France



1. Introduction&lt;br/&gt;Aiming at the nonlinear permanent magnet(NPM) degradation modeling problem in a type of differential magnetic system, firstly, for the NPM magnetization and demagnetization process, the first-order reversal curves of the permanent magnet of different segments is solved based on the Preisach model&lt;sup&gt;[&lt;/sup&gt;&lt;sup&gt;1&lt;/sup&gt;&lt;sup&gt;]&lt;/sup&gt;. Based on this model, a finite element simulation model of the electromagnetic system of a Small Rotation Actuator(SRA) is built, and the model is verified by actual measurement. Combining the simulation data with the physical model, a NPM degradation model is proposed. Based on this model, the single factor analysis of the electromagnetic system is carried out to determine the key parameters of SRA, and a fast calculation model of the degradation process is built. Kriging method&lt;sup&gt;[&lt;/sup&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;sup&gt;] &lt;/sup&gt;is used to perform error fitting, and the SRA magnetic system is optimized with the degradation degree of PEM as the target. The actual measurement results of the prototype are made to verify the effectiveness of the model.&lt;br/&gt;2. Permanent magnet degradation model based on Preisach theory&lt;br/&gt;Usually in the finite element simulation, the permanent magnet B-H curve is set according to the return line model&lt;sup&gt;[&lt;/sup&gt;&lt;sup&gt;3&lt;/sup&gt;&lt;sup&gt;]&lt;/sup&gt;, but there are still large errors for the magnetic system after the magnetization and demagnetization process. An operating point model of PEM is built based on the Preisach theory and applied to the finite element simulation model considering the process of magnetization and demagnetization. The simulation results of the model&#39;s suction characteristics have a smaller error with the actual measurement, and the simulation accuracy is significantly better than the traditional model. At the suction position, the error is the largest, which is only 6.7%. As shown in Figure 1.&lt;br/&gt;After the calculating of the initial state of the actuator, through accelerated tests, the permanent magnet magnetic performance degradation data with time and temperature is obtained, and the function relationship between the degradation degree of magnetic properties of the NPM and temperature and time based on data is deduced. Firstly, analyze the degradation mechanism of the NPM, and the demagnetization rate based on the surface magnetic intensity is determined as the characteristic parameter of magnetic properties of the NPM. The permanent magnets are subjected to degradation tests at different temperatures. Based on the measured data, select the logarithmic function model, combined with Preisach model to build degradation model based on Arrhenius equation. The calculation shows that the model is in good agreement with the measured data.&lt;br/&gt;3. Fast calculation model of electromagnetic system of SRA considering degradation&lt;br/&gt;In order to optimize the structure of the electromagnetic system, it is necessary to determine the key size parameters that have a greater impact on the performance of the electromagnetic system, and build a fast calculation model based on them. First, through the single factor simulation, the key size parameters are determined, and then based on the self-defined model, establish a fast calculation model that takes voltage, armature rotation angle, permanent magnet remanence, and the size parameters as input, and static suction torque as output. Kriging method is used for error correction. The calculation error using this model is not more than 3%, The average calculation time of a single group of electromagnetic torque is 1.07s, which meets the requirements of optimal calculation accuracy and speed.&lt;br/&gt;4. Optimized design and test verification of principle prototype&lt;br/&gt;Based on the completed permanent magnet degradation model and the fast calculation model of the static magnetic torque of the magnetic system which takes voltage, armature rotation angle, permanent magnet remanence, and size parameters as inputs, the optimization objective is the absolute value of the static magnetic torque of the armature at the release position when there are no excitation and pull-in voltage, and at the same time, the tolerance during production and processing is considered, the optimization problem is solved using the NSGAII algorithm. After optimization, the static magnetic torque of the armature at the release position is increased by 29.6% when no excitation is applied. The static magnetic torque under the pull-in voltage is increased by 41.5%, as shown in Figure 2.

**References:**

[1] S. R. Naidu, &quot;Simulation of the hysteresis phenomenon using Preisach&#39;s theory,&quot; in IEE Proceedings A - Physical Science, Measurement and Instrumentation, Management and Education, vol. 137, no. 2, pp. 73-79, March 1990.doi: 10.1049/ip-a-2.1990.0010.&lt;br/&gt;[2] Krige, D.G. A statistical approach to some basic mine valuation problems on the Witwatersrand[J]. Journal of the Southern African Institute of Mining and Metallurgy, 1952, 52(9): 201-203.&lt;br/&gt;[3] Huimin Liang, Jiaxin You, Wenying Yang, and Guofu Zhai. A Type of Subsection Model for a Permanent Magnet Bar and its Leakage Permeance Calculation Method in an Open Magnetic Circuit[J]. Journal of Magnetics, 2014, 19(1), 37-42.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b98f1ca2f62e7ea84fec576cbdf6047a.jpg)
Figure.1 Comparison of simulation calculation results based on Preisach theory and actual measurement results

![](https://assets.underline.io/uploads/markdown_image/1/image/cd381fccd3737f437a706bf0e3dd94c8.jpg)
Figure.2 The performance degradation calculation result of the SRA and the degeneration formula

INTERMAG 2021

 Nonlinear Permanent Magnet Degradation Model and its Application in Magnetic System Optimization

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1. Introduction Aiming at the nonlinear permanent magnet(NPM) degradation modeling problem in a type of differential magnetic system, firstly, for the NPM magnetization and demagnetization process, the first-order reversal curves of the permanent magnet of different segments is solved based on the Preisach model[1]. Based on this model, a finite element simulation model of the electromagnetic system of a Small Rotation Actuator(SRA) is built, and the model is verified by actual measurement. Combining the simulation data with the physical model, a NPM degradation model is proposed. Based on this model, the single factor analysis of the electromagnetic system is carried out to determine the key parameters of SRA, and a fast calculation model of the degradation process is built. Kriging method[2] is used to perform error fitting, and the SRA magnetic system is optimized with the degradation degree of PEM as the target. The actual measurement results of the prototype are made to verify the effectiveness of the model. 2. Permanent magnet degradation model based on Preisach theory Usually in the finite element simulation, the permanent magnet B-H curve is set according to the return line model[3], but there are still large errors for the magnetic system after the magnetization and demagnetization process. An operating point model of PEM is built based on the Preisach theory and applied to the finite element simulation model considering the process of magnetization and demagnetization. The simulation results of the model's suction characteristics have a smaller error with the actual measurement, and the simulation accuracy is significantly better than the traditional model. At the suction position, the error is the largest, which is only 6.7%. As shown in Figure 1. After the calculating of the initial state of the actuator, through accelerated tests, the permanent magnet magnetic performance degradation data with time and temperature is obtained, and the function relationship between the degradation degree of magnetic properties of the NPM and temperature and time based on data is deduced. Firstly, analyze the degradation mechanism of the NPM, and the demagnetization rate based on the surface magnetic intensity is determined as the characteristic parameter of magnetic properties of the NPM. The permanent magnets are subjected to degradation tests at different temperatures. Based on the measured data, select the logarithmic function model, combined with Preisach model to build degradation model based on Arrhenius equation. The calculation shows that the model is in good agreement with the measured data. 3. Fast calculation model of electromagnetic system of SRA considering degradation In order to optimize the structure of the electromagnetic system, it is necessary to determine the key size parameters that have a greater impact on the performance of the electromagnetic system, and build a fast calculation model based on them. First, through the single factor simulation, the key size parameters are determined, and then based on the self-defined model, establish a fast calculation model that takes voltage, armature rotation angle, permanent magnet remanence, and the size parameters as input, and static suction torque as output. Kriging method is used for error correction. The calculation error using this model is not more than 3%, The average calculation time of a single group of electromagnetic torque is 1.07s, which meets the requirements of optimal calculation accuracy and speed. 4. Optimized design and test verification of principle prototype Based on the completed permanent magnet degradation model and the fast calculation model of the static magnetic torque of the magnetic system which takes voltage, armature rotation angle, permanent magnet remanence, and size parameters as inputs, the optimization objective is the absolute value of the static magnetic torque of the armature at the release position when there are no excitation and pull-in voltage, and at the same time, the tolerance during production and processing is considered, the optimization problem is solved using the NSGAII algorithm. After optimization, the static magnetic torque of the armature at the release position is increased by 29.6% when no excitation is applied. The static magnetic torque under the pull-in voltage is increased by 41.5%, as shown in Figure 2.

