Comparative study between two models of a linear oscillating tubular motor

Transcription

1 IOSR Journal of Elecrical and Elecronics Engineering (IOSR-JEEE) e-issn: ,p-ISSN: 3-333, Volume 9, Issue Ver. IV (Feb. 4), PP Comparaive sudy beween wo models of a linear oscillaing ubular moor A.Mazouz. D.Hedjazi. LEB research laboraory-secion: Linear Elecromagneic Tracion Deparmen of elecrical Engineering BATNA Universiy ALGERIA Absrac: The paper describes he performance of linear oscillaing ubular moor and he developmen of is srucure and characerisics of a year oscillaing linear parameric moor. Thus, we have compared our sudy wih ha which uses only one equaion of operaion from an oscillaor moor linear and compared beween he resuls. The oscillaing parameric engine is composed of a reel and a core which can slip inside ha hereof. By connecing he reel o a source of single-phase ension hrough a condenser and a variable resisor, under he condiions of elecromechanical resonance, afer an iniial displacemen of he core, i is hen possible o obain a ranslaor movemen of his las (direc and opposie). The speed of oscillaion can be conrolled by variaion of he capaciy or resisance. Key words: linear moor; linear parameric moor, oscillaing moor I. Inroducion: The inducion parameric moor has excellen execuions in comparison wih he ordinary single-phase moor, since his one uses parameric oscillaions and abnormal phenomena, while he inermien roaion where he invered normal roaion ensures wih asynchronous and synchronous concepion; or an inverse direc displacemen, his can occur in reason of he insabiliy of he parameric oscillaions. This abnormal behavior mus be avoided when an engine wih parameric inducion is used for pracical applicaions. The naure of elecromechanical resonance depends on he presence on wo oscillaing conours, L.C conour wih elecric oscillaions and he core wih mechanical oscillaions which are due o he elecromechanical acion applied o his core, which is similar o he acion of a spring. The energy exchange beween wo conours is carried ou forunaely o he periodic variaion of inducance. he displacemen of he core in he wo direcions, involves he variaion of inducance. Wih a cerain value of he laer, a phenomenon of Ferro resonance engages and an imporan force aracs he core owards a second poin of Ferro symmerical resonance per repor/raio a he poin medium of he reel. I is hen possible o obain a ranslaor movemen of his las (direc and opposie). The speed of oscillaion can be conrolled by variaion of he capaciy, he resisance or he supply volage like by acion on he frequency. The couple or he force only resuls from he variaion of pure inducances. I is hus associaed a deformaion of he magneic circui figure (). shows he ype of oscillaing engine relucan a linear wih springs of balance. The srucure consiss of a coil (4) conneced in series wih a capaciy (5) and (6) resisance limiing curren Ferro resonan, powered by a source (7) single-phase volage as a whole can be equaed wih a saor. Nucleus () consiss of a magneic plae Assembly foam in a circular plasic ube represens he roor. In our work we have modeled mahemaically operaion of linear moor as being moor asynchronous urning; i has wo elecric equaions which govern i, one of he saor and he oher of he roor. The moor consiss of an iron bar moving inside a coil, his coil is conneced in series wih a capacior and his circui is hen fed from an AC volage source. The moor operaes on he basis of resonance in RLC saor circui The (C.I.N.C) presens difficulies of saring and sop, i is used herefore especially in he elecromagneic pichers. Fig () linear oscillaing ubular moor 77 Page

2 Comparaive sudy beween wo models of a linear oscillaing ubular moor Firs model [8]: Elecric equaion of he C.I.N.C. Circui RLC series by is elecric equaion governing is operaion has a model idenical o ha of a machine wih D.C. curren excep for movemen. The elecric equaion of he oscillaory ubular linear moor is an equaion of a circui RLC series wih reel wih iron core fig (): i R L C U Fig () equivalen elecrical schemaic di L dx L.. i R. i. i. d u d x d C () Elecric equaion of he C.I.N.C. Second model: The self-inducion coil coefficien L depends on he peneraion of he nucleus. The calculaion of L is done by considering he inducor as he associaion of an inducance of he air lengh l, wih a self-inducion coefficien L in series wih an inducance iron nucleus of lengh l f, wih self-inducion coefficien of L f and a muual M [8]. This inducance is expressed as: L=L + L f + M Wih: M K L. L f Applying he firs law of Kirchhoff o primary and secondary circui from he C.I.N.C fig (3). We obained: Fig (3). equivalen elecrical schemaic of C.I.N.C 78 Page

