Optimization of Design Correlations for Linear Electromagnetic Motors

Transcription

1 Intenational Jounal of Enegy Engineeing (IJEE) Fe. 0, Vol. Iss., PP Optimization of Design Coelations fo inea Electomagnetic Motos Ame Kh. Massad Assistant pofesso: Hisham Hijjawi College of Technology, An-Najah National Univesity, Nalus, Palestine, Astact-This pape pesents a study of optimization of the geometical coelations of the linea electictomagnetic motos (EMM) to ensue minimum mass and constant mechanical integal output wok. The simplified electomagnetic cicuit was uilt, and mathematical models of the system wee laid out. To show the optimization pocess fo geometical coelations etween main dimensions of the EMM and ensuing minimum mass and constant mechanical integal output wok, two vaiale factos ae used in this pape: pe winding to magnetic coe atio a and height winding to intenal adius of moto. Analyzing the aove optimizations, it s seen that EMM has minimum mass m= when a = 0. and = 0. 88, which is educed y 0 % compaed with the EMM without optimization. Keywods - inea Electo-Magnetic Moto, Geometical Coelations, Minimum Mass Motos, Dimensions, Mechanical Integal Output ok. I. INTRODUCTION inea electictomagnetic motos (EMM) ae a special goup of electical machines that convets electical enegy diectly to mechanical enegy in tanslational motion [-7]. Machines and devices with electomagnetic ecipocating motos completely coespond to this tend; they ae contollale, and thei wok meme, as a ule, is diectly connected to the moto amatue such as pumps, viatos, viomixes, pesses o integally united with it ( hand hammes, hammes) [,3,8]. Using machines and devices with electomagnetic ecipocating motos makes it possile to considealy simplify the mechanical diagam of the devices, incease thei eliaility, impove thei powe chaacteistics, and also to educe the cost and the noise [,3,5,8,9]. As mentioned in [3,,5,0,], industial application of the machines will e moe extensive if thei mass and dimensions decease. The technologgy of mico-electomechanical systems exploes a new way of miniatuizing electomagnetic motos. A vey pomising appoach fo uilding miniatue linea moto is to faicate EMM with minimum mass and mege the motos components in a micoassemly pocess[]. A new method of optimization fo geometical coelations etween main dimensions of the EMM and ensuing maximum mechanical integal output wok of the EMM elated to the volume of the active mateial was invented y a goup of scientists in aatov tate Technical Univesity in aatov, Russia [3]. The geatest advantage of the pocessing technology discussed in this pape is to study the elationship etween the main dimensions of the EMM which gives minimum mass with constant mechanical integal output wok. This study aims to investigate the pefomance impovement of the dimensions and mass of the EMM y optimization of the geometical coelations etween main dimensions of the EMM to ensue minimum mass and constant mechanical integal output wok. II. DECRIPTION OF THE YTEM EMM woking on the eality pinciple of diect convesion of electical enegy to mechanical integal output wok of diect linea motion of the stike is shown in Figue. This EMM is equipped with a cylindical magnetic system of the amoued type two unning cleaances δ, δ and a comined amatue. It consists of an amatue (stike) (maked as shown in the Figue ), a yoke (), a guide case (), a winding (3), a etun sping (6) and a a (5) fo impact enegy tansmission. Hence the comined amatue consists of two pats. A woking stoke of the stike is made unde the effect of magnetic field, eing ceated y the winding when cuent flows in it, and etuns to the initial position unde the effect of sping [,5]. The method invented y a goup of scientists in aatov tate Technical Univesity in aatov, Russia, is used fo optimization geometical coelations etween main dimensions of the EMM, thus ensuing maximum mechanical integal output wok of the EMM elated to the volume of active mateials. In this method, the volume of EMM should e otained fist to do the geometical coelations etween its main dimensions so as to find maximum mechanical - 3 -

2 Intenational Jounal of Enegy Engineeing (IJEE) 3-30 Fe. 0, Vol. Iss., PP. integal output wok. This method has een applied in potale EMM. Due to the limited volume and mass in this method, its application is limited [3]. Theefoe, thee is a need to find maximum mechanical integal output wok. Fig. The EMM design In the electomagnetic cicuit of EMM, geometical optimization coelations etween main dimensions of the EMM, should e done to ensue minimum mass and constant mechanical integal output wok as shown in Figue. Fig. Dimensions used in the electomagnetic cicuit of EMM hee is coss sectional aea of winding, coe is coss sectional aea of cylindical coe, of moto (stike), is height of winding, 3 is width of winding is intenal adius III. THE MATHEMATICA MODE OF YTEM The main equation suggests that the mechanical integal output wok of EMM is equal to the aea etween steady value of cuent (I) and flux linkage in the winding (y ) [6,6,7] as shown in Figue

