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Precise positioning using electrostatic glass motor with diamagnetically suspended rotor
Abstract
This paper presents a novel application of diamagnetic levitation. In combination with electrostatic glass actuators, levitation and synchronous propulsion of a suspended rotor become possible. The proposed compact system finds promising applications in the field of positioning of optical devices. A potent yet cost-effective diamagnetic material for the rotor along with an optimized permanent magnet pattern on the stator will be presented, allowing frictionless suspension of objects weighting several grams. The suggested rotary device allows very precise and smooth synchronous rotation over a wide speed range (1 μm/s-10 m/s). Among the focused applications are precise scanning and the readout of holographic crystals for data storage.
... Virtually all approaches make use of a permanent magnet floater. Though in some cases the possibility of using a ferromagnetic sphere has also been considered [69]. ...
... More relevant work in the macro scale has been done by Bleuler et al. [29], [69] who make use of a diamagnetic graphite plate levitated above a flat and checkerboard planer Halbach array configuration for motor bearing applications (Figure 2-11c). ...
... In comparison to work on the stabilizing machinery, only a few studies have given rigorous treatment to the electrical machine used with diamagnetic bearings. For instance, Bleuler et al. [69] have looked at the use of an electrostatic machine whereby a glass coating is used as charge carrier (Figure 2-12a). The charged glass surface is driven by a three phase electrode assembly. ...
Recent trends in energy production have led to a renewed interest in improving grid level energy storage solutions. Flywheel energy storage is an attractive option for grid level storage, however, it suffers from high parasitic loss. This study investigates the extent to which passive diamagnetic bearings, a form of electromagnetic bearing, can help reduce this parasitic loss. Such bearings require three main components: a weight compensation mechanism (lifter-floater), a stabilizing mechanism and an electrical machine. This study makes use of a new radial modification of an existing linear multi-plattered diamagnetic bearing. Here a prototype is built and analytical expressions derived for each of the three main components. These expressions provide a method of estimating displacements, fields, forces, energy and stiffness in the radial diamagnetic bearing. The built prototype solution is found to lift a 30 [g] mass using six diamagnetic platters for stabilization (between ring magnets) with a disc lifter and spherical floater for weight compensation. The relationship between mass and number of platters was found to be linear, suggesting that, up to a point, increases in mass are likely possible and indicating that significant potential exists for these bearings where high stiffness is not needed – for instance in flywheel energy storage. The study examines methods of reducing bearing (parasitic) losses and demonstrates that losses occur in three main forms during idling: air-friction losses, electrical machine losses, stabilizing machine losses. Low speed (158 [rpm]) air-friction losses are found to be the dominant loss at 0.1 [W/m3]. The focus of this study, however, is on loss contributions resulting from the bearing’s electrical machine and stabilizing machine. Stabilizing machine losses are found to be very low at: 1 × 10−6 [W/m3] – this leaves electrical machine losses as the dominant loss. Such electrical machine losses are analysed and divided into eddy current loss and hysteresis loss. Two components of hysteresis loss are remanent field related cogging loss and remagetization loss. Eddy current losses in silicon steel laminations in an electrical machine are quite high, especially at high speeds, with losses in the order of 1 × 105 [W/m3]. Noting the further high cost of producing single unit quantities of custom lamination-based electrical machine prototypes, this high loss prompts a look at potentially lower cost ferrite materials for building these machines. A commercial sample of soft magnetite ferrite is shown to have equivalent eddy current losses of roughly 1 × 10−13 [W/m3]. The study notes that micro-structured magnetite has significant hysteresis loss. Such loss is in the order of 1 × 10−3 [W/m3] when referring to both remanence related cogging and remagnetization. This study, thus, extends its examination of loss to nano-structured magnetite. Magnetite nano-particles have shown superparamagnetic (no hysteresis) behaviour that promises the elimination of hysteresis losses. A co-precipitation route to the synthesis of these nano-particles is examined. A detailed examination involving a series of 31 experiments is shown to demonstrate only two pathways providing close-to-superparamagnetic behaviour. After characterization by Scanning Electron Microscope (SEM), X-Ray Diffractometer (XRD), Superconducting Quantum Interference Device (SQUID) and crude colorimetry, the lowest coercivity and remanence found in any given sample falls at −0.17 [Oe] (below error) and 0.00165 [emu/g] respectively. These critical points can be used to estimate hysteresis related power loss, however, to produce bulk ferrite a method of sintering or bonding synthesized powder is needed. A microwave sintering solution promises to preserve nano-structure when taking synthesized powders to bulk material. A set of proof-of-concept experiments provide the ground work for proposing a future microwave sintering approach to such bulk material production. The study uses critical points measured by way of SEM, XRD, SQUID characterization (e.g. remanence and coercivity) to implement a modified Jiles-Atherton model for hysteresis curve fitting. The critical points and curve fitting model allow estimation of power loss resulting from remanent related cogging and remagnetization effects in nano-structured magnetite. Such nano-structured magnetite is shown to exhibit hysteresis losses in the order of 1 × 10−4 [W/m3] from remagnetization and 1 × 10−7[W/m3] from remanence related cogging drag. These losses are lower than those of micro-structured samples, suggesting that nano-structured materials have a significant positive effect in reducing electrical machine losses for the proposed radial multi-plattered diamagnetic bearing solution. The lower parasitic loss in these bearings suggests excellent compatibility with flywheel energy storage applications.
