长定子用互补型模块化磁通切换型永磁直线电机优化设计

1、长定子用互补型模块化磁通切换型永磁直线电机优化设计design optimization of a complementary and modularlinear flux-switching permanent magnet motor for longstator applications#4o3525ocao ruiwul, cheng mingl, hua weil, wang xinl, zhao wcnxiang2*1. school of electrical engineering, southeast university, nanjing 210096;2. school

2、of electrical and information engineering, jiangsuuniversity,jiangsu zhenjiang 217>2013abstract: this paper investigate the design optimization of a new modular 1 inear flux-swi tchingpermanent magnet mlfspm motor with complementary, symmetrical and modular structure andcompare its performance wi

3、th the conventional linear flux-switching permanent magnet lfspm . thekey of the proposed st rue ture is that each phase arma ture winding is composed of two coils whosepositions are mutually one half of the stator pole pitch and there arc flux barrier betwecn the twoadjacent "e” models. hence,

4、 the back-emf waveform of each phase is sinusoidal and the three phasemagnet circuits are symmetrical. we first optimize the design and analyze the electromagneticperforma ncc of the proposed mlfspm motor by mca ns of finite cl omen t method fem . then, thest rue turc of the conventional lfspm motor

5、 is also optimized and t hen compared with the proposedmotor based on the same met hod. the results reveal that the proposed motor has sinusoidal andsymmetrical three-phase back-emf waveforms, smaller cogging force, and smaller force ripple thanthe existing motors. moreover, a prototype of the propo

6、sed motor is built to validate the study.keywords: linear motor; permanent magnet motor; flux-switching; modular0 introductionlinear motors produce a direct thrust force without the need of conversion from rotationaltorque to linear force. therefore, they are ideal for rail transportation systemsl-5

7、. theconventional 1 incar permanent-magnct synchronous motor lpmsm exhibits higher efficiencyand higher power density than linear induction motors6. however, in applications with a longstator, such as in urban rail systems, the conve nt io nal lpmsm incvitably results in significant costincrease due

8、 to a large amount of magnets or armature windings set along the long stator. linearswitched reluctance motors lsrm has a simpler and more rugged structure, and a lower systemcost than direct-drive lpmsm due to its simple stator, which only consists of iron7. however,this motor also suffers from the

9、 drawbacks such as higher torque ripples and lower power densitythan the pm motors as in the rotary structure8. hence, how to incorporate the merits of bothhigher power density and simpler, lower cost long stator has attracted more and more attentions. inrecent years, a new kinds of primary pm linea

10、r motors9-14, name 1 y the 1 inear structure ofstator-pm motors15: doubly salient permanent magnet dspm motors16, flux reversalpcrmancnt magnct frpm motors17, and fluxswitching pcrmancnt magnet fspm motors18have attracted wide attentions, in which both the permanent magnets and the armature windings

11、are placed in the same short primary mover, while the long secondary stator is only made of iron.hence, this kind of linear pm motors incorporate the merits of simplestructurc of linear inductionfoundations: this work was partially supported by national natural scienee foundation of china under proj

12、ectof 50907031, the specialized research found for the doctoral program of higher education of china underproject of 20090092110034, the program for postgraduate research irmovation in general universities of jiangsuprovince 2010 under project of x10b 066z, and the scientific research foundation of

13、graduate school ofsoutheast university.brief author introduction:cao ruiwu, 1980- , male, phd. candidate, his research interests include design,analysis, and control of permanent-magnet machines.correspondance author: cheng ming, i960- , male, professor, doc to ral advisor,his teaching and researchi

14、nterest include electrical machincs， motor drives for electrie vehicles, and renewable energy generation. emai1:mchemotors, lsr motors and high power density of lspm motors, which are perfectly suited for longstator application systems.it has been shown that the fspm motor can offer high power densi

15、ty 19, 20, sinusoidalback-emf, and fault-tolerance capabilities21, 22, as compared with the dspm motor. so the4550556065linear structure of fspm motor is investigatcd in this paper. fig.1 shows a rotary 12/14-polefspm motor.its operation principle and electromagnetic performance are investigated and

