United States

I. Introduction and Machine Modeling&lt;br/&gt;Fig. 1 shows the topology of a 6/5 wound field flux-switching machine (WFFSM), which is simple and reliable [1],[2]. However, the armature reaction and the excitation magnetic field are seriously coupled in WFFSM, resulting in a complicated mathematical model. To solve this problem, the mathematical model of 6/5 WFFSM is derived based on the precise inductance parameters considering magnetic saturation calculated by the frozen permeability method in this paper.&lt;br/&gt;The average electromagnetic torque equation is as follows:&lt;br/&gt;&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;e(av)&lt;/sub&gt; =3/2[&lt;i&gt;P&lt;/i&gt;&lt;sub&gt;r &lt;/sub&gt;&lt;i&gt;M&lt;/i&gt;&lt;sub&gt;f &lt;/sub&gt;&lt;i&gt;I&lt;/i&gt;&lt;sub&gt;m &lt;/sub&gt;&lt;i&gt;i&lt;/i&gt;&lt;sub&gt;f &lt;/sub&gt;cos(&lt;i&gt;β&lt;/i&gt;−&lt;i&gt;θ&lt;/i&gt;&lt;sub&gt;mb&lt;/sub&gt;)] − 9/4[&lt;i&gt;P&lt;/i&gt;&lt;sub&gt;r &lt;/sub&gt;&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;m1 &lt;/sub&gt;&lt;i&gt;I&lt;/i&gt;&lt;sub&gt;m&lt;sup&gt;2&lt;/sup&gt;&lt;/sub&gt;&lt;i&gt;&lt;sub&gt; &lt;/sub&gt;&lt;/i&gt;sin(2&lt;i&gt;β&lt;/i&gt;−&lt;i&gt;θ&lt;/i&gt;&lt;sub&gt;b(2)&lt;/sub&gt;)] (1)&lt;br/&gt;In this equation, &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;e(av)&lt;/sub&gt; is composed of constant components of the excitation torque and the reluctance torque, which are related to the current parameters &lt;i&gt;I&lt;/i&gt;&lt;sub&gt;m &lt;/sub&gt;, &lt;i&gt;i&lt;/i&gt;&lt;sub&gt;f &lt;/sub&gt;, &lt;i&gt;β ,&lt;/i&gt; and the inductance parameters &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;f&lt;/sub&gt;&lt;i&gt;&lt;sub&gt; &lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;θ&lt;/i&gt;&lt;sub&gt;mb&lt;/sub&gt;&lt;i&gt;&lt;sub&gt; &lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;m1 &lt;/sub&gt;, &lt;i&gt;θ&lt;/i&gt;&lt;sub&gt;b(2)&lt;/sub&gt;.&lt;br/&gt;II. Verification of Mathematical Model Results&lt;br/&gt;Fig. 2(a) and (b) show the comparisons of the derived torque model and finite-element analysis (FEA) results under different current densities and different electrical angles, respectively. It can be seen that the derived model results are in good agreement with the FEA results.&lt;br/&gt;Fig. 2(c) shows the error between the model and FEA results in average electromagnetic torque. In most areas, the error is within 0.2%. When the current density is 10 A/mm&lt;sup&gt;2&lt;/sup&gt;, the error reaches a maximum of 0.42% due to magnetic saturation.&lt;br/&gt;Fig. 2(d) shows the comparison between the model and the finite-element interpolation of the maximum electromagnetic torque. The error between them is no more than 0.45%.&lt;br/&gt;More derivations and verifications of the mathematical model of 6/5 WFFSM will be shown in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/303c502f39e665f492642f770254637f.jpg)

Fig. 1. Topology of a 6/5 WFFSM.

![](https://assets.underline.io/uploads/markdown_image/1/image/20f8007d70d71600a0b4749b4befd1fd.jpg)

Fig. 2. Verification of mathematical model results.
(a) The torque under different current densities when β=0°. (b) The torque at different electrical angles when the current density is 5A/mm2. (c) The error between the model and FEA results in average electromagnetic torque under normal operation. (d) The electrical angle of maximum electromagnetic torque under different current densities.

