Principle and Analysis of a Novel Linear Synchronous Motor with Half-Wave Rectified Self Excitation

Transcription

1 Principle and Analysis of a Novel Linear Synchronous Moor wih Half-Wave Recified Self Exciaion Jun OYAMA, Tsuyoshi HIGUCHI, Takashi ABE, Shoaro KUBOTA and Tadashi HIRAYAMA Deparmen of Elecrical and Elecronic Engineering, Nagasaki Universiy 1-14 Bunkyo-machi, Nagasaki, Japan Phone: (Ex. 2665), Fax: oyama@ne.nagasaki- u.ac.ip Absrac Principle and analysis of a new ype LSM are presened. The moor is based on half-wave recified brushless exciaion. The field winding is shor-circuied hrough a diode and he armaure winding is convenional -phase windings. As he field flux is conrollable by varying armaure curren, field weakening operaion is possible in high speed region. The experimenal machine is designed and buil. The characerisics are esimaed heoreically and he inducance is compared wih measured value. Key words: Linear Synchronous Moor, Half Wave Recified Self Exciaion. 1 Inroducion Linear synchronous moors (LSM) have been widely used in various indusry applicaions, such as, ransporaion sysem, NC machine ools and home appliances. A perman en magne (PM) ype LSM is used in general applicaion, because he field exciaion is provided wihou DC power supply and he efficiency is high. If a d-axis curren big enough o offse agains he PM flux is provided, he field weakening operaion becomes possible in high speed region. However, a loss by he d-axis curren causes a drop in moor efficiency especially a low orque. In he previous papers, we proposed a half-wave recified brushless synchronous moor [1] [2] []. Balanced -phase currens in he -phase armaure windings of convenional synchronous moor produce he mmf ha has consan ampliude and roaes a synchronous angular velociy ω. If he ampliude of he balanced -phase currens is modulaed by an alernaing wave wih bias frequency ωb, he produced mmf pulsaes a ω b and roaes a ω. This pulsaing mmf induces he emf wih bias frequency ω b in he field winding. The field exc iaion of he half -wave recified brushless synchronous moor is obained by recifying he emf wih a diode conneced in series wih he field winding. In he previous paper [4], we proposed a new ype LSM, which is based on he half-wave recified brushless exciaion principle. In his paper, we describe he self-exciaion and hrus generaion principle of he novel linear synchronous moor wih half-wave recified self exciaion. We also show he experimenal machine and hen esimae he performance by simulaion. 2 Principle of New LSM 2.1 Moor Consrucion Fig. 1 shows a model of he proposed new LSM wih half-wave recified self exciaion. The LSM consiss of followings; (1) A LSM mover whose field winding is shor circuied hrough a diode. (2) A LSM saor wih hree phase armaure windings. () A PWM inverer 2.2 Volage Equaion Fig. 2 shows a dq-axis model of he new LSM. The field winding is shor-circuied hrough a diode. The dq-axis volage equaion is Fig. 1. Configuraion of New LSM.

2 Fig. 2. Equivalen Model on he dq-axis. e = ( d / d) ω + ri d d q ad e = ( d / d) + ω + ri q q d aq e = ( d / d) + ri fd fd a fd (1) The flux linkages are expressed in erms of self-inducance L and muual-inducance M as follows, d dd fd fd q = Li + M i = Li qq = M i + L i fd fdd fd fd (2) Where, e d is he d-axis volage, e q is he q-axis volage, e fd is he field volage. i d is he d-axis curren, i q is he q-axis curren, i fd is he field curren. r a is he saor winding resisance, r fd is he field winding resisance. d is he d-axis flux linkage wih he saor winding, q is he q-axis flux linkage, fd is he flux linkage wih he field winding. The ω is synchronous angular velociy. The mover posiion x in Fig. 1 is he posiion beween he saor a-axis and he mover q-axis. The synchronous angular velociy ω and synchronous mover velociy v s are as follow; π π ω = v x s τ = τ () The origin, x = 0, is defined where he saor a-axis is inline wih he mover q-axis. 2. Principle of Self Exciaion and Thrus Generaion Fig. illusraes he principle of he half-wave recified self-exciaion and hrus generaion. The following -phase currens, which synchronized wih mover posiion, are supplied o he -phase saor windings of Fig. 1; ia = Af()sin ω + 2Icosω ib = Af()sin( ω 2 π /) + 2I cos( ω 2 π /) ic = Af()sin( ω 4 π /) + 2I cos( ω 4 π /) (4) The firs erm on he righ-hand side of equaions (4) is exciaion curren, which varies wih sine of he mover posiion x and whose ampliude is a modulaion funcion A f (). A f () is a riangular wave funcion wih he effecive value of I f and bias frequency ω b. The second erm of he equaion is hrus curren componen. The d-axis curren becomes; i = (/2) A () (5) d f We can, herefor e, obain such a ravelling field as if produced by a single-phase curren i d in he d-axis winding W d which moves synchronously wih he mover. As a resul, a flux linkage M fd i d is generaed on he mover d-axis. The field curren i fd is induced in he field winding o keep he maximum value of he flux. The flux linkage fd is he sum of flux linkages; M fd i d provided by he saor exciaion curren and L fd i fd by he mover field curren. If inducance of he circui is large enough, fd is kep consan and held o i s maximum by he diode. The q-axis curren becomes; i q = I (6) Fig.. Principle of Thrus Generaion.

