In recent years, the rapid advancement of battery EV cars has underscored the critical need for efficient and reliable electric propulsion systems. Among various motor types, the Permanent Magnet Synchronous Motor (PMSM) stands out due to its high efficiency, superior power density, and broad speed range, making it a preferred choice for battery EV car applications. However, optimizing the structural design of PMSMs to enhance performance metrics such as torque ripple, core losses, and average torque remains a complex, multi-objective challenge. Traditional optimization approaches often involve extensive computational simulations, which are time-consuming and inefficient. To address this, we propose a robust optimization strategy based on the Taguchi method, which systematically evaluates the impact of key structural parameters on motor performance with minimal experimental runs. This study focuses on optimizing the stator slot geometry of an interior PMSM for battery EV cars, aiming to reduce torque ripple and iron losses while maintaining required output torque. Through finite element analysis (FEA) and orthogonal experiments, we identify optimal parameter combinations, demonstrating significant improvements in motor performance. The integration of this optimization approach can contribute to the development of more efficient and quieter battery EV cars, aligning with global sustainability goals.
The widespread adoption of battery EV cars is pivotal in reducing greenhouse gas emissions and dependence on fossil fuels. PMSMs play a central role in this transition, as their compact size and high power density enable longer driving ranges and better vehicle dynamics. However, inherent issues like torque ripple can lead to vibrations and noise, affecting the comfort and durability of battery EV cars. Similarly, core losses contribute to energy wastage and thermal management challenges. Therefore, structural optimization of PMSMs is essential to maximize the overall efficiency and reliability of battery EV cars. In this study, we leverage the Taguchi method, a statistical technique renowned for its efficiency in parameter design, to optimize key stator slot dimensions. By combining FEA simulations with orthogonal arrays, we systematically analyze the effects of these parameters on performance indicators, providing a streamlined pathway for enhancing PMSM designs in battery EV cars.
To establish a baseline for optimization, we first developed a detailed electromagnetic model of a 20 kW PMSM using finite element analysis. This motor is designed for battery EV car applications, with a rated speed of 1500 r/min and a torque output suitable for urban and highway driving. The key structural parameters are summarized in Table 1, which outlines the geometric and material specifications used in the simulation. This model serves as the foundation for all subsequent analyses, allowing us to evaluate the initial performance and identify areas for improvement.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Rated Power (kW) | 20 | Stator Inner Diameter (mm) | 210 |
| Rated Torque (N·m) | 135 | Permanent Magnet Thickness (mm) | 1 |
| Rated Speed (r/min) | 1500 | Air Gap (mm) | 1 |
| Number of Slots | 36 | Stator Core Length (mm) | 235 |
| Number of Poles | 4 | Rotor Core Length (mm) | 235 |
| Stator Core Diameter (mm) | 327 | Tooth Width (mm) | 9.98 |
The FEA model was constructed using ANSYS Maxwell, a powerful tool for electromagnetic simulation. We performed both no-load and load analyses to assess the motor’s characteristics. Under no-load conditions, the back electromotive force (EMF) was examined, as it directly influences the torque generation and efficiency in battery EV cars. The back EMF waveform, shown in Figure 2, exhibits a sinusoidal shape with a peak value of approximately 180 V, slightly below the rated phase voltage of 220 V. This indicates good alignment with design expectations and suggests potential for torque optimization. The formula for back EMF is given by:
$$E = k_e \cdot \omega \cdot \phi$$
where \(E\) is the back EMF, \(k_e\) is a constant depending on winding turns, \(\omega\) is the angular speed, and \(\phi\) is the flux per pole. For battery EV cars, minimizing harmonics in the back EMF is crucial to reduce losses and improve smoothness.
Next, we analyzed the cogging torque, which arises from the interaction between permanent magnets and stator slots. High cogging torque can cause vibrations and noise in battery EV cars, impacting driver comfort. The simulation results, depicted in Figure 3, reveal a peak cogging torque of 4.26 N·m, which is acceptable given the rated torque of 135 N·m. However, further reduction is desirable to enhance the performance of battery EV cars. The cogging torque \(T_{cog}\) can be expressed as:
$$T_{cog} = \frac{\partial W}{\partial \theta}$$
where \(W\) is the magnetic co-energy and \(\theta\) is the rotor position. Optimizing stator slot geometry can mitigate this effect.
The air-gap magnetic flux density was also evaluated, as it affects torque ripple and core losses in PMSMs for battery EV cars. Figures 4 and 5 show the flux density waveform and its Fourier analysis under no-load conditions. The fundamental amplitude is 0.53 T, with a third harmonic of 0.26 T. Reducing harmonic content is vital to minimize torque ripple and iron losses, thereby improving the efficiency of battery EV cars. The flux density \(B\) is related to the motor’s electromagnetic torque \(T_e\) by:
$$T_e = \frac{3}{2} p \left( \lambda_d i_q – \lambda_q i_d \right)$$
where \(p\) is the number of pole pairs, \(\lambda_d\) and \(\lambda_q\) are d- and q-axis flux linkages, and \(i_d\), \(i_q\) are the currents. Harmonic distortions in \(B\) can lead to fluctuations in \(T_e\), affecting the drivetrain of battery EV cars.
