Global Sensitivity Analysis of Helmholtz Coils for Enhanced Homogeneous Magnetic Field of Electromagnetic Flowmeters

Helmholtz coils are widely used to generate homogeneous magnetic fields. Various parameters influence the magnetic field strength and homogeneity, including coil shape, size, spacing, winding layers, winding turns, and axial and radial gaps between windings. Previous researches have partially examined these parameters through local sensitivity analysis, where each parameter is varied independently while others are held constant. However, such studies often have limited applicability due to the interdependence of parameters including coil size, spacing, and windings. This work employs a new global sensitivity analysis, reciprocal optimum solution, to investigate the interconnections between these parameters and their effects on magnetic flux density and field homogeneity. This approach eliminates the need to manually optimize variable ranges and mitigates the issues of randomness, uncertainty, and slow convergence by producing both deterministic formulas and a blueprint for designing Helmholtz coils with homogeneous magnetic fields. Using this method, we produced open-source Helmholtz coils development software. This enables users to obtain design parameters for Helmholtz coils for a required homogeneous magnetic field domain, when provided either its cross-sectional diameter or the coil spacing required for the device.