1. Introduction
The electric motor serves as a critical component in electric vehicle powertrains, directly influencing vehicle performance, efficiency, and driving range. Permanent Magnet Synchronous Motors (PMSMs) are widely adopted in electric vehicles due to their high power density and efficiency. However, conventional PMSMs predominantly use neodymium-iron-boron (NdFeB) magnets, which contain expensive rare-earth elements. Recent price volatility and supply-chain vulnerabilities of rare-earth materials have escalated manufacturing costs, necessitating research into cost-effective alternatives. Ferrite magnets offer a low-cost, rare-earth-free solution but exhibit inferior magnetic properties (remanence: 0.4 T vs. 1.2 T for NdFeB). To balance performance and cost, less-rare-earth PMSMs – combining NdFeB and ferrite magnets – emerge as a promising topology for electric vehicle propulsion.
A key challenge in PMSM design for electric vehicles is torque ripple, which causes vibration, acoustic noise, and drivetrain stress. Traditional torque ripple suppression methods, such as stator auxiliary slots or uneven air gaps, often reduce average torque or increase magnetic saturation. This work proposes a novel rotor topology using asymmetric magnetic poles to simultaneously enhance electromagnetic torque and suppress torque ripple while minimizing rare-earth content.
2. Motor Topology and Electromagnetic Analysis
2.1 Proposed Rotor Structure
We propose a less-rare-earth PMSM topology where ferrite magnets partially replace NdFeB magnets. The ferrite magnets are positioned along the *d*-axis centerline, exploiting the motor’s saliency to boost reluctance torque. A comparative analysis is conducted against two benchmark topologies:
- V-type rare-earth PMSM: Uses only NdFeB magnets arranged in a V-shape.
- Rare-earth PMSM with flux barrier: Uses NdFeB magnets and a non-magnetic barrier.
The motor specifications are provided in Table 1.
Table 1: Motor Parameters for Electric Vehicle Application
| Parameter | Value |
|---|---|
| Rated Voltage | 72 V |
| Rated Power | 5 kW |
| Rated Speed | 3000 rpm |
| Stator Outer Diameter | 200 mm |
| Stator Inner Diameter | 141 mm |
| Rotor Outer Diameter | 140 mm |
| Rotor Inner Diameter | 106 mm |
2.2 Electromagnetic Torque Formulation
The electromagnetic torque TeTe in a PMSM comprises permanent magnet torque (TpmTpm) and reluctance torque (TreTre):Te=Tpm+Tre=32P[ψfiq+idiq(Ld−Lq)](6)Te=Tpm+Tre=23P[ψfiq+idiq(Ld−Lq)](6)
where:
- PP: Pole pairs
- ψfψf: Permanent magnet flux linkage
- id,iqid,iq: *d*-axis and *q*-axis currents
- Ld,LqLd,Lq: *d*-axis and *q*-axis inductances
The permanent magnet flux linkage ψfψf relates to the no-load back-EMF (emem):ψf=emωrψf=ωrem
where ωrωr is the electrical angular velocity.
2.3 Comparative Electromagnetic Analysis
Finite Element Analysis (FEA) was performed on all three topologies at 20°C. Key results are summarized below:
*Table 2: Air-Gap Flux Density and Back-EMF Characteristics*
| Topology | Fundamental BgBg (T) | THD (%) | Fundamental EmEm (V) | THD (%) |
|---|---|---|---|---|
| Less-Rare-Earth PMSM | 0.909 | 22.35 | 53.01 | 8.67 |
| V-Type Rare-Earth PMSM | 0.917 | 22.28 | 54.32 | 8.13 |
| Flux-Barrier PMSM | 0.892 | 23.03 | 51.87 | 9.75 |
The *d*-axis and *q*-axis inductances significantly impact reluctance torque. FEA-derived inductance values are:
*Table 3: d-q Axis Inductances and Differences*
| Topology | LdLd (mH) | LqLq (mH) | ΔL=Lq−LdΔL=Lq−Ld (mH) |
|---|---|---|---|
| Less-Rare-Earth PMSM | 1.9686 | 4.3193 | 2.3507 |
| V-Type Rare-Earth PMSM | 1.9919 | 4.3152 | 2.3233 |
| Flux-Barrier PMSM | 1.9249 | 4.3157 | 2.3908 |
The optimal stator current advance angle for maximizing TeTe is 23° electrical. At this angle:
- Less-rare-earth PMSM achieves the highest peak torque (13.54 N·m).
- Flux-barrier PMSM shows the highest torque increase (12.84%), but lower absolute torque.
