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5 – ANALYSIS,

5 – ANALYSIS, CALCULATIONS AND EXPERIMENTS Coils Magnet Material MULTOGAN Material NdFeB dC hC lC d 0.1 mm 2.0 mm 2.2 mm 1.7 mm dM dL BHmax 1.5 mm 5.0 mm 38 MGOe N 2 × 400 0.15 A IC Table 5.4: Parameters of the Helmholtz VCA test setup. at the full stoke expressed in (5.6). For the second, Fmax shall be achieved at the half stroke expressed in (5.7). Fmax = FV CA( ˆ f) ⇒ EV CA = Fmax = FV CA ˆf 2 ⇒ EV CA = 1.5 mm 0 mm 0.75 mm −0.75 mm FV CA(x)dx FV CA(x)dx (5.6) (5.7) The optimization curves in relation to the coil clearance are shown in figure 5.10. A coil energy improvement of around 22 % will be optained for the second case (blue) compared to the first case (red). Furthermore, the maximum coil energy occurs approx- imately at dopt like in the maximum force simulation of the anti-coupled Helmholtz VCA shown in figure 5.9. The same static measurement as described in subsection 5.3 was performed for a Helmholtz VCA setup with the parameters listed in table 5.4. The current was set to a low value to suppress the coil heating. The test setup did also not allow to measure the force at x > −1.5 mm. Figure 5.11 shows the measured force distribution, whereas the curves in the positive x-domain are rotational symmetric mirored as well. The measured curve characteristics are in good agreement with the simulated results plotted in figure 5.7. With the same Helmholtz VCA setup, several dynamic measurements were per- formed to gain conculsions about the eddy current brake effect and the induction with the different coil wirings and couplings. The magnet was thereby moved along the x-axis inside the fixed coils driven by a loudspeaker VCA, which was excited with different shaped signals. 40

5 – ANALYSIS, CALCULATIONS AND EXPERIMENTS Considering the step response measurements showed in figure 5.12, distinct statements about the different wiring of the coils can be made. The anti-coupled setup shows a considerably better damping behaviour and smaller induction voltage peaks. Due to the same winding number of the coils and the opposite axial orientation, the induction peaks will be almost completely suppressed. Furthermore, the eddy current brake effect occurs in both movement directions, what can be deduced from the falling edge of the upper curve in figure 5.12 (right). Thus, this measurement results confirm the selection of the favoured Helmholtz VCA setup for applying it in the MSTS. 41

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