16、 compared witha 12/10-pole fspm motor in 23-24 the results show that its output torque is much higher andits torque ripple is much smaller than the 12/10-pole fspm motor.hence, a liner fspm motorbased on the 12/14-pole rotary fspm motor will be investigated in this paper. a conventionalliner fspm mo

17、tor as shown in fig. 2 a can be obtained by splitting the rotary 12/14-pole fspmmotor as shown in fig. 1 along the radial direction and unrolling it.also, in order to balanee themag net circu it of the end coil, two add iti onal teeth arc added at each end of the primary mover.however, this struetur

18、e suffers from some drawbacks such as unbalanced magnetic circuit for theend coils, bigger cogging force and lower magnet utilization ratio.fig. 2 b and c show themagnet circuit of end coil al at two positions, where the flux-linkage in coils of phase a reach thepositive imum and negative minimum va

19、lue, respectively. it can be seen that the flux-linkagein coil al is excited by one pm at the position shown in fig. 2 b and by two pms at the positionshown in fig. 2 c , which leads to the unbalanced meignet circuit of the end coils in one electricalperiod.fig. 1. the cross-section of the 12/14-pol

20、e fspm motor.in order to solve the problems in the conventional lfspm motor, namely unbalaneed magnetcircuit, big cogging force, and low magnet utilization, a complernentary and modular 1 inear fspmmlfspm motor was proposed and analyzed in 25 this paper further optimizes the design,structure, and ma

21、gnctic performance of this motor and compares it with a conventional lfspm.the rest of the paper is orga nized as fol lows. the basic st rue ture of the proposed mlfspm motoris explained in section ii. in section iii, the effect of some key parameters on the average thrustforce, force ripple, and co

22、gging force of the proposed motor are examined numerically foroptimization. in section iv, the electromagnetic performanee and cogging force are described indetail. in section v, the steady state performance of the prototype mlfspm motor is evaluatedbased on experiments- finally, some conclusions ar

23、e drawn in section vi-2-75armaturewindingaladditionaltoothstatorbfig. 2. the cross-section of the conventional lfspm motor and its unbalanced magnetic circuit principle, a80the conventional lfspm motor, b the positive imum flux-linkage of coil al. c the negative imumflux-linkage of coil al.fig. 3. t

24、he cross-section of the proposed mlfspm motor.851 first-order headlineeachfig. 3 shows the cross-section of the proposed mlfspm motor.phase consists of two“e” -shaped modules whose positions are mutually 入 1 apart:x 1k+1/2 t s9095100where t s is the stator pole pitch, k is a positive integer k 2 eac

25、h “e” -shaped moduleconsists of two "u” -shaped iron, between which a permeinent meignet is sandwiched. the armaturewinding coils are located in the slot and wound around the adjacent tee th of the two "u” -shapedmodules. the two coils of phase a, namely coil al and coil a2, are connected

26、in series. the twopms in the two “e” -shaped modules are magnetized in opposite directions. the structure of phaseb and phase c is the same as that of phase a.for a 3-phase motor, the relative displacement between the module of the adjacent twophases is equal to 入 2 j+l/m t s, where j is a positive

27、integer j5 , m is the number of phasesm 3 there is a flux-barrier between every two adjaccnt "e" -shaped modules. when the movermoves by one stator pole pitch, the phase flux-linkage and back-emf waveforms are bipolar,sinusoidal, complementary and symmetrical.to optimizc the proposed mlfsp

28、m motor，some key paramoters arc defined in fig. 4 andthe detailed original parameters are listed in table i- also, it is necessary to explain the originalvalue of some key parameters and define some coefficients:? different from the rotary fspm motor, the pms are designed a little shorter than the m

29、overteeth. the mover teeth width wmt, the slot open width wms, and the width of the slot under pm-3-wspm satisfy the relationship wmt wms wspm 5/4 as shown in fig.4.? the original value of pm width wpm is designed the same as the moverteeth, i e. wmt wpmt m/4.? the original value of mover yoke heigh

30、t hmy, stator teeth width wst,stator teeth yoke width wsty,110and stator yoke height hsy are designed bigger than the mover teeth.? the mover height hm, the motor stack length lm, and air gap length g are kept constant.? in order to optimize wst, wpm, hmy, hpm, hst, hsy, wsty, some coefficients are