2022 Joint MMM-INTERMAG

Mathematical Modeling of Wound Field Flux-switching Machines Considering Magnetic Saturation

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

I. Introduction and Machine Modeling Fig. 1 shows the topology of a 6/5 wound field flux-switching machine (WFFSM), which is simple and reliable [1],[2]. However, the armature reaction and the excitation magnetic field are seriously coupled in WFFSM, resulting in a complicated mathematical model. To solve this problem, the mathematical model of 6/5 WFFSM is derived based on the precise inductance parameters considering magnetic saturation calculated by the frozen permeability method in this paper. The average electromagnetic torque equation is as follows: Te(av) =3/2[Pr Mf Im if cos(β−θmb)] − 9/4[Pr Lm1 Im2 sin(2β−θb(2))] (1) In this equation, Te(av) is composed of constant components of the excitation torque and the reluctance torque, which are related to the current parameters Im , if , β , and the inductance parameters Mf , θmb , Lm1 , θb(2). II. Verification of Mathematical Model Results Fig. 2(a) and (b) show the comparisons of the derived torque model and finite-element analysis (FEA) results under different current densities and different electrical angles, respectively. It can be seen that the derived model results are in good agreement with the FEA results. Fig. 2(c) shows the error between the model and FEA results in average electromagnetic torque. In most areas, the error is within 0.2%. When the current density is 10 A/mm2, the error reaches a maximum of 0.42% due to magnetic saturation. Fig. 2(d) shows the comparison between the model and the finite-element interpolation of the maximum electromagnetic torque. The error between them is no more than 0.45%. More derivations and verifications of the mathematical model of 6/5 WFFSM will be shown in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/303c502f39e665f492642f770254637f.jpg)

Fig. 1. Topology of a 6/5 WFFSM.

![](https://assets.underline.io/uploads/markdown_image/1/image/20f8007d70d71600a0b4749b4befd1fd.jpg)

Fig. 2. Verification of mathematical model results.
(a) The torque under different current densities when β=0°. (b) The torque at different electrical angles when the current density is 5A/mm2. (c) The error between the model and FEA results in average electromagnetic torque under normal operation. (d) The electrical angle of maximum electromagnetic torque under different current densities.

poster

In high-speed electrical machines, centrifugal forces within the rotor can be first-order constraints on electromagnetic optimisation. This can be particularly acute, even at modest speeds, in interior permanent magnet (IPM) machines in which magnets are retained entirely by the rotor core with no additional mechanical containment. A close-up of one such IPM is shown in Figure 1 with key dimensions defined. The magnets, which are profiled to reduce stress concentrations, act as dead-weights which must be resisted by the single-piece core. The electromagnetic and mechanical design pinch-points are the thickness of the outer rib that closes off the magnet slot (h1) and the separation between magnets (h2). Increasing h1 or h2 enhances mechanical support but at the expense of greater leakage flux. A combined mechanical-electromagnetic optimisation was undertaken using 2D finite element analysis (FEA) to establish an optimal combination of rotor diameter, h1 and h2 to maximise torque density in an 8-pole, 100kW PM machine with a base speed of 4,000rpm and an extended speed range up to 12,000rpm. A maximum localised core stress limit of 240MPa was specified, this being 60% of the yield strength for NO20 alloy. The optimisation was done by systematic consideration of the design space rather than by formal optimisation methods. Rotor diameters from 120mm to 180mm in 15mm increments were considered, and for each diameter values of h1 and h2 which meet the mamximum stress limit at 12,000rpm were identified by structural FEA. For viable combinations of h1 and h2, torque was calculated by FEA for both 30 and 24 slot stators using FLUX2D. The axial length was then scaled to produce rated torque of 239Nm allowing the torque density to be calculated. The optimised rotor design diameter is 165mm and is 103mm long with a fractional-slot winding in a 30 slot stator. The overall machine has an active mass of 40.8kg with corresponds to ~2.5kW/kg. The paper described this optimisation study in detail and draws on the results to explore the nature of the design trade-offs in such rotors and impact of core properties.

![](https://assets.underline.io/uploads/markdown_image/1/image/82808e7b50ab87b074e0d5a79d86f4cb.jpg)

Figure 1 - Close up cross-section of the IPM machine type

![](https://assets.underline.io/uploads/markdown_image/1/image/f2d1a89fc0a74a7d03d6b2d345689207.jpg)

Figure 2 - Finite element predicted flux density at full-load

Combined electromagnetic and mechanical optimisation of an interior permanent magnet rotor

