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Synthesis and Modelling of an Electrostatic Induction Motor Jean-Frédéric Charpentier, Yvan Lefèvre, Emmanuel Sarraute, Bernard Trannoy

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Synthesis and Modelling of an Electrostatic Induction Motor Jean-Frédéric Charpentier, Yvan Lefèvre, Emmanuel Sarraute, Bernard Trannoy Synthesis and modelling of an electrostatic induction motor Jean-Frédéric Charpentier, Yvan Lefèvre, Emmanuel Sarraute, Bernard Trannoy To cite this version: Jean-Frédéric Charpentier, Yvan Lefèvre, Emmanuel Sarraute, Bernard Trannoy. Synthesis and mod- elling of an electrostatic induction motor. IEEE Transactions on Magnetics, Institute of Electrical and Electronics Engineers, 1995, vol. 31 (n° 3), pp. 1404-1407. 10.1109/20.376290. hal-01792424 HAL Id: hal-01792424 https://hal.archives-ouvertes.fr/hal-01792424 Submitted on 15 May 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Open Archive TOULOUSE Archive Ouverte ( OATAO ) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 19944 To link to this article : DOI: 10.1109/20.376290 URL: http://dx.doi.org/10.1109/20.376290 To cite this version : Charpentier, Jean-Frédéric and Lefèvre, Yvan and Sarraute, Emmanuel and Trannoy, Bernard Synthesis and modelling of an electrostatic induction motor . (1995) IEEE Transactions on Magnetics, vol. 31 (n° 3). pp. 1404-1407. ISSN 0018-9464 Any correspondence concerning this service should be sent to the repository administrator: [email protected] SYNTHESIS AND MODELLING OF AN ELECTROSTATIC INDUCTION MOTOR J.F. Charpentier, Y. Lefèvre,E. Sarrauteand B. Trannoy LEEI/ENSEElHT 2. Rue Charles Camichel 31071 Toulouse Cédcx FRANCE A bs tract -- This paper deals wlth a new way of some previous works on the conception of micrometric synthesls and modelllng electrostatlc Induction actuators [6](7][8]. mlcromotors by means of duallty rules from the An E.I.M. requires a revolving electricfield on its stator. magnetic induction machine. An electromechanlcal Such as in Ùle M.I.M. this is achieved by applying a three­ model based on this method is given. Theo, a phasedvoltages source to electrodes equallyaround spaced the computational procedure based on a general Iumped stator. order 10 create an alternating electric field parameter model and an electrlc field calculatlon In code, bas been developed so as to simulate the êlistribution eachphase consists of pair of electrodes feeded dynamlc worklng of these actuators. A comparison with opposite sinusoïdal voltages (Fig. 1). Figure 2 shows 1s made between the computation results and the the final arrangement of the stator of a triphased, two poles model results. Satisfactory agreement between machine. theory and simulation is obtained in most respects. l.lNTRODUCTION -0,SV-sin(rot) Researchon a new typeof actuators have beenundertaken for a few years: the electrostatic microactuators. In these actuators the electromechanical conversion is based on the Fig 1. Creating an altemating electnc rieid electricfield rather than the magneticfield. Likethe classical magnetic machines, electrostatic machines can work on 0,5.V s.sin( wt-2013) -0,5.V s.sin( rot+211/3) differenl principles: electrostatic synchronous motor (E.S.M.), electroquasistatic induction motor (E.l.M.), variable capacitance motor (V.C.M.). For instance the )ç� V.C.M. have beenwidely studiedby many researchers: in the vu;,.,,, U.S.A., Japan and Europe. Sorne prototypes have been designed and fabricated using integrated-circuit �., foi-i � processing.[l][2][3] This paper is concerned with the E.I.M. Sorne authors have already studied this type of machine and developed �� theoretical models based on the theory of electromagnetic 0,5.Vs.sin(ox+2ill3) -0,5.Vs.sin(rot-2[1/3) waves. These models are mainlyadapted forE.I.M. wiÙI the !·1g. L Lreatmg a rotaung eleclnc 11c1<1 rotor made of smooth uniform conductor or a fluid and are not very easy to manipulate for the design. This type of In a M.I.M., due to Lenz's law combined with Ohm's E.I.M. uses charge relaxation to establish its rotor charge law, the revolving magnetic field induces voltages and distribution. It is therefore difficult to optimise its currentsin the rotor windings. According to Lenz'slaw these performances.