France



The ongoing development in the landscape of low power electronics has paved the way for the emergence of autonomous wireless sensor networks (WSNs) to create a smart and responsive environment around us through the Internet of Things (IoT). For instance, efficient WSN performs structural health monitoring of heavy-duty vehicles like train and reports on vital physical parameters and alerts if there are any probable failure to reduce the chances of accidents. Perpetually powering these sensors is one of the critical bottlenecks in realizing a WSN system. The associated maintenance and installation cost [1] of the batteries limits the widespread deployment of the WSNs. The demand for the implementation of battery-less microsystems and the ubiquity of ambient vibrations in an industrial and domestic environment has made the electromagnetic vibration energy harvesters (EM-VEHs) [2] a striking sustainable energy source for powering the WSNs. Compared with the conventionally used narrowband linear VEHs, the nonlinear counterparts [3,4] are much more efficient in harnessing mechanical energy from real-world broadband vibrations owing to their intrinsic wideband frequency response. An effective way of realizing nonlinearity is by tailoring the stiffness of the spring geometry [5.6], which on the other hand depends critically on the thickness of the spring material limiting the scope of geometric alterations. Tapered spring structures on the other hand open up the scope for optimizing the degree of nonlinearity and hence the bandwidth of the VEHs by changing the taper ratio of the spring structure [7]. In this work, we exploit exponential and parabolic tapering to induce stretching based nonlinearity in the spring structure and we explore the overall performance of an optimized tapered EM-VEH that could be a potential candidate for powering WSN involved with railway infrastructure monitoring system.&lt;br/&gt;The EM transducer under consideration works on the Faraday’s principle, in which the relative motion between a pair of coil and magnet induces voltage across the coil, which could be harvested in the form of usable electrical energy. Among the other conventional transducers, owing to the reliability, longevity and large tunable parameters offered, the EM transducers are the most promising ones. We have used the structural mechanics module of COMSOL Multiphysics to explore the effect of tapering on the force-displacement relationship of the spring structures. The broad arm of the spring (length w&lt;sub&gt;1&lt;/sub&gt;) is fixed with the frame and the shorter arm (w&lt;sub&gt;2&lt;/sub&gt;) is attached to the moving load, which is the magnet assembly as shown in Figure 2. We have varied the taper ratio (= w&lt;sub&gt;2&lt;/sub&gt;/w&lt;sub&gt;1&lt;/sub&gt;) of the spring structures from 0.2 to 0.35, keeping the length of the shorter arm fixed to 4mm. Figure 1 depicts the first eigenmodes of the structures exhibiting out of plane displacements. Owing to the atypical stress distribution of these tapered structures, at a larger amplitude of excitation, the vertical displacement of the spring varies nonlinearly with the force. Hence, the restoring force of the spring consists of the linear part responsible for bending of the springs and the nonlinear part responsible for the stretching of the same. As compared with the parabolically tapered spring architectures, the exponentially tapered counterpart exhibits larger displacements for the same taper ratio. This can be attributed to the larger stress distribution on the springs owing to the exponentially reducing area.&lt;br/&gt;We further designed a nonlinear EM-VEH employing exponentially tapered spring having the taper ratio of 0.25 as shown in figure 2. The central paddle of the spring holds the magnet assembly comprising of four NdFeB magnets arranged such that it forms a close loop of magnetic field lines across the coil. To further eliminate the fringing of magnetic field lines and enhance the EM-coupling, block of soft magnetic steel is arranged on both sides of the magnet assembly, resulting in an EM-coupling of 15.2Wb/m. At low acceleration (0.1g), the system’s frequency response resembles with that of a linear VEH, the load power maximizing at 124Hz. As the excitation amplitude increases from 0.1g to 1g, the frequency response becomes gradually non-resonant in nature. When the frequency is swept in the forward direction, the load power changes from 235μW at 124Hz to 1.6mW at 154Hz with 1g acceleration, beyond this point the response suddenly falls off the high energy branch, which is a signature of the effect of induced nonlinearity. But when the frequency is swept in the backward direction, the response follows a lower energy branch, giving rise to the phenomena of multistability, which in turn aids in enhancing the operable bandwidth of frequency that the device offers. At 1g acceleration, the system offers 20Hz of bandwidth. The typical vertical acceleration of a diesel train is around 0.93g [8] with substantial mechanical energy distributed around 100-300Hz (Fig.2d). This developed VEH could be employed to harness this mechanical energy from trains to power the WSNs associated with the railway system responsible for structural health monitoring.

**References:**

[1] J. P. Amaro, R. Cortesão, J. Landeck &lt;i&gt;et al&lt;/i&gt;, &lt;i&gt;IEEE Transactions on Instrumentation and Measurement, &lt;/i&gt;vol. 64, no. 7, pp. 1847-1857&lt;br/&gt;[2] W. Hwang&lt;i&gt; et al.&lt;/i&gt;, &lt;i&gt;Applied Energy, &lt;/i&gt;vol. 243, pp. 313-320, 2019.&lt;br/&gt;[3] S. Roy, P. Podder, and D. Mallick, &lt;i&gt;IEEE Magnetics Letters, &lt;/i&gt;vol. 7, pp. 1-4, 2016.&lt;br/&gt;[4] P. Constantinou and S. Roy, &lt;i&gt;Smart Materials and Structures, &lt;/i&gt;vol. 25, no. 9, p. 095053, 2016.&lt;br/&gt;[5] B. Marinkovic and H. Koser, &lt;i&gt;Applied Physics Letters, &lt;/i&gt;vol. 94, 2009.&lt;br/&gt;[6] D. Mallick, A. Amann, and S. Roy, &lt;i&gt;Smart Materials and Structures, &lt;/i&gt;vol. 24, no. 1, p. 015013, 2014.&lt;br/&gt;[7] K. Paul, A. Amann, S. Roy, &lt;i&gt;Applied Energy&lt;/i&gt;, 2020, 116267, ISSN 0306-2619.&lt;br/&gt;[8] Real vibration, NIPS lab, https://realvibrations.nipslab.org/node/1093.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/211fa84d35c6420218da27712abd9a60.jpg)
Fig 1: First eigenmodes of parabolically (a) and exponentially (b) tapered spring structure with different taper ratio is shown. The force-displacement relation of springs is shown in (c).

![](https://assets.underline.io/uploads/markdown_image/1/image/5a7acb6abd7048009ffd86b9d85325f7.jpg)
Fig 2: Exponentially tapered EM-VEH (a) is designed with taper ratio 0.25. The EM interaction is depicted in (b). Frequency response of the nonlinear VEH is shown in (c) and power spectral density of train vibrations in (d).

INTERMAG 2021

 Design optimization of tapered wideband nonlinear electromagnetic vibration energy harvesters for powering IoT

