OPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS

Transcription

1 OPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS Ronald De Fou Depatment of Electical & Compute Engineeing, The Univesity of the West Indies St. Augustine, Tinidad Emily Ramouta Univesity of Tinidad & Tobago, Point Lisas Campus, Tinidad Juliet Romeo Depatment of Electical & Compute Engineeing, The Univesity of the West Indies St. Augustine, Tinidad Bian Copeland Depatment of Electical & Compute Engineeing, The Univesity of the West Indies St. Augustine, Tinidad Abstact A bushless dc moto can be descibed as an inveted bush dc moto with its magnet being the oto and its stationay windings foming the stato. This design povides many advantages ove the bush dc moto. The opeational chaacteistic of a moto is impotant fo its contol, modeling and deiving optimum pefomance. Howeve, a eview of the liteatue did not pesent moto opeation based on the vaious phenomena occuing in the moto. Smooth and efficient opeation of the bushless dc moto elies on a knowledge of the enegization sequence of the windings and a technique fo its detemination is pesented. The application of the vecto method of analysis to the Copyight 2007 by Ronald De Fou All ights eseved. No pat of this publication may be epoduced in any mateial fom without the witten pemission of the Copyight Owne, except in accodance with the povisions of the Copyight Act 1997 (Act No. 8 of 1997) o unde the tems of a License duly authoized and issued by the Copyight Owne.

2 bushless dc moto togethe with developed enegization sequence, poduced continuous electomagnetic toque utilizing the coss poduct of the peak flux linkage vecto due to the oto magnet and the stato cuent vecto and classifies this moto as an ac synchonous moto. Keywods: Opeational; chaacteistics; bldcm. 1. Intoduction Bushless dc motos ae apidly gaining populaity in the appliance, automotive, aeospace, consume, medical and industial automation industies. As a esult of the absence of mechanical commutatos and bushes and the pemanent magnet oto, bushless dc motos have many advantages ove the bush dc and induction moto [1-6]. Some of the advantages of bushless dc motos ae: (1) High powe density, low inetia and high toque to inetia atio and high dynamic esponse due to the small size, low weight and high flux density neodymium-ion-boon pemanent magnet oto. (2) High efficiency due to the low oto losses as a esult of the absence of cuent caying conductos on the oto and educed fiction and windage losses in the oto. (3) Long opeating life and high eliability due to the absence of bushes and metallic commutatos. (4) Clean opeation due to the absence of bushes, esulting in no bush dust duing opeation and allowing fo clean oom applications. (5) Low audible noise opeation due to the absence of bushes, commutatos and smooth low ai esistance oto. (6) High speed opeation in excess of 80,000 pm is possible, since these motos ae electonically commutated and ae not subjected to the limitations of conventional commutations. (7) Low themal esistance since most of the machine losses occu in the stationay stato, theeby allowing heat dissipation by the pocess of diest conduction. In addition, since the oto losses ae small, heat tansfe to machine tools and wok pieces when these motos ae utilized in machine tools is minimal, theeby educing the effects of heat on the machining opeation. (8) Low EMI/RFI due to the absence of bushes and metallic commutatos. 2

3 As a esult of the above featues, the bushless dc moto has been eplacing othe motos in many industies. The household appliance industy has been one of the fastest gowing end poduct maket fo adjustable speed dives [7]. Bushless dc motos ae now being used in efigeation compessos, washing machines, fans, food pocessing equipment and vacuum cleanes in the household appliance industy. In the automotive industy, bushless dc motos ae being used in fuel pumps, ai-condition blowes and engine cooling fans. The exceptional featues of bushless dc motos descibed above ae esponsible fo thei widespead use in many industies, howeve, a eview of the liteatue did not povide moto opeational chaacteistics based on the vaious phenomena occuing in the moto. Since the opeational chaacteistic of a moto is impotant fo its contol, modeling and deiving optimum pefomance, this pape is focused on the detemination of the enegization sequence of the moto, its effect on electomagnetic toque poduction and the utilization of the toque poduction mechanism fo the classification of the bushless dc moto. 2. Detemination of Enegization Sequence fo Bushless DC Motos Thee-phase bushless dc motos ae opeated by enegizing two of its thee phase windings at a time. Howeve, fo continuous opeation of the moto in a paticula diection of otation, the pai of windings to be enegized is dependent on the oto position. The dependence of phase winding enegization on oto position lies in the fact that the oto magnet of the moto induces voltages in the phase windings duing otation, and efficient moto opeation is accomplished when the enegized windings ae expeiencing thei steady o non-vaying back emf. Hence, knowledge of the back emf of each phase winding as a function of oto position is necessay in the detemination of the phase winding enegization sequence. The detemination of phase winding back emf as a function of oto position fo a thee-phase bushless dc moto was obtained by opeating the bushless dc machine in geneato mode. In this test, a bush dc moto was used as a pime move to dive the thee-phase, two-pole bushless dc machine at constant speed in an anti-clockwise diection. The appaatus used is shown in Fig. 1. The otating flux of the two-pole bushless dc machine oto induces voltages in each phase winding. Fo a thee wie sta connected bushless dc machine, the sta point is not 3

