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TEMPERATURE AND MAGNETIC FIELD ANALYSIS ON AN ACTUATOR BY USING FINITE ELEMENT METHOD N.Füsun SERTELLER M.Ü. Teknik Eğitim fakültesi Elektrik eğitimi Bölümü 34722 Ziverbey / İstanbul [email protected] Abstract: In this research FL 150 D Type contactor's dimensions is used as an actuator. Three types of material, which commonly used in industry, are examined. These studies are executed seperatly two main groups. First study: Immediately before contactor was switched off, magnetic field and force analysis of contactor is carried out using finite element method (FEM) software program. The other studies, immediately after contactor was switched off. Temperature analysis is obtained by a developed program and their comparative results are issued. In this study, Ferro magnetic and joule losses are so lower, they are neglected, and the study is carried out at a certain time interval that plays most significant role in operation of contactor. Keywords Actuator, Electromagnetic Field, Magnetic Material, Finite Element Element, Heat transfer I-INTRODUCTION Contactors play an important role in Electrical Industry and Electrical Devices. The contactors are not only used as switches, they are also used for controlling and supporting measurement. Their effects on electrical circuits are highly important; both magnetic and thermal operation performances have to be known in detail. The attributes of this study done here, computing and analyzing the electromagnetic field and force and temperature distributions, constituting two indispensable researches not only on an actuator but also all electrical equipments. This study brings together magnetic and temperature analysis together in the same structure. However the analyses are studied separately. The complex processes are strictly tried to avoid, and clear expressions brought in the study to make the problems understandable. II- NUMERICAL PROPERTIES BY USING FINITE ELEMENT METHOD a- Magnetic Field and Force Electromechanical energy conversion is possible when the amount of energy stored in the coupling field depends on the relative positions of the mechanical system. The magnetic field density and magnetic field in an actuator system necessitates of the governing electromagnetic equations to predict accurately the system performance. M 2 Bn Sn n 1 2 0 F (1) B is called magnetic force field, n refers to different air gaps in the contactor, M is the total number of air gap, 0 is the permebility of air gap. Finite Element Method (FEM) allowed the problem discretised in the x-y plane by using magnetic vector potential. Drichlet Boundary conditions are entered to solve the problem [1-2]. b-Thermal Equations The problem inherits symmetry with respect to xaxis; it is considered only ( y 0 ) part of the device. The formulation of the problem is given such 2 T ( x, y ) x 2 2 T ( x, y ) y 2 1 s ( x, y ) (2) k Where T is temperature, s , heat source and k thermal conduction coefficient of contactor metal. FEM scheme based on Galerkin method. Linear triangle elements are chosen. In each triangular element, a field function may be approximated by the first order polynomial, application of the weighted residual method we eventually obtain the discretised FEM form of the heat conduction equation in the contactor. III –SIMULATION AND PROGRAMMING RESULTS a- Simulation and Analytical Results for Magnetic force The numerical method is used to solve magnetic force problems in industrial frequency applications, in magnetic vector potential (A=B) formulation. J current density (A/mm2) as a magnetic field source and dirichlet boundary conditions are used for problem to analyze. The problem structure is shown in Fig.1. Fig. 1 (E Type) Contactor with airgap Problem is analyzed for three materials; cast steel, silicon sheet iron and cast iron. After analyzing the problem, equations are built to obtain the force values numerically. The numerical results are given in Fig2. Casting Steel F-B Curves y axis. The algorithm incorporates linear triangular elements that facilitate proper modeling of problem geometry and can represent the field variables in heat conduction problems very accurately. Silicon Sheet Iron Casting Iron 4,50000E+01 4,00000E+01 3,50000E+01 3,00000E+01 F 2,50000E+01 2,00000E+01 1,50000E+01 1,00000E+01 5,00000E+00 3,06361E-01 2,77650E-01 2,52311E-01 2,31452E-01 2,30770E-01 2,47809E-01 2,84674E-01 3,25940E-01 3,70137E-01 0,00000E+00 B Fig 2. F-B relationship curves Fig. 2 shows that the various materials play an important role for contactor’s performance and magnet design [2]. Mathematica program is developed to analyze temperature distribution on contactor. In the FEM analysis, 204 nodes and 320 triangular elements are chosen. This indicates relatively fine meshing structure for this work. The linear system constructed according to Eq.(2) is solved by the preconditioned conjugate gradient algorithm [3]. The numerical results are tested by the Finite Difference Method (FDM) that based on the same number of nodes. This means that in both methods, the temperature is evaluated in the same spatial points. Fig. 3 Temperature distribution in the contactor The test solutions are performed for different contactor materials. It is presented in Fig.3. At first glance, this graph seems to sketch the temperature distribution as a function of only x spatial variable. Actually, it must be interpreted that each adjacent curve also represents the thermal variation along the IV- CONCLUSION This research study examined how relationship between force and magnetic flux is and how this relationship varies as per temperature values. In some operating conditions, to know this information can be highly important. Beside this high thermal state of a contactor affects its magnetic properties. The other point is the using of both analyzing in the same problem is the specialty of the study. Additionally, the study will have been adapted easily on different subjects. Essential ones are magnet design, coupled problems, temperature distribution problems etc. ACKNOWLEDGE The author would like to thank İ. Taşçı and his company Federal Electric for his technical support. REFERENCES [1] K. Miyoshi, H. Shimizu, S.I. Megura, H. Ueteka, N. Hirota, K. Kitazawa” Development of Compact Magnet for High Magnetic Force” IEEE Transaction on Applied Superconductivity, vol 12, no.1, March 2002. [2] A. Benhama, A.C. Williamson, A.B.J. Reece," Virtual work Approach to the computation of Magnetic Force Distribution from Finite Element Method" IEEE ,Proc-Electro. Power Appl. Vol. 147,No. 6, November 2001. [3] D. S. Burnett, “Finite Element Analysis”, Reading, Massachusetts, Addison-Wesley, 1987.