Magnet Mass Research Articles

Piezoelectric Shunt Damping for a Planar Motor Application under Cryogenic Conditions

For several decades, Moore’s law has driven the semiconductor industry, with computational power and production costs as the main drivers. Such drivers have enabled several technological innovations in the mechatronics and dynamics architecture of photolithography machines, used for semiconductor circuits manufacturing. Among current investigations, the use of superconductive magnets would enable higher accelerating stages and, thus, higher throughput and lower manufacturing costs. However, this involves a complex magnet structure that needs to operate at cryogenic temperatures and mechanical resonances at relatively low frequencies as a result of the thermal architecture of the system. The damping options are also limited due to the very low temperature. This paper explores the use of shunted piezoelectric transducers for damping the internal modes of the magnet mass. A classical resistive and inductive RL shunt is considered. The study was conducted both numerically and experimentally on a demonstrator of a superconductive magnet plate concept, where piezoelectric transducers are incorporated to support the superconducting coils. The study demonstrates the effectiveness of piezoelectric shunts as a damping solution at very low temperatures, with limited impact of the temperature variation on the performance.

Resonant Electro-Mechanical Coupling – A Possible Renewable Energy Source

This paper looks at a simple Electro-Mechanical System that is tuned to resonate with both mechanical and electrical resonance. The intention is to couple the system resonance such that the amplitude of the output voltage is increased. The basic setup consists of a forced Mass-Spring System consisting of a speaker driving a mass attached to a tension-spring. The mass is a Neodymium cylindrical magnet. The vertically driven system couples to a magnet coil which sits over the magnet. Thus, by induction a voltage is generated within the coil. The coil is connected in series with a set of electrolytic capacitors. The resulting Resistor-Capacitor-Inductor (RCL) circuit is so designed as to resonate. The idea behind this coupling is to increase the output voltage of the circuit, thereby creating a voltage supply that could be boosted via transformer action, if necessary. Noting that the resulting circuit provides a source of single-phase electricity, such a setup could be used to charge small electronic devices like cellphones and mobile earphone sets. Mechanical resonance is indicated by the erratic vibration of the speaker, spring and magnet system. Knowing the magnet mass and measured resonant frequency the approximate spring constant can be calculated. The resonant frequency is then used as the driving frequency for the electrical circuit consisting of the RCL components. Noting the electric circuit resonance frequency, the approximate capacitance needed can be calculated using the driving frequency and the inductance of the said magnet coil. Using the circuit capacitance and appropriate circuit resistance, the maximised quality factor is sought, therefore the objective of the electric circuit design is to maximise the output voltage. The power generated by the device was found to be less than ~1 W. This system can be optimized to deliver maximum power output at the required resonant frequency, by greatly increasing the coil turns, using closer tolerances between the moving magnet and the wound coil and/or using materials that would ensure added magnetic coupling. Such a system can be used as a possible source of renewable energy especially on reciprocating engines, where exciting forces are available.

Advanced multimaterial shape optimization methods as applied to advanced manufacturing of wind turbine generators

AbstractCurrently, many utility‐scale wind turbine generator original equipment manufacturers are dependent on imported rare earth permanent magnets, which are susceptible to market risks from cost instability. To lower the production costs of these generators and stay competitive in the market, several small wind manufacturers are pursuing continuous improvements to both generator design and manufacturing. However, traditional design and manufacturing methods have yielded marginal improvements in wind power performance. This work presents novel methods to redesign a baseline 15‐kW wind turbine generator with reduced rare‐earth permanent magnets by leveraging cutting‐edge three‐dimensional (3D) printed polymer‐bonded permanent magnets and steel. Symmetric, asymmetric, and multimaterial‐magnet parametrization methods are introduced for shape optimization. We extend the symmetric and asymmetric methods to the back iron in the stator to further investigate the impact and opportunities for performance improvements with lesser active materials. We employ a design‐of‐experiments approach with parametric computer‐aided design for shape generation and evaluate different designs by magneto‐thermal modeling and finite‐element analysis. We use adaptive sampling technique to identify better performing designs with lesser magnet mass, higher efficiency, and lower cogging torque when compared with the baseline generator. Asymmetric pole designs resulted in a magnet mass in the range of 4.77–5.37 kg, which was 27%–35% lighter than the baseline generator, suggesting that a new design freedom exists that can be enabled by advanced manufacturing, such as 3D printing. Shaping the back iron in the stator resulted in material savings in electrical steel of up to 14.62 kg, which was 20% lighter than the baseline stator. We conducted a structural analysis to evaluate an optimized asymmetric rotor design from the point of view of mechanical integrity and air‐gap stiffness. The magnetically optimal shape profile was shown as having a positive impact on the radial stiffness, and an optimal solution was discovered to reduce the structural mass by nearly 30 kg, which was 29% lighter than the baseline.

