France



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.&lt;br/&gt;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.&lt;br/&gt;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,&lt;br/&gt;[2] Chang-Woo Kim, Gang-Heyon Jang, Kyung-Hun Shin, IEEE Transactions on Applied Superconductivity, VOL. 30, NO. 4, June 2020&lt;br/&gt;[3] Navneet Behra, IEEE International Conference on Technologies for Smart-City Energy Security and Power (ICSESP-2018), March 28-30, 2018&lt;br/&gt;[4] Yoshifumi Okamoto, Yusuke Tominaga, Shinji Wakao, IEEE Transactions on Magnetics, VOL. 50, NO. 2, February 2014&lt;br/&gt;[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,&lt;br /&gt;
(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&lt;br /&gt;
magnet specifications (d) side force reduction result

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

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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

poster

—In order to reduce the cogging torque of the permanent magnet (PM) machine more effectively, a novel conception of the regional magnetic compensation (RMC) is introduced. An effective approach from the perspective of dynamic control for cogging torque reduction based on RMC is then proposed, by which the cogging torque could be reduced. Index Terms—Cogging torque, permanent magnet machines, dynamic reduction method, regional magnetic compensation. I. Introduction The cogging torque is an significant issue of the PM machines, which is an inherent shortcoming of PM machines. It leads to mechanical vibration, noise, and deteriorate the performances of the PM machines [1]. A wide variety of design methods for minimizing the cogging torque of PM machines have been comprehensively studied [1-3]. The existing cogging torque reduction methods can be mainly divided into two types: stator design and rotor design techniques. Undoubtedly, these methods can weaken the cogging torque but may result in the degradation of other machine performances, such as the unnecessary harmonics introduction, cost increase, and efficiency reduction, etc. On the other hand, it is impossible to weaken the cogging torque of a PM machine that has already been manufactured. Therefore, weakening the cogging torque from the perspective of dynamic control is worth considering, but few scholars have carried out related research on this. In this paper, a novel cogging torque reduction method based on regional magnetic compensation (RMC) has been proposed. The imbalance property of the magnetic field between adjacent stator teeth has been investigated and the compensation strategy of the regional magnetic field has been researched. The case studies of interior and surface-mounted PM machines show that the proposed method could help to dynamic minimize the cogging torque. II. Finite Element Analysis Of Cogging Torque Cogging torque is caused by the construction of the magnetic circuit of the machine, which is the interaction between the rotor magnetic flux and variable permeance of the air gap due to the geometry of stator slots [4], and it also exists when the machine is not energized. By making accurate analysis and calculation of the cogging torque, the basis for its compensation of the PM machines is created. The net cogging torque at any rotor position, which produced by a surface/interior PM machine can be calculated by [5] TC=∑k=1QS(La∫0hs((Bθb12(rt)−Bθb22(rt))/(2μ0)) (1) where Bθb1 and Bθb2 are the tangential components of flux densities near the adjacent stator teeth, respectively; QS is the number of slots; La is the effective length; hS is the radius of the slot opening. The cogging torque calculation of PM machines will be illustrated and analyzed in this part. III. Regional Magnetic Compensation Strategy According to the analytical formula of cogging torque, it can be known that the tangential flux density on both sides of the slot wall can be compensated by supplying current or voltage on the stator side, the magnetic close component of the cogging torque can be balanced, thus weakening the cogging torque. The cogging torque analytical calculation and the regional magnetic field compensation is shown in Fig. 1. Take a 2-pole, 12-slot surface-mounted PM machine as an example, the current injection scheme for different slots is illustrated in Fig. 2. Further detailed regional magnetic compensation schemes of different machine topologies and their cogging torque reduction results will be reported in the full paper.

**References:**

 [1] W. Fei and Z. Q. Zhu, “Comparison of cogging torque reduction in permanent magnet Brushless machines by conventional and herringbone skewing techniques,” IEEE Trans. Energy Convers., vol. 28, no. 3, pp. 664–674, Mar. 2013. [2] J. Gao, G. Wang, X. Liu, W. J. Zhang, S. D. Huang, and H. M. Li, “Cogging Torque Reduction by Elementary-Cogging-Unit Shift for Permanent Magnet Machines,” IEEE Trans. Magn., vol. 53, no. 11, p. 8208705, Nov. 2017. [3] L. Zhu, S. Z. Jiang, Z. Q. Zhu, and C. C. Chan, “Analytical methods for minimizing cogging torque in permanent-magnet machines,” IEEE Trans. Magn., vol. 45, no. 4, pp. 2023–2031, Apr. 2009. [4] E. H. Abd-Elhameed and M. Iwasaki, "Pulsating torque modeling and compensation for high precision positioning control," 2009 IEEE International Conference on Mechatronics, Malaga, 2009, pp. 1-5. Z. Q. Zhu and D. Howe, “Analytical Prediction of the Cogging Torque in Radial-field Permanent Magnet brushless motors,” IEEE Trans. Magn., vol. 28, no. 2, pp. 1371–1374, Mar. 2009.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/9e00f76d4a91dc15460041f836e5411e.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/50410699d8d89d71f2ac6c6235d0902d.jpg)