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The ongoing development in the landscape of low power electronics has paved the way for the emergence of autonomous wireless sensor networks (WSNs) to create a smart and responsive environment around us through the Internet of Things (IoT). For instance, efficient WSN performs structural health monitoring of heavy-duty vehicles like train and reports on vital physical parameters and alerts if there are any probable failure to reduce the chances of accidents. Perpetually powering these sensors is one of the critical bottlenecks in realizing a WSN system. The associated maintenance and installation cost [1] of the batteries limits the widespread deployment of the WSNs. The demand for the implementation of battery-less microsystems and the ubiquity of ambient vibrations in an industrial and domestic environment has made the electromagnetic vibration energy harvesters (EM-VEHs) [2] a striking sustainable energy source for powering the WSNs. Compared with the conventionally used narrowband linear VEHs, the nonlinear counterparts [3,4] are much more efficient in harnessing mechanical energy from real-world broadband vibrations owing to their intrinsic wideband frequency response. An effective way of realizing nonlinearity is by tailoring the stiffness of the spring geometry [5.6], which on the other hand depends critically on the thickness of the spring material limiting the scope of geometric alterations. Tapered spring structures on the other hand open up the scope for optimizing the degree of nonlinearity and hence the bandwidth of the VEHs by changing the taper ratio of the spring structure [7]. In this work, we exploit exponential and parabolic tapering to induce stretching based nonlinearity in the spring structure and we explore the overall performance of an optimized tapered EM-VEH that could be a potential candidate for powering WSN involved with railway infrastructure monitoring system. The EM transducer under consideration works on the Faraday’s principle, in which the relative motion between a pair of coil and magnet induces voltage across the coil, which could be harvested in the form of usable electrical energy. Among the other conventional transducers, owing to the reliability, longevity and large tunable parameters offered, the EM transducers are the most promising ones. We have used the structural mechanics module of COMSOL Multiphysics to explore the effect of tapering on the force-displacement relationship of the spring structures. The broad arm of the spring (length w1) is fixed with the frame and the shorter arm (w2) is attached to the moving load, which is the magnet assembly as shown in Figure 2. We have varied the taper ratio (= w2/w1) of the spring structures from 0.2 to 0.35, keeping the length of the shorter arm fixed to 4mm. Figure 1 depicts the first eigenmodes of the structures exhibiting out of plane displacements. Owing to the atypical stress distribution of these tapered structures, at a larger amplitude of excitation, the vertical displacement of the spring varies nonlinearly with the force. Hence, the restoring force of the spring consists of the linear part responsible for bending of the springs and the nonlinear part responsible for the stretching of the same. As compared with the parabolically tapered spring architectures, the exponentially tapered counterpart exhibits larger displacements for the same taper ratio. This can be attributed to the larger stress distribution on the springs owing to the exponentially reducing area. We further designed a nonlinear EM-VEH employing exponentially tapered spring having the taper ratio of 0.25 as shown in figure 2. The central paddle of the spring holds the magnet assembly comprising of four NdFeB magnets arranged such that it forms a close loop of magnetic field lines across the coil. To further eliminate the fringing of magnetic field lines and enhance the EM-coupling, block of soft magnetic steel is arranged on both sides of the magnet assembly, resulting in an EM-coupling of 15.2Wb/m. At low acceleration (0.1g), the system’s frequency response resembles with that of a linear VEH, the load power maximizing at 124Hz. As the excitation amplitude increases from 0.1g to 1g, the frequency response becomes gradually non-resonant in nature. When the frequency is swept in the forward direction, the load power changes from 235μW at 124Hz to 1.6mW at 154Hz with 1g acceleration, beyond this point the response suddenly falls off the high energy branch, which is a signature of the effect of induced nonlinearity. But when the frequency is swept in the backward direction, the response follows a lower energy branch, giving rise to the phenomena of multistability, which in turn aids in enhancing the operable bandwidth of frequency that the device offers. At 1g acceleration, the system offers 20Hz of bandwidth. The typical vertical acceleration of a diesel train is around 0.93g [8] with substantial mechanical energy distributed around 100-300Hz (Fig.2d). This developed VEH could be employed to harness this mechanical energy from trains to power the WSNs associated with the railway system responsible for structural health monitoring.

**References:**

[1] J. P. Amaro, R. Cortesão, J. Landeck et al, IEEE Transactions on Instrumentation and Measurement, vol. 64, no. 7, pp. 1847-1857 [2] W. Hwang et al., Applied Energy, vol. 243, pp. 313-320, 2019. [3] S. Roy, P. Podder, and D. Mallick, IEEE Magnetics Letters, vol. 7, pp. 1-4, 2016. [4] P. Constantinou and S. Roy, Smart Materials and Structures, vol. 25, no. 9, p. 095053, 2016. [5] B. Marinkovic and H. Koser, Applied Physics Letters, vol. 94, 2009. [6] D. Mallick, A. Amann, and S. Roy, Smart Materials and Structures, vol. 24, no. 1, p. 015013, 2014. [7] K. Paul, A. Amann, S. Roy, Applied Energy, 2020, 116267, ISSN 0306-2619. [8] Real vibration, NIPS lab, https://realvibrations.nipslab.org/node/1093.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/211fa84d35c6420218da27712abd9a60.jpg)
Fig 1: First eigenmodes of parabolically (a) and exponentially (b) tapered spring structure with different taper ratio is shown. The force-displacement relation of springs is shown in (c).

![](https://assets.underline.io/uploads/markdown_image/1/image/5a7acb6abd7048009ffd86b9d85325f7.jpg)
Fig 2: Exponentially tapered EM-VEH (a) is designed with taper ratio 0.25. The EM interaction is depicted in (b). Frequency response of the nonlinear VEH is shown in (c) and power spectral density of train vibrations in (d).

technical paper

I. INTRODUCTION Due to the ability to maintain system operation after electrical failure, fault-tolerant machines are increasingly used in safety-critical applications, for instance, automobiles, aviation and armament [1]-[2]. In this paper, based on the dual-winding fault-tolerant permanent magnet motor (DFPMM) which not only inherits permanent magnet synchronous motors’ advantages of high torque density and high efficiency but also has high-performance of fault-tolerance, a novel electric machine drive system is proposed and studied. The 12-slot/10-pole DFPMM, with two separate sets of three-phase single-layer concentrated windings wound on alternate teeth, is capable of restricting fault propagation. The drive system is equipped with two independent drive circuits, while only one DC power supply is needed. With the proposed drive system, fault-tolerant performance to cope with open-circuit faults can be implemented by applying corresponding control strategies. Especially when the one-phase open-circuit fault occurs, system utilization rate is larger compared with the traditional drive system. Simulation and experimental results incorporating current, torque and speed under conditions of one-phase open circuit fault are exhibited respectively. The results verify the effectiveness of the proposed fault-tolerant control strategies and the high reliability of the proposed DFPMM motor drive system. II. THE DFPMM SYSTEM CONFIGURATION AND DESIGN The structure of the proposed electric drive system is shown in Fig. 1(a), which contains a DFPMM, two sets of three-phase full-bridge drive circuits, two triacs, six fuses, and an independent 270V DC power supply. The two sets of windings of the DFPMM are independent of each other, and the ABC windings are controlled by T1 to T6, while the XYZ windings are controlled by T7 to T12. The triac TR1 is connected to the neutral point of the ABC windings and the midpoint of the capacitors, and TR2 is in a similar way. Fuses F1-F6 prevent a shoot-through fault caused by a simultaneous breakdown of power switches in the same phase. During normal operation, two independent three-phase bridge drive circuits control the two windings, each with the same power output which is 50% of the total output power, and the two triacs are kept off. III. FAULT TOLERANT CONTROL STRATEGIES Based on the principle of constant magnetomotive force, control strategies after faults occur will be introduced in the full paper in detail. With the double d-q mathematical model of DFPMM, it is a vector control system that consists of two separate speed controllers, current controllers and SVPWM modules for both two sets of windings. When an open-circuit fault occurs in one set of the windings, the corresponding triac will be turned on, forming a power conversion circuit with a neutral point, as the conductive triac will add a degree of freedom to control the system under the fault condition. Meanwhile, two capacitors are used to perform amplitude and phase modulation on the remaining two-phase currents. IV. SIMULATION AND EXPERIMENTAL VERIFICATION Simulation and experiments are carried out under the conditions of open-circuit faults occurring in one phase, to verify the effectiveness of the proposed electric drive system and its control strategies. The test platform is shown in Fig. 1(b). The results are shown in Fig. 2, including three-phase current of the fault set of windings, speed and torque waveforms. Simulation waveforms of current, torque and speed when an open-circuit fault occurs in phase-A with and without the fault-tolerant control strategies are shown in Fig. 2(a) and Fig. 2(b), respectively. And experimental waveforms of current, torque and speed when an open-circuit fault occurs in phase-A with and without the fault-tolerant control strategies are compared in Fig. 2(c) and Fig. 2(d). From these results, the motor with the proposed drive system maintains the normal performance after the fault occurs, by applying the corresponding control strategy. Thus, the damage caused by open-circuit faults can be avoided. V. CONCLUSION In this paper, a highly-reliable DFPMM drive system aiming at ensuring a normal operation after open-circuit faults is proposed. By applying the control strategies and corresponding actions to typical types of faults, both simulation and experiments have done, proving the effectiveness of the proposed highly-reliable electric drive system. It can cope with open-circuit faults in different situations, and it is suitable for safety-critical applications. More detailed theoretical analysis and experimental verification will be presented in the full paper. ACKNOWLEDGEMENT 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 Jiangsu Planned Projects for Postdoctoral Research Funds under Grant 2020Z145.

