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This paper presents an analytical study of the air-gap magnetic field of a surface permanent magnet (SPM) linear, slot-less machine with a Halbach PM configuration, under the no-load condition. While other analytical formulations of the magnetic field generated by PMs are available, they exhibit some drawbacks, such as only providing a Fourier series, or being suitable to determine magnetic field average values, but not local magnetic field distributions. On the contrary, the proposed approach allows the determination of a unique, closed-form formulation for the slot-less machine air-gap field. This is obtained starting from the complex expression of the magnetic field of a conductor, inside the air gap, between two parallel smooth iron surfaces, obtained by means of the method of images. The magnetic field due to an infinitesimal conductor belonging to a current sheet is then integrated along a segment, providing the expression of the magnetic field due to the corresponding linear current density distribution, for current sheets perpendicular or parallel to the iron surfaces. Any Halbach PM segment disposition can, hence, be obtained via a suitable combination of field distributions generated by couples of current sheets with perpendicular and parallel orientation. Lastly, the no-load magnetic field expression with a Halbach array of PMs is retrieved. The proposed analytical model provides an accurate representation of the magnetic field distribution produced by any Halbach array, with an arbitrary number of segments and orientations. Additionally, the results obtained from the proposed analytical expressions are compared with FEM simulations realized by commercial software, and show an excellent agreement. [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]

In this paper, an analytical approach is proposed in developing a lumped parameter thermal model for the stator coils of naturally cooled axial-flux tooth-coil permanent magnet machines. The model comprises one tooth, the coil around it, and the air channels between coils and the teeth supporting structure; each component is subdivided into cuboidal or arc subelements. An expression of the convective exchange coefficient is proposed to take into account the radial position of each tooth. Experimental results validate the proposed model, which can also be used in the design stage of a machine. [ABSTRACT FROM AUTHOR]

Due to the high torque capability, axial flux (AF) permanent-magnet (PM) machines are an interesting solution for direct driven wind energy conversion systems and low-speed motors. However, the structure of such machines makes them sensitive to geometrical imperfections due to manufacturing process. This paper analyzes the effects that various types of geometrical imperfections produce in concentrated coil AF PM generators. In particular, a case study is presented, where the mechanical stresses, the resulting axial force, and the bending torques on the shaft, as well as the circulation current in the winding parallel paths, are calculated. The results obtained by means of an analytical approach are compared with those based on finite element method simulations and are validated by some experimental results on a prototype. [ABSTRACT FROM PUBLISHER]

An analytical method is presented to evaluate the field and global quantities for the operation and design analysis of axial flux permanent-magnet (PM) machines. The method, of general applicability, is based on the definition and superposition of suited field functions, able to accurately model the different singularities of the studied device: PM field distribution, effects of slotting, and radial end effects. Selected explorative FEM analyses are used in order to investigate the field functions shape and to help in identifying their structure and parameters. Then, the flux density distribution is obtained, as a function of the rotor position, taking into account some manufacture dissymmetry effects, such as air-gap offsets and PM rotor disk inclinations. This approach allows to analyze the effect of dissymmetry on the circulation of current among winding parallel paths in no-load operation. Moreover, by using the Maxwell stress tensor, the stress distribution is evaluated, as well as the resultant axial forces and the bending torques on the shaft due to the rotor disk tilts. Several FEM simulations show the soundness of the proposed method, which exhibits high accuracy and great evaluation speed. [ABSTRACT FROM PUBLISHER]