AXIAL GAP ELECTROSTATIC WOBBLE MICROMOTOR

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1 XIL GP ELETOSTTI WOLE MIOMOTO nc TOMESU Soin NTONIU F.M.G. TOMESU Electicl Engineeing Dept. POLITEHNI Univesity uchest ãzvn MOEI ING OMNI uchest The toque vesus ngle mechnicl chcteistic of n xil gp electosttic wole moto is compute y n nlyticl metho. INTODUTION Micoevices n micomotos e suject of incesing inteest ue to thei multiple pplictions in inusty meicine mility n mny othe fiels. The stuctue of micoevices is genelly sujecte to cetin estictions eive fom the mnufctuing pocess which uses integte cicuit technology. Electosttic motos ppe then to e moe convenient thn motos of clssicl type se on electomgnetic foces. Unvoile mnufctuing eos hve stong influence on the evice stuctue t such smll scle n my esult in n uncceptle ispesion of the pefomnce figues. The wole motos [14] which integte s n opetion pinciple the vey vition of the moto igp pesent themselves s pomising ltentive. The esign of micomotos stts fom peliminy pefomnce evlution with view to estlish the nge of the pope esign n mnufctuing equiements. In this espect the evlution of the mechnic chcteistic of the micomoto i.e. the epenence of the ctive toque on the ottion ngle of the oto is of foemost impotnce fo oth the ovell pefomnce evlution n the esign of ppopite iving poceues. The pesent ppe ims t the computtion of n ppoximte mechnic chcteistic of the il gp wole moto otine une some esonle simplifying ssumptions. DEIE MODEL ND SIMPLIFYING SSUMPTIONS The stto of the micomoto une stuy [15] consists in equl sectos of n nnul conucto eposite on n insulto sustte n covee y thin insulting film n the oto is conucting isk tht cn otte oun the suppot point t the sis of its shft with the cicumfeence touching the stto plne t single point. (fig. 1). The opetion of the wole moto is quite simple: The conucting oto isk is pemnently mintine t null potentil y the contct t the suppot point of its shft while ppopite secto pis of the fgmente stto (stto poles) e successively plce t iving potentil. n enegize stto pole secto ttcts the oto isk tening to euce the vege oto stto istnce etween them n thus mkes the oto oll until the contct point of the oto n the stto plne is t the mile I of the enegize stuctue. y enegizing successive pis of stto poles the contct point olls on the stto plne n the oto woles oun the stto xis. The stto is consiee split into 6 equl sectos of ii n covee y n insulting film of thickness e n eltive pemittivity. The oto ius is its shft height is h n the clence of the infeio oto fce ove the supeio stto fce when

2 these e pllel is ( < h). Moeove the oto ius n the oute stto ius e such tht the instntneous contct point of the oto with the stto plne is istnce t ius fom the stto xis. Some simplifying hypotheses e suppose to pply: 1. The shft length h n the oto stto clence e vey smll s compe with the oto ius.. The stto insulto thickness is negligile with espect to the shft length n the oto stto clence;. The insulting gps etween successive stto sectos (poles) e consiee to e extemely now. Fig. 1. Opeting pinciple of micomoto Fig.. Locl stuctue The symmety of the stuctue mkes it sufficient to compute the mechnic chcteistic coesponing to the oto stto contct point tvelling long the cicumfeence of single enegize stto pole when the pi of enegize stto sectos is t the iving potentil n ll othe stto sectos e t null potentil. The geomety of the stuctue une stuy coespons to the complex thee imensionl fiel polem. Howeve since ccoing to the simplifying hypotheses the ngle θ etween the oto n stto fces is vey smll simplifie ppoch my ssume two imensionl electic fiel polem whee the electic fiel lines e loclly noml to the stto pole fces. The ctive electic toque is compute s [678] T W ct. ( ) whee W is the electic co enegy is oto position ngle i.e. the ngle etween the ii of the oto stto contct point n the oe point I septing the enegize stto sectos n () is the oto stto cpcitnce. OMPUTTION OF THE ELETI PITNE The computtion of the electic toque is euce to the computtion of the electic cpcitnce ssocite to the oto n the enegize stto sectos [9] S ( ) sectos enegize sectos x e ( ) enegize whee is the istnce of the cuent point on the enegize stto secto to the stto xis