**References:**

[1] S. R. Naidu, "Simulation of the hysteresis phenomenon using Preisach's theory," in IEE Proceedings A - Physical Science, Measurement and Instrumentation, Management and Education, vol. 137, no. 2, pp. 73-79, March 1990.doi: 10.1049/ip-a-2.1990.0010. [2] Krige, D.G. A statistical approach to some basic mine valuation problems on the Witwatersrand[J]. Journal of the Southern African Institute of Mining and Metallurgy, 1952, 52(9): 201-203. [3] Huimin Liang, Jiaxin You, Wenying Yang, and Guofu Zhai. A Type of Subsection Model for a Permanent Magnet Bar and its Leakage Permeance Calculation Method in an Open Magnetic Circuit[J]. Journal of Magnetics, 2014, 19(1), 37-42.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b98f1ca2f62e7ea84fec576cbdf6047a.jpg)
Figure.1 Comparison of simulation calculation results based on Preisach theory and actual measurement results

![](https://assets.underline.io/uploads/markdown_image/1/image/cd381fccd3737f437a706bf0e3dd94c8.jpg)
Figure.2 The performance degradation calculation result of the SRA and the degeneration formula

poster

1. In this paper, the optimal design of six phase surface inset permanent magnet synchronous generator and motor (SIPMSGM) is proposed considering the power factor and torque ripple. Because of the reluctance torque component by q-axis core thickness of rotor, SIPMSGM has the high torque density but the poor torque ripple. In order to reduce the torque ripple, the tapering is applied to magnet, but the torque density and power factor are decreased. Therefore, the optimal design is proposed using the performance map based on the tapering of magnet and q-axis thickness of core. First, pole-slot combinations are compared with the efficiency and power factor of SIPMSGM. Considering the efficiency and power factor, the initial SIPMSGM is selected for the optimal design. Based on the initial SIPMSGM, the optimal design is performed based on the optimal design parameters. considering the power factor and torque ripple. 2. Introduction As increasing the environment problems such as the greenhouse gas emissions, the ship demands the high efficiency and environmentally friendly. By this trend, the shaft generator and motor (SGM) of hybrid electric ship have been received the attention because of the energy efficiency, noise, and reliability [1]. Therefore, there are the studies on the torque ripple reduction, the high efficiency, the high power factor, and multi-phase winding. Six-phase surface inset permanent magnet SGM (SIPMSGM) has the high power density, the efficiency, the power factor, the reliability because of the reluctance torque and multi-phase winding [2], [3]. However, the torque ripple is increased by the reluctance torque ripple component. Therefore, the design method of the torque ripple reduction must be studied such as the tapering and winding method. This paper is the optimal design of six-phase SIPMSGM considering the power factor and torque ripple based on finite element analysis (FEA). Through the comparison with performance of pole-slot combinations, the initial SIPMSGM is selected. The optimal design parameters are selected as the q-axis core thickness and tapering of magnet. The selected optimal design parameters have the relationship with torque density, power factor, and torque ripple. Therefore, the optimal design is performed through the performance maps considering the objective function and constraints such as the power and voltage limit. Finally, the PTI/PTO performances of the optimal SIPMSGM are analyzed based on FEA. 3. Optimal Design of SIPMSGM SIPMSGM has the reluctance torque by the q-axis core thickness which determines by the q-axis inductance. The reluctance torque of SIPMSGM is expressed as Eq. (1). Tr =mP(Ld -Lq)idiq /4 (1) Where Tr is the reluctance torque, m is the number of phase, P is pole, Ld and Lq are d- and q-axis inductance, respectively, and id and iq are d- and q-axis current. From Eq. (1), the reluctance torque is determined by the q-axis inductance. Furthermore, the q-axis inductance increases as the q-axis core thickness increases. Fig. 1(a) shows the definition of the q-axis core thickness and FEA result according to the q-axis core thickness. As the q-axis core thickness increases, the torque is improved due to the reluctance torque, but the torque ripple increases. In order to reduce the torque ripple, another design parameter is required. The tapering of magnet can reduce the torque ripple because the sinusoidal magnetic flux density. Therefore, the tapering of magnet is selected as the optimal design parameter. Fig. 1(b) shows the definition of the tapering of magnet and FEA result according to the tapering of magnet. According to the tapering of magnet, the torque ripple is reduced as shown Fig. 1(b). As a result, the q-axis core thickness and tapering of magnet are selected as the optimal design parameters considering the torque density and ripple. The optimal design is performed using the performance maps according to the q-axis core thickness and the tapering of magnet. Fig. 2 shows the performance maps according to the design parameters. Considering the constraints of the power, the current density, and voltage limit, the optimal design point is selected to maximize the power factor and minimize the torque ripple. 4. Conclusion In this paper, the optimal design of SIPMSGM is proposed considering the power factor and torque ripple. First, the comparison of pole-slot combinations are performed considering the efficiency, the current density, and power factor. Furthermore, the optimal design is performed using performance maps according to the design parameters. As a result, the optimal design is selected considering the various objective functions. In the full paper, the pole-slot combinations will be added, and the characteristics according to the design parameters will be detail discussed. Moreover, PTI/PTO mode characteristics of the optimal SIPMSGM will be discussed.

**References:**

[1] A.G. Sarigiannidis, E. Chatzinikolaou, and A.G. Kladas, IEEE Trans. Transport. Electrific., Vol. 2, pp. 558-569 (2016) [2] B. Qu, Q. Yang, and Z. Li, Symmetry, Vol. 12, pp. 1-14 (2020) [3] Y. Sun, W. Zhao, and Y. Cheng, IEEE Trans. Veh. Technol., Vol. 69, pp. 9601-9612 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f6efef050c5ee46a9ed6500c452de060.jpg)
Fig 1. FEA result according to the design parameters (a) q-axis core thickness (b) tapering of magnet

![](https://assets.underline.io/uploads/markdown_image/1/image/2aa556999828ed6866f98c1398b5b5fb.jpg)
Fig 2. Performance map according to design parameters

 Study on the Design of Six Phase Surface Inset Permanent Magnet Synchronous Generator and Motor Considering the Power Factor and Torque Ripple