... Liu et al. [16] invented a diamagnetically levitated variable-capacitance micromotor, but the maximum speed was limited to less than 10 r/min, which consequently limited possible applications. Moser and Bleuler [18] proposed a concept to rotate a diamagnetically suspended rotor by an electrostatic glass motor. The idea was interesting, but it was not realized. ...
... Compared with the above-mentioned works and the proposed of [18], this paper reports the first realization of a diamagnetically levitated rotor driven by electrostatic field. The mechanical design of the electrostatic glass motor is quite different (cylindrical in [18] and disk shaped here). ...
... Compared with the above-mentioned works and the proposed of [18], this paper reports the first realization of a diamagnetically levitated rotor driven by electrostatic field. The mechanical design of the electrostatic glass motor is quite different (cylindrical in [18] and disk shaped here). The rotor disc, comprised of pyrolytic graphite and glass, is stably levitated by an array of NdFeB magnets and rotated by the electrostatic forces with the maximum speed of 140 r/min. ...
In this paper, a novel configuration of frictionless diamagnetic levitation combined with electrostatic glass motor is presented. A 12.5mm diameter disc shaped rotor comprised of pyrolytic graphite and glass is fabricated. The rotor disc is levitated stably by the diamagnetic field in five degrees of freedom and driven by the rotating electrostatic field. It is the first time that the combination of both functions is realized. The main advantages of the proposed novel system are non-contact levitation, low energy consumption, and simplicity, which may find promising applications in the fields of spacecraft attitude control (micro gyroscope) or UHV (ultrahigh vacuum environment) technology (optical trap etc.).
... Statically and dynamically stable diamagnetic levitation can easily be achieved at room temperature without the need for an energy supply. These features make diamagnetic levitation appealing for modern micromechanical systems, such as microscale separation or manipulation [11] and micro rotor bearing systems [12][13][14][15][16][17][18][19]. Additionally, the inherent characterization of low stiffness in diamagnetic levitation systems permits their potential application in high-sensitivity sensors [20][21][22][23] and ultralow-frequency energy harvesters [24,25]. ...
... Bleuler et al. [16] demonstrated the rotation of a diamagnetically suspended rotor by an electrostatic glass motor. Su et al. [17] reported a micromachined rotor in which highly oriented pyrolytic graphite was diamagnetically levitated by magnetics and rotated by gas flow. Our previous work [18,19] realized a rotating diamagnetically levitating rotor system driven by an electrostatic field with a maximum rotation speed of 300 r/min. ...
As an innovative, low-power consuming, and low-stiffness suspension approach, the diamagnetic levitation technique has attracted considerable interest because of its potential applicability in miniaturized mechanical systems. The foundation of a diamagnetic levitation system is mathematical modeling, which is essential for operating performance optimization and stability prediction. However, few studies on systematic mathematical modeling have been reported. In this study, a systematic mathematical model for a disc-shaped diamagnetically levitated rotor on a permanent magnet array is proposed. Based on the proposed model, the magnetic field distribution characteristics, diamagnetic levitation force characteristics (i.e., levitation height and stiffness), and optimized theoretical conditions for realizing stable levitation are determined. Experiments are conducted to verify the feasibility of the proposed mathematical model. Theoretical predictions and experimental results indicate that increasing the levitation height enlarges the stable region. Moreover, with a further increase in the rotor radius, the stable regions of the rotor gradually diminish and even vanish. Thus, when the levitation height is fixed, a moderate rotor radius permits stable levitation. This study proposes a mathematical modeling method for a diamagnetic levitation system that has potential applications in miniaturized mechanical systems.
