Abstract The modular structure of modular permanent magnet linear synchronous motor (MPMLSM) is beneficial to simplify the winding manufacturing process and improve the motor performance and fault tolerance rate. As a motor with high efficiency, high thrust density, and high reliability, it has received extensive attention and application in recent years. However, in mass production, the modular structure is more susceptible to machining tolerances. In order to improve the motor performance and better meet the quality requirements, this paper proposes a thrust robustness optimization method considering manufacturing tolerance, which provides help for the optimization design and application of MPMLSM. First, a robust optimization model is established based on design for six Sigma (DFSS), and the optimization objective function is determined according to the sigma level. Then, the Latin Hypercube Sampling (LHS) method is used to sample within the dimensional tolerance range according to the normal distribution law to simulate possible variations in motor dimensions in mass production. A motor design surrogate model based on the Back Propagation Neural Network (BPNN) can calculate the motor performance required for subsequent optimization quickly and conveniently. The training samples of the model are obtained by uniform sampling, and the thrust performance of the samples is simulated by finite element software. Subsequently, the motor performance of the samples obtained by LHS is calculated by the trained surrogate model, and the mean and variance of the whole sample are solved and substituted into the objective function to obtain the fitness value. Finally, Non-dominated Sorting Genetic Algorithm Ⅱ is used for global optimization to obtain the Pareto front and robust optimization schemes. Compared with the deterministic optimization scheme, the effectiveness of the method is verified. Through finite element verification, the determination coefficient of the surrogate model established by BPNN is 0.999 9, and the mean square error is 1.76×10-3. Thus, the motor performance can be calculated quickly and accurately. Under the harsh condition that the allowable thrust variation range (λ) is 2%, the robust optimization scheme can reduce the probability of failure (POF) from 67.32% to 7.96% under condition 1, and from 53.3% to 1.76% under condition 2. Compared with the deterministic optimization scheme without considering tolerance, although the robust optimization design slightly increases the motor volume and thrust ripple, the robustness is improved. At the same time, it can be inferred that the POF of the robust optimization scheme is 0 when λ≥7% under condition 1 or λ≥5% under condition 2. The reduction of failure probability indicates that the MPMLSM robust optimization schemes have higher qualification rates in mass production and are less affected by tolerances. The following conclusions can be drawn: (1) Under the premise of convergence, reducing manufacturing tolerance can reduce the motor volume and make the motor thrust closer to the set value. However, the manufacturing cost is increased. (2) λ mainly affects the thrust fluctuation, and little affects the volume. Under the same volume condition, the thrust fluctuation increases with the increase of λ. (3) In the optimization results, the tooth height and primary polar distance vary with different tolerance conditions, while the remaining variables are optimized to optimum values. (4) The POF of the robust optimization scheme is lower than that of the deterministic optimization scheme, especially when λ is small. Therefore, the robust optimization scheme has better robustness and is more in line with the quality requirement in mass production.
Gong Xixia,Li Yanxin,Lu Qinfen. Thrust Robustness Optimization of Modular Permanent Magnet Linear Synchronous Motor Accounting for Manufacture Tolerance[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 465-474.
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2024, Vol. 39 
