AN INTERACTIVE DESIGN OF THE WINDING LAYOUT IN PERMANENT MAGNET MACHINES

Transcription

1 AN INTERACTIVE DESIGN OF THE WINDING LAYOUT IN PERMANENT MAGNET MACHINES CHANG-CHOU HWANG 1, CHENG-TSUNG LIU 2, HSING-CHENG CHANG 3 Key word: PM machine, Winding layout, CAD program, FEA. Thi paper preent a winding deign technique for three phae permanent magnet (PM) motor. The winding factor and the emf total harmonic ditortion are provided. A computer-aided deign (CAD) program wa developed and implemented uing the Viual Baic language. Finite element analyi (FEA) program wa linked into the CAD program to calculate the motor performance. 1. INTRODUCTION The layout of a winding in an electric machine affect the mmf ditribution and the performance of the machine. The machine deigner mut determine the bet way of placing the winding in a machine in the mot effective manner. For imple configuration thi can be done by hand, but for any valid pole and lot count combination of a machine, a CAD i virtually eential. However, relatively little ha been reported in detail on decribing a procedure for the placement of winding in a motor [1 4]. Hanelman [2], Cro et al. [3], and Hwang et al. [4], preented the winding layout procedure for finding the highet value of winding factor for PM machine with concentrated winding. Thi paper decribe the extention of the previou work [1 4] to determine the procedure of the winding layout for any valid pole and lot combination of PM machine for both concentrated and non-concentrated winding. A CAD program ha been developed and implemented uing the Viual Baic language. It i linked to an FEA program for calculating motor performance. Three example are conidered for illutration. 1 Department of Electrical Engineering, Feng Chia Univerity, Taichung 407, Taiwan, ROC, cchwang@fcu.edu.tw 2 Department of Electrical Engineering, National Sun Yat-en Univerity, Kaohiung, Taiwan, ROC, ctliu@ieee.org 3 Department of Automatic Control Engineering, Feng Chia Univerity, Taichung 407, Taiwan, ROC, hcchang@auto.fcu.edu.tw Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 56, 4, p , Bucaret, 2011

2 388 Chang-Chou Hwang, Cheng-Tung Liu, Hing-Cheng Chang 2 2. BASIC ASSUMPTIONS There are an infinite number of poibilitie for pole and lot count combination and for winding layout. To limit the cope and implify the problem, the following aumption are made: a) The motor i three-phae. b) A balanced winding i conidered. c) Double-layer per lot i ued. Baed on the above aumption, the combination of lot (N ) or teeth and pole (N m ) mut atify the following relationhip: N GCD = 3 ( N, N ) m k, (1) where k i an integer and GCD tand for the greatet common divior. The total number of coil (N c ) i equal to N for the double layer winding. Before conidering the detail of laying out a winding, it i beneficial to define ome item that lead to the following formulation. 3. DEVELOPMENT METHODOLOGY In thi ection, four item for determining the winding layout are defined. Coil pan i the circumferential width of a coil. It i convenient to decribe the coil pan in term of lot. Generally peaking, the coil pan for a coil hould be a cloe to 180 electrical degree ( 0 E) a poible but eldom exceeding thi [2]. The coil pan S in lot can be formulated a N max fix,1, for lap winding S = Nm, (2) 1, for concentrated winding where max(, ) return the maximum of it two argument and return fix( ) the integer portion of it argument. The relative angle of the k th coil (or teeth) i defined a N m θ ( k) ( k 1) c = E k = 1, 2,, N c. (3) N When the coil angle θ c (k) ha a magnitude greater than E, it i corrected by applying the function.

3 3 Interactive deign of the winding layout in PM machine 389 c ( k) = rem θ ( k), 0 ( 360 E) θ, (4) where rem(x, y) i the remainder function which return the remainder of the diviion x/y. For balanced three-phae motor, each of the three phae winding mut produce the ame amplitude and hape back emf, and each emf hould be hifted in phae by E from the other two phae. Hence, the individual phae coil mut be diplaced by E from the coil in other phae. The phae offet in lot K 0 i an integer value computed by K c 2N = ( 1 3q), (5) 3N 0 + m where q i an integer value of 0, 1, 2,, (N m /2) 1. If no uitable integer value of q can be found, then the choen pole and lot combination can not be adopted to contruct a balanced three phae motor. The winding factor (K w ) for each winding group can be calculated a K w = 1 N N ph e ph k = 1 jθc ( k ), (6) where N ph i number of coil per phae. 4. WINDING LAYOUT PROCEDURES Baed on the above formula and aumption, the eential tep for determining valid winding layout are ummarized a follow: a) Input number of lot, N and number of magnet pole, N m. b) Determine coil pan S uing (2), phae offet K 0 uing (5), and coil angle θ c (k) or θ c( k) uing (3) or (4). c) Layout all coil by the ame coil pan and aign coil number for all coil equentially. Select coil number 1 to be the phae reference. d) Determine coil for phae A, and then determine the coil for phae B and C equentially. The phae B coil are hifted K 0 lot from phae A, and phae C coil are hifted 2K 0 lot from phae A. Generally, coil number 1, N c (1) i aigned to be the firt coil of phae A. The econd coil of phae A i elected from the reidual coil number other than N c (1+K 0 ) and N c (1+2K 0 ). The third coil of phae A i elected from the coil number other than elected coil of phae A, B, and C. According to thi procedure, elect N ph = 1/3N c coil for phae A, B, and C repectively. If it i unable to find a uitable value for K 0, that mean the

