scholarly journals Analytical Model to Calculate Radial Forces in Permanent-Magnet Synchronous Machines

2021 ◽  
Vol 11 (22) ◽  
pp. 10865
Author(s):  
Iratxo Gómez ◽  
Gustavo García ◽  
Alex McCloskey ◽  
Gaizka Almandoz
Keyword(s):  
Magnetic Flux ◽  
Permanent Magnet ◽  
Analytical Model ◽  
Experimental Tests ◽  
Synchronous Machines ◽  
Magnetic Flux Density ◽  
Permanent Magnet Synchronous Machines ◽  
Electromagnetic Forces ◽  
Design Variables ◽  
Radial Forces

There are three principal sources of noise and vibration in electrical machines: electromagnetic sources, mechanical sources, and aerodynamic sources. Nowadays, one of the major advantages of permanent-magnet synchronous machines is their torque density. This density is achieved through a high magnetic flux density in the air gap, which is achieved through hard magnets. Unfortunately, in these machines, electromagnetic forces have been identified as the main source of vibration and noise, and high magnetic flux densities make these vibrations and noises more significant. With the aim of better understanding the relationship between electromagnetic forces and design variables, this article, which is the continuation of previous work, firstly describes a study of the sources of magnetic forces in permanent-magnet synchronous machines. Subsequently, an analytical model for the computation of the radial forces originating from electromagnetic sources in permanent-magnet synchronous machines is stated. This model analyzes the forces on both the rotor surface and the base of the stator tooth. The analytical results were corroborated through simulations using the finite element method (FEM) and also by experimental tests performed over two prototypes. The results achieved by the analytical model show good agreement with both FEM results and experimental measurements.

scholarly journals 2-D Analytical Model for Predicting Magnetic Flux Distribution in Slotless Single-sided Axial Flux Permanent-Magnet Synchronous Machines

2019 ◽  
Vol 11 (2) ◽  
pp. 97-105
Author(s):  
A. Ghaffari
Keyword(s):  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Analytical Model ◽  
Permanent Magnets ◽  
Open Circuit ◽  
Synchronous Machines ◽  
Magnetic Flux Density ◽  
Permanent Magnet Synchronous Machines ◽  
Axial Flux

This paper estimates the magnetic flux density components in the slotless single-sided axial flux permanent-magnet synchronous machines (SAFPMSMs). For this purpose, a 2-D analytical model based on the sub-domain method is utilized in which the cross-section of the presented machine is divided into the seven sub-regions such as stator side exterior, stator, winding, air-gap, permanent-magnets (PMs), mover and mover side exterior. Based on the Maxwell equations, the related partial differential equations (PDEs) of magnetic flux density components are formed in each sub-region which are identified as the essential step for obtaining the machines quantities. According to the superposition theorem, two separate steps are implemented for calculating the magnetic flux density components. In the first step, open circuit analysis includes various type of magnetization patterns, i.e. parallel, ideal Halbach, 2-segment Halbach and bar magnet in shifting direction is investigated and armature currents are zero and in the second step PMs are inactive and the magnetic flux density components are originated due to only armature reaction. Eventually, 2-D finite element method (FEM) is determined to confirm the accuracy of the presented analytical approach and an acceptable agreement between the analytical and FEM models can be observed.

scholarly journals Development of Mathematical Models in Explicit Form for Design and Analysis of Axial Flux Permanent Magnet Synchronous Machines

2020 ◽  
Vol 10 (21) ◽  
pp. 7695
Author(s):  
Franjo Pranjić ◽  
Peter Virtič
Keyword(s):  
Magnetic Flux ◽  
Permanent Magnet ◽  
Input Data ◽  
Permanent Magnets ◽  
Synchronous Machines ◽  
Simplified Model ◽  
Magnetic Flux Density ◽  
Axial Component ◽  
Permanent Magnet Synchronous Machines ◽  
Axial Flux

This article proposes a methodology for the design of double-sided coreless axial flux permanent magnet synchronous machines, which is based on a developed model for calculating the axial component of the magnetic flux density in the middle of the distance between opposite permanent magnets, which also represents the middle of the stator. Values for different geometric parameters represent the input data for the mathematical model in explicit form. The input data are calculated by using a simplified finite element method (FEM), which means that calculations of simplified 3D models are performed. The simplified model consists of two rotor disks with surface-mounted permanent magnets and air between them, instead of stator windings. Such a simplification is possible due to similar values of permeability of the air and copper. For each simplified model of the machine the axial component of the magnetic flux density is analyzed along a line passing through the center of opposite permanent magnets and both rotor disks. Values at the middle of the distance between the opposite permanent magnets are the lowest and are therefore selected for the input data at different stator, rotor disks and permanent magnets (PM) thicknesses. Such input data enable the model to consider the nonlinearity of materials.

scholarly journals Analytical Study and Comparison of Electromagnetic Characteristics of 8-Pole 9-Slot and 8-Pole 12-Slot Permanent Magnet Synchronous Machines Considering Rotor Eccentricity

Electronics ◽  
2021 ◽  
Vol 10 (16) ◽  
pp. 2036
Author(s):  
Hoon-Ki Lee ◽  
Tae-Kyoung Bang ◽  
Jeong-In Lee ◽  
Jong-Hyeon Woo ◽  
Hyo-Seob Shin ◽  
...  
Keyword(s):  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Analytical Method ◽  
Synchronous Machines ◽  
Magnetic Flux Density ◽  
Permanent Magnet Synchronous Machines ◽  
General Solutions ◽  
Rotor Eccentricity ◽  
Electromagnetic Characteristics

In this study, a magnetic field is analyzed using an analytical method and compared with the electromagnetic characteristics of 8-pole 9-slot and 8-pole 12-slot permanent magnet synchronous machines considering rotor eccentricity. The magnetic flux density and back electromotive force (EMF) are derived using perturbation theory and electromagnetic theory. First, the Fourier modeling of a permanent magnet is performed through magnetization modeling, and two analysis regions are set based on several assumptions for applying the analytical method. Accordingly, the governing equations of the analysis regions are derived in the form of Poisson and Laplace equations. In addition, the undefined coefficients of the general solutions are calculated through general solutions and appropriate boundary conditions, and the magnetic flux density and back EMF of the air gap region are derived based on the definition of the magnetic vector potential. The results obtained using the analytical method are compared with the finite element method and experimental results. In addition, we perform a torque analysis considering rotor eccentricity and analyze the torque ripple based on rotor eccentricity for two cases involving the pole/slot combination.

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