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Air NdFeB 40 MGOe

Air NdFeB 40 MGOe 0.125mm [Coil:500] 5 – ANALYSIS, CALCULATIONS AND EXPERIMENTS Figure 5.3: A meshed cylindrical single coil VCA (left) and the corresponding FEMM calcualtion result (right). The left vertical border of both images indicates the rotation axis of the half of the cross section. Integrating the magnet field in the green coil area and multiplying it with the defined current results in the Lorentz force. 5.3 Cylindric Single Coil VCA Experiments As first performed experiments, three test VCAs with different self wound coils were constructed and measured for verifying the calculations and simulations. A single point load cell with strain gauges 4 was applied for the force measurement after cal- ibrating it with reference weights. Fixed on a linear positioning table, the load cell carried the magnet, which penetrated into the fixed coil on its x-axis. First of all, the linear force to displacement characteristic FV CA(x) ∝ x was verified by linearly augmenting the coil current IC. A good correlation was established for currents up to IC = 500 mA. However, during the steady state with IC > 0.5 A, the coil was heating up to temperatures of > 100 ◦ C. This caused unlinearities in the FV CA(x) relation due to the coil resistance changement. For all VCA setups, the static force distribution FV CA(x) along the coil axis was measured and compared with the simulations. Figure 5.4 shows the measurement results of a VCA setup with the parameters listed in table 5.2. The cruxes in the negativ x-domain in the mentioned figure indicate the measured values. Due to the test setup, no forces for x > −1.5 mm could be measured. However, when considering 4 www.vishay.com/docs/12002/1004.pdf accessed on June 8, 2008. 34

5 – ANALYSIS, CALCULATIONS AND EXPERIMENTS (4.20) and its curve plotted in figure 4.7, the characteristic for the positive x-domain can be anticipated. Therefore, the curve in figure 5.2 is rotational symmetric mirrored for easier interpretation. All measurement results are in good agreement with the analytic and FEM calculations. Coil Magnet Material MULTOGAN † Material NdFeB dC 0.1 mm dM 2 mm hC 1.75 mm dL 3 mm lC 4.2 mm BHmax 38 MGOe N 500 0.2 A IC Table 5.2: Parameters of the test VCA setup for the static measurements, whereas hC represents the coil winding height, dM the magnet diameter and dL the magnet length (see fig. 6.2). † www.isodraht.de/MHflachd.pdf accessed on June 8, 2008. The MSTS switching mode characterized in figure 2.1 allows to estimate the induced voltage in the coil, which depends on the magnet’s velocity expressed as Uind ∝ −Bx(x) ˙x. (5.1) High induction voltage peaks possibly disturbe the power supply and furthermore complicates the control of the MSTS. However, as an advantage of the induction, the transient period of a weakly damped spring-mass system can be shortened due to the eddy current brake effect. This damping effect shall be utilized during the launch by short-circuiting the coil for achieving lower FH deflections forced by structure shakings. 5.4 Flexible Hinge Experiments The calculations and measurements of the test VCAs confined the range of generate- able Lorentz forces to FV CA ≈ 130 mN. This value was applied for estimating the FH dimensions starting with a blade thickness of h = 50 µm. Its width was defined to b = 5 mm according to the maximum dimension requirement. The following calcula- tion shows the necessary FH blade length of a stage with two parallel blades presented in section 4.1.5. At this stage, Ti-6Al-4V was definitely selected for the MSTS FH structure. Thus, with its Young’s modulus, the required deflection of f = 1.5 mm 35

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