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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
11

Analysis of Passive Attitude Stabilisation and Deorbiting of Satellites in Low Earth Orbit

Hawe, Benjamin January 2016 (has links)
Orbital debris poses a serious threat to ongoing operations in space.  Recognising this threat, the European Commission has funded the three-year Technology for Self Removal (TeSeR) project with the goal of developing a standard scalable Post Mission Disposal (PMD) module to remove satellites from orbit following the completion of their mission.  As the project coordinator and key member of the TeSeR Project, Airbus Defence and Space Germany will invest significant resources in achieving this goal over the course of the project. This thesis details the initial analysis of potential PMD module designs conducted by the author during an internship within the AOCS/GNC department of Airbus Defence and Space Friedrichshafen between 1 April 2016 and 31 August 2016.  Three main concepts, drag sails, drag balloons and Electrodynamic Tethers (EDTs), were evaluated during this time with an emphasis on determining the ability of each design to permit passive attitude stabilisation of the satellite during PMD.  Following the required modification of a pre-existing MATLAB/Simulink model, several key findings were made for each device concept.  It was found that no drag sail designs investigated permitted passive aerodynamic attitude stabilisation at orbit heights above 550 km.  When deorbiting from 800 km, however, the lack of the desired and stable attitude was not found to have a significant increase on the deorbit time or the area‑time product. Drag balloon designs were predicted to be comparatively unstable and less mass efficient for deorbiting purposes, with area‑time products up to approximately 50 per cent higher than the equivalent mass drag sail designs.  In spite of this, unstable drag balloons were found to provide shorter deorbit times than stable balloons due to the contribution of the satellite body and solar array to the total frontal area of the satellite.  This indicated that attitude stabilisation is not required for satellites equipped with drag balloon devices. Modelling of bare EDTs suggested that tethers with lengths of 1000 metres or more would not permit passive attitude stabilisation at an orbit height of 800 km.  Simulation of a 500 metre EDT, however, indicated that passive attitude stabilisation can be achieved with EDT devices and proved that EDTs can generate significantly higher drag forces than aerodynamic devices while possessing a significantly lower device mass.  Following the analysis of these results, a recommendation was made for future work to be aimed at improving the EDT model used in this investigation.
12

PROPULSIVE SMALL EXPENDABLE DEPLOYER SYSTEM (PROSEDS) MISSION AND TELEMETRY SYSTEM OVERVIEW

Kennedy, Paul 10 1900 (has links)
International Telemetering Conference Proceedings / October 23-26, 2000 / Town & Country Hotel and Conference Center, San Diego, California / The National Aeronautics and Space Administration’s (NASA) Marshall Space Flight Center (MSFC) in Huntsville, Alabama will launch the Propulsive Small Expendable Deployer System (ProSEDS) space experiment in late 2000. ProSEDS will demonstrate the use of an electrodynamic tether propulsion system and will utilize a conducting wire tether to generate limited spacecraft power. This paper will provide an overview of the ProSEDS mission and will discuss the design, and test of the spacecraft telemetry system. The ProSEDS telemetry subsystem employs a combination of Commercial Off-The-Shelf (COTS) hardware and launch vehicle telemetry system components to minimize costs as well as power consumption. Several measures were used to aid the conservation of spacecraft power resources. First, the transmitter was modified to limit input power consumption to less that 20 watts while providing approximately two watts Radio Frequency (RF) output power. Secondly, the ProSEDS on board Global Positioning System (GPS) receiver is being used to control input power to the transmitter in order to limit the telemetry operations to occasions when the spacecraft is in proximity to preprogrammed ground station locations.
13

