A. VISHWAKARMA, M. KOMELJ: OPTIMUM DESIGN OF A PERMANENT-MAGNET-BASED SELF-CHARGING DEVICE ... 627–630 OPTIMUM DESIGN OF A PERMANENT-MAGNET-BASED SELF-CHARGING DEVICE FOR A SMARTPHONE OPTIMALNO OBLIKOVANJE SAMO-POLNILNIH NAPRAV NA OSNOVI TRAJNIH MAGNETOV ZA PAMETNE TELEFONE Anubhav Vishwakarma 1,2* , Matej Komelj 2 1 Jo`ef Stefan International Postgraduate School, Ljubljana, Slovenia 2 Jo`ef Stefan Institute, Department K-7, Jamova cesta 39, 1000 Ljubljana, Slovenia Prejem rokopisa – received: 2023-09-09; sprejem za objavo – accepted for publication: 2023-10-22 doi:10.17222/mit.2023.968 A smartphone battery can be charged without an external power source by applying a portable charger that transforms mechani- cal energy into electricity by means of magnetic induction. Its essential part is a permanent magnet made of a rather expensive and, from the point of view of availability as well ecology, problematic material. The magnet is usually assembled from cylin- drical parts. In order to reduce the raw-material consumption and to simplify the production, we propose a single-piece design in the form of a cylinder with notches. By means of the finite-element modelling, we optimize the dimensional parameters and prove that our proposal is more efficient than standard solutions. Keywords: permanent magnet, electric generator, smartphones, self-recharge, finite-element modelling Baterija za pametni telefon se lahko polni tudi brez zunanjega napajanja z uporabo prenosnega polnilca, ki pretvarja mehansko energijo v elektri~no. Njen najbolj pomemben element je trajni magnet, ki je izdelan iz dokaj dragega, te`ko dostopnega in okoljsko problemati~nega materiala. Ta magnet je obi~ajno sestavljen iz cilindri~nih delov. Avtorja ~lanka predlagata z namenom zmanj{anja porabe osnovnih surovin in poenostavitve proizvodnje uporabo enovitega cilindri~nega izdelka z zarezami. S pomo~jo modeliranja na osnovi metode kon~nih elementov sta avtorja optimizirala dimezijske parametre in dokazala, da je njuna re{itev bolj u~inkovita kot so standardne izvedbe. Klju~ne besede: trajni magnet, elektri~ni generator, pametni telefoni, samo-polnitev, modeliranje na osnovi metode kon~nih elementov 1 INTRODUCTION Energy consumption is one of the main problems faced by society. It is of strategic importance to put ef- forts into energy saving during all activities. At the same time, it is also necessary to reduce the consumption of raw-material resources for ecological and economic rea- sons. On the other hand, technological progress is un- stoppable; therefore, the goal must be to stimulate inno- vations, acceptable in the present situation. An example is a smartphone, a small device which is nowadays indis- pensable in many aspects. Although it is not a significant energy consumer, its operation depends on the battery capacity – one of the crucial topics of contemporary ap- plied science. 1,2 It would be desirable to avoid inconve- nient situations occurring due to an empty battery by not burdening the environment or drastically increasing the price of the device. 3 A possible solution is to use a porta- ble battery self-charger, 4,5 which is basically an electric generator producing electricity from the kinetic energy associated with walking or shaking by the phone’s car- rier. 6 Various studies have been conducted to characterize different moving activities as a potential energy source. 7,8 The idea is to exploit human motion, which excites a vibration of the coil in a magnetic field, inducing a volt- age. 9 A scheme of such a charger is presented in Figure 1. So far, the size of the only commercially realized exam- ple exceeds the size of a smartphone. 10 It must be carried separately in a bag, which is inconvenient and reflected in only limited commercial success. 11 The problem is how to produce a sufficiently strong, non-uniform magnetic field using a reasonably small, light and easily manufactured magnet. The fulfilment of the first two criteria obviously contributes to a light weight and small size as well as to a low price of the fi- nal product, needless to say, crucial for the applicability. Similarly, a simplified manufacture without assembling the magnet from different pre-magnetized parts, as it is the case with the existing self-chargers, would certainly have a positive impact too. We propose a design, suitable for additive manufacturing by means of 3d printing, making a single-piece magnet that can be magnetized in a uniaxial direction. It should be small enough to be em- bedded in the housing of the smartphone. The objective is to determine the shape of a tube-like magnet that yields the optimum performance, defined by the esti- mated induced voltage per volume of the magnetic mate- rial. To achieve this goal, we optimize the magnet-geom- Materiali in tehnologije / Materials and technology 57 (2023) 6, 627–630 627 UDK 620.179.14:621.395.721.5 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 57(6)627(2023) *Corresponding author's e-mail: anubhav.vishwakarma@ijs.si (Anubhav Vishwakarma) etry parameters by modelling in the frame of the finite-element formalism. 2 DESCRIPTION OF THE CHARGER As presented in Figure 1, the charger under consider- ation comprises a rectifier circuit, a magnet, and an oscil- lating coil coupled to a pair of strings. 2,12 Whereas the springs must be tuned to match the walking and oscillat- ing-coil frequencies, and the rectifier circuit should sup- ply an appropriate voltage to charge the battery, the focus of the present research is to find the ideal shape of the magnet as the source of the magnetic field. According to the Faraday’s law the induced voltage is expressed as the time derivative of the magnetic flux 13 m : U t i m =− d d (1) m tN B A ()= (2) where N is the number of turns in the coil, A represents the coil’s cross-section, and B denotes the magnetic-flux density. The target average induced voltage is about 10 V. Under consideration is a cylindrical shape with notches, which makes it possible to stick to a planar problem due to the rotational symmetry. The length and the maximum diameter are set to 10 mm and 4 mm, re- spectively, which implies a reasonable size of the device, and, as a rule of thumb, matches to N = 400 turns in the coil. We adopt the magnetic properties of a state-of-the-art sintered magnet (NdFeB-50) with sufficiently high remanent magnetization. An example of the proposed magnet shape is presented in Figure 2, with the dimen- sions defined in Figure 3 and Table 1. Table 1: Magnet dimensions Parameter Notation Inner diameter (D0) Height of the notch (L1) Width of the notch (L2) The notches in the magnet design are the key innova- tion, contributing to a lower weight, reduced consump- tion of the raw material, and the required field inhomo- geneity necessary for a non-zero time derivative in Equation (1). 