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The following paper presents an analytical study of the air-gap magnetic field distribution produced by the armature reaction of a linear machine. Based on the method of images, the magnetic field generated by a current carrying conductor inside the air-gap between two smooth infinitely permeable iron surfaces is modeled as a complex 2D function. The conductor model then becomes a current sheet model and horizontally oriented current sheets are used to model the magnetic field produced by the armature reaction for smooth ferromagnetic surfaces. Focus will be given to the study of the slot opening function in front of energized slots in comparison to the not energized ones of the classical theory pointing out some remarkable differences. Later, the model is extended to slotted geometries using a complex slotting function adapted for energized slots. At last, the Maxwell tensor expressed in complex formulation will be integrated to obtain the force components acting on the machine tooth tips, quantities that will be compared with FEM simulations in order to validate the proposed analytical model. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of the air-gap magnetic field of a Surface Permanent Magnet (SPM) linear machine under no load. By means of the method of images, the complex expression of the magnetic field of a conductor, inside the air gap between two smooth iron surfaces, is retrieved. Then, integrating the conductor expression, the formulation of the magnetic field of a current sheet and thus the one of a SPM, using two vertical current sheets, is obtained. At last, the no-load magnetic field expression, for a generic time instant, of a slotless machine is retrieved. The novelty of the proposed approach is the availability, due to a different calculation approach, of a unique closed-form formulation for the slotless machine air-gap field, a quantity that, in literature, is usually present in Fourier series formulation. Additionally, as a means to calculate integral quantities and show the goodness of the method a complex slotting function is introduced to account for the slotted geometry. Finally, starting from Lorenz's force formulation, the expression of the Maxwell tensor in complex form is retrieved and the contribution of forces, integral of the complex stress tensor quantity, will be calculated and compared with FEM simulations, showing a good agreement also with the analytical slotted model. [ABSTRACT FROM AUTHOR]