Under load conditions, the magnetic flux density distribution was examined to ensure no saturation points, as shown in Figure 6. A uniform distribution with minimal leakage flux was observed, confirming the robustness of the initial design for battery EV car applications. However, to further enhance performance, we proceeded with structural optimization using the Taguchi method.
The Taguchi method is a powerful statistical approach for robust design, enabling efficient optimization with fewer experiments. In this study, we applied it to optimize four key stator slot parameters: stator slot shoulder depth \(H_{s1}\), stator slot length \(H_{s2}\), slot opening width \(B_{s0}\), and stator slot fillet radius \(R_s\). These parameters influence magnetic circuit characteristics and, consequently, the performance of PMSMs in battery EV cars. We defined three levels for each parameter, centered around the initial design values, as detailed in Table 2. An orthogonal array \(L_9(3^4)\) was employed to arrange the experiments, requiring only 9 simulations instead of 81 full factorial runs. This efficiency is particularly beneficial for battery EV car development, where rapid prototyping is essential.
| Factor Level | \(H_{s1}\) (mm) | \(H_{s2}\) (mm) | \(B_{s0}\) (mm) | \(R_s\) (mm) |
|---|---|---|---|---|
| Level 1 | 0.7 | 25 | 3 | 0.6 |
| Level 2 | 1.1 | 30 | 3.8 | 1 |
| Level 3 | 1.5 | 35 | 4.6 | 1.4 |
The orthogonal experimental layout is presented in Table 3, where numbers 1, 2, and 3 correspond to the factor levels. For each combination, we conducted FEA simulations to compute three performance metrics: average torque \(T_{avg}\), iron loss \(P_{Fe}\), and torque ripple coefficient \(K_{mb}\). These metrics are critical for battery EV cars, as they directly impact driving smoothness, energy efficiency, and thermal management. The torque ripple coefficient is defined as:
$$K_{mb} = \frac{T_{max} – T_{min}}{T_{avg}} \times 100\%$$
where \(T_{max}\) and \(T_{min}\) are the maximum and minimum instantaneous torques, respectively. Lower \(K_{mb}\) values indicate smoother operation, which is desirable for battery EV cars to reduce vibrations.
| Experiment No. | \(H_{s1}\) | \(H_{s2}\) | \(B_{s0}\) | \(R_s\) |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 2 | 2 |
| 3 | 1 | 3 | 3 | 3 |
| 4 | 2 | 1 | 2 | 3 |
| 5 | 2 | 2 | 3 | 1 |
| 6 | 2 | 3 | 1 | 2 |
| 7 | 3 | 1 | 3 | 2 |
| 8 | 3 | 2 | 1 | 3 |
| 9 | 3 | 3 | 2 | 1 |
The simulation results for each experiment are summarized in Table 4. The initial design (before optimization) yielded \(T_{avg} = 123.84 \, \text{N·m}\), \(P_{Fe} = 580.52 \, \text{W}\), and \(K_{mb} = 1.93\%\). By comparing these with the orthogonal results, we can identify trends and optimal configurations for battery EV car PMSMs. For instance, Experiment 1 shows a higher average torque and lower torque ripple, indicating potential for improvement.
| Experiment No. | \(T_{avg}\) (N·m) | \(P_{Fe}\) (W) | \(K_{mb}\) (%) |
|---|---|---|---|
| 1 | 133.39 | 502.23 | 1.09 |
| 2 | 123.05 | 568.76 | 1.94 |
| 3 | 123.99 | 640.05 | 1.95 |
| 4 | 122.46 | 516.21 | 1.94 |
| 5 | 123.55 | 569.82 | 1.90 |
| 6 | 124.47 | 659.08 | 1.89 |
| 7 | 123.63 | 517.33 | 1.93 |
| 8 | 135.31 | 600.30 | 1.09 |
| 9 | 126.01 | 663.47 | 1.90 |
To analyze the influence of each parameter, we computed the mean effects for each factor level, as shown in Table 5. For example, the mean average torque for \(H_{s1}\) at level 1 is calculated as:
$$\overline{T}_{avg}(H_{s1} = 1) = \frac{T_{avg}^{(1)} + T_{avg}^{(2)} + T_{avg}^{(3)}}{3}$$
where \(T_{avg}^{(i)}\) are the average torque values from experiments 1, 2, and 3. This analysis helps identify which factor levels minimize iron loss or torque ripple, crucial for enhancing the performance of battery EV cars.
