United States

Introduction&lt;br/&gt;Doubly-Salient machines (DSMs) have simple structure which provides high mechanical robustness and control flexibility, thus are suitable for wind power application [1-2]. However, due to the shortage of rare-earth resources, the rare-earth PM material becomes more and more expensive. In order to reduce the machine cost, decreasing the usage of rare-earth PMs without sacrificing steady torque becomes a hot topic. Consequent pole concept, which uses only half of the PMs with the same magnetization direction, is proposed to save the dosage of PMs [3-4]. Furthermore, rare-earth PMs are replaced with ferrite PMs to avoid the usage of rare earth resources. In this paper, slot-PM-assisted consequent-pole-PM doubly-salient machine (SPMA-CPM-DSM) is proposed. The key is that the consequent-pole ferrite PMs are employed in the stator yoke to reduce the cost and small amount of tangential magnetized rare-earth PMs is placed in the slot opening to improve the torque production. This proposed hybrid magnet design can greatly enhance the PM utilization ratio and reduce PM cost without sacrificing the steady torque.&lt;br/&gt;&lt;br/&gt;Machine configuration&lt;br/&gt;Fig. 1 shows the configuration of three machines. For the conventional DSM, the polarity of yoke ferrite PMs alternates around the circle. For CPM-DSM, the yoke ferrite PMs of one polarity remain while the yoke ferrite PMs of another polarity are replaced with iron core. For SPMA-CPM-DSM, based on the structure of CPM-DSM, tangential magnetized slot rare-earth PMs are added to further enhance the steady torque.&lt;br/&gt;&lt;br/&gt;Electromagnetic performance&lt;br/&gt;Fig. 2 shows the electromagnetic performance of three machines. It can be seen that the flux linkage amplitude, back-EMF amplitude, as well as average torque of CPM-DSM is almost the same as that of conventional DSM. Since the PM usage of CPM-DSM is half of that of conventional DSM, consequent pole structure can reduce the ferrite PM usage without sacrificing the electromagnetic performance of the machine. In addition, with the employment of slot rare-earth PMs, the flux linkage amplitude, back-EMF amplitude, as well as average torque of SPMA-CPM-DSM is 79% higher than that of CPM-DSM, denoting the torque enhancing ability of slot PMs.

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Fig. 1

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Fig. 2

2022 Joint MMM-INTERMAG

A Novel Slot-PM-assisted Consequent-pole-PM Doubly-salient Machine with Hybrid Magnets of Ferrite PMs and Rare-earth PMs

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Introduction Doubly-Salient machines (DSMs) have simple structure which provides high mechanical robustness and control flexibility, thus are suitable for wind power application [1-2]. However, due to the shortage of rare-earth resources, the rare-earth PM material becomes more and more expensive. In order to reduce the machine cost, decreasing the usage of rare-earth PMs without sacrificing steady torque becomes a hot topic. Consequent pole concept, which uses only half of the PMs with the same magnetization direction, is proposed to save the dosage of PMs [3-4]. Furthermore, rare-earth PMs are replaced with ferrite PMs to avoid the usage of rare earth resources. In this paper, slot-PM-assisted consequent-pole-PM doubly-salient machine (SPMA-CPM-DSM) is proposed. The key is that the consequent-pole ferrite PMs are employed in the stator yoke to reduce the cost and small amount of tangential magnetized rare-earth PMs is placed in the slot opening to improve the torque production. This proposed hybrid magnet design can greatly enhance the PM utilization ratio and reduce PM cost without sacrificing the steady torque. Machine configuration Fig. 1 shows the configuration of three machines. For the conventional DSM, the polarity of yoke ferrite PMs alternates around the circle. For CPM-DSM, the yoke ferrite PMs of one polarity remain while the yoke ferrite PMs of another polarity are replaced with iron core. For SPMA-CPM-DSM, based on the structure of CPM-DSM, tangential magnetized slot rare-earth PMs are added to further enhance the steady torque. Electromagnetic performance Fig. 2 shows the electromagnetic performance of three machines. It can be seen that the flux linkage amplitude, back-EMF amplitude, as well as average torque of CPM-DSM is almost the same as that of conventional DSM. Since the PM usage of CPM-DSM is half of that of conventional DSM, consequent pole structure can reduce the ferrite PM usage without sacrificing the electromagnetic performance of the machine. In addition, with the employment of slot rare-earth PMs, the flux linkage amplitude, back-EMF amplitude, as well as average torque of SPMA-CPM-DSM is 79% higher than that of CPM-DSM, denoting the torque enhancing ability of slot PMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/964ca993a62a1567900765fc831a59cd.jpg)

