AC Magnetic Field-Induced Rotation in Levitating Magnetostrictive Wire

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The rotation of magnetostrictive wires under excitation of an alternating axial magnetic field is a phenomenon discovered few years ago. Previous results and a recent mechanical experiment indicate that the appearance of these rotations is related to
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  3180 IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002 AC Magnetic Field-Induced Rotation inLevitating Magnetostrictive Wire C. Luna, V. Raposo, G. Rauscher, and M. Vázquez  Abstract— The rotation of magnetostrictive wires under excita-tion of an alternating axial magnetic field is a phenomenon discov-eredfewyearsago.Previousresultsandarecentmechanicalexper-iment indicate that the appearance of these rotations is related tothe sample vibrations associated to magnetoelastic resonance. Thissurprising behavior is here experimentally reported in polycrys-talline FeNi levitating wires. An introductory analysis consideringthe balance of gravitational, magnetic gradient, and eddy-currentforces is additionally carried out.  Index Terms— Magnetic forces, magnetic levitation, magnetoe-lastic resonance, magnetostriction. I. I NTRODUCTION M ECHANICAL rotation is observed in magnetic wireswithhighmagnetostrictionconstantundertheexcitationof axial alternating magnetic fields at suitable conditions. Thisphenomenon was first reported a few years ago in amorphouswires, which exhibit a simple domain structure [1], [2]. Later, this behavior was detected in wires with crystalline structure [3]and a much more complex domain structure, but always in sam-ples with large enough magnetostriction (positive or negative),as experimentally shown by careful study of this phenomenonin as-cast and annealed FeSiBNbCu wires [4]. Therefore, theac magnetic field-induced rotation is directly correlated withthe magnetostrictive character of the sample. Both the samplelength and field frequency dependence of the wire rotation in-dicate that the appearance of this effect is closely related to theformationofamagnetoelasticstandingwave[1].Thisrotationaleffect has been applied in studies of viscosimetry [5] and whena load is fixed to the end of the wire [6].Similar rotations induced by mechanical vibrations excitedbyamembraneloudspeakerhavebeenrecentlyreportedinmag-netostrictive, nonmagnetostrictive, and even nonmagnetic wires[7]. This fact suggests that the mechanical vibrations, inducedbymagnetoelasticresonanceinonecaseandbytheloudspeakermembrane in the other, result in an effective coherent rotationdetermined by the boundary conditions, such as the friction be-tween the wire and the glass tube holding the wire into the ex-citing coil.Theobjectiveofthisworkhasbeentostudythisphenomenonin a further step, that is, considering the magnetic forces acting Manuscript received February 6, 2002; revised May 22, 2002.C. Luna and M. Vázquez are with the Instituto de Ciencia de Materi-ales de Madrid-CSIC, 28049 Madrid, Spain (e-mail:; Raposo is with the Departamento de Física Aplicada, Universidad de Sala-manca, 37008 Salamanca, Spain (e-mail: Rauscher is with Vacuumschmelze GmbH, D-63450 Hanau, Germany.Digital Object Identifier 10.1109/TMAG.2002.802407. on the wire, placed in a vertical configuration, arising from thenonhomogeneity of the magnetic field created by the excitingsolenoid. In this case, the rotation is observed in levitating mag-netostrictive wire.II. S AMPLES AND  E XPERIMENTAL  T ECHNIQUES Polycrystalline FeNi (Permenorm 5000H2) wires 3 mm indiameter and commercial NiCr wires 1 mm in diameter wereemployed in the experiments. The experimental setup for mea-suring the rotation frequency of wires is shown in Fig. 1. It isbased on the measurement of the interference produced by therotating wire on a laser beam. The wire was placed within aglass tube glued to the inner part of the solenoid generating theexciting ac magnetic field. Further experimental details