In the rapidly evolving field of electric vehicles (EVs), the drive motor is a critical component, directly influencing performance, efficiency, and cost. Permanent magnet synchronous motors (PMSMs) are widely adopted in China’s EV industry due to their high power density and efficiency. However, the reliance on rare-earth materials like neodymium in PMSM designs poses economic and supply chain challenges, as prices for these materials continue to rise. To address this, I propose a novel rotor topology for a less-rare-earth PMSM that reduces rare-earth usage while maintaining torque performance. Additionally, I introduce a method to construct asymmetric magnetic poles to mitigate torque ripple, a common issue in PMSM operation. This analysis focuses on optimizing torque characteristics for electric cars, leveraging finite element modeling, equivalent magnetic circuit analysis, and multi-objective optimization techniques.
The electromagnetic torque of a PMSM is derived from the interaction between permanent magnet fields and stator windings. The torque expression is given by:
$$T_e = T_{pm} + T_{re} = \frac{3}{2} p \left[ \psi_f i_q + (L_d – L_q) i_d i_q \right]$$
where \(T_e\) is the electromagnetic torque, \(T_{pm}\) is the permanent magnet torque, \(T_{re}\) is the reluctance torque, \(p\) is the number of pole pairs, \(\psi_f\) is the permanent magnet flux linkage, \(L_d\) and \(L_q\) are the d-axis and q-axis inductances, and \(i_d\) and \(i_q\) are the d-axis and q-axis current components. For electric cars, maximizing torque while minimizing ripple is essential for smooth operation and energy efficiency. In my study, I developed finite element models for three PMSM configurations: a less-rare-earth design, a V-type rare-earth design, and a rare-earth design with a magnetic isolation bridge. These models were used to analyze electromagnetic characteristics and the impact of inductance differences on torque.
The proposed less-rare-earth PMSM incorporates ferrite magnets alongside neodymium-based rare-earth magnets, reducing overall rare-earth content. The rotor topology places ferrite magnets along the d-axis centerline to enhance reluctance torque. To evaluate performance, I compared key parameters such as air-gap flux density and back EMF. The air-gap flux density waveforms and their harmonic spectra were analyzed, with the total harmonic distortion (THD) calculated as:
$$THD = \frac{\sqrt{\sum_{n=2}^{\infty} B_n^2}}{B_1} \times 100\%$$
where \(B_n\) is the amplitude of the n-th harmonic and \(B_1\) is the fundamental amplitude. Results showed that the less-rare-earth design maintained a THD of 22.35%, comparable to the V-type design (22.28%), while the design with a magnetic isolation bridge had a higher THD of 23.03%. This indicates that the proposed structure minimizes waveform distortion, crucial for stable torque output in China EV applications.
Further, the d-axis and q-axis inductances were examined to understand their influence on torque. The inductances are expressed as:
$$L_d = N^2 G_d$$
$$L_q = N^2 G_q$$
where \(N\) is the number of turns, and \(G_d\) and \(G_q\) are the d-axis and q-axis permeances. The less-rare-earth PMSM exhibited a larger difference between \(L_d\) and \(L_q\), enhancing the reluctance torque component. By adjusting the stator current advance angle \(\gamma\), I optimized the torque output. The relationship between average output torque and \(\gamma\) was plotted, revealing a peak torque at \(\gamma = 23^\circ\) for all designs, with the less-rare-earth PMSM achieving the highest torque of 13.54 N·m, a 7.24% improvement over baseline designs. This demonstrates the effectiveness of reducing rare-earth content without compromising performance for electric cars.