**References:**

[1] B. Wang, J. Wang and A. Griffo, "Stator Turn Fault Detection by Second Harmonic in Instantaneous Power for a Triple-Redundant Fault-Tolerant PM Drive", IEEE Transactions on Industrial Electronics, vol. 65, no. 9, pp. 7279-7289 (2018) [2] X. Jiang, D. Xu and L. Gu, "Short-Circuit Fault-Tolerant Operation of Dual-Winding Permanent-Magnet Motor Under the Four-Quadrant Condition", IEEE Transactions on Industrial Electronics, vol. 66, no. 9, pp. 6789-6798 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3a7fa4ccb4534a2d2dfda84bf2bd5503.jpg)
Fig. 1. The proposed DFPMM drive system. (a) Configuration topology. (b) Test platform.

![](https://assets.underline.io/uploads/markdown_image/1/image/f6b8eac2831d1c3d6d19a84a0d792b69.png)
Fig. 2. The waveforms of three-phase currents, torque, and speed under conditions of phase-A open-circuit fault. (a) Simulation waveforms when no fault-tolerant control strategy is adopted. (b) Simulation waveforms when the fault-tolerant control strategy is adopted. (c) Experimental waveforms when no fault-tolerant control strategy is adopted. (d) Experimental waveforms when the fault-tolerant control strategy is adopted.

 Analysis of Highly Reliable Electric Drive System Based on Dual-Winding Fault-Tolerant Permanent Magnet Motor

The aim of this paper is to investigate the feasibility of a hybrid ferromagnetic bonding in a stack used in electrical machines. In a context of growing energy needs and the absolute need to reduce greenhouse gases, the stakes are high. For instance, with the electrification of aircraft in full development, it is essential to improve the power density of on-board electric actuators. Beyond aeronautics, the advantage of improving machine performance through its intrinsic performance of its materials is that this increase in efficiency does not depend on the application and becomes possible in all sectors of activity. This study which is supported by the French ADEME (Agency of the Environment and the Control of Energy) focuses on steel sheet stack intrinsic performance improvement for electrical machine applications. Generally, a laminated stack is composed by electrical steel sheet. An epoxy-based bonding is often used to ensure a structural cohesion of the stack in order to be manipulated and integrated. It also helps to keep a proper electrical insulation between sheets, limiting eddy current circulation. This study proposes to add iron powder to the epoxy bonding as described on Fig. 1, in order to improve the permeability of the bonding, which is magnetically neutral, becoming then a SMC. However, SMCs are generally used as a magnetic yoke [1] and not as an adhesive layer. The powder load is only intended to exploit a magnetically inert volume. The magnetic flux which will circulate in the packet will do so essentially through the sheets, but the gain in permeability envisaged to make pass more flux under the same magnetic field. The powder load could also improve the thermal conduction along the z axis, improve the thermal performance of the sheet package. Nevertheless, the circulation of eddy currents must remain limited between the sheets and the composite joints. It is necessary to limit the powder load to ensure this. Actually, the method proposed here does not really reproduce the SMC manufacturing process (pressure at temperature of the dielectric mixture - magnetic powder). In the case of a conventional SMC, the process ensures inter-grain isolation [2], making these materials particularly efficient at high-frequency. In the composite joint proposed here, the inter-grain (and therefore inter-sheet) insulation relies only on the residue of the epoxy adhesive around the grains once the sheets have been bonded. The distribution and the quantity of the adhesive being difficult to control, it is essential to keep a sufficient margin, and therefore to limit the powder load. On the other hand, the addition of a magnetic filler has been shown to improve the permeability of a mixture, especially at high frequency [3]. This feasibility study is based on ring core characterization. In order to limit parameters, the thickness and the number of sheets are set, respectively at 0.2 mm and 10 per stack. The thickness of the composite joint is also set at 50 µm. Actually, the powder grains must be large enough to retain interesting magnetic properties. A thickness of 50 µm is a good compromise in the context of a feasibility study. Finally, the only variable parameter is the powder charge. It has been decided to set it at 25%, 50% and 75% of the mass of the composite joint. A joint of the same thickness but loaded at 0% will be used as a reference. The magnetic permeability of the joint is actually determined by the powder volume / joint volume ratio. However, it is much simpler to proceed by mass ratio and to use density to calculate the corresponding volume ratio (4.5%, 13% and 30%). Besides, two types of iron powder are used (AHC 300 and MH300, both 300 mesh for grain size), each with specific properties. Therefore, each ring core corresponds to electrical steel sheet stack with a determined load of specific type of iron powder. Then, ring cores are manufactured and their windings are designed to reach 2 T at 400 Hz and 1000 Hz, and 1 T at 5000 Hz. Specific iron losses (W/kg) are measured and gathered in Fig. 2. This study demonstrates that adding iron powder to adhesive bonding of steel sheet is technically possible. The gain observed is significant and appears promising from the perspective of a more developed study. However, some technical points must be improved. More measurement should be proceeded, including reproducibility measurement. It would appear interesting to charge the adhesive with a metal powder of the same thermal conductivity as iron (or similar) but which would be non-magnetic. It could then be determined whether the performance is improved via magnetic permeability or via thermal conduction. In order to fully characterize these samples, optimization by numerical simulation could be considered, in order to precisely determine the parameters essential to performance. Finally, it seems essential to perform tests on a machine and not on ring cores, in order to ensure the real potential gains.

**References:**

[1] A. Jakubas, P. Gebara, S. Seme, “Magnetic properties of SMC cores produced at a low compacting temperature”. Acta Phys. Pol. A, 131(5), 1289-1293. [2] Y. X. Pang, S. N. B. Hodgson, J. Koniarek, “The influence of the dielectric on the properties of dielectromagnetic soft magnetic composites. Investigations with silica and silica hybrid sol–gel derived model dielectric.” Journal of magnetism and magnetic materials, 310(1), 83-91. [3] Belyaev, B. A., & Tyurnev, V. V. (2018). “Electrodynamic calculation of effective electromagnetic parameters of a dielectric medium with metallic nanoparticles of a given size.” Journal of Experimental and Theoretical Physics, 127(4), 608-619.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/398f5db97656d15612bd89dc54d799a1.jpg)
Fig. 1: Representation of the hybrid bonding in an electrical steel sheet stack.

![](https://assets.underline.io/uploads/markdown_image/1/image/8beea0f22ed5225ed70e5c7b610947ed.jpg)
Fig. 2: Results of specific iron losses measured in the samples for AHC300 and MH300 iron powder, at several frequencies and magnetic flux densities.

 Experimental study of a hybrid bonding in ferromagnetic stacks for electrical machine applications