[4](5] currents produce magnetic effects which counterbalance the The paper shows how to synthesize an another type of evolution of flux in the rotor coi!. In a wound rotor machine E.I.M. from considerations of duality with the familiar ilierotor coils are short-circuited. Relations between the flux magnetic induction machine (M.I.M.). In order to facilitate <l>rand thecurrent Ir in a coil are: the optimisation of this kind of motor Park's equations for this synthesised E.I.M. are inferred from some hypoilieses. e=-d4>/dtand Ir:=e/R (1) Eventually a general lumped parametermode! is given. This last mode( is used to simulate dynamic working of E.I.M. where e is the e.m.f. and to validate the oblainedPark's model. An equivalent induction phenomena can be achieved by means of electric induction. In an E.I.M. the revolving IL SYNTI-IESIS OF THE MACHINE electric field induces voltages and charges on the rotor electrodes.By considerations of duality from thewound rotor In theory the E.I.M. is a close analog of ils familiar M.l.M., the phases of the rotor of an E.I.M. can consist of electromagneticcounterparts. Voltages and electricfiel d play isolated pairs of electrodeslinked with a resistor(Fig. 3). the parts of currents and magnetic field. The qE term in Lorentz force takes place of the jxB Laplace force. The conception of our model is based on this basic idea and considerations of duality with the familiar M.I.M. and on where Qsi, Qri, Vsi, Vri are thecharge and the voltages of the phase on the stator (s) and on the rotor (r); Cs andCr are the coefficients capacitance of a phaseon the stator andon the rotor; Ms is the coefficient of induction between two phases on the stator; Mr is the coefficient o� induction betweentwo phaseson the rotor; a, band c areg1ven by: a= -Msr.cos(0) b= -Msr.cos(0+4IT/3) (4) c= -Msr.cos(0+2I1/3) Relations between the charge Qr and the voltage Vr where Msr is the amplitude of the coefficients of induction between the two electrodesforming a phaseare: between a phase on the stator and a phase on the rotor , and 0 theelectrical angular position of the rotor located fromthe Ir=dQr/dt andVr:= -Rr / Ir phasenumbered one of the stator. (2) As for the M.I.M. the coefficients of equation (3), These relations show that the induced voltages relating charges to voltages, are fonction of the angular counterbalance the evolution of charge on electrodes. The position of the rotor 0. In order to simplify these rel�tions current Ir between the two electrodes play the part of the • the three-phased variables are transformed to ?ew vanabl�s e.m.f. in M.I.M. and can be called current motive force. related to a reference framefixed to the revolvmg field. This reference frame is the analog of the d-q axis and the transformation is the classical Park's transformation. Equation (3) becomes: -Qr r Qs = Css.Vs - msr. Vr �t {Qr = Crr.Vr- msr. Vs (5) ,g.4. electrodes To illustrateour approach we have chosen a three-phased where: rotor E.I.M. One arrangement of a two poles motor is Css=Cs-Ms/2,Crr = Cr-�/2 and msr=3..Msr/2 shown on figure 5. (6) Equation (5) relates the complex values of the ne� �leclrical 0,5.Ys.sin(rot-2TI/3) -0,5.Ys.sin( rot+2[l!3) variables to one another. Under steady cond1ttons and assuming balanced three-phase sinusoïdal fee�ing volta�es applied on the phases of the stator, the elec1r1cal pulsauon ros of the stator variablesand the electrical pulsation rorof the rotor variablesare related to the electrical angular speed of the rotor by theequation: wr+w=ws (7) This equation is the non-zero torque condition. In these 0,5.Vs.sin(rot+2TI/3) -0,5.Ys.sin(rot-2TI/3) conditions all the new variables are constant in the new reference. The current of a phase of the rotor in the new referenceis: III. PARK'S EQUATIONS FOR THE SYNTHESIZED E.I.M dQr . da.r d Ir=--J-Qr = -J-. a.r Qr= J .mr. (C rr. Vr-rnsr. y s ) (8) In order to deduce a relatively simple model of this dt dt dt E.I.M. fewassumptions must be made: space harmonies and saliency effects are neglected. Thus for three-phased E.I.M. From equations (2) and (5) the expression of voltage of a the matrixcapacitance is: rotor phaseis deduced: Me Ms Cs a b C j.ror.msr.Vs 2 2 Vr= (9) Ms Ms [j. ror.Crr+ 1 / Rr] Cs C a b 2 2 Qs2 Ms Ms Vs2v Cs b a Qs3 _ 2 2 • Vs3 We can comparethe equation (9) with theclassic expression Qrl - Mr Mr Vrl (3) a C b Cr forthe magnetic inductionmachine. Qr2 2 [Vr2"] Qr3 Mr Mr Vr3 b a C Cr 2 2 j.ror.msr.Is Mr Mr Ir=�-----= (10) n b a Cr 2 2 [j.oor.Lrr+ Rr] The torque is obtained by the derivative of the electric where reis the electrical torquegiven by (11); tfs,tfv, J and coenergy in the machine with respect to rotor position.
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