 Cogging Torque Dynamic Reduction Based on Regional Magnetic Compensation

I. Introduction PM machines have become more and more popular in various applications due to high torque density and efficiency. There are two typical winding connection methods for PM machines, of which star connection is more widely used. Delta connection is the other one, which leads to higher line current yet smaller line voltage compared to star connection. Therefore, delta connection is usually employed in high-voltage applications. However, circulating currents are likely to occur in delta connection, which can lead to additional copper loss and thus reduced efficiency. In addition, a hybrid star-delta connection has been proposed in the past few years [1]. Compared to star connection, the winding factor is maximized and thus torque density is enhanced by approximate 5.2%. Nevertheless, little literature is found regarding short circuit (SC) and demagnetization for these winding connections. SC and demagnetization are detrimental to the reliabilities of PM machines. SC currents are usually several times larger than working currents, which can generate more heat and accelerate winding insulation aging. In addition, SC can lead to large torque ripple, which can result in vibration and further damage machine components. Moreover, SC current can yield huge magnetic fields against PMs and thus cause irreversible demagnetization. Average torque can be reduced and torque ripple can deteriorate once demagnetization happens [2]. Therefore, comparing SC currents and demagnetization between different winding connections helps determine which connection should be selected when designing PM machines, especially those for safety-critical applications. In this digest, three-phase SC (3PSC) and two-phase SC (2PSC) for star and delta connections are investigated, together with their resultant demagnetization. II. Finite Element Model and Drive Schemes for Star and Delta Connections Finite element method coupled with circuit is employed. A 10-pole/12-slot surface-mounted PM machine is selected for investigation. Practically, SC faults are more likely to happen in the converter than the SPM machine itself because the power electronic devices are usually easier to be damaged than the well-insulated windings. Therefore, the drive schemes for both connections are shown in Fig. 1(a) and (b) for the following analysis. III. Three-Phase Short Circuit and Demagnetization It is assumed that 3PSC happens when all upper switches in Fig.1 (a) and (b) are closed whilst all lower ones are opened to prevent shoot-through. The equivalent circuits are shown in Fig. 1(c) and (e). The 3PSC starts at the rotor position π/2 from open-circuit state and the rotor speed is assumed to be 500rpm during 3PSC. As shown in Fig. 2(a), the star connection shows slightly larger peak currents. Since SC current usually produces a voltage against the back-EMF, the terminal voltage of each phase is approximately 0V during 3PSC for star connection. Therefore, when only the fundamental back-EMF is considered, the 3PSC currents for both winding connections are almost the same. For the star connection, the 3rd back-EMF harmonics are compensated in each loop and does not contribute to the 3PSC currents. However, the 3rd harmonic cannot be compensated in the delta connection and leads to additional 3PSC current component, which reduces peak currents in this 10-pole/12-slot SPM machine. In addition, the demagnetization level is evaluated by torque loss, which is defined as the ratio of the reduction of average torque to pre-demagnetization value. The torque loss for the star and delta connection are 1.84% and 1.53%, respectively. IV. Two-Phase Short Circuit and Demagnetization It is assumed that 2PSC happens when the switches VT1 and VT3 in Fig.1 (a) and (b) are closed whilst the others are opened. The equivalent circuits are shown in Fig. 1(d) and (f). 2PSC heavily depends on start rotor position and only SC currents starting from rotor position π/2 are analyzed as an example. As shown in Fig. 2(b), for the delta connection, the phase B current is approximately twice the SC currents of phase A and C in the opposite directions. This is because the SC loop of winding A and C has twice larger impedance than that of winding B, as shown in Fig.1 (f). Compared to the star connection, the phase B and C peak currents are larger and the phase A current is smaller under this start rotor position. The 2PSC peak currents under different start rotor positions are shown in Fig. 2(c). In addition, the torque loss after 2PSC for delta connection is larger under most start rotor positions, as shown in Fig. 2(d). V. Conclusions It can be concluded which winding connection causes larger 3PSC peak currents and severer demagnetization heavily depends on the 3rd back-EMF harmonic. In addition, delta connection exhibits larger 2PSC peak currents and severer demagnetization under most start rotor positions. In the full paper, hybrid star-delta connection and single-phase SC will be considered. In addition, more analytical analysis and experimental validation will be presented.

**References:**

[1] M. N. F. Ibrahim, A. S. Abdel-Khalik and E. M. Rashad, IEEE Transactions on Energy Conversion, vol. 33, pp. 1015-1024 (2017). [2] L. Wu, Y. Du and Z. Chen, IEEE Transactions on Industry Applications, vol. 56, pp. 2427-2440 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f2d5e681b6a76738fef42a8cf2aa839f.jpg)
Fig. 1. Drive schemes for star and delta winding connections and SC equivalent circuits. (a) Drive scheme, star. (b) Drive scheme, delta. (c) 3PSC equivalent circuit, star. (d) 2PSC equivalent circuit, star. (e) 3PSC equivalent circuit, delta. (f) 2PSC equivalent circuit, delta.

![](https://assets.underline.io/uploads/markdown_image/1/image/072d4c8f3f2cf29649904f0936930c75.jpg)
Fig. 2. SC currents and torque loss. (a) 3PSC current waveforms. (b) 2PSC current waveforms. (c) 2PSC peak currents under different start rotor positions. (d) Torque loss due to 2PSC under different start rotor positions.