1) Introduction Slotless permanent magnet (PM) motors has no tooth and slot structure compared to the slot type motor. Hence, slotless PM motor, there are no cogging torque and low vibration, low noise, high power density, low iron loss [1]. However, since the slotless PM motor does not have a tooth-slot structure, the manufacturing process of the coil is complicated and a lot of time and cost is required. By using 3D printing technology, non-magnetic material tooth-slot structure can be produced, thereby solving the difficulties of manufacturing the conventional slotless PM motor winding. Using the proposed structure, it is structurally simple to manufacture the windings, and the electromagnetic characteristics of the conventional slotless PM motor can be equally taken. 2) Body In this paper, a design method for slotless PM motor that can replace the conventional slotless motor by conducting a study on the non-magnetic material tooth-slot structure using 3D printing technology is proposed. Additionally, in order to improve the power density on the proposed slotless PM motor, a design using an end-turn was conducted. In general slotted motors, cogging torque occurs because the permeance is uneven in the air gap, whereas in slotless PM motors, since slot structure do not exist, the air gap permeance is even and cogging torque does not occur. When the overall size is the equal, slotless PM motor can increase the fill factor more than slotted motor, which can result in greater Back-EMF. In addition, there are the moment of inertia of the rotor is low, so it is advantages high responsive, and the driving safety and control precision are high [2]. Despite these advantages of a slotless PM motor, it is more difficult to manufacture than a slotted motor. The windings of a general slotted motor are overlapped and made into ellipse shape. In this case, if each coil does not be made to the same shape, the coils are meshed. Eventually, this leads to a phase unbalance due to the shape of the windings [3]. In order to solve this difficulty of slotless PM motor manufacturing, a slotless PM motor design using 3D printing technology was conducted. By using 3D printing technology, a non-magnetic (polycarbonate material) tooth-slot structure is printed to structurally support the coil. Then, while having a structurally slotted structure, it is possible to take the power characteristics of a slotless PM motor in terms of electromagnetic. In this process, the response surface method (RSM) was used to conduct optimal design of the slotless PM motor applying 3D printing technology. The objective function was set as torque, power, and efficiency to derive the optimal values of major design parameters. In addition, when a winding is manufactured as the method of a slotted motor, the end-turn of the coil does higher than the stacking length of the stator, which occurs to leakage magnetic flux. An Additional design, high-height stator design, was conducted to improve the power density of the slotless PM motor by using magnetic flus leakage from the end-turn of the winding. A motor design algorithm was established by applying a high-height stator structure that increases the stacking length of the stator by the length of the end-turn that occurs when winding manufacturing. Slotless PM motor applied with this algorithm are designed, manufactured, and experimented. Conventional target slotless motors had a torque of 0.2Nm and a power density of 0.267W/g, whereas the improved slotless PM motor had a torque of 0.25Nm and a power density of 0.326W/g, indicating that the power characteristics were improved. 3) Conclusion In order to solve the difficulty of manufacturing the windings of a slotless Pm motor, a motor design incorporating 3D printing technology was conducted. A method combining the 3d printing injection molded structure with the stator in the motor was derived. When 3D printing injection molded structure was applied, the major design parameters were selected to derive optimal results using RSM to proceed with the optimal design of the motor. Furthermore, in order to improve the power density within a limited size, the design using the leakage magnetic flux of end-turn was additionally conducted. The motor design algorithm that goes through this process was established, and a prototype of the proposed motor was manufactured, and the finite element method (FEM) result and the actual experimental result were compared to verified that the power density was improved.

**References:**

Reference [1] Jung-Moo Seo, “Design and Analysis of Slotless Brushless DC Motor”, IEEE Transactions on Industry Applications, vol. 47, no. 2, pp. 730~735, (2011) [2] Nicola Bianchi, “High speed drive using a slotless PM motor”, IEEE Transactions on Power Electronics, vol. 21, no. 4, pp. 1083~1090, (2006) [3] Jin Hur, “Three-dimensional characteristic analysis of micro BLDC motor according to slotless winding shape”, IEEE Transactions on Magnetics, vol. 39, no. 5, pp. 2989~2991, (2003)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/89c9fda7101456ee4d7c9d86d982b4e4.jpg)
(3D image) proposed motor by applying 3d printing injection molded structure and high-height stator structure

![](https://assets.underline.io/uploads/markdown_image/1/image/df6d9f7c86df5cd279efd21aac97dc93.jpg)
(2D image) proposed motor by applying 3d printing injection molded structure

 A study on improving the power density of slotless motor applying 3D printing technology

The spoke type permanent magnet synchronous motor (PMSM), which is a general ferrite magnetic flux concentrated motor, has a low portion of reluctance torque at the total torque magnitude. Therefore, as a way to increase the reluctance torque, there is a double-layer spoke type PMSM that can maximize the difference in inductance between the d-axis and the q-axis. However, in the double-layer spoke type PMSM, cogging torque, torque ripple, and total harmonic distortion (THD) increase as reluctance torque is maximized, which is the main cause of vibration and noise. In this paper, a method is proposed that provides the same effect as skew without dividing stages of the permanent magnet by dividing the core of the rotor into two types so that it is easy to manufacture according to the number of stages unlike extant skew methods. Based on the method, the reduction of cogging torque and THD was verified by Finite Element Analysis (FEA). 1. Introduction The general interior permanent magnet synchronous motor (IPMSM) uses NdFeB magnets to take advantage of the high airgap magnetic flux density. However, it had an adverse impact on cost of the motor because there are fluctuation of the cost from limited sources of heavy rare earth. Therefore, for stable supply of permanent magnets, a lot of development of a spoke type permanent magnet synchronous motor (PMSM), which is a structure capable of concentrating magnetic flux by using a ferrite magnet having a low magnetic flux density, has been conducting. The spoke type PMSM concentrates the magnetic flux density and can replace the NdFeB magnet used in the extant PMSM with a ferrite magnet. However, in general spoke type PMSM, the portion of reluctance torque is low because the difference in inductance between the d-axis and the q-axis is not large. In order to further utilize this reluctance torque, a double-layer spoke type shape that can maximize the difference in inductance between the d-axis and the q-axis can be used to bigger reluctance torque to improve motor performance. However, increasing the reluctance torque increases cogging torque, torque ripple, and total harmonic distortion (THD), which in turn leads to vibration and noise problems. Therefore, the double-layer spoke type PMSM needs a design that can reduce cogging torque and THD. As a representative method, it can be solved by applying skew to the rotor, but the conventional method of applying skew is not a good method in terms of productivity because it is difficult to manufacture because it divides the stages of the permanent magnet. For ameliorate of the limitation, the shape of the rotor core is divided and cross-stacked into stack1 and stack2 so that the permanent magnet can be inserted in one shape as the conventional shape. Therefore, the shape of the rotor core is divided into stack1 and stack2 so that the permanent magnet can be inserted in one shape as before and cross-stacked. The stack1 cuts the left part fixing the permanent magnet, and the stack2 cuts the right part fixing the permanent magnet to apply the same effect as skew. In this paper, this is expressed as a core skew, and through this core skew, the design to reduce cogging torque, torque ripple, and THD is conducted while considering productivity. 2. Concept of Core Skew The core skew represents the stacking of only cores of opposite shapes when stacking the rotor cores of the motor. The contents of the basic theory are as follows. Fig. 1 shows stack No. 1 and stack No. 2, respectively. Due to the shape of the rotor core, the phases of the airgap magnetic flux density of stack No.1 and stack No.2 are shifted, and when the two stacks are synthesized due to the phase of the shifted airgap magnetic flux density. As shown in Fig. 2, the cogging torque decreases. Also Fig. 1 shows the shape of applying core skew to the conventional model by intersecting and stacking stack No. 1 and stack No. 2 . Through this core skew structure, research to reduce cogging torque, torque ripple, and THD is conducted. Most of the original skew research is conducted in 3D FEA, but since 3D FEA requires a lot of time, first calculate the optimal model using 2D FEA and then proceed with 3D FEA according to the number of steps considering 3D effect. The final result will be revealed on full paper. Acknowledgment This work was supported by the Technology Innovation Program (No. 20011495) funded By the Ministry of Trade, Industry & Energy(MOTIE, Korea), in part by the National Research Foundation of Korea (NRF) Grant funded by the Korean government. (No. 2020R1A2C1013724).

