Design of a Cylindrical Winding Structure for Wireless Power Transfer Used in Rotatory Applications

: A cylindrical joint structure for wireless power transfer (WPT) systems is proposed. The transmitter (Tx) and receiver (Rx) coils were wound on hemicylindrical and cylindrical structures, respectively. The Rx coil rotates freely around the axial direction of the Tx coil. Di ﬀ erent methods of winding the Tx and Rx coils are given and discussed. Electromagnetic ﬁelds (EMFs) around the WPT windings should be lower than the limits set by WPT standards. Therefore, the WPT windings were designed to reduce EMF level and maintain constant power-transfer e ﬃ ciency (PTE). The design procedures of the windings are discussed in detail. EMF analysis was done under di ﬀ erent rotation angles ( α ). The selected design reduced the variation of the mutual inductance ( M ). As a result, it maintained a constant PTE while rotating the Rx coil between 0 ◦ and 85 ◦ . Moreover, leakage magnetic ﬁelds (LMFs) near the WPT coils of the chosen design were reduced by 63.6% compared with other winding methods that have the same e ﬃ ciency. Finally, a prototype was built to validate the proposed idea. Experiment results were in good agreement with the simulation results. The WPT system maintained constant e ﬃ ciency in spite of the rotation of Rx coil, where e ﬃ ciency dropped by only 2.15% when the Rx coil rotated between 0 ◦ and 85 ◦ .


