Electri c Machines and Control Vol. 21 No. 12 Dec :,,,,,,,, 15 kw r /min, : ; ; ; DOI:

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1 Electri c Machines and Control Vol. 21 No. 12 Dec :,,,,,,,, 15 kw r /min, : ; ; ; DOI: /j. emc TM 336 A X Strength analysis and design of high speed interior permanent magnet rotor ZHANG Chao 1 ZHU Jian-guo 2 TONG Wen-ming 1 HAN Xue-yan 1 1. National Engineering Research Center for REPM Machine Shenyang University of Technology Shenyang China 2. University of Technology Sydney Australia Abstract In order to solve the problem of high speed centrifugal force the rotor strength is analyzed for the design of interior permanent magnet rotor. Based on the principle of rotor centrifugal force the analytical formula of rotor strength was deduced. The correctness of analytical calculation was verified by finite element method. In order to improve the mechanical reliability of the rotor the rotor segment structure was adopted. The extra magnetic rib can disperse the centrifugal force of rotor. Also the effect of rib number and size on the strength and leakage performance was analyzed by finite element method. The design rules of the segmented rotor were summarized. Based on the analysis of rotor strength and electromagnetic a high speed interior permanent magnet rotor with rated power of 15 kw and maximum speed of r /min was designed and tested. It provides references for the design of high speed interior permanent magnet rotor. Keywords high speed interior permanent magnet rotor strength analysis flux leakage : ( ) ; ( 2016YFB ) ; ( LGD ) : ( 1988 ),,, ; ( 1958 ),,,, ; ( 1984 ),,,, ; ( 1978 ),,,, :

2 kw r /min kw r /min 8 6 kw r /min kw r /min r /min r /min Fig. 1 Rotor structure with one straight permanent magnet V r /min Table 1 Material properties of permanent magnet rotor 35W270 / kg /m /GPa /MPa

3 x - = M xρ x y dσ y 2. 1 M = ρ x y dσ 1 y - = M yρ( x y) dσ x M = ρ x y dσ x y ρ x y dσ x - = 1 xdσ } A y - = 1 ydσ A 2 Y 2 Y x = 0 3 Fig. 2 2 Direction of centrifugal force 2 3 Fig. 3 Closed region of rotor 3 XY x - Fe = 0 ydσ 1 + XY y - Fe = 1 } ydσ 2 3 D 2 A 1 + A 2 1

4 A 1 y A 2 D 1 Y 4 ydσ 1 = 2 3 R3 o - R 3 i sin α 2 1 } A 1 = α 2 R2 o - R 2 i 4 R o R i α r /min D 2 Y F σ 4 ( ) ydσ 2 = 1 3 R3 i 2sin α 2 + cos α 2 sin α 2 5 A 2 = R2 i α - sinα 2 5 x - PM y - PM = = 0 3 ydσ 3 } A A mm 678 MPa 450 D 3 Y 7 1 ydσ 3 = 3 R3 i cos α 2 sinα R 3 ( i cos α h sinα m ) cos 2 α 7 2 A 3 = b m h m b m h m y 4 F Fe = m Fe y - Feω 2 Fig. 4 Centrifugal force comparison between analytical 8 method and finite element method m Fe ω y F PM = m PM y - PMω 2 9 m PM σ = S F 2bl 11 b l S mm % 1. 2 mm 2. 0 mm 39. 2% 3 y F = F Fe + F PM 10

12 47 6 Fig. 7 7 Stress distribution of different rotor structure 5 Fig. 5 Maximum rotor stress comparison between analytical method and finite element method 6 Fig. 6 Rotor structure with rib Fig.

5 Fig. 7 7 Stress distribution of different rotor structure 5 Fig. 5 Maximum rotor stress comparison between analytical method and finite element method 6 Fig. 6 Rotor structure with rib Fig. 8 8 Relationship between flux leakage and rib number Table 2 Rotor performance with different rib numbers /MPa MPa MPa % % % 5. 4% %

48 21 9 9 Fig. 9 Relationship between rotor performance and rib size with different rib number 1. 5 mm 30 000 r /min 10 a 69. 85 MPa 6.

5 mm 30 000 r /min 1 7 000 r /min 10. 8% 2 106 V 1. 9% 14% 3 21. 1% 9 1 0. 5 mm 2. 5 mm 6% 2 0. 5 mm 2. 5 mm 21. 2% 3 11 Fig.

