Mechanical Deformation and Body Force Density Due to the Generalized Korteweg–Helmholtz Force Density Method Employing the Virtual Air-Gap Scheme

A generalized Korteweg–Helmholtz (GKH) force density method was implemented incorporating the virtual air-gap scheme and the finite-element method for evaluating magnetic body force density and mechanical deformation. Until now, several generalized force calculation methods adopting the virtual air-gap scheme have been developed and successfully applied to contact and mechanical deformation problems. The KH force density method is well known and can be derived with theoretical completeness, and it can be changed into the tensor formulation for calculating force density and total force on the electromagnetic body. This KH is numerically stable compared with the conventional Maxwell (MX) stress tensor method, because it adopts the tensor difference at an interface. However, the KH also has difficulty calculating the contact force density and body force density. Therefore, here, we developed the GKH force density method employing the virtual air-gap scheme. In addition, the mechanical deformation was tested quantitatively and compared with those from the conventional force calculation methods, including the MX, the KH, the equivalent magnetic charge method, and the Kelvin force density method. To verify the mechanical deformation due to the GKH, we implemented the GKH and compared the mechanical deformations between the several numerical results.