Tree-Pase nduction Motor wit Spiral Seet Rotor Mujal Rosas, Ramon; Boix Aragonès, Oriol Member, ; Marín Genescà, Marc TCHNCA UNVRSTY OF CATAONA TSAT, Colom St., 08 Terrassa (Barcelona), Spain Tel.: +0034 / (93) 739.80.35 Fax: +0034 / (93) 739.8.36 mujal@ee.upc.edu boix@ee.upc.edu marin@ee.upc.edu UR: ttp://www.upc.es Abstract mprovements on te torque wit low currents using wit spiral seets are analyzed. Several s and s ave been built combining different constructive and mecanical caracteristics of te related elements: inertias, constructive materials, geometrical sapes of te seets and geometrical disposition of te seets. Tese different types of motors ave been simulated using computer aided tools and ten tested in te laboratory. Finally, four s (000, 500, 500-type A, and 3000 rpm) aving te same constructive parameters, ave been simulated and tested wit te following s types: solid, solid wit diamagnetic rings, drag cup, and simple and double squirrel cage ; tese results ave been compared to tose obtained wit te seven variants of spiral seet presented in tis paper. ndex Terms lectric macines, Special macine, Spiral seet, Tree-Pase asyncronous motor. Tecnical Tracks T: lectrical macines and drives.. NTRODUCTON T e s of conventional asyncronous motors are formed by magnetic seets packed above te saft of te macine. Te rotating magnetic field created by te, induces currents parallel to te saft and so uprigt to te seets []. Tose currents cannot flow between te seets if tey are electrically isolated, being necessary te intervention of conventional squirrel cage rings to close te electric circuit and tus te currents can circulate. n table te basic mecanical caracteristics of some s tested are presented [3]. Tese s ave te same dimensions and tey are assembled to s of 000 rpm, 500 rpm and 3000 rpm, aving te latter te same constructive parameters. Rotor types TAB MAN MCHANCA CHARACTRSTCS OF ROTORS Mass (kg) nertia (kg m ) Kinetic energy at 500 rpm (J). MOTOR WTH SPRA SHT ROTOR Forming a wit spiral sape seets [8], distributed in a radial disposition around te saft, it is possible to generate a magnetic field in te peripery, inducing periperal emf, and currents along te same seets, tat are only active in teir peripery. Te periperal currents of tis ave more section to circulate, compared to a normal cage current. Fig.. Rotors: wit double cage A. Spiral seet s B and C types. Rotor dimensions (mm) Squirrel cage 3.440.77 0-3 33.59 79.5 x 7 Solid 3.60.860 0-3 35.83 79.5 x 7 Solid wit ring 3.580.88 0-3 34.889 79.5 x 7 Diamagnetic ollow 0.60 4.898 0-4 6.046 79.5 x 7 Winding 3.0.465 0-3 30.4 79.5 x 7 Spiral seet, A 3.60.496 0-3 30.793 79.5 x 7 Spiral seet, B 3.36.556 0-3 3.533 79.5 x 7 Spiral seet, D 3.040.40 0-3 9.6 79.5 x 7 Spiral seet, Z 3.30.65 0-3 3.384 79.5 x 7 Figure 4 sows a plain representation of te disposition of te seets [9]. Tere are two zones: one wit active currents going 978--444-666-0/08/$5.00 '008 455
troug and te oter is used to receive te possible returning currents (A returning currents proposal). σ3 σ3 σ σ Fig.. Section of a tree-pase asyncronous torque-motor.. ANAYSS OF CONDUCTVTY Tis section analyzes te distribution of currents vs. te flux density of foil motors wit different electric conductivity (3, and 60 MS/m eac one). Te induction distribution and also te current density in te foils for 5 Hz frequency are analyzed [7]. Figure 0 sows tat increasing conductivity of te material, te current distribution becomes more superficial. From te analysis we can bear out te existence of a field created by te as te conductivity of te material increases. According to te simulations, te net field in te motor is weaker as te produces a bigger field. Tis penomenon is only possible if tere is a bigger pase between te two fields ( and ). Tis space pase means a cange in te resistance and reactance properties in te just as it is foreseeable. A bigger conductivity obviously implies a more inductive loading tat generates a reactive power. Te optimization in te selection of materials relapses in te evaluation of te product of te primary current by te factor of motor power wit te useful couple tat it can develop. Tis conclusion is very important because it is applicable to any part of te motor for deciding te application of te