**References:**

 References: [1] D. G. Dorrell, M.-F. Hsieh, and A. M. Knight, “Alternative rotor designs for high performance brushless permanent magnet machines for hybrid electric vehicles,” IEEE Trans. Magn., vol. 48, no. 2, pp. 835–838, Feb. 2012. [2] M. M. Rahman, K.-T. Kim, and J. Hur, “Design and optimization of neodymium-free SPOKE-type motor with segmented wing-shaped PM,” IEEE Trans. Magn., vol. 50, no. 2, Feb. 2014, Art. ID 7021404. [3] S. I. Kim, S. Park, T. Park, J. Cho, W. Kim, and S. Lim, “Investigation and experimental verification of a novel spoke-type ferrite-magnet motor for electric-vehicle traction drive applications,” IEEE Trans. Ind. Electron., vol. 61, no. 10, pp. 5763–5770, Oct. 2014 [4] K.-C. Kim, “A novel method for minimization of cogging torque and torque ripple for interior permanent magnet synchronous motor,” IEEE Trans. Magn., vol. 50, no. 2, Feb. 2014, Art. ID 7019604. [5] C. Bianchini, F. Immovilli, E. Lorenzani, A. Bellini, and M. Davoli, “Review of design solutions for internal permanent-magnet machines cogging torque reduction,” IEEE Trans. Magn., vol. 48, no. 10, pp. 2685–2693, Oct. 2012. Z. Q. Zhu, Y. Liu, and D. Howe, “Minimizing the influence of cogging torque on vibration of PM brushless machines by direct torque control,” IEEE Trans. Magn., vol. 42, no. 10, pp. 3512–3514, Oct. 2006.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/20e073b7e9911fa2a37b3f23bac05e50.jpg)
Figure 1. Concept diagram of core skew

![](https://assets.underline.io/uploads/markdown_image/1/image/86facd303a35bb5abc3051c8f93d66b9.jpg)
Figure 2. Cogging torque comparison. (a) 1st core skew model cogging torque; (b) Comparison between the conventional model and 1st core skew model.

 A Study on Core Skew for Performance Improvement of Double-Layer Spoke Type PMSM

Most of the modern industrial machinery and automation equipment obtain a straight thrust by using a rotary motor and a gear, which is a power converter. However, in such power transmission, mechanical noise and friction are produced, and vibration loss occurs. Thus, position control, system, and efficiency deteriorate [1]. In contrast, linear motors do not require gears, ball screws, racks, or pinions, which are used for linear motion conversion in general rotating equipment. Hence, they are not affected by problems such as heat generation, inertia, and stiffness deterioration. Thus, they can function at high speed and offer high precision. Among linear motors, permanent-magnet linear synchronous motors are used in various types of equipment, such as compressors, pumps, and Stirling low-temperature coolers, because of their high efficiency, thrust density, and excellent control performance [2]. However, a disadvantage of the permanent magnet linear synchronous motor is the side force, which is inevitably generated by the magnetically coupled structure of the stator and mover. The side force imparts eccentricity to the rotor. Eccentricity of the rotor is that the center of the shaft is not located at the center of the stator. This causes noise and vibration during operation, and in severe cases, renders the motor inoperable [3]. Eccentricity thus decreases the reliability of a system. Once design and manufacture are completed, a spring with higher rigidity should be used to reduce eccentricity. Therefore, side-force reduction is essential at the design stage to secure system reliability and prevent system complexity. In this study, an optimal design of the side force of a short-stroke linear oscillating actuator (LOA) was performed. Owing to the numerous design variables, the optimum design of the motor requires a considerable analysis time. Particularly, the required analysis time increases exponentially for three-dimensional analysis, such as that required for an LOA, if stochastic algorithms such as genetic and particle swarm optimization algorithms are used. To address this problem, approximate optimal design methods that require relatively fewer experimental points have garnered attention [4]. In this study, the response surface methodology (RSM) was used for the optimal design. The RSM can determine the curvature effect and yield a precise optimal solution through repetition of center points and axis points. The main factors causing the side force were investigated through factorial design in this study [5]. The residual magnetic flux density of the permanent magnet, the inner and outer air gaps, and the magnet fill factor were selected as the optimization variables based on factorial design. Based on the selected variables, experimental points were selected via central composite design, which is most commonly used in response surface design. The side force was set as the objective function of the optimization. The back EMF of the original model was set as a constraint to minimize the reduction in the output power. The reliability of the optimization was determined through FEM and experiments involving the manufactured initial LOA model. Fig. 1 (a) show the 3-D analysis model and manufactured initial LOA model. The LOA consists of an outer core, inner core, a coil, and moving magnet. The moving magnet performs reciprocating motion along the z-axis and generates an electromagnetic force. Fig. 1 (b) shows the experimental setup for the LOA. Fig. 2 (a) and (b) show the flux paths of the initial and optimized LOA models, respectively. In the optimized model, the residual magnetic flux density of the permanent magnet was reduced from 1.3 to 1.1, the inner air gap was increased from 0.3 mm to 0.5 mm, and the magnet fill factor was increased from 0.7 to 1. Fig. 2 (c) presents the side force regression model obtained via RSM according to the magnet specifications. Fig. 2 (d) shows the side force optimization result. The side force was reduced by 50% and the back EMF was maintained at 90% when compared with those of the initial LOA model. Further discussions, analysis results, and experimental results are presented in the final paper.

**References:**

[1] I. Boldea and S. A. Nasar, IEEE Trans. Energy Conversion, vol. 14, no.3, pp. 712–717, [2] Chang-Woo Kim, Gang-Heyon Jang, Kyung-Hun Shin, IEEE Transactions on Applied Superconductivity, VOL. 30, NO. 4, June 2020 [3] Navneet Behra, IEEE International Conference on Technologies for Smart-City Energy Security and Power (ICSESP-2018), March 28-30, 2018 [4] Yoshifumi Okamoto, Yusuke Tominaga, Shinji Wakao, IEEE Transactions on Magnetics, VOL. 50, NO. 2, February 2014 [5] W. Yim, K. An, J. Seo, D. Woo and H. Jung, 2010 International Conference on Electrical Machines and Systems, Incheon, 2010, pp. 1268-1272.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9397bc5b548bcd9fa939d9960529c183.jpg)
Fig. 1. (a) 3-D analysis model and manufactured initial LOA model, 
(b) Initial LOA model experiment setup

![](https://assets.underline.io/uploads/markdown_image/1/image/9576aa6fe502b82b6c58b427eafd3f23.jpg)
Fig. 2. (a) flux path of initial model, (b) flux path of optimized model, (c) side force according to 
magnet specifications (d) side force reduction result

 Optimal design of short-stroke Linear oscillating actuator for minimization of side force by using response surface methodology