... Meanwhile, without the need of energy supply, both statically and dynamically stable diamagnetic levitation can be easily achieved at room temperature. These features make diamagnetic levitation quite appealing for modern micro mechanical system such as microscale separation or manipulation [12] and micro rotor bearing system [13][14][15][16][17][18][19][20]. Additionally, the inherent characterization of low stiffness in diamagnetic levitation system permits its potential application in high-sensitivity sensor [21][22][23][24] and ultra-low frequency energy harvesters [25][26]. ...
... For instance, Liu et al. [15][16] invented a diamagnetically levitated variable-capacitance micro motor and successfully realized the continuous rotation operation of motor. Bleuler et al. [17] demonstrated the rotation of a diamagnetically Corresponding author. Tel.: +86 25 84892905. ...
Featured as an innovative powerless and low stiffness suspension approach, diamagnetic levitation technique has trigged intensive interest because of its potential applicability in miniaturized mechanical system. The foundation of diamagnetic levitation system lies in mathematical modeling, which is essential for operating performance optimization and stability predication. However, to date, few literatures concerning the systematic mathematical modeling has been reported. Herein, in this work, a systematic mathematic model for disc-shaped diamagnetically levitated rotor on permanent magnets array is proposed. Based on the proposed model, the magnetic field distribution characteristics, diamagnetic levitation force characteristics (i.e. levitation height and stiffness) expressions and the optimized theorical conditions for realizing stable levitation are achieved. Experiments are also performed to dig out the relationship between levitation height and levitation force. Moreover, the operating stability of rotor under different conditions is evaluated. The experimental results are well in accordance with the theorical predications, confirming the feasibility of this mathematic model.
... Objects that mainly reveal diamagnetic behavior are called diamagnet, which have a magnetic susceptibility χ m that is less than 0. This means that diamagnet will experience a repelling force which is termed diamagnetic force in magnetic fields H. The diamagnetic force can be written as follows [17]: ...
... Further, the angular acceleration of the magnet rotor was calculated based on the fitted speed curve, as is shown in Fig.12.The angular acceleration gradually decreases as the speed decreases, and the relationship between the angular acceleration and the rotation speed is further illustrated in Fig. 13. The rotation speed and the angular acceleration of the magnet rotor are linearly related to each other, which can be expressed as 0.615 = (17) Together with equations (11) and (17), we can obtain the damping torque T T=-I =-0.06 (18) where I = 0.0968 N/m 2 . ...
... Objects that mainly reveal diamagnetic behavior are called diamagnet, which have a magnetic susceptibility χ m that is less than 0. This means that diamagnet will experience a repelling force which is termed diamagnetic force in magnetic fields H. The diamagnetic force can be written as follows [17]: ...
... Further, the angular acceleration of the magnet rotor was calculated based on the fitted speed curve, as is shown in Fig.12.The angular acceleration gradually decreases as the speed decreases, and the relationship between the angular acceleration and the rotation speed is further illustrated in Fig. 13. The rotation speed and the angular acceleration of the magnet rotor are linearly related to each other, which can be expressed as 0.615 = (17) Together with equations (11) and (17), we can obtain the damping torque T T=-I =-0.06 (18) where I = 0.0968 N/m 2 . ...
This paper presents a gas flowmeter by using the rotation of a diamagnetically levitated magnet rotor to measure the gas flowrate. Two highly oriented pyrolytic graphite (HOPG) sheets are introduced to build a diamagnetic levitation structure. By adjusting the distance between the two HOPG sheets, the diamagnetic levitation structure can be tuned to obtain a single potential well which ensures the stable levitation and rotation of the magnet rotor and improves the stability of the sensor. The maximum distance for achieving a single potential well is measured to be 3.1mm. The feasibility of the proposed flowmeter was verified by experiment. The performance of the sensor was tested, and the maximum relative error is 5.56%.
... Moser and Bleuler [101] presented a rotative positioning device based on diamagnetically stabilized levitation in combination with the electrostatic glass actuators. They demonstrated slow and synchronous rotation in the sub-arc second range. ...