Introduction When permanent magnet synchronous machines (PMSMs) are running, electromagnetic forces acting on stator teeth excite vibrations. The electromagnetic forces can be decomposed into concentrated forces at different frequencies by FFT. If phase differences between the concentrated force are zero, zero-mode vibrations are excited. The zero-mode vibrations are generally dominant in PMSMs. Some approaches on optimizing the structure have been proposed for reducing the zero-mode vibrations. In addition, injecting harmonic currents into windings is also effective. However, almost existing methods aims to decrease the amplitude of concentrated forces. This study investigated the method of changing the phase difference between concentrated forces to transform zero-mode vibrations to nonzero-mode vibrations. Methodology The investigation used a finite-element model of surface mounted PMSM with 12 poles 36 slots. Its permanent magnets were optimized for decreasing the amplitude of concentrated forces. The main frequency of the zero-mode vibration of the model is 6 times fundamental frequency. So different 5th harmonic currents were injected into windings for changing phases of concentrated forces. Then, concentrated forces before and after the injection were calculated respectively, and its phase differences were analyzed. Finally, the validity of the injection was verified by calculating vibrations. Result The phase difference between concentrated force was changed from 0 degree to 120 degree after the harmonic injection. Fig.1 shows the vibration before the harmonic injection, and Fig. 2 shows the vibration after the harmonic injection. The zero-mode vibration became the nonzero-mode vibration after harmonic injection and its amplitude was reduced. Conclusion Combining the optimization and the harmonic injection not only reduced the amplitude of the concentrated force, but also changed the phase difference between them. Thus, zero-mode of vibrations can be transformed into nonzero-mode vibrations, and their amplitudes are reduced significantly.

![](https://assets.underline.io/uploads/markdown_image/1/image/afce0516c99d87098d474a957f252dae.jpg)

Fig.1 Acceleration of the core surface without harmonics


![](https://assets.underline.io/uploads/markdown_image/1/image/7888e7f00d1f09385a0829218aa4f9be.jpg)

Fig.2 Acceleration of the core surface with harmonics

Reducing Zero- Mode Vibration for Permanent Magnet Synchronous Machines through Changing Phases of Concentrated Forces

I. Introduction PMSM is widely used in industrial fields because of the advantages of high power density and high efficiency [1-3]. However, torque ripple of PMSM can cause vibration and noise, which are not conducive to the smooth operation of the motor. Consequently, this paper proposes segmented asymmetrical stator design, which can reduce torque ripple without significant drop of average torque. II. Segmented Asymmetrical Stator Design A 6-pole 9-slot PMSM is carried out to analyze the proposed stator design. Then segmented asymmetrical design is carried out to optimize the stator. The main parameters are θ and W. θ is the degree from the middle of teeth to the middle of slot opening. W is the width of the slot opening. From the FEA analysis, it’s easy to find two torques which have opposite ripple phases. The first section is that when θ is 14° and W is 1.2 mm, and the second section is the mirroring of the first. The shapes of the sections and the torques are shown as Fig.1. According to the FFT analysis, the phases of sixth ripples of two sections are 65.9° and -109.3°, and the amplitudes are 0.1961Nm and 0.0763Nm. Adjusting the length ratio of the two sections to 2:5, then the amplitudes of sixth ripples are 0.056Nm and 0.0545Nm. The sixth ripples generated by two sections have the opposite phases and similar amplitudes, so the torque ripple of the whole motor can be decreased. The schematic of segmented asymmetrical stator and the torque waveforms are shown as Fig.2. III. Conclusion This paper proposes a segmented asymmetric stator structure. By optimizing the design parameters and adjusting the length of two stator segments, two torques with opposite ripple phases and similar ripple amplitudes can be obtained, so the two ripples can offset each other thus decreasing the torque ripple of the whole motor. This method doesn’t require PM shape optimization, so the average torque will not decrease significantly.


![](https://assets.underline.io/uploads/markdown_image/1/image/a728e6fa2214b0163d5f6e651ed53cfb.jpg)

Fig.1 Schematics of stator sections and waveform of torques


![](https://assets.underline.io/uploads/markdown_image/1/image/d1df39bc1bae3999d6a298bdff626d34.jpg)