Due to the constant flux of slot PM for relieving-saturation, the effect is limited when it is applied to the variable biased flux machine(VBFM). To address this issue, low coercivity permanent magnet (LC-PM) is applied to slot PM of transverse variable flux tubular linear machine (TVFTLM) to accomplish the dynamic relieving-DC-saturation in the stator core in this paper, and the method to verify the value of magnetizing current is also illustrated. The novel transverse variable flux tubular linear memory machine (TVFTLMM) has merits of higher thrust density, higher overload capacity and lower leakage flux. The key to achieve this is that the remanence of the LC-PM can be varied in coordinate with the magnetizing current which is adjusted online for dynamic-relieving-DC-saturation. I. Introduction Locating tangential magnetization PM at slot opening of motor is an effective method to relieve saturation in the stator core [1]. However, the saturation in the stator core of VBFM is variable, while the flux excited by conventional slot PMs are constant. Therefore, conventional relieving-DC-saturation method cannot cancel VBFM saturation perfectly and may cause further leakage flux. The low coercivity PM (LC-PM) such as Al-Ni-Co is a kind of material whose magnetic status is relatively easy to change via pulsing magnetizing current [2]. Therefore, the LC-PM is a quite suitable candidate for VBFM to alleviate saturation in the core. The transverse flux tubular machine (TFTM) achieving much smaller normal force and decoupling three phases windings has wide application in industry [3]. On the other hand, It is also a kind of VBFM suffered from variable saturation and leakage flux. In this paper, LC-PM material whose magnetization can be regulated online is applied to a novel TVFTLM to increase its overload capability. In this way, when DC excitation changes, the magnetization degree of LC-PM can be adjusted accordingly to cancel the saturation in the core. The methodology of this online flux regulation is also discussed in this paper. II. Design Mechanism and Analysis Method The stator of the motor is composed of 3 separate parts, which have 12 teeth and is arranged alternately with armature windings, field windings and magnetizing windings wounded on teeth, as shown in the Fig.1. The other parts of phase B and C is arranged in line with phase A, and the distance between two neighboring phases is 2kτ+2/3τ, where k is an integer, and τ is pole pitch. The mover of this proposed motor is composed of the laminations with stack thickness of τ, and switched by 60 degrees every τ distance. The LC-PMs are located at slot opening. Together with armature windings, the magnetizing windings are wound on the armature teeth. When armature teeth A1, A3 and A5 aligned with mover teeth at z=0, the magnetic loop of A2, A4 and A6 is open, and the pulsing magnetizing current is applied on M2, M4 and M6 to generate magnetization flux for part of slot LC-PMs, as shown in Fig.1 (a). Vice versa, at z=τ, current is applied on M1, M3 and M5 to magnetize the rest of LC-PMs, which is shown in Fig.1 (c). Fig.1 (e) compares the distribution of no-load flux linkages with constant PMs (CPM) and LC-PMs, where TVFTLM with changeable LC-PMs could cancel the DC components of flux linkages perfectly, regardless of the value of DC excitation. The hysteresis model presented in Fig.1 (f) could demonstrate the operation points of the LC-PMs intuitively. The operation points of the LC-PMs can be determined by magnetic field intensity Hmk and load line. With different excitation modes (e.g., light, rated and over excitation), the operation points of the slot PM can be switched among P1, P2, and P3 by applying magnetizing/ demagnetizing current. Hysteresis model is utilized and coupled with transient finite element method (FEM) for calculation. III. Design Consideration and Results The main initial design parameters of the proposed motor are set as follows. Radius of outer stator Rso=50mm, the split ratio rsp=0.6, field windings turns per slot Ndc=75, armature winding turns per slot Nac=75, and the ratio of pole arc between stator and mover rpole=0.9. The coercivity of the LC-PMs Hc1 is set as -119366 A/m and the remanence Br= 1.05T. In Fig.2, no-load magnetic field distribution of proposed TVF-TLM with LC-PMs and CPMs are compared. It can be seen that with same DC-excitation, the flux density in the core with LC-PMs is lower than that with CPMs regardless of DC excitation, expecially when the excitation current comes to 12A. Therefore, from the perspective of flux distribution, comparing with CPMs, the LC-PMs could further alleviate saturation and improve the performance of motors. IV. Conclusion In this paper, a dynamic relieving-DC-saturation transverse variable flux tubular linear memory machine (TVF-TLMM) is proposed. The memory LC-PMs are innovatively applied on the biased-flux TVF-TLMM to relieve saturation in the core dynamically. The comprehensive design consideration and optimization of the proposed machine will be presented in the full paper. Acknowledgement This work was supported in part by grants from the Hong Kong Research Grants Council, Hong Kong, China, under Project PolyU 152058/17E and PolyU 152143/18E.

**References:**

 [1] X. Zhao, S. Niu and X. Zhang, IEEE Trans. Ind. Electron., vol. 67, p.9571 (2020) [2] H. Yang, Z. Q. Zhu and H. Lin, IEEE Trans. Ind. Electron., vol. 65, p.9168 (2018) [3] X. Zhao and S. Niu, IEEE Trans. Ind. Electron., vol. 66, p. 494 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/34f8ce89ca05b40b527e71e518f407ce.jpg)
Fig.1 Operation Principle of the Motor (a) 2D Cross section at z=0 (b) 3D Model at z=0 (c) 2D Cross section at z=τ (d) 3D Model at z=τ (e) Operation Principle of LC-PMs (f) Hysteresis Model

![](https://assets.underline.io/uploads/markdown_image/1/image/1fc48a4f2dc72ffd1ead3ee4d3743725.jpg)
Fig. 2. Field Distribution. (a) Idc=3A (LC-PMs) (b) Idc=3A (CPMs) (c) Idc=6A (LC-PMs) (d) Idc=6A (CPMs) (e) Idc=12A (LC-PMs) (f) Idc=12A (CPMs)

 Design and Optimization of a Novel Dynamic Relieving-DC-Saturation Transverse Variable Flux Tubular Linear Memory Machine

In recent years, aging of social infrastructure such as bridges and industrial tanks has become a problem. Therefore, robots capable of working in difficult environments are desired. In this study, a novel magnetic actuator system capable of an appearance inspection on complex steel structures with steps was proposed. Fig. 1 shows a diagram of the magnetic actuator capable of a reciprocating movement on a magnetic substance. The magnetic actuator consists of a vibration component, an acrylic frame, four shape memory alloy (SMA) coil springs, eight electrodes, an acrylic semi-cylinder, an acrylic slider and two permanent magnets attached to the bottom of the frame. The vibration component consists of a permanent magnet of ring type, a translational spring, an electromagnet with iron core of the bobbin-type proposed by the authors in a previous paper [1]. The permanent magnet of ring type is NdFeB and is magnetized in the axial direction. The permanent magnet of ring type has an outer diameter of 12 mm, an inner diameter of 9 mm, and a thickness of 8 mm. The surface magnetic flux density measured using a tesla meter was 322 mT. The translational spring was a stainless steel compression coil type having an outer diameter of 12 mm, a free length of 25 mm. The bobbin-type electromagnet was inserted in the translational spring. The actuator has a height of 42 mm, a length of 40 mm, a width of 38 mm, and a total mass of 19 g. This actuator can move in the direction that the vibration component is tilted. Therefore, as shown in Fig. 1, the actuator support part was made to be rotatable. The reciprocating movement of the actuator was realized by tilting the vibration component using the expansion and contraction of four shape memory alloy (SMA) coil springs. After the vibration component is tilted, the acrylic semi-cylinder and the acrylic slider are held by the attractive force of the two permanent magnets even if the input current to SMA coil spring is stopped. Fig. 2 shows the direction of movement due to the expansion and contraction of SMA coil springs. Fig. 3 shows the relationship between the load mass and the vertical upward speed for two directions of movement. This figure shows that the actuator is able to climb upward at 32.1 mm/s while pulling a load mass of 80 g. Fig. 4 shows the relationship between the load mass and the efficiency. The maximum efficiency of the actuator was 28.1 %. In both figures, almost the same movement characteristics were shown even if the direction of movement changes. There are many complicated steps in steel structures such as bridges and tanks. In order to realize the movement of these steps, a magnetic actuator system has been proposed in which two actuators are arranged on flexible silicon rubber as shown in Fig. 5. In this actuator system, two acrylic discs and a ring-type permanent magnet are combined at both ends of the silicon rubber. In addition, two permanent magnets A and B are arranged on the silicon rubber. The total length of this actuator system is 307 mm, and the total mass is 70 g. The diameter of the acrylic disc, the attractive force and position of the permanent magnet, and the rigidity and length of the silicon rubber material were determined in consideration of both step movement and traction characteristics for the actuator system. Details will be shown in a full paper. Fig. 6 shows a situation in which the actuator system moves the step of height H by the cooperative operation of two actuators. This actuator system can move on the step surface very smoothly. The moving situation will be shown as a video at the presentation. Table 1 shows the relationship between the tilt angle of the actuator system α and the speed when the step length L is fixed at 200 mm and the height H is changed to 15 mm, 20 mm, and 25 mm, respectively. The measurement distance with the step length was set at 600 mm. The tilt angle was varied from α = -90° (straight down) to α = 90° (straight up). This actuator system can move in the complex steel structure with the step height of 25 mm.