As a typical contact-free manipulation technique that removes friction and contamination risk, levitation has gradually become a preferred candidate for various applications. Magnetic levitation using diamagnetism, beyond Earnshaw’s theorem, is a kind of passive stable levitation that can be achieved at normal temperatures with no energy input. Appealingly, most seemingly nonmagnetic materials can be levitated in a magnetic field and can stabilize free levitation of magnetic materials. This review focuses on the fundamental principles of magnetic levitation using diamagnetism, with emphasis on its burgeoning applications. The theoretical basis associated with the magnetic levitation using diamagnetism is discussed by elucidating the characteristics of diamagnetic materials, and the key levitation mechanisms are clarified. Afterwards, state-of-the-art applications in various aspects, including sensing and measurement, actuating and micromanipulation, energy harvesting and magnetic gravity compensation, are summarized and compared. Finally, the review concludes with a brief outlook on future perspectives.
... The above references focus on the diamagnetic bearing properties and the rotor is powered by the gas. For the 'active' rotation realisation, Moser and Bleuler proposed a concept to combine the diamagnetic levitation and electrostatic glass motor together to fulfil the rotation function [17]. Liu et al. levitated a gear-shaped pyrolytic graphite rotor and adopted a three-phase axial variable-capacitance motor to drive the rotor. ...
In this work, we introduce a newly developed passive and frictionless diamagnetic contactless suspension rotor with electrostatic glass motor. A 20 mm diameter disc‐shaped rotor comprised of pyrolytic graphite with glass is fabricated. The rotor is diamagnetically and passively levitated by an array of Nd–Fe–B magnets at room temperature without any energy supply. To realise the rotating function, a 700 V high voltage electrostatic glass motor is designed and arranged in the levitation air gap between the rotor and the magnets. To install the stator in this narrow air gap, we fabricated the stator using a flexible printed circuit with 100 μm thickness. The newly developed system is more compact, stable and of high performance. The maximum speed has been improved doubly to 300 rpm in atmosphere. We intend to draw attention to this uncommon levitation and to show that it could be used for micro‐mechatronic system.
... [6][7][8][9][10] The diamagnetic levitation of graphite was also extensively studied and various applications have been proposed. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] A typical experimental setup used for the diamagnetic levitation is a checkerboard arrangement of NdFeB magnet as shown in Fig. 1, where the alternating pattern of magnetic poles generates a magnetic field gradient to support a diamagnetic object in a free space. 13,[18][19][20]24,25 A recent experiment performed a detailed measurement of the levitation height of a graphite piece in this geometry. ...
We theoretically study the diamagnetic levitation and the thermal-driven motion of graphite. Using the quantum-mechanically derived magnetic susceptibility, we compute the equilibrium position of levitating graphite over a periodic arrangement of magnets, and investigate the dependence of the levitation height on the susceptibility and the geometry. We find that the levitation height is maximized at a certain period of the magnets, and the maximum height is then linearly proportional to the susceptibility of the levitating object. We compare the ordinary AB-stacked graphite and a randomly stacked graphite, and show that the latter exhibits a large levitation length particularly in low temperatures, because of its diamagnetism inversely proportional to the temperature. Finally, we demonstrate that the temperature gradient moves the levitating object towards the high temperature side, and estimate the generated force as a function of susceptibility.
... Thus, one direction control is required to be controlled actively to levitate the axis in all directions [4]. There are different ways to control the axis actively, electro dynamically [5,6] (implementing the short-circuited coils), diamagnetically controlled and electrostatically controlled [7]. Cost effectiveness, high stiffness, ability to be used in the miniature designs are some factors that make passive magnetic bearings to become more popular in the industries. ...
... Clara and Antlinge 13,14) investigated a viscositydensity sensor based on diamagnetic levitation. Moser and Bleuler 15) introduced a novel frictionless motor-bearing combination featuring a passive five-degrees-of-freedom suspension system. Chen and Zhou 16,17) designed a diamagnetic bearing for microsystems and investigated the eddy-current effect on the performance of the diamagnetic bearing. ...
We investigated a micro-diamagnetic levitation rotor system (MDLRS) in which the rotor freely levitates above the magnets. To explore the characteristics of the rotor, we carried out numerical simulations of and experiments on the MDLRS. Numerical simulation results show that the steady-state levitation height of the rotor is 130 µm, which is basically consistent with the experimental result (132 µm). Under the actuation of a regulated nitrogen flow, experimental results from the rotation speed of the rotor show that the maximum rate is 500 rpm at a flow rate of 28.16 sccm. Furthermore, an empirical model of the relationship between the flow rate and the rotation speed is proposed.
... Li et al. [24] efficiently applied a magnetic levitated suspension system to an atomic force microscope for the calibration of the lateral force. A diamagnetic rotor suspension was developed in [25] and in [26] for optical devices positioning purposes. ...