Introduction. Additive manufacturing, also known as 3D printing, has experienced a tremendous development over the past twenty years. This process enables fast prototyping and it offers the ability to create complex shapes that would otherwise be difficult to produce using classical techniques. This process has been applied to a wide range of polymer, nowadays different research interests [1] focus on functional materials, such as metals or ceramics, to create components with enhanced physical properties. In this way, electromagnetic systems and power applications could exploit printed soft magnetic materials to be designed in a shorter amount of time and benefit from a wider range of feasible shapes. In this work, additively manufactured inductor made using two different printing feedstock types are presented. The simulation of a new geometry is made using finite element method in an attempt to explore the influence of the form on the flux density distribution. Finally, modeling and magnetic characterizations were carried out to compare the performances with a reference material. The specificity of this work consists in the usage of magnetic materials shaped with 3D printing. 1. Additive manufacturing of magnetic materials. Fabrication of objects is realized through the Fused Deposition Modeling technic. A first approach is to use a feedstock that comes as a filament loaded with metallic particles [2]. For this, two filaments from Proto Pasta and Virtual Foundry were used to produce shapes that could be used in an electrical system, like toroidal or E-shaped inductor. To achieve a greater concentration of the target materials, a pellet type feedstock was also used to perform MIM-like additive manufacturing with material from PolyMIM. In order to get good magnetic performances, the binding polymer has to be removed from the final part, so that it is only composed of the loaded material. Finally, the densification of the object has to be performed through a heat treatment. These last two steps are called debinding and sintering. Both processes will be undertaken in future works. 2. Modeling. In order to predict the behavior and performances of a toroidal inductor, a multi-physical modeling has been realized. It takes into account the analytical computation of the flux density, the thermal behavior due to the losses and the impact of heat on magnetic permeability. This model was then compared to a finite element simulation for validation. The simulation was performed using the software Opera-3D. The whole is put into perspective with practical tests. 3. New printable geometry. The main benefit from creating 3d printed objects is the variety of shapes that becomes accessible [3]. Complex geometry could be considered in the design process to suit requirements or even to modify the behavior of a component without using a different material [4]. To explore this possibility, an inductor with a complex shape was studied using finite element method. It consists in a torus that is distorted, along its axis, in a cyclic manner. The result is a wavy body that can be seen on figure 1.a. This core will be coiled and simulated as if it was made out of a ferromagnetic material. The geometry has been created to follow a wrapped-up sinus curves and to ensure a constant section along the path. This way, the circulation of the magnetic field can be modified without increasing the torus radius. Conductor were placed around each antinodes of the waves. Finally, different amplitudes were tried and the distribution of the magnetic field inside the core was observed. In figure 1.b, we can see that the magnetic field repartition can be tilted depending on the ripple range. 4. Magnetic characterization. To evaluate the performance of the different printed materials, a serie of magnetic characterizations was conducted. For this, the TX42/26/13 ferrite core from Ferroxcube was taken as a reference and several components with the same dimensions were printed with the feedstocks stated previously. Some examples of wound components are shown in figure 2.a. Magnetic variables such as magnetic permeability, maximum flux density and iron losses were observed. As it can be seen in the work of Bollig et al. [5], performances are way smaller than the reference material. This is due to the fact the first materials tested were made out of powder enclosed in a polymer binder, hence the density of magnetic material is very low. In figure 2.b, the magnetic permeability versus the density of the material is presented. Conclusion. To conclude, the use of additive manufacturing with magnetic materials offers a wide range of feasible shapes that can be used advantageously in the design process. However, the performances of such objects need to be improved . In future work, the density of the printed parts will be greatly enhanced by using a pellets based printing process and by going through the thermal treatments. Furthermore, a soft magnetic material that is similar to the reference presented earlier, will be used as feedstock for future prints.

**References:**

[1] Y. Yan, J. Moss, K. D. T. Ngo, Y. Mei, et G.-Q. Lu, « Additive manufacturing of toroid inductor for power electronics applications », in 2016 IEEE Energy Conversion Congress and Exposition (ECCE), Milwaukee, WI, USA, sept. 2016, p. 1-6, doi: 10.1109/ECCE.2016.7854826. [2] Y. Wang, F. Castles, et P. S. Grant, « 3D Printing of NiZn ferrite/ABS Magnetic Composites for Electromagnetic Devices », MRS Proc., vol. 1788, p. 29-35, 2015, doi: 10.1557/opl.2015.661. [3] F. Lorenz, J. Rudolph, et R. Wemer, « Design of 3D Printed High Performance Windings for Switched Reluctance Machines », in 2018 XIII International Conference on Electrical Machines (ICEM), sept. 2018, p. 2451-2457, doi: 10.1109/ICELMACH.2018.8506845. [4] L. Liu et al., « Design and Additive Manufacturing of Multi-Permeability Magnetic Cores », p. 6, 2017. [5] L. M. Bollig, P. J. Hilpisch, G. S. Mowry, et B. B. Nelson-Cheeseman, « 3D printed magnetic polymer composite transformers », J. Magn. Magn. Mater., vol. 442, p. 97-101, nov. 2017, doi: 10.1016/j.jmmm.2017.06.070.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2aa88ee44aa6d76f457a417e97a5c278.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/6ead33b37563f614f48b2d286d42878e.jpg)
Fig.2 Printed samples and magnetic characterization results (effective permeability over material density)

 Additive manufacturing for soft magnetic materials

1 Introduction In aviation field, direct drive permanent magnet (PM) rectifier generator is often used in Multi Electric Airplane (MEA). Multiphase AC windings and rectifier technology make DC generator an excellent DC source with low torque ripple and low voltage ripple. And by regulating the engine speed within specified range, the DC-link voltage can be maintained constant with various electric loading. The key point of designing such a kind of generator, is to predict the electromagnetic and thermal field accurately. To solve the problem above, most research focused on electromagnetic thermal coupling analysis based on computational fluid dynamics (CFD), which can accurately predict temperature distribution [1]. Obviously, CFD-based coupling analysis method is not fit for optimization of direct drive PM rectifier generator for CFD process is time-consuming. In this paper, we aim to adopt lumped parameter thermal network (LPTN) as a substitute to replace the CFD process, implementing an electrical circuit-electromagnetic field-thermal network coupling analysis algorithm, enabling a much faster solution to analyze and optimize a PM rectifier generator. 2 Coupling Analysis 2.1 Electrical Circuit and Electromagnetic Field Coupling Analysis Electrical circuit and electromagnetic field are coupled by electromotive force(EMF). Electromagnetic field analysis takes winding current as the input, and outputs EMF. Electrical circuit analysis takes EMF as the input, and outputs winding current. Electromagnetic field is usually solved by 2D time stepping FEM method. Electrical circuit is solved by branch current method. The coupling relation is so strong that magnetic vector potential and winding current can only be analyzed simultaneously. 2.2 Electromagnetic Field and Thermal Network Coupling Analysis Electromagnetic field analysis takes winding current as input, and outputs iron loss, copper loss, solid loss, etc. Thermal networks analysis takes loss as input, and output temperature of generator parts. The above is just one way coupling (designated as unidirectional) from electromagnetic field to thermal network, which is carried out by transferring and mapping loss data. In this paper, we have also considered the coupling from thermal network to electromagnetic field, involving material property, which will be described in Section 2.3. Here this is called bidirectional coupling method. As for the LPTN model of generator, thermal resistance of each part refers to Mellor’s T-shaped model [2]. The structure of each part is equivalent to a hollow cylindrical structure. Conduction, natural and forced convection are considered in the LPTN model. Model parameters and assumptions will be detailed in the full paper. 2.3 Material Property The temperature dependent material property is measured in the lab. The result is as follows: (1)For permanent magnet, coercivity and remanence decrease with temperature. (2)For silicon steel, the iron loss decreases with temperature. (3)For copper and permanent magnet, the resistivity increase with temperature. 2.4 Implementation Thermal network of generator is modelled and solved in Matlab, and electrical circuit and electromagnetic field are solved in ANSYS/Maxwell. Because the electromagnetic field and the temperature field have different time constant, during each iteration, several periods of electromagnetic field-circuit calculation are need to reach a steady state, followed by LPTN calculation. A control program is coded in Matlab to call thermal solver and Maxwell solver, and to transfer and map loss and temperature dependent material property. The convergence criterion is met if the temperature difference between adjacent iterations is less than 1°C. 2.5 Experiment Validation This prototype machine is an inner rotor PM generator with an integrated fan on the same shaft as rotor. The designed output power is 4.5kW at 7250rpm, and the DC link voltage is 50V. The generator is of 10 poles and 12 slots, filled with six phase double layer winding. The surface mounted PM is sintered SmCo30H. After 5 iterations, the coupled field analysis quickly reached convergence. The PM and winding temperature at each iteration and the corresponding loss is shown in Fig 2 . As shown in Fig 1, a load test has been carried out to validate the accuracy of the bidirectional coupling method. The servo motor drives the prototype at a constant speed and torque meter measures the mechanical torque. The rectifier circuit is connected to the terminal of the prototype. Two thermocouples are embedded in the end windings. Fig 2 shows the measured and simulated results. To illustrate the effect of temperature on electromagnetic field, the simulated result by unidirectional method is provided where the initial temperature is set to 25°C. Due to the consideration of thermal effect on material properties, the simulated result by bidirectional method is more accurate than unidirectional method. The prediction error of the bidirectional coupling method is within 5%. This paper proposed a much faster method to predict the electromagnetic and thermal field of direct drive PM rectifier generator. Lumped parameter thermal network (LPTN) is used as a substitute to replace the CFD process, greatly shortens the solution time. Furthermore, temperature effect on material property is considered, enabling a bidirectional coupling analysis in the paper. The experimental validation shows that the proposed method is enough accurate. The method can be applied to analyze and optimize a PM rectifier generator, as well as other typed motor.

