Cogging torque reduction of Interior Permanent Magnet Synchronous Motor (IPMSM)

Transcription

1 Cogging torque redution of Interior Permanent Magnet Synhronou Motor (IPMSM) Mehdi Arehpanahi* and Hamed Kahefi Department of Eletrial Engineering, Tafreh Univerity, Tafreh, Iran, P.O ,, Mob: Abtrat: In thi paper uing ombination of two eparated idea the torque ripple of Interior Permanent Magnet Synhronou Motor (IPMSM) i redued. Thee two idea are rotor PM egmented and modifying the rotor truture baed on pole-ar ratio of flux barrier optimization. In addition the torque ripple due to the relutane torque omponent dereaed too. Analyi and imulation reult inluding aturation have been performed uing analytial method and Finite Element Method (FEM). The rotor flux barrier onfiguration of the propoed deign i arried out by Repone Surfae Method (RSM) a optimization tehnique whih i verified by FEM. Keyword: ogging torque, PM egmented, pole-ar ratio, aturation and repone urfae method. -Introdution Magneti interation between tator tooth and rotor magnet in IPMSM produe output torque flutuation whih i alled ogging torque. Cogging torque make a noie and vibration in the motor peed. There are everal method for redution of ogging torque uh a permanent magnet egmented [], flux barrier employing in rotor truture [], uing the ontinuum enitive analyi ombined with the FEM for rotor truture deign [3], optimization of hape and poition of nothe in the rotor truture [4]. A modified V-type magnet angle rotor urfae hape a a new deign of IPM motor for eletri air onditioning ytem of Hybrid Eletri Vehile (HEV) i propoed in [5]. Some of thee tehnique are not pratial and they are expenive. In thi paper uing ombination of two eparated idea i.e. PM egmented and pole-ar ratio optimization of the flux barrier a new deign invetigated. Generally the ogging torque equation i omputed by equation () [6] l T R R nn G B nn ( ) ( ) an an in 40 n ()

2 Where l, R, R, n, N, G, B, are rotor length, air permeability, inner and outer rotor radiu, 0 an an, harmoni order, leat ommon multiplier between rotor pole and tator lot, Fourier oeffiient of air gap permeane, flux denity and mehanial angle. Baed on IPMSM truture i.e. permanent magnet are inide in the rotor body, iron bridge urrounding the PM, are in aturation alway therefore thi magneti nonlinearity for aurate analyi of motor behavior mut be onidered [6]. For obtaining the general and optimized deign, at firt the initial deign onidered then the two eparated idea are applied to the initial deign tep by tep. -Calulation of the Lq and Ld Ld and L q (d and q indutane) omputation affeted on motor performane analyi and deign diretly. In addition, in IPMSM, L d i in aturation region beaue the PM flux i roing through the d axi diretion therefore the value of Ld varie with the tator urrent. Then the auray of indutane alulation method in nonlinear ondition (aturation effet) i very important. In thi paper uing [7] thee indutane are alulated whih are expreed in (): L d _ total q q i q d _ PM L d i d L d d _ total i d d _ PM Where d _ total,d _ PM are total flux linkage and PM flux linkage of d axi repetively. Therefore for onidering the aturation the flux linkage due to the tator winding and PM ( ) and flux d _ total () linkage due to the PM alone ( d _ PM ) i omputed eparately then uing equation () the both indutane are obtained. 3-Cogging torque redution of IPMSM 3--Modifying the rotor truture