Design and analysis of a novel low loss homopolar electrodynamic bearing

Lembke, Torbjörn A. January 2005 (has links)
<p>A novel homopolar electrodynamic bearing, together with a suitable permanent magnet drive, have been developed for high-speed applications where low losses and high reliability are essential and exclude the use of ball bearings, and yet where active magnetic bearings offer a too complex system solution. Considered applications are small turbomolecular vacuum pumps, and maintenance free flywheels for energy storage in remote telecom and satellite systems. Other upcoming areas where these bearings offer interesting technical and economic solutions are compressors for fuel cells and heat pumps, applications which normally suffer from short bearing lifetime.</p><p>Unlike active magnetic bearings, forces are produced in electrodynamic bearings without any control electronics, thanks to stabilizing eddy currents induced by permanent magnets. In the novel homopolar concept eddy current losses are reduced to a minimum using a homopolar design with ring magnets instead of multipole or Halbach arrays.</p><p>Currents and forces are simulated using steady state 3D-FEM analysis, which can take velocity into account using an implemented Minkowski transform. From these results an analytical model has been developed, and the results are compared. The results are converted into useful rotordynamic data that is easily understood by machine engineers.</p><p>The bearing has been experimentally tested in a rebuilt turbomolecular vacuum pump up to 90,000 rpm. Bearing forces have been accurately measured on a specially designed spring suspended scales, in which the bearing rotor is powered with the permanent magnet drive. Comparison of measured data with results from the 3D-FEM analysis shows excellent agreement.</p>
14

Eletrofiação de nanofibras poliméricas de poliacrilonitrila e polifluoreto de vinilideno, incorporadas com negro de fumo e ftalocianina de cobre, visando aplicações em dispositivos sensores. / Electrospinning of polyacrylonitrile and polyvynilidene fluoride nanofibers incorporate with carbon black end copper phthalocyanine to applications in sensors devices.

Gomes, Demetrius Saraiva 23 February 2018 (has links)
O presente trabalho tem como objetivo principal a eletrofiação de nanofibras poliméricas de poliacrilonitrila (PAN) e polifluoreto de vinilideno (PVDF), incorporadas com negro de fumo (NF) e ftalocianina de cobre (CuPc), visando aplicações em dispositivos sensores. Inicialmente foram preparadas soluções de PAN puro a 6 % em peso e PVDF puro a 20% em peso e foram misturadas a essas soluções partículas de negro de fumo e ftalocianina de cobre, obtendo soluções de PAN/NF, PVDF/NF, PAN/CuPc e PVDF/CuPc. Foi determinada a viscosidade absoluta das soluções. Realizou-se a eletrofiação para obtenção de nanofibras que foram caracterizadas segundo o diâmetro e morfologia, usando microscópio óptico e microscópio eletrônico de varredura. Para avaliar as interações polímero-polímero, polímero-partícula foram analisadas por espectroscopia FITR e Raman. Com as fibras de PAN/NF foi analisada a resistência e condutância elétrica das membranas usando um picoamperímetro digital, visando aplicação como filtro eletrostático. Foi construído canal na lâmina de silício usando um feixe de laser visando a deposição de fibras dentro do canal usando a técnica de focagem eletrodinâmica com tensão aplicada em máscaras de cobre. Foi usada a técnica da microbalança de cristal de quartzo para determinar a variação de massa adsorvida por membranas de PAN/CuPc e PVDF/CuPc por meio da medida da variação de frequência usando um frequencímetro digital, onde se observou que essas membranas são promissoras para atuar como sensores de vapor de amônia. / The main objective of this work is the incorporation of different particles in order to electrospun polymeric nanofibers of polyacrylonitrile (PAN) and polyvinylidene fluoride (PVDF), aiming at applications in sensor devices. Initially, solutions of PAN pure 6 wt% and PVDF pure 20 wt% were prepared and these solutions were mixed with carbon black (NF) particles and copper phthalocyanine (CuPc), obtaining solutions of PAN/NF, PVDF/NF, PAN/CuPc and PVDF/CuPc. The absolute viscosity of the solutions was determined. The electrospinning was performed to obtain nanofibers that were characterized according to the diameter and morphology, using optical microscope and scanning electron microscopy. To evaluate the polymer-polymer and polymer-particle interactions, FITR and Raman spectroscopy were performed. The resistance and conductance of the membranes electrospun from PAN/NF solution were analyzed using a digital picoammeter, and an increase in the resistance was measured. This result shows that the membrane is suitable to be applied as electrostatic filter. A channel was constructed on the silicon wafer using a laser beam for the deposition of fibers inside the channel using the electrodynamic focusing technique. The quartz crystal microbalance technique was used to determine the applicability of the membranes as sensor layer. The results of PAN/CuPc and PVDF/CuPc membranes suggests that these membranes are promising to act such as ammonia vapor sensors.
15

Mancal magnético híbrido do tipo repulsão com controle uniaxial com amortecimento fornecido por mancal eletrodinâmico. / Repulsion-type hybrid magnetic bearing with uniaxial control using electrodynamic bearing to provide radial damping.

