High-temperature Permanent Magnets Research Articles

Analysis of a passive vibration damper for high-speed superconducting magnetic bearings

Abstract Superconducting magnetic bearings (SMB) based on a combination of high temperature superconductors and permanent magnets enable the realization of self-stabilized high-speed devices with significantly reduced friction. However, external vibration might couple in the bearing resulting in large amplitude oscillations due to a resonance case. A dedicated eddy current damper (ECD) might be used to eliminate these oscillations for a stable operation. The influence of such damping elements was studied for a frictionless SMB twisting system designed to speed up the conventional ring spinning process. Therefore, conductive copper rings with different thicknesses were implemented at different positions into the bearing setup as ECD. Afterward, the SMB setup was analyzed during acceleration using an array of laser distance sensors to record the displacement of the levitating permanent magnet ring in radial and axial direction, respectively. Simultaneously, a numerical model was developed to investigate the influence of the ECDs on the dynamic and static behavior of the SMB in more detail. It was shown that the simulated damping coefficients are in good agreement with the measured values, which allows further optimization of the ECD with the developed numerical model.

Optimizing superconducting magnetic bearings of HTS flywheel systems based on 3D H-[formula omitted] formulation

The superconducting flywheel system exploiting the magnetic coupling between the bulk high temperature superconductors (HTSs) and permanent magnets (PMs) exhibits excellent performance of self-stable levitation, and is promising for power applications. In this paper, we use the H-ϕ formulation combined with moving mesh to establish a full 3D model for the thrust type and journal type bearings in the HTS flywheel system. We then proposed different Halbach schemes to enhance the magnetic flux density of the rotor and thus the coupling, and investigated the levitation force, relaxation characteristics, electromagnetic transient distribution, and temperature characteristics of the bearings. Results show that, under axial zero field-cooled (ZFC) condition, the optimized PM rotor scheme can significantly improve the maximum levitation force and stiffness by 4.0 and 2.3 times respectively for the thrust type bearing, and the maximum levitation force of journal type bearing can be improved by a factor of 5.5. Under the radial ZFC condition, the maximum levitation force and stiffness of the journal type bearing have been increased by 4.9 times and 2.9 times. For the relaxation of both bearings during operation, the optimized PM rotors lead to relatively greater attenuation of levitation force. The proximity of the optimized PM rotors intensifies the magnetic flux movement of the HTS bulks but only brings about a limited temperature rise, and the superconductors still maintain a good low-temperature working environment. This study provides an effective methodology for analyzing the HTS bearing systems and good references for the optimal design of compact HTS flywheel energy storage systems (FESSs).

Development of High-Temperature Permanent Magnet Synchronous Motor for Autonomous Robotic Navigation: A Design and Finite Element Analysis Approach

The traditional industrial robots come with the prime mover, i.e. Electric Motors (EM) which ranges from a few hundred too few kilo watts of power ratings. However, for autonomous robotic navigation systems, we require motors which are light weighted with the aspect of high torque and power density. This aspect is very critical, when the EMs in robotic navigations are subjected to harsh high temperature survival conditions, where the sustainability of the performance metrics of the electromagnetic system of the EMs degrade with the prevailing high temperature conditions. Hence, this research work address and formulate the design methodology to develop a 630 W High Temperature PMSM (HTPMSM) in the aspect of high torque and power density, which can be used for the autonomous robotic navigation systems under high temperature survival conditions of 200°C. Two types of rotor configurations i.e. the Surface Permanent Magnet type (SPM) and the Interior Permanent Magnet type (IPM) of HTPMSM are examined for its optimal electromagnetic metrics under the temperature conditions of 200°C. The 630 W HTPMSM is designed to deliver the rated torque of 2 Nm within the volumetric & diametric constraints of D x L which comes at 80 x 70 mm at the rated speed of 3000 rpm with the survival temperature of 200°C with the target efficiency of greater than 90%. The FEM based results are validated through the hardware prototypes for both SPM and IPM types, and the results confirm the effectiveness of the proposed design methodology of HTPMSM for sustainable autonomous robotic navigation applications.