3. Torque Ripple Suppression via Asymmetric Poles
3.1 Mechanism of Torque Ripple Reduction
Torque ripple (TripTrip) is quantified by the ripple coefficient:Krip=Tmax−Tmin(Tmax+Tmin)/2×100%(18)Krip=(Tmax+Tmin)/2Tmax−Tmin×100%(18)
Initial torque ripple coefficients were:
- Less-rare-earth PMSM: 26.00%
- V-type PMSM: 19.32%
- Flux-barrier PMSM: 23.73%
To suppress torque ripple, we propose an asymmetric pole design (Fig. 13) parameterized by angles α1,α2,α3,α4α1,α2,α3,α4. The equivalent magnetic circuit model (Fig. 15) illustrates two main flux paths:
- Path 1: NdFeB magnets → Air gap
- Path 2: Ferrite magnets → Air gap
Kirchhoff’s laws yield air-gap flux densities:Φg1=2Fy−Fs12(Rg1+Ry),Φg2=2Fn1−Fs12(Rg2+Rnd)(20)Φg1=2(Rg1+Ry)2Fy−Fs1,Φg2=2(Rg2+Rnd)2Fn1−Fs1(20)
where FyFy and Fn1Fn1 are magnetomotive forces, and Rg1,Rg2Rg1,Rg2 are air-gap reluctances. Asymmetry alters the spatial distribution of Φg1Φg1 and Φg2Φg2, reducing harmonic interactions that cause torque pulsations.
4. Multi-Objective Optimization Using TOPSIS
4.1 Optimization Framework
We optimize asymmetric pole angles to maximize average torque (TavgTavg) and minimize torque ripple (KripKrip). The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) algorithm is applied as follows:
- Initial Matrix: X=[X1,X2,…,Xm]X=[X1,X2,…,Xm] for mm candidate designs.
- Data Normalization:
zij=xij∗/∑i=1n(xij∗)2(30)zij=xij∗/i=1∑n(xij∗)2(30)
- Ideal Solutions:
- Positive ideal: Z+=[max(zi1),max(zi2),… ]Z+=[max(zi1),max(zi2),…]
- Negative ideal: Z−=[min(zi1),min(zi2),… ]Z−=[min(zi1),min(zi2),…]
- Distance Calculation:
Di+=∑j=1m(zij−zj+)2,Di−=∑j=1m(zij−zj−)2(32,33)Di+=j=1∑m(zij−zj+)2,Di−=j=1∑m(zij−zj−)2(32,33)
- Relative Closeness:
Ci=Di−Di++Di−(0<Ci<1)(33)Ci=Di++Di−Di−(0<Ci<1)(33)
4.2 Optimization Results
Table 4: TOPSIS Results for Asymmetric Pole Designs
| Configuration | Design | TavgTavg (N·m) | KripKrip (%) | CiCi | Rank |
|---|---|---|---|---|---|
| Single-Pole Asymmetry | 1 | 14.52 | 7.54 | 0.929 | 1 |
| 2 | 15.12 | 9.40 | 0.747 | 2 | |
| N-S Pole Asymmetry | 1 | 11.89 | 10.85 | 0.567 | 5 |
| 2 | 13.15 | 11.01 | 0.577 | 4 |
The optimal design uses single-pole asymmetry (α1=α3=12∘α1=α3=12∘, α2=α4=5∘α2=α4=5∘), achieving:
- Average Torque: 14.52 N·m (+7.24% vs. symmetric)
- Torque Ripple: 7.54% (−35.72% vs. symmetric)
5. Experimental Validation
A prototype (Fig. 25) was built and tested to validate the FEA and optimization results.
5.1 No-Load Back-EMF Test
At 3000 rpm:
- Simulated EmEm: 53.01 V
- Measured EmEm: 54.06 V
- Error: 1.94% (attributed to material property variations).
5.2 Torque Performance Test
Table 5: Torque Characteristics at 3000 rpm
| Parameter | Simulation | Experiment | Error |
|---|---|---|---|
| Average Torque (N·m) | 14.52 | 14.18 | 2.34% |
| Torque Ripple (%) | 7.54 | 7.88 | 3.40% |
Minor discrepancies arise from idealized FEA assumptions (e.g., zero core losses, constant temperature). The results confirm the feasibility of the proposed motor for electric vehicle traction systems.
6. Conclusion
This work presents a comprehensive optimization of a less-rare-earth PMSM for electric vehicles, achieving:
- Rare-Earth Reduction: Ferrite magnets replace 14.3% of NdFeB by volume.
- Torque Enhancement: Reluctance torque utilization increases average torque by 7.24%.
- Torque Ripple Suppression: Asymmetric poles reduce torque ripple by 35.72%.
- Validated Design: Prototype tests confirm FEA accuracy (<3.5% error).
The optimized motor meets the dual demands of cost efficiency and high performance, critical for mass adoption of electric vehicles. Future work will focus on high-speed operation and thermal management.
Appendix: Key Symbols
| Symbol | Description |
|---|---|
| TeTe | Electromagnetic torque |
| TpmTpm | Permanent magnet torque |
| TreTre | Reluctance torque |
| Ld,LqLd,Lq | d/q-axis inductances |
| ψfψf | PM flux linkage |
| KripKrip | Torque ripple coefficient |
| αiαi | Asymmetric pole angles |