 Comparison of Short Circuit and Irreversible Demagnetization between Different Winding Connections in Surface-Mounted PM Machines

Permanent magnet synchronous machines (PMSMs) are widely used in transmission and air-conditioning systems owing to several advantages such as high power density, high efficiency, and compact structure. However, PMSMs have the drawbacks of noise, vibration, and harshness (NVH) caused by the interaction between the magnetic motive force (MMF) of the stator winding and rotor magnets having a high coercive force, significantly affecting the machine characteristics. The NVH of PMSMs is influenced by serious machine operation problems such as eccentricity, rotor mass asymmetry, and axis misalignment, which causes machine faults and breakage. Therefore, it is necessary to consider these problems during the initial design stage. However, among these problems, the rotor mass asymmetry and axis misalignment have an influence on the change in mechanical characteristics, while eccentricity affects the change in the electromagnetic characteristic, which causes an increase in the electromagnetic NVH sources. Previous research has shown that eccentricity affects not only electromagnetic performance but also NVH sources that are related to the machine’s characteristics. Electromagnetic NVH sources can be divided into two types: torque and electromagnetic force characteristics. The torque characteristics are classified as cogging torque and torque ripple. Previous research has shown that NVH characteristics are improved by reducing the torque characteristics. The electromagnetic force characteristics are classified as unbalanced electromagnetic force (UMF) and magnetic pull force (MPF). The MPF is the distribution of the magnetic flux density owing to the MMF of the stator winding, rotor magnets, and slotting effect. Numerous studies emphasizing MPF symmetry have been published. The UMF is caused by changing the magnetic flux density according to the rotating operation, which has been actively studied as the primary cause of NVH along with rotor eccentricity in induction machines. There are a few studies on the UMF of PM machines. Wu, et al. analyzed the UMF harmonic orders using an analytical method along with experimental results. Zhu, et al. analyzed the UMF generated in the models according to different winding patterns with equal specifications and changes in the current waveform according to the shape of the machines. However, the electromagnetic source influence on the NVH caused by eccentricity was not confirmed. Therefore, to analyze the eccentricity influence on each electromagnetic NVH source, we proposed the design of a PMSM with a fractional pole/slot combination, derived the dominant model of the pole/slot combination for each electromagnetic NVH source through a finite element analysis, and carried out a comparative results analysis of the results of the electromagnetic characteristic analysis. The derived pole-slot combination of the models are 8-pole/9-slot. The dominant components of 9-slot is electromagnetic force characteristics, respectively. However, if it is applied eccentricity conditions that increased the torque characteristics. Thus, we analyzed the influence of each NVH source by conducting experiments and electro-mechanical coupled analysis using FEM, and then compared the results with two different operating conditions. The analysis model and concept of eccecntricity used for the electromagnetic excitation analysis are shown in Fig. 1(a). The derived pole-slot combination is the 8-pole/9-slot and 8-pole/12-slot. The concept of the NVH experimental system is shown in Fig. 1(b), to generate eccentricity, an apparatus for moving the stator is applied to the test motor. The characteristic analysis results of electromagnetic excitation are shown in Figs. 1(c) and (d). The NVH source, in the eccenctricity condition is higher than that in a healthy condition. Therefore, the influence on each source can be analyzed. Figs. 2(a) and (b) show the electro-mechanical NVH characteristic analysis results of PMSMs according to the eccentricity. Figs. 2(c) and (d) show the measurement NVH results. This indicates that eccentricity significantly influences the NVH of the PMSMs. Detailed analysis and measurement results are discussed in the full paper.

**References:**

[1] J. Zou, H. Lan, Y. Xu, and B. Zhao, “Analysis of Global and Local Force Harmonics and Their Effects on Vibration in Permanent Magnet Synchronous Machines,” IEEE Trans. Energy convers., vol. 32, no. 4, pp.1523-1532, Dec. 2017. [2] D. Torregrossa, F. Peyraut, B. Fahimi, J. MBoua, and A. Miraoui, “Multiphysics finite-element modeling for vibration and acoustic analysis of permanent magnet synchronous machine,” IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 490–500, Jun. 2011. [3] H. Yang and Y. Chen, “Influence of radial force harmonics with low mode number on electromagnetic vibration of PMSM,” IEEE Trans. Energy Convers., vol. 29, no. 1, pp. 38–45, Mar. 2014. [4] P. Beccue, J. Neely, S. Pekarek, and D. Stutts, “Measurement and control of torque ripple-induced frame torsional vibration in a surface mount permanent magnet machine,” IEEE Trans. Power Electron., vol. 20, no. 1, pp. 182–191, Jan. 2005. [5] 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. [6] D. Y. Kim, M. R. Park, J. H. Sim, and J. P. Hong, “Advanced Method of Selecting Number of Poles and Slots for Low-frequency Vibration Reduction of Traction Motor for Elevator,” IEEE/ASME Trans. Mechatro., vol. 22, no. 4, pp. 1554-1562, Aug. 2017. [7] J. F. Gieras, C. Wang, and J. C. Lai, Noise of Poly-phase Electric Motors. New York, NY, USA: Taylor & Francis, 2006.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/84a39008bc4ccc70facb277b81e18897.jpg)
Figure 1 (a) Analysis model (b) the concept of experimental system (c) UMF analysis results according to Eccentricity (d) Back EMF analysis results according to Eccentricity

