Design and Simulation of a Three-Phase Electrostatic Cylindrical Rotary Micromotor

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1 Intenatonal Jounal of Advanced Botechnology and Reseach (IJBR) ISSN , Onlne ISSN X, Vol-7, Specal Issue-Numbe5-July, 016, pp Reseach Atcle Desgn and Smulaton of a Thee-Phase Electostatc Cylndcal Rotay Mcomoto Sanaz Rezvan and Abolghasem Zabhollah Scence and Engneeng Depatment, Shaf Unvesty of Technology Intenatonal Campus, Ksh Island, Ian ABSTRACT Nowadays the electostatc moto fnds fequent use n mco-electo-mechancal systems (MEMS) whee the dve voltages ae below 100 volts. Usng movng chaged plates n capacto motos ae fa ease to fabcate than cols and on coes. Ths pape pesents a novel desgn of a thee-phase electostatc otay moto. It s shown that the angula velocty of the cylndcal type moto s almost 1.8 tmes geate n compason wth paallel plate type and as the voltage nceases the enhancement of slope ate n the angula velocty of the cylndcal type s moe tangble compaed to the paallel plate type. The effect of changng the gap between oto and stato on the angula velocty s also studed. Key wods: Cylndcal capactos, Electostatc, Mco-motos, MEMS, Desgn, Angula velocty 1. INTRODUCTION Snce 1980 seveal knds of electostatc motos have been studed and fabcated. Electostatc motos ae ntoduced as one of the most pomsng mco-electo-mechancal actuatos fo some easons. Fstly, the plana stuctue n these motos s hghly compatble wth lthogaphy pocesses n ntegated ccuts. Secondly n the mco scale, the electostatc motos ae stonge than electomagnetc actuatos because the foce pe volume atos of electostatc actuatos nceases as the dmenson decease [10,1,3,7]. In moden technology we ae facng an nceasng demand fo MEMS technology. Mcomotos and mcogeneatos ae powe MEMS systems fo enegy conveson between mechancal and electcal domans [4]. Vaous types of electostatc mcomotos have been ntoduced n the past. Vnhas et al. poposed an electostatc sde dve moto. They demonstated that the toque nceases wth lage oto adus, smalle gap between oto and stato and bgge oto teeth and stato electodes wdths [11]. Ghalchechal et al. epoted the desgn, fabcaton and chaactezaton of a otay mcomoto suppoted on mcoball beangs. The mcoball beang technology povdes a unfom and small a gap and a obust mechancal suppot fo the oto. It must be fabcated wth a coatng of slcon cabde flm to educe the fcton othewse the opeaton s not possble [4]. Saos et al. descbed the cylndcal and concal electostatc wobble mcomotos and the advantages. Concal desgn elmnates the need fo a long pvot beang and substantally educes the sze of the moto [9]. Roto pole shapng (RPS) desgn technque s also used to optmze the oto pole slope to maxmze the dvng toque. The sgnfcant low dvng voltage makes the ntegaton of electostatc mcomotos possble wth CMOS as a dvng voltage ccut []. To avod any fctonal contact dung opeaton, povdng pecse, epeatable and elable bdectonal steppng moton wthout