3 The initial deign eleted from [8]. A 9kW, 4 pole, 0V IPMSM with magneti ore (tator and rotor material) harateriti illutrated in figure and motor peifiation lited in appendix. Thi IPMSM i ued for tration appliation. At firt tep, uing Geneti Algorithm a optimization tool, the rotor truture with three limitation whih are defined below, optimized: -air gap limitation 0.6 mm g. mm -PM thikne limitation 8.8mm Wm 9. 6mm 3-PM width limitation 87mm l m 95mm The target funtion i defined by minimization of ogging torque divided by maximum ogging torque T max at any rotor poition whih i expreed in equation (3) T OF min( T max l ) min( 4 T 0 max ( R R ) n0 n N B an in( n N )) (3) Optimization proe uing geneti algorithm arried out by optimization toolbox of MATLAB oftware. The output reult uing analytial approah before optimization (deign) and after optimization by GA (deign) lited in table. T rm i RMS value of ogging torque. Peak-peak and RMS value of ogging torque are the main parameter for torque ripple redution. Peak-peak ogging torque i twie of peak value of ogging torque. Therefore aording to the table information, optimization of rotor truture by GA (deign) ha a low ue related to the initial deign. The ogging torque of deign redued only 4.5% related to the deign Therefore in following etion uing ombination of two idea i.e. PM egmented and flux barrier optimization the ogging torque will be dereaed more. 3--PM egmented There are everal artile in field of IPMSM optimization baed on PM egmented [6-7]. PM egmented i a well-known IPMSM optimization tehnique whih reate iron bridge between PM whih are in aturation alway. Thee iron bridge have two advantage: -Flux linkage of neighboring PM dereaed due to the flux roing through thee path. -inreaing L d beaue iron bridge are plaed through the d axi of the motor. Aording to the figure relation between pole ar and PM egmented number an be deribed by equation (4) m ( ) (4) 3

4 Where,,, m are the number of PM egmented, PM ar length, ar length between egmented PM and a pole ar repetively. The Fourier oeffiient of air gap magneti flux denity B an expreed in equation (5) [6] B an Bg in( n N / ) o( i nn ) n N / p (5) i0 For eliminating the ogging torque equation (5) mut be et to zero expreed in (6) n N / k or i0 o( i nn ) 0. (6) The empirial formula for obtaining the optimized number of PM egmented expreed in (7) [9] n l Where m k B N at max k w, max, w k B, k, l are winding fator, maximum flux denity of eah pole, aturated flux at m denity of iron bridge, flux linkage of PM divided by iron bridge and PM length repetively. By olving equation 6 the optimal value of (7) and obtained. Baed on motor peifiation (in appendix) without PM egmented and above information deign a firt optimization motor obtained. If we employed PM egmentation in to the optimization proe uing (7) four PM egmented with.5 mm Iron Bridge i arried out a eond optimized motor a deign3. The onfiguration and magneti flux denity ditribution of deign3 and ogging torque waveform of two optimized deign (deign, 3) illutrated in figure 3 and 4 repetively. The peak-peak and RMS value of ogging torque of deign3 related to the deign redued 7% and 3% repetively. Table how the performane analyi of two optimized deign. Te and Tr are eletromagneti and relutane torque omponent of output torque repetively. THD_Bg i total harmoni ditortion of air gap magneti flux denity. Aording to the table the motor magnetizing flux (m) and differene between indutane (L q - L d ) of deign3 are dereaed therefore the output power of deign3 (P n ) redued too (almot 8%). But the THD of air gap magneti flux denity of deign3 dereaed in ompare with the deign whih i good. For more redution of ogging torque redeign of IPMSM baed on putting flux barrier in the rotor truture will be done in the next etion. 3-3-Redeign of IPMSM uing optimized flux barrier onfiguration 4