LCA of Recycled (NdDy)FeB Permanent Magnets through Hydrogen Decrepitation

Compared to conventional fossil-fueled vehicles, electric vehicles offer several environmental benefits. However, even electric vehicles are not completely environmentally friendly because many of their parts are not recycled today. These parts, especially the magnets that power them, end up in landfills at the end of the vehicle’s life cycle. This study aims to evaluate the environmental impacts of recycled (NdDy)FeB permanent magnets obtained by means of a novel hydrogen-decrepitation-based, magnet-to-magnet recycling technique. The Life Cycle Assessment methodology was used to compare, on a like-to-like basis, recycled and virgin permanent magnets. The core data provided by an industry partner served as the foundation for modelling the recycling process. Three different functional units were investigated based on three parameters, namely the magnet mass, magnetization coercivity, and energy product. Results revealed that the recycled magnet outperformed the virgin magnet in most impact categories. In terms of carbon footprint, recycling permanent magnets through hydrogen decrepitation would allow for an 18─33% reduction with respect to their production from virgin materials, depending on the assumed functional unit.

A lever-type piezoelectric wave energy harvester based on magnetic coupling and inertial vibration

Wave energy is not easily harvested due to its low-frequency movement. This paper proposed a lever-type piezoelectric wave energy harvester (LPWEH) based on magnetic coupling and inertial vibration. Through four sets of L-shaped lever structures, the LPWEH can fully use the kinetic energy created by wave motion. Using magnetic coupling and inertial vibration excitation methods can realize improved output performance. Meanwhile, using these two non-contact excitation methods can reduce the wear of the piezoelectric sheets. The effects of the installation height of the oscillating lever, the included angle of the oscillating lever, and the magnet mass at the end of piezoelectric sheets on the prototype's output voltage are studied. With the best testing conditions, the LPWEH can achieve an output voltage of 36.93 V and an output power of 16.72 mW at a resistance of 6 kΩ. In tests of wave environment, the LPWEH can light up 34 LEDs. These findings demonstrate that the LPWEH has a promising application for converting wave energy into electric energy, which may be used to supply electricity to some low-energy electronic devices.

Comparison of designs of synchronous machines with integrated torque transformer for renewable energy

Increasing the specific torque of electric machines is an urgent problem for a number of low-speed power electromechanical systems, one of such systems is a wind power plant. Determining the optimal design of a synchronous generator with a built-in torque transformer is important for the further development of wind power. The purpose of the research is to determine the optimal design of a generator with a built-in torque transformer for wind power plants, which is a solution to the problem of creating low-speed, high-torque and relatively compact electric generators, and will make it possible to abandon the gear drive. The paper examines two designs of a direct drive synchronous generator with a built-in torque transformer with two and three air gaps. The calculation is performed using the Comsol Multiphysics software based on the finite element method. The main criteria for comparison are the generator's output power, the maximum torque of the low-speed rotor connected to the wind turbine, the maximum torque per unit volume of the generator, and the maximum torque per unit mass of the permanent magnets. Based on the calculation results, it has been concluded that a synchronous generator with two air gaps has a higher torque per unit volume and torque per mass of permanent magnets, i. e. with the same power, the expenses on active materials will be lower. This type of generator has a higher output power compared to both the direct-drive synchronous generator and the synchronous generator with three air gaps, with the same dimensional parameters.

Determination of the optimal shape of permanent magnets of a given volume providing maximum strength of their magnetic coupling

The ponderomotive force of the adhesion of two permanent magnets depends on their shape. We present the results of determining the optimal shape of ellipsoidal magnets providing maximum magnetic adhesion between them. The interaction of two halves of a magnet, which is an ellipsoid of revolution, and a magnet in the form of a long rod with an elliptical cross section, is analyzed. Analytical formulas for the cohesion forces in these cases are obtained. For a fixed mass or volume of magnets, the problem of optimizing the adhesion force is solved and a geometric shape which provide the maximum adhesion force is determined. It is shown that in the case of a magnet in the form of an ellipsoid of revolution, the maximum adhesion force of its halves (ignoring the magnetic tension on the side surfaces) is achieved at an eccentricity of 0.625958. The magnitude of the maximum adhesion force exceeds the adhesion force of the halves of a uniformly magnetized spherical magnet of the same volume by 1.7%. In this case, the adhesion area of the ellipsoidal magnet will be less than the adhesion area of the spherical magnet by 28%. The optimal form of a bar magnet with an elliptical section with the maximum force of adhesion of its halves at a fixed volume of the magnet is determined. A formula is derived for the ponderomotive magnetostatic force of the interaction between the halves of a bar magnet with an elliptical section and the maximum force of interaction. Numerical estimates for a sintered NdFeB bar magnet showed that the ponderomotive force of interaction with a cross-sectional radius of 5 cm can reach 2 tons per 1 m of length. The results obtained can be used to improve the efficiency of devices based on permanent magnets.