3 We can obain such a ravelling field as if produced by a direc curren iq o he q-axis winding Wq which moves synchronously wih he mover. Then he hrus is obained from he following equaion. π F = ( diq qd i ) (7) τ Assuming ha r a and r fd equal zero, hen he hrus is F = π (1 σ) LII ( σl L ) A () I d f d q f τ (8) Though a pulsaing componen exiss in his hrus as shown in Fig., i is no serious problem for pracical usage by suiable choosing he bias frequency ω b and (σ L d L q ). Experimenal machine Fig. 4 illusraes he designed experimenal moor. Table 1 shows he specifics and consans of he experimenal machine. Fig. 5 shows phoos of he new ype LSM and he mover, which we buil. The full lengh of a saor is 2m. The cushion is aached on boh side in order o proec he mover. A wire ype linear encoder is aached o he mover. (I) The circui parameers such as self - and muual- inducances of saor armaure windings and a mover field winding are esimaed using he FEM analysis. Magneic sauraion of he core is aken ino accoun. (II) The equivalen circui is creaed using he circui parameer s obained a sep (I) and hen he performances are compued by a circui simulaor. 4.2 Inducance and flux linkage By FEM analysis, we obain he maximum value L max and minimum value L min of self inducances of he saor armaure windings, he maximum value M max and minimum value M min of muual inducances beween he armaure windings, he maximum muual inducance M f beween he armaure and he mover field windings, and he maximum self inducance L fd of he field winding. Fig. 6 shows he FEM model of he experimenal moor. The number of elemens is 1075 and he number of nodes is Table 2 shows he esimaed inducances. As FEM sofware, we use "ANSYS", Cyberne Co.. 46mm 0mm 20mm 4 Analysis 0.6mm 8mm 4.1 Procedure Design or analysis is carried ou by he following sequence. 54mm 10mm 10mm 20mm Fig. 4. Dimensions of Experimenal Moor. Table 1. Design Parameers of Experimenal Moor. Raed Oupu 0.8 kw Raed Volage 200 V Raed Curren 4 A Raed Speed 0.5 m/s Number of Poles 4 Saor Lengh 1990 mm Pole Pich 60 mm Sack Heigh 50 mm Windings Double Layer Disribued Pich Winding Diameer 0.8mm Saor Winding 85 urns / pole Mover Winding 00 urns (a) The appearance of LSM. (b) The mover Fig. 5. Phoo of Experimenal Moor.

4 Fig. 6. FEM Model of Experimenal Moor. Table 2. Inducance of Experimenal Moor. Lmax 125.5mH Lmin 97.1mH M max 69.4mH M min 40.4mH M f 240.5mH L fd 976.7mH R s 12.48Ω R m 2.8Ω Here, assuming ha each flux linkages vary wih sinusoidal waveform, he flux linkages are expressed as follows, [ ] [ ][ ] = L i + M i (9) = M [ i ] + L i abc ss abc sf fd fd sf abc fd fd Mmax : Saor Muual-Inducance (x = τ / ) M min : Saor Muual-Inducance (x = 5τ / 6) l s : Saor Leakage Inducance M f : Maximum Saor-Mover Muual Inducance L fd : Maximum Mover Self -Inducance On he exp erimen, a firs, DC resisances of he saor and mover windings are measured by he volage drop mehod. Nex, he inducances are measured using AC curren (60Hz, 1.0A). Fig. 7 shows he measured inducances. The black square mark shows he heoreical inducance using FEM. The experimenal resuls agree well wih he heoreical one. Some errors beween hem may depend on suble difference of boundary condiions and iron core parameer or effec of he punch hole which is used o fix he iron core. Where, L M M aa ab ac [ Lss] = Mab Lbb M bc M M L ac bc cc 1 La Lmcos2ω Ms Lmcos2 ω π 1 2 = Ms Lmcos2 ω π La Lmcos2 ω π 2 Ms Lmcos2 ω π Ms Lmcos2ω 2 Ms Lmcos2 ω π M L cos2ω s m 1 L L cos2 ω π a m (a) Saor winding self-inducance. (b) Saor winding muual-inducance. M sinω f M af 2 M = M = M sin ω π sf bf f M cf 4 M f sinω π [ ] L = ( L + L )/2 a max min L = ( L L )/2 m max min (10) M = ( M + M )/2 = ( L l )/2 s max min a s L max : Saor Self -Inducance (x = τ / 2) L min : Saor Self-Inducance (x = 0) (c) Saor and mover muual-inducance. (d) Mover winding self-inducance. Fig. 7. Measured and Esimaed Inducances.