... Earnshaws' theorem [1] discards the possibility of passive static magnetic levitation, but by taking advantage o f the diamagnetic effect, passive magnetic systems can be stabilized. A diamagnetic material for levitation purposes was already proposed [2], the pyrolytic graphite, and full suspension and asynchronous propulsion of small disc shaped rotors was presented in [3]. Also, one-dimensional magnet arrangements have been investigated and optimized by finite element simulation [4]. ...
This paper presents new results in the field of passive diamagnetic levitation of macroscopic objects. Two dimensional permanent magnet arrays have been analyzed and optimized in order to obtain high thrust force and stiffness for fully passive magnetic levitation at room temperature in all 6 degrees of freedom. Experimental results with strongly diamagnetic materials like pyrolytic graphite indicate that diamagnetic levitation can be an interesting alternative to active magnetic bearings. Possible applications are pointed out and functional experimental prototypes are presented.
... Although diamagnetic forces are very weak, it is indeed possible find diamagnetic materials light enough so that the diamagnetic effect may overcome gravity. We obtained such a stable equilibrium for a piece of graphite over an optimized 2D arrangement of permanent magnets [4, 5].Figure 1: Diamagnetic material levitated over an array of permanent magnetsFig. 1 shows a 7mm diameter pyrolitic graphite disc floating motionless at room temperature, at about 250µm above an array of NdFeB magnets. Small loads can be added to the levitated disc and, if more payload is needed, some weight compensating magnet can be added [5]. ...
We present two types of passive magnetic bearings with a high potential for flywheel applications. Both types are for full contact-free support in all six rigid-body degrees of freedom, both are fully vacuum compatible. Eddy-current losses occur only under dynamic load. Therefore, they allow an essentially loss-less support of a flywheel. The flywheel is supported with low radial stiffness; it is therefore left free to rotate about its principal axis. The magnitude of residual losses can thus be made arbitrarily low by balancing the rotor. The first type proposed is based on the diamagnetic effect. In order to support macroscopic charges, a permanent magnetic bearing in attractive mode is used, e.g. in axial (thrust) direction. In this case, the radial bearing is passively stable. The unstable equilibrium of the attractive-type thrust bearing is stabilized by the diamagnetic effect, in our case a graphite wafer supported above an appropriate array of NdFeB magnets on the stator. This rotor is levitated at standstill as well. A prototype of such a bearing with a rotor mass of about 80g has been built. Larger rotors could easily be supported by this principle. The second prototype does not rely on the diamagnetic effect. It is based on a planar Halbach array and an electrodynamic system with short-circuited coils for the thrust direction, the radial directions being stabilized by passive permanent magnet bearings. This rotor (with vertical rotor, 1.3 kg, of a length of about 30 cm for our test system) rests on a pivot bearing at standstill. This test-system includes a motor-generator of negligible negative radial stiffness, an important requirement due to the relatively low stiffness of the passive bearing system. It levitates above a speed of about 4800 rpm. It also allows the rotor to rotate about the principle axis, so here too the basic limitation on rotational speed is given by the resistance of the rotor to centrifugal stress. Another electrodynamic system with horizontal axis has been designed as well. Both diamagnetic and electrodynamic vertical axis prototypes perform well and seem well suited at least for stationary flywheel systems for various applications as they could run with only very small residual losses. Mobile applications would need higher radial stiffness.
... The major technological challenges encountered are the difficulties of fabricating micro PMs with strong magnetic properties and fine-pitch poles that could be integrated into more complex microfabrication process flow. However, various technologies in this respect have been evolving quickly in recent years [9][10][11] and it is reasonable to anticipate great advance in fabrication capability that could unleash the value of diamagnetic levitation for microsystem applications [12][13][14][15][16][17]. ...
Diamagnetic materials could be utilized with permanent magnets to offer a simple passive solution to micro bearings as a result of scale reduction. In this paper, we investigate the eddy-current effect on the performance of diamagnetic bearings. Due to the good electrical conductivity of some of diamagnetic materials or the intentionally introduced eddy-current damper for vibration control, eddy current could be induced in the diamagnetic bearing with viscous forces opposing the relative motion between the rotor and the stator. Such damping mechanism is analyzed with a thin-sheet model and the image method and compared with that due to aerodynamic effects so as to give an idea of its significance at the microscale. Following the calculation, extracted damping coefficients are employed in a rotor dynamic model to investigate their influence on dynamic behaviors of the bearing. Results indicated that damping provided by eddy-current effects has pros and cons for the performance of the diamagnetic bearing which involves rotational motion. Finally, rundown characteristics of the bearing are evaluated, and the implication for operation scheme is discussed.
