France



I.Introduction&lt;br/&gt;With the development of more electric aircraft (MEA), higher demand for electrical energy is put forward in generation systems. In order to reduce the weight of the aircraft generation system, the requirement on the power density of generator becomes higher [1]. Wound rotor synchronous machines (WRSMs) are most widely used in aircraft applications. However, the reliability of rotating rectifier is low. In addition, the starting processing is complex. Hybrid excitation synchronous machines (HESMs) are recently proposed as the potential candidates for EV drive systems, wind power generation and more electric aircraft, for the air-gap flux can be regulated by field current efficiently.&lt;br/&gt;This paper proposes a new hybrid excited starter-generator (HESG) with magnetic field decoupling topology for MEA applications. The predicted electromagnetic performance is validated by the 3-D finite-element analysis (FEA) model. Finally, the results of FEA are confirmed by the experiments on a 60kVA HESG. The contribution of this paper is to propose a promising HESG to replace WRSMs in aircraft starter-generator applications.&lt;br/&gt;II.Operation Principle and Machine Specification&lt;br/&gt;Table I presents the design requirements of a starter-generator for aircraft generation system. The structure of the HESG with decoupling magnetic field is shown in Fig. 1, it can be seen that the PM side air-gap is larger than EE side air-gap. In order to implement high air-gap flux density, the Halbach-array PM rotor is preferred for the flux concentrating characteristic, low harmonic components and low inductance characteristic. Fig. 2 shows the HESG topology. It can be seen that the PM rotor and the two EE rotors can be installed on the shaft together seamlessly, which can greatly improve the compactness, torque density and power density. As shown in Fig. 3, the magnetic flux path can be divided into axial part and radial part. There is no axial flux in the stator core so that the stator can keep the same with that in WRSM and brings sinusoidal back EMF, which makes it suitable for starter-generator system. Table II provides the main parameters of the designed HESG with decoupling magnetic field.&lt;br/&gt;III.Electromagnetic Performance Analysis&lt;br/&gt;In order to verify the applicability of the new HESG magnetic field decoupling topology for AC starter-generator system, the electromagnetic performance analysis mainly focus on the power characteristics and flux regulation capability. Fig. 4 shows the distribution of magnetic field with different field currents. As shown in Fig. 5, the back-EMF magnitude increases with field current. Fig. 6 shows the output voltage versus output current at 8000r/min for different field currents. It can be seen that the output characteristics can be regulated by field current. The output power versus speed for different field currents is shown in Fig. 7. A 60kVA prototype is manufactured and measured for the verification of previous analysis. The photos of the motor are shown in Fig. 8. The experimental results will be supplemented in the later formal paper.&lt;br/&gt;IV.CONCLUSION&lt;br/&gt;In this paper, a new HESG is proposed for aircraft generation system. The topology and operating principle are described in detail. In addition, the electromagnetic performance of HESG is investigated to verify the applicability of the HESM to a starter-generator system for aircraft applications.

**References:**

[1] Y. Liu, Z. Zhang and X. Zhang, &quot;Design and Optimization of Hybrid Excitation Synchronous Machines With Magnetic Shunting Rotor for Electric Vehicle Traction Applications,&quot; in &lt;i&gt;IEEE Transactions on Industry Applications&lt;/i&gt;, vol. 53, no. 6, pp. 5252-5261, Nov.-Dec. 2017.

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INTERMAG 2021

 Electromagnetic Performance Analysis of a New Hybrid Excitation Synchronous Generator with Decoupling Magnetic Field

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I.Introduction With the development of more electric aircraft (MEA), higher demand for electrical energy is put forward in generation systems. In order to reduce the weight of the aircraft generation system, the requirement on the power density of generator becomes higher [1]. Wound rotor synchronous machines (WRSMs) are most widely used in aircraft applications. However, the reliability of rotating rectifier is low. In addition, the starting processing is complex. Hybrid excitation synchronous machines (HESMs) are recently proposed as the potential candidates for EV drive systems, wind power generation and more electric aircraft, for the air-gap flux can be regulated by field current efficiently. This paper proposes a new hybrid excited starter-generator (HESG) with magnetic field decoupling topology for MEA applications. The predicted electromagnetic performance is validated by the 3-D finite-element analysis (FEA) model. Finally, the results of FEA are confirmed by the experiments on a 60kVA HESG. The contribution of this paper is to propose a promising HESG to replace WRSMs in aircraft starter-generator applications. II.Operation Principle and Machine Specification Table I presents the design requirements of a starter-generator for aircraft generation system. The structure of the HESG with decoupling magnetic field is shown in Fig. 1, it can be seen that the PM side air-gap is larger than EE side air-gap. In order to implement high air-gap flux density, the Halbach-array PM rotor is preferred for the flux concentrating characteristic, low harmonic components and low inductance characteristic. Fig. 2 shows the HESG topology. It can be seen that the PM rotor and the two EE rotors can be installed on the shaft together seamlessly, which can greatly improve the compactness, torque density and power density. As shown in Fig. 3, the magnetic flux path can be divided into axial part and radial part. There is no axial flux in the stator core so that the stator can keep the same with that in WRSM and brings sinusoidal back EMF, which makes it suitable for starter-generator system. Table II provides the main parameters of the designed HESG with decoupling magnetic field. III.Electromagnetic Performance Analysis In order to verify the applicability of the new HESG magnetic field decoupling topology for AC starter-generator system, the electromagnetic performance analysis mainly focus on the power characteristics and flux regulation capability. Fig. 4 shows the distribution of magnetic field with different field currents. As shown in Fig. 5, the back-EMF magnitude increases with field current. Fig. 6 shows the output voltage versus output current at 8000r/min for different field currents. It can be seen that the output characteristics can be regulated by field current. The output power versus speed for different field currents is shown in Fig. 7. A 60kVA prototype is manufactured and measured for the verification of previous analysis. The photos of the motor are shown in Fig. 8. The experimental results will be supplemented in the later formal paper. IV.CONCLUSION In this paper, a new HESG is proposed for aircraft generation system. The topology and operating principle are described in detail. In addition, the electromagnetic performance of HESG is investigated to verify the applicability of the HESM to a starter-generator system for aircraft applications.

**References:**

[1] Y. Liu, Z. Zhang and X. Zhang, "Design and Optimization of Hybrid Excitation Synchronous Machines With Magnetic Shunting Rotor for Electric Vehicle Traction Applications," in IEEE Transactions on Industry Applications, vol. 53, no. 6, pp. 5252-5261, Nov.-Dec. 2017.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/d1a01027692aa59030478c3a38de0002.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/112fdd56d19723570dd66e8465c54e37.jpg)

