An analytic calculation method on air gap flux in permanent magnet. brushless DC motor with ironless rotor

Transcription

1 Intenational Confeene on Enegy and Envionmental Potetion ICEEP 6 An analyti alulation method on ai gap flux in pemanent magnet bushless DC moto with ionless oto Xinghua Wang,Yaolong Sheng andshugang Zhao,, Shool of Eletial Engineeing, Shangdong Univesity, Jinan ity, China wangxinghua@sdu.edu.n Keywods: ionless oto, analyti alulation method, method of equivalent sufaeuents, image method. Abstat.An analyti alulation method about the ai gap magneti field of the high-speed pemanent-magnet bushless DCmoto with ionless oto is pesented in this pape. ased on equivalent sufaeuents method and image method, the mathematial model of the moto is pesented. Then the analytial poession is dedued. And the alulated esults of the method oinides with that of finite element method. It poves the analyti alulation method is exat and eliable. Intodution With the advantages of high powe density, fast tansient esponse and high opeation effiieny, high-speed pemanent magnet bushless DC moto has widely appliation pospets. In this pape, the high speed bushless DC moto applied in the small moleula pump is poposed as the eseah bakgound. Due to its high speed,and the vauumsuounding envionment, its apaity of heat dissipationis vey poo. Theefoe, the stutue of ionless oto is adopted fo the less amatue magneti field andthe weak oto eddy uent loss. In ode to get a easonable and optimal ionless otostutue, the paametes of the moto must be optimized;although the finite element method FEM an auately alulate the pefomane of the moto, it is not onduive to the optimum design beause of it'slow omputational speed. oweve, the analyti alulation method is simple, paameteizable, fast and so on, so it is espeially suitable fo the optimization of the moto. The analyti alulation of the ai gap flux has been deeply studied by sholas. In onfene [], the analyti fomulas of the unloaded ai-gap flux in paallel-magnetized PM synhonous moto ae deived fom equivalent sufaeuents Consideing the ogging of the moto, the ai-gap elative atio pemeability funtion is onstuted by Shwaz-Chistoffel tansfomation. In onfene[], an exat analyti method is applied to ompute ai-gap field. The ai gapfield is solved dietly by the Laplasse equation o the Poisson equation of the thee sub egions of the ai gap, pemanent magnet and slot, but the poess is elatively omplex. In onfene[],the supepositionpiniple is used to dedue the analyti expessions with the seonday ai gap o no magneti mateial inside the magnet. In this pape, equivalent mathematial model of ionless oto stutued high-speed pemanent-magnet bushless DC moto is built based on equivalent sufae uent method and image method. An analyti expession fo the ai gap field of the moto is deived, and the analyti alulation esults ae ompaed with that of finite element method. Finally, it is poved that the analyti alulation method pesented in this pape is oet and auate. The method is suitable fo optimization design of the moto with ionless oto. 6. The authos - Published by Atlantis Pess

2 The piniple of analytial alulation A. Equivalent sufaeuents method of pemanent magnet.in the analysis of eletomagneti field of pemanent magnet moto, the following assumptions ae geneally adopted. the oe pemeability of the stato Fe ; the demagnetization uve of pemanent magneti mateial is linea; the impat of the end of the moto is ignoed; the sufae of the amatue is smooth, and the equivalent ai gap is onsideed. The sufae magnet pole is usually applied in the sufae mounted pemanent magnet moto. The paallel magnetization magneti pole of pemanent magnet bushless DC moto is poposed as an example in this pape. The equivalent model of the equivalent sufaeuents of the pemanent magnetis shown in Fig.. The amplitude of sufaeuents of the the pemanent magnet fae AD is the same as that of the fae C, but they ae in opposite dietion. The uent density an be expessed as J, epesents t the uent deviation fom the ente line of a point on the uve. Similaly, the uent density along the A and CD faes an be expessed as J osξ in this pape.as the paallel magnetization is used, the magneti flux density of A and CD is., ξ is Fig..Model of the equivalentfig.. The mio uent of the line sufae uents of N pole uent a in the feomagneti ylinde. Image method. As to the influenee of the magneti bounday, In this pape, the image method is used to analyze the equivalent sufaeuents.as shown in Fig., when the bounday intefae is a long staight feomagneti ylinde and the line uent is loated in the feomagneti ylinde. The aea within the adius of the ylinde is filled with the vauum,, while the magneti pemeability of feomagneti ylindes aea Fe ; as well as k uent b is the mio uent of the line uent a. C. The model of pemanent magnet moto with ionless oto. Due to the oto oe and the, ab. The line