Yamamoto, Rogério Issamu 10 April 2017 (has links)
Mancais magnéticos com controle uniaxial são mancais híbridos que combinam um mancal radial por imãs permanentes e um mancal axial eletromagnético com controle ativo. Estes mancais, a despeito das vantagens com relação a outras modalidades de mancais magnéticos, têm como principal deficiência a ausência de capacidade de amortecimento de vibrações radiais do rotor. De modo a eliminar tal deficiência, esta tese propõe um novo mancal magnético híbrido que conjuga um mancal com controle uniaxial a um mancal eletrodinâmico. Esta tese tem como objetivo investigar e demonstrar a eficácia desta solução. O objetivo final é apresentar um mancal magnético de elevado desempenho, de arquitetura simples e robusta, com possibilidades de aplicação em máquinas rotativas de alta velocidade. O mancal aqui proposto tem como base um mancal de controle uniaxial cuja arquitetura é definida de modo a apresentar elevada rigidez radial, elevada folga mecânica na porção rotativa, reduzida inércia no rotor, assim como simplicidade na construção e funcionamento. Para tanto, aqui se emprega mancais radiais com imãs disposto em camadas, operando em repulsão. Na direção axial, são usados atuadores eletromagnéticos compatíveis com a elevada rigidez gerada pelos mancais radiais. A estes mancais são associados mancais eletrodinâmicos homopolares de dois tipos, de fluxo magnético axial e de fluxo radial. Definido conceitualmente o novo mancal, protótipos foram desenvolvidos e foram realizados ensaios de validação do conceito do novo mancal, assim como de verificação do desempenho do protótipo. Com relação ao mancal proposto, foi verificada uma levitação estável do rotor e, obtida uma rigidez radial de 44 N/mm mediante uma folga de 2,5 mm. São valores que superam quaisquer resultados encontrados em literatura sobre mancais similares. Em seguida, demonstrou-se, ao menos até uma rotação de 35 Hz (2.100 rpm), a eficácia do mancal eletrodinâmicos de fluxo axial no amortecimento de movimentos assíncronos do rotor. / Single axis controlled magnetic bearings are hybrid bearings that combine a radial bearing based on permanent magnets and an electromagnetic bearing with active control. Such bearings, despite advantages with respect to other modalities of magnetic bearings, present an important problem of absence of vibration damping capability in the radial directions of the rotor. In order to solve this problem, this thesis proposes a new hybrid magnetic bearing that conjugates a single axis controlled bearing with an electrodynamic bearing. This thesis aims investigate and demonstrate the efficiency of the proposed solution. The final goal is to present a magnetic bearing with high capabilities, of simple architecture and robust, with possibilities for applications in high speed rotary machines. The presented bearing has, as the base, a single axis controlled bearing with an architecture suitable for achieving high radial stiffness, large gap in the rotary portion, low rotor inertia, as well as simplicity in its construction and operation. For this, the bearing employs radial bearings based on magnets arranged in layers operating in repulsion mode. In the axial direction, it uses electromagnetic actuators compatible with the high radial stiffness generated by radial bearings. These bearings are associated with electrodynamic homopolar bearings of two types: one of axial magnetic flux and other with radial flux. Once, the new bearing is defined conceptually, tests are conducted to validate the principle of the new bearing, as well, tests to evaluation of the efficiency of the prototype. With respect to the proposed bearing, a stable levitation of the rotor is obtained. Also, a radial stiffness of 44 N/mm is achieved with a gap of 2.5 mm. These values are higher than any results presented in literatures related to similar bearings. Finally, it is demonstrated that at rotations speeds of until 35 Hz (2,100 rpm), the electrodynamic of axial flux is efficient to attenuate asynchronous motions of the rotor.
16