3 Intenational Jounal of Enegy Engineeing (IJEE) 3-30 Fe. 0, Vol. Iss., PP. Fig. 3 Mechanical integal output wok of EMM o the appoximate fomula fo mechanical integal output wok of (EMM) is given y [6,5,7] Electical cuent in the winding is given y I = Iy () hee j is cuent density, K is fill winding facto, jk I = () N N is nume of tuns of wie in winding. Flux linkage in the winding y is given y whee magnetic flux F can e otained y: y =FN = B N (3) coe F = B coe hee B is magnetic flux density. If we sustitute equations (), (3) in equation (), then the output wok of EMM can e ewitten as jk I = ( )( BcoeN ) ÞI = N jb coe K () Magnitude of coss sectional aea of electomagnet active mateials cylindical coe is given y coe = P (5) o Magnitude of coss sectional aea of winding is given y = 3 (6) Fo choosing the optimal geometical coelations etween main dimensions of the EMM in Figue with minimum mass, thee ae two vaiale factos: - 5 -

4 Intenational Jounal of Enegy Engineeing (IJEE) 3-30 Fe. 0, Vol. Iss., PP. a) the atio of pe winding to magnetic coe witten as Cop Coe ) the atio of height winding to intenal adius of moto (stike) Notice that the output wok I is given y the following equation: I coe = (7) jkb To give the minimum mass, we find the elation etween the following vaiales, Then the mass of moto is given y hee coe et =, a = coe m = m + m coe (8) m = KV Þ m =Kav. t is pe density; V is volume of pe in winding. The aveage length of one tun of winding is given y av +. t = Pav = P( ) = P c + ) =P ( c ) av. t ( + hee av is aveage adius of tun of winding. Using magnitude (α), (β ) and (Eq. 6), the magnitude of coss sectional aea of winding may e given y whee: = ( - ) = ( -) ( c- ) = ( ) = c ( c- ) = ( ) 3= - = c- - ; = ; and magnitude of coss sectional aea of winding is given y = c o pe winding to magnetic coe atio can e denoted as ( ) - ( c- ) Þ a = = ap C = + P coe c = Þ = c Mass of winding is given y m = Kav. t (9) - 6 -

5 Intenational Jounal of Enegy Engineeing (IJEE) 3-30 Fe. 0, Vol. Iss., PP. If we sustitute magnitude, K,, av. t in (Eq. 9), we can find the mass of winding m = K ( c-) P ( c+ ) m = 3 P ( c K ) (0) - Consideing that tack of magnetic flux has constant coss sectional aea, the mass of electomagnetic coe may e given y: mcoe = coevcoe Þ mcoe coecoe coe The aveage length of tack of magnetic flux in magnetic coe is given y whee coe is the coe density. coe + = () = () But the magnitude ( ; ) is given y consideing that the coss sectional aea is constant. If we sustitute magnitude, coe we get If we sustitute magnitude coe = P = P = P P = P Þ = P = P Þ = Þ,, coe 3 = = c c =, = ( c ) 3 - = in (Eq. ) to the aveage length of tack of magnetic flux in magnetic = + + ( c-) + c coe = ( + c+ -) c coe and (Eq.5) in (Eq.), the mass of magnetic coe can e found as follows:- 3 m = coe P( + c+ -) (3) c - 7 -

6 Intenational Jounal of Enegy Engineeing (IJEE) 3-30 Fe. 0, Vol. Iss., PP. If we sustitute (Eq.0), (Eq.3) in (Eq. 8), the mass of EMM can e 3 m=õ ( K ( C -) + coe(( + C) + -)) C 3 ap ap m =P ( KaP( + ) + coe(( + ) + + )) () ap+ The esult of Eq. 7 indicates that the multiplie of the following equation is constant coe = a = a ( P ) = I jk The aove esults show that depends on (a ) = (5) jap K I 3 ( ) If we sustitute (Eq. 5) in (Eq. ) and chose magnitude K = 0. [], we get coe 8.93 KP= 0. 3.= ; = 7. 8 hee = m=p coe I ( ) jp K ap ap.3a ( + ) + ( + ) + + ap+ ( ) 3 a 3 coe (6) This equation can e witten y: m= cm( a, ), c= P coe ( jp K I 3 ) æap ö æ apö.3aç + + ç+ + + ap+ m ( a, ) = è ø è ø 3 a Paamete (C) is constant and we can find it fom mateial chaacteistics and integal wok. But the mass of the EMM depends on magnitude of ( a ; ) which indicate dimensions of the EMM. By analyzing the elationship etween mass of the EMM ) (m and magnitude of ( ; ) (Excel), we find the minimum mass magnitude m = whena = 0. and = a with computes pogam - 8 -

