Magnetic Field Simulation of a Miniature Circuit Breaker s Coil

Transcription

1 Magnetic Field Simulation of a Miniature Circuit Breaker s Coil Comparison of Simulation and analitical results on the solenoid axis. Conecici-Lucian Madalin, Munteanu Calin, Purcar Ioan Marius Technical University of Cluj-Napoca Cluj-Napoca 40000, Romania conecici.madalin@gmail.com Abstract This paper presents the computer aided design (CAD) and computer aided engineering (CAE) modeling of a Miniature Circuit Breaker(MCB) in order to analyze the electromagnetic field(emf) distribution. In a first step the detailed three dimensional (3D) CAD model of the MCB is constructed in the CAD environment PTC Creo Elements v Then the exact 3D model is imported in the Ansoft Maxwell v.15 CAE environment and the electromagnetic field distribution computed. The field along the axis of MCB s coil is compared with the analytical solution. Keywords Miniature Circuit Breaker (MCB); Electromagnetic Field (EMF); Solenoid axis ; I. INTRODUCTION Also known as a operated electrical switch, a MCB, is designed to protect a electrical circuit from damage caused by overload or short circuit. It s basic function is to detect a fault condition and interrupt current flow. Unlike a fuse, which operates once and then must be replaced, a circuit breaker can be reset (either manually or automatically) to resume normal operation. In the industrial domain the MCB is used in many buildings, and it s preferred before the old fuses. Especially in installations that require up to 30 ka capacity s, the MCB is a more suitable for this type of applications and devices. They can be found in circuits with motors or large lamps, semiconductors or equipment such as transformers and solenoid valves getting strong pulses. Low voltage MCB s, with a rated current of not more than 100A, normally used for domestic use, nowadays, are often installed in distribution boards along with other electronic devices or signal receivers, thus the electromagnetic field generated by the MCB can become a Electromagnetic interference, or EMI, source for the electronic devices in question[1]. In order to begin the study, first of all we need to conduct a comparison between the simulation and the analytical calculation of the same EMF, all of this in order to see the standard deviation between these two. In order to be able to conduct the study, a low Voltage MCB coil was used, to represent the electro magnetic field that it is generated by it, while a current of 60 A travels through the coil. This first part of the article presents the comparison in question. II. 3D MCB MODEL (CAD) The standard European design of a DIN-rail mounted MCB includes the following components as shown in Fig 1.: 1. Actuator lever-used to manually trip and reset the circuit breaker;. Actuator mechanism- forces the contacts together or apart; 3. Contacts Allow current when touching and break the current when moved apart; 4. Terminals; 5. Bimetallic strip- separates contacts in response to smaller, longer term over currents. 6. Calibration screw- for adjusting trip current after the assembly; 7. Solenoid- Separates contacts rapidly in response to 56

2 high overcurrent; 8. Arc divider/extinguish chamber. Fig1.Inside of a circuit breaker Our complete MCB 3D model used for simulation purposes consists of : the contacts, one terminal, the solenoid and the extinguishing chamber. As for this paper we will use to simulate only the magnetic field over the solenoid coil. The Copper is the main material used in producing coils of any size, shape or application due to it s good conductivity, and low resistivity of 1.68x10-8 (Ω m) at 0 o C. C. Solution type, applying excitation, setup conditions and mashing By studying in this case the Electromagnetic field of a stationary coil we have chosen the Magnetostatic solution setup. In order for the simulation to give out the wanted results, like in the real world, here you have to apply current to the coil wire. At each end of the coil wire we have added a excitation, a current of 60A. The only difference is that at one end the current goes into the coil and at the other end the current comes out. Adaptive Mesh Process was used for the simulation in question. This process is working with numerous passes over the model, and refining the mesh with every pass. There are numerous factors that can influence the meshing process, factors like: geometry of the model, field solutions, also a factor is the percent refinement number which in our case was set to 30%. The refined mesh points are calculated by the field solver and placed in areas where fields are stronger. The list of refined point is then passed on to the meshing procedure which places the points and creates an optimal refined mesh for the next pass over the model[3]. The mesh on our model can be seen in Fig.3. complete model can be seen in Fig.. Fig.. 3D MCB model. III. 3D NUMERICAL SIMULATION (CAE) The numerical simulation is based on finite element analysis using the ANSOFT software.the simulation consists out of the following 4 major steps: A. Importing the 3D model into Ansoft and prepare it for the simulation in question After the model was designed in PTC Creo, the model has to be exported in a suitable format so that Ansoft Maxwell can import the drawn geometry without fault. In our case the file format used was.igs. Other changes that will have to be made in Ansoft are: creating a parallelepiped geometry that covers the entire coil, and later will serve as boundary, also at this point the ends of the coil will have to be extended in order for the conductor faces to touch the boundary geometry[]. This is needed in order to apply excitation currents to the coil. Another preparation that has to be done at this point is to draw a line through the center of the coil which later will serve as the solenoid axis, shown in Fig.3. B. Applying Boundary Conditions and Material Attributes A parallelepiped shape is set to be the boundary region, on which the solving setup is applied. As material for the boundary region chosen was vacuum, and it uses a relative permeability of about 1.57x10-6 Hm -1. The relative permeability of vacuum is in the SI system also denoted by the symbol µ 0. For the coil, as a material was chosen copper. Solenoid axis Fig.3. Meshing on used coil model and solenoid axis D. Validate, Analyze and Represent After all the above parameters are set, we can start the simulation by first validating the model, this will find and present any found issues with the model or the set parameters, and will give a report of the found issues. If all parameters are set the software is ready to start analyzing the problem. Depending on the solution setup (refinement of the solution), and on the hardware used, analyzing the problem can take up to a few hours. 57