3 shaft of the high speed moto ae nonmagneti mateial, they an be appoximately equivalent to vauum. Aoding to the equivalent sufae uent method, the pemanent magnet pole is equivalent to two annula sufae uents, then the mio uent of them is dedued shown as Fig.. The mathematial model of the ai gap field of the moto with ionless oto is established. The mathematial model of the moto is divided into fou solution aeas, and the size of ai gap flux is obtained by the supeposition method. Fig.. Mathematial modelof the ai flux The alulation of ai flux Shown as Fig., The adial ai flux density is woked out by followingeq. and Eq.. A z i ln ρ C A z whee ρ epesents the distane fom any point on the sufae uent density ing to the point os, on the ai gap; epesents the angle between the onneting line of the sufae uent ing and the point on the ai gap iumfeene os of the hoizontal X axis; while, i d ;C is a onstant. and the nomal dietion ased on the above fomula, the adial ai flux density geneated by equivalent sufaeuents ings at the same adius 7. 5mm an be alulated sepaately.the expession of the aiadial flux density is obtained by poesg the flux density expession:

4 μ tan atan μ tan atan tan atan 5 tan atan 6 7 As it shows, epesents the oute adius of the oto, epesents the oute adius of the pemanent magnet. The numeial esult analysis In ode to veify the auay of the analyti alulation method, A pototype moto showed as table is pesented. The ai flux density is espetively woked out by above analyti alulation and FEM in this pape. Table.Pototype paametes paamete value paamete value Phase numbe Inne adius of the stato [mm] 6 Pole numbe Oute adius of the oto [mm] 9 Slot numbe 6 Pemanent magnet thikness [mm]. Numbe of paallel banhes Pemanent magnet mateial onded NdFe Oute adius of the stato [mm] Magnetizing method Paallel Length of ion oe [mm] ated speed [pm] 7 Fig. shows the ompaison between analytial esults and that of finite element method.as we an find out fom the figue,the hollow pat in the esult of finite element analysis is aused by the stato slots. Theefoe, negleting the influene of stato slot, the two esults ae basially onsistent with eah othe. It poves the analyti method pesented in this pape is oet and exaet. 5

5 Fig.. Compaison between esults of analyti method and FEM Conlusion The ionless otostutueis vey effetive fo eduing otoeddy uent loss in high speed motos. The analyti alulation method of ai flux is a poweful tool fo the design and optimization of this kind of moto. The mathematial model of ionless oto stutue is deived based on equivalent sufaeuents method and image method in this pape, and the ai gap flux of the moto is alulated by it. The alulation esults is fit with that of FEM, Itpoves that the analyti alulation method of the ai gap flux pesented in this pape is oet and effetive. Aknowledgements This wok was finanially suppoted bynational Key Sientifi Appaatus Development of Speial Item YQ9. efeenes [] Pan Yuanzhang,ang Yuqi,and uang Kefeng: Analytial Calulation of No-Looad Ai-Gap Magneti Field of Sufae Pemanent Magnet Synhonous Moto [J]. Explosion-poof Eleti Mahine, Vol. 7, No. 6, pp. -5 [] Li Jiebao, Jing Libing, Zhou Xiaoyan, Zhang Yuejin: Exat Analytial Method fo Sufae-Mounted Pemanent-Magnet ushless Motos[J]. Tansations of China Eletotehnial Soiety, Vol. 7, No., pp [] Shen Jianxin, Chen Ligen: Analytial Calulation of Aigap Field in -Pole PemanentMagnet ushlessmoto with Paallel-Magnetisation[J]. Eleti Mahines&Contol Appliation, Vol. 6, No., pp. 7-6