In the context of global efforts toward carbon neutrality and sustainable transportation, the development of pure electric vehicles has become a focal point of automotive innovation. Among various propulsion systems, dual-motor configurations coupled with planetary gear mechanisms offer superior performance in terms of dynamic response, torque distribution, and redundancy. However, under high-speed and heavy-load conditions, the friction-induced heat generation at gear meshing interfaces in these systems can lead to scuffing failures, significantly impacting the reliability and efficiency of the electric vehicle car. This study addresses this critical issue by establishing a transient multi-physics finite element analysis model based on thermal-structural coupling theory. The primary objective is to investigate the thermal effects on gear teeth, particularly in the planetary gear system of a dual-motor pure electric vehicle power coupling mechanism, and to provide insights for preventing gear failure. The integration of numerical modeling and finite element simulation allows for a comprehensive analysis of temperature distributions, thermal stresses, and deformations, which are essential for optimizing the design and operation of electric vehicle car transmissions.
The planetary gear system, comprising a sun gear, planet gears, and a ring gear, is a core component in the dual-motor electric vehicle car coupling mechanism. Its compact design and high power density make it ideal for transmitting torque efficiently, but the inherent sliding friction during meshing generates substantial heat, especially at high rotational speeds. This heat accumulation can cause localized temperature spikes, leading to lubricant breakdown and surface damage, ultimately compromising the performance of the electric vehicle car. To mitigate these risks, we developed a mathematical model for the temperature field based on thermal elastohydrodynamic lubrication theory, coupled with finite element analysis using Ansys Workbench. By examining the transient thermal behavior and structural responses, we aim to enhance the durability and efficiency of power coupling systems in dual-motor pure electric vehicles.
The friction heat flux density at the gear meshing interface is a key factor influencing the temperature rise. According to Hertzian contact theory, the contact pressure at any meshing point C can be expressed as:
$$P_c = \frac{\pi}{4} \sqrt{\frac{F_{nC}}{\pi \left( \frac{1 – \mu_1}{E_1} + \frac{1 – \mu_2}{E_2} \right) L \rho_C}}$$
where \( F_{nC} \) is the normal force at point C, \( \mu_1 \) and \( \mu_2 \) are the Poisson’s ratios of the driving and driven gears, \( E_1 \) and \( E_2 \) are their elastic moduli, \( L \) is the contact line length, and \( \rho_C \) is the comprehensive curvature radius. The contact half-width \( a \) is given by:
$$a = \sqrt{\frac{4F}{\pi b} \cdot \frac{1 – \nu_1}{E_1} + \frac{1 – \nu_2}{E_2} \cdot \rho_C}$$
For the dual-motor electric vehicle car system, the gear geometric parameters are summarized in Table 1. These parameters are critical for calculating the thermal and mechanical loads during operation.
| Name | Number of Teeth | Module (mm) | Pressure Angle (°) | Tooth Width (mm) |
|---|---|---|---|---|
| Sun Gear | 15 | 2 | 20 | 15 |
| Planet Gear | 30 | 2 | 20 | 15 |
| Ring Gear | 75 | 2 | 20 | 15 |
The material selected for the gears is 304 steel, commonly used in automotive applications for its strength and thermal properties. The thermal and structural parameters are listed in Table 2, which are essential for the finite element analysis of the electric vehicle car coupling mechanism.
