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1 Publication P2 Sami Ruoho and Anteo Akkio. 27. Mixed-gade pole design fo pemanent magnet synchonous machines. In: Poceedings of the 5th Intenational Aegean Confeence on Electical Machines and Powe Electonics and 7th Intenational Symposium on Advanced Electomechanical Motion Systems Joint Confeence (ACEMP 27 & Electomotion 27). Bodum, Tukey. -2 Septembe 27. Pages ISBN Institute of Electical and Electonics Enginees (IEEE) Repinted, with pemission, fom IEEE. This mateial is posted hee with pemission of the IEEE. Such pemission of the IEEE does not in any way imply IEEE endosement of any of Aalto Univesity's poducts o sevices. Intenal o pesonal use of this mateial is pemitted. Howeve, pemission to epint/epublish this mateial fo advetising o pomotional puposes o fo ceating new collective woks fo esale o edistibution must be obtained fom the IEEE by witing to pubs-pemissions@ieee.og. By choosing to view this document, you agee to all povisions of the copyight laws potecting it.

2 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < Mixed-Gade Pole Design fo Pemanent Magnet Synchonous Machines,2 Sami Ruoho, Anteo Akkio Laboatoy of Electomechanics, Helsinki Univesity of Technology, FIN-25 TKK, Finland 2 Neoem Magnets Oy, FIN-284 Ulvila, Finland Abstact This pape intoduces a design idea of a new kind of pole stuctue with diffeent magnet gades used in one pole: the Mixed-Gade Pole Design. This stuctue offes impoved demagnetization potection and also bings potential cost savings by optimizing the use of dysposium in Nd-Fe-Bpemanent magnet mateial. A new demagnetization model with an exponential function is also intoduced. The new design idea is compaed with a taditional one-gade design by using finite element method electomagnetic simulations combined with the demagnetization model. Finally, the benefits of the new pole stuctue ae discussed. Index Tems Demagnetization, finite -element methods, pemanent magnets, magnetic field modeling, mixed-gade pole. I. INTRODUCTION M ODERN lage pema nent magnet electic motos may have vey lage magnet poles. Fo pactical and manufactuing easons, a single magnet cannot be vey big, thus a single pole in a lage machine may consist of tens of magnets. If a pole is wide, one pole may have seveal magnets also in cicumfeential diection. This opens inteesting possibilities in a machine constuction. Nomally, a pole consists of one magnet mateial gade, which is selected as a compomise of flux poduction and demagnetization esistance. Howeve, by using moe than one magnet gades in one pole, seveal technical and economical benefits can be gained: a pole stuctue manufactued using seveal magnet mateial gades can have bette esistance against ievesible demagnetization while giving moe flux at the same time. This kind of mixed-gade pole design can also be cheape than a single gade pole. Manuscipt eceived July 7., 27. This wok was suppoted in pat by the Finnish Cultual Foundation. S. Ruoho is with the Laboatoy of Electomechanics, Helsinki Univesity of Technology, FI-25 TKK. He is also woking pat time at Neoem Magnets Oy (phone: ; sami.uoho@tkk.fi) A. Akkio is with the Laboatoy of Electomechanics, Helsinki Univesity of Technology, FI-25 TKK anteo.akkio@tkk.fi Patial ievesible demagnetization of magnets in electical machines has ealie been modeled with a two-line model in FEM envionment by Kim et al. [][2], Kang et al. [3][4] and Lee et al. [5]. They have used two diffeent kinds of linea models. Diffeent eal hysteesis models have also been used to model demagnetization, fo example by Rosu et al. [6]. Enokizono et al. [7] have used the theoy of otation magnetization to model magnetization of assembled anisotopic DC-moto magnets with FEM. Faooq et al. [8] have used a pemeance netwok to model demagnetization. In thei model they have assumed that the whole magnet has unifom magnetization, and thus unifom patial demagnetization. Howeve, they suggest that the magnet should be divided in seveal sections, which might have diffeent demagnetization. Boucheit et al. [9] have used the supeposition theoem to model demagnetization. In thei model, the ai-gap flux density has two components: one fo undemagnetized magnets and the othe one is a fault component epesenting demagnetization. Ooshima et al. [] have calculated analytically the maximum allowed stato cuent befoe demagnetization. Some demagnetization models have been compaed by Ruoho et al. []. In this pape, a simple and fast model based on an exponent function is intoduced to make the modeling of demagnetization fast and simple. This model allows pefomance calculations of electical machine afte some ievesible demagnetization. The benefits of this model ae an easy implementation and a fast calculation. This model also allows an accuate modeling of eal hysteesis cuves of NdFe-B magnet mateials. In this pape, a new mixed-gade pole design is intoduced and simulated in the FEM envionment using a new exponent function based demagnetization model. II. MIXED-GRADE POLE DESIGN A. Basic Idea Nd-Fe-B-magnet mateial is manufactued in diffeent gades. Some gades offe highe demagnetization esistance and highe woking tempeatues, while othe gades offe highe emanence. Unfotunately, high emanence and high demagnetization esistance o intinsic coecivity, cannot exist in the same magnet gade (Fig ).

