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5 – ANALYSIS,

5 – ANALYSIS, CALCULATIONS AND EXPERIMENTS Component Node Material cH / J kgK λT / W mK m / kg ɛ / - Coil 1 Cu 385 393 0.2 · 10 −3 0.6 Magnet 2 NdFeB 9 † 502 ‡ 0.31 · 10 −3 0.5 Fixed part 3 Steel 444 67 6 · 10 −3 0.5 Moving part 4 Steel 444 67 4 · 10 −3 0.5 Table 5.1: Thermal and material properties of the nodes 1 to 4 of the thermal network configuration (fig. 5.1). Listed are the heat capacity cH, the coefficient of thermal conductivity λT , the mass m and the defined thermal efficiency ɛ. † www.johnsonmag.com, ‡ www.shnfb.com accessed on June 8, 2008. Coil Temperature / °C 120 110 100 90 80 70 60 50 40 30 40 50 60 Electronic Board Temperature / °C 70 80 90 Figure 5.2: Thermal analysis curves of the moving coil concept (red) and the moving magnet concept (blue). The average power dissipation of the coil is set to PC = 0.6 W and a MSOP temperature to 45 ◦ C. 32

5.2 Finite Element Calculations 5.2.1 Electromagnetic FEM 5 – ANALYSIS, CALCULATIONS AND EXPERIMENTS First estimations of FV CA for the coil dimensioning were performed with (4.15). How- ever, force measurements of different loadspeaker VCAs and voice coil motors showed, that this simple mathematical model cannot be applied for the dimensioning of the MSTS VCA. As a powerful tool, the FEMM 2 electromagnetic simulation software was used for the design progress. FEMM solves planar and axisymmetric problems for electro- and magnetostatic setups. The results of the FEM calculations are in good agreement with the performed test measurements. The left part of figure 5.3 shows a cylindic single coil VCA setup meshed with triangles. Since FEMM solves axisymmetric problem in 2D, just the half of a cylindrical VCA’s cross section must be sketched. The parameters of the magnet, the coil and the surrounding air 3 are directly indicated inside of the corresponding countours. As result of the calculation, the right part of the figure shows the field lines and the magnet field distribution represented with graded colors. The generated Lorentz force will be determined by integrating the coil area and results as a planar vector. 5.2.2 Mechanical FEM Applying the mathematical model for the mechanical deflection calculation presented in (4.2) shows results, which are in a good agreement with the FEM calculations performed with NASTRAN. Therefore, this formula was mainly applied for the di- mensioning of the FH structure. For experimenting with more complicated FH shapes, the calculations must be per- formed with FEM. The mechanical FEM model was generally meshed with tetrahe- drons of an adequate mesh size for reducing the calculation time. 2 The Finite Element Methode Magnetics (FEMM) solver is a freeware tool an can be downloaded at http://femm.foster-miller.net accessed on June 8, 2008. 3 Air must be defined as surrounding medium for the DM. The permeability and permittivity of air and vacuum (space condition) almost conicide, that this fact practically can be disregarded for the flight model. 33

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