Research Article Design and Analysis of Linear Fault-Tolerant Permanent-Magnet Vernier Machines

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1 e Scientific Word Journa, Artice ID 4838, 8 pages Research Artice Design and Anaysis of Linear Faut-Toerant Permanent-Magnet Vernier Machines Liang Xu, Jinghua Ji, Guohai Liu, Yi Du, and Hu Liu Schoo of Eectrica and Information Engineering, Jiangsu University, Zhenjiang 223, China Correspondence shoud be addressed to Jinghua Ji; jjh@ujs.edu.cn Received 22 January 24; Accepted 3 March 24; Pubished 26 March 24 Academic Editors: H. Bai, L. Jian, J. Liang, and W. Zhao Copyright 24 Liang Xu et a. This is an open access artice distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the origina work is propery cited. This paper proposes a new inear faut-toerant permanent-magnet (PM) vernier (LFTPMV) machine, which can offer high thrust by using the magnetic gear effect. Both PMs and windings of the proposed machine are on short mover, whie the ong stator is ony manufactured from iron. Hence, the proposed machine is very suitabe for ong stroke system appications. The key of this machine is that the magnetizer spits the two movers with moduar and compementary structures. Hence, the proposed machine offers improved symmetrica and sinusoida back eectromotive force waveform and reduced detent force. Furthermore, owing to the compementary structure, the proposed machine possesses favorabe faut-toerant capabiity, namey, independent phases. In particuar, differing from the existing faut-toerant machines, the proposed machine offers faut toerance without sacrificing thrust density. This is because neither faut-toerant teeth nor the fux-barriers are adopted. The eectromagnetic characteristics of the proposed machine are anayzed using the time-stepping finite-eement method, which verifies the effectiveness of the theoretica anaysis.. Introduction Currenty, inear machines have been appied to numerous direct-drive appications such as urban rai transit. It is we known that inear induction machine (LIM) has been appied to the metro traction system in many cities. The inearmachinepossessestheadvantagesoftheenhanced train cimbing abiity and the reduced train turning radius. This in turn means increased cornering abiity and improved stabiity. However, the efficiency and the power factor of thelimarereativeyow[]. In order to overcome these drawbacks, the research on inear permanent-magnet (PM) synchronous machine has been increasingy prompted. However, its cost becomes a chaenging issue for ong stroke appications, since PM or copper cost increases with the system ength. To sove the cost issue, severa primary-pm inear machines which are the counterpart of stator-pm rotary machines have been considered [2 6]. The common characteristic of the primary-pm inear machine is that both thepmsandwindingsareontheshortprimarymover.ithas been identified that this topoogy can reduce the cost for ong stroke system. The inear fux-reversa PM (LFRPM) machine retains the advantage of the primary-pm inear machine which is being cost effective for ong stroke appications [2]. However, the thrust density of the LFRPM machine is reativey ow becausetheeakagefuxofpmsistooarge,hencereducing theeffectivefuxdensityinairgap. Anotherattemptistheinearfux-switchingPM(LFSPM) machine. In recent years, the design procedure and optimization of the LFSPM machine have been investigated []. It has been identified that this machine has a high air gap fuxdensityduetothefuxconcentrationeffect[2]. Hence, compared with the existing LFRPM machine, it can provide greater thrust density under the same condition. However, theneedofahigherpmvoumeforthelfspmmachineeads to the drastic increase of manufacturing costs. Recenty, the concept of magnetic gear (MG) has been presented and anayzed [7 ]. By using the principe of fux fied moduation, the vernier PM (VPM) machine can offer improved torque density [2 ]. Aso, it has a simper structure differing from MG machine. In addition, in order to enhance the reiabiity of the VPM machine, a new fauttoerant VPM machine was proposed in [2]. Its faut-toerant

