Calculating the magnetic force of solenoid inductor wound by rectangular cross‐section wire

Abstract A new semi‐analytical expression is presented based on two integrations for calculating the magnetic force of a solenoid inductor wound by rectangular cross‐section wire. The authors simplified the solenoid inductor coil to a collection of circular coils, and the current density of the coils in the radial direction which was inversely proportional to its radius is considered. The obtained expressions can be implemented by adaptive Gaussian quadrature integration with MATLAB programming. In addition, they used the filament method and the finite element method to calculate the magnetic force on the solenoid inductor coil. The correctness of the semi‐analytical expressions was verified by comparing the results of the semi‐analytical numerical method with those of the filament method and the finite element method, respectively. The derived semi‐analytical expressions of magnetic force allow a low computational time compared with the filament method and the finite element method to a specific accuracy. The calculation results show that: the solenoid inductor coil tends to compress in the axial direction, and the axial magnetic force on the outermost coils is the largest; the solenoid inductor coil tends to expand outward in the radial direction, and the radial magnetic force on the intermediate coil is the largest.