Introduction
Wireless power transfer (WPT) systems have proven their reliability and have become a widely used technique. A WPT system transfers power for many applications, such as implantable medical devices (IMDs) [1][2][3], the charging of electric vehicles (EVs) [4][5][6][7][8][9], autonomous underwater vehicles (AUVs) [10], unmanned aerial vehicles (UAV) [11], robotic systems [12], light detection and ranging equipment [13], and the Internet of Things (IoT) [14][15][16]. In addition, it is used in some appliances, for instance, smartwatch straps [17], smartphones [18], battery-powering systems [19], and electrical drones [20,21]. Earlier, many research works investigated different types of structures, such as pancake coils, square coils, and circular coils [22,23]. Recently, in order to extend the transfer area, three-dimensional (3D) geometries have been proposed. For example, a rectangle-shaped resonant cavity was presented [1]. It charged multiple IMDs in a freely behaving animal. A WPT system made of a bowl-shaped transmitter (Tx) coil and a box-shaped receiver (Rx) coil was investigated and could be embedded in an in-ear hearing aid [24]. Hou, et al. [25] fabricated 3D windings for the WPT system. Moreover, Ha-Van et al. [26] studied an omnidirectional WPT system with a cube-shaped Tx coil that could be a possible way of charging portable devices. Many other structures were reported in [27]. However, those structures only considered fixed coils without built-in rotatory parts. The transferred power (P) across the gap, given in Equation (1), is proportional to frequency (f), mutual inductance (M), and the square of the Tx current (I2) [28]. The design of the proposed WPT system can be optimized by maximizing the mutual inductance and reducing its fluctuation at different rotation angles (α). Mutual inductance is given by Equation (2).
where k is the coupling coefficient, LTx is the self-inductance of the Tx coil, and LRx is the selfinductance of the Rx coil. LTx and LRx depend on the resonators' geometries. Several variables were considered to parametrize the coils, as follows. Turn numbers are given as NTx, NRx, where NTx is the number of turns of Tx coil and NRx is the number of turns of Rx coil. Number of winding layers are given as single-layer (SL) winding and double-layer (DL) winding. In addition, the space between turns and variation in the z-axis position, which affects the value of the coupling coefficient, was considered. Therefore, there are many possibilities for winding Tx and Rx coils on a joint structure. Some winding models are illustrated in Figure 2. Figure 2a is a hemicylindrical winding method of Tx and Rx coils that can be written as DL (64, 50), where 64 is the number of turns of the Tx coil, and 50 is the number of turns of the Rx coil. Figure 2a-c shows very high coupling coefficients (close to 0.4). In such models, the fluctuation of mutual inductance with rotation is very high. For example, Figure 3 displays the variations of mutual inductance and coupling coefficient of the winding structures that are given in Figure 2c. M variation reached 95% when the Rx coil rotated between 0° and 85°. Therefore, efficiency drops a lot in this case. In addition, a high coupling could result in a frequency-splitting issue, thus reducing output power. For choosing the right model, low variations of mutual inductance while rotating the Rx coil should be considered. Thus, a WPT system maintains constant efficiency. The coupling coefficient between the studied models ranged between 0.08 and 0.5. In further steps, the chosen model should consider low-leakage magnetic fields, which is explained in the next section. The transferred power (P) across the gap, given in Equation (1), is proportional to frequency (f ), mutual inductance (M), and the square of the Tx current (I 2 ) [28]. The design of the proposed WPT system can be optimized by maximizing the mutual inductance and reducing its fluctuation at different rotation angles (α). Mutual inductance is given by Equation (2).
where k is the coupling coefficient, L Tx is the self-inductance of the Tx coil, and L Rx is the self-inductance of the Rx coil. L Tx and L Rx depend on the resonators' geometries. Several variables were considered to parametrize the coils, as follows. Turn numbers are given as N Tx , N Rx , where N Tx is the number of turns of Tx coil and N Rx is the number of turns of Rx coil. Number of winding layers are given as single-layer (SL) winding and double-layer (DL) winding. In addition, the space between turns and variation in the z-axis position, which affects the value of the coupling coefficient, was considered. Therefore, there are many possibilities for winding Tx and Rx coils on a joint structure. Some winding models are illustrated in Figure 2. Figure 2a is a hemicylindrical winding method of Tx and Rx coils that can be written as DL (64, 50), where 64 is the number of turns of the Tx coil, and 50 is the number of turns of the Rx coil. Figure 2a-c shows very high coupling coefficients (close to 0.4). In such models, the fluctuation of mutual inductance with rotation is very high. For example, Figure 4 displays the variations of mutual inductance and coupling coefficient of the winding structures that are given in Figure 2c. M variation reached 95% when the Rx coil rotated between 0 • and 85 • . Therefore, efficiency drops a lot in this case. In addition, a high coupling could result in a frequency-splitting issue, thus reducing output power. For choosing the right model, low variations of mutual inductance while rotating the Rx coil should be considered. Thus, a WPT system maintains constant efficiency. The coupling coefficient between the studied models ranged between 0.08 and 0.5. In further steps, the chosen model should consider low-leakage magnetic fields, which is explained in the next section.
The transferred power (P) across the gap, given in Equation (1), is proportional to frequency (f), mutual inductance (M), and the square of the Tx current (I2) [28]. The design of the proposed WPT system can be optimized by maximizing the mutual inductance and reducing its fluctuation at different rotation angles (α). Mutual inductance is given by Equation (2).
where k is the coupling coefficient, LTx is the self-inductance of the Tx coil, and LRx is the selfinductance of the Rx coil. LTx and LRx depend on the resonators' geometries. Several variables were considered to parametrize the coils, as follows. Turn numbers are given as NTx, NRx, where NTx is the number of turns of Tx coil and NRx is the number of turns of Rx coil. Number of winding layers are given as single-layer (SL) winding and double-layer (DL) winding. In addition, the space between turns and variation in the z-axis position, which affects the value of the coupling coefficient, was considered. Therefore, there are many possibilities for winding Tx and Rx coils on a joint structure. Some winding models are illustrated in Figure 2. Figure 2a is a hemicylindrical winding method of Tx and Rx coils that can be written as DL (64, 50), where 64 is the number of turns of the Tx coil, and 50 is the number of turns of the Rx coil. Figure 2a-c shows very high coupling coefficients (close to 0.4). In such models, the fluctuation of mutual inductance with rotation is very high. For example, Figure 3 displays the variations of mutual inductance and coupling coefficient of the winding structures that are given in Figure 2c. M variation reached 95% when the Rx coil rotated between 0° and 85°. Therefore, efficiency drops a lot in this case. In addition, a high coupling could result in a frequency-splitting issue, thus reducing output power. For choosing the right model, low variations of mutual inductance while rotating the Rx coil should be considered. Thus, a WPT system maintains constant efficiency. The coupling coefficient between the studied models ranged between 0.08 and 0.5. In further steps, the chosen model should consider low-leakage magnetic fields, which is explained in the next section.