... Even though Earnshaw's theorem [3] states that perfect (i.e., in all degrees of freedom) passive magnetic levitation is impossible and that therefore at least one degree of freedom has to be mechanically [4], actively [5] (by means of an active magnetic bearing), electrodynamically [6], [7] (by means of conductive surfaces or short circuited coils), electrostatically or diamagnetically [8] controlled, these types of bearings are quite often sufficient for many applications [9]- [11]. ...
Passive magnetic bearings are an attractive alternative to conventional ball bearings in applications where wear and tear must be minimal and cost or construction restrictions ban the use of active magnetic bearings. They also find applications as miniaturized high-speed bearings where no other low-friction solutions are available. We show that, for a given cylindrical construction volume, an optimized repulsive bearing design with respect to a maximal radial stiffness can be found. This optimal configuration is independent of the aspect ratio of the bearing, but is determined by the width of the air gap between rotor and stator. Our method can determine the optimal configuration for any bearing geometry. We develop a design for a miniaturized high-speed bearing as an example.
The rotation of circular and annular pyrolytic graphite (PG) disks levitating above circular magnet arrays can be used for a novel method of magnetic manipulation, whereas the condition of stable levitation has not been figured out yet. In this article, a method to analyze the diamagnetic forces sustained by levitated PG is proposed to investigate the mechanism of stable levitation. When using this method, the whole PG disk is divided into multiple regions according to the distribution of magnetic field in order to determine the resultant diamagnetic force. With the help of the method, the exclusive levitation height of PG disk was determined, and the relationship between the relative size of circular and annular disks to magnet and its ability of stable levitation was clarified. The proposed method is the first one able to investigate the position stability of levitated PG and provides insights into local forces without heavy workload of finete element method (FEM) calculation. The analysis results are verified by the simulation of distribution of potential energy and can be a new way of magnetic manipulation.
In this paper, a miniaturized energy harvester is presented to scavenge gas flow energy. A magnet rotor with three teeth evenly distributed on the edge was introduced into the energy harvester, and it is frictionlessly levitated between two highly oriented pyrolytic graphite (HOPG) sheets. The energy harvester is designed to operate at a single stable equilibrium, so as to improve the stability of the rotor. The optimal incident angle of the gas flow was determined to be 83°. On the basis of the optimal angle, two different configurations of the energy harvester were proposed. Configuration A includes one nozzle, while Configuration B has two centrosymmetric nozzles. The maximum flow rate that enables Configurations A to work stably is limited, which can be increased by thickening the magnet rotor. The maximum voltage of configuration A was 0.28 V at a flow rate of 1500 sccm for the 4.5 mm thick rotor. Configuration B can run stably at any flow rate bigger than 250 sccm and the induced voltage increases with the driving flow rate. At the flow rate of 3000 sccm, the energy harvester of Configuration B can generate a maximum voltage of 3 V and light up tens of light-emitting-diodes (LEDs).
We theoretically study the diamagnetic levitation and the thermal driven motion of graphite. Using the quantum mechanically derived magnetic susceptibility, we compute the equilibrium position of levitating graphite over a periodic arrangement of magnets, and investigate the dependence of the levitation height on the susceptibility and the geometry. We find that the levitation height is maximized at a certain period of the magnets, and the maximum height is then linearly proportional to the susceptibility of the levitating object. We compare the ordinary AB-stacked graphite and a randomly stacked graphite, and show that the latter exhibits a large levitation length particularly in low temperatures, because its diamagnetism is inversely proportional to the temperature. Finally, we demonstrate that the temperature gradient moves the levitating object towards the high-temperature side, and estimate the generated force as a function of susceptibility.
Througout history, the suspension or levitation phenomenon have always attracted the humanity’s imaginary to the astonishing possibility of reproduce the birds’ behavior and defy gravity, that had maintained us limited to the ground.
In addition to all the levitation methods, the magnetic levitation technique is the one that has attracted more interest currently and has the most promising technologies to the market, mainly to the passengers’ transportation and at the industry level, to impact in a positive way the whole society, contributing to their wellbeing.
Under this favorable scenarium to the magnetic levitation, this work will first analize in details all the suspension methods previously developed, doing a retrospective of the acoustic, optical, aerostatic, aerodynamic and electrostatic’s techniques, describing the each one’s operating principle, their advantages and disadvantages, and their main applications.