![](https://assets.underline.io/uploads/markdown_image/1/image/4eee758d9a0e9c24b511c0483b44bfbf.jpg)
Figure 2 Experimental and analysis results of NVH according to eccentricity: (a) healthy conditions analysis results (b) eccentricity conditions analysis results (c) healthy conditions measurement results (d) eccentricity conditions measurement results

 Analysis and Experimental Study for Electromagnetic and Mechanical Characteristic of Permanent Magnet Synchronous Machines according to Eccentricity

I Introduction Owing to their characteristics of easy manufacturing, convenient transportation and high fault-tolerant capacity, the modular permanent magnet synchronous machines (PMSMs) are favored by various industrial applications, such as electric vehicle and wind turbine applications [1]. However, due to the manufacturing tolerance, the additional mechanical gaps between the modules are inevitable which will affect the magnetic field distribution and hence the electromagnetic performances. The influences of the inevitable mechanical gaps between the modules in a three-phase PMSM has been investigated in [2-5]. Unfortunately, the influences of the additional gaps between the modules in a six-phase modular machine have not been covered. Moreover, the different influences of the modular structures on PMSMs with symmetrical or asymmetrical six-phase winding layouts are not investigated. II Development of the different six-phase winding layouts and the modular machines The symmetrical and asymmetrical six-phase windings layouts 12-slot/14(10)-pole PMSMs can be obtained by analyzing the the slot star diagram of a conventional 12-slot/14(10)-pole three-phase PMSM with double-layer FSCW as shown in Fig. 1. The mutual inductances between adjacent phases are nonzero as shown in Table I, which will decrease their magnetic isolation capacity. To improve this situation, all the double-layer slots are divided into two single-layer slots so that three 24-slot/14(10)-pole six-phase PMSMs with unequal teeth can be obtained. And, the modular stators are employed. For the asymmetrical six-phase machine, there is only one modular method—one module with one coil (Design A). For the symmetrical six-phase machine, there can be two different modular methods—one modular with one coil (Design B) and one modular with one-phase (Design C) (one phase possesses two adjacent coils). The different modular methods will introduce different additional mechanical gaps which cannot be avoided resulting from the manufacture limitations and tolerances, as shown in Fig. 1. These mechanical gaps will have significant influences on the electromagnetic performances of the modular machine. III Influences of the modular stators on the performances In this section, the performance such as winding factor, no-load air-gap flux density, on-load torque and short-circuit current, are investigated. For the sake of comparison, all the dimensions of the three modular stator PMSMs are the same as shown in Table II and Fig. 2. Since the slot area is fixed, the sum of the width of coil-wound tooth (t1) and the width of non-wound tooth (t2) is the same when the width of the coil-wound tooth varies. The additional mechanical gap varies from 0.5 mm to 5 mm. By injecting rated sine currents, the on-load torques can be obtained as shown in Fig. 3. It can be clearly found that the average torques of the three machines all decrease with the increase in mechanical gap width. When the mechanical gaps are relative small, i.e. 0~1 mm, the average torques are in direct proportion to t1. However, due to the serious saturation in the non-wound teeth, this rule will disappear. This is why, the average torques drop more rapidly with the increase in mechanical gap width when t1 is relatively large. The average torques of Design C are the most smooth ones, which indicates that the modular method of Design C can avoid deep saturation. The fault-tolerant machine requires that the short-circuit current should be closed to the rated current. The short-circuit currents of the three modular machines are investigated as shown in Fig. 4. For Design A and B, it can be seen that the short-circuit current decreases with the increase in mechanical gaps when t1 smaller than 24mm, which results from the reduced back-electromagnet force (back-EMF). The short-circuit will rapidly increase with the increase in mechanical gap width when t1 bigger than 24mm, which results from the reduced self-inductance when deep saturation occurs. For Design C, with different winding tooth width, the amplitudes of the short current are almost deprived of the influence of the width of the mechanical gaps. IV Conclusion This paper presents three different modular six-phase PMSMs. For the asymmetrical six-phase machine, there is only one modular method—one module with one coil (Design A). For the symmetrical six-phase machine, there can be two different modular methods—one modular with one coil (Design B) and one modular with one-phase (Design C) (one phase possesses two adjacent coils). For Design A and B, the mechanical gaps between the modules will make the performances bad significantly. While, Design C almost insulates from the influcence of the addtional mechanacal gaps.