| Factor | Level | \(T_{avg}\) (N·m) | \(P_{Fe}\) (W) | \(K_{mb}\) (%) |
|---|---|---|---|---|
| \(H_{s1}\) | 1 | 126.81 | 570.35 | 1.66 |
| 2 | 123.49 | 581.70 | 1.91 | |
| 3 | 128.32 | 593.70 | 1.64 | |
| \(H_{s2}\) | 1 | 126.49 | 511.92 | 1.65 |
| 2 | 127.30 | 579.63 | 1.64 | |
| 3 | 124.82 | 654.20 | 1.91 | |
| \(B_{s0}\) | 1 | 131.06 | 587.20 | 1.36 |
| 2 | 123.84 | 582.81 | 1.93 | |
| 3 | 123.72 | 575.73 | 1.93 | |
| \(R_s\) | 1 | 127.65 | 578.51 | 1.63 |
| 2 | 123.72 | 581.72 | 1.92 | |
| 3 | 127.25 | 585.52 | 1.66 |
Further, we performed analysis of variance (ANOVA) to quantify the contribution of each factor to the performance metrics. The variance \(S_f\) for a factor \(f\) is computed as:
$$S_f = \sum_{i=1}^{n} (y_i – \bar{y})^2$$
where \(y_i\) is the result at level \(i\), \(\bar{y}\) is the overall mean, and \(n\) is the number of levels. The results, presented in Table 6, indicate that \(B_{s0}\) has the largest influence on average torque (58.78% contribution) and torque ripple (60.22%), while \(H_{s2}\) dominates iron loss (96.53%). This insight guides the selection of optimal parameters for battery EV car PMSMs, ensuring balanced performance improvements.
| Factor | Variance for \(T_{avg}\) | Contribution to \(T_{avg}\) (%) | Variance for \(P_{Fe}\) | Contribution to \(P_{Fe}\) (%) | Variance for \(K_{mb}\) | Contribution to \(K_{mb}\) (%) |
|---|---|---|---|---|---|---|
| \(H_{s1}\) | 4.07 | 20.31 | 90.89 | 2.60 | 0.0151 | 12.59 |
| \(H_{s2}\) | 1.07 | 5.34 | 3376.55 | 96.53 | 0.0156 | 13.01 |
| \(B_{s0}\) | 11.78 | 58.78 | 22.33 | 0.64 | 0.0722 | 60.22 |
| \(R_s\) | 3.12 | 15.57 | 8.21 | 0.23 | 0.0170 | 14.18 |
| Total | 20.04 | 100 | 3497.98 | 100 | 0.1199 | 100 |
Based on the mean effects and ANOVA, we determined the optimal parameter combination for battery EV car PMSMs: \(H_{s1} = 0.7 \, \text{mm}\) (level 1), \(H_{s2} = 25 \, \text{mm}\) (level 1), \(B_{s0} = 3 \, \text{mm}\) (level 1), and \(R_s = 0.6 \, \text{mm}\) (level 1). This configuration prioritizes low torque ripple and iron loss while maintaining adequate average torque, which is essential for the smooth and efficient operation of battery EV cars. The optimized parameters are summarized in Table 7.
| Optimization Parameter | \(H_{s1}\) (mm) | \(H_{s2}\) (mm) | \(B_{s0}\) (mm) | \(R_s\) (mm) |
|---|---|---|---|---|
| Optimal Value | 0.7 | 25 | 3 | 0.6 |
We then conducted a final FEA simulation with this optimal set and compared the results with the initial design, as shown in Table 8. The optimized PMSM exhibits significant improvements: average torque increased to 133.39 N·m, iron loss reduced by 13.5% to 502.23 W, and torque ripple decreased by 43.5% to 1.09%. These enhancements are highly beneficial for battery EV cars, as they lead to better energy efficiency, reduced thermal stress, and smoother acceleration, ultimately contributing to longer battery life and improved driving experience.
| Performance Metric | Before Optimization | After Optimization |
|---|---|---|
| \(T_{avg}\) (N·m) | 123.84 | 133.39 |
| \(P_{Fe}\) (W) | 580.52 | 502.23 |
| \(K_{mb}\) (%) | 1.93 | 1.09 |
In conclusion, this study demonstrates the effectiveness of the Taguchi method for structural optimization of PMSMs in battery EV cars. By integrating finite element analysis with orthogonal experiments, we systematically optimized stator slot parameters to achieve substantial reductions in torque ripple and iron loss. The proposed approach requires fewer simulations compared to traditional methods, making it a practical tool for accelerating the development of high-performance motors for battery EV cars. Future work could expand the optimization to include additional parameters like permanent magnet geometry or employ three-dimensional FEA to account for end effects. Moreover, combining the Taguchi method with other optimization algorithms, such as genetic algorithms or response surface methodology, may yield even better results. As the demand for battery EV cars continues to grow, such advancements in motor design will play a crucial role in enhancing vehicle efficiency, reliability, and sustainability.
The implications of this research extend beyond individual motor components; by improving PMSM performance, we contribute to the broader adoption of battery EV cars, which are essential for reducing carbon emissions and promoting clean transportation. The Taguchi-based optimization framework presented here can be adapted to other motor types or engineering systems, offering a versatile solution for robust design in the automotive industry. We encourage further exploration of these techniques to unlock new potentials in electric vehicle technology, ensuring that battery EV cars remain at the forefront of the global shift towards sustainable mobility.