technical paper

I. Introduction The conventional modulating ring in a coaxial magnetic gear is composed of a sequence of ferromagnetic blocks. The rotating cylinder planetary gear (RCPG) proposed by Davey et al borrowed the conventional topology but replaced the ferromagnetic blocks with free-spinning magnetized cylinders called planet gears [1]. The planet gears enhance the modulating effect and hence the torque density, since they themselves are a source of magnetomotive force (MMF). Davey's team reported 79% increase of torque density over a conventional coaxial gear of comparable dimension [1]. In the operation of the RCPG, the planet gears move to new angular position corresponding to each updated relative position of the two rotors. It is a prerequisite to know these angular positions of planet gear for the calculation of the performance such as torque. Since the planet gears are unconstrained, they move to zero-torque positions. However, finding these positions is mathematically a difficult optimization with a large number of unknowns and strong internal coupling. A custom optimization algorithm combining splines, quadratic interpolation and response surface method was implemented for these positions that minimize the maximum torque on the planet gears. This algorithm was proved to be the most effective though it converged more slowly than the other algorithms that Davey's team had tried [1]. Alternatively, Wang et al proposed that the total magnetic energy stored in the gear should be minimum (or maximum magnetic coenergy) when all the planet gears settle in their equilibrium positions [2]. Wang's team found the positions of planet gear corresponding to the minimum stored magnetic energy, by using gradient-based Broydon–Fletcher–Goldfarb–Shanno (BFGS) and three preconditioning techniques, respectively. The BFGS algorithms converge apparently faster than Davey'ss custom algorithm. However, two of the preconditioning techniques need flux-tracing finite element (FE) calculation with or without non-magnetized cylinders. The other technique seems analytical and consequently saves the preconditioning cost, but it was not described in detail [2]. This digest proposes a BFGS algorithm with an alternative analytical preconditioning technique for the angular positions of planet gear corresponding to the minimum stored magnetic energy. The algorithm can quickly find these angular positions for each relative position of the two rotors in the operation of the gear. II.Description of Proposed Preconditioned BFGS The proposed preconditioning technique estimates the angular position of a planet gear depending on the polarities of the closest neighboring magnets on the rotors. This estimate can be easily formulated if the two closest neighboring magnets have different polarity, but it is difficult for some special relative positions of the planet gear and the two rotors. For example, the closest neighboring magnets have same polarity, as shown in Fig. 1 (a) and (b), or the distances from the planet gear to the two neighboring magnets on a rotor are equal, as shown Fig 1 (c) and (d). The angular position of planet gear (given by the direction of polarity, shown as the red arrow in Fig. 1) in each special case is found by the BFGS without preconditioning. The preconditioned BFGS relies on this result to formulate the presetting of angular position for each special case in the performance calculation of RCPG. The calculation of gradient in the BFGS algorithm was also improved to ensure the convergence to the global optimum. The formulation of the proposed preconditioning and the improved gradient calculation will be given in the full paper. III.Performance Calculation With Preconditioned BFGS The proposed preconditioned BFGS was used to calculate the torque for each relative position of the planet gears and the rotors in the running of a magnetic gear with 4 inner poles, 40 outer poles and 22 planet gears. Randomly initialized and flux-tracing preconditioned BFGS algorithms were also used respectively to calculate the torque. The latter algorithm makes two-dimensional (2-D) FE calculation of the flux distribution in the magnetic gear with the conventional modulators of the same dimension as the planet gears, and initializes each planet gear's angular position for the BFGS optimization according to the field direction in the center of the corresponding conventional modulator. Fig. 2 (a) compares the performances of the three BFGS algorithms for the optimization at a certain relative position of the planet gears and the rotors. The randomly initialized, flux-tracing preconditioned and proposed preconditioned BFGS algorithms made 21, 16 and 14 iterations, and calculated the stored magnetic energy by FE for 474, 348 and 279 angular position cases in total, respectively, until the convergence. The running of the magnetic gear with different initial angles of the inner rotor was simulated by FE and the proposed preconditioned BFGS. Fig. 2 (b) shows the torque-initial-angle curve given by this simulation. IV.Conclusion This digest proposes an analytically preconditioned BFGS algorithm for the performance calculation of RCPG. With the preset angular positions of planet gear, the BFGS converges fast and significantly saves the cost for the FE simulations of the full-range operation of RCPG. The full paper will discuss the application of other algorithms to the analysis of RCPG.

**References:**

[1] K. Davey, et al, IEEE Transactions on Industry Applications, vol. 52, no. 3, pp. 2253–2260 (2016) [2] R. Wang, et al, IEEE Magnetics Letters, vol. 7, Art. no. 1303805 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/24aefc2a2086278c9a4c40b19bcdde82.jpg)
Fig. 1. Special preconditioned cases

![](https://assets.underline.io/uploads/markdown_image/1/image/0e9bc3bec8e9ad352ffbbbf0931f3000.jpg)
Fig. 2. Performances of BFGS algorithm and torque capacity curve.

 Optimization Algorithms for Performance Calculation of Rotating Cylinder Planetary Gear

Axial flux magnetic-geared double-rotor machines (AMGDRMs) are characterized as a potential core component of the power splitting system in hybrid electric vehicles (HEVs). Conventional AMGDRMs suffer from low mechanical strength due to high axial magnetic force. In this paper, an interior-modulating-rotor axial flux magnetic-geared double-rotor machine (IMR-AMGDRM) is proposed to solve this problem. An analytical model of the IMR-AMGDRM is proposed to predict the magnetic field distribution and electromagnetic performances. Since analytical model is based on 2-D geometry, a 2-D approximation of IMR-AMGDRM which has similar output performance to 3-D finite element analysis (FEA) is presented based on the permanent magnet (PM) magnetic energy equivalent principle. Utilizing subdomain method, the magnetic field distribution and electromagnetic performances are calculated. Finally, the accuracy of the proposed analytical model is validated by 3-D FEA. Index Terms—Analytical model, axial flux, magnetic-geared machine, double-rotor machine. I. Introduction Axial flux magnetic-geared double-rotor machines (AMGDRMs), which enable high torque density, have been considered a promising candidate for power splitting in hybrid electric vehicles (HEVs) [1]. However, conventional AMGDRMs suffer from low mechanical strength due to high axial magnetic force. To enhance mechanical strength, an interior-modulating-rotor axial flux magnetic-geared double-rotor machine (IMR-AMGDRM) which can reduce axial magnetic force dramatically is proposed in this paper. Fig. 1 (a) and (b) illustrate the configuration of the proposed IMR-AMGDRM. As axial flux type machine, IMR-AMGDRMs have complex 3-D magnetic circuits. 3-D finite element analysis (FEA) can offer accurate results by taking into account the nonlinear factors such as magnetic saturation and flux leakage. But the major drawback of 3-D FEA is serious time cost. Analytical model which is much lower time-consuming provides an alternative for electromagnetic performance prediction in the initial design procedure. In this paper, an analytical model of the IMR-AMGDRM is proposed. The geometry of analytical model is derived based on PM magnetic energy equivalent principle to guarantee similar output performance to 3-D FEA. The solution to analytical model is calculated by subdomain method. To evaluate the accuracy of the proposed analytical model, the results computed by analytical model and that of 3-D FEA are compared. II. Configuration of IMR-AMGDRM In conventional configuration, the inner and outer rotors are the permanent magnet (PM) rotor and the modulating rotor, respectively. Since the modulating rotor is closer to the PM rotor than stator, the modulating rotor suffers from high axial magnetic force. Furthermore, the modulating rotor is hollow and thus the low mechanical strength of modulating rotor becomes the major drawback of conventional configuration [1]. To solve this problem, the IMR-AMGDRM which switches positions of the PM rotor and the modulating rotor is proposed. In interior-modulating-rotor configuration, as shown in Fig. 1 (a) and (b), the PM rotor is between the modulating rotor and stator, i.e. the inner and outer rotors are the modulating rotor and the PM rotor, respectively. Owing to that the PM rotor suffers from reverse axial magnetic forces from both sides simultaneously, the total axial magnetic force is dramatically reduced. Hence, although the outer rotor is hollow in both configurations, the axial magnetic force of interior-modulating-rotor configuration is significantly decreased, leading to higher mechanical strength and reliability. III.Geometry of 2-D Approximation Generally, the unrolled section of axial flux machine at mean radius is used as 2-D approximation. However, few references are found to evaluate the electromagnetic performance equivalence of such approximation. To make the electromagnetic performance of 3-D model and 2-D approximation equal, the amount of magnetic energy of the PM should remain unchanged after approximation, i.e. PM magnetic energy equivalent principle [2]. A 2-D approximation of IMR-AMGDRM which has identical output performance is presented by using PM magnetic energy equivalent principle. IV. Analytical Calculation of IMR-AMGDRM The proposed analytical model is illustrated in Fig. 1 (c). It can be seen that the model consists of four subdomains. Region i, I, II and III represent the ith slot of the modulating rotor, the inner air gap, the PM rotor and the outer air gap, respectively. Utilizing subdomain method, the magnetic field distributions in the inner and outer air gaps are obtained by the solution of Laplace’s and Poisson’s equations. Then, the electromagnetic performances such as no-load back EMF, torque and axial force can be derived from the calculated magnetic field distributions. Comparisons of computation accuracy between analytical model and 3-D FEA is shown in Fig. 2. As can be observed, the results of analytical model are well consistent with that of 3-D FEA, validating the proposed method.