**References:**

 [1] B. Bickel, J. Franke, and T. Albrecht, “Manufacturing cell for winding and assembling a segmented stator of PM-synchronous machines for hybrid vehicles,” in Proc. 2nd Int. EDPC, Oct. 2012, pp. 1–5. [2] Z. Q. Zhu, Z. Azar, and G. Ombach, “Influence of additional air gaps between stator segments on cogging torque of permanent-magnet machines having modular stators,” IEEE Trans. Mag., vol. 48, no. 6, pp. 2049–2055,Jun. 2012. [3] G. Dajaku and D. Gerling, “Low costs and high-efficiency electric machines,” in Proc. 2012 2nd Int. Electr. Drives Prod. Conf. (EDPC), Oct. 15–18, 2012, pp. 1–7. [4] G. J. Li, Z. Q. Zhu, W. Q. Chu, M. P. Foster, and D. A. Stone, “Influence of Flux Gaps on Electromagnetic Performance of Novel Modular PM Machines,” IEEE Trans. Energy Convers., vol. 29, no. 3, pp. 716-726, Sept. 2014. [5] G. J. Li, Z. Q. Zhu, M.Foster, and D. Stone, “Comparative Studies of Modular and Unequal Tooth PM Machines Either With or Without Tooth Tips,” IEEE Trans. Magn., vol. 50, no. 7, 8101610, July 2014.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c7d72a6eb79b24e702e24265576ac0d9.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/80cdcd47954ab9f66b951f6c3e7c8a89.jpg)

 Comparative Studies of Six-Phase PMSMs with Modular Stator Under Pre-Fault and Post-Fault Conditions

this paper proposes segmented asymmetrical stator design to reduce torque ripple for permanent magnet synchronous motor (PMSM). By changing the design parameters of the segmented stator, a specific phase difference of the two torque ripples can be generated by two sections of the stator, so the ripples can offset each other to reduce the torque ripple. A 14-pole 12-slot PMSM is carried out to analyze the proposed stator design, and the correctness of the method is verified by finite element analysis (FEA). I. Introduction Permanent magnet synchronous motor (PMSM) is widely used in industrial fields because of the advantages of high power density and high efficiency [1]. However, torque ripple of PMSM can cause vibration and noise, which are not conducive to the smooth operation of the motor. So, it’s of great necessity to reduce the torque ripple. Generally, magnet shape optimization is carried out to reduce torque ripple, but this method also decreases the average torque [2]- [3]. Consequently, this paper proposes segmented asymmetrical stator design, which can reduce torque ripple without significant drop of average torque. II. Mechanism of Torque Ripple Electromagnetic torque is generated by back EMF and current. Assuming that the input current is a standard sinusoidal wave, then average torque is generated by the current and the fundamental of back EMF, while torque ripple is generated by the current and the harmonics of back EMF. The conventional method is to optimize the shape of permanent magnet. In this way, the amplitude of back EMF harmonics can be reduced so as to achieve the decrease of the torque ripple. However, the fundamental of back EMF is also reduced so the average torque decreases obviously. The proposed method is not to reduce the back EMF harmonics, but to create two groups of harmonics which are staggered by a certain phase to make them cancel each other. In this way, the torque ripple is reduced and the average torque can be maintained. III. segmented stator design A 14-pole 12-slot PMSM is carried out to analyze the proposed stator design. For the conventional symmetrical structure, the average torque is 53Nm and the torque ripple is 3.05%. 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. Given several θ and W, finite element analysis (FEA) is used to calculate the performance of the motor. A total of 120 schemes are calculated by FEA and the results are analyzed. Fast Fourier Transform (FFT) are applied to the torque results to obtain the harmonics distribution of the torque ripples. From the analysis, it’s easy to find two torques which have similar ripple amplitude and opposite phase. The model A is that when θ is 12° and W is 4.4, and the model B is that when θ is 18° and W is 4.4. The details of the torque results are shown as Fig.1. It can be seen from Fig.1 that the amplitudes of sixth torque ripple are 0.4664 and 0.7719, and the phases are -109° and 74°. The amplitudes of twelfth torque ripple are 0.1484 and 0.1512, and the phases are -165° and 28°.Both the sixth and the twelfth torque ripples of the two models have similar amplitude and opposite phase. So the torque ripple can be reduced sharply if the two torque waveforms are superimposed. According to the above analysis, the stator core can be designed in sections. The stator core can be divided into two parts in the axial direction, and the laminations of the two parts are made according to model A and model B respectively. Then the segmented stator is used for FEA calculation, the average torque is 52.5 Nm and the torque ripple is 0.93%. The torques of segmented stator and relevant comparison models are shown in Fig.2. It can be seen from Fig.2 that although the FEA results of segmented stator structure are not entirely consistent with the average results of model A and model B, the torque ripple of the motor can be effectively reduced without obvious reduction of average torque. The torque ripple is obviously reduced from 3.05% to 0.93%, and the average torque is only reduced from 53Nm to 52.5Nm. IV. Conclusion This paper proposes a segmented asymmetric stator structure. By segmenting the stator and designing each section, the torque ripples generated by different sections can cancel each other, so as to weaken the torque ripple. This method doesn’t require permanent magnet shape optimization, so the torque will not decrease significantly. The validity and accuracy of the segmented asymmetrical stator structure are verified by FEA calculation.