Design and analysis of a novel low loss homopolar electrodynamic bearing

Lembke, Torbjörn A. January 2005 (has links)
A novel homopolar electrodynamic bearing, together with a suitable permanent magnet drive, have been developed for high-speed applications where low losses and high reliability are essential and exclude the use of ball bearings, and yet where active magnetic bearings offer a too complex system solution. Considered applications are small turbomolecular vacuum pumps, and maintenance free flywheels for energy storage in remote telecom and satellite systems. Other upcoming areas where these bearings offer interesting technical and economic solutions are compressors for fuel cells and heat pumps, applications which normally suffer from short bearing lifetime. Unlike active magnetic bearings, forces are produced in electrodynamic bearings without any control electronics, thanks to stabilizing eddy currents induced by permanent magnets. In the novel homopolar concept eddy current losses are reduced to a minimum using a homopolar design with ring magnets instead of multipole or Halbach arrays. Currents and forces are simulated using steady state 3D-FEM analysis, which can take velocity into account using an implemented Minkowski transform. From these results an analytical model has been developed, and the results are compared. The results are converted into useful rotordynamic data that is easily understood by machine engineers. The bearing has been experimentally tested in a rebuilt turbomolecular vacuum pump up to 90,000 rpm. Bearing forces have been accurately measured on a specially designed spring suspended scales, in which the bearing rotor is powered with the permanent magnet drive. Comparison of measured data with results from the 3D-FEM analysis shows excellent agreement. / QC 20101026
17

Magnetic Transduction for RF Micromechanical Filters

Forouzanfar, Sepehr 21 February 2012 (has links)
The use of electrostatic transduction has enabled high-Q miniaturized mechanical resonators made of non-piezoelectric material that vibrate at high and ultra high frequencies. However, this transduction technique suffers from large values of motional resistance associated with the technique, limiting its use for interfacing to standard 50 RF circuits. Piezoelectric transduction has advantages over the electrostatic method because of its comparable to 50 motional resistance. However, the technique requires use of thin film piezoelectric materials with the demonstrated Qs that are much lower than their corresponding non-piezoelectric resonators. This research proposes use of electrodynamic transduction, reports analytic and experimental studies on electrodynamic transduction for RF application, highlights the method’s advantages, and lists the contributions. The use of Lorentz-force transduction for RF micromechanical filters proposed in this work is pursued by experimentally evaluating the transduction technique implemented for microfabricated designs. By fabricating single and coupled microresonators in a few different fabrication technologies, including CMOS35, the performance of the Lorentz-force driven microresonators is studied. Using a laser vibrometer, the actual performance, including the displacement and velocity of the moving points of the microstructures’ surfaces, are measured. The mode shapes and resonance specifications of the microstructures in air and vacuum derived by laser vibrometer provide data for characterizing the employed Lorentz-force transduction technique. Furthermore, the results from the electrical measurements are compared to the micromechanical resonators’ frequency response obtained from the mechanical measurements by laser vibrometer. The significantly low values of motional resistance computed for the differently fabricated designs demonstrate the advantage of Lorentz-force transduction for RF filter applications. Should a device similar in size be driven electrostatically, the motional resistance would be multiple orders of magnitude higher. This research reports the experimental results obtained by examining a Lorentz- force transduction application for developing RF micromechanical filters. The results demonstrate the Lorentz-force transduction’s advantages over other transduction methods used for RF μ-mechanical filters. Compared to electrostatic transduction, the Lorentz-force method provides greater electromechanical coupling, multiple orders of magnitude lower motional resistance, the independence of the filter center frequency from the bias voltage, higher power handling, and no requirement for bias lines, which decreases the work in microfabrication. Unlike piezoelectric transduction, the electrodynamic technique requires no piezoelectric material. Use of non-piezoelectric materials provides more flexibility for resonator material in the IC-compatible fabrications. Power handling in electrodynamic transduction has fewer limitations than other transduction techniques because the higher power needed in electrostatic or piezoelectric methods requires a higher voltage, which is limited by the breakdown voltage. The higher power in Lorentz-force-based transduction demands a larger current. The larger current produces heat that is removable by applying an appropriate cooling technique.
18