2 2 The Scientific Word Journa capabiity was improved by introducing the faut-toerant teeth. However, its torque density has aso been reduced due to the reduced sot area. The purpose of this paper is to design and anayze a new inear faut-toerant PM vernier (LFTPMV) machine, which combines the advantages of the faut-toerant machine and vernier machine, thus offering high thrust and high fauttoerant capabiity. Aso, in order to obtain the high fauttoerant capabiity, the proposed machine adopts a deicate compementary structure, rather than conventiona fauttoerant teeth or fux-barriers structure in [, 2]. Hence, the desired faut-toerant capabiity is obtained without resuting in the reduction of the thrust density. In addition, the detent force of the proposed machine aso reduced due to the compementary structure. Thus, the thrust performance of the proposed machine is improved. 2. Topoogy and Operation Principe Figure compares the topoogies of the existing inear vernier hybrid (LVH) machine and the proposed LFTPMV machine. Figure 2 shows the schematics of their armature windings. It shoud be noted that the schematic of armature windings of the proposed machine significanty differs from that of the existing one. In the proposed machine, the armature windings of every phase are reversey connected in series. Phase C, for exampe, is composed of two concentrated armature windings, namey, C and C 2.Thepositionsofboth windings are mutuay λ = (j±/2) τ p apart (τ p is the stator poe pitch). Moreover, there is the magnetizer which connects the two adjacent mover modues. It shoud be noticed that the materia of this magnetizer is the same as other parts of the mover. Thus, the magnetizer and the two mover modues are processedintoawhoeprimarymoverwhichcansimpifythe manufacturing process and assemby process. Between two adjacent phases beonging to one mover modue, the distance equas to τ s =(k±/m) τ p (k=3is a positive integer and m=3isthephasenumber).theproposedmachineadopts two PMs on the surface of each primary tooth. Compared with the existing one, the consumption of PM materia can be reduced and PMs can be easiy mounted. It aso shows that the movercoreoftheproposedmachineconsistsoftwomodues, named mover and mover 2. According to the operation principe of fux fied moduation, the reationship among the overa PM pairsm p PM,the number of stator teeth n r,andthepoepairsofthespatiafied distribution p is given by n r =p PM ±p. () It shoud be noted that if the PMs do not entirey fi air gap aong the eve direction, the vaue of p PM is not equa to the number of a existing PM poe pairs amounted on theiron.theexistinglvhandproposedlftpmvmachines aso operate according to the operation principe of MG. However, both of them have reativey arge sot openings and there are no PMs in the sot openings which are not the same as the ones in [7 ]. Hence, ()shoudberevisedwhen it is used for the existing LVH and the proposed LFTPMV machines. Mover A B C A 2 B 2 C 2 Stator τ s λ τ p Magnetizer Mover Mover 2 A B C A 2 B 2 C 2 Stator τ s λ τ p Tooth tip Tooth root Stator poe pitch Figure : Comparison of topoogies. Existing LVH machine. Proposed LFTPMV machine. A A A B C A 2 B 2 C 2 B C A B C A 2 B 2 C 2 B C Figure 2: Schematics of armature windings. Existing LVH machine. Proposed LFTPMV machine. X X Y Y Z Z

3 The Scientific Word Journa 3 To anayze the two machines in this paper, the magnetic resistance and saturation of the stee are considered to benegigibe.theeffectivemagneticmotiveforce(mmf) produced by the PMs can be expressed as F (x) = m=,3, F m cos ( 2πp PM eff x ), (2) where x is the mover position, p PMeff is the effective number of PM poe pairs on the primary mover, F m is the ampitude of the m order component of MMF, and is the primary ength of the machine. Ony considering the fundamenta component, theeffectivemmfofthepmscanbesimpifiedandexpressed as F (x) =F cos ( 2πp PM eff x ). (3) Permeance coefficient changes with secondary moving and its toothed structure. Hence, both the moving veocity and corresponding secondary position infuence the permeance coefficient. The permeance coefficient can be expressed as P (x, t) =P + i=,2,3 P i cos 2πn r (x Vt), (4) where P is the direct current component in permeance coefficient, P i is the ampitude of the i order component of permeance coefficient, n r isthenumberofthestator teeth, and V is the secondary veocity. Ony considering the fundamenta component, the permeance coefficient can be simpified and expressed as P (x, t) =P +P cos 2πn r (x Vt). () The air gap magnetic fux density can be expressed as B (x, t) =F(x) P (x, t) =F P cos 2πp PM eff x + 2 F P cos 2π (p PM eff +n r )x 2πn r Vt + 2 F P cos 2π (n r p PMeff )x 2πn r Vt. In (6), the first term represents a static magnetic fied that cannot induce votage in the primary windings. The second term represents short waveength magnetic fied produced by PMs and stator teeth, showing that the traveing speed of magnetic fied is sow. The third term represents ong waveength magnetic fied, showing that the traveing speed of magnetic fied is fast that can induce more considerabe votage