3 When the software finishes analyzing the problem we are able to represent the results, either in field Overlaid plots, graphic plots or numerical values. Represented in Fig.4. is the Electromagnetic field generated into the vacuum by the coil. field[4]. Fig.5. Solenoid representation If the solenoid in Fig.5. is considered, by applying the right hand rule on it, the magnetic field generated on the z-axis will point to the right, assuming that the solenoid is tightly wound. In order to calculate, the magnitude of the magnetic field, at any given point on the z-axis, the solenoid has to be separated into single loop segments with a infinitesimally small length of dz. In order to be able to calculate the magnetic filed in this infinitesimally small length segment we have to have the current circulating this ring (1)[5]. (1) In this case n equals the number of turns N per unit length L shown by (). () Fig.4. Electromagnetic field surrounding the coil IV. ANALYTHICAL REPRESENTATION OF THE MAGNETIC FIELD ON THE SOLENOID AXIS OF THE COIL A helical coil of wire, tightly wound, whose diameter is smaller than its length is also called a Solenoid. The Solenoid, after it s connected to a current source, will generate on the center axis of the solenoid, or otherwise called a solenoid axis,a magnetic field which essentially is uniform. The magnetic field on the outside of the coil is far weaker. This can be observed also from our simulation result shown in Fig.4. The Solenoid has a large number of potential uses thanks to its ability to change it s magnetic field rather easily, by just changing the Current that flows through it. By using a single loop, of current, to create a magnetic field, the result would be relatively small, this due to the small size of the magnetic permeability constant or µ 0. In order to produce a usable magnetic field for other applications there are solution, increasing the current, or increase the number of loops of current. By using the same wire coiled around several times, and the same current, the same effect can be generated of creating a stronger Magnetic Considering the current circulation in the ring we can calculate the Magnetic Field on axis of the ringerror! Reference source not found.error! Reference source not found.(3) : μ (3) By integrating the magnetic filed on the axis of thering onto the entire length of the solenoid axis we get (4), and by solving the integral we get (5): μ (4) μ (5) By using the theory from above, we are able to calculate the magnetic field generated by our coil on it s solenoid axis. In order to do this we have to have the dimensions of the model. In Table I we have the values of our model used for this calculation[6]. V. COMPARISON BETWEEN THE NUMERICAL AND ANALYTICAL RESULTS A. Analytical results The results have been calculated for a coil with N = 7.5 turns and L= m. The current through coil is 60A, see Table I. 58

4 TABLE I VALUES USED FOR THE ANALYTHICAL MODEL µ0 n [I]=A x x1 x R So by applying the values from Table I and (5) we get the following values for x equal to 0 to 16. Values of the magnetic field alongside the solenoid axis are shown in Table II. Values are first calculated in Tesla [T] and then converted in militesla in order to compare values to simulation results. From this table we will extract and represent the magnetization curve to be compared to the simulation result. TABLE II VALUES OF MAGNETIC FIELD OBTAINED x Bx=[mT] Fig.7. Numerical results from the simulation C. Comparison Of Results By comparing the two results we can see that both methods gave similar results. We have to compare the values of the maximum magnetic field value of both methods and the values of the markers on the Maxwell graphic to the 0 and 16 th value to have a conclusive comparison because the result until the markers show the attenuation curve of the magnetic field. In the Fig.8. below we can observe the difference between B. Numerical simulation results In our example, we used basically the same dimensions from the Table I on the model from Fig.1. In order to extract the values from our model, the solenoid axis shown in Fig. 3. had to be drawn. In our model the solenoid axis is a bit longer than the coil due to the fact that the attenuation curve of the magnetic field can be represented more visible. The axis in our model has a length of about 5 mm. In the Fig.7. the graphical representation of the magnetic field along the solenoid axis, obtained as a result of the simulation, can be observed. the two values: Fig.8. Comparison between analytical calculated results and numerical simulated results We can observe that the magnetization curve is very similar one to another, also that the values are similar in magnitude, the only difference is a standard deviation of results of 0.6 [mt] which can be determined by a small deviation a the axis of the model trough the coil center, caused by a error in finding the center of the coil. 59

5 VI. CONCLUSIONS This method of analyzing results and compare them between one another can be used in this kind of simulations, also to reassure yourself that the results obtained in the simulation are plausible ones and no major error is interfering with the simulation. The electromagnetic filed generated by the MCB coil can be found using Maxwell 3D FEM models, and the magnetization curve can be represented on the Solenoid axis. In order to reassure the results a analytical calculation can be establish and used to determine a potential cause of an error if such appears. REFERENCES [1] YanYan Luo,JianGuo Lu (S.M of IEEE),ZhiGang Li Study of Reliability Test and Analysis for Miniature Circuit Breakers, Electrical Apparatus Institute 33# Hebei University of Technology, pp , 00; [] Yi Wu, Mingzhe Rong, Jian Li, and Jianyong Lou Calculation of Electric and Magnetic Fields in Simplified Chambers of Low- Voltage Circuit Breakers State Key Laboratory of Electrical Insulation for Power Equipment, Xi an Jiaotong University, Xi an , China, 006; [3] Dumitru Pop, Liviu Neamt, Radu Tirnovan, Dorin Sabou 3D Finite Element Analysis of a Miniature Circuit Breaker Technical University of Cluj-Napoca, 013; [4] Said R. Marandi, The Magnetic Near-Field Of A Solenoid Canadian Space Agency, pp. 1-4,Vol1.1996; [5] John T. Conway, Exact Solutions for the Magnetic Fields of Axisymmetric Solenoids and Current Distributions, Ieee Transactions On Magnetics, pp , Vol. 37, No. 4, July 001; [6] H. B. Dwight, The magnetic field of a circular cylindrical coil, Phil. Mag., vol. 38, pp , 1931; 60