**References:**

 [1] Yapeng Jiang , Dong Wang, Junquan Chen, "Electromagnetic-Thermal-Fluidic Analysis of Permanent Magnet Synchronous Machine by Bidirectional Method," IEEE Transactions on Magnetics, vol.3, no.54, pp. 1-5, 2018. [2] Mellor P.H, Roberts D, Turner D.R, "Lumped parameter thermal model for electrical machines of TEFC design," IEEE PROCEEDINGS-B, vol.138, no.5, pp.205-218, 1991.

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 Coupled Electromagnetic and Thermal Analysis of Permanent Magnet Rectifier Generator Based on LPTN

I. Introduction Variable flux memory machines (VFMM) equipped with low coercive force (LCF) aluminum-nickel-cobalt (AlNiCo) magnets [1]-[4] can achieve high efficiency over a wide operation range by applying a current pulse to magnetize the LCF magnets with negeligible copper loss. Thus, VFMM is widely recognized as a competitive candidate for traction applications. For elevating the the electromagnetic performance of VFMMs, hybrid usage of high coercive force (HCF) and LCF magnets are applied in VFMMs. A novel hybrid-magnet-circuit VFMM (HMC-VFMM) is proposed in [5], which combines the design concepts and strengths of VFMMs with parallel and series magnetic circuit of HCF and LCF magnets. Due to the special hybrid magnetic circuit design, it is essential to provide an insightful understanding about the nonlinear hysteresis behavior of the LCF working point considering the resultant effects of parallel and series branches and to analyze the magnetic field variation phenomenon of the developed HMC-VFMM due to the transient current pulse by an effective solution. This paper attempts to reveal and investigate a balanced bidirectional-magnetization effect of the proposed HMC-VFMM, i.e., the required demagnetizing and remagnetizing current levels are basically similar, which will benefit the inverter rating reduction and online flux control. The balanced bidirectional-magnetization effect is analytically revealed by using a simplified Fourier-series based hysteresis model. In addition, the numerical hysteresis model is programmed with FE model so as to accurately investigate the magnetization characteristics of HMC-VFMM. Finally, the experimental results on a prototype are carried out to verify the theoretical analyses. II. Machine configuration and working principle The proposed 21-slot/4-pole HMC-VFMM is investigated, in which the cross-section is illustrated in Figs. 1(a). The proposed HMC design is characterized by a dual-layer PM structure. For the parallel branch, the “U”-shaped hybrid PM arrangement is employed. For the series branch, the HCF PMs form a spoke-type flux concentration type. The proposed HMC-VFMM can combine the advantages of wide flux regulation range in parallel type and excellent on-load demagnetization withstand capability in series type. The variable-flux principle of the proposed HMC-VFMM can be illustrated by the open-circuit field distributions under different magnetization states (MSs) in Fig. 1(b). It can be observed that the air-gap flux can be flexibly adjusted by applying a transient magnetizing or demagnetizing current pulse. Meanwhile, due to the variable flux property, the losses at different speeds and loads can be also manipulated to realize efficiency improvement over a wide operating range. III. Analytical Analysis of Balanced Bidirectional-Magnetization Effect The nonlinear hysteresis characteristics of the LCF PMs used in the proposed HMC-VFMM can be characterized by a simple Fourier-series based hysteresis model as shown in Fig. 2(a). The PM working point can track along different recoil lines by applying a specific remagnetizing or demagnetizing current pulse. The underlying mechanism of the balanced bidirectional-magnetization effect can be physically characterized by hysteresis curves of the LCF PM in Fig. 2(b). The load line of the HMC design is placed between the two load lines of the parallel and series cases, which allows a better balance between the magnetizing and demagnetizing current amplitudes. Meanwhile, the oversized inverter rating issue for either parallel or series VFMMs can be well avoided by appropriately reducing maximum remagnetizing currents. The detailed analysis and investigation of magnetization characteristics of HMC-VFMM will be given in the full paper.

**References:**

[1] V. Ostovic, "Memory Motors," IEEE Ind. Appl. Mag., vol. 9, no. 1, pp. 52-61, Jan./Feb. 2003. [2] H. Liu, H. Lin, Z. Q. Zhu, M. Huang, and P. Jin, "Permanent Magnet Remagnetizing Physics of a Variable Flux Memory Motor," IEEE Trans. Magn., vol. 46, no. 6, pp. 1679-1682, 2010. [3] Yu, C. and K. T. Chau . "Design, Analysis, and Control of DC-Excited Memory Motors," IEEE Trans. Energy Convers., vol. 26, no. 2, pp.479-489, 2011. [4] N. Limsuwan, T. Kato, K. Akatsu, and R. D. Lorenz, "Design and Evaluation of a Variable-Flux Flux-Intensifying Interior Permanent-Magnet Machine," IEEE Trans. Ind. Appl., vol. 50, no. 2, 2014. [5] H. Yang, S. Lyu, H. Lin, Z. Q. Zhu, H. Zheng and T. Wang, "A novel hybrid-magnetic-circuit variable flux memory machine," IEEE Trans. Ind. Electron., vol. 67, no. 7, pp. 5258-5268, 2020.

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Fig. 1 VFMM topology and open-circuit field distributions under different magnetization states. (a) Topology. (b) Open-circuit field distributions under different magnetization states.

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Fig. 2 Illustration of Fourier-series based hysteresis model. (a) Simplified view for illustrating the variable flux principle. (b) Numerical representation.

 Investigation of Balanced Bidirectional-Magnetization Effect of a Novel Hybrid-Magnet-Circuit Variable Flux Memory Machine

The first energization of a power transformer in an energy distribution system is a critical issue in the transformer’s lifetime since the high currents experienced by the device in these conditions. Such currents are primarily due to magnetization of the iron core, which exhibits memory phenomena and saturation. Further, the initial phase strongly affects dynamics and could push the core in a saturation state, which, in turn, reduces the primary coil impedance and hence enables the current to rise (up to 10-15 times the full load current). This transient current is usually referred to as inrush current [1,2] and can be very dangerous for the device, causing electrodynamic stress, dissipations and consequent heating of the electrical insulations, harmonics production and their circulation in the power system. Such magnetizing currents focused great attention in the analysis of large transformers. The latest research activity was basically focused on the modeling, at the macroscopic scale, of the magnetization processes taking place in the transformer’s core, strongly affecting the circuit’s dynamics. The effort was therefore aimed to plug into the circuit model a suitable hysteresis operator. Different proposals discussed the effects of hysteresis models (e.g., Preisach, Jiles Atherton (J-A), etc., [3,4]) on the global behavior of the transformer dynamics, with particular emphasis to model’s accuracy and computational weight, [5,6]. The J-A model offers a tool to describe hysteresis, but it is able to describe too simplified memory phenomena, [3] and requires a nontrivial parameters identification (e.g., through a nonlinear optimization). Conversely, Preisach model (PM) provides a memory description that fits with the real macroscopic processes but requires some expertise and a large of measured data (i.e., first order reversals), which limits its use in non-specialized frameworks, as power circuits and industrial electronics. Therefore, the availability of well-behaved hysteresis operator suitably simplified with respect to, e.g., the Preisach model, would represent an interesting contribution to this field. In the present contribution, the core magnetization modeling of a power transformer in a network is provided through a Preisach-based operator (i.e., it is characterized by the Preisach memory updating rules), [7] offering a simpler implementation, inverse operator availability and a reduced set of measured data, than PM. Such operator, as detailed hereafter, is based on a weighted linear superposition of elementary operators (Play operators, see, [7]) and will be referred to as Prandtl-Ishilinskii (P-I) operator. Further, due to its simpler structure and reduced numbers of parameters, it allows the inrush current process analysis in a wide range of magnetization conditions with low effort. The P-I model, describing the B-H characteristic, along with the circuit’s equations, referred to the same circuit as in [6], are reported in Fig. 1. In the first frame, Pr[.] is the play operator, while μ(r) is a weight function and the saturation magnetization, Ms = 1.5T. In the second frame, R1 is the primary resistance, E the voltage amplitude, while F is the hysteresis operator linking the flux linkage to the primary current. The secondary current is assumed zero during the analysis. The model so conceived is able to fairly describe the behavior of a realistic core, as shown in the same figure. The circuit’s behavior has been preliminary tested in the same conditions as in [6]. However, in Fig. 2 its behavior has been studied in conditions where the great arise of (inrush) currents clearly appears. In the same figure the impact of hysteresis with respect to a memoryless description is outlined. Aim of the paper will be a thorough testing of the proposed model, in terms of accuracy, computational efficiency for the analysis of inrush currents phenomena in power transformers. The characteristics of the hysteresis operator would allow an immediate analysis of the basic magnetic parameters affecting the inrush currents dynamics. In particular, the influence of remanence, coercive field and permeability at current reversal, will be investigated. For the latter (initial permeability at the branch start), during the transient, the material experiences an up and forth current variation, allowing the branching to arise and to affect (in the starting part of the branch characterized by low permeability) the whole current dynamics. Such effect, which strongly relies on the initial magnetization state of the iron core (Mr), could be easily described by the proposed model and of course, cannot be taken into account when a nonlinear memoryless modeling is employed.