After, this undergraduate project will present all the possible magnetic levitation schemes, with their respective mathematical analysis, highlighting the academic, industrial, transportation, and consumer goods state of the art, indicating the MagLev trains’ projects, and the machinery manufacturers with this technology.
Português:
Ao longo da história, o fenômeno da suspensão ou da levitação de objetos sempre atraiu a atenção e o imaginário da humanidade para a possibilidade surpreendente de reproduzir o comportamento das aves e desafiar a ação gravitacional, que nos mantinham limitados ao solo.
Dentre todos os métodos de levitação de objetos, a técnica de levitação magnética é a que atrai mais interesse atualmente e que possui maior capacidade de apresentar tecnologias promissoras ao mercado, sobretudo no setor de transporte de passageiros e na área industrial, e impactar de maneira positiva grande parte da sociedade, contribuindo para o seu bem-estar.
Sob este cenário favorável para a levitação magnética, este trabalho se propõe a primeiramente analisar em detalhes todas as formas de suspensão de objetos anteriormente desenvolvidas, realizando uma retrospectiva sobre as técnicas acústica, óptica, aeroestática, aerodinâmica e eletrostática, descrevendo o princípio de funcionamento de cada uma delas, as suas vantagens e desvantagens e as aplicações em que são frequentemente encontradas.
Em seguida, este trabalho apresenta todas as possíveis variações da levitação magnética, com as respectivas formulações matemáticas de seus sistemas de levitação, ressaltando o estado da arte das suas aplicações acadêmicas, industriais, de meios de transporte ou de bens de consumo, indicando os projetos de trens MagLev, e fabricantes de máquinas e equipamentos dotados desta tecnologia.
Stabilized passive magnetic levitation at room temperature can be realized with the help of diamagnetism. This paper researches the condition of the diamagnetic levitation and introduces the experiments of diamagnetic levitation using the diamagnetic material of graphite successfully. According to the theory of diamagnetic levitation, a micro-switched reluctance motor with a levitated rotor was designed.
A novel micro-machined diamagnetic stable-levitation system (MDSLS) which is composed of a free permanent magnetic rotor, a ring lifting permanent magnet and two diamagnetic stabilizers was presented. The static and dynamic stable characters of MDSLS were analyzed. The coupled non-linear differential equations were used to describe six-degree-of-freedom motion of the levitated rotor, and the equivalent surface current and combined diamagnetic image current method were utilized to model the interaction forces and torques between the lifting permanent magnet and rotor permanent magnet and also between the rotor permanent magnet and diamagnetic substrates. Because of difficulty to get analytical solution, the numerical calculation based on Runge-Kutta method was used to solve the dynamic model. The vibration frequencies were identified by fast Fourier transform (FFT) analysis. According to their resonance characteristics and parameters, the translational and angular dynamic stiffness were also calculated. The results show that the levitation of the rotor in MDSLS is stable, and the MDSLS is potential for the application in levitation inertial sensor.
An electromagnetic levitation system comprising a detuned microwave cavity is investigated. The cavity takes the form of a ring-resonator supporting a TM mode, the fields of which generate suspension forces on an unattached 'free' wall of the cavity. The electromagnetic forces over the surface of the free-wall or 'float', which in the most basic format takes the form of a flat disc, are determined by solving the modal equations for a range of possible levitated positions of the float, both aligned and misaligned. These force estimates are then used to determine the dynamic responses of the disc-shaped float to assess the stability and robustness of the suspension mechanism.
In this paper, we mainly describe about a performance of the successive acceleration motion of the asymmetrical shaped diamagnetic graphite (PG) plate in zero electrical power supply. The unique contact free motion of PG plate by using our novel technique was previously reported at the Maglev 2006 conference in Dresden, Germany. Since that time, some experiments revealed that the acceleration motion of PG plate was depend on the edge shape of PG plate sample. In the future planning, we would like to develop the continuous linear and rotation drive system by using this novel technique with edge shape effect of PG plate.