4 accessible and the thee esistos labeled R, in sta connection wee used to obtain machine phase voltages fom line to the sta point n fomed by the thee esistos. Fig. 1 Bushless DC Machine Opeated as a Geneato The esulting geneated phase voltages as functions of oto position θ, elative to the stato fo the two-pole, thee-phase bushless dc machine ae shown in Fig. 2(a). These geneated phase voltages ae tapezoidal in natue, having flat tops of 120 electical degees and positive and negative slopes each of 60 electical degees. Thei magnitudes fo a paticula bushless dc machine ae dependent on the speed of otation of the machine. The thee geneated phase voltages e an, e bn and e cn ae displaced 120 electical degees fom each othe as shown in Fig. 2(a), and thei vaiations ae dependent on oto position, since, dλ dθ dλ dλ e = =. = ω (1) dt dt dθ dθ whee, e is the geneated voltage, λ is the flux linkage, θ is the oto position and ω is the angula velocity of the oto. Fom Eq. (1), the geneated voltage wavefom is a function of oto position, theeby poviding an indication of the oto position at any time. The wavefoms of Fig. 2 eveal that fo a two-pole machine, one electical cycle of geneated wavefom was completed in one mechanical evolution of the oto. Howeve, in the case of a fou-pole oto, thee would be two electical cycles of geneated voltage wavefom fo one mechanical evolution of the oto. Fig. 2(a) eveals that two phase voltages ae of constant value fo 60 electical degees and fo a sta connected stato as shown in Fig. 3, line voltage wavefoms can be dawn fom two phase voltages. These line voltage geneated wavefoms e bc, e ca and e ab ae shown in Fig. 2(b). Since two phase windings of a sta connected bushless dc moto ae expeiencing a constant 4

5 geneated line voltage fo 60 electical degees, then efficient opeation of the moto is obtained when the two enegized windings ae expeiencing thei constant back emf. Fig. 2 Bushless DC Moto Voltages (a) Geneated Phase Voltages e an, e bn and e cn (b) Geneated Line Voltages e bc, e ca and e ab (c) Supply Line Voltages V bc, V ca and V ab Hence, the geneated line voltage wavefoms shown in Fig. 2(b), which ae functions of oto position θ, ae used to detemine the sequence of enegization of the moto windings fo a paticula diection of otation. Theefoe, fo anti-clockwise opeation of the bushless dc moto, using Fig. 2(b), and stating with oto position at θ = 0, the winding pais should be enegized in the sequence ac, bc, ba, ca, cb, ab and ac again, with each winding pai being enegized fo 60 electical degees [8-9]. It must be noted that fo clockwise opeation of the bushless dc moto, the sequence of enegization of the winding pais must be evesed and would take the fom ab, cb, ca, ba, bc and ac. 5

6 Fig. 3 Sta Connected Bushless DC Moto Fig. 2(c) shows the line voltages fo efficient moto opeation, placing the supply voltages in phase with the geneated o back emf line values. The line supply voltages ae geate than the line back emfs to ensue that electomagnetic toque is developed by the machine. The development of the enegization sequence fo a thee-phase bushless dc moto, as a function of oto position and hence back emf, fo otation in a paticula diection has been lacking in the liteatue. The mateial pesented above can be used in the absence of the manufactue s data to detemine the enegization sequence of a bushless dc moto. 3. Toque Poduction and Opeation of BLDCM Using Vecto Analysis The theoy of vecto analysis of a thee-phase stato, justifying the existence and location of vecto cuents and voltages and the equality of scala and vecto cuent magnitudes was pesented in [10]. A coss sectional view of a two-pole, thee-phase bushless dc moto is shown in Fig. 4. The oto magnet is shown with a educed diamete and hence an enlaged ai-gap fo illustation puposes. The two-pole oto is assumed to be otating at a constant angula velocity ω ad/sec in an anticlockwise diection. At the instant of obsevation in Fig. 4, it s d-axis which is defined as the cente of the south pole is at the position θ = 0, which coesponds to the θ = 0 point on the hoizontal axes of the wavefoms in Fig. 2. At this oto position θ = 0, winding pai ac would begin to expeience thei constant back emf E ac due to the effect of the oto magnet on the stato windings as shown in Fig. 2(b). Hence, at this oto position θ = 0, winding pai ac must be enegized with a supply voltage of V ac volts to oppose the constant back emf E ac pesently 6

