋅v_t)0.67⋅(F_n)−0.067⋅ρ0.464 | Average elastohydrodynamic oil film thickness |
2.2 Churning Power Loss (P_G)
Churning power loss results from the resistance imparted by the lubricant as the gears rotate, leading to energy dissipation. According to ISO/TR 14179-1, churning power loss (P_G) comprises three components: smooth outer diameter churning loss (P_C1), smooth disk churning loss (P_C2), and tooth surface churning loss (P_C3).
P_G=P_C1+P_C2+P_C3
where:
- P_C1, P_C2, and P_C3 are calculated using respective formulas based on gear dimensions, lubricant properties, and operational conditions.
Table 2: Formulas for Churning Power Loss Components
| Component | Formula |
|---|---|
| P_C1 | P_C1=7.37⋅f_g⋅μ_0⋅n3⋅D4.7⋅L⋅A_g⋅10−26 |
| P_C2 | P_C2=1.474⋅f_g⋅μ_0⋅n3⋅D5.7⋅A_g⋅10−26 |
| P_C3 | P_C3=7.37⋅f_g⋅μ_0⋅n3⋅D4.7⋅b⋅R_f⋅tanβ⋅A_g⋅10−26 |
2.3 Bearing Power Loss (P_z)
Bearing power loss (P_z) includes friction power loss, churning and windage loss, and seal friction loss. The SKF equation is utilized to calculate the friction torques, comprising rolling friction torque (M_r), sliding friction torque (M_s), drag torque due to lubricant (M_d), and seal friction torque (M_e).
P_z=9549M_r+M_s+M_d+M_e⋅n
Table 3: Formulas for Bearing Friction Torques
| Torque Component | Formula |
|---|---|
| Rolling Friction Torque (M_r) | M_r=G_r⋅v0.6⋅n |
| Sliding Friction Torque (M_s) | M_s=f_1⋅G_s |
where G_r and G_s are functions of bearing type, load, speed, and lubricant properties.
3. Simulation Modeling and Analysis Using Amesim
3.1 3D Model Establishment
A 3D model of the helical gear system, including a pair of helical gears, two transmission shafts, and four roller bearings, was created for simulation in Amesim. This model facilitates a detailed observation of the transmission structure and characteristics.
3.2 Amesim Simulation Model
The Amesim simulation model incorporates the 3D model, gear parameters, and bearing settings. The gear and bearing parameters are summarized in Tables 4 and 5, respectively.
Table 4: Gear Parameters
| Parameter | Small Gear | Large Gear |
|---|---|---|
| Number of Teeth | 18 | 79 |
| Module (mm) | 1.75 | 1.75 |
| Tooth Width (mm) | 30 | 30 |
| Pressure Angle (°) | 25 | 25 |
| Helix Angle (°) | 30 | 30 |
Table 5: Bearing Parameters
| Parameter | Large Gear Bearings | Small Gear Bearings |
|---|---|---|
| Average Diameter (mm) | 40 | 40 |
| Friction Coefficient | 2.5e-4 | 2.5e-4 |
| Speed-dependent Friction Coefficient | 2 | 2 |
| Moment of Inertia (kg·m²) | 1 | 1 |
| Viscous Friction Coefficient [N·m/(r/min)] | 0.05 | 0.05 |
The simulation results provide insights into the various types of power losses during helical gear rotation.
The results indicate that sliding friction power loss dominates over rolling friction power loss, highlighting the importance of reducing sliding friction in optimizing gear performance.
Churning power loss varies with rotational speed and lubricant properties, offering potential avenues for reduction through lubricant optimization.
Bearing power loss primarily comprises friction torques, with a notable contribution from sliding friction.
3.4 Parametric Analysis
A parametric study was conducted by varying gear parameters to assess their impact on total power loss.
The results reveal that:
- Increasing the number of teeth on the large gear reduces total power loss.
- Wider tooth widths and deeper immersion depths lead to higher total power losses.
- Increasing the helix angle and pressure angle exhibit contrasting effects on total power loss.
Table 6: Parametric Study Results
| Parameter Variation | Effect on Total Power Loss |
|---|---|
| Increasing Large Gear Teeth | Decrease |
| Increasing Tooth Width | Increase |
| Increasing Immersion Depth | Increase |
| Increasing Helix Angle | Increase |
| Increasing Pressure Angle | Decrease |
4. Conclusion
This paper presents a comprehensive simulation and analysis of power loss in helical gears using Amesim software. By establishing detailed simulation models and employing theoretical calculations, the study reveals the various types of power losses and their contributing factors. Through parametric analysis, optimal gear parameters for minimizing total power loss were identified, providing valuable insights for gear design and optimization. The findings underscore the importance of reducing sliding friction and optimizing lubricant properties to enhance helical gear efficiency.