Static Performance Analysis and Optimization of High-Speed Solenoids Integrated with Permanent Magnets and Annular Flanges

To enhance the performance of high-speed solenoids (HSSs) in control systems, two improved structural designs incorporating a permanent magnet (PM) and an annular flange (AF) are proposed based on the parallel magnetic circuit principle. Their static electromagnetism performances were thoroughly investigated by the finite element method. Furthermore, multi-objective optimization combined with the response surface method and NSGA-II was carried out. The results indicate that the electromagnetic energy conversion efficiency and electromagnetic force of HSSs can be promoted by applying a PM and an AF: for the first improvement design just employing a PM, increasing the PM height improves energy conversion efficiency and mitigates magnetic saturation within the main pole, and for the second improvement design employing both a PM and an AF, the electromagnetic energy conversion efficiency and electromagnetic force of HSS can be further promoted. In the end, based on the Pareto optimal solution set, the optimized design increases the net electromagnetic force by 18.8% and reduces the peak current by 18.8%. This is the result of applying the optimization scheme, which is beneficial for increasing the dynamic response speed of the HSS valve and reduce its energy loss.