Design and Finite Element Analysis of Planetary Wheel Reducer for Electric Vehicle

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:

  1. Single-stage 9:1 reduction ratio in compact package
  2. Maximum stress 25% below material limits under peak torque
  3. Planet gear load sharing efficiency > 98%
  4. 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.

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