Design Procedures for High Efficiency
Different methods of winding the Tx and Rx coils were obtained. In Figure 4, twelve different coil designs are displayed. In Figure 4a, the Tx and Rx coils took the same shape of hemicylindrical structures, and could be denoted as DL (64, 50). In Figure 4h, the Tx and Rx coils took the same shape of hemicylindrical structures and could be denoted as SL (32,25). As mentioned before, a constant PTE during the rotation of the Rx coil depends on mutual inductance and coupling coefficient, which follows the winding structure. Different methods of winding the Tx and Rx coils resulted in different values of the coupling coefficients and mutual inductances, as illustrated in Figure 5. DL (64, 50) and SL (32,25) designs had very high values of M and k. However, cost, volume, and weight were higher than those of other models. In addition, for the magnetically coupled resonant (MCR) WPT design, the k value could not be very high. Therefore, the design could be selected as one of the models that are marked in black in Figure 5.

Design Procedures for High Efficiency
Different methods of winding the Tx and Rx coils were obtained. In Figure 4, twelve different coil designs are displayed. In Figure 4a, the Tx and Rx coils took the same shape of hemicylindrical structures, and could be denoted as DL (64, 50). In Figure 4h, the Tx and Rx coils took the same shape of hemicylindrical structures and could be denoted as SL (32,25). As mentioned before, a constant PTE during the rotation of the Rx coil depends on mutual inductance and coupling coefficient, which follows the winding structure. Different methods of winding the Tx and Rx coils resulted in different values of the coupling coefficients and mutual inductances, as illustrated in Figure 5. DL (64, 50) and SL (32,25) designs had very high values of M and k. However, cost, volume, and weight were higher than those of other models. In addition, for the magnetically coupled resonant (MCR) WPT design, the k value could not be very high. Therefore, the design could be selected as one of the models that are marked in black in Figure 5.

Design Procedures for High Efficiency
Different methods of winding the Tx and Rx coils were obtained. In Figure 4, twelve different coil designs are displayed. In Figure 4a, the Tx and Rx coils took the same shape of hemicylindrical structures, and could be denoted as DL (64, 50). In Figure 4h, the Tx and Rx coils took the same shape of hemicylindrical structures and could be denoted as SL (32,25). As mentioned before, a constant PTE during the rotation of the Rx coil depends on mutual inductance and coupling coefficient, which follows the winding structure. Different methods of winding the Tx and Rx coils resulted in different values of the coupling coefficients and mutual inductances, as illustrated in Figure 5. DL (64, 50) and SL (32,25) designs had very high values of M and k. However, cost, volume, and weight were higher than those of other models. In addition, for the magnetically coupled resonant (MCR) WPT design, the k value could not be very high. Therefore, the design could be selected as one of the models that are marked in black in Figure 5.

Design Procedures for High Efficiency
Different methods of winding the Tx and Rx coils were obtained. In Figure 4, twelve different coil designs are displayed. In Figure 4a, the Tx and Rx coils took the same shape of hemicylindrical structures, and could be denoted as DL (64, 50). In Figure 4h, the Tx and Rx coils took the same shape of hemicylindrical structures and could be denoted as SL (32,25). As mentioned before, a constant PTE during the rotation of the Rx coil depends on mutual inductance and coupling coefficient, which follows the winding structure. Different methods of winding the Tx and Rx coils resulted in different values of the coupling coefficients and mutual inductances, as illustrated in Figure 5. DL (64, 50) and SL (32,25) designs had very high values of M and k. However, cost, volume, and weight were higher than those of other models. In addition, for the magnetically coupled resonant (MCR) WPT design, the k value could not be very high. Therefore, the design could be selected as one of the models that are marked in black in Figure 5.    The simulations of the WPT system were conducted with Ansys Maxwell 3D and Ansys Simplorer for cosimulation. Series-series (SS) compensation topology was considered. Resonant frequency was 950 kHz. Figure 6 illustrates the efficiency of each SS-compensated WPT system at a resonant frequency of 950 kHz. On the basis of the value of the coupling coefficient (shown in Figure  5) and the efficiency values in Figure 6, the chosen design was DL (30,16). Figure 6b displays the DL efficiency (30,16).  The simulations of the WPT system were conducted with Ansys Maxwell 3D and Ansys Simplorer for cosimulation. Series-series (SS) compensation topology was considered. Resonant frequency was 950 kHz. Figure 6 illustrates the efficiency of each SS-compensated WPT system at a resonant frequency of 950 kHz. On the basis of the value of the coupling coefficient (shown in Figure 5) and the efficiency values in Figure 6, the chosen design was DL (30,16). Figure 6b displays the DL efficiency (30,16). The simulations of the WPT system were conducted with Ansys Maxwell 3D and Ansys Simplorer for cosimulation. Series-series (SS) compensation topology was considered. Resonant frequency was 950 kHz. Figure 6 illustrates the efficiency of each SS-compensated WPT system at a resonant frequency of 950 kHz. On the basis of the value of the coupling coefficient (shown in Figure  5) and the efficiency values in Figure 6, the chosen design was DL (30,16). Figure 6b Figure 7 presents the relation between frequency, load, and efficiency, showing that the system was steady at low and high loads.
Electronics 2020, 9, x FOR PEER REVIEW 7 of 13 DL (30,16) self-inductances were LTx1 = 120.68 µH and LRx1 = 52.068 µH. Figure 7 presents the relation between frequency, load, and efficiency, showing that the system was steady at low and high loads.