**References:**

 [1] M. Q. Wang, D. C. Tong and P. Zheng, IEEE Trans. Ind. Electron., vol. 66, no. 1, pp. 806-817( 2019). [2] Kim J S, Lee J H, Song J Y, and Kim D W, IEEE Trans. Magn., vol. 53, no. 6, 8105304(2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6f461fd509eebd7cd34868edda2a46ab.jpg)
Fig. 1. IMR-AMGDRM. (a) Overall view of configuration. (b) Exploded view of configuration. (c) Analytical model.

![](https://assets.underline.io/uploads/markdown_image/1/image/464feedb2617c359e0d07874766cd2b5.jpg)
Fig. 2. Comparisons between analytical model and 3-D FEA. (a) Axial flux density distribution in the inner air gap. (b) Axial flux density distribution in the outer air gap. (c) The static torque characteristic. (c) The static axial force characteristic.

 Analytical Modeling of an Axial Flux Magnetic-Geared Double-Rotor Machine with Interior-Modulating-Rotor

Magnetic lead screw (MLS) is a new type of linear actuator with high force density. Its output force depends not only on the arrangement of the permanent magnet (PM), but also on the materials used for the PMs, and the different materials of the PM directly affect the cost of the MLS. Therefore, based on this, a proposed MLS is given based on the combination of PM structure and magnetization direction and the combination of different PM materials. Compared with the traditional structures, it can not only improve the output force of the MLS, but also reduce the cost of the MLS. The results show that the size of air gap, the size of PM and the proportion of different materials combinations have great influence on the performance and cost of MLS. Finally, the performance of the proposed structure is compared with the traditional structures. The results show that the output force is increased by 21.5% and the cost is reduced by 21.4% under the same volume of MLS and PM. Index Terms — MLS, PM structure, magnetization direction, output force, cost. I.Introduction In recent years, as a new type of high force density linear actuator, magnetic lead screw (MLS) has been widely used in many fields, ranging from CNC machine tools, wave power generation to artificial heart [1-3]. MLS is similar to mechanical lead screw, which can convert linear motion into rotary motion, and vice versa. Compared with mechanical lead screw, MLS has the characteristics of inherent overload, minimum friction and low maintenance [4]. But for the existing applications and MLS structure, in addition to its output force is still low, there is also a problem of high cost caused by the use of high-performance PM materials in order to improve the output force of the MLS. Based on the above problems, a proposed MLS is given based on the combination of PM structure and magnetization direction and the combination of different PM materials, which improves the output force and decreases its cost. Detailed proposed structure introduction and operation principle are introduced in the second part. In the third part, the influence of the main parameters on the output force and cost is designed and optimized, and finally the size parameters of the structure are given. Finally, the performance of the proposed model is simulated and compared with the traditional structures to verify the superiority and economy of the proposed model. II.Structure and Operation Principle Compared with the traditional MLS structures, the proposed structure is shown in Fig. 1. The blue block and red block are radially magnetized PMs, in which the blue block is rectangular shape and the red block is salient pole shape, and both are made of NdFeB material. Green and yellow block are axially magnetized PMs with rectangular shape, and are made of other materials. Compared with the traditional halbach magnetizing array, this structure has higher output force and lower cost, and the structure is not difficult to process. The detailed operation principle of MLS is introduced in this paper. Fig.1. The proposed model. III.Design and Optimization The main design point of MLS is how to design the 3D structure of PM. There are three kinds of processing and installation structures, which are cylindrical, spiral and discrete surface mounted. In this part, the three structures will be compared in detail and the advantages and disadvantages of the description, and finally choose the appropriate shape for processing. After the structure is determined, the structure of the PM is optimized, mainly discussing the influence of the size of the air gap and PM on the output force and its cost of the MLS. In addition, the combination of different materials also has a great impact on the performance and cost of MLS, such as NdFeB, Ferrite, SmCo and Alnico. Finally, the best set of structural parameters of the MLS is obtained through the optimization, and the specific description is shown in the full text. IV.Results and Conclusion After design, optimization and analysis, the output force of the proposed model is shown in Fig. 2. It can be seen that the output force has increased by 21.5%. Moreover, after calculation, the cost of the proposed MLS is reduced by 21.4%, and the weight of the proposed MLS is also reduced by 8.6% due to the use of the combined materials of NdFeB and Ferrite, in which the proportion of NdFeB is 75.9% and Ferrite is 24.1%. In particular, limited by the number of words and pictures, we choose the traditional MLS for comparison, in which the PMs are rectangular and are made of NdFeB material. Fig.2. Performance comparison of the proposed model.

**References:**

[1] R. K. Holm, N. I. Berg, M. Walkusch, P. O. Rasmussen and R. H. Hansen, "Design of a Magnetic Lead Screw for Wave Energy Conversion," in IEEE Transactions on Industry Applications, vol. 49, no. 6, pp. 2699-2708, Nov.-Dec. 2013. [2] N. I. Berg, R. K. Holm and P. O. Rasmussen, "Theoretical and Experimental Loss and Efficiency Studies of a Magnetic Lead Screw," in IEEE Transactions on Industry Applications, vol. 51, no. 2, pp. 1438-1445, March-April 2015. [3] J. Ji, Z. Ling, J. Wang, W. Zhao, G. Liu and T. Zeng, "Design and Analysis of a Halbach Magnetized Magnetic Screw for Artificial Heart," in IEEE Transactions on Magnetics, vol. 51, no. 11, pp. 1-4, Nov. 2015, Art no. 8108604. [4] Z. Ling, J. Ji, J. Wang and W. Zhao, "Design Optimization and Test of a Radially Magnetized Magnetic Screw with Discretized PMs," in IEEE Transactions on Industrial Electronics, vol. 65, no. 9, pp. 7536-7547, Sept. 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/813f2c217de6006d1e11f97bf88afb43.jpg)
The proposed model