Nonlinear motion characteristics of the high-temperature superconducting levitation system with boundary crack

High-temperature superconducting levitation systems have nonlinear behaviors, such as the period-doubling bifurcation and chaotic vibration under external excitation, in connection with the nonlinear hysteresis interaction between the high-temperature superconductors (HTSC) and permanent magnet. The HTSC is a non-ideal type II superconductor in which the fracture is generated internally during manufacturing, and the material properties are brittle. The HTSC tends to crack under a strong magnetic field and electromagnetic force, and its internal defects are likely to cause structural damage with the variable Lorentz force. The fracture performance of the superconducting magnetic levitation system will affect the temperature variation of HTSC, in which the temperature is coupled with the internal electromagnetic force. In this paper, we analyze the fracture characteristics of the HTSC in nonlinear vibration with thermal effect. A superconducting magnetic levitation system model with boundary cracks is applied to study the coupling of multiple physical fields in dynamic processes. The Maxwell equation and superconducting electromagnetic constitutive equation are used to obtain the superconductor’s current density, and the temperature is calculated through the heat conduction equation. The superconducting magnetic flux flow and creep model is applied to analyze the magnetic flux motion inside the superconductors. We compare the superconducting levitation system’s electromagnetic force, temperature, and current density with four critical current densities. The numerical results show that the critical current density of superconductors significantly impacts bifurcation motion, and the temperature of the crack tip of the superconductors varies greatly during vibration, causing the superconductor to lose its superconductivity.

Magnetocrystalline anisotropy of interstitially and substitutionally Sn-doped MnBi for high temperature permanent magnet applications

First-principles calculations were performed to calculate the electronic structures of low temperature phase (LTP) MnBi (Mn50Bi50) and substitutionally and interstitially Sn-doped MnBi [Mn50Bi25Sn25, (Mn0.5Bi0.5)66.7Sn33.3]. Brillouin function predicts the temperature dependence of saturation magnetization M(T). Sn substitution for Bi in MnBi (Mn50Bi25Sn25) changes the magnetocrystalline anisotropy constant (Ku) from −0.202 MJ/m3 (the in-plane magnetization) for LTP MnBi to 1.711 MJ/m3 (the out-of-plane magnetization). In comparison, the Ku remains negative but slightly decreases to −0.043 MJ/m3 when Sn is interstitially doped in MnBi [(Mn0.5Bi0.5)66.7Sn33.3]. The Curie temperature (TC) decreases from 716 K for LTP Mn50Bi50 to 445 K for Mn50Bi25Sn25 and 285 K for (Mn0.5Bi0.5)66.7Sn33.3. Mn50Bi25Sn25 has a lower magnetic moment of 5.034 μB/f.u. but a higher saturation magnetization of 64.2 emu/g than (Mn0.5Bi0.5)66.7Sn33.3 with a magnetic moment of 6.609 μB/f.u. and a saturation magnetization of 48.2 emu/g because the weight and volume of the substitutionally Sn-doped MnBi are smaller than the interstitially Sn-doped MnBi. The low Curie temperature and magnetization for Sn-doped MnBi are attributed to the high concentration of Sn. Thus, future study needs to focus on low Sn-concentrated MnBi.

Hard Magnetic Properties and the Features of Nanostructure of High-Temperature Sm-Co-Fe-Cu-Zr Magnet with Abnormal Temperature Dependence of Coercivity

This paper presents methods and approaches that can be used for production of Sm-Co-Fe-Cu-Zr permanent magnets with working temperatures of up to 550 °C. It is shown that the content of Sm, Cu, and Fe significantly affects the coercivity (Hc) value at high operating temperatures. A decrease in the content of Fe, which replaces Co, and an increase in the content of Sm in Sm-Co-Fe-Cu-Zr alloys lead to a decrease in Hc value at room temperature, but significantly increase Hc at temperatures of about 500 °C. Increasing the Cu concentration enhances the Hc values at all operating temperatures. From analysis of the dependence of temperature coefficients of the coercivity on the concentrations of various constituent elements in this alloy, the optimum chemical composition that qualifies for high-temperature permanent magnet (HTPM) application were determined. 3D atom probe tomography analysis shows that the nanostructure of the HTPM is characterized by the formation of Sm2(Co,Fe)17 (2:17) cells relatively smaller in size along with the slightly thickened Sm(Co,Cu)5 (1:5) boundary phase compared to those of the high-energy permanent magnet compositions. An inhomogeneous distribution of Cu was also noticed in the 1:5 phase. At the boundary between 1:5 and 2:17 phases, an interface with lowered anisotropy constants has developed, which could be the reason for the observed high coercivity values.