**References:**

1. J. Si, S. Zhao, H. Feng and R. Cao, Chinese Journal of Electrical Engineering, vol. 44, p. 67-73(2018) 2. W. Zhao, T. A. Lipo and B.-I. Kwon, IEEE Transactions on Industrial Electronics., vol. 61, p. 5779-5787(2014) 3. D. Wu and Z. Q. Zhu, IEEE Transactions on Magnetics, vol. 51, p. 1-4(2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3e74da84394619607f70d0edbc605b1e.jpg)
Fig.1 Structures and torque analysis of asymmetrical models

![](https://assets.underline.io/uploads/markdown_image/1/image/753d00020fd38f4003146832df524af2.jpg)
Fig.2 Segmented asymmetrical stator structure and torque results of the models

 Segmented asymmetrical stator structure of PMSM to reduce torque ripple

I. INTRODUCTION With the development of electric drive technology, all electric and hybrid control has been more and more used in aerospace, and the integrated electric engine fuel pump on the aircraft has many potential advantages: compared with the traditional system using mechanical drive pump, the fuel control system is lighter, smaller, simpler and more efficient. Therefore, the fuel pump motor also plays an important role in electric drive control. The existing dual-winding fault-tolerant permanent magnet machine (DWFT-PMM) is generally designed with a rated speed of 5000rpm, rated power of 10kW and rated torque of 20Nm, the cooling mode is air cooling [1]. In [1], the optimized DWFT-PMM owns the advantages of physics isolation, strong magnetic isolation, inhibiting the short circuit current, small cogging torque ripple and high fault tolerance by designing and optimizing the air gap surface shape and anti short-circuit reactance parameters. It is precisely because of these advantages that existing DWFT-PMM as a fuel pump motor has a broad application and the idea of continuing to optimize this motor is worthwhile. However, in practical application, due to the speed demand of aviation fuel pump motor reaching 6000rpm or even higher, the demand for power and torque is relatively reduced, and the cooling mode is changed from air cooling to oil cooling. This paper aims to optimize the parameters of the existing DWFT-PMM. To improve the performance of DWFT-PMM and make it successfully used in the aviation field, the design and optimization of aviation fuel pump motor based on DWFT-PMM are proposed and studied in this paper. Firstly, according to the design specifications, the design and performance optimization scheme of the fuel pump motor is proposed and finally determined. Then, to verify the performance of the motor, the comparative analyses of the DWFT-PMM are showed in simulation and experiment, and the finite element analysis (FEA) results are given in terms of the sizing and volume, electromagnetic torque, no-load back EMF in simulation and experiment, etc. Based on the design and optimization results, the prototype is manufactured, and the experimental results of loss analysis are given. Finally, the conclusion is drawn. II. DESIGN AND PERFORMANCE OPTIMIZATIONS Fig.1 shows the comparison of two-dimensional (2-D) model and three-dimensional (3-D) model of DWFT-PMM before and after optimization along with the optimized prototype. It is indicated from models in Fig. 1(a) that the inner and outer diameters of the stator and rotor are reduced to achieve the optimization goal. The optimization goal also includes reducing the peak value of no-load back EMF to increase the speed, the cooling mode changed from air cooling to oil cooling, and reducing the copper loss, iron loss and mechanical loss. Fig. 1(b) shows the prototypes before and after DWFT-PMM optimization. III. FINITE ELEMENT ANALYSIS VERIFICATION According to the design and optimization parameters, no-load back-EMF waveforms of DWFT-PMM are shown in Fig .2(a) before and after optimization. The electromagnetic torque waveforms of DWFT-PMM before and after optimization are shown in Fig. 2(b). More detailed simulated verification will be presented in the full paper. IV. EXPERIMENTAL VERIFICATION The no-load back-EMF waveforms in experiment are respectively shown in Fig. 2(c). The former is when DWFT-PMM is running at the 2000r/min, and the latter is when the optimized DWFT-PMM is running at the 5000r/min. V. CONCLUSION This paper presents and studies the comparison and analysis of DWFT-PMM. According to the actual requirements, the speed of the fuel pump motor is higher and the cooling mode is oil cooling. So, the flow chart of the design and performance optimization of the existing DWFT-PMM is established. Then, the size of the stator and rotor and the number of coil turns of the fuel pump motor are designed and optimized. The performance of the optimized DWFT-PMM is analyzed by FEM from the aspects of inductance, cogging torque ripple, no-load back EMF, short circuit current, electromagnetic torque, and loss. Finally, the simulated and experimental results show that the optimized DWFT-PMM has the advantages of higher speed, better heat dissipation, smaller size, higher reliability, and more practicability. More detailed theoretical analysis, simulated and experimental verification will be presented in the full paper. ACKNOWLEDGMENT This work was supported in part by the National Natural Science Foundation of China under Project 51807094, and in part by the Project funded by China Postdoctoral Science Foundation under Project 2020M671499, and in part by High-level Innovative Entrepreneurial Talent Introduction Program of Jiangsu Province under Project [2019]20, and in part by Jiangsu Planned Projects for Postdoctoral Research Funds under Grant 2020Z145.

**References:**

[1] Xuefeng Jiang, Shaoshuai Wang, Qiang Li, Yufei Gao, “Design and optimization of dual-winding fault-tolerant permanent magnet motor,” CES Transactions on Electrical Machines and Systems, vol.3, no.1, pp.45- 53, (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f2da28df7f90375fba2fec3189951abf.jpg)
Fig. 1. The proposed DWFTPMM. (a) Comparisons the 2-D of and the 3-D model. (b) Comparison of prototype.

