In the context of the global “dual carbon” strategy, the development of high-efficiency, low-cost traction motors for electric cars has become a critical engineering challenge. As an electrical engineering graduate, I have focused my research on the design and analysis of a permanent magnet synchronous motor (PMSM) that employs a composite magnet rotor structure. The motivation for this work stems from the urgent need to reduce reliance on expensive rare-earth permanent magnets while maintaining high performance in electric cars. Traditional single-rare-earth PMSM drives often suffer from high material cost, difficult flux regulation at high speed, and risk of irreversible demagnetization under extreme thermal or overload conditions. To address these drawbacks, I propose a hybrid magnet topology combining NdFeB and ferrite magnets in an interior permanent magnet rotor. In this paper, I present a complete design procedure, electromagnetic performance evaluation, thermal management study, and control system verification for a 75 kW, 6000 r/min motor intended for an electric car.
1. Design Requirements and Operating Characteristics
An electric car traction motor must satisfy demanding driving cycles covering frequent start, acceleration, hill climbing, and high-speed cruising. The design targets adopted in this research are based on a commercial electric car platform. Table 1 lists the main vehicle specifications, and Table 2 gives the motor performance indicators.
| Parameter | Symbol | Value |
|---|---|---|
| Curb mass | mc | 1870 kg |
| Frontal area | A | 2.85 m² |
| Maximum speed | Vm | 120 km/h |
| Rated speed | Vn | 60 km/h |
| Transmission efficiency | ηt | 0.92 |
| Rolling resistance coefficient | f | 0.012 |
| Tire rolling radius | r | 0.2413 m |
| Final drive ratio | i0 | 11.5 |
| Gear ratio | ig | 8.3 |
| Aerodynamic drag coefficient | CD | 0.3 |
| Rotational inertia factor | δ | 1.1 |
| Insulation class | — | H |
| Parameter | Symbol | Value |
|---|---|---|
| Rated power | PN | 75 kW |
| Rated speed | nN | 6000 r/min |
| Maximum speed | nmax | 16000 r/min |
| Rated torque | TN | 120 N·m |
| Peak torque | Tmax | 310 N·m |
| Efficiency | η | ≥95% |
| Rated phase voltage | UN | 230 V |
| Efficiency ≥90% area ratio | — | ≥84.9% |
| 0–100 km/h acceleration time | t0–100 | ≤7 s |
The tractive force demand of an electric car at constant speed can be expressed as:
$$F_t = \frac{1}{\eta_t}\left( m_c g f + \frac{C_D A V^2}{21.15} \right)$$
For maximum acceleration performance, the peak power requirement is calculated from:
$$P_{\max} = \frac{1}{\eta_t t_a}\left( \frac{1}{2} m_c \delta \frac{V_a^2}{3.6^2} + \frac{2}{3} m_c g f V_a + \frac{C_D A V_a^3}{21.15 \times 2.5} \right)$$
The motor’s rated torque can be derived from the rated power and speed:
$$T_N = 9550 \frac{P_N}{n_N}=9550\times\frac{75}{6000}=119.4\ \text{N·m}$$
The base speed, constant-power speed ratio, and overload factors are key to meeting the electric car acceleration and hill-climb requirements. In my design, the torque overload factor is 2.5, the power overload factor is 2.33, and the constant-power speed ratio is 2.67.
2. Electromagnetic Dimensioning and Structural Selection
I began the electromagnetic design using the classical sizing equation:
$$D_{i1}^2 L_{ef} = \frac{6.1 \times 10^3}{\alpha_p’ K_{Nm} K_{dp} A B_\delta} \times \frac{P’}{n_N}$$
For a traction motor with oil-spray cooling, I selected an electric loading A = 505 A/cm and an air-gap flux density Bδ = 1.0 T. The resulting key dimensions are listed in Table 3.
| Geometric parameter | Value (mm) |
|---|---|
| Stator outer diameter | 220 |
| Stator inner diameter | 148 |
| Rotor outer diameter | 146.3 |
| Rotor inner diameter | 48 |
| Active stack length | 95 |
| Air-gap length | 0.85 |
To achieve a reasonable compromise between torque capability and high-speed operation for an electric car, I compared several pole-slot combinations: 8P72S, 6P72S, and 8P48S. The winding factor and harmonic suppression results are presented in Table 4.
