With the rapid advancement of electric vehicle (EV) technologies in China, the demand for high-performance drive motors has surged. As a key component, the motor core significantly influences energy efficiency and power density. Traditional core lamination methods, such as riveting and welding, often lead to increased iron losses and reduced magnetic performance. In contrast, adhesive bonding techniques offer superior insulation and tighter lamination, reducing eddy current losses and enhancing overall motor efficiency. However, the production efficiency of adhesive motor core processing equipment remains a bottleneck, primarily due to suboptimal drive system selection and parameter settings. In this study, we address these challenges by developing a comprehensive multi-objective optimization approach based on grey theory, aiming to improve the accuracy of drive device selection and parameter configuration for rotary lamination mechanisms in China EV applications.
The rotary lamination mechanism is integral to the production of adhesive motor cores, combining functions such as blanking, rotating, and stacking electrical steel sheets. In typical progressive die setups, this mechanism operates in conjunction with glue application systems to achieve continuous production. However, inefficiencies in drive system coordination often limit the overall equipment effectiveness. We focus on optimizing the drive system—specifically servo motors—by considering factors like transmission mechanisms, load inertia matching, and motion profiles. Our methodology ensures that the selected parameters minimize production costs while maximizing throughput, which is critical for scaling up China EV component manufacturing.
To determine the appropriate transmission mechanism, we evaluated various coupling methods, including couplings, gears, and synchronous belts. Synchronous belt drives were selected for their absence of backlash, ability to cover larger distances, and reduced impact during operation. The transmission efficiency $\eta_1$ for synchronous belts is typically 0.98. In cases where additional torque reduction or inertia matching is required, gear reducers may be incorporated, with an efficiency $\eta_2$ of 0.98. The overall transmission ratio $i$ and mechanical efficiency $\eta$ are given by:
$$ i = i_1 i_2 $$
$$ \eta = \eta_1 \eta_2 $$
where $i_1$ is the synchronous belt ratio (range 1–3) and $i_2$ is the gear reducer ratio (common values: 3, 4, 5, 7, 8, 10). For initial calculations, we assume no reducer ($i_2 = 1$), but the model adapts if performance criteria are not met.
Load parameters are derived from operational requirements, such as the production rate $m$ (in strokes per minute, spm), rotation angle $\alpha$, and time allocation. The rotation cycle $t_0$ and theoretical rotation time $t’$ are calculated as:
$$ t_0 = \frac{60}{m} $$
$$ t’ = \frac{60}{m} \cdot \frac{1}{f} $$
where $f$ is a time coefficient (range 1–4, typically 4). The critical speeds for triangular and rectangular motion profiles are:
$$ n_{\text{max}} = \frac{60 \alpha}{\pi t’} $$
$$ n_{\text{min}} = \frac{30 \alpha}{\pi t’} $$
These translate to servo motor speed requirements:
$$ n_{2\text{max}} = n_{\text{max}} i_{\text{max}} $$
$$ n_{2\text{min}} = n_{\text{min}} i_{\text{min}} $$
with $i_{\text{min}} = 1$ and $i_{\text{max}} = 3$. The maximum acceleration time $t’_{\text{max}}$ is half the rotation time for trapezoidal motion, which is preferred for its balance between speed and mechanical stress.
Inertia matching is crucial for dynamic performance. The load inertia $J_\omega$ reflected to the motor shaft includes contributions from the rotary mechanism $J_1$, pulley $J_2$ (negligible), and reducer $J_r$ (if used). The equivalent load inertia is:
$$ J_\omega = \frac{J_1}{\eta i^2} + J_2 + J_r $$
To ensure optimal power transfer and controllability, the load-to-motor inertia ratio $M = J_\omega / J_M$ should satisfy $M \leq 3$, with $M = 1$ ideal. We incorporate a safety factor $k_1$ (1.0–1.3) to account for unmodeled components:
$$ J_{\omega 0} = k_1 J_\omega $$
$$ J_M = J_{\omega 0} $$
The total system inertia becomes:
$$ J_{\omega 1} = J_{\omega 0} + J_M = 2k_1 \frac{J_1}{\eta i^2} + 2J_r $$
Key components’ inertia values are summarized below:
| Component | Inertia (×10⁻⁴ kg·m²) |
|---|---|
| Pulley | 4.8 |
| Rotary Sleeve | 25.7 |
| Die | 2.8 |
| Clamping Ring | 2.3 |
| Rotor Core | 1.6 |
| Total $J_1$ | 3943.5235 |
For motion profiling, we adopt a trapezoidal velocity curve with acceleration time $t_1$, constant velocity time $t_2$, and deceleration time $t_3$ (equal to $t_1$). The total rotation time is:
$$ t = t_1 + t_2 + t_3 $$
Given the rotation angle $\alpha$ and acceleration $a_1$, the relationship is:
$$ t = \frac{900 \alpha a_1 + \pi^2 n_1^2}{30 a_1 \pi n_1} $$
where $n_1$ is the mechanism’s steady-state speed. The motor speed $n_2 = n_1 i$, and acceleration at the motor shaft is:
$$ a_{10} = \frac{\pi n_2}{30 t_1} $$
Thus, the rotation time simplifies to:
$$ t = \frac{30 \alpha i}{\pi n_2} + t_1 $$
Torque calculations include acceleration torque $T_{a1}$, negligible friction torque $T_f$, and root-mean-square torque $T_{\text{rms}}$ for thermal validation:
$$ T_{a1} = J_{\omega 1} a_{10} = \left(2k_1 \frac{J_1}{\eta i^2} + 2J_r\right) \frac{\pi n_2}{30 t_1} $$
$$ T_{\text{rms}} = \sqrt{\frac{2 T_{a1}^2 t_1}{t_0}} $$
Peak torque and power are:
$$ T_{a2} = T_{a1} + T_f $$
$$ P = \frac{T_{a2} n_2}{9550} $$
We conducted parametric sweeps over motor speed $n_2$ (120–720 rpm, step 10), transmission ratio $i$ (1–3, step 0.1), and acceleration time $t_1$ (1–41 ms, step 1). Combinations satisfying $t \in [0.99t’, 1.01t’]$ were retained, yielding 847 valid sets. Sample parameters are shown below:
| $n_2$ (rpm) | $i$ | $t_1$ (s) | $t$ (s) | $T_{a2}$ (N·m) | $P$ (kW) | $T_{\text{rms}}$ (N·m) |
|---|---|---|---|---|---|---|
| 240 | 1.1 | 0.037 | 0.0828 | 497.79 | 12.51 | 234.54 |
| 240 | 1.1 | 0.038 | 0.0838 | 484.69 | 12.18 | 231.44 |
| 240 | 1.2 | 0.033 | 0.0830 | 468.98 | 11.79 | 208.68 |
To identify the optimal set, we applied grey relational analysis, a method effective for multi-objective decision-making under uncertainty. The steps include:
- Defining reference sequences for minimized peak torque, power, and RMS torque.