31、defined as:wst? m 42kmyhmy? m 23115kstywsty? m 4kpm l, kpm w are the ratios of the changed pm length and width to the original one,respectively, khst, khsy are the ratios of the chcinged steitor teeth height and stator yoke height to theoriginal value, respectively.wpmhmyhpmhmwmtwmst mhstwstlusulwlu

32、dsavwstyhsyt shs120fig. 4. the design parameters of the "e" -shaped module and stator.tab. 1design specifications of the mlfspm motorratedspeed,vm/s1.5moverstacklength,lmmm120moverpolepitch,t mmm42statorpolepi tch,t smmtm*12/14movertoothwidth,wmtmmt m/4moverslotmouthwidth,wmsmnunt m/4slotw

33、idthunderpm,wspmmmt m/4moverheigh t，hmmm50moveryokeheight,hmymm0. 75* t m/2magnetheight,hpmmm0. 9* hmmagnetwidth,wpmmmitemsoriginal parameters0. 9* hmairgaplength,gmm1statortoothwidth,wstmm1. 5* t m/4statorteethyokewidth,wstymin1. 5* t m/4statortoothheight,hstmm15statoryokeheight,hsymm20statorheight

34、,hsmm35numberofturnspercoil,ncoil116currcntdensityjsa/mm25.82 design optimization1251301351402.1 optimization of kst and magnet dimensionsbecause the cogging torque of the rotary fspm motor is sensitive to the rotor teeth width 26,the coefficient kst is also optimized first in this paper for the pro

35、posed mlfspm motor.fig. 5 a shows the rms value of the back-emf at rated speed for kst in the range of 1 to 1. 5while keeping other paramoters constant. it can be seen that when kst is about 1. 1, the back-emfreaches the imum value. also, the peak to peeik value of cogging force fcog, average thrust

36、force favg and thrust force ripple f_ripple at the rated current density are calculated by means offem as shown in fig. 5 b . obviously, f_avg reaches the imum value and f_ripple emdf cog all reach the minimum value at kst 1. 1. the detailed values of the back-emf, favg,f_ripple, and f_cog at differ

37、ent kst are listed in table 11. hence, in this stage, kst 1. 1 is adopted.as aforcmcntioned，the original pm width is the same as a quarter of mover pole pitch, t m/4.in fact, the pm dimensions should be optimizcd according to the actual requirement. there aretwo methods to reduce the pm height, neim

38、ely reducing the pm length from top and from bottom.the current research shows that reducing the pm length from top can offer higher force ability byusing the same pms 26. hence, this method is also adopted as shown in fig. 6. based on thismethod, pm dimensions arc calculated by using fem. the avera

39、ge thrust force at given currentdensity and original parameters when kpm_l in the range of 1 to 0.7 and kpm_w in the range of 1 to0. 6 are 1 is ted in table ttt. it can be seen from table th that the pm utilization ratio when kpm_l 1and kpm w in the range of 1 to 0. 6 is bigger than that when kpm w

40、1 and kpm_w in the range of 1 to0. 7. also, f_avg reaches the imum value when kpm_w 0. 8 and kpm_l 1, which is about 104.9%of the one with the original pm dimensions but using 80% pm volume- moreover, favg atkpm_w 0. 7 and kpm_l 1 is about 99. 1% of the one at kpm_w 0. 8 and kpm_l 1. hence, to save

41、theexpensive pm material, kpm w 0. 7 and kpm l 1 arc adopted for the ncxt step work.6059710700690680120105907560571.11.21.31.41. 56601.11.21.31.41. 530150fig. 5. back-emf and force performances of mlfspm motor versus kst. a back-emf. b thrust force, forceripple, and cogging force.tab. 2 electromeign

42、etic performances of the mlfspm motor as a function of kstemf vf cog nf avg nf ripple n1.159. 781.259. 691. 359.211.458. 351.557. 1159. 4585. 2839. 9863.6540. 7945.9678. 27694. 26683. 66668. 96698. 66702.13700. 5377. 08 48.4772. 5969. 9963102. 64155fig. 6. schematic ofpm optimization.tab. 3kpm_laver