| q | y/τ | Kd | Kq | Kdq | Suppressed harmonics |
|---|---|---|---|---|---|
| 2/5 | 5/6 | 0.9659 | 0.9659 | 0.933 | 5, 7 |
| 4/5 | 5/6 | 0.9577 | 0.9659 | 0.925 | 5, 7 |
| 1 | 2/3 | 1 | 0.866 | 0.866 | 3 |
| 8/5 | 5/6 | 0.9556 | 0.9659 | 0.9231 | 5, 7 |
| 2 | 5/6 | 0.9659 | 0.9659 | 0.933 | 5, 7 |
| 3 | 8/9 | 0.9598 | 0.9848 | 0.9452 | 9 |
After evaluating the rated torque performance under the same inverter current for each pole-slot combination, I selected the 8-pole/72-slot configuration because it offers a balanced combination of high winding factor, low torque ripple, and low cogging torque for high-speed electric car applications.
The stator winding uses a double-layer, distributed, three-phase Y-connected configuration with two parallel branches. The stator slots are open slots with the dimensions listed in Table 5.
| Parameter | Value (mm) |
|---|---|
| Hs0 | 0.6 |
| Hs1 | 1.5 |
| Hs2 | 20.2 |
| Bs1 | 2.95 |
| Bs2 | 2.95 |
3. Rotor Topology Comparison
In designing the rotor for an electric car PMSM, the interior configuration is preferred due to its superior reluctance torque contribution and flux-weakening capability. I constructed three motor models that share the same stator, housing, magnet total volume, and material grade (initially NdFeB only), but have different rotor magnet layouts: double-V, V+1, and U+1. Schematic descriptions of these configurations are listed in Table 6.
| Label | Description | Magnet arrangement |
|---|---|---|
| Type A | Double-V | Two symmetric V-shaped layers on each pole |
| Type B | V+1 | One V-shaped pair plus one central bar magnet |
| Type C | U+1 | One U-shaped pair plus one central bar magnet |
Using finite-element analysis (FEA), I evaluated the rated torque at 120 A and the peak torque at 320 A for all three structures. The results are summarized in Table 7.
| Quantity | Double-V | V+1 | U+1 |
|---|---|---|---|
| Rated torque @120 A (N·m) | 120.47 | 115.39 | 104.96 |
| Peak torque @320 A (N·m) | 319.86 | 312.49 | 304.34 |
The double-V structure exhibits the highest torque capability because of better flux concentration and a more sinusoidal air-gap field distribution. Therefore, I selected the double-V topology for the subsequent composite magnet design.
4. Composite Magnet Arrangement
To reduce the consumption of rare-earth NdFeB material, I proposed replacing part of the magnet layers with low-cost ferrite or AlNiCo magnets. In the double-V topology, there are four magnet segments per pole labelled 1–4. I systematically investigated five possible positions for introducing non-rare-earth material, as shown in Table 8.
| Case | Non-rare-earth layer | Rare-earth layer |
|---|---|---|
| ① | 1,2 | 3,4 |
| ② | 1,3 | 2,4 |
| ③ | 2,3 | 1,4 |
| ④ | 1,4 | 2,3 |
| ⑤ | 2,3 (with spacing) | 1,4 |
For the initial study, AlNiCo was used as the non-rare-earth candidate. At the rated current of 120 A, I recorded the rated torque for each case:
| Case | Rated torque (N·m) | Deviation from target |
|---|---|---|
| ① | 89.18 | −25.7% |
| ② | 89.50 | −25.4% |
| ③ | 120.43 | +0.36% |
| ④ | 83.24 | −30.6% |
| ⑤ | 96.52 | −19.6% |
Only case ③ produced a rated torque that matches the 120 N·m target. In this arrangement, the two inner magnet pockets located near the rotor q-axis are made of non-rare-earth material, while the two outer pockets that form the V apex retain NdFeB. This configuration realizes the same level of active flux while using significantly less rare-earth content.