5 Suitable flux barrier onfiguration ha a great effet on ogging torque redution. The flux barrier tranfer the PM flux in to the air gap then the air gap magneti flux denity will be inreaed. For obtaining the optimal plaement of flux barrier in the rotor body three parameter of flux barrier (pole-ar0, pole-ar and pole-ar) mut be well alulated for obtaining the minimum ogging torque. Figure 5 illutrate the typial flux barrier and pole-ar poition in the rotor body. We have three degree of freedom for modifying the rotor flux barrier. In order to finding uitable poition of flux barrier into rotor body ome limitation mut be onidered whih are lited in table 3. Uing magneto tati FEM analyi and Repone Surfae Method (RSM) a optimization tehnique, optimal poition of flux barrier in the rotor body obtained. The output power held ontant during optimization proe by air gap magneti flux denity B g limitation whih i depited in table 3. Figure 6 how 3D output RSM reult for minimizing the ogging torque (R). The minimum point obtained by pole-ar0=64.0 degree, pole-ar=83.38degree, pole-ar=88.4 degree with the minimum ogging torque value 0.47 N.m/m. Thi deign i alled deign4. Magneti flux denity ditribution of deign4 illutrated in figure 7. The output parameter of deign4 are lited in table 4. Thi optimization deign in ompare with the deign and deign3 ha ome advantage: The air gap flux denity i more inuoidal due to the lowet THD of Bg The ogging torque i dereaed more related to other deign (T rm =0.7 N.m/m) But in thi deign the output power inreaed due to the inreaing the relutane torque omponent Tr and low inreaing in eletromagneti torque Te. Inreaing the relutane torque reate a torque ripple in addition of ogging torque in the output torque. In thi paper an optimized deign uing ombination of flux barrier onfiguration with PM egmented propoed. 4-Propoed deign Uing PM egmented the THD of air gap magneti flux denity and relutane torque omponent will be dereaed. By employing RSM for optimum poition and onfiguration of flux barrier the torque ripple will be dereaed. In other word, optimization of flux barrier onfiguration redound to inreaing the L d and dereaing the Lq-Ld whih affet on redution of relutane torque without dereaing the output torque. Flowhart of the propoed deign illutrated in figure 8. At firt, the initial deign (whih an be deign) defined. 5

6 Uing RSM the onfiguration of flux barrier obtained then the initial value of ar between PM, ' ' for eleting the uitable number of PM egmented alulated. If air gap magneti flux denity 0.68T Bg 0. 7T thi deign will be optimized otherwie the value of i inreaed by one and the inner loop of flowhart will be repeated till the magneti flux denity i to be in range. Finally propoed deign performane whih i alled deign5 i ompared with other deign in table 5. The number of PM egmented i 4 with.4 mm iron bridge width. The peak value of magneti flux denity in the air gap i 0.7 T. Magneti flux denity and magneti flux line of propoed deign hown in figure 9a and 9b repetively. Aording to the table 5 information, propoed deign ha the lowet value of air gap flux denity THD i.e. 0%. The output power of propoed deign i very loe to the pre-defined value (9 kw) and value of Lq-Ld i dereaed related to the deign4 too therefore the relutane torque i redued related to the deign4. The ogging torque of propoed deign i dereaed 6% i.e. 0.4 N.m/m in ompare with the deign. 5-Conluion In thi paper uing ombination of two eparated idea i.e. PM egmented in rotor body and optimized deign of uitable flux barrier an optimized deign of IPMSM baed on ogging torque redution propoed. Optimization proe arried out by Repone Surfae Method (RSM). In propoed deign whih i alled deign5 the ogging torque i dereaed 6% related to the uual deign (deign) and in addition the Lq-Ld value of that i redued too. The THD value of the air gap magneti flux denity of propoed deign ha the lowet value related to the other deign whih i equal to the 0%. Referene [] R.Dutta, M. F. Rahman, Deign and Analyi of an Interior Permanent Magnet (IPM) Mahine With Very Wide Contant Power Operation Range, IEEE Tranation on Energy Converion, 3( ), pp. 5-33, (008). [] Fang and J.-P. Hong",Flux-barrier deign tehnique for improving torque performane of interior permanent magnet ynhronou motor for driving ompreor in HEV" onferene in vehile power and propulion, pp , (009). [3] Kim Dong Hun, II-Han Park Lee, Joon Ho and Chang-Eob Kim, Optimal hape deign of iron ore to redue ogging torque of IPM motor, IEEE Tranation on Magneti, 39(3), pp , (003). 6