Fig. 1

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Fig. 2

poster

Wireless Sensor Network (WSN) node communication, which is used to gather information on a wide range of sensors, uses wireless communication that does not require wiring, but power is supplied via wired or battery[1]. In order to manufacture many small switches as battery-less, an economical self-powered generating application excluding additional elements such as piezoelectric elements are required. In addition, small electromagnetic induction studies are required because mechanical kinetic energy must be converted into electrical energy in a small spatial structure including pushbuttons[2]-[4]. This paper proposes a self-powered generating apparatus applicable to two-gang wireless switches. The electromagnetic induction phenomenon follows Faraday's law, which generates induced voltage when the magnetic field passing through the coil changes at time. Electromagnetic induction self-powered generating apparatus require magnets and conductors that generate electromotive force to create magnetic fields. Figure 1 shows the proposed new two-gang switch structure and magnetic flux flow. The right side of the Conventional one-gang switch magnetic material 2 was opened and magnet 2 and magnetic material 4 were added. The coil is in common use and is assumed to have the same winding resistance and inductance for comparison with the conventional one-gang switch. The no-load back Electromotive Force(EMF) waveforms of the convolutional one-gang switch and the proposed two-gang switch are shown in Figure 2. In the two-gang switch, when the switch lever 1 and 2 are operated, the no-load back EMF waveform is divided into a positive direction and a reverse direction. Therefore, the switch can be miniaturized because sensors are not required to distinguish each push operation. And the performance has been improved to the induced voltage ratio 84% of the one-gang switch. Later, the mechanism of the proposed two-gang switch will be described in full paper to compared with the existing one-gang switch mechanism, and optimum design according to the detailed shape will also be added.

![](https://assets.underline.io/uploads/markdown_image/1/image/33736a113bbb6f59cecf559e4bb10040.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/5293f40d9593827569e10290f9fb930c.jpg)

Design of Battery-less Wireless Switch that Share Coils in common using Electromagnetic induction Energy Harversting Mechanism

Design of Battery-less Wireless Switch that Share Coils in Common Using Electromagnetic Induction Energy Harversting Mechanism

Hydrogen is considered as a potential energy carrier, because there is no greenhouse polluting gas (such as carbon dioxide) generated during the energy releasing process. Water electrolysis is the best way to obtain pure hydrogen, but its low energy efficiency greatly limits its wide application. Hydrogen is a diamagnetic substance that can be manipulated by an external field. The various locomotion behaviors of the hydrogen bubbles under different magnetism are first shown in Fig.1. Fig. 1(a) shows that hydrogen bubbles move upward from the surface of the graphite electrode when the voltage of 150V is applied. Fig1. (b) shows that hydrogen bubbles evolving from graphite electrode slightly move towards the upper right when the magnet S-pole is faced with the cathode. This motion indicates that the magnetic field may help detach the bubbles from the surface of graphite electrode because of the micro-magnetohydrodynamic (MHD) effect. Fig.1 (c) shows that hydrogen bubbles move towards the right more significantly when the graphite electrode is changed to a platinum electrode, which is a paramagnetic material with a higher magnetic susceptibility than graphite. This result shows that the paramagnetic property will further enhance the locomotion of the bubbles and detach bubbles from the electrode more quickly. Figs. 2(a) and 2(b) respectively show a platinum electrode faced with a magnet generates a greater increase in the current density and conductivity of the water under the same applied voltage. In this paper, electrodes with different magnetism are adapted to hydrogen production in water electrolysis. The various moving behaviors of the bubbles under the different magnetism of electrode and the field conditions will be demonstrated in the full paper and the effects of working parameters related to magnetism and water electrolysis are discussed as well.

