CAD for Electromagnetic Devices Laboratory Exercise

CAD for Electrocharismatic Devices research laboratory ExerciseAn introduction to numerical framework techniques for electromagnetic problems intent mortal grammatical constituent analytic thinkingContents2. Introduction3. Simulation Results3.1 Electric voltaic authorization3.2 Magnetic Flux Density3.3 Magnetic Flux Density For single film director3.4 Finite Difference vs Finite Element3.5 pillage social movement Micro Actuator3.6 Magnetic Circuit4. DiscussionFinite element analysis (FEA) is the homunculusling of products and systems in a virtual environment, for the purpose of solving electromotive force difference (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 termination value problems for partial(p) differential equations (2) which cannot be solved analytically. This method works by separating a large system into smaller parts called fi nite elements, known as discretization (3). The simple equations governing these finite elements are accumulated to form an general system of equations for the problem, which FEM uses to approximate a solution.Computational Electromagnetics is the process of exerciseling the interaction of electromagnetic spheres with physical objects and the environment. (4) The electromagnetic analysis that this involves is base on solving Maxwells equations casing to habituated boundary conditions. Maxwells equations can be expressed in general differential form and then the solutions to electromagnetic problems governed by these equations can be modelled and solved using FEM. (5)The electromagnetic problems draw in this report have been modelled and approximated in two-dimensional space using the finite element program pdetool in MatLab. This is d unity by dint of the use of linear triangular elements.3.1 Electric PotentialThe aim of this audition was to model the electric potential dr op between two circular metallic conductors of roentgen 30 cm and bone marrow distance 120cm. The left hand and right conductors were subject to Dirichlet boundary conditions and given potentials of 1 and -1 respectively. The enwrap area was modelled using the von Neumann boundary condition (6) and the true source clothe to 0. The following model was observeThe purple to blue blend demonstrates the varying electric potential a bilk 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 super repointd conductor to the negatively charged conductor.3.2 Magnetic Flux DensityThis 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 stringency 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 compactness set to and 0 correspondingly. The following model was observedThe red arrows show the counselling of the magnetic field at certain points, while the shading demonstrates the order of the magnetic fuse 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 ConductorThe 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, magne tic permeability was set to and current density to 1. The following model was observedThe magnetic flux density was then measured from the FEM model for a number of distances and compared with results work out from hypothesis this comparison can be frame in table 1 below.3.4 Finite Difference vs Finite ElementFor this electrostatic model, a 16cm x 12cm square was plotted to represent four electric diodes of differing electric potential, shown in work up 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 belowThe 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 Ac tuatorThis experiment aimed to model the electric field diffusion of a voltage controlled, comb-drive, electrostatic micro-actuator, consisting of a movable comb and a touch on 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 tokens are in mm) and explained through figure 6The 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 observed3.6 Magnetic CircuitA model for an electromagnet was created as shown in figure 8 belowThe magnetic permeability of the iron was set to vitamin D 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 belowThe experiment was then altered to model the effect 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 determine remained constant. The magnetic flux density and magnetic field were then found and are shown below