best materials. Supposing te reactance variation in te very small, since its frequency is weak, it is possible to approac te variation of te angle of temporary pase out between te current and te electromotive force as: θ arctg ( K σ ) Were σ is te conductivity. Now, te widt variation of B in relation to te variation gives: r and B () R + j X () Fig. 3. Flux and current densities simulations for different conductivity values. Motor wit spiral seet type A. Wit teir corresponding module : r R + X Finally, making a series development: σ60 σ60 r X ( R j X ) X Grapically te dependence of te current module wit te conductivity, for very small R gives: K K σ R 3 R + X (3) (4) (5) 456
Je, MA/m Current (A) Current density (MA/m ) m[je], MA/m Conductivity (S) Fig. 4. Current-conductivity in a motor wit spiral seet. σ Re[Je], MA/m a) Te obstacles of air tat finds te flow facilitate te creation of a caracteristic reluctance of te motor. Tis penomenon facilitates in transitory a very quick answer. Te ig reluctance also comes accompanied by a low inertia tat also supposes a low mecanical and electric time constant. Current density (MA/m ) Je, MA/m m[je], MA/m Re[Je], MA/m V. CURRNT DNSTY DSTRBUTON Troug FMM simulations te distribution of current density in te [6] can be determined. Te real component of tis current density is represented in grey (figure 3). Seet Seet Current density (MA/m ) Je, MA/m m[je], MA/m Re[Je], MA/m b) c) Fig. 5. Current density distribution. Seet 3 t is important to remark te evolution of current density wit te radius, wic is represented by sine wave function as it was expected. Tis current density versus te radius follows a yperbolic distribution, in particular, follows a yperbolic tangent. Te values of some electric magnitudes can also be observed in tese graps. For example, te value of te maximum current density in te is approximately.6 A/mm. Fig. 6. Current density distribution a) seet, b) seet, c) seet 3. V. THRMA VAUS Termal experiments demonstrate tat te motors present different caracteristics wit respect to conventional squirrel cage motor, since te current, tat is te main cause of te increase of te temperature in te winds, practically does not cange wen canging te load [8]. Tis makes tese motors able to work in regimes wit ig slip witout canging teir termal conditions. Tis fact is almost impossible in squirrel cage motors. On te oter and, te spiral seet motors are more resistive tan squirrel cage motors and we can appreciate an increase of temperature wit respect to squirrel cage s wen tey are working in te same conditions, but it is in any case muc smaller tan te increase tan undergoes oter s like te solid. 457
00 80 Temperature (ºC) 60 40 0 0 0 0 0 30 40 50 60 70 Time (min) S.5% S0% S5% S.5% S0% S5% Fig. 7. Termal test of motor wit spiral seet at 3000 rpm: evolution of - temperature. V. MCHANCA NRTAS AND OSSS Te study of mecanical losses due to te bearings, fan and air friction as been made, getting reasonable values compared to te rest of conventional motors []. Te inertias are very similar to squirrel cage motor values; and in te worst case a ligt inertia increase in te spiral seet motor are detected, wic ave not te macined. Fig. 9. Torque (red) and speed (blue) in a start-stop cycle of a motor wit spiral seet type A. V. PARASTC CURRNTS Using simulation and test of normal section it is possible to know te induction in (figures 0 and ). ine a Fig. 0. Magnetic simulation wit FMM. ine a represents te section of simulation. Fig. 8. Torque (red) and speed (blue) in a start-stop cycle of a motor wit squirrel cage. Finally, te experiments done to test mecanical resistance in long term operation were satisfactory because, altoug tese s ave not been tougt for periods wit prolonged operations, tey ave not undergone any type of deformation. Magnetic induction (T) Re[Bn], Tesla Bn, Tesla m[bn], 0 0 0 30 40 Fig.. Magnetic induction. Seet at 3000 rpm, c3 MS/m, μ4000 H/m, and f 3.33 Hz. 458
