THE INFLUENCE OF THE MAGNETIC NON-LINEARITY ON THE MAGNETOSTATIC SHIELDS DESIGN

Transcription

1 THE INFLUENCE OF THE MAGNETIC NON-LINEARITY ON THE MAGNETOSTATIC SHIELDS DESIGN LIVIU NEAMŢ 1, ALINA NEAMŢ, MIRCEA HORGOŞ 1 Key wods: Magnetostatic shields, Magnetic non-lineaity, Finite element method. The analytical magnetostatic shields design appeas to be vey simple and is based on the lineaity of the magnetic mateial. The main poblem begins with the eal behavio of the mateial on diffeent applied magnetic field. An impopiate choose of mateial can offe a high designed efficiency of the shield but a vey poo eal efficiency in applied field. The pesent pape analyses, using Finite element method, the efficiency of magnetostatic shields in tems of mateials and applied magnetic field. Taking in mind that, geneally, mateials with the highe magnetic pemeability have coesponding low satuation points some guidance in mateial choosing can be outlined. 1. INTRODUCTION Due to the explosion of the hadwae and softwae technologies in the last decade, the design of the electomagnetically devices becomes moe and moe dependent on the numeical methods of electomagnetic field computation, especially on the Finite element method, FEM. Also the optimization is now a pocess developed unde FEM technologies. The easy way to accomplish the non lineaity and the complicated stuctue of the mateials, geat accuacy of the simulation, educed costs, speed of analysis pemit to take into account a lot of models (geomety, mateials, loadings, ) and choose the best fitting of a desied imputed condition. Actually design method of magnetostatic shields is based on analytically computation of the magnetic field intensity inside the shields by consideing the lineaity of the magnetic mateials. In the pesent pape a cylindical shield model was consideed to illustate the influence of non-lineaity in its efficiency. Thee diffeent magnetic mateials have 1 Noth Univesity of Baia Mae, liviu_neamt@ubm.o Anghel Saligny Technical College, Baia Mae Rev. Roum. Sci. Techn. Électotechn. et Éneg., 53, Suppl., p , Bucaest, 008

2 130 Liviu Neamţ, Alina Neamţ, Micea Hogoş been selected and a value of shield efficiency in diffeent applied fields was tageted as a esult of the FEM design pocess.. ANALYTICAL DESIGN OF THE CYLINDRICAL MAGNETOSTATIC SHIELDS A cylindical tube is placed in a unifom magnetostatic field, localized in ai, with its axis pependicula with espect to field diection (Fig. 1). The efficiency of the magnetostatic cylindical shield is given by the attenuation facto: B0 A =, (1) whee B 0 and B i ae the flux densities befoe and afte shielding, espectively. B i Fig. 1 Cylindical shield model with notations. Using the notations given in Fig. 1, the efficiency can be analytically computed. Consideing the lineaity of the magnetic mateial ( constant) [1], its expession becoming: A = ( 1+ ) ( 1 ) 4 i e Some appeciations about the maximum flux density of applied field suppoted by the mateial of the shield until the magnetic satuation become not negligible can be done taking into account the maximum value of flux density in the mateial, B m, also analytically computed [1]:. ()

3 3 Magnetostatic shields design 131 i + 1+ ( e i + 1 ( e B0 1+ B. m = i i + 1+ ( 1) + 1 ( e e + i + 1 ( e (3) These values have to be compaed with the values fom the (B, H) cuve of the mateial, to evaluate the diffeence between the constant taken into calculus and the eal value. Of couse elation (3) and the values of fom (B, H) cuve geneate an unending cycle of computations so expession (3) being only an image of mateial behavio. 3. FEM BASE DESIGN OF THE CYLINDRICAL MAGNETOSTATIC SHIELDS Magnetic field distibution in tansvesal section of the inteest domain is given by the Maxwell equations educed fo magnetostatic plane-paallel egime and leads to a Laplace equations: 1 A = 0. ( B) FEM solving [] of (4) tough its associated functionals: (4) 1 1 F( A) = ( A) ( A)d s, s (5) pemits to calculate the flux density anywhee in the simulated domain, the attenuation facto becoming easily to detemine. All simulations wee done using FEMM 4.1 softwae [3]. Constucting the models implies choosing the oute and intenal diamete of the shields and the magnetic mateial.

4 13 Liviu Neamţ, Alina Neamţ, Micea Hogoş 4 The feomagnetic mateials consideed in FEM simulations ae: low cabon steel, 1010 Steel with a constant elative magnetic pemeability (linea consideation of mateial) = 90.6, cobalt ion Hipeco 50 with = 350 and nickel alloys Mu metal with = The magnetic chaacteistics ae illustated in Fig.. Fig. Relative magnetic pemeability of inteested feomagnetic mateials. Fo having the possibilities to compae the efficiency of shielding fo diffeent mateials the cylinde geomety was selected in tems to each the same attenuation facto with unsatuated mateials. Thee configuations with feomagnetic mateials descibed above whee FEM analyzed and the esulted atios, intenal/oute diamete, ae summaized in Table 1. Also the analytical calculations ae made and the esults ae pesented as a compaison of methods. Table 1 Compaison of the analytical and FEM esults Feomagnetic A B mateial i [T] i / e i / e (imposed) (analytically computed) (FEM computed) 1010 Steel Hipeco Mu metal Both simulations ae consideed fo a value of flux density of the field befoe shielding B 0 = T.