6 Fig. 9 Relationship between rotor performance and rib size with different rib number 1. 5 mm r /min 10 a MPa b MPa mm 1. 5 mm 10 1 Fig10 Stress distribution of rotor 50. 6% % % r /min 1. 5 mm 2. 5 mm r /min r /min 10. 8% V 1. 9% 14% % mm 2. 5 mm 6% mm 2. 5 mm 21. 2% 3 11 Fig. 11 Interior permanent magnet rotor 0. 5 mm 2. 5 mm 87. 6% Magtrol r /min r /min A 30 A 4% 15 kw r /min %

12 49 Fig. 13 Fig. 12 5 12 13 Platform for load test Characteristics of motorefficiency IEEE Transactions on Industrial Electronics 2014 1 2 50. 1 YAMAZAKI K KUMAGAI M.

7 12 49 Fig. 13 Fig Platform for load test Characteristics of motorefficiency IEEE Transactions on Industrial Electronics YAMAZAKI K KUMAGAI M. Torque analysis of interior permanent-magnet synchronous motors by considering cross-magnetization variation in torque components with permanent-magnet configurations J. IEEE Transactions on Industrial Electronics WANG K ZHU Z Q OMBACH G et al. Average torque improvement of interior permanent-magnet machine using third harmonic in rotor shape J. IEEE Transactions on Industrial Electronics J ZHANG Fei TANG Renyuan CHEN Lixiang et al. Study of the reactance parameters of permanent magnet synchronous motors J. Transactions Of China Electrotechnical Society J WU Zhenyu QU Ronghai LI Jian. Multi-field coupling rotor design for surface-mounted high-speed permanent magnet machine J. Electric Machines and Control J ZHANG Chao ZHU Jianguo HAN Xueyan. Rotor strength analysis of high-speed surface mounted permanent magnet rotors J. Proceedings of the CSEE GERADA D MEBARKI A BROWN N L et al. High-speed e- lectrical machines technologies trends and developments J.. IEEE Transactions on Indus- 2 and Control PM synchronous machine rotors J try Applications mm Orleans LA J ZHANGFengge U Guanghui WANG Tianyu et al. Ventilation system design and research on wind friction loss of rotor surface of MW high-speed permanent magnet motor J. Electric Machines 8 LOVELACE E C KEIM T A LANG J H. Mechanical design considerations for conventionally laminated high-speed interior 9 HONDA Y YOKOTE S HIGAKI T et al. Using the halbach magnet array to develop an ultrahigh-speed spindle motor for machine tools C / / Industry Applications Conference 1997 New 10 BINDER A SCHNEIDER T KLOHR M. Fixation of buried and surface-mounted magnets in high-speed permanent magnet syn-

8 50 21 chronous machines J. IEEE Transactions on Industry Applications J J CHEN Yuanyang HAN Zeying CHEN Yangsheng. Mechanical ZHANG Tao ZHU Huangqiu SUN Xiaodong et al. Strength a- strength analysis of high interior permanent magnet motor J. nalysis on high-speed permanent magnet rotor using finite element Small & Special Electrical Machines method J. Electric Machines and Control FENG Chai LI Yi LIANG Peixin et al. Calculation of the maximum mechanical stress on the rotor of interior permanent-magnet synchronous motors J. IEEE Transactions on Industrial Electronics JANNOT X VANNIER J C MARCHAND C et al. Multiphysic modeling of a high-speed interiorpermanent-magnet synchronous machine fora multiobjective optimal design J. IEEE Transactions on Energy Conversion KIM S YONGIN S K KIM Y et al. A Novel rotor configuration and experimental verification of interior pm synchronous motor for high-speed applications J. IEEE Transactions on Magnetics M ( : ) 檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪 QIANG Song WEN Hualiu. Control of a cascade STATCOM with star configuration under unbalanced conditions J. IEEE Transactions Power Electronics STATC OM J YI Guiping HU Renjie JIANG Wei et al. Influence of grid voltage unbalance on STATCOM and the countermeasure J. Transactions of China Electrotechnical Society MMC-HVDC J LIANG Yingyu YANG Qixun LIU Jianzheng et al. Deadbeat direct power control for MMC-HVDC under unbalanced grid voltages J. Transactions of China Electrotechnical Society D-STAT- COM J ZHANG Maosong WANG Qunjing LI Guoli et al. Study on robust current and neutral-point potential control for the D-STAT- COM based on NPC three-level inverter J. Proceeding of the CSEE D-STATCOM L 2 J ZHANG Maosong LI Shangsheng ZHA Xiaoming etal. Robust L 2 performance criteria design for cascaded-statcom J. Proceeding of the CSEE ( : )

34 22 f t = f 0 w t + f r t f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A B s Fig. 1

34 22 f t = f 0 w t + f r t f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A B s Fig. 1 22 2 2018 2 Electri c Machines and Control Vol. 22 No. 2 Feb. 2018 1 2 3 3 1. 214082 2. 214082 3. 150001 DOI 10. 15938 /j. emc. 2018. 02. 005 TM 301. 4 A 1007-449X 2018 02-0033- 08 Research of permanent