Optimal design of brushless DC motor for electromobility propulsion applications using Taguchi method

Abstract This paper presents the optimal design of the permanent magnet brushless DC (BLDC) motor for electromobility propulsion applications. Two BLDC machines were analyzed: (a) – exterior rotor machine, and (b) – interior rotor machines The optimization of both motors structures was executed by the Taguchi method. The device structure was described by three design variables. The functional parameter (efficiency) and the economic parameter (total mass of the permanent magnets) were included in the objective function. The BLDC motors have been modelled using a finite element method (FEM). Finally, the functional parameters for both motor constructions were compared. The selected results of the calculations were presented and discussed.

A Novel Multi-Criteria Local Latin Hypercube Refinement System for Commutation Angle Improvement in IPMSMs

The commutation angle, γ, of an interior permanent magnet synchronous motor's (IPMSM) vector diagram, plays an important role in compensating the back electromotive force (back-EMF); both under phase current variations and an extended speed range, is required by the application. This commutation angle is defined as the angle between the fundamental of the motor phase current and the fundamental of the back-EMF. It can be utilised to provide a compensating effect in IPMSMs. This is due to the reluctance torque component being dependent on the commutation angle of the phase current even before entering the extended speed range. A real-time maximum torque per current and voltage strategy is demonstrated to find the trajectory and optimum commutation angles, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</i> , where the level of accuracy depends on the application and available computational speed. A magnet volume reduction using a novel multi-criteria local Latin hypercube refinement (MLHR) sampling system is also presented to improve the optimisation process. The proposed new technique minimises the magnet mass to motor torque density whilst maintaining a similar phase current level. A mapping of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</i> allows the determination of the optimum angles, as shown in this paper. The 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> generation Toyota Prius IPMSM is considered as the reference motor, where the rotor configuration is altered to allow for an individual assessment.

Bifurcations and nonlinear dynamics of asymmetric tri-stable piezoelectric vibration energy harvesters

Tri-stable piezoelectric vibration energy harvester (TPVEH) with asymmetric potential wells has lower potential difference and more unstable potential wells than the symmetric counterpart, which may benefit to improve the energy harvesting performance. Although some progress has been made, there is still few research on the asymmetric TPVEH compared to the symmetric counterparts. The bifurcation mechanism of equilibrium solutions, the transition mechanism of multi-stability state and the nonlinear dynamics of the asymmetric TPVEH are different from those of the symmetric one, and have not been well explored at present. This work presents an asymmetric TPVEH which is composed of a piezoelectric linear oscillator (PLO) and a magnet–mass–spring oscillator (MMSO) to theoretically and experimentally investigate the bifurcations, the transition mechanism and the nonlinear dynamics. A general nonlinear dynamic model of the asymmetric TPVEH is derived and its equilibrium solutions are calculated to reveal the bifurcation and transition mechanism. The steady-state response solutions and their stability analysis are successively deduced to theoretically investigate the nonlinear dynamics and the enhancing mechanism of energy harvesting. Experiments are consequently performed to validate the theoretical results. The results show that the MMSO can not only change the distribution position of the stable and unstable equilibrium points, but also change the potential barriers height by adjusting the horizontal interval in real-time. In addition, suitable spring stiffness of the MMSO benefits to enhance the dynamic response outputs and frequency bandwidth. Compared to the symmetric TPVEH, the asymmetric TPVEH can access the interwell oscillations more easily and generate larger response outputs over a wide frequency range under lower excitation level. For the suitable spring stiffness of 1000 N/m, the maximum voltage, power obtained by experiments and the acceleration threshold for snap-through of the asymmetric TPVEH are 7 V, 4.8 × 10−5 W and 8 m/s2, respectively, which are far better than the symmetric TPVEH, whose corresponding values are 3 V, 0.8 × 10−5 W and 18 m/s2, respectively.

