3 3 0095 EL ECTR ICMACH I ESADCO TROL Vol3 o3 May 009,, 3, 4 (., 70048;., 70048; 3., 70069; 4., 7007) :,,, : ;,;,,, : ; ; ; : TH333 : A : 007-449X (009) 03-0349- 07 Axial magnetic force model for large outer diameter m ultiannularnesting permanent magnetic bear ings TIA Lulin, L I Yan, TIA Q i 3, L I Zhihang 4 (. College ofw ater and Electricity Engineering, Xi an University of Technology, Xi an 70048, China;. College ofmechanics and Instrument Engineering, Xi an University of Technology, Xi an 70048, China; 3. Department ofmath, orthwest University, Xi an 70069, China; 4. College of communication Engineering, Xidian University, Xi an 7007, China) Abstract: To enhance permanent magnetic bearings( PMB) magnetic force, the new construction for large out er diameter multiannularnesting PMB was designed. Based on the axial magnetic force mathematic model of radial magnetization biannular PMB which coincide with experiment results, connected with the structure character of large outer diameter multiannularnesting PMB and linearity addition p rincip le, the axial magnet ic force analytical model of radial magnetization large outer diameter multiannularnesting PMB was construc ted. The model showed that the axial magnetic force of this type PMB was proportional to the second power of residual magnetism induction density, and that the magnetic force decreased with an increase in magnetic an nular radial gap s and increased with an increment in the number of magnetic annulus and the total magnetic conductivity of magnetic circuit. It also showed that the magnetic force increased with the increment of axial excursion in normal range. The magnetic pole face of this type PMB was fully used, the number of gaps in magnetic annulus which brought magnetic force was increased, so the axial magnetic force increased marked ly. The test and finite element calculated values verify the accuracy of the model. Key words: permanent magnetic bearings; radial magnetization; axial magnetic force; analytical model : 008-07 - 7 : (959 - ),,,, ; (960 - ),,, ; (988 - ),,,; (987 - ),,,
350 3,,,,, [ - 0 ],,,,,,,,,,,, [ ],, = 4,, h, 5; 3 4 h L,L g, d, b 3 a4, 5 4 -, / /, /,,,,, 3 3, 4 5 3 / t ) [ ] = 0 L ln (R /R ), : R ; R ; L ; 0 = 4 0-7 H /m, ) k =, ( = L ln[ ( d h) / d ], () L ln d h (k - ) (h L g ) (k - ) h d (k - ) (h L g ) (k - ) h k :, [ ] ), () g = 0(R L g /) LL g, L g z : R ; z k gk = 0[R k ( h L g ) / ]L ( h L g ), ( h L g ) z (3) k -, ; ; 3; 4 ; 5 Fig. Structure of large outer diametermultiannularnesting PMB : R = d / h, (4) R k = d / h - h ( k - ) ( h h L g ), (5) k - 3)
3 35 D - h, [ ] = 0 S S, S =R (R L ), = 0 (D - h ) (D - h L ) /, (6) D = d h ( h h 4) = 0 V /L p j, L g ) ( - ) : V ; L p j V = d L /4, L p j (L /4) t v = ( d /4), = 4 0 d L / (L d ) (7) 5) / t k = k - k = lnv L (h L g ) z 0 L (h L g ) - k = = gk d h h L g d h L g - h (k - ) (h h L g ) 0 (D - h ) (D - h L ) L d 4 0 d L, (8) (d h) [d h (k - ) (h L g ) (k - ) h ] k = d [d (k - ) (h L g ) (k - )h ] k = 3 F z = [ ] R p j L m t R p j LL m t B r L z, (9) 0 (R L g /) L g : R p j ; L m ; t ; B r F