7 [4] Gyu-Hong Kang, Young-Dae Son, Gyu-Tak Kim and Jin Har A Novel Cogging Torque Redution Method for Interior-Type Permanent-Magnet Motor, IEEE Tranation on Indutry Appliation, 45(),, pp. 6-67, (009). [5] Young-Un Park, Ju Hee Cho, Dong-Howa Chang and Ji-Young So, A rotor hape deign of interior PM motor for reduing ogging torque in eletri air-onditioning ytem of HEV,International Conferene on Eletrial Mahine and Sytem (ICEMS), pp , (03). [6] Dutta, S. Sayeef, and M. Rahman, "Cogging torque analyi of a egmented interior permanent magnet mahine, Eletri Mahine & Drive Conferene, IEMDC07, pp , (007). [7] Lee, Seong Taek, "Development and Analyi of Interior Permanent Magnet Synhronou Motor with field exitation truture " PhD thei, Univerity of Tenneee, (009). [8] Mehdi Arehpanahi and Vahid anaei, "optimal deign of interior permanent magnet motor f with wide flux weakening range " Sientia Irania D (05) (3), pp [9] Rukmi Dutta, A Segmented Interior Permanent. Magnet Synhronou Mahine with. wide fieldweakening range PHD thei, The Univerity of New South Wale,,(007). Appendix IPMSM PARAMETERS Symbol Quantity Value Dy Outer tator diameter 70.7 mm D Inner tator diameter 57. mm Q number of tator lot 36 l fe ative mahine length mm A lot tator lot area 47. mm bt tator tooth width 6 mm b o lot opening mm g Air gap length 0.8 mm D h haft diameter 50 mm D r rotor ore diameter 55.5 mm V m Magnet volume mm 3 W m Magnet thikne 8.5 mm L m Magnet width 96.8 mm PM relative permeability H PM oerive fore 890 ka/m B r PM reidual flux denity. T 7

8 B(T) H (A/m) Figure. magneti ore harateriti of propoed IPMSM Figure : PM and flux barrier onfiguration Figure 3. Magneti flux denity ditribution of deign3 Figure 4. Cogging torque of deign and deign3 8

9 Pole-ar Pole-ar Pole-ar0 Figure 5. Flux barrier onfiguration ued in deign4 Figure 6. Output reult of RSM for deign4 Figure. Magneti flux denity ditribution of deign4 9

10 Initial deign Initial Optimization uing RSM PM egment number alulation 0.68 T Bg 0. 7 T No Inreaing ye end Figure 8. Flowhart of propoed deign a Figure 9. Propoed deign a: magneti flux denity ditribution b: magneti flux line b Table : motor parameter before/after optimization Air gap (mm) Rotor diameter (mm) PM length (mm) PM width (mm) PM thikne (mm) Ld (mh) Lq (mh) T max (N.m/m) T rm (N.m/m) Deign Deign

11 Table : omparion of deign and deign3 Ld(mH) Lq(mH) Lq-Ld(mH) m(mweb) Tr(N.m/m) Te(N.m/m) Pn(KW) THD Bg(%) Deign Deign Table 3: limitation of optimization for deign4 Pole-ar0 (degree) Pole-ar (degree) Pole-ar (degree) Bg (T) interval Table 4: omparion of deign and deign4 Deign Ld(mH) 0.98 Lq(mH) 6. Lq- Ld(mH) 5. m(mweb) 580 Tr(N.m/m).8 Te(N.m/m) 40.3 Pn(KW) 8.8 T rm (N.m/m) 0.44 THD Bg(%) 3 Deign Table 5: omparion of all deign Ld(mH) Lq(mH) m(mweb) Tr(N.m/m) Te(N.m/m) Pn(KW) THD Bg(%) T rm(n.m/m) Deign Deign Deign Propoed deign Mehdi Arehpanahi wa born in Kermanhah, Iran, in 978. He reeived a BS degree from Tabriz Univerity in 000, and MS and PhD degree from Amirkabir Univerity of Tehnology, Tehran, Iran, in 003 and 009, repetively. He i urrently Aitant Profeor in the Eletrial Engineering Department of Tafreh Univerity, Iran. Hi reearh interet inlude work on omputational eletromagneti, eletrial mahine deign and drive. Hamed Kahefi wa born in bouher, Iran, in 987. He obtained a BS degree from Perian gulf Univerity Iran, in 00, and an MS degree in Eletrial Engineering (Power Sytem), in 04, from Tafreh Univerity, Iran. He i urrently teahing in the Ilami azad Univerity of buhehr, Iran