![](https://assets.underline.io/uploads/markdown_image/1/image/1c277bb1460ff3db5480660c4301df2b.jpg)

3-D view of Magnetic flux flow by conventional two-gang switch when the switch lever 1 is tilted down


![](https://assets.underline.io/uploads/markdown_image/1/image/96c0d30aef3aea0cae37e7ed0f9c5710.jpg)

Fig.2 (a) Current density vs. Charging voltage (b) Conductivity vs. Charging voltage for the different electrodes with and without the effect of magnetic field.

The Effect of Magnetism and Magnetic field on Locomotion of Hydrogen and Hydrogen Production Efficiency

I. Introduction Arc permanent magnet (PM) machines (APMMs) can directly connect the load without auxiliary devices, which are promising in large telescope drives [1] [2]. However, the conventional APMM with rotor PM suffers from a low PM utilization. In this paper, two new dual-stator consequent pole flux reversal APMMs (DS-CPFRAPMMs) are proposed and studied. The topologies and operation principles of the proposed machines are described. The electromagnetic performances of machines are analyzed by finite element analysis. II. Machine Topology and Operation Principle Fig. 1 shows the topologies of the proposed DS-CPFRAPMMs, which are named as machines I and II, respectively. It can be seen that both machines consists of two stators and one rotor, and each stator is composed of three modules. The three-phase concentrated windings are wound on the teeth of stator, which can offer the merits of short end length and low copper loss. Besides, the alternatively PMs and iron poles are placed on the top of stator teeth, which forms a consequent pole PM arrangement. The polarities of PMs on the inner and outer stators are opposite for machine I, while those are the same for machine II. Moreover, the rotor structures of machines I and II are also different. For machine I, the iron-only rotor is designed with double-sided salient poles. However, for machine II, the rotor is made up of separated iron poles. For both machines, each stator module and rotor forms a 12 stator-slot/11 rotor-pole combination. The operation principles of DS-CPFRAPMMs are based on the flux modulation effect, and the torque of machines are generated by taking advantage of the modulated air-gap field harmonics. III. Electromagnetic Performance Evaluation As shown in Fig. 2 (a) and (b), machine II has higher no-load phase flux linkage and back-EMF than machine I. According to Fig.2 (c), the average torque of machine II is 20.7% higher than that of machine I. However, machine I has a relatively low cogging torque. In addition, compared with machine II, machine I has a better over-load torque capability. More detailed design considerations and electromagnetic performance comparison results will be presented in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/3f365398ffc60be5268039dea92d3af6.jpg)

Fig. 1

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Fig. 2

Comparative Study of New Dual-Stator Consequent Pole Flux Reversal Arc Permanent Magnet Machines

Axial-flux magnetic-geared double-rotor machines (AMGDRMs) are verified a promising candidate for power splitting in hybrid electric vehicles (HEVs) [1]. However, in conventional AMGDRM, as can be seen in Fig. 1. (a), the modulating rotor is set in middle of stator and the permanent magnet (PM) rotor. Hence, the modulating rotor suffers from high axial magnetic force from the side of the PM rotor, resulting in low mechanical strength. In this paper, a new AMGDRM with interior-modulating-rotor is proposed to solve the problem of low mechanical strength. As shown in Fig. 1. (b)-(d), the PM rotor is set in middle of stator and the modulating rotor in proposed AMGDRM. Owing to that the PM rotor suffers from reverse axial magnetic forces from both sides simultaneously, the total axial magnetic force is dramatically reduced. The 3-D finite element analysis (FEA) simulation results shown in Fig. 1. (e) and (f) verify the low axial magnetic force property of proposed AMGDRM. Based on the magnetic-field modulating principle, the operating principle of proposed AMGDRM is investigated, and the speed and torque characteristics are also given. For the pole-pair configuration with ps=3, ppm=20, pm=23, the simulated magnetic field distribution and its spectrum verify the operating principle, as shown in Fig. 2. (a) and (b). As shown in Fig. 2. (c) and (d), the no load back electromagnetic force (EMF) verifies the speed characteristic. Fig. 2. (e) and (f) show that the torques of stator, the modulating rotor and the PM rotor are always in direct proportion, validating the torque characteristic. A simplified analytical model, as shown in Fig. 2. (g), is proposed to investigate the influence of geometry parameters. Based on it, the analytical description of the magnetic field is deduced by magnetomotive force (MMF) and permeability functions. The influences of ferromagnetic pole-piece and PM on torque output are investigated. Fig. 2. (h) shows that the optimal pole-arc coefficient is about 0.3 at any thickness of ferromagnetic pole-piece, which agrees well with the proposed analytical model. As shown in Fig. 2. (i), the optimal thickness of PM is about 3mm and torque output rises with the pole-arc coefficient of PM increasing.

