0 0 06 0 Electri c Machines and Control Vol. 0 No. 0 Oct. 06 5006 DOI 0. 5938 /j. emc. 06. 0. 008 TM 53 A 007-449X 06 0-0055- 09 The oretical and experimental research on axial and radial magnetic force of axial magnetic bearing ZHANG Yun-peng GAO Shu-ning LIU Shu-qin LI Hong-wei XUE Bo-wen School of Electrical Engineering Shandong University Jinan 5006 China Abstract In order to simplify magnetic levitation system supported by axial magnetic bearings axial and radial magnetic force of axial magnetic bearing is studied in this paper. Based on spatial distribution of magnetic flux in the gap equivalent circuit model was created and the mathematic formula of axial and radial magnetic force in axial magnetic bearing was deduced by virtual work method. Magnetic flux density and field distribution in the gap of axial magnetic bearing were obtained by finite element method. On three-dimensional force measuring experimental platform axial and radial magnetic force of axial magnetic bearing was measured. The change law of magnetic force in terms of exciting current i axial gap g and radial displacement Δr was analyzed and physical mechanism was discussed based on theoretical and simulation results. These results provide reference for research of magnetic suspension system in multi-degree-of-freedom supported by axial magnetic bearings. Keywords magnetic bearing magnetic equivalent circuit axial magnetic force radial magnetic force finiteelement method 05-07 - 9 5053 300 BS0DX03 05JC04 98 99 958 979 99
56 0 0-3 4-6 7-3 Fig. Distribution model of axial magnetic bearing air gap permeance - 3 9 5 - G 6 ~ G 8 G G G ' 7-8 G 3 G 4 G ' 3 G ' 4 G 5 G 6 G 5 G ' 6 ' G 7 G 8 G 7 G ' 8 '
0 57 Fig. Equivalent magnetic circuit of axial magnetic bearing. i g 9 Δr F z g Δr i F r g Δr i 3G ' 4 G i g Δr = G G 3G 4 G' = G 3 G 4 G ' 3 G ' 4 μ 0 R πr - 4Δr 8Δr g Δr g 5G ' 6 G o g Δr = G G ' G 5G 6 G' G 5 G 6 G ' 5 G ' 6 G 7 G 8 G' 7G ' 8 = G 7 G 8 G ' 7 G ' 8 F z = W μ 0 R 3 R π R 3 - R - 4Δr g } g F r = W 7 8Δr Δr Δr g ~ 3 6 7 G i G o R F z g Δr i F r g Δr i R R 3 g Δr F z g Δr i = W g = - G i F mi g - G o F mo g = μ 0 N i f i R πr - 4Δr G a g Δr = g = G i G o μ 0 R πr - 4Δr 8Δr g Δr g πt - 4Δr μ 0 R R 3 g 8Δr Δr g 3 H m = Ni N i Φ g = H m G a = Ni μ 0 R πr - 4Δr 8Δr g Δr g πt - 4Δr μ 0 R R 3 g 8Δr Δr g 4. F z i g F z i /g 5 5-3 W m = F mg / W g = W g W g = F mig in / F mog out / 6 F mi = f i NI F mo = f o NI f i f o 9 6Δr Δr g μ 0 N i f o R 3 R πt - 4Δr g 6Δr Δr g 8
58 0 F r g Δr i = - G i F mi e - G o F mo e - μ 0 N i f i R 4 g - 6g Δr g = f o R 3 R 9 3 B z B r r = 0 Δr = 0 B z B r r = 0 mm F z F r Δr 4 a B z 3 4 b i g Δr B r Table Parameters of axial magnetic bearing R /mm 8 R /mm 6 R 3 /mm 0 /mm 0 /mm 0 /mm 45 /mm 5 / 00 g /mm 0 - Δr /mm 0-3 Fig. 3 3 Fig. 4 Finite element simulation model of axial magnetic bearing 4 / / 4 a 4 b ATI Mini40 4 Spatial distribution of magnetic flux density 5 a 5 b
0 59 g Δr F z! B A 0 i μ 0 F x F y F z F z B A = 槡 F x F y F r μ 0 8 B z i i 0 Fig. 6 6 F z i Axial force F z dependence on current i 5 Fig. 5 Magnetic force measurement system for axial magnetic bearing 4 F z g Δr i F r g Δr i i g Δr i g Δr Fig. 7 Radial force F r dependence on current i 4. F z F r i 6 F z i g = 0. 5 mm7 F r i F z = F miμ 0 πr F moμ 0 π R 3 - R g F i miμ 0 πr F moμ 0 π R 3 - R - 3 3 9 7 F r i 4. F z g 8
60 0 F z! /g 4. 3 F r g i =. 4 A Δr = mm F r g 9 g! /g 9 F r! /g F r Fig. 8 8 Magnetic flux density B dependence on current i 0 Fig. 0 Axial force dependence on axial air gap with radial displacement 9 Fig. 9 Axial force dependence on axial air gap without radial displacement 8 /g / Δr g Δr = mm 0 8 F z! /g B z /g Fig. Magnetic flux density B z dependence on /g F z! /g 9 i =. 4 A Δr = mm B z /g 3 B z /gb z! /g 0 4. 4 F z Δr g 3 8 8 F z g
0 6 8 F z g Δr i μ 0N i f R f o R R i 3 N /m 8 B z 0 πt - 4Δr g A F z 0 Δr < 0. 5 mm F z = 3. 08 03 Δr 4 Fig. 4 F z r Axial force F z dependence on radial displacement Δr Fig. F r g Radial force factor F r dependence on axial air-gap g 4. 5 F r Δr 9 i i F r Δr 5 9 F r Δr! = - F miμ 0 R F moμ 0 R 3 R 4 g 6 3 g F r = Fig. 3 Normalized axial forceand radial force Δr Δr = 0 dependence on axial air-gapg. 5 0 3 N /m Δr K r 4 a
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