![](https://assets.underline.io/uploads/markdown_image/1/image/dffae9c2b87389d02da5ebb1d06a6e7e.jpg)
Performance comparison of the proposed model

 Optimization Design of Performance and its Cost of a Novel Magnetic Lead Screw by Combination of Different Permanent Magnet Materials

I. INTRODUCTION Non-permanent magnet machines are having growing interest recently due to the volatility of permanent magnet (PM) prices. Variable flux reluctance machine (VFRM) is a non-permanent magnet machine and it is a candidate for high-performance applications such as electric vehicles [1,2]. There are several slot/pole combinations of VFRM, such as 6/4, 6/5, 6/7, and 12/10 [3,4]. The 6/4 topology has a large torque ripple [5]. The 6/5 and 6/7 topologies have low torque ripple, but they have an unbalanced magnetic force (UMF) issue which causes mechanical stress and acoustic noise due to the odd rotor poles [6]. The 12/10 topology has a low torque ripple and balanced UMF. Although the structure of the VFRM is similar to the switched reluctance machine (SRM), VFRM has DC winding in the stator as well as three-phase AC windings. Therefore, the back-EMF waveform of the armature winding is sinusoidal. The control of the VFRM is easier than SRM due to the sinusoidal back-EMF. There is a magnetic coupling between armature and field winding because they have a common flux path as seen in Fig. 1. However, the field winding is fed by a DC current while armature windings have an AC current. In this study, the magnetic coupling between armature and field winding is analyzed and how VFRM can operate having DC and AC windings is explained. II. FLUX LINKAGE ANALYSIS OF FIELD WINDING Every tooth of VFRM has a field winding as shown in Fig. 1. Blue ones are field windings, red, green and yellow ones are armature windings. Firstly, the field winding is separated and called DC1, D2, D3, DC4, DC5, and DC6. Field windings are excited by DC current while armature windings are not excited. The flux of a single excited magnetic circuit is determined by Eq. (1). θ=NI/R(θr) (1) Where N is turns number, I is current, R is magnetic reluctance and θr is rotor position. The magnetic reluctance of the motor depends on rotor position because effective airgap changes with rotor position. Flux linkages of DC field windings and resultant flux linkage of field winding are obtained using the FEA, as shown in Fig. 2. Reluctance function of DC1 winding is obtained by FFT analysis of flux linkage, turns number and DC current. R0 is the DC component of reluctance, n is harmonic order, Rn is the magnitude of nth harmonic, and α is the angle of harmonic with respect to rotor position. RDC1=R0+∑Rnsin(nθr+α) (2) Flux linkage of DC1 winding is obtained using Eq. 1 and Eq. 2. Each of stator and rotor poles are not aligned at the same time, so there is a phase difference between DC windings. Therefore, the flux linkage of the DC2 winding is given in Eq. 4. λDC1(θr)=λ0+∑λnsin(nθr+α) (3) λDC2(θr)=λ0+∑λnsin(nθr+α+π/3) (4) Eventually, resultant flux linkage of when all DC windings are connected series is obtained by Eq. 5. λT(θr)=6λ0+∑λnsin(nθr+α)+∑λnsin(nθr+α+π/3) +∑λnsin(nθr+α+2π/3)+∑λnsin(nθr+α+3π/3)+∑λnsin(nθr+α+4π/3)+∑λnsin(nθr+α+5π/3) (5) λT(θr)=6λ0 (6) As shown in Fig. 2, all of the AC components eliminate each other and the resultant flux linkage has only a DC component. In this analysis, armature windings are not excited. Also, both field and armature windings are excited and flux linkage of the field winding is obtained by FEA, core material is assumed it has infinite magnetic permeance. Although magnitudes of the harmonic orders are changed, all AC components are eliminated and resultant flux linkages consist of DC components. Flux linkage of field winding has little harmonic if core material is steel, due to the magnetic saturation and leakage flux. These results could not be presented in this digest due to the figure limits. However, all of the results will be given in the final paper. III. CONCLUSION VFRM has DC field winding and armature windings in the stator. Although armature and field windings have a common flux path and magnetic coupling, field winding can be excited by DC current. Thus, the flux linkage of the DC field winding is analyzed while armature windings are excited by AC current. The field winding is separated, and flux linkages of every winding are obtained by FEA. Every winding has a DC biased AC flux linkage. However, all DC windings are connected series, AC components of resultant flux are eliminated. Eventually, field winding has only a DC component even if there is a magnetic coupling between armature and field windings. The magnetic circuit of analysis and results at full load will be given in the final paper due to the figure limits of the digest.

**References:**

1. T. Raminosa, D. A. Torrey and A. M. El-Refaie, IEEE Trans. on Industry Applications, Vol. 52, p. 2129, (2016) 2. T. Raminosa, A. M. El-Refaie and D. A. Torrey, IEEE Trans. on Industry Applications, Vol. 53, p. 3496, (2017) 3. X. Liu and Z. Q. Zhu, IEEE Transactions on Magnetics, vol. 49, p. 3020 (2013) 4. . J. T. Shi, X. Liu and Z. Q. Zhu, IEEE Transactions on Magnetics, Vol. 50, (2014). 5. J. Feng, L. Huang and Z. Q. Zhu, IEEE Transactions on Energy Conversion, Vol. 34. p.1135 (2019) 6. X. Liu and Z. Q. Zhu, IEEE Transactions on Industry Applications, Vol. 50. p. 3675 (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/746d6e18f4498238f67fb44609dbefd9.jpg)
Fig. 1 Structure and windings of 12/10 VFRM

![](https://assets.underline.io/uploads/markdown_image/1/image/1be7ef569c9266b81d7244046b273b53.jpg)
Fig. 2. Flux linkage variation of DC windings

 Analysis of Magnetic Coupling Between Armature and Field Windings of Variable Flux Reluctance Machine