5 5 Magnetostatic shields design 133 The diffeences appeas to be insignificant but in tems of shield thickness came to be extaodinay, e.g. fo Hipeco 50 and i = 0.5 m it s 11.5 mm vesus 16 mm and ae due to incoect value of elative magnetic pemeability (choused constant fo linea mateial). The effect will stat to become moe accentuated with the inceasing of the magnetic flux density of the initial field. Opeating with the FEM computed values of geomety, fo each mateial, it was simulated using FEM the magnetostatic shielding effect fo an inceasing set of values of magnetic flux density of the applied field. In accoding to magnetic chaacteistic of the mateials the satuate effect becomes moe apidly seen. Fo example the Mu metal compotment can be easily outlined using the magnetic spectum and the distibution of the magnetic flux density inside of the shield fo B 0 = T, in Fig. 3a and fo B 0 = T, in Fig. 3.b. a Fig. 3 The magnetic spectum and the distibution of the magnetic flux density: a) B 0 = T; b) B 0 = T. The maximum magnetic flux density in the shield mateial eaches T and the magnetic field intensity the values of A/m, in the second case. The value analytically detemined (3) goes to a double value, T fo flux density and A/m fo magnetic field intensity. The FEM elative magnetic pemeability evaluation indicates a value of fa fom the constant pemeability of The satuation of the feomagnetic mateials deceases the eal attenuation facto. The effect is moe visible fo the mateials with highe elative pemeability because, geneally, them have coesponding low satuation points (Fig. ). The attenuation facto fo diffeent values of magnetic flux density of the non-shielded field and mateials, as esults fom FEM simulations, is illustated in Fig. 4. b

6 134 Liviu Neamţ, Alina Neamţ, Micea Hogoş 6 Fig. 4 The attenuation facto FEM computed. Some elevant infomations egading these esults ae easily to deive: the attenuation facto follows the magnetic chaacteistics of mateial: stated with an initial magnetic pemeability, eaching maximum value and the satuation affected section; it is not enough to choose the geomety and the mateial fo a magnetostatic shield with an tageted shielding effect; the behavio in the applied field (depending by the value of magnetic flux density) has to be analyzed; it is had to done the poblem in analytically mode; the lineaity of mateial conducting to inadequate esults, dealing with non-lineaity ceating vey complicated poblems most of them insolvable; FEM is one of the best ways to accomplish the poblem due the easiness of dealing with non-linea mateials, complicated geomety, speed of analyses and low costs involved; the economical aspects of the design ae eady to be appeciate tacking into account that the shields constucted fom these thee mateials have the same initial attenuation facto, the diffeence being the shield thicknesses. 4. CONCLUSIONS As a conclusion, based on above mentioned, the authos tied to point a stategy to design a magnetostatic shield, following these steps: selection of the available feomagnetic mateials fo the shield (available fom manufactue), analytically choosing the oute and intenal diamete of the shields in coelation with the magnetic mateial (),

7 7 Magnetostatic shields design 135 coection of the geomety fo all choused mateials using FEM simulations at a vey low magnetic flux density of the applied magnetic field (to avoid the magnetic satuation effect fo all mateials), evaluation of the coected shields at maximum expected magnetic flux density of the non-shielded magnetic field; some of the feomagnetic mateials can be eliminate if the satuation points ae low; FEM simulations of the shields configuation fo diffeent values of applied magnetic flux density (at least between the lowest value and the maximum expected one) dawing the vaiations of the attenuation facto in tems of applied magnetic flux density and feomagnetic mateials; choosing the best fitting shields tageting an technical and economical optimum. To exemplifying the method let consideed that we need an attenuation facto of 39.73, fo a non-shielded magnetic field in ange of T and 0.01 T. All steps ae aleady coveed in the pesentation of the pape, except the last one. Only two feomagnetic mateials cove the desied attenuation: 1010 Steel and Hipeco 50. In the studied ange of flux density both geneate the appopiate minimum and maximum values fo efficiency of shielding (neithe unde the 39.73). Electomagnetically judging, both ae identically, the economical and mechanical aspects being those who make the diffeence: e.g. fo 1m intenal diamete the 1010 Steel thickness is 46 mm and the Hipeco 50 thickness is 16 mm. The manufactue pocess, the pice of mateials, the weight and dimensions of the shields must to be compaed to find an optimum. Received on 15 Septembe, 007 REFERENCES 1. G. Hotopan, Compatibilitate Electomagnetică, Edit. Tehnică, Bucueşti, J. Jin, The Finite Element Method in Electomagnetics, John Wiley & Sons, New Yok, D. Meeke, Finite Element Method Magnetic, Uses Manual,