Next, I compared two non-rare-earth materials, AlNiCo and ferrite, when placed in the selected positions. The electromagnetic performance and material cost are presented in Table 10.
| Quantity | AlNiCo + NdFeB | Ferrite + NdFeB |
|---|---|---|
| Rated torque @60 A (N·m) | 51.3 | 50.4 |
| Peak torque @320 A (N·m) | 305.68 | 301.2 |
| No-load line-to-line back-EMF (V) | 642.1 | 585.79 |
| Total magnet cost (RMB) | 532.92 | 463.95 |
The ferrite-based composite motor has slightly lower torque, but the much lower no-load back-EMF offers better flux-weakening behavior at high speeds. Ferrite is also more economical than AlNiCo. Through the above trade-off study, I selected the final composite magnet motor with ferrite + NdFeB in the double-V configuration. Compared with a pure NdFeB motor, the rare-earth usage is reduced by about 40%, and the overall magnet cost is reduced by 16.6% for the electric car traction system.
5. Electromagnetic Performance Analysis by Finite Element Method
5.1. No-Load Field Distribution and Air-Gap Flux Density
The no-load magnetic flux density distribution was analyzed to verify that the iron-core flux densities are within reasonable limits. The stator teeth peak at 1.78 T, the stator yoke at 1.47 T, and the flux barriers at 1.93 T. The no-load air-gap flux density waveform is shown with an amplitude of 0.983 T, which is within the recommended range of 0.8–1.3 T for interior PM machines used in electric cars.
5.2. Inductances and Flux Linkages
The self-inductance of one phase, as well as the d-axis and q-axis inductances, were evaluated under no-load conditions. The phase self-inductance peak is 0.84 mH, while the q-axis inductance is 1.17 mH, close to the theoretical 1.5 times the self-inductance peak. The permanent-magnet flux linkage can be obtained from the back-EMF:
$$\psi_d = \frac{E_p}{\omega_e}$$
At the rated speed of 6000 r/min, with a pole-pair number of 4:
$$\omega_e = \frac{2\pi n_N p}{60} = \frac{2\pi\times 6000\times4}{60}=2513.3\ \text{rad/s}$$
The calculated d-axis flux linkage is 0.115 Wb, which agrees well with the simulated value. The q-axis flux linkage is almost zero, which confirms correct axis alignment.
5.3. Three-Phase Back-EMF
The no-load back-EMF waveforms of the three phases were simulated at 6000 r/min. The fundamental amplitude is 219.6 V, which is lower than the rated phase voltage of 230 V, leaving enough margin for field-weakening operation of the electric car at maximum speed. A harmonic analysis shows that the 3rd and 5th harmonics are the dominant components. Although the waveform is not perfectly sinusoidal, its distortion is acceptable.
5.4. Cogging Torque
To ensure low vibration and noise in the electric car, I analyzed the cogging torque. The peak-to-peak cogging torque is 2.04 N·m, which is only 1.7% of the rated torque. This is significantly below the commonly used 3% limit, demonstrating that the selected slot/pole combination and rotor shaping are effective.
5.5. Rated Load Torque and Torque Ripple
At the rated operating point with a phase current amplitude of 120 A and a current angle of 40°, the electromagnetic output torque is shown in Figure 3. The average torque is 119.18 N·m, matching the rated requirement. The torque ripple at rated load is about 6.1%, which is acceptable for an electric car motor but can be further reduced through control optimization.
5.6. Demagnetization Withstand Capability
Because ferrite has a lower coercivity than NdFeB, demagnetization may occur under high demagnetizing ampere-turns. Using the finite-element method, I applied rectangular demagnetizing currents of 60 A, 120 A, 180 A, 240 A, 300 A, 360 A, 420 A, and 480 A to the ferrite magnet portions. The onset of demagnetization occurs at approximately 270 A (2.25 times rated current), while severe demagnetization appears only above 390 A (3.25 times rated current). This provides excellent overload ability for the electric car during emergency acceleration and regenerative braking.
5.7. Efficiency Map
Figure 4 presents the efficiency map over the entire torque-speed operating envelope. The peak efficiency is 95%, and the region with efficiency higher than 90% occupies more than 60% of the operating area. Such a distribution is well-suited for the typical driving cycles of an electric car, where most operating points lie in the medium-speed, medium-torque region.