Coaxial magnetic gears (MGs) create non-contact speed change by using a ferromagnetic slotted rotor between an inner and outer magnetic rotor with dissimilar magnet pole-pairs. In 2001, Atallah et al. demonstrated that a coaxial surface mounted permanent magnet MG with a gear ratio Gr = 5.5, could be designed to operate with a peak volumetric torque density of 100Nm/L [1]. This is approximately twice the continuous operating torque density of a motor. If a higher gear ratio is utilized, then the motor size can be reduced thereby increasing the overall performance of a magnetically geared drivetrain. To-date most studies have concluded that coaxial MGs are only capable of operating at a high volumetric torque density at a relatively low gear ratio, typically less than 1:8 [2]-[5]. The reason for the reduction in torque density at higher gear ratios is explained by the increased discrepancy between the inner and outer rotor magnet pole count as well as the pole pitch. For instance, Gouda [2] conducting a limited sweep analysis in which the magnet thickness and modulation thickness was varied and concluded that the peak volumetric torque density was close to a Gr=5 gear ratio and the torque density greatly reduced with increased gear ratios. More recently Gardner [3] came to the same conclusion. Gardner studied three different coaxial MG designs and computed that the lowest gear ratio design, Gr = 4, had a significantly higher torque density. In many applications a high gear ratio is required. In order to design a coaxial MG with a high gear ratio multistage MG designs must currently be utilized [6]. However, using a multistage MG complicates the mechanical structure and decreases the torque-per-kilogram of the rare earth permanent magnets. The object of this paper is to further investigate the performance of higher gear ratio designs, Gr&gt;20. In this paper the authors demonstrate, for the first time, that a coaxial MG can be simultaneously designed with both a high gear ratio, Gr&gt;20, and high torque density. In order to do this a complete design sweep of three key radial geometric sweep parameters (ri1, ro1, l2) is conducted using the MG design illustrated in Fig.1. In this MG design the laminated (M19) modulator is supported using an inner bridge and G11 Garolite rods (not shown). A pole-slot combination defined as (p1, n2, p3) = (1, 22, 21) is used to demonstrate the performance capability. When the outer rotor is stationary, a gear ratio of Gr = n2/p1 = 22 is obtained. In the design study the outer rotor is composed of a four-segment Halbach array (N48) rotor structure and the inner rotor is composed of a single pole-pair created by a single diametrically magnetizing NdFeB (N48) cylinder magnet. Note that the torque ripple is mitigated by choosing a pole-slot combination that minimizes the greatest common divisor (gcd) defined as: CT = gcd(2p1, n2) [7]. However, when CT = 1, an odd number modulation rotor slot number is obtained but this then creates a large radial force on the cage rotor due to the unsymmetrical slot number. Thus, the design with a CT = 2 was selected. In the illustrated design a 2-D finite element analysis model was used in which the outer rotor radius was fixed at ro3 = 60mm and the axial stack length was d = 60mm. The active material mass and volumetric torque density performance for the design example is shown in Fig. 2. Fig. 2 was created by simultaneously sweeping the three radial parameters. The inner rotor values were swept across values: (ri1, ro1)=([8, 10, … 30], [30, 32, … 50]) and the cage rotor radial thickness was simultaneously swept across the range shown in the legend of Fig. 2. The resulting pareto-front is evident. The peak volumetric torque occurred when (ri1, ro1, l2) = (8 mm,44 mm, 5/16”) and this yielded a peak computed volumetric and mass torque density of Tv = 380.5 Nm/L and Tm = 59.4 Nm/ kg respectively. The peak torque for the design was T = 258.2 Nm. The volumetric and mass torque density were computed using Tv=T/(dπro3^2) and Tm = T/(mm+ ms), where mm = mass of the magnets and ms = mass of the laminations. By studying Fig. 2. it can be seen that a design can be obtained that has an impressively high torque density whilst still having a high gear ratio. The authors believe this has not been demonstrated before. In order to understand the reason for this high performance, the full paper presents a comparison in performance for the lower performing high gear ratio design presented in [2] – [5] with the MG design presented here. A field and torque harmonic analysis are used to demonstrate that whist a higher gear ratio does lead to a lower torque density, if a complete sweep analysis is used, then the reduction in torque density performance with a high gear ratio is much less than previously demonstrated.

**References:**

[1] K. Atallah and D. Howe, IEEE Trans. Magn., vol. 37, no. 4, p. 2844, July 2001. [2] E. Gouda, S. Mezani, L. Baghli, IEEE Trans. Magn., vol. 47, no. 2, p. 439, Feb. 2011. [3] M. C. Gardner, M. Johnson and H. A. Toliyat, 2018 IEEE Energy Conv. Congress and Expo., Portland, OR, 2018, p. 5005. [4] D. J. Evans, Z. Q. Zhu, 2011 IEEE Intern. Elect. Mach. Drives Conf., Niagara Falls, ON, 2011, p. 1403. [5] E. Park, C. Kim, S. Jung, Intern. Conf. Elect. Mach. Sys., Jeju, Korea, p. 2529, Oct. 7-10, 2018. [6] M. C. Gardner, M. Johnson, H. A. Toliyat, IEEE Trans. Energy Conv. Vol. 34, no. 2, p. 665, June 2019. [7] G. Jungmayr, J. Loeffler, B. Winter, IEEE Trans. Ind. App., vol. 52, no. 5, p. 3822, Sept.-Oct. 2016.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/ec91cbc6f43b7fed3076279e99e01552.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/a250a46fc226ab68f10790bf829ca181.jpg)

 Investigating the Performance Potential of High Gear Ratio Coaxial Magnetic Gears.

I. Introduction Recently, compressed air has been used in many applications and compressors tend to high energy efficiency and high-power density, which becomes a hot issue and draws more and more interest. As a powerful candidate, permanent magnet (PM) machine including PM located on rotor and stator is an excellent candidate for the compressors [1]. However, due to the increase of rotation speed and rotor diameter, the rotor integrity for PM located on rotor becomes a critical issue. Although bandings have been installed in rotor, they inevitably increase the air-gap width and rotor loss and hence reduce the torque capability of the machine. Meanwhile, the electrical machines driven compressors has challenges in machines cooling, sizing and loss. The PM located on the stator, namely the flux-switching PM machines (FSPMMs), have been an intense topic of research for the high-speed compressors. And the torque density is comparable to the conventional rotor-PM machines. By combining the armature winding and excitation source in the stator, its rotor is a robust steel sheet lamination, a passive single material and salient pole rotor, making it inherently suitable for high-speed applications. Hence, there is a feasible solution to integrate the machine with the compressor, which combines the function of motor drive and compressor. In additional, the self-cooling capability of this topology is another important advantage due to its forced convection flow to the stator, rotor, magnet and winding generated by the rotor rotation, especially in high power density applications, which is robust in harsh environment. Even though the conventional topology (12/10 FSPMMs) can achieve more symmetrical phase back-EMF waves, it is not optimistic in terms of core loss under high-frequency excitation. A feasible design with the lowest possible slot-poles (6/4 FSPMMs) for three-phase windings is proposed by Li et al. [2], which possesses the lowest fundamental frequency for the given speed. The purpose of this paper gives a suitable structure for high-speed axial flow compressors based on the topology of FSPM machines. In order to minimize the size of compressor system, a design of dual-stator 6/4 FSPM machine-compressor is proposed. The electromagnetic performance of C-core and E-core topology is calculated and analyzed by the 3-D finite element analysis (FEA). The design is electromagnetically and aerodynamically coupling since the structure of rotor has significant effects on both the machine and compressor. For better fitting high-speed operation and generating compressed air, the rotor with asymmetric pole-width is used and optimized. II. Machines Topology The FSPM machines are attractive in ultra-high-speed application due to its robust rotor. A specification of 10 kW, 30 krpm dual-stator FSPM machines is designed and analyzed by 3-D FEA. For given speed, the dual-stator structure is a promising solution to minimize the fundamental frequency of the source system. Fig. 1 (a) and (b) show the topology of C-core and E-core stator of FSPM. The electromagnetic performance of two stator topology is analyzed and compared such as average torque, torque ripple and over load capability. As shown in Fig. 1 (c), the front rotor is offset-ed by 45° mechanically with respect to the rear rotor and the even harmonics are counteracted in the total flux linkage based on this topology. In order to better air flow, the asymmetric rotor poles are used in the integrated 6/4 FSPM machines. The parameters of the rotor are optimized in terms of electromagnetics and aerodynamics. III. Results The design of integrated machines-compressor based on the lowest slot-pole numbers is proposed. By the FEM analysis, the electromagnetic and aerodynamic performance of the proposed machines is calculated and compared. Fig. 2 (a) and (b) show the 3-D flux density distribution of the C-core and E-core 6/4 FSPM machines at no-load condition. Fig.2 (c) show the torque characteristic of two FSPM machines with different stator cores at on-load condition. The torque ripple of the machine with E-core stator reduce 25.7% than the one with C-core stator. The optimized E-core FSPM machine-compressor is verified to generate better torque characteristic and overload capability. Furthermore, after optimizing rotor topology, the E-core stator FSPM machines is a good candidate for axial-flow compressors, especially in higher rotation speed.