than the short waveength magnetic fied. Hence, the thirdtermischosenastobeeffectiveharmonictomatchwith (6) Ampitude Ampitude Mover position (mm) Frequency (Hz) Figure 3: PM MMF waveform and spectra. PM MMF waveform. Spectra. the poe pairs of primary windings, resuting in the foowing reationships: p wi = n r p PMeff, (7) G r = n r p wi, (8) V fux =G r V, (9) where p wi isthenumberofprimarywindingpoepairs,g r is the gear ratio, and V fux is the speed of the traveing magnetic fied. It can be found that (7) sightydiffersfrom(), because the primary sot openings of the proposed machines aso infuence the harmonic components of the PMs. Hence, the p PMeff must be confirmed and satisfied with (7) in order to use MG effect and obtain high thrust. For the existing LVH machine, Figure 3 shows the PM MMF waveform and its spectra. It is noticed that 2, the number of the actua PM poe pairs, is not the highest ampitude, due to the primary sot openings. Aso, it reveas that the 8-order harmonic is the main harmonic component. Therefore, the effective number of PMs is p PMeff =8,andthe number of stator teeth is n r =2. According to (7), the poe pairs produced by primary windings shoud be p wi =2.

4 4 The Scientific Word Journa Peak back-emf (V) Peak to peak detent force (N) C tip C tip =C root Figure 4: Peak vaue of back-emf with respect to c tip C root C tip =.2 Figure : Peak to peak vaue of detent force with respect to c root. 3. Optimization The parameters of the stator tooth, such as c tip and c root,can infuence the performance characteristics of the proposed machine, where c tip is defined as the ratio of stator tooth tip width to the stator poe pitch and c root is defined as the ratioofstatortoothrootwidthtothestatorpoepitchas shown in Figure.In[6], the authors exhibited that stator tooth dimensions affect the average thrust of the machine. Aso, the vaue of the c root has negigibe impact on the average thrust of the existing machine. In contrast, the vaue of the c tip has significant impact on its average thrust. Based on these constraints, back eectromotive force (back-emf) optimization of the proposed machine can be simpified when the vaue of the c root is defined the same as the vaue of the c tip.figure4 shows the peak vaue of back-emf of the proposed machine with respect to the vaue of the c tip. Itcanbeobservedthatthepeakvaueofback-EMFreaches maximum when the c tip equas.2or.2.figureshows the peak to peak vaue variation of detent force of the proposed machine with respect to the c root when the c tip is chosen as.2. It can be known that the optimized c root is from. to.7. To maximize peak back-emf and minimize peak to peak detent force of the proposed machine, c tip and c root are chosen as.2 and., respectivey. 4. Performance Anaysis 4.. Moduar Structure. The open-circuit fied distributions under ony PM excited are investigated based on finiteeement method. Figure 6 shows the no-oad magnetic fied distributions of the proposed machine at different mover positions. Position A is defined as the origina mover position. Positions B, C, and D represent when the mover goes to the eft from position A by /4, /2, and 3/4 stator poe pitches, respectivey. The mover goes haf stator poe pitch (8 )frompositiona to position C. Itcanbeobserved that PM fux distributions of position A in the mover 2 are very simiar to those of position C in the mover. Aso, PM fux distributions of position B in the mover 2 are very simiar to those of position D in the mover. Therefore, it can be concuded that the change of fux distributions in both parts of the mover has difference in time for haf of eectrica period. Meanwhie, since there are very few fux ines which pass the magnetizer, the whoe mover can be regarded as two independent modues with compementary magnetic circuit. Therefore, the proposed machine can be anayzedbyoneofbothmodues,ratherthanonewhoe modue, which faciitates the interpretation of the MG effect in the proposed machine. Thus, for either of the two modues, theeffectivenumberofpmsisp PMeff =9, the number of stator teeth is n r =, and the poe pairs produced by primary windings are p wi =.Obviousy,theycansatisfy(7). Figure 7 shows the no-oad magnetic fied distributions in the mover at position A. Figure7 shows the no-oad fux radia density in the mover at position A, which is moduated by the stator teeth. It is very crucia to anayze the no-oad density in the air gap and its harmonics. Figure 7(c) depicts the corresponding harmonic spectra. There are many asynchronous space harmonics in the air gap as the moduation of the stator teeth. Owing to the principe offuxfiedmoduation(8), the