| Thermal and Structural Parameter | Value |
|---|---|
| Young’s Modulus (GPa) | 193 |
| Poisson’s Ratio | 0.3 |
| Density (kg/m³) | 8000 |
| Specific Heat Capacity (J·kg⁻¹·K⁻¹) | 500 |
| Thermal Conductivity (W·m⁻¹·K⁻¹) | 16.3 |
| Thermal Expansion Coefficient (K⁻¹) | 1.73 × 10⁻⁵ |
The relative sliding velocity at any meshing point C is calculated as:
$$V_{gC} = V_{1C} – V_{2C} = \frac{2\pi n_1 g_{yC} (1 + r_1 / r_2)}{60 \times 1000}$$
where \( n_1 \) and \( n_2 \) are the rotational speeds of the driving and driven gears, and \( g_{yC} \) is the position on the line of action. The friction coefficient \( f_C \) is derived from empirical relations:
$$f_C = 0.002 \left( \frac{F_{tC}}{0.001b} \right)^{0.2} \cdot \left( \frac{2(\rho_{1C} + \rho_{2C})}{0.001\cos \alpha (V_{1C} + V_{2C}) \rho_{1C} \rho_{2C}} \right)^{0.2} \eta^{-0.05X_R}$$
Here, \( F_{tC} \) is the tangential load, \( b \) is the tooth width, \( \eta \) is the dynamic viscosity of the lubricant, and \( X_R \) is the surface roughness factor. The friction heat flux density \( Q_C \) is then:
$$Q_C = \gamma f_C P_C V_{gC} \times 10^6$$
with \( \gamma = 0.95 \) representing the fraction of frictional energy converted to heat. For the planetary gear system in the dual-motor electric vehicle car, the heat distribution between gears is governed by the heat partition coefficient \( \beta \):
$$\beta = \frac{\sqrt{\lambda_1 \rho_1 c_1 V_{1C}}}{\sqrt{\lambda_1 \rho_1 c_1 V_{1C}} + \sqrt{\lambda_2 \rho_2 c_2 V_{2C}}}$$
where \( \lambda \), \( \rho \), and \( c \) denote thermal conductivity, density, and specific heat capacity, respectively. The average heat flux densities over a meshing cycle are:
$$\bar{Q}_{1C} = \frac{t_{1C}}{T_1} Q_{1C}, \quad \bar{Q}_{2C} = \frac{t_{2C}}{T_2} Q_{2C}$$
with \( t_{1C} = 2a / (v_{1C} \cdot 1000) \) and \( T_1 = 60 / n_1 \). These equations form the basis for the temperature field analysis in the electric vehicle car gear system.
Convective heat transfer plays a significant role in dissipating the generated heat. For the gear end faces, the convective heat transfer coefficient \( h_d(t) \) is given by:
$$h_d(t) = \frac{\lambda_0 \pi n r h}{30 v_0} \left( \frac{\rho_0 v_0 c_0}{\lambda_0} \right)^{0.66} \left( \frac{\pi n}{30 v_0 \sin \alpha} \right)^{0.5}$$
where \( \lambda_0 \) is the thermal conductivity of the lubricant, \( n \) is the gear speed, \( r \) is the pitch radius, \( h \) is the working tooth height, \( \rho_0 \) is the lubricant density, \( c_0 \) is its specific heat, and \( v_0 \) is the kinematic viscosity. For the meshing surfaces, the coefficient \( h_m(t) \) is:
$$h_m(t) = \frac{0.0863 \lambda_0 (\pi n r h / 30 v_0)^{0.618} (\rho_0 v_0 c_0 / \lambda_0)^{0.35}}{d}$$
with \( d \) as the pitch diameter. Using lubricant properties (density 910 kg/m³, specific heat 1870 J·kg⁻¹·K⁻¹, thermal conductivity 0.3 W·m⁻¹·K⁻¹), we computed the convective coefficients for different operating conditions, as shown in Table 3. These values are crucial for setting boundary conditions in the finite element model of the electric vehicle car coupling mechanism.
| Name | Speed (r/min) | End Face Convective Coefficient (W·m⁻²·K⁻¹) | Meshing Face Convective Coefficient (W·m⁻²·K⁻¹) |
|---|---|---|---|
| Sun Gear | 2000 | 277 | 850 |
| 3000 | 509 | 1275 | |
| 4000 | 679 | 1700 | |
| Planet Gear | 2000 | 389 | 648 |
| 3000 | 715 | 972 | |
| 4000 | 953 | 1296 | |
| Ring Gear | 2000 | 518 | 458 |
| 3000 | 953 | 687 | |
| 4000 | 1264 | 916 |
The steady-state temperature field within a gear tooth is governed by the three-dimensional heat conduction equation for a homogeneous, isotropic material with no internal heat source:
$$\lambda \left( \frac{\partial^2 t}{\partial x^2} + \frac{\partial^2 t}{\partial y^2} + \frac{\partial^2 t}{\partial z^2} \right) = 0$$
Boundary conditions include Robin conditions for non-meshing surfaces, Neumann conditions for meshing surfaces with heat flux, and combined conditions for convective heat transfer. For example, on the meshing surface:
$$-\lambda \frac{\partial t}{\partial n} = h_m(t) (t_w – t_f) – Q_w$$
where \( Q_w \) is the average heat flux density. Solving these equations numerically using MATLAB, we obtained the temperature distribution on the sun gear tooth meshing surface, as illustrated in the results section. This approach ensures accurate thermal analysis for the dual-motor electric vehicle car system.