2 feedback contol, a flexual suspenson of the oto s employed n a thee-phase otay steppe mcomoto [8]. Even though, manufactung of the mcomotos has eceved a geat deal of attenton, thee ae only a few studes about cylndcal desgn of electostatc otay mcomoto. Thus, n ths pape, fo the fst tme we poposed a novel cylndcal desgn fo mcomotos to ncease the angula velocty fo hgh speed applcatons. To nvestgate the advantages of cylndcal capactos, the mechancal chaactestcs of ou poposed desgn s compaed to the conventonal paallel plate capactos. The est of the pape s oganzed as follows: n secton II the mathematcal modelng of cylndcal desgn s dscussed. In the next sectons the smulaton esults fo the poposed desgn and compason study between two models s pesented.. MATERIAL AND METHODS.1 Mathematcal Modelng.1.1 Cylndcal Capactos In the poposed desgn fo mcomoto, cylndcal capactos ae used nstead of paallel plate capactos. Fgue 1 depcts a cylndcal capacto wth a sold cylndcal conducto of adus a and chage q that s coaxal wth a cylndcal shell of neglgble thckness that has adus b a and chage q. In ths case the lengths of the capactos L should be much geate than adus b, thus we can neglect the fngng effect of the electc feld that occus at the end of the cylnde [5]. In the followng fomulaton ε s the elatve pemttvty of the mateal. Hee the mateal s a, thus ε =1 and F / m s the vacuum pemttvty. E s the electc feld n the egon a b. The aea of the vtual cylnde wth adus s denoted wth A. The emanng paametes ae shown n fgue 1. The electc chage s calculated as follows [5]: q 0 EA 0 ( L) (1) Thus the electc feld s [5]: q E L () 0 The potental dffeence between the two cylndes s calculated by: q d q b V Eds ln L L a b (3) ( ds d) 0 a 0 Capactance s calculated by: q C (4) V Thus we have: L C 0 (5) ln( b ) a Electc potental enegy can be expessed as [6]: 1 U So t can be calculated as: CV (6) 1 L ( U 0 ) V (7) ln( b ) a.1. Dvng Foce fo Pole Msalgnments The followng equaton can be used to deve the electostatc foces n the decton n whch msalgnment occus [6]: U F (8) x Fgue s the schematc model of ou poposed desgn fo the otay mcomoto. The msalgnment of the electodes s n the L decton, thus by calculatng the patal devatve of U wth espect to L we obtan: FL ln( b ) a 0 V (9) Fgue 1 Cylndcal capacto [5] Sanaz Rezvan, et al. 918

3 F L s the dvng foce to otate the mcomoto. In the pmay desgn thee ae 6 poles on the oto and 8 poles on the stato. The oto poles ae connected n an altenatng sequence wth thee dstnct electcal phases. Each phase actvates one thd of oto poles ndependently. When a gven phase s actvated, a voltage dffeence between the coespondng oto poles and the opposng stato poles geneates an electostatc foce. Howeve the adal component of the electostatc foce actng on the oto s canceled due to the symmety, the tangental component geneates a global toque. The electostatc toque tends to ealgn the poles of the stato and the actvated oto phase[]. The tangental foce F t, j exeted on a sngle oto pole j can be estmated usng the cylndcal capacto as follows: 0 Ft, j V ln( b (10) ) a Whee V s the voltage appled on the assocated phase. Fgue The schematc model of ou poposed cylndcal otay mcomoto.1.3 Dvng Toque fo Mcomoto Rotaton The electostatc toque T appled on the oto by one phase s: n 0 T Ft, j n V j 1 ln( b (11) ) a By puttng T I whee I s the mass moment of neta and s the angula acceleaton of the oto, the angula velocty of the oto can be calculated. n s the numbe of actve poles pe phase.. Smulaton Chaactestcs The dmensons of two poposed motos ae lsted n table 1. To acheve an mplct compason, the dmensons of poposed cylndcal moto ae assumed equal wth the paallel plate capacto moto. Fo smulatng the eal functon, 19 poles ae placed on the otos. Slcon s chosen fo moto mateal. Table 1 Values fo both moto paametes Symbol m Quantty Cylndcal capacto moto Paallel plate capacto moto Roto adus 450 m 450 m b Roto poles adus 50 m - Roto poles heght m g Gap between oto and stato 1.5 m 1.5 m n No. of actve poles pe phase V Voltage appled to each phase 100 V 100 V Moto mateal densty 3 kg m 3 kg m - Rato of poles n stato to oto RESULTS Whle some paametes of the motos ae changed the angula veloctes of both types of motos ae calculated and the esult s as below: 3.1 Effect of Alteng the Voltage on Angula Velocty The angula velocty of both type of motos fo dffeent voltages ae calculated. Fgue 3 depcts the behavo of motos as the voltage nceases. It can be seen that the cylndcal type moto poduces a geate value of angula velocty than the paallel plate type. The angula velocty of the cylndcal type moto s almost 1.8 tmes geate n compason wth paallel plate type. Ths s due to the dffeence between magntudes of constant paametes n cylndcal and paallel plate Sanaz Rezvan, et al. 919