Modeling and Characteristic Analysis of Combined Beam Tri-Stable Piezoelectric Energy Harvesting System Considering Gravity

The emergence of the vibration energy harvesting system makes it possible for wireless monitoring nodes in coal mines to realize self-power supply. In order to reveal the influence of gravity effect on the response characteristics of the combined beam tri-stable piezoelectric energy harvesting system (CTEHS), the system’s nonlinear magnetism is calculated according to the principle of point magnetic charge dipole, and the system’s nonlinear resilience is obtained through experimental measurements and nonlinear fitting methods. Based on the Lagrange equation, the system’s electromechanical coupling motion model considering gravity is established. The system’s motion equation is solved numerically based on the Runge–Kutta algorithm, and the effects of the end magnet mass and the initial vibration point on the bifurcation behavior, potential energy, and system output performance are investigated by emulation and experiment. The research shows that the magnet’s gravity effect causes a change in the stable equilibrium position and the system’s motion state and also causes the system to generate additional gravitational potential energy, which leads to a potential asymmetric well of the system. Under the consideration of magnet gravity, the appropriate end magnet mass and initial vibration point can not only reduce the system’s requirements for external excitation strength but also effectively improve the system’s response and output. This research provides a new theoretical basis for the optimal design of the tri-stable piezoelectric energy harvesting system.

Electromagnetic Design of Single-Phase Permanent Magnet Linear Oscillation Actuator Considering Detent Force Minimum

This article proposes an improved tubular single-phase permanent magnet linear oscillation actuator (SP-PMLOA) considering eliminating detent force for direct drive compressor applications. First, the flux tube method and Maxwell stress tensor are used to derive the end force and cogging force formulations based on the magnetic flux leakage of the magnet rings. Then, a novel model with minimum detent force is presented by finite element parametric sweeping. Finally, the electromagnetic performance of the three SP-PMLOAs is compared using 2-D finite element analysis (FEA), whose merits are evaluated, and the thermal distribution of the optimal PMLOA is analyzed using 3-D FEA. The predicted results show that the proposed structure not only can significantly reduce the detent force and the mover axial length but also can increase the thrust force-moving magnet mass ratio.

A zero power current and frequency sensor for smart grid applications

Obtaining real time feedback on the amplitude and frequency of current flowing through power lines is of significant importance to smart grids. This paper investigates the use of a zero power multifunctional device (sensor and energy harvester) to solve this challenging problem. The passive device combines a piezoelectric cantilever with a hard magnet mass in order to couple the AC magnetic field from the power line to the device to generate an oscillating kinetic force at the frequency of the current. The proposed device is passive, but the transmission of the data requires the use of wireless sensor nodes, which requires power. The piezoelectric cantilever acts as both a passive sensor and a kinetic energy harvester to power the wireless sensor nodes. This study investigates the effects on both the sensor sensitivity and energy harvesting power density as a function of the type of wire (stranded vs solid wires), stiffness of the cantilever, and pull strength of the magnet for high current applications. The results demonstrate that stranded wires have a slight reduction in sensitivity from 1.12 V A−1 to 0.98 V A−1 for solid and stranded wire. The stiffness of the cantilever also affects the sensitivity and energy harvesting performance, where stiffer beams resulted in high power density and sensitivity. Increasing the magnet thickness and pull strength resulted in increased power density and bandwidth but it also effects the optimal spatial location of the magnet in relation to the wire. The device was also validated as a frequency sensor with a resolution of <1 Hz, and could be further optimized in the future. The results of this study validate the potential use of the device as a multifunctional sensor/energy harvester for smart grid applications.

Thermodynamics of heterogeneous equilibria in the In-In2 O3 system using Knudsen effusion mass spectrometry.