7 Intenational Jounal of Enegy Engineeing (IJEE) 3-30 Fe. 0, Vol. Iss., PP. IV. VAIDATION The esults of this study using the mathematical model and compute pogam (Excel) ae pesented in Tale. TABE I OPTIMA OUTION OF THE EMM Data of EMM Initial design Optimal design values m (kg) values a (mm) (mm) (mm) (mm) 3 (mm) (mm) , V. CONCUION This study conducts the optimal stuctual design to enhance the EMM pefomance y impoving the dimensions and mass, whee the mathematical models of system ae laid out. Fo efficient optimal design, this mathematical model is used to find the elationship etween mass of the EMM (m) and magnitude of ( a ; ), then y the compute pogam (Excel), the minimum mass magnitude is otained. By analysis of the geometical optimization coelations etween main dimensions of the EMM, the minimum mass m = is otained when a = 0. and = Accoding to the compaison of EMM with and without optimization, the mass deceases y 0%. REFERENCE [] G. McPheson, R. aamoe, An Intoduction to Electical Machines and Tansfomes, second edition, John iley & ons, 990. []. Coy, The Natue of inea Induction Motos, Machine Design, pp. 3, 98 [3] E. R aithwaite, A Histoy of inea Electic Motos, MacMillian, 987. [] J, Gieas, inea Induction Dives, thid edition, Oxfod cience Pulications, New Yok, 99. [5] M. Riaz, inea Electical Machines, Couse Notes of EE 580, Univesity of Minnesota, 995. [6] M. Poloujadoff, The Theoy of inea Induction Machiney, Oxfod Univesity Pess, 980. [7] K. Hyniova, A. tisky, J. Honcu, A. Kuczek, Active uspension ystem with inea Electic Moto, EA Tansactions on ystems, Issue, Vol. 8, pp , 009. [8] E. Matkevičius,. Radzevičius, Foces of hift of the Electomagnetic Moto, Electonics and Electical Engineeing. Kaunas: Technologija, Issu 6 Vol. 70, pp [9] K. Hyniova, A. tisky, J. Honcu, A. Kuczek, Active uspension ystem with inea Electic Moto, EA Tansactions on ystems, Issue, Vol. 8, pp , 009. [0] H. Isfahani, M. Eahimi, H. esani, Design Optimization of a ow-peed ingle-ided inea Induction Moto fo Impoved Efficiency and Powe Facto, IEEE Tansaction on Magnetics, Issu, VO., pp [] J. Eastham, Novel synchonous machines: inea and disc, Poc. Inst. Elect. Eng., vol. 37, pp. 9 58, Jan. 990 [] H. Gatzenk, et al, A Novel vaiale Reluctance Mico-moto fo linea Actuation, Poc. Actuato, Bemen, pp , 000. [3] A.Kh. Massad, I.M. Husainov, Optimization of dimensions of electomagnetic pecussion machines, New technologies on the ailway tanspot and in the education, U,aatov, 00. [] G.G. Ugaov, and othes, linea electomagnetic dive of the pess, MKN Pulishes B0J7/ (033569), Moscow,000. [5] V. Neiman, and othes, linea electomagnetic motos (MKN Pulishes BJ7/ , Moscow, ). [6] G. Ugaov, and othes, A potale electomagnetic dive fo impulse technologies, VINITI Pulishes 97-B00, Moscow, 000. [7] A. Malov, and othes, Electomagnetic Hammes, Novosiisk, Nauka Pulishes,

8 Intenational Jounal of Enegy Engineeing (IJEE) 3-30 Fe. 0, Vol. Iss., PP. Ame. Kh. Massad was on in Jenin, Palestine in 970. He got his B.c. in electomechanical engineeing, and Ph.D. degee in Electical Engineeing complexes and systems fom aatov tate Technical Univesity, aatov, Russia in the yea 00. He is a Head of electical and mechanical engineeing depatment in Hisham Hijjawi college of technology in Palestine, 0- pesent. His majo eseach inteests ae in the aea of optimization design of linea electomagnetic motos