fundamenta fux traves at the speed times of the speed of the secondary. Namey, G r = Back-EMF. Figure8 compares the back-emf waveforms inducedinwindingc,windingc 2, and phase C of the proposed machine at rated speed. Figure 9 shows their harmonics anaysis resuts. The back-emf waveforms of phase C are the overap of both winding C and winding C 2. It can be seen that the even harmonic components of back-emf greaty decrease, resuting in the phase back-emf being more symmetrica and sinusoida. This is due to the fact that the two modues of the proposed machines have the compementary magnetic circuits. Another reason is that the two concentrated armature windings beonging to one phase are reversey connected in series as is shown in Figure 2. Figure confirms that the three-phase back-emf waveforms are very symmetrica and sinusoida Detent Force. Figure shows the detent force of the proposed machine. The detent force of the two modues of the proposed machine can be separatey cacuated by using FEM. In Figure, they are noted as modue and modue 2.

5 The Scientific Word Journa.8 (c) Fux density (T) Mover position (mm) (d). Comparison In order to evauate the proposed LFTPMV machine as compared with the existing LVH machine, they are designed based on the same number of phases, rated speed, stack ength, winding turns, number of stator teeth, number of mover teeth, and stator poe pitch. According to the abovementioned design procedure, a 3-pahse 6/2-poe LFTPMV Fux density (T) Poe pairs (c) Figure 7: No-oad magnetic fied distributions in the mover at position A. No-oad air gap fux density. (c) Spectra. 6 4 Back-EMF (V) 4.4. Inductance. Figure 3 shows the fux pattern, in which a the PMs are unmagnetized and ony phase C is excited. It can be seen that amost a of the produced fuxes pass the armature teeth of phase C, rather than other armature teeth. This means that the proposed machine decoupes the phases. Figure 4 compares the sef-inductance and the mutua inductance of the proposed machine. It can be cacuated that the ratio of the mutua inductance to the sefinductance of the proposed machine is ony 4.4%. Hence, the proposed machine inherenty possesses the desired fauttoerant capabiity. 4 Figure 6: No-oad magnetic fied distributions at different stator positions. Position A. Position B. (c) Position C. (d) Position D. As shown, the waveform of detent force of modue 2 is simiar to the one of modue, which shifts 8 aong the horizonta axis. Hence, there are 8 phase ange differences between the two modues. The sum of modue and modue 2 is defined as anaytica sum. The whoe means the tota detent force, which is cacuated directy by using FEM. Figure 2 shows the waveforms of anaytica sum and whoe. It shoud be noticed that the waveform of anaytica sum is very simiar to the whoe one Phase C Winding C Winding C2 Figure 8: Winding and phase back-emf waveforms. 36

6 6 The Scientific Word Journa A n /A (%) Harmonics order Detent force (N) Winding C Winding C 2 Phase C Modue Modue 2 Anaysis sum Figure 9: Harmonics anaysis of winding and phase back-emfs. Figure : Partia and sum detent forces of proposed machine. Back-EMF (V) Phase A Phase B Phase C Figure : Three-phase back-emf waveforms. Detent force (N) Anaysis sum Whoe Figure 2: Comparison of detent forces based on both methods. and a 3-pahse 6/2-poe LVH machines are designed. Their major specifications are isted in Tabe. The eectromagnetic performances of the two machines arequantitativeyanayzedusingfem.itcanbefoundthat the proposed machine requires % PMs of the existing one. Since PM materia is much more costy, the proposed machine takes the significant advantage of ower cost. Tabe 2 compares the sef-inductance and the mutua inductance of the existing machine and the proposed machine. It iustrates that the sef-inductance of the proposed machine is arger than that of the existing machine because the proposed machine has smaer tota (magnetic) air gap ength [7].Itcanbecacuatedthattheratioofthe mutua inductance to the sef-inductance of the proposed LFTPMV machine is much ower than that of the existing LVH machine, reveaing that each phase of the proposed machine is essentiay decouped from other phases. That is to say,theproposedmachinepossessesenhancedfaut-toerant capabiity. Figure compares their back-emf waveforms under the conditionsofthesamearmaturewindingturnsandspeed. It can be found that the proposed machine generates higher back-emf than the existing machine. Therefore, the thrust of Figure 3: Magnetic fied distributions ony excited by armature current. Inductance (mh) L(A, C) L(B, C) L(C, C) Figure 4: Comparison of inductances.