The In-In2 O3 system is regarded as a potential low-temperature source of gaseous indium oxide (In2 O) when obtaining functional materials by physical vapor deposition techniques. To date the vaporization thermodynamics of the system have been investigated in few studies, the results of which are contradictory. The study of the In-In2 O3 system was performed using Knudsen effusion mass spectrometry in the temperature range 930-1210 K, with a magnet mass spectrometer (MS-1301). Quartz effusion cells heated by a resistance furnace were employed. It was established that In(g) and In2 O(g) are the major vapor species over heterogeneous mixtures (In(l) + In2 O3 (s)) and the gaseous oxide In2 O is predominant. The partial pressures of the vapor species were determined and the quantitative vapor composition was calculated. Based on the experimental data, a p-x section of the In-In2 O3 system phase diagram at 1060 K was constructed. The standard enthalpies of reactions accompanying vaporization of the In and In2 O3 mixtures were evaluated using the second- and third-law methods. The standard enthalpy of formation of In2 O(g) was derived from the enthalpies of reactions obtained. The predominance of In2 O in the equilibrium vapor over heterogeneous mixtures (In(l) + In2 O3 (s)), along with its high partial pressure at relatively low temperatures, substantiate the In-In2 O3 system to be suitable for physical vapor deposition methods. The obtained results can be used for physical vapor deposition parameter adjustment and optimization. The standard enthalpy of formation of In2 O(g) obtained in an independent way in the present work is in good agreement with that from our previous In2 O3 (s) vaporization study.

Design and Experiments of a Galloping-Based Wind Energy Harvester Using Quadruple Halbach Arrays

This study aims to develop a device for harvesting electrical energy from low-speed natural wind. Four linear Halbach arrays are adopted to design a high-performance galloping harvester with the advantage of high durability and efficiency at low-frequency vibrations. The results of magnetic field analysis reveal that there are optimal sizes of the main and transit magnets of the Halbach arrays and coil to obtain the maximum magnetic flux density normal to the coil. The experimental and simulation results show that the electrical external load resistance significantly affects the vibration amplitude and the galloping onset velocity of the harvester. The results also reveal that the performance of the original design using the quadruple Halbach array was lower than that of the existing harvester because of the heavy magnet mass embedded in the tip prism. The modified design, reducing mass, improved the performance by four times compared to the original design.

The CERN-MEDICIS Isotope Separator Beamline.

CERN-MEDICIS is an off-line isotope separator facility for the extraction of radioisotopes from irradiated targets of interest to medical applications. The beamline, between the ion source and the collection chamber, consists of ion extraction and focusing elements, and a dipole magnet mass spectrometer recovered from the LISOL facility in Louvain-la-Neuve. The latter has been modified for compatibility with MEDICIS, including the installation of a window for injecting laser light into the ion source for resonance photo-ionization. Ion beam optics and magnetic field modeling using SIMION and OPERA respectively were performed for the design and characterization of the beamline. The individual components and their optimal configuration in terms of ion beam extraction, mass separation, and ion transport efficiency is described, along with details of the commissioning and initial performance assessment with stable ion beams.

CERN-MEDICIS: A Review Since Commissioning in 2017.

The CERN-MEDICIS (MEDical Isotopes Collected from ISolde) facility has delivered its first radioactive ion beam at CERN (Switzerland) in December 2017 to support the research and development in nuclear medicine using non-conventional radionuclides. Since then, fourteen institutes, including CERN, have joined the collaboration to drive the scientific program of this unique installation and evaluate the needs of the community to improve the research in imaging, diagnostics, radiation therapy and personalized medicine. The facility has been built as an extension of the ISOLDE (Isotope Separator On Line DEvice) facility at CERN. Handling of open radioisotope sources is made possible thanks to its Radiological Controlled Area and laboratory. Targets are being irradiated by the 1.4 GeV proton beam delivered by the CERN Proton Synchrotron Booster (PSB) on a station placed between the High Resolution Separator (HRS) ISOLDE target station and its beam dump. Irradiated target materials are also received from external institutes to undergo mass separation at CERN-MEDICIS. All targets are handled via a remote handling system and exploited on a dedicated isotope separator beamline. To allow for the release and collection of a specific radionuclide of medical interest, each target is heated to temperatures of up to 2,300°C. The created ions are extracted and accelerated to an energy up to 60 kV, and the beam steered through an off-line sector field magnet mass separator. This is followed by the extraction of the radionuclide of interest through mass separation and its subsequent implantation into a collection foil. In addition, the MELISSA (MEDICIS Laser Ion Source Setup At CERN) laser laboratory, in service since April 2019, helps to increase the separation efficiency and the selectivity. After collection, the implanted radionuclides are dispatched to the biomedical research centers, participating in the CERN-MEDICIS collaboration, for Research & Development in imaging or treatment. Since its commissioning, the CERN-MEDICIS facility has provided its partner institutes with non-conventional medical radionuclides such as Tb-149, Tb-152, Tb-155, Sm-153, Tm-165, Tm-167, Er-169, Yb-175, and Ac-225 with a high specific activity. This article provides a review of the achievements and milestones of CERN-MEDICIS since it has produced its first radioactive isotope in December 2017, with a special focus on its most recent operation in 2020.