6. Loss Analysis and Thermal Management
6.1. Loss Calculation at Rated Condition
For the 75 kW, 6000 r/min electric car motor, the copper loss is the dominant component. The copper loss is calculated as:
$$P_{Cu}=3I^2R$$
With a stator resistance of 0.02376 Ω and a phase current of 120 A:
$$P_{Cu}=3\times120^2\times0.02376=941.6\ \text{W}$$
Using Bertotti’s separation model, the iron loss is expressed as:
$$P_{Fe}=P_h+P_c+P_e$$
where:
$$P_h = k_h f B_m^2,\quad P_c = k_c f^2 B_m^2,\quad P_e = k_e f^{1.5} B_m^{1.5}$$
The calculated iron loss at rated frequency is 133.4 W, and the eddy-current loss in the magnets is 6.73 W. The material properties used for the electromagnetic and thermal analysis are listed in Table 11.
| Part | Material | Specific heat (J·kg⁻¹·K⁻¹) | Density (kg·m⁻³) | Thermal conductivity (W·m⁻¹·K⁻¹) |
|---|---|---|---|---|
| Housing / oil baffle | Aluminum alloy | 871 | 2719 | 202.4 |
| Stator / rotor core | JFE_35JN210 | 460 | 7600 | 30 |
| Winding | Copper | 385 | 8933 | 401 |
| Magnet (NdFeB) | N42EH | 460 | 7500 | 7.6 |
| Magnet (Ferrite) | Y40 | 837 | 4900 | 2 |
6.2. Natural Air Cooling Analysis
First, I performed a thermal analysis with no external cooling system. The resulting peak temperatures are listed in Table 12.
| Component | Winding | Magnets | Stator core |
|---|---|---|---|
| Peak temperature (°C) | 184.1 | 173.9 | 177.7 |
These temperatures exceed the H-class insulation limit and cause irreversible demagnetization risk for the ferrite magnets. Therefore, an oil cooling system becomes mandatory.
6.3. Cooling Structure Design
I evaluated two oil jacket configurations: U-type and C-type channels. At a coolant flow rate of 0.5 L/min, the temperatures of the motor components were simulated. The results are summarized in Table 13.
| Cooling structure | Winding (°C) | Magnets (°C) | Stator core (°C) |
|---|---|---|---|
| U-type | 137.8 | 113.5 | 123.2 |
| C-type | 146.6 | 133.5 | 134.8 |
The U-type structure provides superior thermal performance because the coolant enters and exits at the same side, creating a more uniform axial flow and better heat extraction along the active parts of the electric car motor.
6.4. Effect of Coolant Flow Rate
The cooling performance is strongly influenced by the oil flow rate. I simulated the flow rates of 0.5 L/min, 1.0 L/min, and 1.5 L/min. The resulting peak component temperatures are listed in Table 14.
| Flow rate | Winding (°C) | Magnets (°C) | Stator core (°C) |
|---|---|---|---|
| 0.5 L/min | 137.8 | 113.5 | 123.2 |
| 1.0 L/min | 124.4 | 100 | 109.8 |
| 1.5 L/min | 119.5 | 95.3 | 105 |
An increase in flow rate from 0.5 to 1.0 L/min reduces the winding temperature by 13.4 °C, while a further increase from 1.0 to 1.5 L/min only lowers it by another 4.9 °C. Therefore, I selected the U-type oil jacket with a coolant flow rate of 1.0 L/min as the final cooling system for the designed motor. At this flow rate, the peak magnet temperature is exactly 100 °C, which is safe for the ferrite–NdFeB combination in the electric car application.
7. Control System Design for Full-Speed-Range Operation
7.1. Mathematical Model of the PMSM
For the interior PMSM in an electric car, the d-q axis voltage equations are:
$$u_d = R i_d + L_d \frac{di_d}{dt} – \omega_e L_q i_q$$
$$u_q = R i_q + L_q \frac{di_q}{dt} + \omega_e L_d i_d + \omega_e \psi_f$$
The electromagnetic torque equation is given by:
$$T_e = \frac{3}{2} p \left[ \psi_f i_q + (L_d – L_q) i_d i_q \right]$$
Because the interior PMSM has saliency, Ld < Lq, and the reluctance torque can be exploited by injecting a negative d-axis current. The parameters of the two motor versions I used in control comparisons are given in Table 15.