4 capacto fomulas. Futhemoe, t s appaent that as the voltage nceases, the angula velocty of the cylndcal type has a shape ncease compaed to the paallel plate type. Fgue 3 Angula velocty vesus voltage fo both cylndcal type and paallel plate type mcomotos 3. Effect of Alteng the Gap between Roto and Stato on Angula Velocty Fgue 4 shows that ou poposed cylndcal type moto gves us an almost double magntude of angula velocty compaed to paallel plate type moto. It can be seen that as the gap between oto and stato nceases the angula velocty deceases. In ths case the ate of decement s slowe n the paallel plate type. Fgue 4 Angula velocty vesus gap between oto and stato fo both cylndcal type and paallel plate type mcomotos 4. CONCLUSION A novel desgn of a thee-phase electostatc otay mcomoto was poposed. The poposed cylndcal type mcomoto s compaed to the conventonal paallel plate type. It was shown that an electostatc mcomoto usng cylndcal capacto poduces a lage value of the angula velocty compaed to paallel plate capactos. The angula velocty of the cylndcal type moto s almost 180 pecent geate than that of paallel plate type. It s shown that as the voltage nceases the angula velocty of the cylndcal type has a shape ncease compaed to the paallel plate type. The effect of alteng the gap between oto and stato s also studed. It can be seen that as the gap between oto and stato s ased the angula velocty deceases and the ate of decement s slowe n the paallel plate type. The advantages of ou poposed cylndcal capactance mcomoto make t sutable fo desgn optmzaton of mcomotos fo hgh speed applcatons, namely mcodllng. 5. REFERENCES 1. Bat, SF., et al. (1988). Desgn consdeatons fo mcomachned electc actuatos, Sens Actuatos;14(3) pg Basha, MA., et al. (007). Desgn and Fabcaton of an Electostatc Mcomoto wth a Low Opeatng Voltage, The 14th Intenatonal Confeence on Sold-State Sensos, Actuatos and Mcosystems, Lyon, Fance. 3. Fan, LS., et al. (1988). IC-pocessed electostatc mco-motos. Poceedngs of the IEEE Intenatonal Electon Devces Meetng., pg Ghalchechan, N., et al. (008). Desgn, Fabcaton and Chaactezaton of a Rotay Mcomoto Suppoted on Mcoball Beangs - Jounal of Mcoelectomechancal systems, VOL. 17, NO. 3, pg Hallday, et al. (004) Fundamentals of Physcs, 7th Ed, Wley, 138 p., ISBN Sanaz Rezvan, et al. 90

5 6. Hsu, TR. (008). MEMS & Mcosystems: Desgn, Manufactue, and Nanoscale Engneeng, John Wley &Sons. 7. Jacobsen, SC., et al. (1989). The wobble moto: an electostatc, planetay-amatue, mcoactuato. Poceedngs of the IEEE Mco Electo Mechancal Systems Wokshop, pg Saajlc, E., et al. (010). Thee- Phase Electostatc Rotay Steppe Mcomoto wth a Flexual Pvot Beang. Jounal of Mcoelectomechancal systems, VOL. 19, NO., pg Saos, T., et al. (00). Investgaton of Cylndcal and Concal Electostatc Wobble Mcomotos, Elseve Jounal, Mcoelectoncs Jounal 33, pg Tmme, WSN., et al. (1987). Desgn Consdeatons fo a pactcal electostatc mco-moto, Sens Actuatos;11() pg Vnhas, HF., et al. (006). Optmzed Desgn of an Electostatc Sde-Dve Mcomoto, ABCM Symposum Sees n Mechatoncs Vol. pg Sanaz Rezvan, et al. 91