3 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 Magnet mateial gade in a synchonous machine should be selected to be able to esist the wost demagnetizing situation in the machine. The whole magnet mateial in the machine is taditionally selected accoding to the wost point in a magnet pole, which usually is in the leading o tailing edges. Othe positions in the pole might have easie conditions. This means that if a magnet pole is constucted using seveal individual magnets, like lage poles typically ae, these individual magnets can be made of diffeent magnet mateial gades, because each individual magnet has to endue diffeent demagnetizing conditions. The basic idea of this mixed-gade pole design is that the magnetic popeties of a pemanent magnet in a pemanent magnet pole stuctue can be a function of position. Moh and Odo have intoduced a simila stuctue aleady in 97s to esist amatue eaction in feite magnet based DC moto [2]. They also intoduced a manufactuing method suitable fo manufactuing feite magnets with highe intinsic coecivity in the othe end. If the mixed-gade pole design is used in lage synchonous machines with Nd-Fe-B-magnets, thee can also be economical benefits. B. Technical Benefits With mixed-gade pole design seveal technical benefits can be expected: demagnetization esistance and flux shape can be optimized. Eddy-cuent losses can also be degeased. Demagnetization esistance can be impoved by using a mateial with highe intinsic coecivity in places, whee demagnetization in the fault situations is the most pobable. This nomally means that a high intinsic coecivity mateial would be used on the edges of a pole. In the middle of the pole, less intinsic coecivity will be needed in many cases. Thus, a mateial with highe emanence could be used in the middle. With this stuctue, moe sinusoidal flux density distibution fom a pole is also possible. The mixed-gade design equies that a pole is constucted using many individual magnets in cicumfeential diection. These individual magnets can be electically insulated fom each othe and so the eddy-cuent losses in a pole stuctue can be minimized. Dy-content (w-%) 35 3 Magnet Gades Dy-content Intinsic Coecivity (ka/m),4,3,2,,9 Fig.. Axially pessed magnet gades (cicles) of a Euopean manufactue and the elative Dy-metal content of these magnet gades. C. Economical Benefits Nd-Fe-B-magnets contain ae eath metals, especially Neodymium (Nd) and Dysposium (Dy) fo some one thid of thei weight. Diffeent Nd -Fe-B-gades can be manufactued by adjusting the elative amount of Nd and Dy. In high intinsic coecivity magnets, which ae the tempeatue esistant moto gades, the quantity of Dy can be up to % of weight o even moe. In high emanence magnets, the content of Dy can be vey low (Fig. ). At the end of 26, the pices of Nd and Dy wee as follows: Neodymium-metal 3 USD/kg and Dysposium-metal USD/kg. These pices have been lately inceasing vey apidly: The aveage pices of Nd and Dy duing wee aound 7 USD/kg and 28 USD/kg, espectively. So the pices have quadupled in just two yeas (Fig 2). Dysposium is much moe expensive than Neodymium. This means that if the elative quantity of Dy can be deceased in a magnet, the pice of the magnet will also be deceased. Because moden lage PM machines can have up to seveal tons of magnet mateial, a saving in the amount of Dy can cause a significant cost eduction. Remanence (T) III. EXPONENTIAL FUNCTION DEMAGNETIZATION MODEL Ievesible demagnetization of pemanent magnets has been modeled with a two-line model by Kim et al. [] [2]. Thei model is simple, easy to implement and fast. Real hysteesis models ae also used in FEM envionment to model demagnetization [6]. The implementation of these models can be moe difficult. With complex hysteesis models longe calculation times can also be expected. In some cases, especially, with Newton-Raphson iteation, complex hysteesis models can lead to convegence poblems in FEM solution [3].