Design Procedures for Low-Leakage Magnetic Fields
Maintaining low-leakage magnetic fields (LMFs) around Tx and Rx coils is another key point of WPT design. Figure 8 illustrates a comparison of the magnetic-field density (B) of different WPT systems (given in Figure 4). B was calculated around the coils' vicinities. The worst winding scenario was DL (64, 50), which had very-high-leakage magnetic fields (LMFs) of 74.67 µT. In addition, DL (64, 50) had a very high value of coupling coefficient at α = 0°, and this value dropped close to zero at α = 85°. On the basis of the efficiency value given in Figure 6, and the magnetic-field-density value presented in Figure 8, the chosen design was the same as DL (30, 16) (dark green), which had a low LMF level of 27.1 µT. This value is almost the same as the exposure limit that was set by ICNIRP-2010. Therefore, the chosen design decreased LMFs by 63.6% compared with DL (64, 50), which has similar efficiency. Moreover, the magnetic-field density of the chosen design at different rotation angles (0°-85°) is illustrated in Figure 9. With the rotation of the Rx coil, B was reduced. Furthermore, Figure 10 displays the B of SL (32,25). Compared with the best selected design, the level of LMFs was decreased by 22.5%.

Design Procedures for Low-Leakage Magnetic Fields
Maintaining low-leakage magnetic fields (LMFs) around Tx and Rx coils is another key point of WPT design. Figure 8 illustrates a comparison of the magnetic-field density (B) of different WPT systems (given in Figure 4). B was calculated around the coils' vicinities. The worst winding scenario was DL (64, 50), which had very-high-leakage magnetic fields (LMFs) of 74.67 µT. In addition, DL (64, 50) had a very high value of coupling coefficient at α = 0 • , and this value dropped close to zero at α = 85 • . On the basis of the efficiency value given in Figure 6, and the magnetic-field-density value presented in Figure 8, the chosen design was the same as DL (30, 16) (dark green), which had a low LMF level of 27.1 µT. This value is almost the same as the exposure limit that was set by ICNIRP-2010. Therefore, the chosen design decreased LMFs by 63.6% compared with DL (64, 50), which has similar efficiency. Moreover, the magnetic-field density of the chosen design at different rotation angles (0 • -85 • ) is illustrated in Figure 9. With the rotation of the Rx coil, B was reduced. Furthermore, Figure 10 displays the B of SL (32,25). Compared with the best selected design, the level of LMFs was decreased by 22.5%.   Alpha='0deg' Alpha='90deg' Figure 9. Magnetic-field density of chosen design of DL (30,16) at different rotation angles of Rx coil.
There are some models that have almost the same level of LMFs as those of the chosen design, such as DL (24,16), as shown in Figure 11 at different rotation angles. Nevertheless, on the basis of efficiency values, DL (30,16) had efficiency of 97.9%, whereas DL (24, 16) had efficiency of 87.1%. Figure 11. Double-layer winding model DL (24,16) at different rotation angles of Rx coil.