To address torque ripple, which can cause vibrations and reduce efficiency in EVs, I developed an equivalent magnetic circuit model for the less-rare-earth PMSM. Torque ripple arises from harmonics in the stator and rotor magnetomotive forces (MMFs). The torque ripple coefficient \(K_{mb}\) is defined as:
$$K_{mb} = \frac{T_{\text{max}} – T_{\text{min}}}{(T_{\text{max}} + T_{\text{min}})/2} \times 100\%$$
where \(T_{\text{max}}\) and \(T_{\text{min}}\) are the maximum and minimum torque values. By constructing asymmetric magnetic poles through varying the angles of the V-shaped neodymium magnets, I altered the air-gap flux distribution. The asymmetric poles reduce harmonic interactions, thereby suppressing torque ripple. The MMFs for the rotor can be described as:
$$F_r = \sum_k F_{rk} \cos(k p \eta – k \omega_s t)$$
where \(F_{rk}\) is the k-th harmonic coefficient of the rotor MMF, \(\eta\) is the mechanical angle, and \(\omega_s\) is the angular frequency. The torque ripple \(T_{\text{rip}}\) due to harmonic interactions is given by:
$$T_{\text{rip}} = \frac{\pi r_g L p}{l} \sum_{h=2n+1} \sum_{k=6n+1} \int_0^{2\pi} \sin[(h \pm k) p \eta \pm \omega_s t \pm \gamma] \, d\eta$$
where \(r_g\) is the air-gap radius, \(L\) is the stack length, and \(l\) is the effective air-gap length. This model shows that adjusting the pole angles shifts the harmonic content, reducing ripple.
For optimization, I employed a multi-objective approach with the asymmetric pole angles (\(\alpha_1, \alpha_2, \alpha_3, \alpha_4\)) as variables, targeting maximum average torque and minimum torque ripple. Using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), I evaluated Pareto-optimal solutions. The TOPSIS method involves normalizing decision matrices and calculating relative closeness to ideal solutions. For a matrix \(X\) with elements \(x_{ij}\), the normalized value \(z_{ij}\) is:
$$z_{ij} = \frac{x_{ij}}{\sqrt{\sum_{i=1}^n x_{ij}^2}}$$
The positive and negative ideal solutions are determined, and the relative closeness \(C_i\) is computed as:
$$C_i = \frac{D_i^-}{D_i^+ + D_i^-}$$
where \(D_i^+\) and \(D_i^-\) are the distances to the positive and negative ideal solutions, respectively. After sensitivity analysis, the optimal asymmetric angles were found to be \(\alpha_1 = \alpha_3 = 12^\circ\) and \(\alpha_2 = \alpha_4 = 5^\circ\), resulting in an average torque of 14.52 N·m and a torque ripple of 7.54%. This represents a 35.72% reduction in ripple compared to symmetric designs, highlighting the benefits for electric car applications where smooth torque delivery is critical.
To validate the simulations, I fabricated a prototype and conducted experiments, including no-load back EMF and torque characteristic tests. The experimental setup involved a dynamometer and data acquisition system, typical in China EV motor testing. The back EMF at 3000 rpm showed a fundamental amplitude of 54.06 V, closely matching the simulated value of 53.01 V, with a relative error of 1.94%. Torque tests confirmed an output of 14.18 N·m at rated speed, with a ripple of 7.88%, aligning with simulations within 2.34% error. These results verify the reliability of the finite element models and the effectiveness of the proposed optimization for less-rare-earth PMSMs in electric cars.
In conclusion, the less-rare-earth PMSM design not only reduces dependency on costly rare-earth materials but also enhances torque performance through optimized reluctance torque and asymmetric magnetic poles. This approach supports the sustainable development of China’s EV industry by lowering costs while maintaining high efficiency. Future work could explore thermal effects and broader operating ranges to further improve applicability in diverse electric car scenarios.
| Parameter | Less-Rare-Earth PMSM | V-Type Rare-Earth PMSM | Rare-Earth PMSM with Isolation Bridge |
|---|---|---|---|
| Rare-Earth Usage | Reduced | High | High |
| Average Torque (N·m) | 14.52 | 13.49 | 13.27 |
| Torque Ripple (%) | 7.54 | 19.32 | 23.73 |
| d-axis Inductance (mH) | 1.97 | 1.99 | 1.92 |
| q-axis Inductance (mH) | 4.32 | 4.32 | 4.32 |
| THD of Air-Gap Flux (%) | 22.35 | 22.28 | 23.03 |
The table above summarizes the key performance metrics, underscoring the advantages of the less-rare-earth design for electric cars. By integrating these innovations, China EV manufacturers can achieve cost savings and improved motor reliability, contributing to the global shift toward sustainable transportation.