can befound in [2]–[4]. In the “conventional” experiment, where the wire does not levitate, the solenoid is placed onto a planar glasspiece, so that the wire also rests on that glass. A current is fedthe coil from a function generator coupled with an amplifier toproduce an axial alternating magnetic field.In the experiment where the wire levitates, the solenoid isheld 10 cm above the planar glass. In this case, a “levitation”distance is defined as the distance between the middle points of the coil and the levitating wire (see Fig. 1).III. R ESULTS AND  D ISCUSSION  A. Rotation Without Levitation The ac field-induced rotation of magnetostrictive wires ap-pearsataspectrumoffrequenciesfortheexcitingmagneticfieldwith fundamental and higher harmonics [1], [2]. The inset in Fig. 2 shows the rotational spectrum of the polycrystalline FeNiwire for an ac magnetic field of 15.2 kA/m.Thedependenceoftherotationfrequencyofthewirewiththeamplitudeoftheacexcitingfield(538Hz)isplottedinFig.2.Asobserved, there is a very noticeable influence of the ac excitingfield amplitude. For the rotation of the wire to be observed, aminimum threshold value is required. In fact, vibrations of thesampleareoftenobservedbeforethatoccurs.Increasingtheam-plitude results in an increase of the rotation frequency of thewire until a maximum is reached.  B. Levitation Levitation of the wire in the vertical configuration, as shownin Fig. 1, is achieved through alternating magnetic force gener-ated by the exciting coil that periodically balances gravitation.A vertical oscillatory motion then results. The magnetic force is, where is the magnetic moment of the 0018-9464/02$17.00 © 2002 IEEE  LUNA  et al. : AC MAGNETIC FIELD-INDUCED ROTATION IN LEVITATING MAGNETOSTRICTIVE WIRE 3181 Fig. 1. Schematic diagram of the experimental setup for rotation measurements of levitating wires.Fig. 2. Dependence of rotation frequency of the FeNi wire on exciting ac fieldamplitude (field frequency of 538 Hz). The inset shows the rotational spectrumobtained at 15.2 kA/m of the exciting field amplitude. sample and is the magnetic field strength of the solenoid. Asa consequence of the nonhomogeneity of the magnetic field atthe ends of the solenoid, the generated magnetic force tries tomaintain the wire at the center of the solenoid. The magneticfield strength at the vertical axial coordinate is(1)where , , and are the number of turns, the length and the ra-dius of the solenoid, respectively. The srcin of the coordinateis taken at themiddle position of thesolenoid. Then, theverticalmagnetic force becomes(2) Fig. 3. Levitation distance as a function of amplitude of exciting field for arange of field frequency. Inset shows the dependence of the levitation distanceon the exciting field frequency obtained at several values of field amplitude. where is the th component of the magnetic moment of thesample and(3)The frequency of the vertical oscillatory displacement of thewire is the same as the exciting field frequency of the mag-netic. This can be easily observed by the eye for frequenciesin the range of a few hertz. The amplitude of the oscillationsdecreases as field frequency increases. These oscillations are aconsequence of the balance between the magnetic force tryingtocenter the wireat themiddle ofthe solenoid,where van-ishes and the opposing gravitational force .Fig. 3 shows the dependence of the levitation distance (be-tween the centers of the solenoid and the wire) on the excitingfield amplitude for a range of frequencies. The evolution of thelevitation distance on the exciting field frequency is given in the  3182 IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 5, SEPTEMBER 2002 Fig. 4. Spectrum of rotation frequencies for levitating FeNi wire obtained at15.2 kA/m. Inset shows dependence of the levitation distance on exciting fieldfrequency obtained at 15.2 kA/m. inset of Fig. 3, the parameter now being the amplitude of the acfield. This evolution where increasing the frequency results