![](https://assets.underline.io/uploads/markdown_image/1/image/eecd067d24e5fa092591902ffab9b456.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/9c410cd88934435eacfebcf8dee444bf.jpg)

Investigation of an Axial-Flux Magnetic-Geared Double-Rotor Machine with Interior-Modulating-Rotor

Electromagnetic Characteristic Analysis of an Axial-Flux Magnetic-Geared Double-Rotor Machine with Interior-Modulating-Rotor

Coaxial magnetic gear (CMG) is a novel transmission device, which is widely used in the field of low speed and high torque transmission. In order to improve the output torque of CMG, a novel CMG with convex Halbach arrays and Spoke structure is proposed in this paper. The permanent magnets of the inner rotor are Convex-T alternating arrangements. The PMs of the outer rotor are combination of Spoke structure and Halbach arrays. The Spoke part is magnetized along the tangential direction, and the Halbach part is magnetized along the radial direction. Using the unilateral effect of Halbach arrays, the air gap side magnetic field is strengthened and the yoke side magnetic field is weakened. In order to reduce the amount of iron, it is considered to slot on the outer rotor. The topological structure of CMG with 4 inner and 17 outer poles is established. The proposed CMG has the same volume size as the conventional CMG and the same amount of permanent magnets. The two-dimensional finite element method is used for simulating the proposed CMG. The magnetic field and electromagnetic torque of the CMG are calculated. Compared with the conventional CMG, the results show that the proposed CMG can effectively enhance the air gap flux density, reduce the non-working harmonic in the air gap, and the output torque is increased by 41.78%. This is of great significance to improve the torque density of the CMG.

![](https://assets.underline.io/uploads/markdown_image/1/image/b3f6ba7e8de407dca94f6d9125466bde.jpg)

Fig. 1 The topology of the proposed CMG


![](https://assets.underline.io/uploads/markdown_image/1/image/5d78f96dc717fcc508bb5864dcadac5b.jpg)

Table 1. Torque comparison

A Novel Coaxial Magnetic Gear with Convex Halbach Arrays and Spoke Structure

Due to the magnetic field modulation of the modulating ring, a large number of harmonics can generate in the air gap. These harmonics act on the permanent magnet and magnetic ring, resulting in large eddy current losses and iron losses. In order to improve the harmonics in the air gap and reduce the losses, a novel magnetic gear with Halbach and copper bar is proposed in this paper. The permanent magnets (PMs) of the inner rotor adopted Halbach arrays. The iron yoke of outer rotor is slotted and add copper bar. The air gap flux density, output torque and loss of the magnetic are compared by finite element method. Compared with conventional magnetic gear, the results show that the proposed magnetic gear not only improves the air gap magnetic density and weakens the unworked harmonics, but also increases the output torque from 140.07Nm to 142.64Nm, reduces the eddy current loss by 32.24% and the iron loss by 16%. This model provides a new idea for loss analysis and optimization of coaxial modulated magnetic gear.