**References:**

[1] Hiroyuki Yaguchi and Shun Sakuma : Improvement of a Magnetic Actuator Capable of Movement on a Magnetic Substance, IEEE Transactions on Magnetics, Vol. 52, No. 7, Article#: 10.1109/TMAG.2016.2533433 (2016).

**Images:**

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![](https://assets.underline.io/uploads/markdown_image/1/image/d7f5946c566ae4650e385034679c76ce.jpg)

 A novel magnetic actuator system for appearance inspection of complex iron structures

Linear oscillating actuators (LOAs) are devices that make reciprocating movements at a certain frequency. Therefore, LOAs can be classified according to the movement type, such as the moving-core type, moving-coil type, and moving-magnet type. The moving-core-type LOA has the advantage of easily increasing the permanent magnet usage and the output, but the price of the LOA becomes more expensive as the magnet usage increases. The moving-coil-type LOA has the highest output density compared to other types, but its disadvantage is that it is difficult to manufacture. Most LOAs used in practical applications are of the moving-magnet type. The moving-magnet type makes the mover light and suitable for high-speed operation, which is the most efficient way of increasing LOA output [1]. A novel design of a single-phase short-stroke LOA has been developed for application in refrigeration compressors and other similar equipment because of its advantages, such as high transmission efficiency and simple structure [2]. However, the performance of the LOA is difficult to evaluate due to its reciprocating linear motion. Additionally, unlike rotating machines, measuring the magnetic force of LOAs can be complicated. Therefore, LOA analysis and performance evaluation are essential not only via applying the finite-element method (FEM) analysis but also experimental verification. Experimental studies of the electromagnetic force and output of LOAs have been conducted by various researchers [3]. In this study, the structural and magnetic characteristics of a moving-magnet-type LOA are determined and verified through the analysis and experiment of mover stroke and current based on the operating frequency and applied voltage. Because the operation of the LOA is most efficient at the resonance frequency, it is essential to consider the operating frequency in the electromagnetic design. Finally, the change of the resonance frequency according to the mechanical load is confirmed, and the most efficient operation range is confirmed. Figure 1(a) illustrates the structure of the LOA. The LOA is fixed to the outer core, coil, and inner core, and has a structure in which the permanent magnet makes a linear reciprocating motion in the z-axis direction. The flux path and flux density are depicted in Figure 1(b). The permanent magnet makes a reciprocating motion in the z-axis direction and changes the direction of the main magnetic flux flowing in the outer core, which generates a counter electromotive force. Figure 1(c) shows a manufactured LOA component and experimental set. AC power is applied through the function generator and the voltage is amplified through the amplifier. The mover's stroke is measured through a displacement sensor. Figure 2(a) displays an analysis model considering the mechanical load of the LOA. The LOA is analyzed considering both the electrical system and mechanical load. The mechanical loads include the spring coefficient, damping coefficient, and mover mass. Under no-load conditions, the spring coefficient and mover mass act as mechanical loads, and the effects of force and damping from the loads are negligible. Figure 2(b) shows the current and stroke based on the applied voltage and frequency. Both cases show the most efficient operation at the resonance frequency. Therefore, the operating frequency of the LOA should be similar to the resonance frequency, and the LOA operation becomes less efficient as the difference between the resonance frequency and operating frequency increases. Detailed analysis and experimental results will be presented in the full paper.

**References:**

[1] J. Wang, D. Howe, and Z. Lin, “Design Optimization of Short-Stroke Single-Phase Tubular Permanent-Magnet Motor for Refrigeration Applications,” IEEE Trans. Industry App., vol. 57, no. 1, pp. 327–334, Jan., 2010. [2] T. Ibrahim, J. Wang, and D. Howe, “Analysis and Experimental Verification of a Single-Phase, Quasi-Halbach Magnetized Tubular Permanent Magnet Motor wit Non-Ferromagnetic Support Tube,” IEEE Trans. Mag. vol. 44, no. 11, pp. 4361-4387, Nov., 2008. [3] Z. Q. Zhu, and X. Chen, D. Howe, and S. Iwasaki, “Electromagnetic Modeling of a Novel Linear Oscillating Actuator,” IEEE Trans. Mag. vol. 44, no. 11, pp. 3855-3858, Nov., 2008.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/78af974295edeea6e81a05823492bbd8.jpg)
Fig. 1 (a) Analysis model of linear oscillating machine, (b) magnetic flux density and flow of linear oscillating machine due to PM, (c) outer core and experimental set.

![](https://assets.underline.io/uploads/markdown_image/1/image/54e8c4440204d478ec6729ed88cb4fd0.jpg)
Fig. 2 (a) Analysis model of linear oscillating machine considering mechanical load, (b) stroke and current analysis results and experimental results based on applied voltage and frequency

 Operating Characteristic Analysis and Verification of Short-Stroke Linear Oscillating Actuators Considering Mechanical Load