![](https://assets.underline.io/uploads/markdown_image/1/image/bd64d249f73840e196d7baa6603ec893.jpg)
Fig. 2. Simulation and experimental comparison results of DWFT-PMM before and after optimization. (a) The comparison of no-load back EMF in simulation. (b) The comparison of the electromagnetic torque in simulation. (c) The comparison of no-load back EMF in experiment.

 Comparison and Analysis of Dual-Winding Fault-Tolerant Permanent Magnet Motor for Aviation Fuel Pump Applications

1.In recent years, electromagnetic renewable energy systems such as wind turbines have become an important research direction. It can be seem more and more commonly to use surface-mounted permanent magnet generators and mostly installed in coastal areas. In order to improve the reliability of the generator, permanent magnet elements are used in the internal structure. In the research of this article, an enhanced permanent magnet salient pole generator that improving the magnetic flux is proposed. The demagnetization phenomenon of the motor is the transient magnetic performance of the fault. The two-pole alternator device is shown as Figure 1. For concept of the rotor core structure, a sinusoidal waveform is generated between the surface and the air gap magnetic flux density. At each magnetic pole of the two permanent magnet phenomena, it shown the symmetry magnetization directions with mirror condition are embedded. In two pole generators, non-magnetic materials are generally used to guide the path of magnetic flux [1]. Due to the placement of permanent magnets, the radial magnetic field will be stronger. To change the angle between the two left and right permanent magnets, it will show the demagnetization performance of the magnetic field in the magnetic pole. Therefore, the AC two-pole generator in this research with two forms is proposed. The first one, it is the naked motor form of the No Cover (NC), as shown in Figure 1, and the other is an iron-based amorphous alloy material is used to cover the whole generator. Due to this changing of the magnetic pole and the spatial magnetic field, it apply a different permanent magnet motors with a magnetic material shell and a shell-less structure to observer their magnetic field distribution, is obtained. The demagnetization area of the demagnetization area is measured by the power analyzer and Tesla measuring instrument. The harmonic measurement results of different shell shapes are shown in Figure 2, which the demagnetization area is magnetized in the direction magnetic flux density node coverage. As shown in Figure 2, the amorphous alloy shell-clad magnetic pole generator has the highest demagnetization rate in the permanent magnet area near the bottom of the pole shoe. This is because the side frame of the pole shoe is certainly changed the leakage flux. The magnetic flux path is affected by the demagnetization performance. In contrast, due to the magnetic field distribution characteristics of the different casings, the demagnetization of the generator armature in the two forms of magnetic field distribution is not completely symmetrical. The experimental measurement of the surface of the amorphous shell shows that the magnetic flux at the inner and outer center points is about 1.2-2.4 (mT), and the magnetic flux distribution at the four corners is about 0.6-1.0 (mT), which is relatively weak before NC type of the generator. The experimental target is to define the influence of demagnetization on electromagnetic parameters, and summarize the magnetic flux distribution of permanent magnet salient pole motors in the demagnetization and amorphous housings, which is used as a reference for the design of such type motors. 2. Theory and Method The rotating field alternator shown in the figure below is the most widely used generator [2,3]. In this type of generator, direct current from another power source flows through the windings on the rotor by means of slip rings and brushes is obtained. By this way, a rotating electromagnetic field with a fixed polarity can be maintained, and the rotating magnetic field of the rotor extends outward and passes through the armature windings embedded in the surrounding stator. When the rotor rotating, an AC voltage is induced in the windings because the magnetic field of the first polarity and the other polarity penetrates them. Because the output power comes from a fixed winding, the output can be connected through a fixed terminal. The advantage of this structure is indicated that there are no sliding contacts and the entire output circuit is continuously insulated and can handle a large amount of current. 3. Experimental discussion and conclusion This research is a single-phase two-pole alternator, which apply a NC type of the generator, to produce an average AC voltage of 37V, current of 0.11A, power factor of 0.99, P power of 4.11 watts, Q of 0.48VAR, and S of 4.14VA during operation. Besides, for CO type of the generator with amorphous material, it is produce an average AC voltage of 37.03V, current of 0.14A, power factor of 0.99, P power of 3.97 watts, Q of 0.43VAR, and S of 4 VA. This results of the CO type is much better than NC type of the generator. This research focuses on observing the comparison between the bare generator and the structure covered with the amorphous shell. At the same time, it observes the electric energy generated by the generator and the harmonic state. It can be carried out by measuring the voltage and current without interrupting the generator. From the perspective of THD (Total harmonic distortion) performance, the third, fifth, and seventh order waves have the most serious impact on the generator. Of course, the generator with an amorphous shell structure has better magnetic properties and power.