**References:**

[1] Gerada D, Mebarki A, Brown N L, et al. High-speed electrical machines: Technologies, trends, and developments[J]. IEEE Transactions on Industrial Electronics, 2013, 61(6): 2946-2959 [2] Liu M , Li Y , Sixel W , et al. Design and Testing of Low Pole Dual-stator Flux-Switching Permanent Magnet Machine for Electric Vehicle Applications[J]. IEEE Transactions on Vehicular Technology, 2019, PP(99):1-1.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/65a9694b1204d088dfcbc8e8506afb68.jpg)
Fig. 1. Topology of 6/4 FSPM machines. (a) C-core dual-stator. (b) E-core dual-stator. (c) Design parameters of rotor .

![](https://assets.underline.io/uploads/markdown_image/1/image/6a40f9af98ca6d5787928acb0d498802.jpg)
Fig. 2. The performance characterization of the FSPM machines. (a) Flux density distribution of C-core FSPMMs at no-load condition. (b) Flux density distribution of E-core FSPMMs at no load condition. (c) The torque characteristic of the machines with different stator cores.

 Design and Analysis of Dual-Stator Flux-Switching Permanent Magnet Machine-Compressor with Asymmetric Rotor Poles

The contra-rotating propeller (CRP), a complex propulsion device that produces thrust by two oppositely rotating propellers, can be used for applications like unmanned underwater vehicles, power generations and aero propulsions [1]. The CRP propulsion system requires two output shafts with equal and opposite torques. Nowadays, there are three ways to achieve the above function. Compared with the schemes which are driven by two independent machines or one conventional machine connected to gear box, the contra-rotating double-rotor machine (CRDRM) directly drives the CRP, which is the most competitive scheme due to the advantages like as high transmission efficiency, low noise and compact volume. However, the existing CRDRM schemes have several inevitable problems. Due to the existence of electric brushes, slip rings and rotating windings, the CRDRM scheme which is achieved by the coaxial rotation of armature winding and rotor has problems of poor reliability and difficult dynamic balance. Moreover, the heat dissipation becomes more difficult when the rotating winding is placed inside the machine. The other kind of CRDRMs adopts the way of double-rotor and stator with two sets of windings in the middle of two rotors, which has the severe heat dissipation problems [2]. Therefore, the research of the brushless CRDRM with easier heat dissipation is a main developed direction in CRP propulsion applications. In this paper, a transversely-dislocated magnetic-field modulated brushless double-rotor machine (TDMFM-BDRM) is proposed to solve the above problems. The TDMFM-BDRM is composed of a stator, a transversely-dislocated modulating (TDM) rotor and a permanent-magnet (PM) rotor, as shown in Fig. 1 (a)-(b). The stator ring windings, which is similar with the tubular linear machine, are distributed along the axial direction. The spoke-type PMs of the PM rotor are distributed along the circumferential direction. Moreover, the special structure of the TDMFM-BDRM is its TDM rotor, as shown in Fig. 1 (c)-(d), which is composed of the magnetic blocks and non-magnetic support. The magnetic blocks of one modulating group are regularly distributed along the oblique direction, and the number of modulated groups is equal to the pole-pair number of PMs. The proposed TDMFM-BDRM combines the structural characteristics of transverse-flux machines and the modulated theory of magnetic-field modulated machines. Therefore, the proposed TDMFM-BDRM has the following advantages: (1) it has high reliability due to the elimination of electric brushes and slip rings; (2) it has better heat dissipation condition because the stator is next to the frame; (3) compared with conventional machine, it has more design freedom because of the decoupling of electric load and magnetic load; (4) the stator ring winding has no end winding, which can save a lot of space of the machine system. Different from the conventional magnetic-field modulated machines, the main flux path of the TDMFM-BDRM is three-dimensional, and its operating principle cannot be explained by the conventional magnetic-field modulated theory. Therefore, the special magnetic-field modulated principle of the TDMFM-BDRM is investigated in detail. According to the theoretical analysis, the equal and opposite torques can be generated on the two rotors of the TDMFM-BDRM, and the speed difference of the two rotors can be controlled by the adjusting the frequency of stator currents. Therefore, the coaxial contra-rotating operating mode of the two rotors can be achieved. Furthermore, the operating principle and design method of the TDMFM-BDRM are analyzed in detail. The torque and speed characteristics are shown in Fig. 2 (a), where ps, fs, τs, and vs are the pole-pair number, frequency, pole pitch, and speed of stator axial magnetic-field, respectively; Tm, nm, and TPM, nPM are the electromagnetic torques and rotation speeds of transversely-dislocated modulating ring rotor and PM rotor, respectively; pPM is the pole-pair number of the PM rotor; pm is the number of magnetic blocks of one modulating group. In order to verify the validity of the proposed structure and theory, a 3-D finite element model is established and the calculated results are shown in Fig. 2 (b)-(e). The calculated results agree well with the theoretical results. The full paper will present the detailed magnetic-field modulated theory, design principle and contra-rotating performance analysis of the proposed TDMFM-BDRM.

**References:**

[1] H. Shin, J. Chang, and D. Hong, “Design and characteristics analysis of coaxial magnetic gear for contra-rotating propeller in yacht,” IEEE Transacrions on Industrial Electronics, vol. 67, no. 9, pp. 7250-7259, Sep. 2020. [2] G. Liu, G. Qiu, J. Shi, et al, “Study on counter-rotating dual-rotor permanent magnet motor for underwater vehicle propulsion,” IEEE Transactions on Applied Superconductivity, vol. 28, no. 3, Apr. 2018, Art. no. 0601905.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4b738b175f52241ad798b907425b55ad.jpg)
The structure, sectional drawing and expanded drawing of the TDMFM-BDRM

![](https://assets.underline.io/uploads/markdown_image/1/image/6e43f78c236edc084367c11caaa79ddb.jpg)
The characteristics and simulation results of the TDMFM-BDRM

 A Transversely-Dislocated Brushless Double-Rotor Machine Based on Magnetic-Field Modulation for Contra-Rotating Propeller