I. Introduction The electrical energy can be directly converted to the linear mechanical energy through linear motors. Containing no transmission mechanisms, linear motors have many remarkable advantages, such as high speed and high positioning accuracy. Therefore, linear motor servo systems have received more and more attentions in academic and industrial fields in recent decades [1-6]. However, the testing methods for the linear motor servo systems is not well elaborated and researched compared with conventional rotary motors. Among all the indexes of the linear motor servo systems, the position loop stiffness defined as the ratio between the dynamic disturbing force and the consequent maximal position deviation is an important one to evaluate the closed-loop performances of linear motor servo systems. In the conventional position loop stiffness testing systems, the weight lifting, hydraulic, and the rotating motor plus ball screw are three common loading methods. Nevertheless, some inherent defects exist in these loading methods, such as low repeatability, complex system structure, and low dynamic response. In [7], a novel position loop stiffness testing method for the linear motor servo systems is proposed, in which a high thrust linear voice coil motor is served as the loading motor. This paper will focus on the electromagnetic analysis and cooling design of the proposed high thrust linear voice coil motor. II. Configuration and Model The configuration of the position loop stiffness testing platform for linear motor servo system is shown in Fig. 1. The linear voice coil motor is connected to the tested linear motor by a load sensor, and the tested linear motor operates in position loop state. The thrust generated by the linear voice coil motor can be seen as a step disturbance for the linear motor servo system. Therefore, low thrust ripple performance of the loading motor is required to improve the testing accuracy of position loop stiffness. The cooling structure is also needed to increase the force density and decrease the motor mass. Basically, the magnetic charge method can be used to calculate the magnetic flux density of permanent magnet, and the image method is applied to consider the influence of ferromagnetic boundary [8-9]. The thrust expression with different parameters is obtained using Lorentz force equation. III. Thrust Analysis and Cooling Design In this section, the influence of the parameters on the thrust and thrust ripple are analyzed based on the established model. To enhance the structural strength of primary, two layers arrangement are selected and two layers coils are inserted into a common coil frame. Additionally, the cooling structure for the high thrust linear voice coil motor is designed. The water channels are evenly distributed in the coil frame. To further improve the cooling effect and realize thermal shielding of primary, two aluminum sheets are fixed onto both sides of the primary with heat-conducting glue. The cooling effect is analyzed using temperature field simulation. IV. Experiment To verify the related analysis, a prototype of the high thrust linear voice coil motor is manufactured. The thrust linearity test shows that the thrust varies linearly with the current. The rated thrust is 800N when the current is 9.6A. the experiment values of thrust match well with the ones from analysis and FEM. The thrust ripple within 4mm displacement is less than 1%, which could provide a nearly constant thrust during stiffness testing. In addition, the temperature test is achieved. The temperature rises of the primary with and without the cooling water are compared. The aluminum sheets could quickly transfer the coils heat to the coil frame, and the surface temperature of primary with cooling is 37 degrees under 12A coil current. V. Conclusion In this paper, a linear voice coil motor is analyzed and designed. Considering the practical requirements in the stiffness testing of linear motor servo system, high thrust and low thrust ripple are two critical indexes. Additionally, the effective cooling structure is important. The related experimental results show a good agreement with the analytical model and finite element simulation results.

**References:**

[1] W. Zhao, J. Zheng, J. Wang, IEEE Trans. Ind. Electron., vol. 63, no. 4, pp. 2072–2082, Apr. 2016. [2] Q. Lu, Y. Li, X. Huang, IEEE Trans. Magn., vol. 51, no. 11, pp. 8108804, Nov. 2015. [3] Y. Fujimoto, T. Kominami, and H. Hamada, IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1383–1392, Mar. 2009. [4] Y. Gao, R. Qu, J. Li, D. Li, and F. Chen, IEEE Trans. Magn., vol. 53, no. 6, 7001905, Jun. 2017. [5] Z. Liu, W. Zhao, J. Ji, IEEE Trans. Magn., vol. 51, no. 7, 8105807, Jul. 2015. [6] H. Zhang, B. Kou, Z. Q. Zhu, IEEE Trans. Ind. Electron., vol. 65, no. 12, pp. 9853–9862, Dec. 2018. [7] H. Zhang, B. Kou, Y. Zhou, ICEMS Conference, Harbin, 2015. [8] S. A. Nasar and G. Y. Xiong, IEEE Trans. Magn., vol. 24, no. 3, pp. 2038–2044, May 1988. [9] S. H. Lee, S. B. Park, S. O. Kwon, IEEE Trans. Magn., vol. 42, no. 4, pp.1327-1330, Apr. 2006.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d4e8d9f3608916dcdb7f56ffad01ea1f.jpg)
Fig. 1. Configuration of the position loop stiffness testing platform for linear motor servo system.

![](https://assets.underline.io/uploads/markdown_image/1/image/a359460ad8f8de83524842499e11821e.jpg)
Fig. 2. Prototype of the high thrust linear voice coil motor.

 Design and Analysis of a High Thrust Linear Voice Coil Motor using for the Stiffness Test of Linear Motor Servo System

The electrodynamic suspension system (EDS) is used for levitation and guidance[1]. The principle of the EDS system is electromagnetic induction. This system has basically no damping factor against the vertical oscillation of the bogie. Once the vertical oscillation of the bogie occurs by the external disturbance, it does not converge immediately. Thus, the additional damping system is needed. Fig.1 shows the coils for the EDS system[2]. Passive damper system is installed to improve the damping factor. However, the damper coil current of this system is delayed by its self-inductance. When the direction of the bogie oscillation is same to the direction of the damping force, the damper coils amplifies the oscillation. To improve the damping factor, the semi-active damper system is installed. The damper coils are switched according to the oscillation velocity of the bogie and the magnetic force generated by the damper coils. The operation velocity of the train is v = 120[m/sec]. At this speed, the bogie is capable of levitation stability because the electromagnetic force is large. However, at low speed such as the velocity v = 60 - 80[m/sec], the damping factor is small. So, it is difficult to keep levitation stability[3]. This paper examines optimal shape and installation position of the damper coil at the low speed. As a typical application of the EDS system, this paper discusses about the JR Maglev system. EDS system is used for levitation and guidance. The levitation force is generated by the SC coil attached to the bogie. The eight-figure null-flux connection is used for the levitation coils on the ground. When the bogie passes the center of the eight-figure coils, the levitation force is generated to the bogie. The current induced in the levitation coils is calculated. EDS system has an air coil system and modeled as electric circuits. The mutual inductance between the SC coils and levitation coils is calculated from the electric circuit equations. And, to solve the electric circuit equations, the current of the levitation coils is calculated. Also, the motion of the bogie is calculated from the motion equations. By repeating these procedures, the transient motion of the bogie is given. Runge-Kutta method is used to solve these equations[4]. The optimal shape of damper coils is analyzed using the energy consumption. The bogie is forced to oscillate in the vertical direction and run at the velocity v = 60 - 80[m/sec]. The bogie oscillates based on free oscillation of the bogie without the damper coils. The energy consumption of the damper coil in one cycle of the oscillation is considered to evaluate damping factor. When the energy Wt takes negative peak, the damper coils are optimal shape. According to previous research[5], the width of the damper coils indicated as optimal around the width w = 0.8[m] because change in the number of flux linkage is greatest. Therefore, the width of the damper coils is considered at w = 0.7 - 0.9[m]. The height of the damper coils indicated as optimal around the height of the levitation coils because electromagnetic force works between the damper coils and levitation coils. Therefore, the height of the damper coils is considered at h = 0.30 - 0.40[m]. Fig. 2(a) shows energy consumption. the weight of the damper coil is constant at 10.31[kg]. The optimal height of the damper coils is around h = 0.35[m] regardless of velocity and switching system. This is almost the same as the height of levitation coils. The width of the damper coils in the semi-active system is smaller than in the passive system. This result is thought to be related to the chain flux change. At the high speed, change in the number of flux linkage of the damper coils increase. So, the energy Wt at the velocity v = 80[m/sec] is larger than at the velocity v = 60[m/sec]. Optimal installation position of the damper coils on the bogie is discussed. In this study, for damper coils are installed on each side of the bogie as the installation position of the damper coils zd = -0.40 - 0.40[m]. Fig. 2(b) shows the dependence of energy on the position of the damper coils at the velocity v = 60[m/sec]. From Fig. 2(b), there are two position where the energy becomes small regardless of the velocity and damper system. This position is related to the position of the levitation coils. So, the result is that there are two optimal installation positions of the damper coils. In the semi-active damper system, the energy Wt change sharp in value at the position zd = -0.12, 0.29[m]. This is because the number of switching change around this position. The optimal installation position of the damper coils is the same regardless of velocity. However, in the passive damper system, at the velocity v = 80[m/sec], the optimal installation position of damper coils is lower than at the velocity v = 60, 70[m/sec]. Because the weight of the bogie balances with the levitation force. The levitation position of the bogie at the high speed is higher than at the low speed. In conclusion, the optimal shape of the damper coils at the velocity v = 60 - 80[m/sec] is almost the same as at the velocity v = 120[m/sec]. However, the optimal installation position of the damper coils at the velocity v = 60 - 80[m/sec] is higher than at the velocity v = 120[m/sec]. Because the levitation position of the bogie at the low speed is lower than at high speed.