3 Comparaive sudy beween wo models of a linear oscillaing ubular moor di dl dx di dm dx U Rb. i L. i.. M. i. i. d d dx d d dx d C di dl f dx di dm dx U RN. i Lf. i.. M. i. d dx d d dx d Afer simplifying we ge: dl di di dm U. dx d d dx dl f di di dm U ( RN. v). i L f. M. i.. v dx d d dx du C i C. d ( Rb. v). i L. M. i. v U C () C: he capaciance, L : he inducance of he air, L f : he inducance of he core, M: he muual inducance, U and U: respecively he volage of he coil and he core circuis, i and i : respecively he currens of he coil and he core circuis, R b and R n : are respecively he resisances of he coil and he core, This expression can be wrien in he following marix form: [ ] [ ][ ] [ ][ ] [ ] [ ] (3) This is a deferenially equaion non linear and non homogeneous wih second member. The magneic force f m is expressed by he following formula: ( ) (4) f m ( ) F.cos wm. f m : is he magneic force acing on he bar, Where: m: is he masse of he bar, x: he posiion of he cenre of he bar, The resulan movemen is he summer of wo oscillaing periodic of bea (w m, w ) and a deferen ampliudes. : Frequency mechanical oscillaion of he nucleus. Mechanical model of he C.I.N.C. Non damped oscillaory mechanical sysem has he form fig (3) Wih a condiion: Fig (3) : Oscillaing mechanical sysem unamorized ( ) (5) w k m : Source frequency. : Frequency criical resonance. wr 79 Page

4 Comparaive sudy beween wo models of a linear oscillaing ubular moor Comparison of wo models: The firs model equaion (), gave simulaion resuls presened in figures (.,.,.3,.4). Cons by he simulaion resuls of our model equaion () are illusraed by he figures (.,.,.3,.4,.5,.6,.7), and comparison of resuls beween he wo models allowed us o conclude concordance of he wo works. The linear moor oscillaing parameric single consiuion, i operaes on he basis of an elecric Ferroresonance occurs in a saor consising of an RLC circui where he coil iron core. Solving he sysem of mahemaical equaions describing he behavior of he moor requires compuer skills. In he case of he Ferro- resonance ransiens are generally long-ime simulaion sudies are significan cos. The Ferro resonance phenomenon is very sensiive o parameer values and iniial condiions are unknown in pracice, we need o sudy for each possible combinaion, which is no normal. To arrive a soluions, differen mahemaical mehods are used. Our case is o rea he problem by simulaion using MATLAB. Fig. variaion of he oal inducance in funcion of(x) Fig. variaion of he speed in funcion of (x) Fig.3 variaion of he inducance L f of funcion of (x) 8 Page

5 L L Lf Comparaive sudy beween wo models of a linear oscillaing ubular moor Fig.4 variaion of he force in funcion of he ime Fig. variaion of he inducance L f in funcion of he ime Fig. variaion of he inducance L in funcion of he ime Fig.3 variaion of he oal inducance L in funcion of he ime. 8 Page

6 v v M Comparaive sudy beween wo models of a linear oscillaing ubular moor Fig.4 variaion of he muual in funcion of he ime. Fig.5 variaion of he force in funcion of he ime x Fig.6 variaion of he speed in funcion of (x) Fig.7 variaion of he speed in funcion of he ime. 8 Page

7 Comparaive sudy beween wo models of a linear oscillaing ubular moor II. Conclusion The comparison made in his aricle, among us o conclude concordance of he resuls obained, so we can say ha i is possible o use boh models o modeling a ubular linear moor wih oscillaion, on he oher hand we are ineresed in a possible model is he magneic force which is deduced from he oal inducance of he coil evaluae he laer is a he cener of he coil a a value close o.[h] for boh models wihou forgeing of course he oal curren. So i imperaive for any sudy on he linear moors ubular o swing hrough he operaion of he deerminaion of he oal inducance of he coil. We noe ha he resuls obained by he model () are similar o hose of he Model (). Where one can see ha he evoluion of inducive and capaciive volages are he same and nearly equal o he resonan poins giving he form of elecrical pumping. Bibliography []. s. Kikuchi and K. Ishikawa «A New Type 4-Legged Linear Parameric Moor wih Excellen Performance» []. IEEE Transacions on magneic, vol. 33, No. 5, Sepember 997. [3]. IEEE Transacions on magneic, vol. 34, No 4, July 998. [4]. Yorshinori Misuo Nasusaka Koichi Murakami, «Anomalous phenomena in he performance of he parameric moors» [5]. K. Ishikawa and M. Ishizuka and S. Kikuchi, Performance Characerisics of A New Type of Linear Parameric Moor Wih Double Driving Surfaces, IEEE Transacions on magneic, vol. 34, No 4, July 998. [6]. B.Z.Kaplan, «A noe on parameric machines» Proc. IEEE, vol.54, p. 898, 966. [7]. D. HEDJAZI and A. Chaghi and.abdessamed, Modeling and characerizaion of High Performance Linear Oscillaing Parameric Moor, Jee Journal of Elecrical Engineering, vol. 7, N,Poiechnica of Timisoara, Romania. ISSN , 7. [8]. K. Ishikawa and S. Kikuchi, «Improvemen of he Performance characerisics of a linear parameric moor wih Open Magneic Circui» IEEE Transacions on magneics, vol. 35, No. 5, Sepember 999. [9]. E.A.Mandrela, «Comparison of he performance of a lnear relucance oscillaing moor operaing under AC supply wih one under DC supply» IEE ransacions on energy conversion, Vol.4 N 3, Sepember 999. []. A.MAZOUZ, D.HEDJAZI A.CHAGHI, Calculaion and visualizaion of inducances and magneic force of a coil iron nucleus, IOSR-JEEE. Vol 9, N, 4, 83 Page