Dimensionless Analysis of Axial Magnetic Force and Stiffness in Cylindrical Permanent Magnets and Coils

This paper establishes an equivalent model between cylindrical permanent magnets and solenoids. Based on the magnetic charge theory and Coulomb’s model, an expression for the axial magnetic force is derived, and then derived the dimensionless axial magnetic force formula. Through further differentiation, the dimensionless axial stiffness formula is obtained. An in-depth analysis is conducted on the impact of dimensionless parameters on axial stiffness. The process of dimensionless calculations eliminates interference caused by differences in unit systems, revealing the intrinsic relationship between magnetic stiffness and the geometric and material properties of the magnets. This provides a theoretical basis for the optimization of electromagnetic device design and holds extensive application value in both engineering and scientific research fields.