3 METHODOLOGY The complete flow chart of the magnet-modelling procedure is presented in Figure 4. The finite-element calculations of the magnetic flux density were carried out with FEMM software. 14,17 The first-type (Dirichlet) boundary conditions and a triangular mesh were applied. Its density was determined A. VISHWAKARMA, M. KOMELJ: OPTIMUM DESIGN OF A PERMANENT-MAGNET-BASED SELF-CHARGING DEVICE ... 628 Materiali in tehnologije / Materials and technology 57 (2023) 6, 627–630 Figure 3: Magnet dimensions and black arrows present the magneti- zation direction Figure 1: Schematic of the charger Figure 2: Schematic diagram of the proposed permanent-magnet shape for the self-generation system Figure 4: Complete flow chart of the magnet-modelling procedure on the basis of the convergence tests. 15,16 Figure 5 pres- ents the meshing for the magnet geometry under consid- eration. The mesh is denser close to the magnet, where the field gradients are more pronounced. The time de- pendence of the calculated flux is modelled by examin- ing various displacements between the coil and the mag- net assuming a harmonic motion. For simplicity, the angular frequency was set to =1s –1 . The time derivative in Equation (1) is carried out in terms of the finite-difference method, and the av- erage value B of the magnetic-flux density for a given cross-section is applied in Equation (2). 4 RESULTS AND DISCUSSION The following geometry parameters yielding the opti- mum performance were optimized: L1 (height of the notch), L2 (width of the notch), and the inner diameter of the tube (D0) of the magnet. The optimization criterium was the induced voltage divided by the magnet volume. We adopted the simplest optimization procedure by fixing one and optimizing the other two parameters at the first stage. It makes sense to compare the calculated out- put average voltage normalized to the volume of a partic- ular magnet with notches. First, we fixed the diameter D0 and plotted the normalized voltage for four different notch heights L1 as functions of the notch width L2 in Figure 6. Although a bigger notch certainly contributes to a smaller volume and simultaneously to a less homog- enous magnetic field, there is obviously an optimum combination of L1 and L2 corresponding to 4 and 6, re- spectively in Figure 6. In the second stage, we applied this combination L1 and L2 and examine the influence of the diameter D0. To check the stability of our solution, we fixed the width L2 to 6 and present the results of several values of L1. Again, L1 equals four yields the highest normalized volt- age for diameter D0 value equals 8 giving the optimum set of the three parameters. To prove that our concept makes sense, we present a comparison between the calculated voltages resulting from applying the optimized magnet geometry and dif- ferent conventional solid (without notches) magnets magnetized uniaxially (Normal), axially (Axis) as a se- quence of segments magnetized periodically in the left or right direction, and along the Halbach pattern (Halbach): Figure 8. Although the solid magnets, particularly the one magnetized along the Halbach pattern, might yield a higher absolute voltage, the benefit of the notches due to a reduced amount of the used material is obvious and even a non-optimum solution (L1 equals 5) gives a higher normalized voltage. A. VISHWAKARMA, M. KOMELJ: OPTIMUM DESIGN OF A PERMANENT-MAGNET-BASED SELF-CHARGING DEVICE ... Materiali in tehnologije / Materials and technology 57 (2023) 6, 627–630 629 Figure 5: Meshing for the considered magnet Figure 7: The calculated normalized voltage for L2 fixed to 6 for dif- ferent values of L1 as functions of the inner diameter D0 Figure 6: Voltage vs. volume as a function of the notch width L2 for different values of the notch height L1 and a fixed value of D0 5 CONCLUSION The subject of our investigation was a self-charging device for portable electronics, for example, smartphones, adopting magnetic induction generated by a permanent magnet surrounding an oscillating coil. The focus was on the magnet geometry, to save raw material and to simplify the production. Therefore, we introduced notches in a uniformly magnetized tube-like magnet, which at the same time contribute to the required non-homogeneity of the produced magnetic. A compari- son with the performance of conventional cylindrical magnets of equal outer dimensions proved that our pro- posal, which can be produced by means of 3d printing, indeed yielded the highest output voltage normalized to the volume of the consumed material. The overall result might contribute to the general efforts for sustainable de- velopment. Acknowledgments The presented work is financially funded by the Slovenian Research Agency (ARRS) under the Young Researcher Fellowship under project no. PR-09862. 6 REFERENCES 1 C. R. Saha, T. O’Donnell, N. Wang, P. 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Komelj, Design of a Smart Phone Self-Charg- ing Device Based on Permanent Magnets, Adv Transdiscipl Eng., 27 (2022), 507–513, doi:10.3233/ATDE220787 17 https://www.femm.info/wiki/HomePage A. VISHWAKARMA, M. KOMELJ: OPTIMUM DESIGN OF A PERMANENT-MAGNET-BASED SELF-CHARGING DEVICE ... 630 Materiali in tehnologije / Materials and technology 57 (2023) 6, 627–630 Figure 8: Comparison between our proposal and conventionally mag- netized solid magnets of magnets of tube-like shape