4 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 Pice of Dy (USD/kg) Dy Nd Pice of Nd (USD/kg) Linea model Satuated Demagnetized Demagnetized Applied Field (ka/m),5,5 -,5 - -,5-2 Flux Density (T) Yea Fig. 2. Pices of Dy- and Nd-metals. An exponent function model is used hee to model ievesible demagnetization (Fig 3). The model is based on the following equation, descibing the HB-cuve of satuated Nd- Fe-B mateial in the fist, second and patly in thid quadant: B = B + m K (K + H) 2 m H C e () C is a constant needed fo unit convesion. C = T. This model is easy to implement using emanence (B ), slope of HB-cuve (µ ), intinsic coecivity ( J H c ) and one exta paamete K, which descibes the shapness of the knee in a cuve (Fig 4). Paamete K 2 depends on the othe quantities. Its value is obtained fom equation: K 2 ln ( B = + ( m ) m K J H c ) C H This exponent function model follows vey accuately the eal cuve of NdFeB-mateial (Fig 5). The simulations ae made with a time-stepping FEM. The flux density at each time step is fist calculated using a linea model fo the magnet mateial, whee only emanence and slope ae defined. Afte the solution has conveged, a woking point fo each element of pemanent magnet mateial is checked. If the woking point is too fa on the negative H-axis when compaed to the cuve given by the exponent function, the emanence of that element is educed to bing the woking point back to the B-H-cuve (Fig. 3). If thee have been changes in the emanences of the elements duing these checks, the flux density at the time step will be ecalculated using the updated emanence values and checked again. J c (2) Fig. 3. Ievesible demagnetization of Nd-Fe-B-magnet modeled with the exponent function model. The woking point (cicle in figue), which is calculated using the linea model, is educed to a cuve descibed by the exponent function, if the woking point is too fa on the negative H-axis. -6,E-5-2,E-5-8,E-6,5 -,5 -, Applied Field (ka/m) Fig. 4. The effect of paamete K. IV. MODELING WITH AN EXAMPLE MACHINE A. Example Machine A six-pole salient pole synchonous machine was used to simulate the mixed-gade pole design. The same kind of machine was used by Rosu et al. [6]. The main paametes of the moto ae pesented in Table I. The pole of the machine was constucted using fou magnets in the cicumfeential diection (Fig 6). The FEM simulations wee done using diffeent magnet gades in diffeent positions.,5 - Flux Density (T)

5 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 D. Discussion The fist ow solution in Table III based totally on mateial shows the highest EMF but afte a 3-phase shot cicuit, the dop of EMF is 2 %. This is vey high and means, that the fist stuctue cannot be used. The second ow solution in Table III shows a quite high EMF, which dops only 2 % afte the fault. The thid ow solution based on mateial 3 has the lowest EMF in the beginning, but suvives the fault with pactically no dop in EMF. TABLE I MAIN PARAMETERS OF MODELED SIX POLE MACHINE Paamete: Value Fig. 5. Exponent function model (gay cuves) compaed with measued Nd-Fe-B-magnet cuves (black cuves). Oute diamete of the stato 2 mm Ai gap diamete 795 mm Coe length 26 mm Numbe of stato slots 72 Connection Sta Rated voltage 69 V Rated powe. MW Symbol TABLE II ND-FE-B-MAGNET GRADES USED IN CALCULATIONS B in 2 C (T) JH c in 2 C (ka/m) B in 8 C (T) JH c in 8 C (ka/m) Fig. 6. Six pole machine with fou magnets pe pole. B. FEM Modeling The simulations wee done using time-stepping based FEM using Newton-Raphson method as solve. Fist-ode elements wee used. Thee wee 88 elements and 937 nodes. Fist the machine electomotive foce (EMF) of the machine was calculated. Afte that a thee-phase shot cicuit was modeled. The total demagnetization was then detemined by calculating the EMF again. The simulations wee done using thee diffeent magnet gades. The magnet gades ae descibed in Table II. The magnet tempeatues wee assumed to be 8 C. C. Results The esults of calculations ae descibed in Table III. The fouth ow solution, which is the fist mixed-gade pole design in a Table III, shows the highest EMF afte 3-phase shot cicuit. The stating EMF is only 2 % less than on the fist ow. This stuctue also suvives the fault without demagnetization. The last ow solution is based on the magnet gades and 3. Afte the fault, the EMF has dopped 6 %. An impotant thing to note concening this pole stuctue is that this pole demagnetizes fist fom the cental magnets made of mateial, which has the lowest intinsic coecivity. In this design case, the ievesible demagnetization of machine should be less than 5 % afte a shot cicuit situation. This means that the fist calculated stuctue cannot be used and the last one is baely toleable. If the demagnetization toleance of ow two (based totally on mateial 2 ) in Table III is not satisfying, the taditional method in design wok is to change the magnet gade to the next one having a geate intinsic coecivity, like to the mateial on ow thee based totally on mateial 3. Howeve, by using the mixed-gade pole design descibed on ow fou, the same demagnetization toleance against a 3-phase shot cicuit can be achieved while having less eduction in EMF. The solution on the ow fou is supeio compaed to the othe solutions pesented, because solution on ow fou has the highest EMF afte the fault.