![](https://assets.underline.io/uploads/markdown_image/1/image/b5ef11c5aede8123fe1e41bc167e4dae.jpg)

Fig. 1 CMG topology

![](https://assets.underline.io/uploads/markdown_image/1/image/7c5e67019eea1285df1e2bfa719e821e.jpg)

Table I Torque ripple



Loss Analysis of Magnetic Gear with Halbach Arrays and Copper Bar

Magnetic-geared double-rotor machines (MGDRMs) are verified a promising candidate for power split application [1]. However, there remains undesired torque ripple in conventional MGDRM. A new MGDRM with ironless stator, as shown in Fig. 1. (a), is proposed. The ironless stator structure can eliminate stator slot effect and enable a more flexible winding configuration, resulting in low torque ripple. The simplified model of the proposed machine, as shown in Fig. 1. (b), is proposed. Thus, based on the magnetic-field modulating principle, the operating principle is investigated, and the speed and torque characteristics are also deduced. For the pole-pair configuration with ps=3, ppm=20, pm=23, the simulated magnetic field distribution and its spectrum verify the operating principle, as shown in Fig. 1. (c) and (d). As shown in Fig. 2. (a) and (b), the no load back electromagnetic force (EMF) with low distortion verifies the speed characteristic. Fig. 2. (c) shows that the torque ripple of the proposed machine is 0.18%, validating the low torque ripple property. Furthermore, the torque ratio equals the theoretical value (i.e. pole-pair ratio). Fig. 2. (d) shows that the torques of stator, the modulating rotor and the PM rotor are always in direct proportion, validating the torque characteristic. Based on the simplified model shown in Fig. 1. (b), the analytical model consisting of magnetomotive force (MMF) and permeability functions is deduced to investigate the influence of key geometry parameters. The influences of ferromagnetic pole-piece and PM on torque output are investigated. Fig. 2. (e) shows that the optimal pole-arc coefficient of the modulating rotor is about 0.2, which approximately agrees with the proposed analytical model. It can be seen in Fig. 2. (f) that the torque output rises with the increment of ferromagnetic pole-piece thickness in the beginning and remains approximately unchanged when thickness is larger than 7mm. As shown in Fig. 2. (g) and (h), torque output rises with the pole-arc coefficient of PM increasing and the optimal thickness of PM is about 3mm, respectively. The trends of all above simulated results can be explained by the analytical model, validating the proposed model.

![](https://assets.underline.io/uploads/markdown_image/1/image/b0ebdb01a9ad9891d1d8419b54aa70c1.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/529c5b2024706364e5ca02465348f1e5.jpg)

A Novel Ironless Stator Magnetic-Geared Double-Rotor Machine

1. Introduction A 12-slot-8-pole switched reluctance motor (SRM) has benefits in many applications due to no permanent magnet, low-cost, and simple and robust rotor structure [1]-[4]. However, noises and vibrations of the 12/8 SRM are large due to its large torque ripple. In order to solve this problem, a 12/10 SRM with a star connection has been proposed, which has less torque ripple [5], [6]. In this paper, we propose a 12/10 SRM with a hex connection. The hex connection does not need a neutral point, and the stator has a short coil end height. Therefore, the size of the motor with the hex connection becomes smaller. The characteristics of the hex connection was compared with the star connection through 2D finite element analysis. 2. Comparison Fig. 1 shows a 12/10 SRM, inverter, hex and star connections. The stator has a 6-phase concentrated winding from A-phase to F-phase, and the in-phase coils are connected in series. The torque ripple and efficiency of the 12/10 SRM with hex and star connections are compared, where the voltage application timing is adjusted to satisfy an output power of 1 kW. Figs. 2 (a), (b) and (d) show the torque and current waveforms, and efficiency, respectively. Fig. 2 (c) shows the ratio of each harmonic component against the fundamental component in the coil current. From Fig. 2 (a), the torque ripple ratio of the hex connection model is less than that of the star connection model. This is because, from Fig. 2 (c), the coil current of the hex connection model has the third harmonic components. From Fig. 2 (d), the efficiency of the hex connection model is larger than that of the star connection model. This is because, from Fig. 2 (c), the ratio of the DC and fundamental components in the coil current is different between the hex and star connection models. 3. Conclusion A 12/10 SRM with the proposed hex connection is superior to that with the conventional star connection in terms of a torque ripple and efficiency. In the final paper, the difference between hex and star connections is theoretically described using a mathematical model. Furthermore, their load characteristics are compared by carrying out measurements on a prototype.

