Comparison of Three Analytical Methods for the Precise Calculation of Cogging Torque and Torque Ripple in Axial Flux PM Machines

Abstract

A comparison between different analytical and finite-element (FE) tools for the computation of cogging torque and torque ripple in axial flux permanent-magnet synchronous machines is made. 2D and 3D FE models are the most accurate for the computation of cogging torque and torque ripple. However, they are too time consuming to be used for optimization studies. Therefore, analytical tools are also used to obtain the cogging torque and torque ripple. In this paper, three types of analytical models are considered. They are all based on dividing the machine into many slices in the radial direction. One model computes the lateral force based on the magnetic field distribution in the air gap area. Another model is based on conformal mapping and uses complex Schwarz Christoffel (SC) transformations. The last model is based on the subdomain technique, which divides the studied geometry into a number of separate domains. The different types of models are compared for different slot openings and permanent-magnet widths. One of the main conclusions is that the subdomain model is best suited to compute the cogging torque and torque ripple with a much higher accuracy than the SC model.

A Simple and Efficient Quasi-3D Magnetic Equivalent Circuit for Surface Axial Flux Permanent Magnet Synchronous Machines

“…Then the total magnetic field strength can be obtained by summation of both the effects of the non-linear magnetic characteristics and the eddy currents. Afterwards, the total reluctivity is available and can be substituted in (7) and (10) to obtain the residual function r and the Jaccobian matrix J respectively. Skin effect can be accounted for by expressing the flux density distribution in the lamination thickness as a series using a set of skin-effect basis functions as described in [23].…”

“…In this machine, only 1 over 10 of the machine can be simulated. The details of this machine can be found in [7]. This machine has a higher cogging torque amplitude.…”

“…Several numerical and analytical techniques were developed and used over last decades [2]- [4]. Although numerical techniques, such as 3D and 2D finite element (FE) analysis [5]- [7], are the most accurate techniques to model electric machines, they are not preferable in early design stages due to their expensive computational burden.…”

“…These models can nicely predict the air gap flux density and therefore predict the cogging torque and torque ripple efficiently. A comparative study between different concepts of Fourier based subdomain (SD) models and conformal mapping techniques for AFPMSM and radial flux permanent magnet synchronous machines (RFPMSMs) has been presented in [7], [14] respectively. For the calculation of the no load voltages, the result is satisfactory for all models.…”

A 3D Dynamic Lumped Parameter Thermal Network of Air-Cooled YASA Axial Flux Permanent Magnet Synchronous Machine

“…However, they are still very time-consuming. Therefore, fast and accurate analytical models were developed in [4][5][6][7]. These models are capable of calculating all the electromagnetic quantities (cogging torque, torque ripple, iron losses, permanent magnet (PM) losses, inductances, and no load and full load voltages) in a very efficient way.…”