7 expeienced by the windings. The magnitude of the supply voltage must be geate than the constant back emf developed by the windings as shown in Fig. 2(c) and sufficient to develop electomagnetic toque to sustain the oto speed. Fig. 4 Stato And Roto Vectos Fo Two-Pole, Bushless DC Moto The enegization of stato winding pai ac with supply voltage V ac and the esulting phase cuents ae shown in Fig. 5(a). The enegization of winding pai ac esults in the cuents i a though winding aa' and i c though winding cc' espectively, whee, ia = ic. These cuents establish stationay cuent vectos i a and i c along the positive magnetic axis of winding aa' and negative magnetic axis of winding cc' espectively [10]. The vecto addition of these two stationay cuent vectos i a and i c, esults in the esultant stationay cuent vecto i ac as shown in Fig. 4. 7

8 Fig. 5 Enegization Sequence of Two-Pole, Thee-Phase Stato At this oto position θ = 0, the esultant stationay cuent vecto i ac, is displaced fom the oto flux vecto φ by an angle of 120 electical degees. The esultant stationay stato flux m vecto φ ac, poduced by cuent vecto i ac, establishes a magnetic south pole at the aow head of the φ ac vecto, while a noth magnetic pole exist at the aow head of the oto flux vecto φ m. The inteaction of these flux vectos φ ac and φ m develops electomagnetic toque, esulting in the oto and its flux vecto being pulled towads the esultant stationay stato flux vecto φ ac, causing otation of the moto in an anti-clockwise diection. The electomagnetic toque T e developed by the machine is given by the coss poduct of peak flux linkage vecto λ m (whee, λm = N φ ) and cuent vecto i ac [11], hence, m ( φ ) T e = λm i ac = N m i ac (2) T e = N φ i Sinα k (3) m ac whee, φ m is the oto flux vecto, α is the angle between vectos φ m and i ac in Fig. 4, and k is the unit vecto whose diection is pependicula to the plane in which φ m and i ac exists. Eq. (3) 8

9 indicates that the developed electomagnetic toque vaies with the magnitude of the esultant stationay cuent vecto i ac and Sin α, since, N and φ ae constants. m The utilization of the developed enegization sequence fo the bushless dc moto, fo oto positions in the ange 0 θ 60 esulted in the electomagnetic toque equation pesented in Eq. (3). The electomagnetic toque developed by the moto poduced anticlockwise otation, esulting in an incease in the angle θ fom its 0 position. This incease in the angle θ in an anticlockwise diection, esults in a decease of angle α fom its initial 120, theeby inceasing the electomagnetic toque developed by the moto, povided thee is no decease in the magnitude of the esultant stationay cuent vecto i ac. When α = 90, the developed toque is maximum, but as α deceases and eaches 60, the developed electomagnetic toque deceases to the value when θ was 0. When θ > 60 in Fig. 2(b), the back emf in winding pai ac is no longe at its constant value fo this speed of opeation, and the electomagnetic toque developed fo α < 60, would be less than the values obtained fo 0 θ 60 and 60 α 120. If winding pai ac emains enegized up to the point whee θ = 120, the angle between the vectos φ m and i ac would be α = 0, and the electomagnetic toque developed using Eq. (3) would be zeo. In addition to zeo toque being developed at θ = 120, the oto would be locked in this zeo toque position, since the noth pole of the oto magnet would be aligned with the south pole poduced by esultant stationay flux vecto φ. Hence, fo continuous toque poduction ac and otation of the moto and efficient enegy convesion fom electical to mechanical, winding pai ac must not emain enegized fo θ > 60. Examination of Fig. 2(b), eveals that at θ = 60, winding pai bc has just begun to expeience its constant back emf E bc, hence, winding aa' must be commutated and winding bb' bought into conduction with winding cc'. That is, winding pai bc must be enegized with V bc at θ = 60 as shown in Figs. 2(c) and 5(b). The enegization of winding pai bc with supply voltage V bc esults in the cuent i b though winding bb' and i c though winding cc'. These cuents establish stationay cuent vectos i b and i c, along the positive magnetic axis of winding bb' and negative magnetic axis of winding cc' espectively. The vecto addition of these two cuent vectos i b and i c, esults in the esultant stationay cuent vecto i bc as shown in Fig. 4. At this oto position θ = 60, the 9