![](https://assets.underline.io/uploads/markdown_image/1/image/8caada62ef3ce8cd7d940df0d8393ae3.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/8eea51f0a9c37974ea51fc9d65152adf.jpg)

12/10 Switched Reluctance Motor with a Hex Connection

12/10 Switched Reluctance Motor with a Hex Connection

Switched reluctance motor (SRM) is a kind of doubly salient variable reluctance motor, which has the advantages of simple structure, reliable operation and large starting torque. The motor has the problem of large torque ripple, which causes vibration and noise during operation. In order to reduce torque ripple, a switched reluctance motor with hybrid excitation segmented rotor (HESSRM) is presented in this paper. Firstly, in HESSRM, aluminum block is used instead of silicon steel sheet rotor, the fan-shaped rotor core is embedded into the non-magnetic aluminum block, and stator has full pitch three phase windings. The permanent magnet is embedded in the stator tooth and its magnetization direction is consistent with the excitation direction of the winding. Secondly, in order to further reduce the torque ripple, the switch-on and switch-off angles of the power converter should be optimized. Finally, a three-phase 12/8 pole HESSRM model is established. Through parametric simulation, the optimal position and size of the permanent magnet are obtained, and the electromagnetic properties of the motor such as flux linkage, air gap magnetic field and torque are calculated. Compared with the conventional SRM, the average output torque of the proposed HESSRM is increased by 36.49% and the torque ripple is reduced by 36.41%.

![](https://assets.underline.io/uploads/markdown_image/1/image/ca22d7878c3bb8b3bc5be84ebbcbcf72.jpg)

Topology of HESSRM

![](https://assets.underline.io/uploads/markdown_image/1/image/27a3eab5e71eaef78f8b2f4d554a5d0e.jpg)

Torque comparison

Torque Characteristic of Switched Reluctance Motor with Hybrid Excitation Segmented Rotor

The magnetic circuit of switched reluctance motor(SRM) has a non-sinusoidal structure, and the switching performance of the control circuit changes with the period, resulting in complex electromagnetic performance, therefore, it is difficult to accurately calculate the core loss of SRM. Considering that SRM is affected by both alternating magnetization and rotational magnetization, an improved vector Play model is proposed for finite element analysis. This model not only satisfies the rotational hysteresis loss property but also improves the calculation accuracy of the core loss in the alternating field[1]. The traditional loss separation model can get accurate results for core loss calculation of motor under sinusoidal excitation, but this method can not be fully applied to the SRM under non-sinusoidal excitation. To verify the accuracy of the finite element simulation results, the magnetic flux density of stator and rotor core of SRM is decomposed into radial component and tangential component, The finite element model of SRM and the flux density waveform of typical points are shown in fig.1 and fig.2 respectively. For eddy current loss and excess loss, Fourier decomposition method is used to decompose the radial component and tangential component flux density of the motor into a series of sinusoidal magnetic density waveform, which is calculated by accumulation. For hysteresis loss, the equivalent elliptic loop(EEL) method was used to model the hysteresis loop in time domain[2]. This model divides the magnetic field intensity into reversible component and irreversible component, therefore, the calculation accuracy of dynamic hysteresis loss is improved. The accuracy of the improved vector Play model can be verified by comparing the results of core loss calculation with the finite element simulation results.

![](https://assets.underline.io/uploads/markdown_image/1/image/b9d2a71a116dc1d4557a3660e4ff5173.jpg)

Fig.1 A two-dimensional model of a 12/8 structure switched reluctance motor

![](https://assets.underline.io/uploads/markdown_image/1/image/8270b60bfc73e0a089ae857b2c913cb1.jpg)

Fig.2 (a) Magnetic flux density waveform of stator pole (b) magnetic flux density waveform of rotor pole (c) magnetic flux density waveform of rotor yoke

A Novel Slot-PM-assisted Consequent-pole-PM Doubly-salient Machine with Hybrid Magnets of Ferrite PMs and Rare-earth PMs

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