Wit tis distribution, te e.m.f. results: φ B S S B ws wst t t cos (6) Were S is te magnetic circuit area, a constant in tis case. Tensión (V) Voltage (V) Fig.. MF distribution (distance from axis). Te current induced by tis MF in seets can be calculated using te respective electric circuits, remembering tat current flow inside te seets. MF F.e.m () () Fig. 3. Vertical coordinate defining te current sense cange. Tis distribution is due to te MF in te upper area of te seets inducing a iger current in tis section. Te maximum current can be calculated (r is te eigt of te seets from te axis center): Raxis R Current íneas de lines intensidad k A R dr k ln ( A r) A k A dr k ln ( A r) A R axis Posición (mm) Posición (x) Position (x) Posición () Position () ( R s) R ( + ) seet R R ρ (9) seet ( R s) (7) (8) ( A ) ( ) ( R + R ) k ln (0) A Raxis) ( A R ) ( A ) k ln A Raxis) ( A R ) ρ ( ) seet R s ( ( )) R s () Were te constants A, K, y k, are values tat adjust te electromagnetic field equation; s is a parameter tat depends upon te current circulating troug te upper seet area. Also, is te seet radius; e axis te seet tickness (mm); σ is te seet conductivity (S m/mm ) and is te lengt. As te induction is a function of te radial position of considered section, wic is known; it is possible to calculate de constants A and K: K Bmin R R Bmax Bmax ; A () ( A ) B B R K Bmin ; K Bmin ( A R ) (3) ( A R ) And k is a constant function of maximum emf: k ; k max ) ( A r ) ( A R (4) m Z ξ max max (5) m Z ξ Were: - m and m number of pases of and. - Z and Z number of turns and seets of and. - ξ and ξ distribution factors for and. All te terms are known except te radial coordinate wic corresponds to cange of sense in current along te sape profile. (A) Current (A) min max Posición c (mm) Fig. 4. Distribution of te active current along te radial seet of te. 459
Wit te coordinate known, it is possible to calculate te total seet current, by integration of te current equation between te upper a lower limits of te seet: upper R lower R k ( ) ρ seet ( A ) ln A Raxis ) ( A R ( R ) ( R (6) d s) s) k ( ) ρ seet (7) d ( A ) ( R s) ln A Raxis) ( A R) ( R s) Te ring per-seet current and te total currents are: ring per seet upper lower (8) total ring ring per seet p Te torque is related to tis total current: τ R R R R n B( r) ( r) d seets π K k ( A ) ρ seet ( A ) ln A Raxis ) ( A R ( ( R s)) ( R s) d ) (9) (0) V. CONCUSON Wit a proper coice of te materials and constructive sapes, it is possible to obtain low starting current of induction motors. Tis will not suppose a decrease in teir torque values, and at te same time, teir life is extended considerably and te maintenance is reduced. Tese motors present a ig starting torque related to sortcircuit current. Tis caracteristic makes tem adequate for drives in wic we were asked to ave a ig number of starting and stops per our. ts main inconvenience is te ig cost of te tools used in te configuration of te seets, so tat tey sould be fabricate in mass production. Nowadays tere are many electrical drives of te mentioned caracteristics, wit increased demands. ACKNOWDGMNT Te autors would like to acknowledge te economic support from te Ministerio de Ciencia y Tecnología de spaña under te DP 004-0380 Researc Project. RFRNCS [] Xiaodong i, Qing Wu, Subasis Nandi Performance Analysis of a Tree- Pase nduction Macine Wit nclined Static ccentricity Transactions on ndustry Applications, vol. 43, no., marc/april 007. [] D. Gonen, Analysis of a -Pase Drag-Cup nduction macine. Transactions On Power Apparatus And Systems, Vol. Pas-85 No., January, 996. [3] J.F. indsay T.H. Barton. Parameter dentification For Squirrel Cage nduction Macines Transactions On Power Apparatus And Systems, Vol. Pas-85 No., January, 996. [4] Mujal, Ramón. Humet, uís Asyncronous Motor wit spiral seet CM-000. p. 477-48, 8-30 August. Helsinki-Finland, 000. [5] Mujal, Ramon. Asyncronous motor wit spiral seet. mprovement of te functional caracteristics of te asyncronous motors CMS-00. p. 80-84, August 8-0. Senyang-Cina, 00. [6] Mujal, Ramon. Tree-pase asyncronous motor wit spiral seet. Performance improvement of te tree-pase induction motors. SC-00. 6-8 August. Tsukuba (Japan). [7] Mujal, Ramon. Tree-pase Asyncronous motor wit spiral seet Material effects and analysis. nternational lectrical Macines and Drives Control. p. 688-694, -4/3 Madison-UU, 003. [8] Mujal, Ramón. "lectromagnetic of te induction motor wit spiral seet ". P' 05, -5/9 Dresden-Germany, 005. [9] Mujal, Ramón. "Analysis of te induction motor wit spiral seet ". CM 06, 04-06/9 Crete-Greek, 006. 460