For many low-speed electrical machine applications it is usually cost effective to employ a high-speed machine together with a mechanical gearbox. This can also minimise system size and weight. The gearbox however brings disadvantages in terms of reliability, acoustic noise, mechanical vibration and the need for lubrication and maintenance. For the case of offshore wind turbines with high service life the disadvantages are compounded by the high cost of gearbox replacements. To eliminate these concerns in offshore wind applications, it is commonplace to delete the gearbox and use a direct drive machine, but care is required to ensure the size, mass and cost of the system do not become unfeasible. The Pseudo Direct Drive (or PDD®) is a magnetic and mechanical integration of a magnetic planetary gear with a permanent magnet generator. A magnetic equivalent to a planetary gear is embedded within a permanent magnet generator. This integrated approach is used to reduce the size and mass of the machine without recourse to a mechanical gearbox. By doing this the disadvantages of using a mechanical gearbox are avoided, but the size of the generator is minimised. This paper discusses the design, build and test results of a 200,000Nm, 500kW PDD machine shown in Fig 1. This is the world’s largest PDD machine and serves as a technology demonstrator for a larger 10MW project, providing validated data for this new class of machine at this size. The discussion presented includes the principle of operation of magnetically geared machines, and specifically how this is applied in the design of very large machines. The magnetic gear embedded in the generator is described and the equivalence of a mechanical planetary system with analogous components (sun, planets and ring) is detailed. The high torque is reacted magnetically and there is no mechanical contact between the shafts. The inclusion of this single stage magnetic gear gives the same uplift in performance to the generator system, i.e. increased rotor speed, reduced airgap torque and increased efficiency whilst allowing the size and mass of the generator to be minimised. The key design features of a highly integrated magnetic gear are discussed:- ● The magnetic components service both the generator and the gear; hence the losses can be assumed to be shared and minimised, leading to very high system efficiencies ● The compliant nature of the gear leads to the attenuation of drive train oscillations and reduces acoustic noise. ● There is no lubrication of the gear element (except bearings) and the service interval can be extended accordingly. ● The integrated magnetic gear is placed in the centre of the machine and does not increase the overall volume envelope. ● Small size means higher power machines may be built with existing facilities designed for direct drive generators. This paper gives quantitative experimental data of a 500kW, 200,000Nm magnetically geared PDD wind turbine generator that was designed, built and tested as part of the DemoWind Programme funded under the European Research Area Network. Key operating data is shown, including verified electromagnetic parameters. Component thermal traces verify the thermal and operation models with an exemplar case presented at 80% load showing a 70°C rise in winding temperature. Dynamic operating data is presented as a measured 10minute recorded trace of speed, torque, current and electrical power whilst the machine is operated with a real-world input profile example at nominal 10m/s wind speed conditions, this verifies the performance of the machine in realistic wind conditions. The results presented confirm both the accuracy of the underlying analysis models and the suitability of the generator system as a wind turbine machine. Finally, the verified data is used to provide Levelized Cost of Energy (LCOE) analysis for a 10MW system (performed independently). The LCOE calculations are based on OPEX, CAPEX and Energy production models comprising 17 sub-categories upon which the influence of the PDD efficiency, mass, CAPEX and operational parameters can be individually evaluated. The results show a reduction in LCOE of 2.8% and 2.5% when the PDD system is compared to the equivalent direct-drive and mid-speed geared systems respectively as detailed in Fig.2

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2fc5625af5504e957c7e8d3a8a5b8a8a.jpg)
Fig. 1. 200,000Nm, 500kW PDD generator on test

![](https://assets.underline.io/uploads/markdown_image/1/image/53494368d068af346a6f950f995e5d77.jpg)
Fig. 2. Source of LCOE savings of PDD compared to alternative drivetrains

 Design, Build and Test of a Magnetically Geared Generator for Wind Turbine Applications INVITED

Tidal turbine generators are submerged in water, which means reliability is a critical criterion, arguably even more than efficiency. The objective of this paper is to discuss the main electromagnetic design aspects of a flooded permanent magnet (PM) direct-drive generator for tidal turbines. In a flooded generator design, the stator-rotor gap is filled with sea water instead of air, as shown in Fig. 1. The reasons to consider flooded direct-drive generators are to get rid of highly pressurized rotary seals that keep the water outside the nacelle which holds the generator; additionally, a flooded design could also improve cooling. This could result in a higher power density generator and/or potentially better performance. As a ramification of the flooded design, however, protective sleeves (also called cans) are needed to shield the magnets, iron and windings from sea water [1]. The paper mainly focuses on the following three aspects of the generator, which could provide useful guidelines for the design of flooded generators. I. WINDING TYPE SELECTION Fractional slot windings are cheaper and easier to manufacture than distributed windings [2]. In large direct-drive generators, it may also result in lower copper losses, improving the lifetime cost of the generator. However, because of the higher space harmonic content of the fractional slot windings, they could cause high eddy current losses in the rotor magnets and the rotor sleeve if it is conductive [3]. In contrast, a distributed winding is costlier to manufacture, especially in a flooded design due to larger end windings, but contains much lower space harmonics. These aspects need to be carefully considered while selecting a winding layout for the flooded generator. II. SLEEVE MATERIAL SELECTION For the stator, a non-conductive sleeve is strongly preferred. Even at no-load, the losses in a conductive stator sleeve due to rotating magnets would be too high for a reasonable design. On the other hand, for the rotor a conductive sleeve may be acceptable. In this study, we compared the eddy-current losses in the rotor sleeve of a flooded generator with different sleeve materials, ranging from highly conductive metallic materials, such as stainless steel to non-conductive glass fiber. Whereas the glass fiber has no loss, it is not as robust against water ingression as metallic materials [4]. Consequently, a thicker layer of glass fiber would be necessary compared to the metallic sleeve. This would increase the volume of the magnets required, increasing the generator cost. Thus, the selection of sleeve material should be based on multiple aspects, such as losses in the sleeve, material strength, water-proofing properties, thermal performance of the generator, winding layout, etc. rather than just losses. III. THERMAL ANALYSIS The effect of flooding the generator on the temperature distribution is analyzed in this section. For this purpose, a flooded generator was compared with a similarly sized airgap generator (both are 300 kW at 30 rpm and both contain a rotor sleeve). Consequently, we assumed that the loss distribution in the airgap and the flooded generator is the same. Figure 2 shows the influence of flooding the stator-rotor gap on the magnet and the slot temperatures in a flooded and an airgap PM generator with fractional slot windings (non-negligible rotor losses). The figure also illustrates the effect of using materials with different electrical conductivities on the temperature distribution inside the machine. It is clearly seen that the materials with higher conductivity exhibit higher temperature in the magnets and in the stator slots on account of higher eddy current losses in the rotor. For the corresponding decrease in the magnet temperature on flooding, there is an increase in the temperature of the stator slot. This is because of the better heat transfer in the flooded stator-rotor gap compared to the airgap. Whether the net heat transfer is from the rotor-to-stator or vice-versa would depend on the losses in the rotor and the stator, rotor-to-ambient thermal path via the stator iron and rotor-to-ambient thermal via the shaft and bearings, etc [5]. In the case of glass fiber (GRP) sleeve, it is seen that the magnet temperature in the airgap design is more than the flooded design. This is because in this case magnet (or rotor) temperature is less than the slot (or stator) temperature in the airgap design. As a result, on flooding the heat transfer improves enhancing the heat transfer to the rotor, which increases the magnet temperature rather than decreasing it [5].

**References:**

[1] O. Krovel, R. Nilssen and S. Skaar, in Proceedings of ICEM, 2004. [2] A. El-Refaie, IEEE Transactions on Industrial Electronics, vol. 57, no. 1, pp. 107-121, 2009. [3] F. Wani, U. Shipurkar and H. Polinder, in 13th European Wave and Tidal Energy Conference, Napoli, Italy, 2019. [4] L. Bian, J. Xiao and J. Zeng, Journal of Composite Materials, vol. 46, no. 25, pp. 3151-3162, 2012. [5] F. Wani, J. Dong and H. Polinder, in 13th International Conference on Electrical Machines (ICEM), Alexandroupolis, Greece, 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e77fcd839c90ba32859760e499dd9002.jpg)
Fig. 1. A representative diagram of a flooded permanent magnet generator (not drawn to scale).