7 The Scientific Word Journa 7 Back-EMF (V) Proposed Existing Figure : Comparison of back-emf waveforms. Thrust (N) Proposed Existing Figure 7: Comparison of thrusts. Detent force (N) Proposed Existing Figure 6: Comparison of detent force waveforms. the proposed machine is arger than that of the LVH machine when both machines operate at the same speed and eectric oading. Figure 6 compares their detent forces. It can be observed that the peak to peak vaue of the detent force of theproposedmachineismuchsmaerthantheoneofthe existing one. Figure 7 showsthethrustwaveformsoftheproposed machine and the existing machine under brushess AC operation with the root mean square (RMS) vaue of 6 A. In order to evauate the thrust performance of the two machines, a thrust fuctuation coefficient (K F ) is defined as Tabe : Design parameters of existing LVH and proposed LFTPMV machines. Existing Proposed Number of phases 3 3 Rated speed (m/s).6.6 Stack ength (mm) 2 2 Mover ength (mm) Number of stator teeth 2 2 Winding turns per phase Stator poe pitch (mm) 6 6 Air-gap ength (mm).. Number of PMs 24 2 C tip.2.2 C root.. PM materia NdFeB NdFeB Magnet remanence (T).2.2 Magnet reative permeabiity.. Magnet voume (cm 3 ) Mover/stator core materia DW46- DW46- Tabe 2: Comparison of sef-inductance and mutua inductance. L (mh) M (mh) M/L (%) Existing LVH machine Proposed LFTPMV machine K F = F max F min F avg = F rip F avg, () where F max is the maximum of thrust, F min is the minimum of thrust, F avg is the average vaue of thrust, and F rip is the vaue of thrust rippe. It can be cacuated that the average thrust of the proposed machine is 332 N and the corresponding K F is 7.8%, whie the thrust and its rippe of the existing machine are 278 N and 3.3%, respectivey. It indicates that the proposed machine possesses the better thrust performance. 6. Discussions and Concusions In this paper, a new LFTPMV machine has been proposed which is suitabe for high thrust and ong stroke appications. The parameters of the stator tooth, c tip and c root, have been optimized for the maxima peak back-emf and minima detent force. However, the p PM number and sot openings ength aso woud have significant impacts on the magnetic oading and power density. Furthermore, for the proposed LFTPMV machine, its faut-toerant capabiity woud change with varied p PM number and sot openings

8 8 The Scientific Word Journa ength. These issues are very critica for improved eectromagnetic performance of the proposed machine. Therefore, it shoud be cosey studied in the future work. On the other hand, since the ratio of the mutua inductance to the sef-inductance of the proposed machine is very sma, the proposed machine inherenty possesses the desired fauttoerant capabiity. Compared with the existing faut-toerant machines, the proposed machine offers desired faut-toerant capabiity without sacrificing thrust density because neither faut-toerant teeth nor the fux-barriers are adopted. Due to the moduar and compementary structure, the three-phase back-emf waveforms are more symmetrica and sinusoida. The detent force of the proposed LFTPMV machine is much smaer than that of the existing LVH machine. The proposed machine not ony offers arger back-emf but aso reduces the cost of PMs. A of these advantages make the proposed machine an exceent candidate for high thrust and high reiabiity appications such as urban rai transit system. Confict of Interests The authors decare that there is no confict of interests regarding the pubication of this paper. Acknowedgments This work was supported by the Nationa