Fig.2 Schematic of segmented asymmetrical stator and waveform of torques

Segmented Asymmetrical Stator of PMSM for Torque Ripple Reduction

1.Study and Objective This research proposes a single-phase tow pole N-S stator core alternator, which uses a neural network algorithm (NNA) to predict the harmonic and power characteristics. This study, the generator is composited with a two-pole N-S rotor and a dual-coil which is defined as surface mounted permanent magnet synchronous motor (PMSM) structure [1,2]. This generator, it is driven by an external motor to generate single phase power. The prediction and comparison of power and harmonic analyzed by the NNA method with sensor and single chip, can be obtained. 2.Theory and Method This research uses a small 2-pole synchronous alternator, as shown in Figure 1. The synchronous generator is need to be driven by the synchronous speed by an external motor. The internal magnetic flux distribution of the synchronous generator is not a regular sine wave. The induced potential of the armature winding is a distorted sine wave. This research proposes recurrent neural network (RNN) to observe as performance of the generator, as shown in the Figure 2. The dynamic storage tank has internal weights, which define the internal circulation connection, and link to the dynamic library of the output layer through the output weights. The input is the parameters of voltage (V), current (A), real power (P), apparent power (Q), reactive power (S), etc. as the neuron weights to the output [3]. 3.Experimental discussion and conclusion This research is a single-phase two-pole alternator, which produces an average AC voltage of 37V, current of 0.11A, power factor of 0.99, P of 4.11 watts, Q of 0.48VAR, and S of 4.14VA during operation. This research focuses on learning the trained neural network system with a recursive state neural network. From the perspective of THD (Total harmonic distortion) performance, the third, fifth, and seventh harmonic have the most serious impact on the generator, and the harmonic situation of the motor can be predicted through the neural-like recognition system.

![](https://assets.underline.io/uploads/markdown_image/1/image/e112c39634735785b6160ef4ee98d6a0.jpg)


Figure 1 The two pole single phase generator harmonic performance detection by NN method


![](https://assets.underline.io/uploads/markdown_image/1/image/fd619c022a600e24d7449959e7548ea2.jpg)


Figure 2 Harmonic measurement and power factor performance

Effects of Harmonic and Power of Single-Phase Two-Pole Permanent Magnet Synchronous Generator

Motors are replacing conventional internal combustion engines in many applications to deal with fossil fuel crises and to reduce carbon emissions, and permanent magnet synchronous motors (PMSMs) are widely used in many fields due to their advantages such as a high power and high efficiency [1]-[4]. The torque and speed curve (TN curve) can be obtained by performing repetitive time-consuming finite element analysis (FEA) for each current phase angle. Therefore, this paper proposes initial state FEA (ISF) to derive the TN curve of the PMSMs that can reduce the analysis time and guarantee satisfactory accuracy. The average torque of the PMSMs can be calculated using the average flux linkage of each phase coil and input current. For the ISA, to reduce the calculation burden, the FEA is conducted at the initial rotor position, which means the number of the step is one, and the TN curve of the PMSM can be calculated using the flux linkage value of the ISF. Fig. 1 shows the d and q axis transformed flux linkage waveform obtained by the ISF and full period FEA (FPF) when the number of the step is 120 and the application is surface-mounted PMSM. The ISF result is marked with pink circle and located on the point, where the electrical angle is zero. The d and q axis flux linkages obtained by the ISF have 0.38% and 0.09% error compared with average FPF result. Using the flux linkage and input current, torque can be calculated. Fig. 2 show the torque according to the current phase angle calculated with the ISF and FPF. The maximum error rate was 0.37% and occurred at zero electrical degree, and the average error rate of the torque according to the current phase was 0.33%. Considering the calculation time of the ISF was 83% reduced compared with the FPF, the accuracy of the ISF is acceptable. The detailed explanation of TN curve deriving process of various types of PMSMs and verification of the ISF will be described at the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/aa9194d1def7af1ce9a6c204a975feb8.jpg)

Fig. 1. Comparison of the d and q axis flux linkage obtained by the ISF and FPF.


![](https://assets.underline.io/uploads/markdown_image/1/image/d1d8c57ae0b899d2047dcd3123cbc6b8.jpg)

Fig. 2. Comparison of the calculated torque according to the current phase angle using the ISF and FPF.

Novel Method of Deriving Torque and Speed Curve of the Permanent Magnet Synchronous Motor Using Initial State Finite Element Analysis