STUDIES RELATED TO COULOMBIC FISSIONS OF CHARGED DROPLETS AND HYGROSCOPIC BEHAVIOR OF MIXED PARTICLES

Hunter, Harry Cook, III 01 January 2011 (has links)
This dissertation describes two independent studies related to charged aerosols. The first study examines the role of electrical conductivity on the amounts of charge and mass emitted during the break-up of charged droplets via Coulombic fission. The second study examines the hygroscopic behavior of mixed particles. The results from both studies are presented here in detail along with an in-depth discussion of pertinent literature and applications in modern technologies. Charged droplets break-up via a process termed Coulombic fission when their charge density reaches a certain level during which they emit a portion of their charge and mass in the form of progeny microdroplets. Although Rayleigh theory can be used to predict the charge level at which break-ups occur, no equivocal theory exists to predict the amounts of charge or mass emitted or the characteristics of the progenies. Previous investigations have indicated that the electrical conductivity of a charged droplet may determine how much charge and mass are emitted during its break-up via Coulombic fission. To further examine this supposition, charged droplets having known electrical conductivities were observed through multiple break-ups while individually levitated in an electrodynamic balance. The amounts of charge and mass emitted during break-ups were determined using a light scattering technique and changes in the DC null point levitation potentials of the charged droplets. Here, electrical conductivity was found to increase and decrease the amounts of charge and mass emitted, respectively, while having no effect on the charge level at which break-ups occurred. The findings of this investigation have significant bearing in nanoparticle generation and electrospray applications. The hygroscopic behavior of atmospherically relevant inorganic salts is essential to the chemical and radiative processes that occur in Earth’s atmosphere. Furthermore, studies have shown that an immense variety of chemical species exist in the atmosphere which inherently mix to form complex heterogeneous particles with differing morphologies. However, how such materials and particle morphologies affect the hygroscopic behavior of atmospherically relevant inorganic salts remains mostly unknown. Therefore, the effects of water insoluble materials, such as black carbon, on the hygroscopic behavior of inorganic salts were examined. Here, water insoluble solids were found to increase the crystallization relative humidities of atmospherically relevant inorganic salts when internally mixed. Water insoluble liquids however, were found to have no effect on the hygroscopic behavior of atmospherically relevant inorganic salts. The findings of this investigation have significant bearing in atmospheric modeling.
19

Magnetic Transduction for RF Micromechanical Filters

Forouzanfar, Sepehr 21 February 2012 (has links)
The use of electrostatic transduction has enabled high-Q miniaturized mechanical resonators made of non-piezoelectric material that vibrate at high and ultra high frequencies. However, this transduction technique suffers from large values of motional resistance associated with the technique, limiting its use for interfacing to standard 50 RF circuits. Piezoelectric transduction has advantages over the electrostatic method because of its comparable to 50 motional resistance. However, the technique requires use of thin film piezoelectric materials with the demonstrated Qs that are much lower than their corresponding non-piezoelectric resonators. This research proposes use of electrodynamic transduction, reports analytic and experimental studies on electrodynamic transduction for RF application, highlights the method’s advantages, and lists the contributions. The use of Lorentz-force transduction for RF micromechanical filters proposed in this work is pursued by experimentally evaluating the transduction technique implemented for microfabricated designs. By fabricating single and coupled microresonators in a few different fabrication technologies, including CMOS35, the performance of the Lorentz-force driven microresonators is studied. Using a laser vibrometer, the actual performance, including the displacement and velocity of the moving points of the microstructures’ surfaces, are measured. The mode shapes and resonance specifications of the microstructures in air and vacuum derived by laser vibrometer provide data for characterizing the employed Lorentz-force transduction technique. Furthermore, the results from the electrical measurements are compared to the micromechanical resonators’ frequency response obtained from the mechanical measurements by laser vibrometer. The significantly low values of motional resistance computed for the differently fabricated designs demonstrate the advantage of Lorentz-force transduction for RF filter applications. Should a device similar in size be driven electrostatically, the motional resistance would be multiple orders of magnitude higher. This research reports the experimental results obtained by examining a Lorentz- force transduction application for developing RF micromechanical filters. The results demonstrate the Lorentz-force transduction’s advantages over other transduction methods used for RF μ-mechanical filters. Compared to electrostatic transduction, the Lorentz-force method provides greater electromechanical coupling, multiple orders of magnitude lower motional resistance, the independence of the filter center frequency from the bias voltage, higher power handling, and no requirement for bias lines, which decreases the work in microfabrication. Unlike piezoelectric transduction, the electrodynamic technique requires no piezoelectric material. Use of non-piezoelectric materials provides more flexibility for resonator material in the IC-compatible fabrications. Power handling in electrodynamic transduction has fewer limitations than other transduction techniques because the higher power needed in electrostatic or piezoelectric methods requires a higher voltage, which is limited by the breakdown voltage. The higher power in Lorentz-force-based transduction demands a larger current. The larger current produces heat that is removable by applying an appropriate cooling technique.
20

Mancal magnético híbrido do tipo repulsão com controle uniaxial com amortecimento fornecido por mancal eletrodinâmico. / Repulsion-type hybrid magnetic bearing with uniaxial control using electrodynamic bearing to provide radial damping.