10 esultant stationay cuent vecto i bc, is displaced fom the oto flux vecto φ by an angle of m 120 electical degees. The inteaction of these vectos i bc and φ develops electomagnetic m toque, esulting in the oto and its flux vecto being pulled towads the esultant stationay stato flux vecto φ, causing otation to continue in an anti-clockwise diection. The pocess of bc toque poduction continues until θ = 120 and a new winding pai ba is bought into conduction as shown in Fig. 2(c). Similaly, the enegization of the othe phase windings shown in Figs. 5(c) to (f), esults in the poduction of esultant stationay cuent vectos i ba, i ca, i cb and i ab espectively as shown in Fig. 4. These esultant stationay cuent vectos occupy a fixed position in the stato. They ae displaced fom each othe by an angle of 60 electical degees and thei magnitudes ae dependent on the cuent flowing in the phase windings. The electomagnetic toque developed by the machine is not constant thoughout each 60 movement of the oto and is given by T = λm i Sinα k (4) e xy whee, x is the phase winding teminal connected to the positive end of the supply voltage, y is the othe phase winding teminal connected to the negative end of the supply voltage and α is in the ange 60 α 120. The electomagnetic toque developed by the moto fo a fixed stato winding cuent I fo one evolution of the oto and ignoing the electomagnetic toque developed duing commutation is shown in Fig. 6 [11]. Fig. 6 Electomagnetic Toque Developed in One Revolution 10

11 The events descibed above fo efficient opeation of the two-pole, thee-phase bushless dc moto, showing the ange of oto positions fo a pai of windings to emain enegized, the coesponding back emf of the enegized windings and the coesponding electomagnetic toque developed ae summaized in Table 1 below. Table 1 Roto Position, Constant Back EMF, Windings Enegized and Toque Developed Roto Position Range Constant Back EMF Windings Enegized Electomagnetic Toque Developed 60 α θ 60 E ac ac λ m i ac Sinα 60 θ 120 E bc bc Sinα 120 θ 180 λ m i bc E ba ba Sinα λ m i ba 180 θ 240 E ca ca λ m i ca Sinα 240 θ 300 E cb cb Sinα 300 θ 360 λ m i cb E ab ab Sinα λ m i ab 4. Classification of Bushless DC Moto Electic motos ae classified into two main categoies, namely bush dc and ac bushless motos as shown in Fig. 7 and pesented in [1]. Bush dc motos ae made up of statos consisting of poles poduced by pemanent magnets o dc excited magnets, which give ise to static magnetic fields acoss the oto. The oto of these bush dc motos consists of windings connected to mechanical commutatos to facilitate the application of a dc powe souce. Cuent flow though these oto windings takes place though cabon bushes which make contact with the commutatos, theeby poducing a magnetic field and a cuent vecto which emains in a elatively fixed position elative to the stato. The elatively stationay cuent vecto of the oto inteacts with the stationay magnetic field of the stato, developing electomagnetic toque given by the coss poduct of these two vectos. Fig. 8(a) shows the bush dc machine stationay flux 11

12 linkage vecto φ N and the elatively stationay oto cuent vecto s i The electomagnetic toque developed by the machine is given by: ( φ ) sepaated by an angle α. T e = N i. (5) s Thee-phase ac machines ae divided into two categoies, synchonous and asynchonous. The statos of synchonous and asynchonous ac machines ae supplied with thee-phase ac voltages and the esulting thee-phase ac cuents poduce a otating cuent vecto and magnetic field, both of which ae of constant magnitude and otate at the angula velocity of the supply voltage. Fig. 7 Classification of Electical Motos The diffeence between synchonous and asynchonous machines lies in the fact that the oto of an asynchonous machine deives its electical enegy fom the stato by the pocess of induction to poduce the oto s cuent vecto and magnetic field. This pocess esults in the speed of the oto being lowe than that of the stato s otating magnetic field. Howeve, the otos of synchonous machines possess thei own magnetic field in the fom of fixed magnets o dc excited magnets and do not depend on induced cuents fom the stato s magnetic field. This esults in the oto of synchonous machines having the same speed as the stato otating cuent 12