Vertical Magnetic Field Distribution Characteristics of Triple-Peak Halbach Array PMG and Its Engineering Application in HTS Maglev Train

The maglev train has a broad application prospect in the field of high-speed transportation, which is based on the high-temperature superconductor permanent magnet guideway (HTS-PMG) maglev system. The optimized design of the permanent magnet guideway (PMG) configuration is of great significance to improve the overall performance of the system and reduce the cost. In this article, a triple-peak Halbach array PMG is proposed, which is suitable for the HTS-PMG maglev system based on square single-seed melt-texture YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_x</i> block with a width of 40 mm. Through theoretical calculations, the influence of structural parameters of triple-peak Halbach array PMG on the vertical magnetic field distribution characteristics is revealed, that is, increasing the proportion of horizontally magnetized permanent magnet (vertically magnetized permanent magnet) is conducive to enhancing the vertical magnetic field in the regions close to (far away from) PMG. Furthermore, combined with the engineering application of HTS-PMG maglev train, an optimized triple-peak Halbach array PMG sample is fabricated. And the reliability of the theoretical model of triple-peak Halbach array PMG is verified by simulation and experimental measurements. Based on the optimized PMG, a full-scale HTS-PMG maglev train test line with a length of 22 m and a standard gauge of 1.435 m (in China) is built up, and the manned test is successfully carried out, which shows the feasibility of the triple-peak Halbach array PMG in large-scale engineering application of the HTS-PMG maglev train.

Influence of exchange coupling interaction on coercivity in 2:17-type SmCo-based high temperature permanent magnets

The intergranular exchange coupling interaction in Sm(CobalFe0.10Cu0.10Zr0.03)7.2 high temperature permanent magnets with different isothermal aging time was studied. The magnet isothermally aging for 24 h with higher coercivity at room temperature exhibits a weaker exchange coupling, while that aging for 4 h with a relatively small temperature coefficient of coercivity shows a stronger exchange coupling. Microstructure and microchemistry analysis indicated that Cu gradually enriches in the cell boundaries with the prolongation of isothermal aging time, decreasing the exchange coupling strength. Theoretical analysis results revealed that with the increase of temperature, the cells gradually get exchange decoupled and demagnetized independently, and the exchange coupling strength between cells decreases, which slows down the decline of coercivity. It is proposed that an optimized temperature coefficient of coercivity requires a stronger exchange coupling at room temperature, conducing to a more significant compensation effect with the increase of temperature.

Equivalent Models of Critical Current and Magnetization for Calculating the Magnetic Field in Simply Connected Structures Made of HTS Bulk and HTS Tape

This paper proposes a way to represent the anisotropic nonlinear superconducting properties using a discrete model for magnetization with the corresponding critical parameters, equivalent to the Power Law model for currents. This simplified model makes it possible to analyze magnetic systems with superconducting elements in a stationary mode, which reduces the calculation time. Using of proposed model is demonstrated by the calculation of force interactions between high-temperature superconducting (HTS) samples and permanent magnet in zero-field-cooling (ZFC) and field-cooling (FC) modes. HTS bulks in the form of a prism and stack made of HTS tape are considered. The calculation of the electromagnetic field was carried out using the method of integral equations for field sources. The data of calculations are compared with the results of experimental studies.

Accurate Calculation of Iron Loss of High-Temperature and High-Speed Permanent Magnet Synchronous Generator under the Conditions of SVPWM Modulation

The high-temperature and high-speed permanent magnet synchronous generator (HTHSPMSG) is the core component ensuring the efficient and safe operation of the high-speed aircraft power supply system. At present, the existing iron loss model fails to meet the requirements for the precise calculation of the iron loss of HTHSPMSG under high-temperature and high-frequency conditions. In this paper, a 40 kW, 18,000 rpm HTHSPMSG is used to study the accurate calculation of iron loss at an ambient temperature of 350 °C. Considering the influence of high temperature and high frequency on the loss and performance of electromagnetic materials, a test platform for the loss performance of the magnetic core materials is established. Then, according to the loss performance of the electromagnetic material, the corresponding iron loss coefficient is fitted by the variable coefficient iron loss separation model. In addition, the digital twin field-circuit co-simulation method is proposed to guarantee the accuracy of the iron loss calculation. Then, the influence of carrier frequencies and modulation ratios on the iron loss characteristics of the HTHSPMSG under the conditions of SVPWM modulation is studied. Lastly, the effectiveness of the proposed method is verified by the experimental results, which provide a reference for the accurate analysis of iron loss of the same type of HTHSPMSG.

