This paper presents a simple and efficient magnetic equivalent circuit (MEC) model for surface axial flux permanent magnet synchronous machines. The MEC model is used to solve all the electromagnetic properties of the machine including the no load, full load voltages, cogging torque, torque ripple, and stator iron core losses. Moreover, this approach can be extended for all surface permanent magnet synchronous machines. The main novelty of this approach is the development of a static system, which accounts for the rotation. The model takes into account the rotor rotation via time-dependent permanent magnet magnetization sources. The static system matrix facilitates a very fast solving. In addition, to take into account the three-dimensional (3-D) effect, a multislicing of the machine in the radial direction is done. This boosts the simulation time to only 60 s for six slices and 50 time steps including the nonlinear behavior of the stator elements with a great accuracy. Additionally, the number of elements in the MEC can be adjusted to reduce the computational time. This model is verified by means of 3-D and two-dimensional (2-D) multislice finite-element models. In addition, experimental validations are also provided at the end.

To facilitate the active magnetic bearing (AMB) design and analysis, an accurate and fast model that considers both rotor eccentricity and the saturation effect is necessary. In this article, a novel hybrid analytical model (HAM) for effective calculation of the magnetic field of the AMB is proposed. Eccentricity and local saturation are considered in the proposed HAM. In the proposed HAM, the stator and rotor are modeled by elementary subdomains (ESDs) and the air-gap is modeled by magnetic equivalent circuit (MEC). Direct coupling between the solutions in the ESD regions with MEC completes the whole model matrices. Compared to the existing literature, the proposed model considers both the rotor eccentricity and material nonlinearity. The effectiveness and accuracy of the proposed HAM are validated by both the finite element model and experimental results. The results show that the proposed HAM can accurately predict the magnetic quantities of the AMB.

To find the temperature rise for high power density yokeless and segmented armature (YASA) axial flux permanent magnet synchronous (AFPMSM) machines quickly and accurately, a 3D lumped parameter thermal model is developed and validated experimentally and by finite element (FE) simulations on a 4 kW YASA machine. Additionally, to get insight in the thermal transient response of the machine, the model accounts for the thermal capacitance of different machine components. The model considers the stator, bearing, and windage losses, as well as eddy current losses in the magnets on the rotors. The new contribution of this work is that the thermal model takes cooling via air channels between the magnets on the rotor discs into account. The model is parametrized with respect to the permanent magnet (PM) angle ratio, the PM thickness ratio, the air gap length, and the rotor speed. The effect of the channels is incorporated via convection equations based on many computational fluid dynamics (CFD) computations. The model accuracy is validated at different values of parameters by FE simulations in both transient and steady state. The model takes less than 1 s to solve for the temperature distribution.

Integrated onboard battery charger (IOBC) is an emerging technology that charges electric car battery packs utilizing the same circuitry for electric propulsion, reducing the cost and weight of an EV. During charging, while ensuring zero-average torque to avoid rotation, permanent magnets (PMs) synchronous motors with fractional slot concentrated winding (FSCW) may be subjected to irreversible demagnetization due to sub and super space harmonics with relatively high magnitudes. This paper presents the design and optimization of six-phase surface-mounted permanent magnet (SPM) and interior permanent magnet (IPM) motors with FSCW considering the impact of PM demagnetization during IOBC. A detailed thermal and demagnetization analysis is conducted to identify the risk of PM demagnetization during propulsion and IOBC modes. The performance and demagnetization risk for SPM and IPM motors with different power ratings used in commercial EVs are compared at various operating conditions. In the integrated charging process, grid-to-vehicle and vehicle-to-grid power circulations are practically implemented. Simulations are conducted using a three-dimensional finite element analysis. Experimental results of a 15 kW IPM motor are provided for further verification.

The aim of this paper is to calculate the static eccentricity (SE) of a double rotor axial flux permanent magnet (AFPM) machine by using a general analytical model. The flux density in the air gap under healthy conditions is calculated firstly, where the axial and circumferential magnetic flux densities are obtained using a coupled solution of Maxwell’s equations and Schwarz-Christoffel (SC) mapping. The magnetic flux densities under SE conditions are calculated afterwards using a novel bilinear mapping. Some important electromagnetic parameters, e.g., back electromotive force (EMF), cogging torque and electromagnetic (EM) torque, are calculated for both SE and healthy conditions, and compared with the finite element (FE) model. As for the double rotor AFPM, SE does not contribute much effect on the back EMF and EM torque, while the cogging torque is increased. At each calculated section, FE models were built to validate the analytical model. The results show that the analytical predictions agree well with the FE results. Finally, the results of analytical model are verified via experimental results.

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.