An analytical optimization approach of the submersible solenoid valve constrained in a specific small volume is presented. In order to maximum the electromagnetic force, thermal model and electromagnetic model are constructed, and five radial dimensions are optimized when the main limiting quantity is the maximum allowed temperature. A numerical optimization calculation is performed in order to verify the proposed analytical approach. The optimal solution of the numerical calculation is compared with the solution of the analytical approach, which shows a good agreement between the two methods. A thermal analysis of the optimal submersible solenoid valve based on AYSYS is also performed to verify the thermal model. A comparative study between the experimental and simulated static characteristics of the optimal submersible solenoid valve is also performed. The results show that the proposed analytical approach is correct.

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