I.Introduction The saliency is essential using the method of high-frequency injection-based sensorless control[1]. The saliency in the spatial impedance is built by the spatial saturation on the leakage flux paths in for the structurally symmetrical ac machines. In [2],the stator or rotor bridge is inserted to generate saliency but the performance of torque is not considered. This paper investigates that the design of slot builds up the saliency for the surface mounted permanent magnet machine (SMPMSM) and parameters of design can be guaranteed the performance of torque by the Back Propagation network (BP net). II.Design method for SMPMSM Saliency Considering the saturation of flux AC machine makes the difference of d- and q- axes leakage inductances so that the saliency is acquired. Lots of flux linkages penetrate stator slots from the flux distributions of SMPMSM in Fig. 1. Because of leakage linkages, the saliency is acquired but it will bring the deterioration of performance of torque . To guarantee the performance of torque,the approach of optimum design needs to be investigated.The parameters of structure of the slot are shown in Fig.2. III.BP net for optimal parameters The approach of BP net is used in order that parameters are optimum for the set of average torque and the saliency level. The design steps are shown in the followed flowchart in Fig.3. After 7463 samples being trained, the results of regressions of the designed BP net are shown in Fig.4. The optimum parameters are selected according to the minimum of absolute error between FEM and BP predict results. Herein, 18 sets of data are tested and the results are listed in TABLE 1. The assumption is that the excepted salient ratio is equal to 1.2, and the optimum scheme is the17th because that the error of (T/I)aver for the 17th scheme is minimum as shown in TABLE 1.

![](https://assets.underline.io/uploads/markdown_image/1/image/e1d061e39fe342265d1c58cadad6d010.jpg)

Fig.1.Flux distribution of SMPMSM

Fig.2.Diagram of structure of the slot

![](https://assets.underline.io/uploads/markdown_image/1/image/75ffc117dc582330a2f7bb367ebf916e.jpg)

Fig.3.Flowchart for design of parameter using the BP net approach

Fig.4.The regression result of designed BP net

TABLE 1 The results of torque current ratio and salient ratio by the FEM and BP predict

Design and Selection of Optimum Slot Parameters for SMPMSM Saturation Saliency with BP Net Approach

Although the inner rotor permanent magnet (IRPM) motor and the outer rotor permanent magnet (ORPM) motor have different rotor structures, the analysis method of magnetic field is the same. An analytical method for calculating the no-load magnetic field of ORPM motor in the stator static coordinate and the rotor motion coordinate is presented in [1], this analysis method is based on the transformation of coordinate system, and does not consider the change of rotor structure. The magnetic field distribution calculation method of surface mounted permanent magnet motor is presented in [2], but unified inner/outer rotor structural permanent magnetic motor magnetic field calculation method is not given. Equivalent calculation of IRPM motor and ORPM motor with the same structure size is of great significance for motor design and performance analysis. In this paper, an equivalent analytical calculation theory of IRPM motor and ORPM motor is presented. The IRPM motor and ORPM motor with the same geometric size are established, as shown in Figure 1. The effects of curvature effects on magnetic field calculation is considered [3], and establish a unified calculation model. The complete unified computational theory derivation will be presented in the full paper. In order to verify the correctness of the equivalent calculation theory proposed in this paper, the finite element method (FEM) model and equivalent calculation model of the two motors are established according to Fig. 1. The FEM results and equivalent model results of air gap flux density component, output torque and other electromagnetic performance are compared. The comparison results show that the unified calculation model established in this paper is correct and has high calculation accuracy. Fig. 2 shows the comparison between the FEM results of the normal and tangential components of no-load air gap magnetic flux density and the equivalent calculation model. The complete electromagnetic performance comparison results will be given in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/3b8f6fd695489b2e21fba76a685772ef.jpg)

Equivalent Analytical Calculation Theory of Inner Rotor and Outer Rotor Permanent Magnet Motor

With the advantages of high efficiency, high power density and wide constant power speed range, interior permanent magnet synchronous motor (IPMSM) is widely used in industrial, home applications, electric vehicles and other fields [1]. The magnetic equivalent circuit (MEC) model and finite element model (FEM) have been widely used in motor design. However, the MEC model has the disadvantage of low calculation accuracy, and the FEM model has the shortcomings of calculation time and occupy more computational resources [2]. The subdomain model is an optimal method for the initial design and optimization of the motor, which achieves a good compromise between the precision and the time of the magnetic field calculation [3]. In this paper, a hybrid model for magnetic field calculation considering rotor slots effect is proposed, which is improved the method in [3]. To take armature reaction into account, the IPMSM rotor is usually assumed to be a toothless model to simplify calculations [3], as shown in Fig.1. However, this simplified analytical model is difficult to accurately consider the armature reaction magnetic field. Considering that the relative permeability of the permanent magnet, a simplified and improved model of rotor structure is presented in this paper. The rotor is equivalent to a slotted rotor, when solving armature reaction magnetic field, the permanent magnet is equivalent to air. In order to verify the correctness of the subdomain model proposed in this paper, the analytical calculation results and the FEM results of the air gap magnetic flux density of the general simplified model and the simplified model in this paper are compared. The results show that the accurate subdomain model proposed in this paper has better accuracy. On the other hand, the computation time of the proposed subdomain model and FEM are compared. This paper proposed an improved simplified subdomain model, which reduced the computation time remarkably while maintaining high accuracy. The complete analytical method derivation will be presented in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/8f394af37c8ab0480c5a6e56276fd270.jpg)