![](https://assets.underline.io/uploads/markdown_image/1/image/98fb2f2d28af815d02e8628cf2f594ca.jpg)
Fig. 2. Temperature of the magnets and the slots is shown as a function of different rotor sleeve materials. Electrical conductivities of the materials are: Stainless steel 304L—1.30e6 S/m ; Inconel alloy 718—0.80e6 S/m ; Titanium SP700—0.61e6 S/m; Glass reinforced plastic (GRP)—0 S/m [5].

 Flooded Permanent Magnet Direct-drive Generator for Tidal Turbines INVITED

I. Introduction There are many studies on axial flux permanent magnet machines (AFPMMs) due to their compactness [1]. The conventional AFPMMs comprise a stator and two rotors. In general, the stator with toroidal windings or overlapping windings is sandwiched between two rotors [2][3]. Toroidal windings have shorter ends than overlapping windings, which can reduce copper loss and ending effect. However, this structure also wastes the ends of windings, which means that the windings are not utilized sufficiently. To some extent, it reduces the torque density of the machine. This paper proposes a novel axial-radial flux permanent magnet machine (ARFPMM) to solve the problem. In the ARFPMM, the endings of windings are also used to produce torque with little increase of volume, which results in the improvement of torque density. II. Structure of ARFPMM The proposed ARFPMM integrates both axial-flux and radial-flux machines in a compact space, which improves the torque density. As shown in Fig. 1(a), the ARFPMM is composed of one stator, two axial rotors and one radial rotor. Because the end of overlapping windings is useless, the machine adopts toroidal windings. Thus, the stator is equipped with opening slots on three faces. Permanent magnets are mounted on the surface of rotors. The radial rotor is fixed and aligned with two axial rotors, which can avoid the tilt of axial rotors and generation of harmonics in flux density per phase. The inner and outer diameters of permanent magnets on axial rotors are the same as those of stator. Similarly, the height of permanent magnets on radial rotor is equal to that of stator. In order to suppress air-gap flux density harmonics and get more sinusoidal waveform of air-gap flux [4], the permanent magnets are arranged as Halbach-array. It can also increase the flux density in the air gap. The magnetization direction of PMs is related to the number of segments per pole pair. As shown in Fig. 1(b), each pole pair is divided into six segments, so the magnetization direction of each segment varies 60° in turn. III. Design and Analysis Compared with integer-slot concentrated windings, fractional-slot concentrated windings can enhance flux-weakening capability and reduce cogging torque [5]. Therefore, a 20 pole 24 slot fractional-slot concentrated-winding machine is chosen. In the case, the winding factor is 0.966. It is related to the no load back electromotive force (EMF) which can be calculated as equation (1). E0=4.44fkwNΦ10 (1) Where f is the electric frequency of the machine, kw is the winding factor, N is the number of coils per phase in series, Φ10 is the magnetic flux. In the ARFPMM, three rotors are used to increase the magnetic flux in air gap. The result of 3D FEA for back EMF is shown in Fig. 2(a). Fig. 2(b) is the fast Fourier transform of back EMF. It shows that the maximum harmonic is the third order harmonic, which can be neglected due to the star-connection of three phase windings. Because the magnetic flux in air gap is increased under the same operating state, the torque of ARFPMM is also increased. Fig. 2(c) shows the torque of the machine at rated conditions when the current is 7 A and rotor speed is 600 rpm. In the condition, the average torque is 41.63 Nm and the torque density is 28.58 Nm/L. The torque ripple is 3.4 Nm, 8.1% of the rated torque. As shown in Fig. 2(c), the peak-peak value of cogging torque is 3.26 Nm. IV. Conclusion This paper proposes a novel ARFPMM with a unique structure of two axial rotors and one radial rotor, and implements its design and FEA. Due to the Halbach-array PMs, the main harmonics of back EMF is the third order harmonic, which is negligible when the windings are connected in star-connection. Compared with conventional AFPMM, the structure increases the torque through increasing the magnetic flux through windings per phase. Thus, the ARFPMM reaches an extremely high torque density of 28.58 Nm/L. On the other hand, fractional-slot concentrated winding configuration reduces the cogging torque, of which the peak-peak value is only 3.26 Nm. Acknowledge This work is supported in part by NSFC (52077186&51677159), in part by STIC of Shenzhen Municipality (JCYJ20180307123918658), and in part by ITF (ITP/027/19AP), HK.

**References:**

[1] W. Tong, S. Wang, S. Dai and S. Wu, et al, "A Quasi-Three-Dimensional Magnetic Equivalent Circuit Model of a Double-Sided Axial Flux Permanent Magnet Machine Considering Local Saturation," in IEEE Transactions on Energy Conversion, vol. 33, no. 4, pp. 2163-2173, Dec. 2018. [2] M. F. H. Khatab, Z. Q. Zhu, H. Y. Li and Y. Liu, "Comparative study of novel axial flux magnetically geared and conventional axial flux permanent magnet machines," in CES Transactions on Electrical Machines and Systems, vol. 2, no. 4, pp. 392-398, Dec. 2018. [3] M. Aydin and M. Gulec, "Reduction of Cogging Torque in Double-Rotor Axial-Flux Permanent-Magnet Disk Motors: A Review of Cost-Effective Magnet-Skewing Techniques With Experimental Verification," in IEEE Transactions on Industrial Electronics, vol. 61, no. 9, pp. 5025-5034, Sept. 2014. [4] Z. Song, C. Liu, K. Feng, H. Zhao and J. Yu, "Field Prediction and Validation of a Slotless Segmented-Halbach Permanent Magnet Synchronous Machine for More Electric Aircraft," in IEEE Transactions on Transportation Electrification, vol. 6, no. 4, pp. 1577-1591, Dec. 2020. [5] G. De Donato, F. Giulii Capponi, A. Rivellini and F. Caricchi, "Integer-slot vs fractional-slot concentrated-winding axial-flux permanent magnet machines: Comparative design, FEA and experimental tests," 2011 IEEE Energy Conversion Congress and Exposition, Phoenix, AZ, 2011, pp. 3120-3127.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/697cf24946ef7e94bfba61f933056aa6.jpg)
Fig. 1 Structure of ARFPMM. (a) Topology overview, (b) Halbach-array PMs

![](https://assets.underline.io/uploads/markdown_image/1/image/a06dfaf0b07a6b05f86f78b37c8eff73.jpg)
Fig. 2 Back EMF and torque analyzed by FEA. (a) Back EMF waveform, (b) Fast Fourier transform of back EMF, (c) Electromagnetic torque and cogging torque

Electromagnetic Performance Analysis of a New Hybrid Excitation Synchronous Generator with Decoupling Magnetic Field

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Electromagnetic Performance Analysis of a New Hybrid Excitation Synchronous Generator with Decoupling Magnetic Field

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Optimization Algorithms for Performance Calculation of Rotating Cylinder Planetary Gear

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