Experiment Results and Validation
To validate the selected design (DL (30, 16)), a prototype was built. Series-series (SS) topology was chosen. The experiment setup is given in Figure 12. Multistrand Litz wire was used to wind the coils. This reduced the skin effect and power losses at high frequency. In addition, radio-frequency (RF) mica capacitors were used for better performance of the WPT system. The measured parameters are given in Table 1, where R1 and R2 (Ω) are the resistances of Tx and Rx windings, respectively; and CTx and CRx (nF) are the compensation capacitors of Tx and Rx coils, respectively.   There are some models that have almost the same level of LMFs as those of the chosen design, such as DL (24,16), as shown in Figure 11 at different rotation angles. Nevertheless, on the basis of efficiency values, DL (30,16) had efficiency of 97.9%, whereas DL (24, 16) had efficiency of 87.1%.
There are some models that have almost the same level of LMFs as those of the chosen design, such as DL (24,16), as shown in Figure 11 at different rotation angles. Nevertheless, on the basis of efficiency values, DL (30,16) had efficiency of 97.9%, whereas DL (24, 16) had efficiency of 87.1%. Figure 11. Double-layer winding model DL (24,16) at different rotation angles of Rx coil.

Experiment Results and Validation
To validate the selected design (DL (30, 16)), a prototype was built. Series-series (SS) topology was chosen. The experiment setup is given in Figure 12. Multistrand Litz wire was used to wind the coils. This reduced the skin effect and power losses at high frequency. In addition, radio-frequency (RF) mica capacitors were used for better performance of the WPT system. The measured parameters are given in Table 1, where R1 and R2 (Ω) are the resistances of Tx and Rx windings, respectively; and   Figure 11. Double-layer winding model DL (24,16) at different rotation angles of Rx coil.

Experiment Results and Validation
To validate the selected design (DL (30,16)), a prototype was built. Series-series (SS) topology was chosen. The experiment setup is given in Figure 12. Multistrand Litz wire was used to wind the coils. This reduced the skin effect and power losses at high frequency. In addition, radio-frequency (RF) mica capacitors were used for better performance of the WPT system. The measured parameters are given in Table 1, where R 1 and R 2 (Ω) are the resistances of Tx and Rx windings, respectively; and C Tx and C Rx (nF) are the compensation capacitors of Tx and Rx coils, respectively.
Electronics 2020, 9, x FOR PEER REVIEW 10 of 13 Figure 12. Experiment setup of WPT system. The input and output voltages are displayed in Figure 13. The output voltage slightly changed when Rx coil rotated. The voltages are presented at four angles between 0° and 85°.  The input and output voltages are displayed in Figure 13. The output voltage slightly changed when Rx coil rotated. The voltages are presented at four angles between 0 • and 85 • .
The chosen design had low fluctuations of mutual inductance while rotating the Rx coil. The measured and simulated mutual inductances are presented in Figure 14. Simulated mutual inductance is always larger than measured mutual inductance. The simulations gave ideal values of the coils' inductances and mutual inductance. However, measurements take into consideration some factors such as losses. In addition, in the fabricated prototype, the distance between the Tx and Rx coils was slightly different than that in the simulated model, so the coupling coefficient in the simulation was 0.13, whereas the measured one was 0.11. Therefore, simulated mutual inductance was larger than the measured mutual inductance. The measured M varied between 9.94 µH at α = 0 • , 11.56 µH at α = 60 • , and 10.033 µH at α = 85 • . This affected the measured efficiency. A network analyzer (E5061B) was used for measuring the S-parameters at the resonant frequency of 943 kHz. Ports 1 and 2 were connected to the Tx and Rx coils, respectively. Power-transfer efficiency (PTE) could be obtained in terms of the linear magnitude of the S-parameter (|S 21 |) [26]. In Figure 14, PTE was given according to rotation angle. The measurements indicated that the given WPT system could maintain almost constant PTE in spite of rotation. At α = 0 • , PTE = 83.50%; at α = 30 • , PTE = 84.24%; at α = 60 • , PTE = 85.01%; and at α = 85 • , PTE = 81.35%. Thus, PTE was increased by 1.51% when the Rx coil rotated from 0 • to 60 • , and dropped by only 2.15% when the Rx coil rotated between 0 • and 85 • . The input and output voltages are displayed in Figure 13. The output voltage slightly changed when Rx coil rotated. The voltages are presented at four angles between 0° and 85°. The chosen design had low fluctuations of mutual inductance while rotating the Rx coil. The measured and simulated mutual inductances are presented in Figure 14. Simulated mutual inductance is always larger than measured mutual inductance. The simulations gave ideal values of Electronics 2020, 9, x FOR PEER REVIEW 11 of 13 the coils' inductances and mutual inductance. However, measurements take into consideration some factors such as losses. In addition, in the fabricated prototype, the distance between the Tx and Rx coils was slightly different than that in the simulated model, so the coupling coefficient in the simulation was 0.13, whereas the measured one was 0.11. Therefore, simulated mutual inductance was larger than the measured mutual inductance. The measured M varied between 9.94 µH at α = 0°, 11.56 µH at α = 60°, and 10.033 µH at α = 85°. This affected the measured efficiency. A network analyzer (E5061B) was used for measuring the S-parameters at the resonant frequency of 943 kHz. Ports 1 and 2 were connected to the Tx and Rx coils, respectively. Power-transfer efficiency (PTE) could be obtained in terms of the linear magnitude of the S-parameter (| |) [26]. In Figure 14, PTE was given according to rotation angle. The measurements indicated that the given WPT system could maintain almost constant PTE in spite of rotation. At α = 0°, PTE = 83.50%; at α = 30°, PTE = 84.24%; at α = 60°, PTE = 85.01%; and at α = 85°, PTE = 81.35%. Thus, PTE was increased by 1.51% when the Rx coil rotated from 0° to 60°, and dropped by only 2.15% when the Rx coil rotated between 0° and 85°. Figure 14. Simulated and measured mutual inductance, and efficiency according to rotation angle.