An Improved Hybrid Method for Magnetic Field Calculation in Spoke PM machine

For non-contact, low-loss and controllable support, active magnetic bearings (AMB) are increasingly used in turbomachineries, continuously improving the operating speed and power density of turbomachineries [1,2]. However, as an active support system, improper design of the AMB controller may arouse modal resonance of the rotor-AMB system and lead to poor system performance. It is necessary to analyze the dynamic characteristics of the rotor-AMB system for the AMB controller design [3]. With disk structure, the rotor-AMB system has coupling vibration modes between the disks and the shaft. Traditional analytical modeling methods of rotor dynamics can hardly analyze the dynamics characteristics of the multi disks rotor-AMB system. To solve the dynamic modeling problem, this paper establishes the dynamic model of the multi disks rotor-AMB system of maglev turbomachineries using the two-dimensional finite element method based on Euler Bernoulli beam theory. As shown in Fig. 1, four virtual spring dampers are introduced in the radial direction to connect the disk and the shaft. The connection characteristics of the spring dampers are described by the angular stiffness and angular damping coefficient. The partition coefficient determines the radial relative position of the spring dampers and distributes the mass and inertia between the disk and the shaft, and the coupling model of the disks and the shaft is established. The angular stiffness and angular damping coefficients are identified from the system modes test data, and the division coefficient is obtained using multi-objective genetic optimization algorithm. Finally, a test rig is built as shown in Fig. 2(a) and the effectiveness of the proposed dynamic modeling method of the multi disks rotor-AMB system is verified through experiments as shown in Fig. 2(b).

![](https://assets.underline.io/uploads/markdown_image/1/image/a9dd064fec52630508d3b0718dfa755a.jpg)

Fig.1 Multi disks rotor system and coupling vibration model

![](https://assets.underline.io/uploads/markdown_image/1/image/7222e5b4114ddba636a2a24193328130.jpg)

Fig.2 Test rig and comparison between dynamic model results and experiments

Dynamic Modeling of Multi Disks Rotor System of Maglev Turbomachineries

Sleeve or bolting is applied to a permanent magnet synchronous generator (PMSG) to prevent defects caused by shattering. Bolting is more useful than the sleeve in manufacturing processes; however, the magnetic flux is reduced by the material characteristics of bolting. In addition, permanent magnet machines exhibit an overhang structure because the end effect causes leakage flux. Therefore, the axial length of the rotor must be considered in 3D analysis according to the overhang structure. However, the analysis is time-intensive for the 3D model with diverse and complex design variables. In this study, we performed a semi-3D analysis of a PMSG considering the bolting and overhang structure. The analysis time of a PMSG must be reduced because of the complex structure. Hence, we propose a semi-3D analysis for the 2D model by considering the operating point of the magnet in the 3D analysis. The operating point of the permanent magnet was calculated using magnetic energy analyses of the 2D and 3D models. Variations in the operating point were applied to the 2D analysis models, which were separated according to the permanent magnets and bolting regions. Then, a circuit parameter was derived using the semi-3D analysis and applied to the equivalent circuit of the generator. Characteristic analysis was performed using the superposition method. The results of the semi-3D model analysis were compared with those of the 3D model analysis. Figs. 1(a), (b), and (c) show the manufactured model. Fig. 2(a) shows the analysis model. Fig. 2(b) shows the variation in the operating point of the permanent magnet. Figs. 2(c) shows the output characteristic results from the comparison between the 3D and semi-3D models. We confirmed that the results of the semi-3D and 3D model analyses are congruent. Detailed data and experimental data is presented in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/b3d3b3536eccb58e234ae1715b043e4c.jpg)

Figs. 1. Manufactured model: (a) experimental set, (b) stator, (c) rotor

![](https://assets.underline.io/uploads/markdown_image/1/image/8a5fb512170e0ca742075f05c20bed37.jpg)

Figs. 2. (a) Analysis model, (b) demagnetization curve, and load power characteristic curve: (c) power-voltage curve

Semi 3D Analysis of a Permanent Magnet Synchronous Generator Considering Overhang Structure Using 2D Finite Element Analysis and Equivalent Magnetic Circuit

Mathematical Modeling of Wound Field Flux-switching Machines Considering Magnetic Saturation

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