Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets. Part 2: Radial Magnetization

Ravaud, Romain; Lemarquand, Guy; Lemarquand, V.

doi:10.1109/tmag.2009.2025315

Cited by 110 publications

(56 citation statements)

References 28 publications

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“…The vast majority of this attention has been given to the purely coaxial geometries [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. More recently the focus has been shifted to calculation of the mutual inductance and magnetic force between circular coils with lateral and angular misalignments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

Babić

Akyel

2012

IEEE Trans. Magn.

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Abstract-This paper presents a new general formula for calculating the magnetic force between inclined circular loops placed in any desired position. This formula has been derived from the Lorentz force equation. All mathematical procedures are completely described to define the coil positions that lead to a relatively easy method for calculating the magnetic force between inclined circular loops in any desired position. The presented method is easy to understand, numerically suitable and easily applicable for engineers and physicists. The obtained formula is given in its simplest form from the already existing formulas for calculating the magnetic force between inclined circular loops. We validated the new formula through a series of examples, which are presented here.

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Section: Introductionmentioning

confidence: 99%

Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

Babić

Akyel

2012

IEEE Trans. Magn.

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“…[30,31] The NS effect can also be displayed by constrained buckled tube [32] , buckled beam [33] or multiple magnet [34] systems. Whereas our system is demonstrated to display NS under quasi-static loading, it should be pointed out that a number of these previous studies [3,[30][31][32] measured the dynamic modulus.…”

Section: General Rightsmentioning

confidence: 99%

Double‐Negative Mechanical Metamaterials Displaying Simultaneous Negative Stiffness and Negative Poisson's Ratio Properties

Hewage¹,

Alderson²,

Alderson³

et al. 2016

Advanced Materials

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Intuitively, materials become both shorter and wider when compressed along their length.Here we show how a composite material or structure can display a simultaneous reversal in the direction of deformation for both the axial and transverse dimensions, corresponding to negative values of effective stiffness and effective Poisson's ratio, respectively. A negative Poisson's ratio [1] (NPR or auxetic [2] ) host assembly stabilising (otherwise unstable) embedded negative stiffness [3] [4,5] Metamaterials include negative refractive index [6] and negative effective mass density [7] materials finding use in, for example, electromagnetic and acoustic cloaking/lensing applications, respectively. Examples of mechanical metamaterials are negative compressibility transition, [4] NPR [1] and NS [3] materials.Auxetic materials and structures exist, and are stable in the unconstrained state, at the nanoscale (e.g. crystalline forms of silica, [8] zeolites [9] and cellulose [10] ), microscale (microporous polymers [11] and microfabricated truss-like structures [12] ) and macroscale (composite laminates, [13] foams, [14,15] honeycombs [16] and patterned elastomeric spherical shells [17] ). Enhanced shear modulus, [18] energy absorption [19] and indentation resistance [20] are some of the benefits known for auxetic materials and structures. [21] Periodic arrangements of sub-units leading to auxetic behaviour include truss, [16,22] corner-sharing polygon, [23,24] and hybrid truss-polygon [25] frameworks, and particle assemblies. [26,27] NS materials and structures, on the other hand, are thermodynamically unstable unless stabilised by an external constraint.[28] Examples of NS materials include polymethacrylimide (PMI) foams, [16] honeycombs and lattices, [29,AA1,AA2] and certain crystals (VO 2 , BaTiO 3 )undergoing constrained phase transformation. [30,31] The NS effect can also be displayed by constrained buckled tube [32] , buckled beam [33] or multiple magnet [34] systems. Whereas our system is demonstrated to display NS under quasi-static loading, it should be pointed out that a number of these previous studies [3,[30][31][32] measured the dynamic modulus. Dynamic loading of NS materials can give rise to beneficial temporary effects demonstrated, for example, in 3 3 composite systems containing NS inclusions or elements which display extreme stiffness [30] and vibration damping [3,32] responses.Our 'double-negative' mechanical metamaterial displaying simultaneous negative Poisson's ratio and negative stiffness properties comprises an auxetic host framework constraining embedded NS elements. The framework consists of a regular array of interlocked rigid hexagonal sub-units with 3 male and 3 female keys per sub-unit, arranged in an alternating fashion around the six sides of the hexagon [27] (Figure 1...

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“…Two different approaches, namely, Lorentzian [16][17][18] and Coulombian [20][21][22][23][24][25] are available to determine the forces. In former approach the permanent magnet is considered as planes with equivalent currents, while the equivalent charge density in the later one.…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…Analytical approach is faster investigation method as compared to the latter ones for the parametric study. The analytical equations for determining the magnetic field [9][10][11][12][13][14], force and stiffness [15][16][17][18][19][20][21][22] in bearings with axial, radial and perpendicular polarizations are presented by the many researchers recently. However in these works, the ring magnets are concentric, which might not be prevailing in actual scenario.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Radial Magnetized Permanent Magnet Bearing Characteristics

Bekinal¹,

Anil²,

Jana³

2013

PIER B

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Abstract-With an increase in the number of high speed applications, researchers have been concentrating on permanent magnet bearings due to their suitability. This paper presents a mathematical model of a permanent magnet bearing made of ring magnets with radial polarizations. Coulombian model and vector approach are used to estimate the force, moment and stiffness. A MATLAB code is developed for evaluating the envisaged parameters for three degrees (translational) of freedom of the rotor. Comparison of force and stiffness results of the presented model with that reported in the literature and also with the results of 3D finite element analysis shows good agreement. Then, it is extended to analyse stacked ring magnets with alternate radial polarizations. Finally, the cross coupled stiffness values in addition to the principal stiffness values are presented for the elementary structure and also for stacked structure with three ring permanent magnets with alternate radial polarizations.

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Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets. Part 2: Radial Magnetization

Cited by 110 publications

References 28 publications

Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

Double‐Negative Mechanical Metamaterials Displaying Simultaneous Negative Stiffness and Negative Poisson's Ratio Properties

Analysis of Radial Magnetized Permanent Magnet Bearing Characteristics

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