The rapid advancement of electric car technologies, particularly in the China EV sector, has intensified the demand for high-performance drive motors. As a critical component, the motor core significantly influences energy efficiency and power density. Traditional core manufacturing methods, such as riveting and welding, often lead to increased iron losses and reduced magnetic performance due to localized fixation and inadequate lamination. In response, adhesive bonding technology has emerged as a superior alternative, enabling tighter lamination and reduced eddy current losses. However, the production efficiency of adhesive motor core processing equipment remains a bottleneck, primarily due to suboptimal drive system selection and parameter settings in rotary lamination mechanisms. This study addresses these challenges by developing a comprehensive multi-objective optimization approach based on grey theory, aiming to enhance the accuracy of drive device selection and parameter configuration for improved processing efficiency in electric car applications.
The rotary lamination mechanism, integral to adhesive core production, performs functions including blanking, rotating, and stacking electrical steel sheets. Inefficiencies in this mechanism often stem from mismatched timing between process steps, limiting overall production rates. Our research focuses on optimizing the drive system—typically a servo motor—by refining the selection process and parameter settings. The methodology involves determining transmission mechanisms, calculating load parameters, ensuring inertia matching, and validating operational parameters through rigorous analysis. By leveraging grey theory, we formulate a systematic approach to multi-objective optimization, prioritizing minimal torque, power consumption, and root mean square torque while adhering to production constraints.
Transmission mechanisms play a pivotal role in the performance of rotary lamination systems. Synchronous belt drives are preferred for their absence of backlash, reduced impact during operation, and cost-effectiveness compared to couplings or gear drives. The transmission efficiency $\eta_1$ for synchronous belts is typically 0.98, while gear reducers, used when additional torque or inertia reduction is needed, exhibit an efficiency $\eta_2$ of 0.98. The total transmission ratio $i$ and mechanical efficiency $\eta$ are calculated as follows:
$$i = i_1 i_2$$
$$\eta = \eta_1 \eta_2$$
where $i_1$ and $i_2$ represent the synchronous belt and gear reducer ratios, respectively. For instance, common reducer ratios in the PLN115 series range from 3 to 10, with moments of inertia between $1.933 \times 10^{-4}$ and $3.256 \times 10^{-4}$ kg·m². The stroke rate $m$ (in strokes per minute, spm), rotation angle $\alpha$, and time coefficients determine the operational cycle. The theoretical rotation time $t’$ and cycle time $t_0$ are derived as:
$$t_0 = \frac{60}{m}$$
$$t’ = \frac{60}{m} \cdot \frac{1}{f}$$
Here, $f$ denotes the time coefficient, with a practical range of 1 to 4. The trapezoidal motion profile is adopted for its balanced operation time and reduced motor impact, contrasting with triangular or rectangular profiles that induce higher stresses or impractical constant speeds. Critical motor speeds are defined by:
$$n_{\text{max}} = \frac{60 \alpha}{\pi t’}$$
$$n_{\text{min}} = \frac{30 \alpha}{\pi t’}$$
These values guide the servo motor selection, ensuring compatibility with the China EV industry’s requirements for high-speed production.
Load parameters are crucial for inertia matching and dynamic performance. The load moment of inertia $J_\omega$ incorporates components from the rotary mechanism, pulleys, and reducers, adjusted for mechanical efficiency:
$$J_\omega = \frac{J_1}{\eta i^2} + J_2 + J_r$$
where $J_1$, $J_2$, and $J_r$ represent the inertia of the rotary mechanism, small pulley, and reducer, respectively. An inertia amplification factor $k_1$ (1.0 to 1.3) accounts for uncalculated components, yielding the final load inertia $J_{\omega0} = k_1 J_\omega$. The servo motor rotor inertia $J_M$ should satisfy $J_{\omega0} \leq 3J_M$ for optimal dynamic response, with a target inertia ratio $M = J_M / J_{\omega0} = 1$ to enhance controllability and power conversion rates. The total system inertia is then:
$$J_{\omega1} = J_{\omega0} + J_M = 2k_1 \frac{J_1}{\eta i^2} + 2J_r$$
Key load parameters for a typical rotary lamination mechanism are summarized in the table below:
| Parameter | Value |
|---|---|
| Stroke rate $m$ (spm) | 180 |