zk = k R pj L m t R pj LL m t B r Lz 0 (h L g ) [R k (h L g ) /] (0), F z = F z F z F z( - ) = R pj L m t R pj LL m t B r Lz - 0 (h L g ) k = R k (h L g ) / () L m = h, () R p j = [ d h - h ( - ) ( h h L g ) ] / (3) (4) (5) () (3) (), F z = h B r L z L/ t h - / [ d h - h ( - ) (h h L g ) 0 (h L g ) - d L g h h k = 3 (d h L g ) / h - h (k - ) ( h h L g ) (4), 3, 4 5, F z F zr F za 3 / t gk () () ; k = 0(R k L g /) LL g, k -, (5) L g z R k = d / h (k - ) (h h L g ), k - (6) d [ ] g = 0 ( d 4 086d), d dg d 0 4 ( b z) 086d (7) d d g 0 [ ( d - d ) 4 086 ( d d ) ], DD - h Dg 0 [ (D - h ) h b z 086 (D - h ) ], (8) bz, z
35 3, t k = k - k = gk dg Dg lnv L L g z - 0 LL g k = d h L g ( k - ) ( h h L g ) 0 {d / [ 4 ( b z) ] 086d (D - h ) [h / ( b z) 63 ]} (9) 3 F zr F zrk = (9) k R p j L m t R p j L L m t B r L z 0 L g (R k L g /) (0), F zr = F zr = R p j L m t R p j L L m t - B r L z 0 L g k = R k L g / () ()(3)(6) (), h L/ t h - / [d h - h ( - ) (h h L g ) - B r L z 0 L g k = ( d L g ) / h ( k - ) ( h h L g ) () 33 F za dfeb, [ ] B r H c L m t B m = B r S m H c L m t,, g g = B m S m = R p j LB m = R p jlb r H c L m t R p j LB r H c L m t = B r h / t h / {L [ d h - h ( - ) ( h h L g ) ]}, (3) : B m ; S m ; H c ; B r = r 0 H; r d5 h,, g / F =, 0 S :, S F za = B r h / t h( L) - / [d h - h ( - ) (h h L g ) ] ( 0 ) { / d / [ 4 (D - h ) h ] } (4) 333 F z = F zr F za (5), 4 5, / t (8) ;F zr (4), 5,,, F za B r h / t h( L) - / [d h - h ( - ) (h h L g ) ] ( 0 ) / d (6) 4 dfeb,45, :B r = 35 4 T; H ch = 947 035 ka /m; H ci 955 ka /m, (BH) max =336360 kj /m 3 ; 80 B r = 38 T; H c = 000 ka /m ; = 3 8 0-6 H /m; r =098 : = 4; h = 5mm; h = mm; L g = mm; d = 6 mm; b = 3 mm 4 5 z = mm,f zf : L = 8 9 mm 8 mm Table FEM ca lcula ted results L /mm F zf / 3 4 4 75 5 06 6 3 7 39 8 5 9 57 0 43 5 46 0 40
3 353 4, 4 5 L = 8 mm, (8) (4) = 699 37 949 3 0- z 039 034 575 t F z 64 54008z / ( z 68658 ) F z, F zf, 6%, 36%,3 (644 74 0-3 z t Table M odel calcula ted results and FEM ca lcula ted results z/mm F z / F zf / 0 0 05 68 7 0 33 40 5 9 00 0 44 5 5 86 8 30 30 97 35 344 36 40 359 334 45 366 35 50 366 348 55 36 34 60 35 334 65 340 33 70 35 304 75 309 79 80 9 57 4, 3 4 (7) t g L m = h = 5 = 0 mm, R p j = 9 mm, R = 8 mm, L = 8 mm, L g = mm, B r = 38 T, r = 098(7) (9) 006 88 35) / ( 0 ) F z 505 79z / (8784 0 / t 5 /9) L m = h = 0 mm, R p j = 345 mm, R = 33 mm, h = mm, L = 8 mm, L g = mm, B r = 38 T, r = 098(7) (9) t (6038 65 0-4 z 0076 388 3) / ( 0 ) 3 4 F z 84z / (8784 0 / t 5 /345) F z F z 3,3F z = F z F z, F z z 3 : 4 3(, ; 3, 4 ) Table 3M odel calculated results(, ; 3, 4 two biannular PM B) z/mm F z / 3 4 F z / F z / 0 0 0 0 05 7 4 3 0 34 7 6 5 50 40 90 0 63 53 6 5 75 64 39 30 85 74 59 35 9 83 75 40 97 9 88 45 0 97 98 50 03 0 05 55 03 06 09 ; ; 3 F ig. Curve of ax ia lmagnetic force and ax ia l excursion for permanen t magnetic bear ings 60 0 09 0 65 99 0 70 96 07 75 93 04 80 89 0 99