| Parameter | Single NdFeB PMSM | Composite magnet PMSM |
|---|---|---|
| Phase resistance (Ω) | 0.02376 | 0.02376 |
| d-axis inductance (mH) | 0.5979 | 0.5389 |
| q-axis inductance (mH) | 1.2172 | 1.209 |
| PM flux linkage (Wb) | 0.0988 | 0.0938 |
7.2. Maximum Torque per Ampere Control
For the constant-torque region below the rated speed, I used the Maximum Torque per Ampere (MTPA) strategy. The MTPA problem is formulated as:
$$\min_{i_d,i_q} i_s^2 = i_d^2 + i_q^2$$
$$\text{subject to}\quad T_e = \frac{3}{2} p \left[ \psi_f i_q + (L_d – L_q) i_d i_q \right]$$
Using the Lagrange multiplier method, the optimal d-axis current is obtained from:
$$i_d = \frac{\psi_f – \sqrt{\psi_f^2 + 4(L_d – L_q)^2 i_q^2}}{2(L_d – L_q)}$$
For a given torque command, the q-axis current can then be determined from the torque equation.
7.3. Flux Weakening Control
At speeds above the rated value, the inverter voltage reaches its limit. The voltage and current constraints are:
$$u_d^2 + u_q^2 \le U_{\max}^2$$
$$i_d^2 + i_q^2 \le I_{\max}^2$$
Under steady-state and high-speed conditions, the resistive voltage drop can be neglected; then the voltage limit becomes an ellipse in the d-q plane:
$$\left(L_q i_q\right)^2 + \left(L_d i_d + \psi_f\right)^2 \le \left(\frac{U_{\max}}{\omega_e}\right)^2$$
In the flux-weakening region, a negative d-axis current is used to reduce the air-gap flux, thereby allowing operation beyond the base speed. The control system automatically switches MTPA to flux-weakening based on the voltage error. I designed a hybrid MTPA-FW controller for the electric car motor, and the overall control block diagram is shown in Figure 5.
7.4. PI Controller Tuning
I used pole-zero cancellation for the current loops. The current-loop gains are:
$$K_{pc} = \omega_c L_{dq}, \quad K_{ic} = \omega_c R$$
where ωc is the current-loop bandwidth in rad/s. The speed-loop gains were derived using the symmetric optimum method:
$$K_{sp} = \frac{J \omega_s}{K_T}, \quad K_{si} = \frac{\omega_s}{u} K_{sp}$$
Here, u is the phase-margin factor and KT is the torque constant. The specific gains used in the simulations were tuned for both the single-rare-earth and the composite-magnet motor.
8. Dynamic Response and Acceleration Performance Analysis
8.1. Zero-to-Hundred Acceleration Time
The acceleration capability of the electric car is directly related to the traction force of the motor. The tractive force at the wheels is:
$$F_t = \frac{T_e i_g i_0 \eta_t}{r}$$
The acceleration time is:
$$t = \frac{\delta m_c}{3.6} \int_{V_1}^{V_2} \frac{1}{F_t – F_f – F_w} \, dV$$
Using the vehicle parameters in Table 1 and the motor torque-speed envelope, I calculated the 0–100 km/h times for both motor versions. The results are presented in Table 16.
| Motor type | Acceleration time (s) |
|---|---|
| Single NdFeB PMSM | 5.77 |
| Composite magnet PMSM | 5.98 |
Both motors satisfy the design target of below 7 s. The composite magnet motor is only 0.21 s slower, while offering a significant reduction in magnet cost and improved flux-adjustment capability.
8.2. Speed Regulation Performance below the Base Speed
Using the MTPA controller, I simulated speed transients from 0 to 2000 r/min and then to 4000 r/min, followed by a regenerative braking command to 1000 r/min. The dynamic performance indices are compared in Table 17.
| Speed range (r/min) | Motor type | Time (s) | Overshoot |
|---|---|---|---|
| 0–2000 | Single NdFeB | 3.65 | 2.38% |
| 0–2000 | Composite | 2.85 | 1.49% |
| 2000–4000 | Single NdFeB | 9.82 | 1.19% |
| 2000–4000 | Composite | 8.75 | 0.80% |
| 4000–1000 | Single NdFeB | 13.85 | 6.43% |
| 4000–1000 | Composite | 11.96 | 3.20% |
At every speed step, the composite magnet motor reaches the target speed faster and with a smaller overshoot. This improvement is partly because the lower permanent-magnet flux linkage weakens the inductive coupling, which reduces the settling time of the current loop. Better dynamic behavior directly affects the drivability of the electric car.