Rogério Issamu Yamamoto 10 April 2017 (has links)
Mancais magnéticos com controle uniaxial são mancais híbridos que combinam um mancal radial por imãs permanentes e um mancal axial eletromagnético com controle ativo. Estes mancais, a despeito das vantagens com relação a outras modalidades de mancais magnéticos, têm como principal deficiência a ausência de capacidade de amortecimento de vibrações radiais do rotor. De modo a eliminar tal deficiência, esta tese propõe um novo mancal magnético híbrido que conjuga um mancal com controle uniaxial a um mancal eletrodinâmico. Esta tese tem como objetivo investigar e demonstrar a eficácia desta solução. O objetivo final é apresentar um mancal magnético de elevado desempenho, de arquitetura simples e robusta, com possibilidades de aplicação em máquinas rotativas de alta velocidade. O mancal aqui proposto tem como base um mancal de controle uniaxial cuja arquitetura é definida de modo a apresentar elevada rigidez radial, elevada folga mecânica na porção rotativa, reduzida inércia no rotor, assim como simplicidade na construção e funcionamento. Para tanto, aqui se emprega mancais radiais com imãs disposto em camadas, operando em repulsão. Na direção axial, são usados atuadores eletromagnéticos compatíveis com a elevada rigidez gerada pelos mancais radiais. A estes mancais são associados mancais eletrodinâmicos homopolares de dois tipos, de fluxo magnético axial e de fluxo radial. Definido conceitualmente o novo mancal, protótipos foram desenvolvidos e foram realizados ensaios de validação do conceito do novo mancal, assim como de verificação do desempenho do protótipo. Com relação ao mancal proposto, foi verificada uma levitação estável do rotor e, obtida uma rigidez radial de 44 N/mm mediante uma folga de 2,5 mm. São valores que superam quaisquer resultados encontrados em literatura sobre mancais similares. Em seguida, demonstrou-se, ao menos até uma rotação de 35 Hz (2.100 rpm), a eficácia do mancal eletrodinâmicos de fluxo axial no amortecimento de movimentos assíncronos do rotor. / Single axis controlled magnetic bearings are hybrid bearings that combine a radial bearing based on permanent magnets and an electromagnetic bearing with active control. Such bearings, despite advantages with respect to other modalities of magnetic bearings, present an important problem of absence of vibration damping capability in the radial directions of the rotor. In order to solve this problem, this thesis proposes a new hybrid magnetic bearing that conjugates a single axis controlled bearing with an electrodynamic bearing. This thesis aims investigate and demonstrate the efficiency of the proposed solution. The final goal is to present a magnetic bearing with high capabilities, of simple architecture and robust, with possibilities for applications in high speed rotary machines. The presented bearing has, as the base, a single axis controlled bearing with an architecture suitable for achieving high radial stiffness, large gap in the rotary portion, low rotor inertia, as well as simplicity in its construction and operation. For this, the bearing employs radial bearings based on magnets arranged in layers operating in repulsion mode. In the axial direction, it uses electromagnetic actuators compatible with the high radial stiffness generated by radial bearings. These bearings are associated with electrodynamic homopolar bearings of two types: one of axial magnetic flux and other with radial flux. Once, the new bearing is defined conceptually, tests are conducted to validate the principle of the new bearing, as well, tests to evaluation of the efficiency of the prototype. With respect to the proposed bearing, a stable levitation of the rotor is obtained. Also, a radial stiffness of 44 N/mm is achieved with a gap of 2.5 mm. These values are higher than any results presented in literatures related to similar bearings. Finally, it is demonstrated that at rotations speeds of until 35 Hz (2,100 rpm), the electrodynamic of axial flux is efficient to attenuate asynchronous motions of the rotor.

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