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 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 Analytical Model of the Slotless Double-Sided Axial Flux Permanent-Magnet Brushless Machines

2020 ◽  
Vol 12 (1) ◽  
pp. 38-50
Author(s):  
A. Ghaffari
Keyword(s):  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Analytical Model ◽  
Design Stage ◽  
Magnetic Flux Density ◽  
Magnetic Vector Potential ◽  
Axial Flux ◽  
Internal Rotor ◽  
Analytical Approaches

Analytical approaches, if possible, are suggested for saving the simulation time in the design stage of the electrical machines. This benefit is highlighted when the optimization issues including too many iterations are desired. Hence, this paper presents a 2-D analytical model for magnetic field distribution based on the sub-domain method in a slotless double-sided axial flux permanent-magnet (PM) brushless machines (AFPMBMs) with internal-rotor-external-stators. According to this method, the machine cross-section is divided into the appropriate number of sub-regions and the related partial differential equations (PDEs) extracted from Maxwell equations are formed for magnetic vector potential in each sub-region. Applying curl on the obtained results leads to calculating the magnetic flux density components in each sub-region. Based on the superposition theorem, the analytical procedure is utilized in the two separate steps where in the first step the magnetic flux is originated by only PMs with various magnetization patterns (i.e., parallel, ideal Halbach, 2-segment Halbach and bar magnet in shifting magnetization patterns) and the armature currents are zero. In the second step, all PMs are inactivated and only armature currents affect the magnetic flux distribution. Finally, the obtained analytical results are compared with those of the Finite element method (FEM) to confirm the accuracy of the proposed analytical model. The extracted results reveal the benefit of the analytical model for replacing instead of the FEM to predict the magnetic flux density component in the presented AFPMBMs in a shorter time.

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.

scholarly journals Design of a New 1D Halbach Magnet Array with Good Sinusoidal Magnetic Field by Analyzing the Curved Surface

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2522
Author(s):  
Guangdou Liu ◽  
Shiqin Hou ◽  
Xingping Xu ◽  
Wensheng Xiao
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Permanent Magnets ◽  
Air Gap ◽  
Curved Surface ◽  
Magnetic Flux Density ◽  
Sinusoidal Magnetic Field ◽  
The Magnetic Field

In the linear and planar motors, the 1D Halbach magnet array is extensively used. The sinusoidal property of the magnetic field deteriorates by analyzing the magnetic field at a small air gap. Therefore, a new 1D Halbach magnet array is proposed, in which the permanent magnet with a curved surface is applied. Based on the superposition of principle and Fourier series, the magnetic flux density distribution is derived. The optimized curved surface is obtained and fitted by a polynomial. The sinusoidal magnetic field is verified by comparing it with the magnetic flux density of the finite element model. Through the analysis of different dimensions of the permanent magnet array, the optimization result has good applicability. The force ripple can be significantly reduced by the new magnet array. The effect on the mass and air gap is investigated compared with a conventional magnet array with rectangular permanent magnets. In conclusion, the new magnet array design has the scalability to be extended to various sizes of motor and is especially suitable for small air gap applications.

scholarly journals The Air Gap and Angle Optimization in the Axial Flux Permanent Magnet Motor

1970 ◽  
Vol 110 (4) ◽  
pp. 25-29 ◽  
Author(s):  
C. Akuner ◽  
E. Huner
Keyword(s):  
Magnetic Flux ◽  
Permanent Magnet ◽  
Permanent Magnets ◽  
Air Gap ◽  
Magnetic Flux Density ◽  
Permanent Magnet Motor ◽  
Axial Flux ◽  
Flux Change ◽  
Torque Values ◽  
The Impact

In this study, the axial flux permanent magnet motor and the length range of the air gap between rotors was analyzed and the appropriate length obtained. NdFeB permanent magnets were used in this study. Permanent magnets can change the characteristics of the motor's torque. However, the distance between permanent magnets and the air gap will remain constant for each magnet. The impact of different magnet angles for the axial flux permanent magnet motor and other motor parameters was examined. To this aim, the different angles and torque values of the magnetic flux density were calculated using the finite element method of analysis with the help of Maxwell 3D software. Maximum torque was obtained with magnet angles of 21°, 26°, 31.4°, and 34.4°. Additionally, an important parameter for the axial flux permanent magnet motor in terms of the air gap flux was analyzed. Minimum flux change was obtained with a magnet angle of 26°. The magnetic flux of the magnet-to-air-gap is under 0.5 tesla. Given the height of the coil, the magnet-to-air-gap distance most suitable for the axial flux permanent magnet motor was 4 mm. Ill. 11, bibl. 4, tabl. 2 (in English; abstracts in English and Lithuanian).http://dx.doi.org/10.5755/j01.eee.110.4.280

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