Natura Science Foundation of China (27794, 62734, and 3772), by the Natura Science Foundation of Jiangsu Province (BK227), by the Priority Academic Program Deveopment of Jiangsu Higher Education Institutions, and by the Fund Program of Jiangsu University for Exceent Youth Teachers. References [] F. J. T. E. Ferreira and A. T. de Ameida, Nove mutifux eve, three-phase, squirre-cage induction motor for efficiency and power factor maximization, IEEE Transactions on Energy Conversion,vo.23,no.,pp. 9,28. [2] M.Cheng,W.Hua,J.Zhang,andW.Zhao, Overviewofstatorpermanent magnet brushess machines, IEEE Transactions on Industria Eectronics, vo. 8, no., pp. 87, 2. [3] W. Zhao, M. Cheng, X. Zhu, W. Hua, and X. Kong, Anaysis of faut-toerant performance of a douby saient permanentmagnet motor drive using transient cosimuation method, IEEE Transactions on Industria Eectronics, vo.,no.4,pp , 28. [4] W. Zhao, M. Cheng, W. Hua, H. Jia, and R. Cao, Back- EMF harmonic anaysis and faut-toerant contro of fuxswitching permanent-magnet machine with redundancy, IEEE Transactions on Industria Eectronics, vo.8,no.,pp , 2. [] R.Cao,M.Cheng,C.Mi,W.Hua,andW.Zhao, Comparison of compementary and moduar inear fux-switching motors with different mover and stator poe pitch, IEEE Transactions on Magnetics,vo.49,no.4,pp.493 4,23. [6] W. Zhao, M. Cheng, K. T. Chau, and C. C. Chan, Contro and operation of faut-toerant fux-switching permanent-magnet motor drive with second harmonic current injection, IET Eectric Power Appications,vo.6,no.9,pp.77 7,22. [7]K.Ataah,S.D.Caverey,andD.Howe, Design,anaysis and reaisation of a high-performance magnetic gear, IEE Proceedings: Eectric Power Appications,vo.,no.2,pp.3 43, 24. [8] L.JianandK.T.Chau, Acoaxiamagneticgearwithhabach permanent-magnet arrays, IEEE Transactions on Energy Conversion,vo.2,no.2,pp ,2. [9]L.Jian,W.Gong,G.Xu,J.Liang,andW.Zhao, Integrated magnetic-geared machine with sandwiched armature stator for ow-speed arge-torque appications, IEEE Transactions on Magnetics, vo. 48, no., pp , 22. [] L. Jian, G. Xu, J. Song, H. Xue, D. Zhao, and J. Liang, Optimum design for improving moduating- effect of coaxia magnetic gear using response surface methodoogy and genetic agorithm, Progress in Eectromagnetics Research, vo.6,pp , 2. [] L. Jian, K. T. Chau, and J. Z. Jiang, A magnetic-geared outerrotor permanent-magnet brushess machine for wind power generation, IEEE Transactions on Industry Appications,vo.4, no.3,pp ,29. [2] G.Liu,J.Yang,W.Zhao,J.Ji,Q.Chen,andW.Gong, Design and anaysis of a new faut-toerant permanent-magnet vernier machine for eectric vehice, IEEE Transaction on Magnetics, vo.48,no.,pp ,22. [3] L. Jian, G. Xu, C. C. Mi, K. T. Chau, and C. C. Chan, Anaytica method for magnetic fied cacuation in a ow-speed permanent-magnet harmonic machine, IEEE Transactions on Energy Conversion,vo.26,no.3,pp ,2. [4] E. Spooner and L. Haydock, Vernier hybrid machines, IEE Proceedings: Eectric Power Appications,vo.,no.6,pp.6 662, 23. [] L. Jian, J. Liang, Y. Shi, and G. Xu, A nove doube-winding permanent magnet fux moduated machine for stand-aone wind power generation, Progress in Eectromagnetics Research, vo. 42, pp , 23. [6] Y.Du,K.T.Chau,M.Chengeta., Designandanaysisofinear stator permanent magnet vernier machines, IEEE Transactions on Magnetics,vo.47,no.,pp ,2. [7] I. Bodea, J. Zhang, and S. A. Nasar, Theoretica characterization of fux reversa machine in ow-speed servo drives the poe-pm configuration, IEEE Transactions on Industry Appications,vo.38,no.6,pp.49 7,22.

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