For the finite element analysis, we imported a simplified planetary gear model into Ansys Workbench, focusing on one planet row to reduce computational cost while maintaining accuracy. The gears were meshed with tetrahedral elements for the teeth and free mesh for the end faces, resulting in 341,336 elements. The mesh quality was verified through the Jacobian ratio, which averaged 0.965, indicating good element shape. The thermal loads, including friction heat flux and convective coefficients, were applied with an ambient temperature of 50°C. The steady-state temperature field is shown in Figure 1, revealing a maximum temperature of 54.778°C near the sun gear root, consistent with numerical predictions of 55.899°C (error less than 2%). This validates the model for the electric vehicle car application.
Subsequently, the temperature field results were mapped to the structural analysis as a boundary condition to evaluate thermal stresses and deformations. In the static structural simulation, the planet gears were fixed, while torques of 100 N·m on the sun gear and 500 N·m on the ring gear were applied to simulate operational loads. Constraints included cylindrical supports for the sun and ring gears (restricting axial and radial movements) and fixed supports for the planet gears. The equivalent stress distribution under thermal-structural coupling is depicted in Figure 2, with a maximum stress of 328.25 MPa occurring at the sun gear root. This stress level is within the yield strength of 304 steel, but it highlights the critical region for potential scuffing in the electric vehicle car gear system.
The deformation analysis, shown in Figure 3, indicates a maximum displacement of 0.015949 mm on the planet gear teeth, which is negligible for normal operation. However, to assess the impact of thermal effects, we compared the stress results with and without temperature field consideration. Under identical torque and constraints but excluding thermal loads, the maximum stress reduced to 305.44 MPa (Figure 4), a difference of 22.81 MPa. This demonstrates that friction-induced heating significantly increases stress concentrations, emphasizing the importance of thermal-structural coupling in the design of dual-motor electric vehicle car transmissions.
We further investigated the influence of rotational speed on the temperature field under a constant torque of 100 N·m. As summarized in Table 4, higher speeds lead to increased friction heat flux and convective coefficients, resulting in elevated gear temperatures. For instance, at 1000 r/min, the maximum temperature is 54.778°C, while at 4000 r/min, it rises to 61.195°C. The temperature distribution pattern remains similar, with hotspots consistently at the sun gear root due to its fewer teeth and higher meshing frequency. These findings are crucial for optimizing cooling strategies in electric vehicle car powertrains.
| Speed (r/min) | Maximum Temperature (°C) | Location of Maximum Temperature |
|---|---|---|
| 1000 | 54.778 | Sun Gear Root |
| 2000 | 57.432 | Sun Gear Root |
| 3000 | 59.876 | Sun Gear Root |
| 4000 | 61.195 | Sun Gear Root |
The mechanical torque transmission in the electric vehicle car system is analyzed using the torque formula:
$$M_a = 9549 \frac{P}{n}$$
where \( P \) is power and \( n \) is speed. The gear ratio is determined by:
$$i = \frac{n_1}{n_2} = \frac{z_2}{z_1}$$
allowing calculation of planet and ring gear speeds. Thermal stresses induced by temperature rises affect gear tooth deflection, with the yield stress given by:
$$\sigma_f = K \cdot \sigma_c$$
where \( K \) is the yield modulus and \( \sigma_c \) is the ultimate stress. Integrating these mechanical principles with thermal analysis provides a holistic view of system performance.
In conclusion, this study establishes a robust thermal-structural coupling finite element model for the planetary gear system in a dual-motor pure electric vehicle power coupling mechanism. The analysis reveals that the sun gear root is the most vulnerable to scuffing due to higher friction heat generation and stress concentrations. The inclusion of thermal effects increases the maximum stress by 22.81 MPa compared to purely mechanical analysis, underscoring the necessity of coupled field simulations. As rotational speed increases, gear temperatures rise proportionally, but the overall distribution pattern remains unchanged. These insights can guide the design of more durable and efficient transmissions for electric vehicle car applications, contributing to the advancement of sustainable transportation. Future work may explore advanced lubrication methods or material enhancements to further mitigate thermal issues in high-performance electric vehicle car systems.