High-temperature superconducting guidance force enhancement by a novel permanent magnet guideway for maglev curve negotiation

In order to enhance the guidance force, adding the high-temperature superconducting (HTS) bulks and permanent magnets in lateral direction is the simplest way especially in curve negotiation situations. However, as the core component of maglev system, permanent magnet guideway (PMG) consists of a huge amount of NdFeB magnets along the operation line. Hence, it means a huge construction cost to add the magnets in lateral direction. To help solving this issue, this paper discusses a PMG improvement methodology based on the widely-used two-pole Halbach PMG. This proposed novel PMG can enhance the guidance force by only adding air intervals between neighbor magnets and the flux-concentration irons and raising the onboard HTS bulks’ width accordingly. Firstly, a 2D electromagnetic theoretical model of the HTS bulk-PMG maglev system was built in the COMSOL Multiphysics. Then, under the different external magnetic fields of the PMGs with different air intervals, levitation and guidance performances of the typical onboard HTS bulk array at typical working conditions were discussed. The results showed that, with the suitable HTS bulks’ width, the guidance force can increase with the intervals increasing in a range. And the HTS maglev system adopting this idea can achieve a guidance force growth of about 41%. This PMG idea is appropriate for curve negotiation situations because of its higher ratio of the guidance force to the levitation force, without changing the basic magnetic circuit and the magnet block number of the previous linear PMG.

The Effects of Temperature on the Dynamic Characteristics of High-Temperature Superconductor and Permanent Magnet Interaction System

The effects of temperature on the dynamic characteristics of a high-Tc superconductor (HTS) and permanent magnet (PM) system at different field cooled (FC) gaps and different masses are studied theoretically and experimentally. Results indicate that the resonant frequency of the HTS-PM system decreases with increasing FC gap or mass at different temperatures. Although decreasing temperature augments stiffness of the interaction force between the HTS and the PM. The effect of decreasing temperature on stiffness and resonance frequency is more significant at a smaller FC gap. It means that the enhancement of lowering temperature on stiffness and resonant frequency also depends on the magnetic field gradient.

Influence of Exchange Coupling Interaction on Coercivity in 2:17-Type SmCo-Based High Temperature Permanent Magnets

Influence of Exchange Coupling Interaction on Coercivity in 2:17-Type SmCo-Based High Temperature Permanent Magnets

Effect of post-solutionizing cooling rate on microstructure and magnetic properties of 2:17-type Sm-Co-Fe-Cu-Zr magnets

The fabrication of 2:17-type Sm-Co-Fe-Cu-Zr magnets that have served as the strongest high-temperature permanent magnets for nearly half a century requires a strict processing control to form full cellular nanostructure. Considering that slow cooling after solution-treatment may enable a more homogeneous temperature field inside the chamber and more slight magnetic properties difference among the magnets in mass production than rapid cooling, here we performed a comparative study on a model magnet Sm25Co46.9Fe19.5Cu5.6Zr3.0 (wt%) to investigate how the post-solutionizing cooling rate affects the microstructure and magnetic properties. In comparison with the rapid cooling condition, slow cooling produces coarser cellular nanostructure and lower defects density at the solution-treated state. Such initial microstructural difference leads to slower 1:5 H growth kinetics and slower defects dissociation kinetics during the subsequent aging process, characterized by the smaller fraction of 1:5 H cell boundary phase and the higher density of remanent defects in the slowly-cooled final magnets. Since the 1:5 H phase plays a dominant role on the coercivity and the remanent defects are harmful to hard magnetic properties, further work reveals that longer aging time can promote the formation of 1:5 H phase and to reduce the harmful defects for achieving better magnetic performance in the slowly-cooled magnets. These findings may be helpful for achieving uniform magnetic performance in mass production of 2:17-type Sm-Co-Fe-Cu-Zr magnets.

