CAD for Electromagnetic Devices Laboratory Exercise

CAD for Electromagnetic Devices Laboratory Exercise An introduction to numerical modelling techniques for electromagnetic problems using finite element analysis Contents 2. Introduction 3. Simulation Results 3.1 Electric Potential 3.2 Magnetic Flux Density 3.3 Magnetic Flux Density For Single Conductor 3.4 Finite Difference vs Finite Element 3.5 Comb Drive Micro Actuator 3.6 Magnetic Circuit 4. Discussion Finite element analysis (FEA) is the modelling of products and systems in a virtual environment, for the purpose of solving potential (or existing) structural or performance issues. (1) FEA is the practical application of the finite element method (FEM), a numerical technique for approximating solutions to boundary value problems for partial differential equations (2) which cannot be solved analytically. This method works by separating a large system into smaller parts called finite elements, known as discretization (3). The simple equations governing these finite elements are accumulated to form an overall system of equations for the problem, which FEM uses to approximate a solution. Computational Electromagnetics is the process of modelling the interaction of electromagnetic fields with physical objects and the environment. (4) The electromagnetic analysis that this involves is based on solving Maxwells equations subject to given boundary conditions. Maxwells equations can be expressed in general differential form and therefore the solutions to electromagnetic problems governed by these equations can be modelled and solved using FEM. (5) The electromagnetic problems outlined in this report have been modelled and approximated in two-dimensional space using the finite element program pdetool in MatLab. This is done through the use of linear triangular elements. 3.1 Electric Potential The aim of this experiment was to model the electric potential between two circular metallic conductors of radius 30 cm and centre distance 120cm. The left and right conductors were subject to Dirichlet boundary conditions and given potentials of 1 and -1 respectively. The enclosed area was modelled using the Neumann boundary condition (6) and the current source set to 0. The following model was observed: The purple to blue shading demonstrates the varying electric potential across the model, with V = 0 at the midpoint of the two conductors as anticipated due to the equation†¦ The electric field is visualised through the red arrows, confirming the expectation that the current would flow from the positively charged conductor to the negatively charged conductor. 3.2 Magnetic Flux Density This experiment aimed to model the magnetic field between two cylindrical, current-carrying conductors of radius 5cm and centre distance of 60cm. The magnetic permeability of both conductors was set to and the current density set to 1 and -1 respectively. The enclosed area was modelled using Dirichlet boundary conditions with magnetic potential set to 0, and the magnetic potential and current density set to and 0 correspondingly. The following model was observed: The red arrows show the direction of the magnetic field at certain points, while the shading demonstrates the magnitude of the magnetic flux density, clearly highlighting that the strength of magnetic flux decreases with distance away from the conductors. The current in each conductor is given by the equation , where J is the current density and A is the cross sectional area of the conductor. Using this equation yields a current of 7.85mA for the left conductor and -7.85mA for the right conductor. 3.3 Magnetic Flux Density For Single Conductor The experiment from 3.2 was then replicated using a single, circular, current-carrying conductor of radius 0.2cm. The boundary conditions for the enclosed area remained the same while, for the conductor, magnetic permeability was set to and current density to 1. The following model was observed: The magnetic flux density was then measured from the FEM model for a number of distances and compared with results calculated from theory; this comparison can be found in table 1 below. 3.4 Finite Difference vs Finite Element For this electrostatic model, a 16cm x 12cm square was plotted to represent four electric diodes of differing electric potential, shown in figure 4. The dielectric permittivity of the electric diodes was set to 1 and the electric potential and electric field for the system was modelled as shown below: The variation of electric field between the positive and negative diodes is represented through the shading and the electric field lines are shown in black. Values for the electric potential at particular geometric coordinates were then measured from the FEM model and compared against the results calculated from FDM; this comparison can be found in table 2. 3.5 Comb Drive Micro Actuator This experiment aimed to model the electric field distribution of a voltage controlled, comb-drive, electrostatic micro-actuator, consisting of a movable comb and a fixed comb, with the latter containing four fingers. The dimensions of the comb were specified as follows: w=1, d=1, dl=0.6 and Lc=3 (all figures are in mm) and explained through figure 6: The movable comb was given a potential of 5V and the fixed comb a potential of -5V to simulate a 10V applied voltage. The electric potential of the enclosed area was set to 0 and the space charge density to 0 as well. The following model, demonstrating electric field distribution, was observed: 3.6 Magnetic Circuit A model for an electromagnet was created as shown in figure 8 below: The magnetic permeability of the iron was set to 500 and current density 0. The coil was represented in the model by two rectangles either side of where the coil appears in figure 6, one with positive and one with negative current density. Given that the current in the coil is 10 A-turns, the current density is given by the equation, where A is equal to the area of the approximated coil. The magnetic permeability of both the coil and the enclosed area were set to and models for the magnetic flux density and magnetic field were achieved. These are shown below: The experiment was then altered to model the effects of the coil if the material of the magnet was plastic, with a relative permeability of 1, and therefore the magnetic permeability of the magnet was set to . All the other values remained constant. The magnetic flux density and magnetic field were then found and are shown below:

“The Lemon Tree” Essay

Film Viewing Assignment The film that I watched is called â€Å"The Lemon Tree† directed by Eran Riklis. The actors spoke in both Arabic and Hebrew, as its plot involved both Palestinians and Israelis. The film took place in the West Bank, Palestine. A middle-aged Palestinian widow named Salma Zidane lives on a property that belongs to her great grandparents. On this property is a field of lemon trees planted by her grandparents themselves when they were alive. This field provides her with a steady source of income and, I believe, a hidden sense of pride.In the film, she gets new neighbors living right across from her. They live exactly on the green line border between Israel and the West Bank. To her disadvantage, her new neighbor is the Israeli Defense Minister and his family. Not to my surprise however, the Defense Minister declares Salma’s field of trees as a threat to the Minister’s safety and quickly tries to initiate an order to uproot them. So, in turn, S alma tries to fight this order. She calls upon Ziad Daud, a young lawyer, to help her save her trees.What greatly interested me, however, was the invisible bond that had developed between Salma and the Minister’s wife, Mira Navon. This woman was portrayed as unhappy with her life in her new house and feels bad for Salma and her situation. They come from two separate worlds, yet they share similar feelings as individuals, rather than as Palestinians and Israelis. This was something I had hoped all viewers would notice and take into regard. Most of the time, the Palestinian-Israeli conflict is never viewed as neutral.Both peoples are criticized, and in my belief, the Palestinians are targeted more harshly than the Israelis. Yet my point is that it is refreshing to see representatives from both parties seen as individuals who struggle with everyday problems, rather than entire minorities battling this ongoing situation. For the most part, this film did a great job of capturing l ife in Palestine and some Israel from a physical standpoint. It captured everything that I, as a Palestinian, am used to seeing.The entire plot was unique yet very accurate in its depiction of what the Israelis will do to sabotage the people and land that mark the very existence of a once peaceful Palestinian state. However, I did not appreciate the romance that occurred between Salma and her lawyer, Ziad. This is completely inaccurate of the Palestinian mentality. Since this was an independent film about a conflict that not many people are completely aware of, viewers will subconsciously or even consciously get a solid idea as to how the Palestinians behave from it.As I know them, Palestinians are very respectful people. They respect themselves and as far as being men and women, they know where they stand. Though a person can argue that Salma felt vulnerable due to the situation that she was in and the fact that she had no man in her life to really comfort her, one has to understan d that there are so many Palestinian families that have lost their husbands/wives/ siblings/kids and they do not invoke shame onto whatever is left of their family through romantic affairs.Yes, she was depressed, and yes she is alone, but the typical Palestinian woman will look to God, not another man, to help her get through her problems. Granted, this film does not depict the entire minority as a whole, but it is implied that Salma represents them. So being the representation of the Palestinians, she is scandalous and insecure. Meanwhile, the Israeli family is very clean and well-kept. They are shown as happy and celebrative at their house-warming party; While Salma and the visitors that we see are quite depressing.In class, we have very briefly discussed the Palestinian-Israeli conflict. It is an extremely controversial and sensitive issue, for we couldn’t even make it through twenty minutes on the subject without having a very defensive intruder raise his voice in the cla ss. Though we have learned that both the Jews and the Arabs have inhabited this land since a time that anthropologists cannot even track, it is still appalling to me how such people can be so inhumane. There is so much evidence, when searched for correctly and accurately, that the Palestinian existence is weakening.Cities are being attacked, villages demolished or evacuated, bombings, and families being destroyed are all brutal factors of the evidence. It is distinctly known through the Middle East that Israelis are destroying olive and lemon trees that are hundreds of years old. What is the point of this? To what extent is this humane and indicative of their desire for peace? Just typing about the topic enrages me. This film, produced by an Israeli, could have done a better job of portraying the Palestinians as stronger people. Though there are some nice aspects about the film, there is a lot that I would have changed.

The Key to Successful Sixth Grade Persuasive Essay Samples

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The Atomic Bomb Of The United States Entered Into The...

In December of 1941, the United States entered into the second World War after the Japanese attacks on Pearl Harbor. Due to these attacks and the dangerous rumors sprouting of German bomb builders, the U.S. decided to put efforts towards constructing the ultimate weapon of mass destruction: the Atomic Bomb. With billions of dollars and over 100,000 people, the Manhattan Project was founded to affirm these efforts by U.S. military and scientists. By the Manhattan Project we saw the unfortunate destruction of Japanese cities, the incredible advances in the world of science, and the threats of the cold war resulting in measures to protect against modern nuclear threats. The first origins of the Manhattan Project began as early as 1930, with physicists such as Albert Einstein, who knew of the power of the single atom. Though it wasn’t until later in the decade that German physicists were able to take those thoughts produce the first artificial nuclear reaction, and even document t he theory. Due to the publication of the theory, many people began to realize the immense power that could come from such a tremendous reaction of atoms. Then, in 1939, a letter was sent to the Franklin Roosevelt, the President of the U.S. at the time, warning of the German research developments. The letter in question was in-part sent by Albert Einstein, who along with the proceeded warnings, also advised Roosevelt to allow sufficient funding for research and development of the technology on AmericanShow MoreRelatedTruman s Choice Was A Good One989 Words   |  4 PagesOn August 6, 1945, a bomb with the force of 20,000 tons of TNT, was dropped on the Japanese city of Hiroshima. Three days later a similar bomb was dropped on the city Nagasaki. Both cities were effectively eradicated and so was there people. 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