- Normalizing data via min-max scaling:
$$ y_j(g) = \frac{x_j(g) – \min_g x_j(g)}{\max_g x_j(g) – \min_g x_j(g)} $$
- Computing deviation sequences $\Delta_j(g) = |y_j^0(g) – y_j(g)|$, where $y_j^0(g)$ is the ideal value (minimum).
- Calculating grey relational coefficients:
$$ \gamma_{jg} = \frac{\min_j \min_g \Delta_j(g) + \rho \max_j \max_g \Delta_j(g)}{\Delta_j(g) + \rho \max_j \max_g \Delta_j(g)} $$
with resolution coefficient $\rho = 0.5$.
- Averaging coefficients to obtain grey relational grades $\gamma_g$, with higher values indicating better performance.
Results for selected sets are:
| Set | $\gamma_{jg}$ (Torque) | $\gamma_{jg}$ (Power) | $\gamma_{jg}$ (RMS) | $\gamma_g$ |
|---|---|---|---|---|
| 1 | 0.8802 | 0.9782 | 0.4943 | 0.7843 |
| 2 | 0.8846 | 0.9830 | 0.4995 | 0.7890 |
| 3 | 0.8898 | 0.9887 | 0.5405 | 0.8063 |
The optimal parameters were: motor speed 560 rpm, transmission ratio 3, acceleration time 30 ms. This corresponds to a motor rotor inertia of 0.0494 kg·m², peak torque 193.085 N·m, RMS torque 81.92 N·m, power 11.3223 kW, and rotation time 83.5714 ms. We selected a 15 kW servo motor for safety margin, with detailed specs below:
| Parameter | Value |
|---|---|
| Rated Power | 15 kW |
| Rated Torque | 95.5 N·m |
| Peak Torque | 286 N·m |
| Rated Speed | 1500 rpm |
| Rotor Inertia | 0.0315 kg·m² |
Validation confirmed a load inertia ratio $M = 1.57 \leq 3$, ensuring good dynamic response. Adjusted acceleration time $t_p = 29.76$ ms met timing constraints. Torque and power checks satisfied:
$$ T’_{a2} = \frac{\pi n_2}{30 t_1} \left(J_M + k_1 \frac{J_1}{\eta_1 i^2}\right) = 159.383 \, \text{N·m} < 286 \, \text{N·m} $$
$$ P’ = \frac{T’_{a2} n_2}{9550} = 9.35 \, \text{kW} \leq 15 \, \text{kW} $$
$$ T’_{\text{rms}} = \sqrt{\frac{2 T’_{a1}^2 t_1}{t_0}} = 67.35 \, \text{N·m} < 95.5 \, \text{N·m} $$
We developed a software tool to automate this selection process, enhancing accessibility for China EV manufacturers. Further optimization increased the production rate from 180 to 200 spm, boosting efficiency by 11.1% without hardware changes. This demonstrates the method’s scalability for electric vehicle components.
To verify general applicability, we tested the approach on two stator core lamination mechanisms. Parameters and results are summarized below:
| Stator Type | $m$ (spm) | $\alpha$ (rad) | $J_1$ (kg·m²) | Optimal $n_2$ (rpm) | $i_1$ | $i_2$ | $t_1$ (ms) |
|---|---|---|---|---|---|---|---|
| 1 | 210 | $\pi/2$ | 0.334 | 2788 | 2.5 | 7 | 48.7 |
| 2 | 170 | $\pi$ | 0.412 | 2350 | 1.8 | 5 | 61.6 |
Both cases aligned with empirical selections, validating the method’s robustness. The adhesive motor core processing equipment, integrated with a hydraulic press and progressive die, produced cores meeting dimensional tolerances (e.g., outer diameter 149.0401 mm ±0.063 mm, thickness 60.3354 mm ±0.5 mm). Surface quality and glue distribution were satisfactory, underscoring the practicality for China EV supply chains.
In conclusion, our grey theory-based optimization significantly enhances the efficiency of adhesive motor core processing for electric vehicles. By streamlining drive selection and parameters, we achieve higher production rates and lower costs, supporting the growth of China’s EV industry. Future work will explore real-time adaptive control and integration with digital twins for smart manufacturing.