43、age thrust force for different magnet dimensionskpm_w10.90.80.70.60.90.80.7702. 13 703. 72698. 75685. 78727. 06 721.87709. 95691.02736. 36 724. 25706. 59683. 02729. 53 711.53689. 25662. 37705. 69683.4657. 63628. 741601652.2 optimization of kst and magnet dimensionssince the original mover yoke heigh

44、t is chosen big enough to avoid magnetic saturation,coefficient kmy is optimized in the range of 0. 75 to 0. 55. meanwhile, the coil number and appliedcurrent density are kept constant, which means that the applied phase current and copper loss wil 1increase with the reducing of hmy. the elcctromagn

45、ctic performances of the proposed mlfspmmotor including the back emf, f_avg, f_ripple, f_cog, and the average thrust force per unitcopper loss f_avg/pcu are calculated as shown in fig. 7. it can be seen that f_avg and f_ripplevary inversely as coefficient kmy. when kmy is smaller than 0. 65 the back

46、 emf decreases obviouslywith kmy, which is caused by the mover yoke saturation due to the decrease of mover yoke wi dth.also, f_avg/pcu decreases with kmy obviously when kmy is smaller than0. 65. the reason is that thecopper loss is proportional to slot area. moreover, the cogging force ripple also

47、reaches around theminimum value at kmy 0. 65. so, by considering the saturation, copper loss and cogging force,kmy 0. 65 is chosen for the next step work.1.241.21. 161. 121.081.0410. 960. 921.041.031.021.0110. 990. 980. 970. 960. 550.60. 650.70. 75175180fig. 7. back-emf and force performance at diff

48、erent kmy.2. 3 optimization of stator teeth and yoke heightthe original dimension of stator teeth and yoke are chosen to avoid the magnetic flux leakageand magnetic saturation. to save the stator materieil, coefficients khst and khsy are optimized in thissection. fig. 8 shows the back-emf and f_avg

49、when khst is in the range of 1 to 0. 6, namely hst inthe range of 15 mm to 9 nun. it can be seen that when khst is smaller thcin 0.9, the coefficient ofmagnetic flux leakage increases. in theory, khst 0. 6 is acceptable because the rms value ofback-emf is about 0.98 and f_avg is about 0.988 of the o

50、riginal dimension. however, to reducethe effect of magnctic flux leakage in the prototype motor，khst 0.8 is adopted in this paper.0. 990. 980. 970. 960.60.70.80.9185190fig. 8. back-emf and average thrust force at different khst.fig. 9 shows f_avg, back-emf, f_ripple, and f_cog of the proposed mlfspm

51、 motor whenkhsy is in the range of 1 to 0. 5, namely hsy in the range of 20 mm to 10 mni it can be seen thatwhen khsy is smellier than 0. 75, the back emf wind average thrust force decreases, while f_rippleand f_cog vary inversely as coeff icient khsy. also, f_ripple and f_cog arc around the minimum

52、value when khsy 0.75. hence, khst 0. 8 and khsy 0. 75 are chosen for the next step work.1.61.41.2f_ripple1.2 1. 110.90.8f avgf_cog0.80.50. 6250. 75khsy0. 875195200205fig. 9. back-emf and force performance at diffcrcnt khsy.2.4 optimization of kstsince the cogging force of the proposed mlfspm motor i

53、s sensitive to coefficient kst, in thissection kst is optimized again. fig. 10 shows f_avg, back-emf, f_ripple, and f_cog waveformsof the proposed mlfspm motor versus kst. it can be seen that when kst1.1, f_cog and f_ripplereach the minimum value, while f avg and back emf arc about 99.35% and 99.34%

54、 of theimum value at kst 1 2, respectively- also, the detailed values of the back-emf, f avg,f_ripple, and f_cog at different kst are listed in table tv. hence, kst 1.1 is chosen to be theoptimal dimension for the proposed mlfspm motor in this paper. up to now, the key parametersof the proposed motor have been optimized. the optimal dimensions of the proposed motor arecompared with the original one in table v. obviously, the cogging force, thrust force ripple, andpm volume of the optimized structure is about 36. 8%, 49- 9%, and 70% of that of the