3 is the ngle etween the position vecto of the sme cuent point n the position vecto of the oto stto contct point n x is the locl igp (fig. ). Using the nottions ppeing in fig. which epesents n xil s section of the moto pssing though the oto stto contct point two equtions hol s ( h ) θ h sinθ h θ sinθ. Une the simplifying hypotheses the secon eqution gives ( h ) θ. tn tnθ sinθ θ h so tht ( h ) ( h ) 1 H tn 1 θ. Fig.. xil s section Fig. 4. igp evlution ccoing with the nottions ppeing in fig. 4 one cn eily otin tht ( h ) x H 1 1 n consequently the cpcitnce esults s epesente in fig. 5 [1] whee ( ) ( h ) e ( ) 1 ( ) 1( ) 1( 1) 1( ) ( ) ( ) ( ) ( ) ( ) ( tn 1) tn ln ( ) tn ( ) 1

4 tn ctn e h 1 1. OMPUTTION OF THE PPOXIMTE MEHNI HTEISTI The ppoximte mechnic chcteistic toque vesus ottion ngle e h T is compute s the eivtive of pmete epenent integl [11] s T ln. Fig. 5. oto stto cpcitnce Fig. 6. Mechnic chcteistic The opetion of the micomoto supposes the tnsfe of the enegizing potentil to successive stto pole pis. This wy the ovell mechnic chcteistic of the moto cn e eive s the peioic epetition of the ove one pole pi mechnic chcteistic s epesente in fig. 6 with the peio one y the pole pitch of /. The usul mechnic chcteistic toque vesus evolving spee cn then e eive with efeence to pticul iving poceue iming t elting the evolving spee with the switching te of the enegize pole pis.

5 ONLUSIONS The ppoximte mechnic chcteistic of n xil gp electosttic wole moto ws compute une esonle simplifying hypotheses fo t comptile with cuent ctul eliztions. Moeove the fomule otine fo the oto stto cpcitnce coul e use in the computtion of the toque vesus cuent iving chcteistic of the wole moto. It is woth mentioning tht the numeicl esults otine following the simplifie nlyticl poceue expose ove compes successfully with othe pulishe esults [1]. KNOWLEDGEMENTS Thnks e ue to the stff of the Numeicl Methos Lotoy n to collegues in the Goup of Theoeticl Electicl Engineeing of the Electicl Engineeing Deptment "Politehnic" Univesity of uchest. EFEENES 1.. Legteneg E. eenscholt J. vn M. Elwenspoek n Electosttic Lowe Stto xil Gp Polysilicon Wole Moto Pt I : Design n Moeling IEEE JMEMS ol. 7 No. 1 Mch 1998 pp Legteneg E. eenscholt J. vn M. Elwenspoek n Electosttic Lowe Stto xil Gp Polysilicon Wole Moto Pt II : Fiction n Pefomnce IEEE JMEMS ol. 7 No. 1 Mch 1998 pp D. Smpe.J. Sngste.L. euen U. Wlle Multistto LIG Ficte Electosttic Wole Motos with Integte Synchonous ontol IEEE JMEMS ol. 7 No. June 1998 pp J. Sngste.D. Smpe ccucy ssessment of D n D Finite Element Moels of Doule Stto Electosttic Wole Moto IEEE JMEMS ol.6 No. June 1997 pp Mcovei Micomoto electosttic fulnt Gution thesis Deptment of Electicl Engineeing Polytechnic Univesity of uchest. 6. J. n lel Electomgnetic Fiels McGw-Hill ook ompny New Yok H.. Hus J.. Melche Electomgnetic Fiels n Enegy Pentice Hll Englewoo liffs J.J nc Tomescu F.M.G. Tomescu. Mãculescu zele electotehnicii âmp electomgnetic Mtixom uchest. 9. nc Tomescu F.M.G. Tomescu zele electotehnicii Sisteme electomgnetice (Lectue Notes) Deptment of Electonics n Telecommunictions Polytechnic Univesity of uchest M.L. Smolenski Tele e integle neefinite Eitu Tehnicã uchest 197 pp K.P. Ikovlev Înumãto mtemtic si tehnic Eitu Tehnicã uchest 1964 pg. 17.