**References:**

[1] R. Yacamini, C.Eng., and A. Abu-Nasser, IEE Proceedings, Vol. 133, Pt. B, No. 1, 1986. [2] J.C. Yeh, C.E. Lin, C.L. Huang, Electric Power Systems Research 30, 93-102, 1994. [3] I. D. Mayergoyz, Springer, 1991. [4] D.C. Jiles, D.L. Atherton, J. of Magnetism and Magnetic Materials, vol. 61, 1–2, pp. 48-60, 1986. [5] A. A. Adly, IEEE Trans on Magnetics, vol. 37, no. 4, 2001. [6] X. Wang, D. W. P. Thomas, M. Sumner, IEEE Trans. on Magnetics, 44, 3, 2008. [7] C. Visone, M. Sjöström, Physica B: Condensed Matter, vol. 343, 1–4, pp. 148-152, 2004.

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 Impact of hysteresis phenomena in time and frequency analysis for inrush currents in power transformers

The vibration of the machine is always cared, since it may influence the stability and reliability characteristics. Some indirect-testing methods for the multi-unit permanent magnet synchronous machine have been proposed in order to measure the parameters and characteristics of the machine without any mechanical load. The aim of this paper is to calculate and analyze the vibration of the machine in the indirect-testing method, and discuss the difference of the vibration characteristics between the indirect-testing situation and the direct-testing situation. The calculation error is discussed in this paper. To validate the analysis, the calculated radial electromagnetic force and vibration are compared with the test results of a multi-unit PMSM prototype. I.Introduction The high-power low-speed permanent magnet synchronous machine (PMSM) is typically applied in high-power fields, such as electric propulsion, for their excellent operating characteristics of high efficiency and high torque density. To reinforce the reliability and reduce the power capacity of one phase, a novel multi-unit structure has been proposed [1]. Much effort has been devoted to the electromagnetic analysis, the drive strategy and the testing method of the multi-unit PMSM [2]-[6]. In order to avoid using the mechanical load, non-mechanical-load indirect-testing methods for some important characteristics of the multi-unit PMSM have been proposed. The important characteristics are tested in the non-mechanical-load testing situation, where some unit-motors run as motor and some unit-motors run as generator. However, the vibration analysis of the multi-unit PMSM in the non-mechanical-load testing situation have not been mentioned in literature so far. The PMSM is always required to have a smooth and quiet operation when used in electrical propulsion or military appliances [7]-[9]. If the vibration characteristics of the electrical machine are too bad, it may cause the mechanical fault of the system. Thus, vibration and acoustic noises in the PMSM are considered a critical issue[10]-[11]. In this paper, the radial electromagnetic force and vibration of the multi-unit PMSM in the non-mechanical-load testing situation are calculated and analyzed. The difference of the vibration between different operating situations are discussed. II.The calculation of the radial electromagnetic force and vibration The principle of virtual work is now used as a matter of routine to compute the electromagnetic torque for its excellent advantages of high accuracy and minor calculation. According the virtual work method, the electromagnetic torque of the multi-unit PMSM can be expressed. And combining the voltage equations, the magnetic flux of the machine can be expressed by the function of the electromagnetic parameters. The multi-unit PMSM can perform in the situation that some unit-motors are running as the motor and some unit-motors are running as the generator. In this situation, the parameters and characteristics (including the currents, losses, torque, etc) of the machine can be obtained without using the mechanical load. It can be considered the non-mechanical-load indirect-testing situation. Thus, the magnetic density distribution in the non-mechanical-load indirect-testing situation can be obtained. Furthermore, the radial electromagnetic force are calculated according to the magnetic density. To calculate the vibration, besides the radial electromagnetic force, the modal analysis is also necessary. In this paper, the transient structural analysis is performed using the modal superposition method. The mechanical structure model of the multi-unit PMSM is established. And the natural frequencies of the structure are obtained. The displacement response of the calculated radial electromagnetic force can be calculated based on the established mechanical structure modal model. To validate the calculated displacement response, the modal test and the response test are performed. The test bench for the vibration of the PMSM prototype in the non-mechanical-load indirect-testing situation is shown in Fig. 1. The frequencies of the harmonic components in the calculated results are in a satisfactory agreement with those in the test results. The displacement response in the non-mechanical-load indirect-testing situation is shown in Fig.2. It can be seen in Fig.2 that there are some additional harmonic components of the acceleration because of the additional radial electromagnetic force in the non-mechanical-load indirect-testing situation. The variety of the additional harmonic components are influenced by the rotating speed fluctuation and the asymmetric currents in the phases.The additional harmonic components in the displacement response are also discussed in this paper.

**References:**

[1] B. Zhang, Y. Liu, and G. Feng, “Study on low voltage high power multi-branch permanent magnet synchronous motor,” in Proc. Conf. Power and Energy Engineering, Aug. 2010. pp. 747–755. [2] P. Zhao, G. Yang, and J. Liu, “Multi-unit motor parallel drive system for electric vehicle application,” in Proc. IEEE conf. Vehicle Power and Propulsion, Aug. 2008.pp. 747–755. [3] B. Zhao, J. Zou, G. Hao, J. Zou, and Y. Xu, “Asymmetry of inductance and torque ripple of multi-unit permanent magnet synchronous motor,” in Proc. Conf. International Conference of Electrical Machines and Systems, Aug. 2011. pp. 747–755. [4] Zeng Depeng, Zou Jibin, Xu Yongxiang, “An Indirect Testing Method for the Torque Ripple of Multiunit Permanent Magnet Synchronous Machines, IEEE Transactions on Industrial Electronics, 2020, 67(4): 2734-2743. [5] Zeng Depeng, Zou Jibin, Xu Yongxiang, “Analysis and Discussion of the Indirect Testing Method for the Losses of Permanent Magnet Synchronous Machines, IEEE TRANSACTIONS ON MAGNETICS, 2018, 54(11). [6] Zou Jibin, Zeng Depeng, Xu Yongxiang, “AnIndirect Testing Method for the Mechanical Characteristic of Multiunit Permanent-Magnet Synchronous Machines With Concentrated Windings, IEEE Transactions on Industrial Electronics, 2015, 62(12): 7402-7411. [7] Islam, R , and I. Husain . "Analytical Model for Predicting Noise and Vibration in Permanent-Magnet Synchronous Motors." IEEE Transactions on Industry Applications 46.6(2010):2346-2354. [8] Fakam, Mathias , M. Hecquet , and V. Lanfranchi . "Design and Magnetic Noise Reduction of the Surface Permanent Magnet Synchronous Machine Using Complex Air-Gap Permeance." 2014 Ninth International Conference on Ecological Vehicles and Renewable Energies (EVER) IEEE, 2014. [9] Xing, Zezhi , et al. "Reduction of Radial Electromagnetic Force Waves Based on PM Segmentation in SPMSMs." IEEE Transactions on Magnetics PP.99(2020):1-1. [10] Zhang, Qinghu , et al. "Analysis and Calculation of Radial Electromagnetic Force of Circular Winding Brushless DC Motor." IEEE Transactions on Industrial ElectronicsPP.99(2019):1-1. [11] Shin, Hyeon Jae , et al. "Vibration Analysis and Measurements Through Prediction of Electromagnetic Vibration Sources of Permanent Magnet Synchronous Motor Based on Analytical Magnetic Field Calculations." IEEE Transactions on Magnetics48.11(2012):4216-4219.