Temperature dependence of magnetization processes in Sm(Co, Fe, Cu, Zr)z magnets with different nanoscale microstructures

The characteristic microstructure of Sm(Co,Fe,Cu,Zr)z (z=6.7–9.1) alloys with SmCo5 cell walls in Sm2Co17 cells, all intersected by Zr-rich platelets, makes them some of the best performing high-temperature permanent magnets. Plentiful research has been performed to tailor their microstructure at the nanoscale; but due to its complexity, many questions remain unanswered about the effect of the individual phases on the magnetic performance at different temperatures. Here, we explore this effect for three different Sm(Co,Fe,Cu,Zr)z alloys by deploying high-resolution magnetic imaging via in situ transmission electron microscopy and three-dimensional chemical analysis via atom probe tomography. We show that their microstructures differ in terms of SmCo5 cell-wall and Z-phase size and density as well as the Cu concentration in the cell walls and demonstrate how these features influence the magnetic domain size and density, thus forming different micromagnetic spin structures. Moreover, we illustrate that the dominant coercivity mechanism at room temperature is domain-wall pinning and show that magnets with a denser cell-wall network, a steeper Cu gradient across the cell-wall boundary, and thinner Z-phase platelets have a higher coercivity. We also show that the coercivity mechanism at high temperatures is domain-wall nucleation at the cell walls. Increasing the Cu concentration inside the cell walls decreases the temperature of transition between pinning and nucleation, significantly decreasing the coercivity with increasing temperature. We, therefore, provide a detailed explanation of how the microstructure on the atomic to nanoscale directly affects the magnetic performance and provide detailed guidelines for an improved design of Sm(Co,Fe,Cu,Zr)z magnets.

Quantitative analysis of pinning-hardened intrinsic coercivity of Sm(CoFeCuZr)z (z = 7.0–7.8) high-temperature permanent magnets

SmCo-based permanent magnets possessing high Curie temperature and outstanding magnetocrystalline anisotropy are of great scientific and technological value on high temperature applications. It is widely accepted the coercivity mechanism as well as its temperature dependence is closely related to the microstructure and microchemistry. However, direct domain wall pinning observation with Lorentz microscopy is extremely difficult to explore the strength of domain wall pinning under high temperature and strong magnetic field. The quantitatively understanding of coercivity mechanism such as micromagnetic simulations cannot be carried out without the intrinsic magnetism of 1:5H and 2:17R inside the cellular microstructure of SmCo sintered magnets. Up to nowadays, there are no methods to directly measure the intrinsic magnetism of nanometer scale 1:5H and 2:17R, which retards the exploring of coercivity mechanism especially at high temperature. Herein, we prepared Sm(CoCuFeZr)z high-temperature permanent magnets with the ratio z values ranging from 7.0 to 7.8 and measured the microchemistry of 1:5H and 2:17R phases with transmission electron microscopy. Then single-phase solid solution samples with the same composition as 1:5H and 2:17R phases were prepared and the high temperature magnetic properties are measured directly. The coercivity mechanism can be well explained based on the difference of domain wall energy density qualitatively, including the abnormal temperature dependence of coercivity. More importantly, the quantitatively calculated coercivity according to the pinning-hardened coercivity theory with the obtained intrinsic parameters were found to agree well with the experiment results. Our work on the intrinsic magnetism of 1:5H and 2:17R phases at varying temperatures may offer important guidance for compositions design of the magnets with higher performance.

Revisiting the pinning sites in 2:17-type Sm-Co-Fe-Cu-Zr permanent magnets

It is still an open debate whether the 1:5H cell boundaries (CBs) or the intersections of 1:3R platelets and 1:5H CBs are the strong pining sites for the cellular nanostructured 2:17-type Sm-Co-Fe-Cu-Zr high temperature permanent magnets despite that they have been widely applied in advanced industries since 1970s. Herein, through tuning the volume fraction of Zr-enriched 1:3R platelets by varying the second-step aging time, the pinning behavior in a model magnet Sm25Co44.9Fe21.5Cu5.6Zr3.0 (wt%) was investigated. The results show that the volume fraction of 1:3R platelets can be effectively enlarged without changing the cell size (i.e. the volume fraction of CBs) by extending the aging time at 400 °C. Microscopic TEM characterizations combined with macroscopic magnetic measurements reveals that the locally thickened 1:3R platelets after long-term second-step aging reduce the effective pinning area by interrupting the magnetic domain walls at CBs, weakening the average pinning strength and the coercivity of the magnet. Consequently, our work supports that the 1:5H CBs act as the dominating pinning sites instead of the intersections of 1:3R platelets and 1:5H CBs, which may provide an important insight towards understanding the hard magnetism of pinning-controlled permanent magnets.