4 390 Chang-Chou Hwang, Cheng-Tung Liu, Hing-Cheng Chang 4 combination of N m and N can not be ued for contructing a three phae balanced winding motor. e) Link to the FEA program and calculate the motor performance. f) Determine the total harmonic ditortion (THD) of the phae back-emf for each winding group. The THD i defined by K 1/2 2 = 100 k, (7) 1 k = 2 THD U U where U 1 i the fundamental component of the back-emf and U k i the k th order harmonic component. A flow diagram howing the main routine i illutrated in Fig. 1. The method ued for finding poible winding layout et hown in Fig. 1 i illutrated in detail in Fig. 2. A CAD program ha been developed and implemented uing the Viual Baic language. It i linked to an FEA program for calculating motor performance. Fig. 1 A flow-chart for winding layout.

5 5 Interactive deign of the winding layout in PM machine 391 Fig. 2 A flow-chart for finding poible winding layout et in Fig EXAMPLES Table 1 how an example of the winding layout for an 8-pole/9-lot (8P/9S) permanent magnet bruhle dc motor. It ha four different value of K w and

6 392 Chang-Chou Hwang, Cheng-Tung Liu, Hing-Cheng Chang 6 therefore claifie four group of winding configuration. Screen for winding Group 1 Type 1 and Group 2 Type 4 are diplayed in Fig. 3 and 4. Table 1 Winding layout for 8p/9 motor Winding method Phae A Phae B Phae C K w THD (%) Type Group 1 Type Type Type Group 2 Type Type Group 3 Type Type Group 4 Type Fig. 3 Screen for winding Group 1 Type 1. Fig. 5 illutrate the winding layout for phae A winding of Type 1. Fig. 6 and 7 how a family of back-emf waveform at a peed of rpm and the phae back-emf harmonic content for Type 1, 2, 3, and 4. It i een that Type 1 (Group1) ha the highet amplitude and the mot trapezoidal phae emf waveform due to the highet winding factor. Thi make it the mot appropriate for bruhle dc operation. Type 4 (Group 2) ha the lowet THD, and hence make it mot uitable for ynchronou operation. Type 9 (Group 4) ha the lowet amplitude, and it ha the mallet winding factor.

7 7 Interactive deign of the winding layout in PM machine 393 Fig. 4 Screen for winding Group 2 Type 4. Back EMF (V) Fig. 5 Phae A winding layout for Type 1. Type-1 Type-4 Type-7 Type Time (m) Fig. 6 Back emf waveform for Type 1, 4, 7, and 9.

8 394 Chang-Chou Hwang, Cheng-Tung Liu, Hing-Cheng Chang 8 12 Back EMF (V) Type-1 Type-4 Type-7 Type Harmonic Number Fig. 7 Back emf harmonic content for Type 1, 4, 7, and 9. Reult for two more example for 4P/9S and 12P/9S are lited in Table 2 and 3. It i een that 4P/9S ha four group and nine type and 12P/9S ha only one group and one type winding layout. Table 2 Winding layout for 4p/9 motor Winding method Phae A Phae B Phae C K w THD (%) Type Group 1 Type Type Type Group 2 Type Type Group 3 Type Type Group 4 Type Table 3 Winding layout for 12p/9 motor Winding method Phae A Phae B Phae C K w THD (%) Group 1 Type CONCLUSIONS Thi paper ha propoed a winding deign technique for three-phae PM motor. Detailed graphic deign method are provided with a Viual Baic program. It i linked with an FEA program for calculating motor performance. The technique wa illutrated with three example of different number of magnet pole and the ame number of lot. Thi technique can be applied to any valid

9 9 Interactive deign of the winding layout in PM machine 395 pole and lot combination of three-phae PM motor, it i very efficient to find all poible winding configuration for any PM motor and lit all winding configuration by the value of winding factor. ACKNOWLEDGMENTS Thi work wa upported by the National Science Council of Taiwan through grant number NSC E MY2. Received on February 8, 2011 REFERENCES 1. J. R. Henderhot Jr., T. J. E. Miller, Deign of Bruhle Permanent-Magnet Motor, Magna Phyic Publihing and Clarendon Pre, Oxford, D. Hanelman, Bruhle Permanent-Magnet Motor Deign, The Writer Collective, Cranton, Rhode Iland, J. Cro, P. Viarouge, Synthei of High Performance PM Motor With Concentrated Winding, IEEE Tran. Energy Conv., 17, (2002). 4. C. C. Hwang, S. P. Cheng, C. M. Chang, Deign of High-Performance Spindle Motor With Concentrated Winding, IEEE Tran. Magn., 41, 971 (2005).