| Rotation angle $\alpha$ (rad) | $\pi/3$ |
| Synchronous belt efficiency $\eta_1$ | 0.98 |
| Reducer efficiency $\eta_2$ | 1 (if no reducer) |
| Minimum transmission ratio $i_{\text{min}}$ | 1 |
| Maximum transmission ratio $i_{\text{max}}$ | 3 |
| Cycle time $t_0$ (s) | 1/3 |
| Theoretical rotation time $t’$ (s) | 1/12 |
| Minimum motor speed $n_{2\text{min}}$ (r/min) | 120 |
| Maximum motor speed $n_{2\text{max}}$ (r/min) | 720 |
| Maximum acceleration time $t’_{\text{max}}$ (s) | 41 |
Rotation time optimization involves analyzing the trapezoidal velocity profile, where total time $t$ comprises acceleration ($t_1$), constant velocity ($t_2$), and deceleration ($t_3$) periods. Assuming equal acceleration and deceleration rates $a_1$ and $a_2$, the relationship is expressed as:
$$t_1 = \frac{\pi}{30} \cdot \frac{n_1}{a_1}$$
$$t = \frac{900 \alpha a_1 + \pi^2 n_1^2}{30 a_1 \pi n_1}$$
The servo motor’s stable speed $n_2 = n_1 i$ and acceleration time $t_1$ determine the motor’s angular acceleration $a_{10} = \pi n_2 / (30 t_1)$. The total rotation time simplifies to:
$$t = \frac{30 \alpha i}{\pi n_2} + t_1$$
Torque and power calculations are essential for servo motor sizing. The acceleration torque $T_{a1}$ and root mean square torque $T_{\text{rms}}$ are derived as:
$$T_{a1} = J_{\omega1} a_{10} = \left(2k_1 \frac{J_1}{\eta i^2} + 2J_r\right) \frac{\pi n_2}{30 t_1}$$
$$T_{\text{rms}} = \sqrt{\frac{2(T_{a1} + T_f)^2 t_1}{t_0}}$$
where $T_f$ represents the constant velocity torque, negligible in well-lubricated systems. The maximum output torque $T_{a2} = T_{a1} + T_f$ and power $P$ are:
$$P = \frac{T_{a2} n_2}{9550} = \frac{\left(2k_1 \frac{J_1}{\eta i^2} + 2J_r\right) \pi n_2^2}{30 \times 9550 t_1}$$
Initial drive parameter selection involves evaluating combinations of motor speed $n_2$ (120–720 r/min), transmission ratio $i_1$ (1–3), and acceleration time $t_1$ (1–41 ms). The grey theory-based multi-objective optimization minimizes $T_{a2}$, $P$, and $T_{\text{rms}}$ while ensuring $t \approx t’$. Data sequences are normalized, and grey relational coefficients $\gamma_{jg}$ are computed as:
$$\gamma_{jg} = \frac{\min_j \min_g \Delta_j(g) + \rho \max_j \max_g \Delta_j(g)}{\Delta_j(g) + \rho \max_j \max_g \Delta_j(g)}$$
where $\rho = 0.5$ is the distinguishing coefficient. The grey relational degree $\gamma_g$ averages these coefficients across objectives, identifying optimal parameters. For a case study, the optimal set includes $n_2 = 560$ r/min, $i = 3$, and $t_1 = 30$ ms, yielding $J_M = 0.0494$ kg·m², $T_{a2} = 193.085$ N·m, $T_{\text{rms}} = 81.92$ N·m, $P = 11.3223$ kW, and $t = 83.5714$ ms. A 15 kW servo motor is selected, with verification confirming adherence to inertia matching ($M = 1.57 \leq 3$), torque ($T’_{a2} = 159.383$ N·m < 286 N·m), power ($P’ = 9.35$ kW ≤ 15 kW), and $T’_{\text{rms}} = 67.35$ N·m < 95.5 N·m.
To enhance applicability, the methodology is programmed into a software tool, streamlining drive selection. Further optimization increases the stroke rate to 200 spm, elevating efficiency by 11.1% without hardware changes. This approach is validated on additional stator core configurations, demonstrating consistent alignment with practical motor parameters and underscoring its relevance to the electric car industry, particularly in the China EV market.
Experimental validation involves an adhesive motor core processing platform comprising a hydraulic press, progressive die, and servo motor. The platform produces rotor cores with critical dimensions—outer diameter, inner diameter, thickness—within tolerances. Surface inspection reveals no adhesive overflow or scratches, ensuring high installation precision. Shape parameter deviations are below 0.1 mm, though thickness variability (standard deviation 0.14054 mm) persists due to material inconsistencies. The results confirm that cores meet operational standards for electric car drives, supporting the optimization’s practical efficacy.
In conclusion, this study establishes a grey theory-driven framework for optimizing adhesive motor core processing equipment, achieving precise drive selection and parameter setting. The method eliminates trial-and-error approaches, reducing costs and boosting production efficiency by 11.1%, with broader implications for the China EV sector. The integrated software tool and experimental verification underscore the reliability of this approach, offering a robust solution for enhancing electric car motor performance and supporting sustainable transportation goals.