Conclusions
In this paper, a new cylindrical winding structure for WPT systems was proposed. In the proposed design, the Tx coil was wound on a hemicylindrical structure, and the Rx coil was wound on a cylindrical structure. Therefore, the Rx coil could freely rotate within the Tx coil. Different winding methods were presented and compared. The best winding method reduced the leakage of magnetic fields (LMFs) and maintained constant power-transfer efficiency (PTE), while rotating the Rx coil. Design procedures were discussed in detail. Moreover, EMF analysis was done under different rotation angles between 0° and 85°. The leakage of magnetic fields in the coils' vicinities of the chosen design was reduced by 63.6% compared with other winding methods with the same efficiency. Thus, the given design reduces the cost, weight, shielding (if required), and volume of designed WPT coils. A prototype was built to validate the chosen design. Measurements confirmed that variations of mutual inductance were very low, where M varied between 9.94 µH at α = 0° and 10.03 µH at α = 85°. As a result, the WPT system maintained a constant PTE. Efficiency was decreased by only 2.15% when the Rx coil rotated from 0° to 85°. The proposed WPT system is a good choice

Conclusions
In this paper, a new cylindrical winding structure for WPT systems was proposed. In the proposed design, the Tx coil was wound on a hemicylindrical structure, and the Rx coil was wound on a cylindrical structure. Therefore, the Rx coil could freely rotate within the Tx coil. Different winding methods were presented and compared. The best winding method reduced the leakage of magnetic fields (LMFs) and maintained constant power-transfer efficiency (PTE), while rotating the Rx coil. Design procedures were discussed in detail. Moreover, EMF analysis was done under different rotation angles between 0 • and 85 • . The leakage of magnetic fields in the coils' vicinities of the chosen design was reduced by 63.6% compared with other winding methods with the same efficiency. Thus, the given design reduces the cost, weight, shielding (if required), and volume of designed WPT coils. A prototype was built to validate the chosen design. Measurements confirmed that variations of mutual inductance were very low, where M varied between 9.94 µH at α = 0 • and 10.03 µH at α = 85 • . As a result, the WPT system maintained a constant PTE. Efficiency was decreased by only 2.15% when the Rx coil rotated from 0 • to 85 • . The proposed WPT system is a good choice for power transfer for applications that require angular movements.