354 3 F zf 4,4F z = F zr F za, 5, F zf 5, F zs 5 3 35%, 79%, 8%, 47% 4 Table 4D em on stra tion results com par ison F ig. 3 3FEM flux lines for fourannularnesting PM B 43, 4 5 4 : X5K,, 957B KISTLER, 957BKISTLER, 957BKISTLER 5070, 5070 z/mm F zr / F za / F z / F zf / F zs / 0 0 4 4 49 43 05 68 4 09 4 07 0 3 40 7 75 70 5 9 38 30 6 6 0 43 37 80 85 77 5 86 34 30 34 3 30 30 3 35 336 346 35 343 9 37 370 366 40 359 7 386 379 375 45 366 4 390 405 38 50 366 388 40 380 55 36 0 38 398 376 60 35 8 370 39 36 65 340 6 356 386 357 70 35 4 339 368 340 75 309 3 38 30 80 9 303 96 98 ; ; 3 ; 4957B KISTLER; 5X5K F ig. 4 4Sketch map of test L = 8 mm,z = 0, (9)(3), g 706 0-4 W b, ( ) B g 35 T, (D - h ) h, mm, ( ) (8)(4)(6) / t 098 [458 4 0-3 (9 z ) 004 5 ] /, F zr = F z 468 785 z / ( / t 5 /08), F za 408 58 / ( / t 5 /08) F zr F za, F zs 5 F ig. 5Ax ia l magnetic force and ax ia l excursion for large outer d iam eter fourannularnesting PM B ; ; 3 5 :,
3 355 5 45 dfeb : d = 300 mm, h = 0 mm, L = 0 mm, h = mm, = 3 mm 4 5, L g z =3 mm,m atlab( 8) ( 4), 5 5 :, 5 Table 5M odel ca lcula ted results 6 D /mm F z / 30 73 57 480 40 437 760 50 69 66 040 60 3 7 99 540 70 3 65 39 600,, : ;, ;,,, : [ ],,,. [ J ]., 007, 7 (6) : 57-6. TIA Lulin, L I Yan, WAG Shanshi, et al. netism Research on mag engineering analytical calculation method for bibarrel shaped radial permanent magnetic bearings[ J ]. CSEE, 007, 7 (6) : 57-6. Proceedings of the [ ],,,. [ J ]., 007, 7 (36) : 4-45. TIA Lulin, L I Yan, TIA Q i, et al. Research on the axial mag netic force of axially magnetized biannularshaped permanentmag netic bearings[ J ]. Proceedings of the CSEE, 007, 7 ( 36) : 4-45. [ 3 ] OHJ I T, MUKHOPADHYAY S C, LWAHARA M, et al. Perma nent magnet bearings for horizontaland verticalshaft machines: A comparative study[ J ]. Journal of Applied Physics, 999, 85 (8) : 4648-4650. [ 4 ],,,. [ J ]., 008, 8 () : 73-77. TIA Lulin, YAG Xiaoping, L I Yan, et al. Analyticalmagnetic force model for permanent magnetic guideway and permanent mag netic bearings [ J ]. Tribology, 008, 8 () : 73-77. [ 5 ]. [ D ]. :, 004. [ 6 ],,,. [ J ]., 008, 9 (0) : 63-66. TIA Lulin, L I Yan, TIA Q i, et al. Research on the radial magnetic force of axial p lacement and axialmagnetization multian nularshaped PMB [ J ]. China M echanical Engineering, 008, 9 (0) : 63-66. [ 7 ],,,. [ J ]., 008, 3 (6) : 6-3. TIA Lulin, J IA Rong, YAG Guoqing, et al. Research on the magnetic field and magnetic force of a permanent magnet affixed to a p lane magnetizer[ J ]. Transactions of China Electrotechnical Soci ety, 008, 3 (6) : 6-3. [ 8 ] OHJ I T, ICH IVAMAA S. ew conveyor system based on a passive magnetic levitation unit having repulsivetype magnetic bearings [ J ]. Journal of M agnetism and M agneticm aterials, 004, 7-76. [ 9 ] HAMLER A, GOR ICA V. Passive magnetic bearing[ J ]. Journal of M agnetism and M agnetic M aterials, 004, 379-380. [ 0 ] YOET J P, LEMARQUAD G, HEMMERL I S, et al. Stacked structures of passive magnetic bearings[ J ]. Journal of Application Physics, 99, 70 (0) : 6633-6635. [ ],,,. [ J ]., 007, 6 (9) : 6-9. TIA Lulin, L I Yan, YAG Guoqing, Research on the axialmag netic force of radial magnetization bibarrelshaped PMB [ J ]. M e chanical Science and Technology, 007, 6 (9) : 6-9. [ ],. [M ]. :, 984. ( :)