6 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 Pole Magnet Stuctue (using symbols of table II) TABLE III RESULTS EMF (V) EMF afte 3- phase shot cicuit (V) Demagne -tization % % % % % Pole stuctue --- means that all the magnets in the pole ae manufactued using the magnet mateial. Pole stuctue means, that the edges of the pole ae made using magnet mateial gade 3 and the middle pats mateial 2.

7 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 V. CONCLUSION A new design idea, the mixed-gade pole design was descibed, and its technical and economical benefits wee discussed. By using diffeent magnet mateial gades in a single pole stuctue, the demagnetization esistance can be optimized while keeping the EMF as high as possible. This kind of mixed-gade pole design also minimizes the use of dysposium in Nd-Fe-B-magnet, which will cause a cost eduction. A new demagnetization model based on an exponential function was descibed and compaed to measued hysteesis cuve of a Nd-Fe-B-sample. The model was implemented in FEM analysis and used to simulate a 3-phase shot cicuit of an example machine. The new demagnetization model appeaed to be easy to implement, fast in calculations and it followed the eal demagnetization behavio of Nd-Fe-B-magnet the quite well. A six-pole salient pole machine was used to simulate the mixed-gade pole design. The demagnetization pefomance of the machine was modeled. The pefomances of diffeent pole stuctues based on diffeent magnet gades wee compaed. A stuctue based on the mixed-gade pole design showed the best popeties against demagnetization. REFERENCES [] K-C. Kim, S-B. Lim, D-H. Koo, J. Lee, The Shape Design of Pemanent Magnet fo Pemanent Magnet Synchonous Moto Consideing Patial Demagnetization, IEEE Tansactions on Magnetics, vol 42, no., Octobe 26, pp [2] T.H. Kim, S-K. Choi, C-L. Ree, J Lee, Effect of Design Vaiables on Ievesible Pemanent Magnet Demagnetization in Flux- Revesal Machine, Poceedings of the Eighth Intenational Confeence on Electical Machines and Systems, ICEMS 25, Septembe 25, Vol, pp [3] G.-H. Kang, J. Hu, H-G. Sung, J.-P. Hong, Optimal Design of Spoke Type BLDC Moto Consideing Ievesible Demagnetization of Pemanent magnet, Sixth Intenational Confeence on Electical Machines and Systems, ICEMS 23, Volume:, pp , 23. [4] G.-H. Kang, J. Hu, H. Nam, J-P. Hong, G-T. Kin, Analysis of Ievesible Magnet Demagnetization in Line-Stat Motos Based on the Finite-Element Method, IEEE Tans. Magn., Vol 39, pp , 23. [5] B-K. Lee, G-H. Kang, J. Hu, D-W. You, Design of Spoke Type BLDC Motos with High Powe Density fo Taction Applications, IEEE Industy Applications Confeence, Conf 39, vol 2, pp , 24. [6] M. Rosu, J. Saitz, A. Akkio Hysteesis Model fo Finite-Element Analysis of Pemanent-Magnet Demagnetization in a Lage Synchonous Moto Unde a Fault Condition, IEEE Tansactions on Magnetics, vol 4, no. 6, June 25, pp [7] M. Enokizono, M. Kumoi, S. Kawano, Finite Element Analysis of Anisotopic Magnetic Mateials Taking Rotation Magnetization into Account, IEEE Tansactions on Magnetics, vol 3, no. 5, Septembe 994, pp [8] J. Faooq, S. Saii, A. Djedi, A. Miaoui, Use of Pemeance Netwok Method in the Demagnetization Phenomenon Modeling in a Pemanent Magnet Moto, IEEE Tansactions on Magnetics, vol 42, no. 4, Apil 26, pp [9] A. Boucheit, S. Saii, A. Djedi, A. Miaoui, Analytical and Numeical Modelling of Demagnetization Phenomenon in a Pemanent Magnet Moto, 6 th Intenational Confeence on Electical Machines, ICEM 24, Septembe, Cacow, Poland, vol, pp [] M. Ooshima, S. Miyazawa, A. Chiba, F. Nakamua, T. Fukao, A Roto Design of a Pemanent Magnet-Type Beaingless Moto Consideing Demagnetization, Powe Convesion Confeence, Nagaoka, August 997, vol. 2, pp [] S. Ruoho, E. Dlala, A. Akkio, Compaison of Demagnetization Models fo Finite-Element Analysis of Pemanent Magnet Synchonous Machines, unpublished. [2] F. Odo, A. Moh, Two-component magnets fo DC motos, IEEE Tansactions on Magnetics, Vol. MAG-3, No. 5, Septembe 977, pp [3] Hantila, F.I.; Peda, G.; Vasiliu, M. Polaization method fo static fields, IEEE Tansactions on Magnetics, Vol. 36, Issue 4, Pat, July 2, pp