**References:**

[1] A.Seki, J.Kitano and S.Miyamoto, “Dynamics of the bogie of a maglev system with guideway irregularities”, IEEE Trans. on Magnetics vol.32, No.5, pp5043-5045, 1996. [2]Takenori Yonezu;Ken Watanabe;Erimitsu Suzuki;Takashi Sasakawa, “Study on Electromagnetic Force Characteristics Acting on Levitation/Guidance Coils of a Superconducting Maglev Vehicle System”, IEEE Trans. on Magn. Vol. 53, no. 11, 2017. [3]T.Okubo, S.Ohashi, N.Ueda, “Effective Control Method of the Active Damper System against the Multi Directional Vibration in the Superconducting Magnetically Levitated Bogie”, IEEE Trans. on Appl. Supercond., Vol.26, No.4, Jun. 2016, Art. no. 3601804. [4]S.Ohashi and T.Ueshima, “Control Method of the Semi-Active Damper Coil System in the Superconducting Magnetically Levitated Bogie Against Vertical and Pitching Oscillation”, IEEE Trans. on Magn. vol.48, No.11, pp4542-4544, 2012. [5]S. Ohashi, “Weight Reduction of the Damper Coils in the Superconducting Magnetically Levitated Bogie”, IEEE Trans. on Magn. Vol. 54, no. 11, 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c3b3e7740c2c0958320fd916a0bb2b5d.jpg)
Superconducting magnetically levitation system and the damper coil

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Energy consumption

 Study on the Optimal Shape and Installation Position of the Damper Coils at the Low Velocity Range in Electrodynamic Suspension System

1.Background Nowadays, more and more vehicles are starting to use an automotive display to enhance vehicle infotainment function with high resolution, large screen, and highly accurate in-touch technology, especially haptic feedback. The linear vibration motor is attached to the automotive display to provide efficient haptic performance. A permanent magnet with high remanence can generate massive flux inside a linear vibration motor and cause high acceleration. However, it also causes lots of static magnetic flux leakage in front of the display, potentially having indirect adverse effects on passenger’s implanted medical devices. International Commission on Non-Ionizing Radiation Protection (ICNIRP) guidelines [1] are applied to occupational exposures and exposure of the general public. Many individuals are wearing implanted ferromagnetic or electronic medical devices sensitive to magnetic fields. ICNIRP guidelines mention that the statice magnetic field at or below the 0.5 mT will not create a health hazard on implanted medical devices from studies to date. The prototype linear vibration motors are designed for use in an organic light-emitting diode (OLED) display panel, a thin display that each pixel emits light itself individually. Owing to the display's thinness, the prototype linear vibration motor ware placed around the center of the display. In contrast, liquid crystal display (LCD) pixels require backlight units (BLUs) to emit lights. The BLUs cover the entire display that makes the LCD panel thicker than the OLED panel; thus, the prototype can no longer be used. The available space for placing linear vibration motors are in the bezels around the LCD panel, requiring a slim-width linear vibration motor with acceptable haptic performance and less static magnetic flux leakage (&lt; 0.5 mT). 2. Analysis methods Maxwell's equations [2] are employed to do the magnetostatic analysis by considering the nonlinearity and hysteresis of magnetic material. The electromagnetic-mechanical coupled method is used to verify the linear vibration motor's haptic performance with the finite element method. 3. Prototype The linear vibration motor consists of an electromagnetic system and a mechanical system. The electromagnetic system includes a voice coil, a top plate, a permanent magnet, and a yoke. The mechanical system consists of an inserted frame, an upper frame, a lower frame, and a plate. The full model, half model, an exploded view of the prototype are shown in Figure 1(a). The final slim linear vibration motor has a smaller size than the prototype, and it has an added magnet to provide an opposite magnetic flux to lower magnetic flux leakage at the measured position, shown in Figure 1(b). The magnetic flux leakage is defined as the magnetic flux that does not pass through the air gaps of the voice coil or other parts of the electromagnetic system. The measured positions are in front and behind of linear vibration motor with an 11.30mm distance. The measurement results in front and behind the prototype are 1.60 mT and 11.70mT, while the analysis results are 1.59 mT and 11.69 mT. The experiment setup to measure magnetic flux leakage is Kanetec Tesla Gauss meter, and the measurement results are shown in Fig. 2(a). Based on the E-M coupled method, the analysis results of displacement and acceleration on dummy jig of the prototype are obtained and verified by the experiment results. The measurement setups for measuring displacement and acceleration are Klippel and vibration tester (Type BK 2120C2). 4. Novel design The slim model is designed to satisfy the requirement of the automotive LCD display panel. With a new upper frame shape, the slim model can be inserted into an automotive display in two directions, while the prototype only can be inserted in one direction. Based on a previous study [3] (application of magnetic shielding), the upper frame of the slim model is made by magnetic material (sus 430), which can create another magnetic circuit to make magnetic flux coming back to yoke. Magnetic circuit design includes voice coil design, added yoke design, added magnet design, and magnetic circuit optimization. Secondly, the movable parts of the linear vibration motor include yoke, magnet, and top plate. The inserted frame is treated as spring, and the thickness of the inserted frame's bridge has a dominant influence on resonance frequency. To maintain the same resonance frequency as the prototype (around 130Hz), the thickness of the inserted frame's bridge is changed from 2.30mm to 1.90mm. With a combination of the above designs, the final slim model's analysis results show that magnetic flux leakages in front and behind the slim model are 0.10 mT and 0.43 mT. Both sides are lower than 0.5 mT. There are 93.71%, 96.32% decreased from the prototype. Samples are manufactured and used to do the experimental measurement. 5. Conclusion The current study proposes a width slim linear vibration motor with a novel magnetic circuit design to achieve low static magnetic flux leakage. Haptic performance of linear vibration motor includes the displacement of movable mass and acceleration on dummy jig, shown in Fig. 2(b). The final slim model has the same resonance frequency as a prototype, around 130 Hz, and it has higher displacement than the prototype due to the smaller movable mass. Eventually, the experiment results are in good agreement with the analysis results.

**References:**

1.International Commission on Non-Ionizing Radiation Protection. Guidelines on limits of exposure to static magnetic fields. Health Physics., Vol. 96(4), pp. 504-14 (2009 Apr 1) 2.Monk P. Finite element methods for Maxwell's equations. Oxford University Press., (2003 Apr 17) 3.Jiang ZX, Park KH, Kim JH. Analysis and Design of a New Linear Vibration Motor Used to Reduce Magnetic Flux Leakage in In-Vehicle Infotainment. Applied Sciences., Vol.10(10), pp. 3370 (2020 Jan)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6e6ddbd98125d7b2e61ba693da429676.jpg)
Fig.1 Model comparison between prototype and slim model_Final

![](https://assets.underline.io/uploads/markdown_image/1/image/2889d6a55e76aef872060e0d7c230ac7.jpg)
Fig.2 Resutls comparion between experiment and analysis

Nonlinear Permanent Magnet Degradation Model and its Application in Magnetic System Optimization

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