La lévitation est un moyen fascinant de se soustraire à l'action de la gravité. Le diamagnétisme est le seul phénomène physique permettant une lévitation stable, statique et passive à température ambiante. Toutefois, cet effet magnétique est généralement insignifiant aux échelles usuelles. Parmis les différents moyens d'augmenter l'amplitude de ce phénomène, la réduction d'échelle est une voie prometteuse. Ces travaux contribuent à l'exploration des possibilités et des potentialités de la lévitation dans le domaine des microsystèmes. La diminution en taille permet d'une part d'augmenter les forces diamagnétiques volumiques et d'autre part de diminuer les forces diamagnétiques absolues. Ces propriétés ont été mises en oeuvre à travers la conception et la fabrication de microcapteurs (accéléromètre, inclinomètre, capteur de force) et de microactionneurs (manipulation de microparticule par inclinaison ou au moyen d'un laser). Ces réalisations ouvrent des perspectives novatrices et des fonctionnalités nouvelles dans le micromonde.
The stable levitation of magnets is forbidden by Earnshaw's theorem, which states that no stationary object made of magnets in a fixed configuration can be held in stable equilibrium by any combination of static magnetic or gravitational forces1, 2, ³. Earnshaw's theorem can be viewed as a consequence of the Maxwell equations, which do not allow the magnitude of a magnetic field in a free space to possess a maximum, as required for stable equilibrium. Diamagnets (which respond to magnetic fields with mild repulsion) are known to flout the theorem, as their negative susceptibility results in the requirement of a minimum rather than a maximum in the field's magnitude2, 3, ⁴. Nevertheless, levitation of a magnet without using superconductors is widely thought to be impossible. We find that the stable levitation of a magnet can be achieved using the feeble diamagnetism of materials that are normally perceived as being non-magnetic, so that even human fingers can keep a magnet hovering in mid-air without touching it.
This paper studies electrostatically suspended induction motors (ESIM). The ESIM possesses the rotating ability of an ordinary electrostatic induction motor, in addition to providing contactless support by electrostatic suspension. To accomplish these two functions, a feedback control strategy and the operating principle of an ordinary electrostatic induction motor are used. The stator possesses electrodes which exert the electrostatic forces to the rotor and are divided into a part responsible for suspension and one for rotation. Two rotor types are utilized: a polished glass disk without any surface treatment, and a polished glass disk covered with a thin layer of conductive material (ITO layer) on only one side. In this paper, the structure and the operational principle of the ESIM are described, followed by the experimental system and control strategy for stable suspension and rotation. Experimental results show that the glass disk has been rotated with a speed of approximately 70 rpm while being suspended stably at a gap length of 0.3 mm. The ESIM can be utilized as a rotating device for dielectric materials like glass in ultra-high vacuum and clean-room environments.
The use of diamagnetic levitation for micromechanical bearings is
discussed. The simple system of a magnetic sphere supported by a
diamagnetic material has an analytic solution for the vertical force;
this solution is used to illustrate the fundamental properties of
diamagnetic levitation. Work by previous researchers to diamagnetically
levitate magnets with masses as large as tens of grams using external
fields, as well as micrometer-scale levitation of diamagnetic materials,
is discussed. Calculations presented suggest modern magnets on the order
of 100 to 300 μm will self-levitate over diamagnetic materials
without supporting external fields. This suggests a number of noncontact
micromechanical bearing applications, such as for microrobotics and
highly sensitive sensors. Diamagnetic bearing are typically limited to
light-load applications. To alleviate this limitation, a noncontact,
hybrid diamagnetic air bearing is proposed for light-load/low-speed to
high-load high-speed use without the start-up problems normally
associated with self-pumping air bearings. A preliminary analysis of the
hybrid bearing concept suggests that squeeze film effects may allow
virtually the full drive load to be applied at start-up, provided
lateral acceleration is high
This paper reports the successful electrostatic suspension of
dielectric materials. In order to implement a stable suspension, the
electrostatic forces exerted on a dielectric are actively controlled on
the basis of the measured suspension gap lengths. The principle of
electrostatic force generation for dielectrics is different from that
for conductors. By utilizing a stator electrode pattern containing many
boundaries over which potential differences exist, the suspension
characteristics, such as dynamic stability, suspension initiation time
and stiffness of lateral motion are greatly improved. The dynamic model
of the suspension system and the influence of the resistivity of a
dielectric on the closed-loop stability are described, followed by the
experimental apparatus and stabilizing controller. As dielectric
objects, glass plates have been suspended electrostatically at a gap
length of about 0.3 mm. Apart from the structure of the stator
electrode, the suspension initiation time is also influenced by air
humidity, glass type, supplied voltage and gap length, which have been
experimentally explored. Experimental results on the lateral dynamic
characteristics are also presented
Suspensions magné,tiques partiellement passives
- J Delamare
J. Delamare, " Suspensions magnétiques partiellement passives, " in Diss. LEG, Grenoble, 1994.