**References:**

1. Chang-Hung Hsu* and Yi Mei Huang, “Performance of the Noise and Vibration of the AC/DC Signal for a Permanent Magnetic DC Motor,” IEEE Transactions on Magnetics , Early Access Articles. Accepted Publishing on the web 28 July 2020. 2. Chang-Hung Hsu* and Chia Wen Chang,“Permanent Magnetic Brushless DC Motor Magnetism Performance depends on Different Intelligent Controller Response,” Transactions of the Canadian Society for Mechanical Engineering , Accepted Publishing o n 6 August 2020. 3. Chang-Hung Hsu*, “Fractional Order PID Control for Reduction of Vibration and Noise on Induction Motor,” IEEE Trans. on Magnetics, vol. 55, no. 11, pp. 6700507-1-7, 2019.(SCI, Impact Factor: 1.651)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a3a72bd192d71cd6c84d1268b30247b6.jpg)
Figure 1. The AC generator with (without) tank composited with amorphous alloy in magnetic flux and performance testing results

![](https://assets.underline.io/uploads/markdown_image/1/image/df0c33a2f0625b4ad6c380d94087f48e.jpg)
Figure 2. The experimental results of the two types of AC generator in harmonic performance with cover (CO) amorphous slice (or without NC, No cover).

 Research on Improving Magnetic Flux of Permanent Magnet Synchronous Generator Shell with Amorphous Alloy

— This paper presents a design optimization method for improving annual energy production (AEP) of wind direct-drive permanent magnet generators. Unlike the traditional efficiency optimization method that only improves the rated point efficiency, the proposed method is to improve the overall efficiency of the generator during the operation cycle by matching the maximum power point trajectory of the wind turbine. The periodic loss model of the permanent magnet synchronous generator (PMSG) is established and further constituted as the objective functions, and the genetic algorithm is used to find the Pareto solution between multiple objective functions. Compared with the traditional design method, higher AEP is achieved by the proposed method. 1. Introduction Design optimization for generators is an important approach to promote wind energy conversion systems (WECSs) more efficient, reliable, and cost-effective. Some studies have discussed the optimization methods to improve the operating efficiency of the PMSGs in WECSs [1-3]. The works of literature adopt stochastic algorithms to optimize the analytical efficiency to find the preferable generator structural parameters, such as the genetic algorithm in [1], deterministic optimization algorithm in [2], and evolutionary algorithm in [3]. However, most of the efficiency models in the literature are based on the single function, which is usually rated conditions with rated speed, which means that only the efficiency in the rated state is optimized without considering the entire operating cycle. This is not suitable for WECSs, because of climatic and geographical factors, wind turbines rarely work under rated conditions. Therefore, the classical efficiency optimization method is likely to cause a reduction in AEP. In this paper, a novel design optimization method for PMSGs is presented to maximize the AEP. First, the aerodynamic model of the wind turbine is introduced to predict the relationship between maximum output power and optimum shaft speed, and the wind speed distribution is investigated to obtain the featured operating points with multiple wind speeds. Second, the generator loss models of the multiple featured points are formulated as objective functions, and the genetic algorithm is utilized to solve multi-objective issues. Finally, the proposed optimization is verified by simulation and experiment. 2. Maximum Power Point Trajectory of Wind Turbines The achievable mechanical power obtained from the wind turbine is given by Ρm=0.5ρR2Vω3Cp where Cp is the wind turbine power coefficient. To maximize Cp, the optimal mechanical speed ωr must match the wind speed Vω. Based on the aerodynamic model, the optimal mechanical speeds at different operating powers are obtained, as shown in Fig. 1. Therefore, the typical operating conditions (power, speed) of the generator have been obtained and can be used to assist in the construction of periodic loss models. 3. Optimization Process The loss models of PMSG under the 5 typical wind speeds are established and used as the objective functions, and their weighting coefficients are derived based on the Rayleigh distribution of wind speed. Next, the genetic algorithm is selected to simultaneously optimize the operating efficiency of PMSG at multiple speeds and powers. The efficiency is about 94.78% at the wind speed of 4 m/s, 95.58% at 6 m/s, 96.14% at 8 m/s, 96.69% at 10 m/s, 97.31% at 12m/s, respectively. Considering the wind distribution of the site, the overall efficiency can be achieved by about 96.18%. Finally, the prototype of the designed PMSG is manufactured according to the optimized solution, as shown in Fig. 2. The detailed optimization process and results will be reported in the full paper.

**References:**

[1] Q. Wang, S. Niu, and L. Yang, “Design Optimization of a Novel Scale-Down Hybrid-Excited Dual Permanent Magnet Generator for Direct-Drive Wind Power Application,” IEEE Trans. Magn., vol. 54, p. 8100904, (2018). [2] T. Bazzo, J. Kolzer, R. Carlson, “Multiphysics Design Optimization of a Permanent Magnet Synchronous Generator,” IEEE Trans. Ind. Electron., vol. 64, pp. 9815–9823, (2017). [3] C. L. Sabioni, M. F. O. Ribeiro, and J. A. Vasconcelos, “Robust Design of an Axial-Flux Permanent Magnet Synchronous Generator Based on Many-Objective Optimization Approach,” IEEE Trans. Magn., vol. 54, p. 8101704, (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5589184358a96e6020e65cbed18f03ee.jpg)
Fig. 1. Characteristics of output power and rotational speed of wind turbine at several typical wind speeds

![](https://assets.underline.io/uploads/markdown_image/1/image/2b86062fea534fc789c5e42d6de8bb11.jpg)
Fig. 2. The prototype of 2 MW wind direct-drive PMSG.

 Annual Energy Production Design Optimization for PM Generators Considering Maximum Power Point Trajectory of Wind Turbines

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

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