模块化永磁直线同步电机考虑制造公差的推力鲁棒性优化

Thrust Robustness Optimization of Modular Permanent Magnet Linear Synchronous Motor Accounting for Manufacture Tolerance

模块化永磁直线同步电机(MPMLSM)具有效率与推力密度高、可靠性和可加工性好等优点,非常适用于长行程运输系统;缺点是批量生产中性能易受到加工公差的影响。针对这一问题,该文提出了一种考虑制造公差的综合多目标鲁棒优化设计方法。首先,基于六西格玛设计方法建立了鲁棒优化模型;其次,采用拉丁超立方采样方法在尺寸公差范围内根据正态分布规律进行抽样,模拟大规模生产时电机尺寸受公差影响可能会出现的各种变化;再次,在尺寸优化范围内均匀抽样构成足够的训练样本,由有限元软件仿真这些抽样方案的推力性能,并基于反向传播神经网络建立电机设计代理模型;然后,应用该代理模型对拉丁超立方采样得到的样本进行电机性能的计算,求解样本整体对应的各优化目标的均值与方差,进而计算多目标优化的适应度;最后,采用非支配排序遗传算法Ⅱ进行全局优化,得到鲁棒优化方案,与不考虑公差的确定性优化方案相比,验证了该方法的有效性。鲁棒优化方案虽然略微增加了电机体积和推力波动,但是其失效概率低,受公差影响小,更加符合产品批量生产过程中的质量要求。

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 AlgorithmⅡis 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 0.9999,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 whenλ≥7%under condition 1 orλ≥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)λmainly affects the thrust fluctuation,and little affects the volume.Under the same volume condition,the thrust fluctuation increases with the increase ofλ.(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 whenλis small.Therefore,the robust optimization scheme has better robustness and is more in line with the quality requirement in mass production.