8.3. Speed Regulation Performance in the Flux-Weakening Region
For high-speed operation, the MTPA-FW controller was tested by stepping the speed from 0 to 8000 r/min, then from 8000 to 16000 r/min, followed by deceleration to 8000 r/min and finally to 0 r/min. The results are summarized in Table 18.
| Speed range (r/min) | Motor type | Time (s) | Overshoot |
|---|---|---|---|
| 0–8000 | Single NdFeB | 6.85 | 1.23% |
| 0–8000 | Composite | 5.92 | 0.64% |
| 8000–16000 | Single NdFeB | 20.35 | 0.53% |
| 8000–16000 | Composite | 19.17 | 0.04% |
| 16000–8000 | Single NdFeB | 27.75 | 2.16% |
| 16000–8000 | Composite | 26.64 | 1.08% |
| 8000–0 | Single NdFeB | 33.68 | 2.41% |
| 8000–0 | Composite | 32.28 | 1.21% |
The composite magnet motor consistently exhibits shorter transition times and lower overshoots in the deep flux-weakening region. This occurs because the ferrite magnet has a relatively lower coercivity, and the magnetic flux state can be more easily changed by the d-axis current. Since the permanent flux linkage of the composite motor is 0.0938 Wb compared to 0.0988 Wb for the NdFeB motor, a smaller negative d-axis current is required to satisfy the voltage limit at any speed. This reduces the current-margin loss and improves the dynamic torque response. Consequently, the composite magnet PMSM provides superior speed-adjustment quality and energy-efficiency potential for the electric car.
9. Conclusion and Outlook
In this research, I have carried out a systematic design and performance analysis of a 75 kW, 6000 r/min composite magnet permanent magnet synchronous motor for use in electric cars. The key conclusions of my work are summarized as follows:
(1) Among the double-V, V+1, and U+1 rotor configurations with identical stator and magnet volume, the double-V structure provides the highest rated and peak torque. By replacing the inner magnet layers with ferrite magnets, the motor retains nearly the same rated torque (119.18 N·m) while reducing the magnet cost by 16.6% and dramatically lowering the consumption of rare-earth NdFeB materials.
(2) The composite magnet motor was then analyzed by finite-element analysis under no-load and rated-load conditions. The air-gap flux density amplitude is 0.983 T, the no-load back-EMF is 219.6 V, and the cogging torque peak-to-peak value is only 2.04 N·m. The demagnetization study shows that the ferrite magnets can tolerate demagnetizing currents up to 270 A without severe demagnetization, giving an overload margin of more than 2.25 times the rated current. The efficiency map shows a peak efficiency of 95%, with 60% of the operating area having efficiency above 90%. All of the electromagnetic characteristics meet the requirements of a modern electric car.
(3) In terms of thermal management, I analyzed a U-type oil-cooling jacket. With a coolant flow rate of 1.0 L/min, the hottest component (the winding) reaches 124.4 °C, while the permanent magnets saturate at 100 °C—both values are within safe operating limits for the selected materials.
(4) A full-speed-range vector control system combining Maximum Torque per Ampere and flux-weakening control was designed and applied to both the single NdFeB PMSM and the composite magnet PMSM. The composite magnet motor achieves a 0–100 km/h acceleration time of 5.98 s, slightly less than 5.77 s for the NdFeB motor, but it shows faster dynamic response and lower overshoot at every speed transient, including deep flux-weakening operation up to 16000 r/min. This demonstrates that the composite magnet architecture is a promising solution for high-performance, low-cost electric car traction motors.
Future work will involve building and testing a prototype of the composite magnet motor to validate the simulation results, as well as optimizing the torque ripple at rated load by using advanced current waveform injection or more elaborate rotor shaping. Additionally, to further justify the advantages for electric cars, I plan to couple the motor model with a full vehicle dynamics simulator and evaluate driving-cycle efficiency, thermal cycling, and long-term reliability. The continued development of reduced-rare-earth permanent magnet machines will facilitate the broader adoption of electric cars in a cost-effective and environmentally sustainable manner.