5 4. Performance characerisics For compuing he performance characerisics, he circui simulaor "SIMPLORER", Ansof Co., is used. The model of no only he LSM bu also he conrol sysem is creaed, and he ime varying characerisics of curren, flux linkage, and hrus are compued. Using he flux linkage of he equaion (9), he -phase volage are wrien as follows. [ e ] = [ R ][ i ] + p[ ] abc s abc abc e = ri + p fd fd fd fd (11) Where, p is differenial operaor. Since each inducance is a funcion of mover posiion, he equaion (11) changes as follows. ( ) [ e ] = [ R ][ i ] + p [ L ][ i ] + abc s abc ss abc M sf ifd = [ Rs][ iabc] + ( p[ Lss] )[ iabc] + [ Lss] ( p[ iabc] ) + ( p M sf ) i + M fd sf ( pi fd ) (12) ( [ ] ) ( )[ ] ( [ ]) ( pi fd ) e = ri + p M i + L i fd fd fd sf abc fd fd = ri + p M i + M p i + L fd fd sf abc sf abc fd (1) On he basis of he above equaion, he LSM model was consiued using he circui simulaor and is shown in Fig. 8. In his model, he -phase armaure windings and he field winding shor-circuied by a diode are modeled by analog elemens. The Bemf_a, Bemf_b, and so on modeled by volage source are back emf developed on he each winding. The back emf and hrus are defined by he equaions in he simulaor. Bu hese equaions are omied here. Fig. 9 shows he conrol sysem model. The conrol sysem consiss of a gae drive circui and a PWM inverer. The hrus characerisics are compued using above simulaion model. In his simulaion, he exciaion ampliude command If = 1.0A, he hrus curren command I = 4.0A, synchronous mover velociy v s = 0.5m/s (f = 4.17Hz), bias frequency ω b = 60Hz. Fig. 10 shows he simulaed waveforms of command curren and inverer oupu curren. Inverer oupu curren is well followed o command value a inverer inpu volage V in = 180V. Fig. 11 shows he field winding curren, field winding flux linkage and hrus waveform. Though a pulsaing componen exiss in his hrus, average hrus is 55.7N a hrus curren command I = 4.0A. Fig. 8. Simulaion Model of Experimenal Moor. Fig. 9. Simulaion Model of Conrol Sysem. Fig. 10. Saor Curren of a-phase.

6 5 Conclusions A novel linear synchronous moor wih half-wave recified self-exciaion was proposed and he principle, analysis and experimenal LSM were described. The inducance was compued using he FEM and compared wih he experimenal resuls. The performance characerisics were simulaed by he circui simulaor. Now, he drive sysem of his LSM is under es. We will repor he oupu characerisic s es resuls and he opimum design for reducing he pulsaing hrus in fuure. Fig. 11. Simulaion Resuls. Fig. 12 shows he performances including effec of varying he exciaion ampliude command from I f = 1.2A o 0.8A a = 0.48s. Speed reference v s = 0.5m/s (Frequency f = 4.2 Hz) and hrus curren command I = 4.0 A. The field curren i fd induced in he field winding pulsaes a bias frequency ω b = 60Hz. I is confirmed ha he field curren, flux linkage and hrus can be conrolled easily by he exciaion command. Reference [1] J. Oyama, S. Toba, T. Higuchi and E. Yamada, "The Characerisics of Half-Wave Recified Brushless Synchronous Moor", Proc. of Beijing ICEM, Vol. 2, pp , [2] J. Oyama, T. Higuchi, T. Abe and E. Yamada, "Characerisics of Half -Wave Recified Brushless Synchronous Moor wih Permanen Magnes", Proc. of European Conference on Power Elecronics and Applicaions, vol., pp , [] J. Oyama, T. Higuchi, T. Abe and E. Yamada, "Analysis of Half-Wave Recified Brushless Synchronous Moor wih Permanen Magnes", Conference Record of IEEE Indusry Applicaions Sociey Annual Meeing, pp , [4] J. Oyama, T. Higuchi, T. Abe, H. Tanaka and E. Yamada, "A Novel Linear Synchronous Moor wih Half-Wave Recified Self Exciaion", The Third Inernaional Symposium on Linear Drives for Indusry Applicaions, pp , Fig. 12. Field Flux Conrol.