A study of a new hybrid vibration energy harvester based on broadband-multimode

To improve the energy conversion efficiency and working frequency bandwidth of a single frequency piezoelectric vibration energy harvester, a new type of hybrid vibration energy harvester is developed which is combined with the mechanism of piezoelectric and electromagnetic energy conversion. The system comprises of a PZT cantilever beam, an elastic suspended magnetic mass, a magnet block attached to the end of the cantilever beam and a resonator. The addition of resonator can not only increase the mode, but also adjust the frequency of harvester flexibly. Nonlinear magnetic force of magnet block not only broadens the frequency band and improves the output performance of the system, but also changes the resonant frequency to make the harvester have better adjustable performance. On this basis, an improved electromechanical coupled analytical model of continuum is proposed which can be solved by the Runge-Kutta algorithm and the influence of different factors (the mass and spring stiffness of the resonator, as well as the electromechanical coupling coefficient, electromagnetic coupling coefficient, magnet mass and magnetic flux) on the output are analyzed. According to the prototype of the vibration energy harvester developed, an experimental system was built. The performance of the independent and hybrid energy harvesters is evaluated by experimental and analytical methods. The peak output voltage of the piezoelectric part was about 4 times that of the electromagnetic part. The peak output current of the electromagnetic part is about 30 times that of the piezoelectric part. The study results show that the proposed new hybrid vibration energy harvester can achieve a wider frequency range and multimodal vibration energy harvesting. In addition, the bandwidth and power of the harvester can be dynamically adjusted by changing the resonator or electromechanical coupling coefficient, and the bandwidth of the harvester can also be adjusted by changing the quality and characteristics of the magnet.

Vaporization thermodynamics of In2 O3 by Knudsen effusion mass spectrometry. The standard enthalpy of formation of In2 O(g).

In2 O3 is one of the most important semiconductor oxides in modern electronics. Vacuum deposition methods are often used for the preparation of In2 O3 -based nanomaterials. Thus, vaporization thermodynamics is of key importance for process control and optimization. Since the literature data on the vapor composition and partial pressure values for In2 O3 are contradictory, vaporization thermodynamics of In2 O3 needs to be clarified. Vaporization behavior of In2 O3 was studied using the Knudsen effusion technique in the temperature range 1400-1610 K. Quartz effusion cells were employed. A magnet mass spectrometer with an ordinary focus and a sector-type analyzer was used. Heating of samples and molecular beam ionization were performed by electron impact. The operating ionizing electron energy was 75 eV. A specially designed experiment allowed us to determine the individual mass spectrum of the In2 O molecule and, thus, to interpret the mass spectrum of the vapor registered during In2 O3 vaporization. The composition of the equilibrium vapor was quantified and the partial pressures of the vapor species were determined. On the basis of the experimental data, the standard enthalpies of some gaseous and heterogeneous reactions taking place during In2 O3 vaporization and the standard enthalpy of formation of In2 O(g) were calculated. The presence of In species in the vapor over In2 O3 was confirmed and the vapor composition was quantified. Thermodynamic characteristics of In2 O3 vaporization were obtained and a value of the standard enthalpy of formation of In2 O(g) was recommended. These data can be used for further thermodynamic calculations and for evaluating parameters for the synthesis and exploitation of In2 O3 -containing materials.

Cost Minimization of a Permanent Magnet Eddy Current Brake by Multiobjective Particle Swarm Optimization Based on Nonlinear Reluctance Network Modeling

Design optimization of a permanent magnet eddy current brake (PM-ECB) is performed by applying multiobjective particle swarm optimization (MO-PSO) for cost minimization. A previously designed and patented PM-ECB is used as a reference model in the study. A quasi-3-dimensional (3D) analytical modeling approach based on a reluctance network considering the actual structure of the reference PM-ECB is proposed and verified. The Gauss–Seidel method is used as a nonlinear solver for the reluctance network modeling, and the braking torque is calculated considering both the skin effect and the armature reaction. Multiobjective optimization is developed by applying a particle swarm algorithm, and a 3D Pareto front is provided to demonstrate all non-dominating design points. Three cost functions, viz. rated braking torque, magnet mass, and magnetic flux density of the yoke, are selected as the objectives for the optimization problem, and the optimum design point is addressed in detail. The optimized design is validated by 3D-FEA and experiments. The results indicate that a 40% reduction in the magnet volume could be brought about by the optimized PM-ECB design with practically the same braking torque. Further, a 40% cost reduction in the optimized brake could be achieved compared with the reference one.