Force calculation of magnetized bodies in contact using Kelvin's formula and virtual air-gap

In this paper it is shown that Kelvin's formula can be implemented in a simple way using the external field, which is calculated from the virtual air-gap scheme recently proposed by the authors. External fields of all finite elements come from only one FEM solution. This implementation provides consistent numerical results of force calculation whether a magnetic body is in contact with another or not. The validity of this proposed method for magnetic force calculation is shown by numerical comparisons with other well-known methods.