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 Vibration analysis of the multi-unit permanent magnet synchronous machine in the non-mechanical-load indirect-testing situation

1 Introduction In a dynamical mass-spring system with many discrete mass points, when the spring has nonlinearity, a special localized vibration mode occurs in which only a limited number of masses vibrate. This is called the intrinsic localized mode (ILM) [1]. Many researchers have been interested in the ILM because of its unique features that are not found in the linear systems. Particularly in mobile ILMs [2], in which the kinetic energy of the system is localized in a small number of masses and the localized energy propagates to adjacent masses, have high potential for engineering applications through experiments [3,4]. However, the shape, frequency and speed of the ILM were determined by the parameters of the dynamic vibration system (mass, spring constant, and initial vibration). Hence, control of the generated ILM was not possible and therefore, there has been no significant progress in engineering applications. Here, we propose a new magnetic spring structure that can variably handle the nonlinear spring characteristics of dynamic vibrating systems. In this paper we would like to describe the ILM in dynamic vibrating systems. Then, a variable magnetic spring structure (VMS structure) is proposed, and the variable magnetic spring properties are verified from the finite element analysis (FEA) results of the proposed structure. Lastly, by solving the differential equations of the dynamic oscillating system, we show the possibility of controlling the ILM by varying the nonlinear spring properties of the dynamic vibrating system. 2 Variable magnetic spring structure For ILM generation, multi-mass and nonlinear springs are required. Since we are dealing with rotating bodies, the mass is replaced by inertia and the nonlinear spring has restoring torque. A large number of rotating bodies with the same inertia are connected by nonlinear restoring torques with neighboring rotating bodies. The nonlinear restoring torques structure with VMS is shown in Fig. 1(a). The VMS consists of two rotors, the outer rotor with electromagnets and the inner rotor with interior permanent magnets (IPM). The outer rotor coil consists of two phases with opposite phases and applies DC current. The magnetic flux due to permanent magnet is shown by the solid blue loop, and the magnetic flux due to the applied current is shown by the dotted red loop. The restoring torque of the VMS is generated by the relative angle between the inner and outer rotors. Fig. 1(b) shows the relationship between the relative angle and the restoring torque when 2A/mm2 to 8A/mm2 is applied to the two-phase coil with opposite phases obtained from the FEA. The restoring torque T can be approximated as follows: T=k3θ3+k1θ...(1) Here, θ is the relative angle (rad), k1 (Nm/rad) is the spring constant, and k3 (Nm/rad) is the nonlinear coefficient. Also, the nonlinear ratio is defined as . It decreases continuously from 20.52 at an applied voltage of 2A/mm2 to 11.99 at 8A/mm2. 3 Control of ILM In this chapter we numerically solve the differential equations for a rotating nonlinear mass-spring system. The equation of motion with consideration of the nonlinear coefficients of the rotating spring in Fig. 2(a) is the following differential equation Jd2θn/dt2=k1n+1(i)(θn+1-θn)+k3n+1(i)(θn+1-θn)3-k1n(i)(θn-θn-1)-k3n(i)(θn-θn-1)3...(2) Here, J is the inertia of the VMS, θn is the absolute angle of the nth VMS, k1n(i) is the linear spring constant at current density i between the (n-1)th and nth VMS, and k3n(i) is the nonlinear spring coefficient at current density i between the (n-1)th and nth VMS. Fig. 2 shows the numerical results of the differential equation (2). There are 21 VMS’s used, and the inertias are all 1.34×10-4 kg×m2. Initially, the oscillations were such that the ILM was generated from the center. Magnetic springs of 2A/mm2 (nonlinear ratio 20.52) and 4A/mm2 (nonlinear ratio 16.25) were used as shown in Fig. 1(b). In (b-1), a magnetic spring with a nonlinearity factor of 20.52 was used for the entire simulation time. This resulted in the initial ILM remaining centered until the end of the simulation. In (b-2), we used a magnetic spring of 20.52 for the simulation time of 0-1 sec, and changed k1,3-5~0 to a magnetic spring of 16.25 for 1-2 sec. In 2-3 seconds, k1,3-5~10 were changed to magnetic springs of 16.25. From (b-1) and (b-2), it is clear that the ILM can be controlled by changing the nonlinear rate of the magnetic spring. In the final paper, we will discuss the cause of the nonlinear magnetic spring property of the proposed VMS structure by FEA, and furthermore, discuss the movement speed and trend of ILM according to the nonlinear rate.

**References:**

[1] S. Takeno, K. Kisoda, and A.J. Sievers, Progress of Theoretical Physics Supplement, No. 94, pp. 242-269 (1988). [2] M. Kimura, R. Tsujisaka, T. Hikihara, Y. Taniguchi, and Y. Matsushita, A study on reflection of moving intrinsic localized modes at a junction of two different nonlinear lattices, 2014. [3] Y. Watanabe, M. Nishimoto, and C. Shiogama, Nonlinear Theory and Its Applications, IEICE, vol. 8, pp. 146-152, 2017. [4] S. Lee, K. Hirata, M. Kato, Electrical and Electronic Engineering (ISEF), Nancy, France, 2019, pp. 1-2, doi: 10.1109/ISEF45929.2019.9097039.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e64e22e28e1532cd6e9efdacc9622225.jpg)
Fig.1 (a) Proposed VMS structure. (b) The relative angle and the restoring torque by applied current density.

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Fig.2 (a) Spring-mass system. (b) Numerical result of ILM with VMS.

 A New Method to Control Intrinsic Localized Mode Using a Variable Magnetic Spring Structure

Harvesting of the ambient radio-frequency (RF) energy is of great interest to address the increasing energy demand for emerging applications, e.g., the internet of things, wearable devices, various sensors and implants, and 3D integrated circuits. To use the weak ambient RF power density for such applications, we need rectifiers capable of operating much below 1 μW RF power with high efficiencies. However, the development of such technologies is severely limited by the conventional semiconductor rectifiers [1], which fail to operate in the weak RF limit. We propose a new rectifier concept [2], simultaneously utilizing the spin-orbit torque (SOT) and the Hall effect, that can provide ~200 μV DC voltage from a 500 nW of radio-frequency (RF) power using existing materials, with a power conversion efficiency as high as 71%. The DC voltage strength can be efficiently enhanced to ~300 mV from the same RF power with a series array of such devices while matching the low impedance of the receiver antenna. We estimate a very high curvature coefficient of the proposed rectifier, in the order of 104 V-1, where the theoretical limit of conventional Schottky diodes is determined by the inverse of the thermal voltage q/kBT ~ 40 V-1 [3]. Various SOT materials are being extensively studied for efficient current-induced switching of scaled ferromagnets for memory applications (see, e.g., Ref. [4] and references therein). Here, we propose a new application of SOT in the rectification of weak RF by coupling it to conventional Hall devices. The basic idea can be explained using a Hall bar and a solenoid connected in parallel, see figure. A current-carrying conductor placed in a magnetic field (B) exhibits a voltage drop in the direction orthogonal to both the current and the B-field, known as the Hall effect. If a fraction of the current flows through a solenoid underneath the Hall bar to generate the B-field, the Hall voltage will be unidirectional irrespective of the current direction, leading to a rectification. We propose a structure where such a solenoid is replaced with a bilayer consisting of a material exhibiting SOT and a ferromagnet (FM) with a low anisotropy energy barrier. We design the device such that the current equally divide between the Hall and the SOT layers. The FM magnetization, on average, follows the fraction of the current flowing in the SOT layer, provided that the current can produce sufficiently strong SOT. The FM applies an effective B-field to the Hall layer and thus leads to a similar rectification case as described in the solenoid case. The Hall effect and spin-orbit-torque are both proportional to current density, which improves inversely with device cross-sectional area, providing the largest signals at the nanoscale. To make the proposed rectifier sensitive to weak RF current, we need a material with a high SOT factor, an FM with low anisotropy energy, and a low Gilbert damping constant. An FM with low anisotropy energy is typically achieved by lowering the total magnetic moment or by tuning the FM thickness to optimize near the transition point between in-plane and perpendicular anisotropies or by using isotropic geometries. We consider a soft ferrite with a very low anisotropy field and a low total magnetic moment, that is expected to easily follow a SOT induced by a weak RF current. Such a low anisotropy energy magnets can achieve a wide frequency bandwidth of operation, depending on the total magnetic moment in the FM and the angular momentum conservation [5]. We simulate the magnetization dynamics using the stochastic-Landau Lifshitz Gilbert equation, which considers the stochastic nature of such low anisotropy energy magnets due to the presence of thermal noise. We can further optimize the device structure and use emerging materials to enhance the figure-of-merits at even lower RF power. The proposed device can lead to important new technologies addressing the alarming energy issues in the era of the internet of things, wearable devices, and densely integrated 3D circuits. This work is supported by the Center for Energy Efficient Electronics Science (E3S), NSF Award 0939514.