A Two-Dimension Force Model Between High-Temperature Superconducting Bulk YBaCuO and Halbach-Type Permanent Magnet Guideway

With the merits of self-levitation, self-stabilization, zero magnetic drag, environment-friendliness, and low energy consumption, high-temperature superconducting (HTS) maglev is regarded as one of the main technology modes for the future rail transit. For the researches on the lateral-vertical coupled dynamics of the HTS maglev, there is still a lack of lateral-vertical coupled force model that can characterize the macroscopic force between high-temperature superconductor and permanent magnet guideway (PMG). In this article, a scanning experiment of levitation force and guidance force in a selected area on the vertical plane was carried out, and the law of levitation force and guidance force changing with coordinates was studied as well. Moreover, the finite element method was used to calculate the magnetic field distribution of the Halbach-type PMG, meanwhile, the Lorentz force formula was utilized to analyze the influence law of PMG's magnetic field on the levitation force and guidance force. On the basis of this research, a 2-D force model that neglects the hysteretic between high-temperature superconductor and PMG was established. By comparing the simulation results of the model with the measured data of the experiment, it is found that both of them are in good agreement, which verifies the reliability of the proposed model. The 2-D force model is very helpful to the future research and calculation of the dynamics of the HTS maglev.

Fe content influence on the microstructure of solution-treated Sm-Co-Fe-Cu-Zr alloys

There is a great interest towards further enhancing the energy product of the most prominent high temperature permanent magnets Sm-Co-Fe-Cu-Zr by raising Fe content. Here we investigated the Fe content influence on microstructure of the solution-treated precursors, which is essential for designing subsequent aging conditions to develop desired cellular nanostructure. The combined X-ray diffraction (XRD) and transmission electron microscopy (TEM) investigations reveal that raising Fe content from 16.2 to 23.5 wt% in the solution-treated Sm25CobalFexCu5.6Zr3.0 (wt.%) alloys increases the 2:17R ordering degree (or its fraction) and decreases the density of stacking faults (SFs). In comparison with the Fe-16.2 wt% sample without cellular structure, the Fe-19.5 and Fe-23.5 wt% samples exhibit fine cellular nanostructure, the higher the Fe content, the larger the nanocells. Unlike the Fe-16.2 and Fe-19.5 wt% samples with homogeneous elemental distributions in the matrix, the Fe-23.5 wt% sample shows elemental segregations, thus leading to localized cellular nanostructures. Further comparative investigations show that raising Fe content has a similar influence on the microstructure to that by extending aging time on the Fe-16.2 wt% alloy, which indicates that the alloys with higher Fe content are easier to form equilibrium phases. These findings may provide important information to design proper aging condition for achieving desired cellular nanostructure in the Fe-rich Sm-Co-Fe-Cu-Zr permanent magnets.

Stator Optimization of Wind Power Generators With High-Temperature Superconducting Armature Windings and Permanent Magnet Rotor

Electrical machines with high-temperature superconducting (HTS) armature windings can benefit from high power density and efficiency. Furthermore, by using permanent magnets (PM) on the rotor, the cryogenic system can be significantly simplified compared with the fully superconducting (SC) machines or the machines with SC field windings. Compared with the conventional electrical machines, the performance of machines with HTS armature windings can be more sensitive to the design parameters due to the interaction between the operating current and the flux density. In this article, the influence of stator geometry on the machine with HTS armature windings and PM rotor is investigated. By considering the interaction between the operating current and the flux density, an iteration procedure for calculating the operating current of the HTS armature windings is proposed. A 10-MW surface-mounted PM wind power generator with HTS armature windings is studied by the finite element analysis. It is found that machines with different coil angle have different behaviors when changing the tooth width and the dimensions of tooth tips, which is different from conventional electrical machines. A new design and optimization method is then developed. Finally, the optimal design is identified with global optimization.