inanincreaseofthelevitationdistanceshouldbenoted.Inordertointerpretit,theeffectofinducededdycurrentsshouldbeconsid-ered. Therefore, an additional magnetic field and forceare involved in the motion. As opposes ,theeffectivemagneticforcebalancinggravitationisreducedandthe levitation distance increases. Experimentally, the presenceof such eddy currents is further supported by the detected in-crease of temperature of the wire. This force arising from eddycurrents depends on geometry, resistivity, and permeability of thesampleandincreaseswiththefrequencyoftheexcitingmag-netic field. An additional experiment has been performed on acommercial NiCr wire of which the resistivity is 110 cm,larger than that of the FeNi wire (45 cm), and the radiusand susceptibility are comparatively smaller. In this case, thelevitation distance remains constant within the range of the in-vestigated frequencies and the increase of temperature is verymodest. C. Rotation in Levitating Magnetostrictive Wires Magnetostrictive wires can exhibit both levitation andac field-induced rotation. The rotational spectrum of levitatingFeNi wire for the same field amplitude as that of the inset inFig. 2 is shown in Fig. 4. Two new resonance peaks are nowobserved. While for nonlevitating wire, rotation was observedat 538 and 1075 Hz, the four frequencies of the spectrumnow observed are 360, 541, 721, and 1080 Hz. Assuming thefundamental frequency were at 180 Hz, the other resonancefrequencies would correspond to higher harmonics (neverthe-less, no rotation is detected at 900-Hz frequency). The largernumber of observed frequencies could be associated with thereduction of the friction in levitation.Fig. 5 shows the rotation frequency and levitation distance asa function of the amplitude of the exciting field. A similar result Fig. 5. Rotation frequency dependence on exciting field amplitude forlevitating FeNi wire obtained at 541 Hz. Inset shows dependence of thelevitation distance on exciting field amplitude obtained at 540 Hz. as that shown in Fig. 2 is now obtained with a maximum rota-tion at a given field amplitude. Again, vibrations are observedbefore a threshold amplitude is reached. Eventually, an incre-ment of the diameter of the glass tube results in stronger trans-verse vibrations induced by magnetoelastic resonance and thetransverse instability of the levitation that finally may not giverise to coherent rotation.IV. C ONCLUSION Alternating magnetic field-induced rotation in levitatingmagnetostrictive wire has been reported. The results can beuseful for the development of novel rotor devices.A CKNOWLEDGMENT The authors would like to thank Dr. A. P. Zhukov for helpfulcomments.R EFERENCES[1] H. Chiriac, C. S. Marinescu, and T.-A. Ovári, “Large gyromagneticeffect in FeSiB amorphous wires,”  IEEE Trans. Magn. , vol. 33, pp.3349–3351, Sept. 1997.[2] F. J. Castaño, M. Vázquez, D.-X. Chen, M. Tena, C. Prados, E. Pina,A. Hernando, and G. Rivero, “Magneto-mechanical rotation of magne-tostrictive amorphous wires,”  Appl. Phys. Lett. , vol. 75, pp. 2117–2119,1999.[3] V. Raposo, T.-A. Ovári, and M. Vázquez, “AC field induced rotationof magnetostrictive nickel wires,”  IEEE Trans. Magn. , vol. 37, pp.2705–2707, July 2001.[4] V. Raposo, A. Mitra, Y. F. Li, and M. Vázquez, “Spontaneous mechan-ical rotation of as-cast and annealed FeSiBNbCu wires under high-fre-quency axial AC field,”  J. Phys. D: Appl. Phys. , vol. 34, pp. 1346–1351,2001.[5] M.Vázquez,F.Castaño,T.A.Ovari,V.Raposo,andA.Hernando,“Newviscosimeter based on the ac field induced rotation of magnetostrictiveamorphous wires,”  Sens. Actuators , vol. A 91, pp. 112–115, 2001.[6] T.Sugino,M.Takezawa,T.Honda,andJ.Yamasaki,“Basicloadcharac-teristics of magnetostrictive amorphous wire micro-rotor,”  IEEE Trans. Magn. , vol. 37, pp. 2871–2873, July 2001.[7] V. Raposo, C. Luna, and M. Vázquez, “Rotation in magnetic wire in-duced by AC field and mechanic vibrations,”  J. Magn. Magn. Mater. , tobe published.
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