**References:**

[1] S. Hemour et al. IEEE Trans. Microw. Theory Tech. 62, 965–976 (2014). [2] S. Sayed, S. Salahuddin, and E. Yablonovitch, to appear in Appl. Phys. Lett. (2021). [3] J. Karlovský, Solid-State Electronics 10, 1109 – 1111 (1967). [4] S. Sayed et al., arXiv:2010.01484 (2020). [5] S. Sayed et al., Phys. Rev. Applied11,054063 (2019).

**Images:**

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(a) Basic concept of rectification explained using a Hall bar and a solenoid sharing the same current. The magnetic field on the Hall bar, applied by the solenoid reverses when we reverse the current direction. Thus the Hall voltage remains of the same polarity irrespective of the current direction. (b) The proposed spin-orbit torque (SOT) rectifier, where the solenoid is replaced with a bilayer of a SOT material and a soft ferromagnet (FM). The FM follows in the current in the SOT material and applies a magnetic field to the Hall layer, similar to the solenoid case.

 Spin-orbit torque rectifier for energy harvesting from weak radio-frequency

This paper analyzes the influence of harmonic back-EMFs, especially the third harmonic back-EMF, on the flux-weakening performance of interior permanent magnet synchronous motor (IPMSM). First, IPMSM model and the back-EMF harmonics components of IPMSM are studied. Then, the commonly used flux-weakening control methods are introduced briefly. Finally, the influence of back-EMF harmonics on the flux-weakening performance is analyzed in detail from the perspective of voltage limit. The analysis is validated with the simulation. 1. Introduction IPMSM has been widely explored due to its excellent performance such as high efficiency and high power density. In many applications of IPMSM such as electric vehicles, a wider speed range is usually required, and flux-weakening control is usually adopted to obtain higher speeds. The flux-weakening range of permanent magnet motor is very limited, because the magnetic field of the permanent magnet cannot be adjusted. Generally speaking, IPMSM has a wider flux-weakening speed range than surface permanent magnet synchronous motor (SPMSM) because of the salient-pole structure [1]. Based on the current vector control, there are two typical flux-weakening control methods [2]: one is the feedforward control method, which requires the accurate IPMSM mathematical model parameters. The other is the feedback control method, which uses the PI regulator to compensate the demagnetizing current. The feedback control method can be further divided into two categories: flux-weakening control based on dual current regulators and flux-weakening control based on variable voltage angle. The dual current regulators method is still based on current vector control, but suffers from the conflict of two voltages saturation. There is no current regulator in the initial variable voltage angle method. However, the single d-axis current regulator or single q-axis current regulator methods are developed to plan the current locus and improve the dynamic performance [3]. Regardless of the different flux-weakening methods, its essence is to offset the permanent magnet back-EMF at high speeds by applying the demagnetizing current, and relieve the conflict of back-EMF and inverter voltage limit. However, the demagnetizing current can only counteract the fundamental back-EMF. The back-EMF of IPMSM has rich harmonic back-EMFs. The reason is that the permanent magnet flux linkage contains the harmonic components. Among these harmonics, the third harmonic is the most obvious. At high speeds, the high third harmonic back-EMF can also reach the inverter voltage limit like the fundamental back-EMF. However, there is no demagnetizing current offsetting it. This paper will analyze the influence of the harmonics back-EMFs on the flux-weakening performance of IPMSM. The rest of the paper is organized as follows: Section 2 introduces the IPMSM model and harmonics back-EMFs; Section 3 gives a profile of existing flux-weakening method; Section 4 analyzes the influence of harmonics back-EMFs on the flux-weakening performance of IPMSM. 2. IPMSM Model and back-EMF harmonics Flux-weakening control is based on the current vector control architecture, which is implemented in synchronous rotating (d-, q-axis) coordinate system. Through coordinate transformation, all variables in the IPMSM mathematical model, including the back-EMF, become DC components. However, this mathematical model only considers the fundamental back-EMF and does not consider the harmonic components in the back-EMF. In fact, due to the permanent magnet shape and the magnetization direction, the back-EMF contains rich harmonic components. Especially for IPMSM, since its permanent magnets are embedded in the rotor, it is more difficult to optimize the permanent magnets shape than the surface mount structure. Therefore, IPMSM contains more harmonics in the back EMF than SPMSM. Fig.1 shows a IPMSM’s back-EMFs. It can be seen that they are not standard sine waves. Through FFT analysis, the THD of back-EMF reaches 10.25%, and the main harmonics are the third harmonic. 3. Dual current regulators based flux-weakening method This paper adopts the commonly used dual current regulators based flux-weakening method. The principle of this method is adding a voltage feedback regulator. When the reference voltage exceeds the inverter voltage limit, a negative demagnetizing current is generated through the PI regulator, and then a voltage that cancels the fundamental back-EMF is generated to eliminate the saturation of the reference voltage. 4. The influence of harmonic back-EMFs on the flux-weakening performance. The essence of flux-weakening control is to counteract the high back-EMF through the voltage generated by the demagnetizing current. However, the demagnetizing current in the d-axis can only offset the fundamental back-EMF. The harmonic back-EMFs are also very large at high speeds, and can also cause saturation of the inverter voltage. Fig.2 shows the back-EMFs of the IPMSM operating in the flux-weakening condition. In the simulation, the inverter voltage limit is set as 150V. It can be seen that through applying d-axis demagnetizing current, the fundamental back-EMF has been suppressed. But the amplitudes of the harmonics back-EMFs reach 130V, which is very close to the inverter voltage limit. In other words, for higher speeds, the harmonics back-EMFs will reach the inverter voltage limit, which will prevent the speed from continuing to rise. This proves that the harmonics back-EMFs will seriously affect the range of flux-weakening control.

**References:**

[1] N. Bedetti, S. Calligaro and R. Petrella, "Analytical Design and Autotuning of Adaptive Flux-Weakening Voltage Regulation Loop in IPMSM Drives With Accurate Torque Regulation," in IEEE Transactions on Industry Applications, vol. 56, no. 1, pp. 301-313, Jan.-Feb. 2020 [2] Wang J, Wu J, Gan C, et al. Comparative study of flux-weakening control methods for PMSM drive over wide speed range[C]. 2016 19th International Conference on Electrical Machines and Systems (ICEMS) 2016: 1-6. [3] Z. Zhang, C. Wang, M. Zhou and X. You, "Flux-Weakening in PMSM Drives: Analysis of Voltage Angle Control and the Single Current Controller Design," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 7, no. 1, pp. 437-445, March 2019.

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