Force Calculations in 3-D Cylindrical Structures Using Fourier Analysis and the Maxwell Stress Tensor

Analytical modeling is still a very effective manner to calculate the magnetic fields in permanent magnet devices. From these magnetic fields, device quantities, e.g., force, emf, or inductance, can be calculated. This paper presents a semianalytical technique, based on a 2-D Fourier series to represent the magnetic field, to describe the force components due to permanent magnets in 3-D cylindrical structures. The Maxwell stress tensor method is selected to calculate these force components in the cylindrical coordinate system. The method is analytically evaluated by inserting the analytical expressions describing the magnetic fields. The obtained force equations avoid the use of numerical integration of the magnetic fields resulting in a fast and accurate force calculation method. An example of a 3-D cylindrical structure is modeled and validated by means of a magnetostatic finite element analysis (FEA), and excellent agreement is found.