13 vecto and magnetic field. Although the oto speed of asynchonous machines ae lowe than the speed of the stato otating flux, the speed of the oto flux is the same as that of the stato flux. The stato cuent vectos, oto flux vectos and thei speeds, togethe with the oto speed of synchonous and asynchonous machines ae epesented in Figs. 8(b) and 8(c). In Fig. 8(b), the oto flux vecto and stato cuent vecto of the asynchonous machine ae otating at the angula velocity of the supply voltage ω s, while the oto otates at an angula velocity ω m which is lowe than ω s. Howeve, the oto s flux vecto and stato cuent vecto and the oto of a synchonous machine all otate and the angula velocity of the supply voltage ω s as shown in Fig. 8(c). The electomagnetic toque developed fo synchonous and asynchonous machines in Fig. 8 is given by ( φ ) T e = N i s.. (6) Fig. 8 Flux and Cuent Vectos of Electical Machines (a) Bush DC Moto (b) Asynchonous Machine (c) Synchonous Machine It is clea fom Fig. 8, that dc machines ae chaacteized by stato flux vecto and oto cuent vecto both occupying a elatively fixed position in the machine space, while, ac machines ae chaacteized by oto flux vecto and stato cuent vecto both otating at the angula velocity of the stato supply voltage within the machine space. The enegization of a pai of stato phase windings of a bushless dc moto fo 60 electical degees esults in the poduction of a otating 13

14 oto flux vecto and a stationay stato cuent vecto. This clealy does not fit the classification of a dc machine, although the stato windings ae enegized with a dc supply duing this inteval. In addition, examination of the oto flux vecto and the stato cuent vecto ove a cycle as shown in Fig. 4, also eveal thei non-stationay natue, with the stato cuent vecto always leading the oto flux vecto and they complete an electical cycle in the same time. Futhe to this, the line voltage wavefoms of Fig. 2 ae not dc, but altenating in natue and ae simila to the tapezoidal back emf of the moto when opeated as a geneato. These popeties clealy indicate that the bushless dc moto is an ac synchonous moto although the stato windings ae enegized by dc voltages and the toque-speed chaacteistics of the moto is simila to that of the bush dc moto [12]. 5. Conclusion Smooth and efficient opeation of the bushless dc moto elies on the knowledge of the enegization sequence of the windings. This sequence which is supplied by moto manufactues, can be obtained by opeating the moto in geneato mode and employing the technique pesented in this pape. The application of this enegization sequence, which is a function of oto position, poduces esultant stationay cuent vectos, which inteact with the oto flux linkage vecto to develop electomagnetic toque. Hence the vecto method of analysis, when applied to bushless dc motos, displays the toque poduction mechanism in the moto and pesents a poweful insight into the physical phenomena occuing in the moto. In addition, the coss poduct used in the computation of the developed electomagnetic toque of the moto, evealed the impotance and necessity of phase winding commutation in ode to sustain continuous moto opeation. Finally, the chaacteization of the bushless dc moto as an ac o dc moto was addessed. The chaacteistics of the moto clealy indicate that it is an ac synchonous moto, although the stato windings ae enegized by dc voltages and the toquespeed chaacteistics of the moto is simila to that of the bush dc moto. Refeences 1. Pillay P. and Kishnan R., Application Chaacteistics of Pemanent Magnet Synchonous and Bushless dc Motos fo Sevo Dives, IEEE Tans. Industy Applications, vol. 27, no. 5, Sept./Oct

15 2. Babyak R., New Bidge to Bushless, Appliance Manufactue, Sept Schille H. and Weiman I., Low-Cost Toque, Appliance Manufactue, Jan., Lloyd J. D., and Sood P. K., Defining ASD, Appliance Manufactue, Aug., Yedamale P., Bushless DC (BLDC) Moto Fundamentals, AN855 Micochip Technology Inc., July Hill C., An Intoduction to Low Voltage DC Motos, AN10293_1 Philips Semiconductos, Ma., Kapoch T., Diving the Futue, Appliance Manufactue, Sept De Fou R., A Self-Stating Method and an Appaatus fo Sensoless Commutation of Bushless DC Motos WIPO Publication No. WO 2006/ A1 July 13, De Fou R., A Self-Stating Method and an Appaatus fo Sensoless Commutation of Bushless DC Motos TT Patent TT/P/2006/00070, 27 Octobe, De Fou R., Ramouta E., Romeo J., and Copeland B., Vecto Analysis of a Thee-Phase Stato, Open Access, Mach 30, De Fou R., Ramouta E., Romeo J., and Copeland B., Pulsating Toque in Bushless DC Motos, Open Access, Mach 30, J. R. Hendeshot and THE Mille, Design of Bushless Pemanent-Magnet Motos, Magna Physics Publishing and Claendon Pess Oxfod,