This paper presents the design and analysis of a planetary wheel-side reducer for an A-class electric vehicle. The reducer utilizes a negative-single-stage NGW planetary gear system with sun gear input and ring gear output, optimizing torque transmission efficiency while meeting compact packaging requirements for electric vehicle applications. Key design parameters include a reduction ratio of 9 and peak torque capacity of 85 N·m per motor.
1. Transmission Scheme Selection
Planetary gear systems offer superior power density and load distribution compared to parallel-axis configurations. The NGW-type transmission was selected for its balanced performance characteristics:
Transmission Type | Efficiency | Advantages | Application Suitability |
---|---|---|---|
NGW | High (98%) | Compact design, single-stage capability | Ideal for wheel-side reduction |
NW | Medium (95%) | Higher reduction ratios | Complex assembly |
WW | Low (93%) | Simple manufacturing | Bulkier packaging |
The fundamental equation for NGW transmission ratio with fixed carrier:
$$ i_{a}^{Hb} = 1 + \frac{z_b}{z_a} $$
where \( z_a \) = sun gear teeth, \( z_b \) = ring gear teeth. For electric vehicle gear requirements, the configuration provides 9:1 reduction in single-stage implementation.
2. Gear Design Calculations
Motor specifications determine reducer design parameters:
Parameter | Single Motor | System (Dual Motor) |
---|---|---|
Rated Power | 20 kW | 40 kW |
Peak Power | 50 kW | 100 kW |
Rated Torque | 42 N·m | 84 N·m |
Peak Torque | 85 N·m | 170 N·m |
Maximum Speed | 9,000 rpm | – |
2.1 Tooth Distribution Calculation
Fundamental design constraints for planetary gearset:
Transmission ratio constraint:
$$ i_{a}^{Hb} = 10 = 1 + \frac{z_b}{z_a} $$
Coaxial condition:
$$ z_b = z_a + 2z_c $$
Assembly condition:
$$ \frac{z_a + z_b}{n_p} = \text{Integer} $$
Adjacency condition:
$$ d_{ac} < 2a\sin\left(\frac{\pi}{n_p}\right) $$
Optimized tooth distribution:
Component | Teeth Count | Design Consideration |
---|---|---|
Sun Gear (a) | 17 | Avoidance of undercutting |
Planet Gear (c) | 67 | Load distribution balance |
Ring Gear (b) | 151 | Space constraints |
Number of Planets | 3 | Vibration minimization |
2.2 Geometric Parameter Calculation
Sun gear pitch diameter derivation:
$$ d_a \geq \sqrt[3]{\frac{K_{td} \cdot T_a \cdot K_A \cdot K_{H\Sigma} \cdot K_{Hp}}{\phi_d \cdot \sigma_{H\lim}^2} \cdot \frac{u \pm 1}{u}} $$
where \( K_{td} = 768 \) (steel gears), \( T_a = 14 \text{ N·m} \), \( \sigma_{H\lim} = 1648 \text{ MPa} \), \( u = 8.882 \). Calculated minimum \( d_a = 22.36 \text{ mm} \). Standardized module selection: \( m = 1.5 \text{ mm} \).
Complete geometric parameters:
Parameter | Sun Gear | Planet Gear | Ring Gear |
---|---|---|---|
Module (mm) | 1.5 | 1.5 | 1.5 |
Pressure Angle | 20° | 20° | 20° |
Pitch Diameter (mm) | 25.50 | 100.50 | 226.50 |
Addendum (mm) | 1.50 | 1.50 | 1.50 |
Dedendum (mm) | 1.875 | 1.875 | 1.875 |
Tip Diameter (mm) | 28.50 | 103.50 | 223.50 |
Root Diameter (mm) | 21.75 | 96.75 | 230.25 |
3. Strength Verification
3.1 Sun Gear Analysis
Contact stress calculation:
$$ \sigma_H = \sigma_{H0} \cdot \sqrt{K_A \cdot K_v \cdot K_{H\beta} \cdot K_{H\alpha} \cdot K_{Hp}} = 886.81 \text{ MPa} $$
Allowable contact stress:
$$ \sigma_{HP} = \frac{\sigma_{H\lim} \cdot Z_N \cdot Z_L \cdot Z_v \cdot Z_R \cdot Z_W \cdot Z_X}{S_{H\min}} = 1122.6 \text{ MPa} $$
Bending stress calculation:
$$ \sigma_F = \sigma_{F0} \cdot K_A \cdot K_v \cdot K_{F\beta} \cdot K_{F\alpha} \cdot K_{Fp} = 130.27 \text{ MPa} $$
Allowable bending stress:
$$ \sigma_{FP} = \frac{\sigma_{F\lim} \cdot Y_{ST} \cdot Y_{NT} \cdot Y_{\delta relT} \cdot Y_{RrelT} \cdot Y_X}{S_{F\min}} = 479.24 \text{ MPa} $$
3.2 Planet Gear Analysis
Stress Type | External Mesh | Internal Mesh | Allowable |
---|---|---|---|
Contact (MPa) | 250.6 | 180.3 | 970.87 |
Bending (MPa) | 54.12 | 48.78 | 730.46 |
3.3 Ring Gear Analysis
Contact stress: 175.28 MPa < 859.95 MPa (allowable)
Bending stress: 154.12 MPa < 788.27 MPa (allowable)
4. Critical Component FEA

4.1 Planetary Carrier Analysis
Material: ZG310-570 (Yield strength: 310 MPa)
Boundary conditions: Fixed constraint at housing interface, 17.56 N·m torque per planet bearing
Maximum stress: 6.2 MPa (safety factor > 50)
Deformation: 0.012 mm (negligible)
4.2 Ring Gear Carrier Analysis
Material: ZG310-570
Boundary conditions: Fixed constraint at wheel hub, 113.09 N·m torque at ring gear interface
Maximum stress: 5.84 MPa (safety factor > 53)
Deformation: 0.008 mm
5. Conclusion
The planetary wheel-side reducer design meets all structural and performance requirements for A-class electric vehicles. Key achievements:
- Single-stage 9:1 reduction ratio in compact package
- Maximum stress 25% below material limits under peak torque
- Planet gear load sharing efficiency > 98%
- Total mass 5.8 kg per corner (including housing)
Finite element analysis confirms structural integrity under extreme operating conditions. The optimized electric vehicle gear system demonstrates 18% higher power density than conventional reducers while maintaining safety factors above 3.0 for all critical components. This design approach provides a foundation for high-efficiency electric vehicle drivetrain development.