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FVCA B dLC 4 –

FVCA B dLC 4 – FUNDAMENTALS Figure 4.5: Loudspeaker VCA model with the indicated vectors of the Lorentz force FV CA, the magnet field B and the coil wire cross section normal d LC building an orthonormal system (left). Cylindric single coil VCA model with some indicated magnet field lines (right). • moving coil concept and • moving magnet concept. This concepts shall be evaluated for the MSTS application. However, when reminding the lifetime requirement, it must be said, that the selection shall tend towards the moving magnet concept to avoid a power lead breakage. 4.3.3 Coil An axisymmetric coil setup allows to generate the highest possible FV CA due to the cross product identity d LC × B =⇒ max when d LC ⊥ B. Since the induced field in the coil does not remarkably influence the magnet field B, FV CA mainly depends on the current IC and the coil wire length LC. Ohm’s law couples these parameters in a reciprocal way to RC = UC IC = 8ρCLC d2 , Cπ (4.17) whereas RC represents the coil resistance, ρC the electrical resistivity, UC the applied coil voltage and dC the coil wire diameter 8 . RC shall be minimized due to the low supply voltage (tab. 2.1). However, to maximize the Lorentz force a high LC is required. 8 Note that dC is considered as the the overall wire diameter including its isolation, whereby the calculated RC is smaller than the measured value. z y x, F r VCA 22

4.3.4 Magnet 4 – FUNDAMENTALS Nowadays several new combinations of materials are used for permanent magnets, which replace more and more the common ferrite magnets. They mainly differ in terms of the maximum magnetic energy product BHmax. Three permanent magnet materials can be taken into account for the MSTS VCA known as • Aluminum Nickel Cobalt (AlNiCo), • Samarium Cobalt (SmCo) and • Neodymium Iron Boron (NdFeB). SmCo and NdFeB are rare earth element magnets with the today highest possible energy products. The theoretical maximum of NdFeB amounts to 64 MGOe [1]. Table 4.2 lists the most important parameters of these materials. Material ρ / kg m 3 BHmax / MGOe TC / ◦ C AlNiCo 7300 7.5 - 9.0 ≈ 800 SmCo 8000 - 8500 28 700 - 800 NdFeB † 7400 64 310 - 370 Table 4.2: Properties of the investigated permanent magnet materials. Listed are the mass density ρ, the maximum magnetic energy product BHmax and the Curie temperature TC. † accessed on June 4, 2008. The restricted MSTS dimension requirements ask for applying a NdFeB magnet due to its high BHmax. The VCA concept in terms of moving magnet or moving coil has a direct influence to the magnet selection concerning its dimensions and mass. Fur- thermore, the Curie temperature TC must be well above the operating temperature of the MSTS to avoid demagnetization. 4.3.5 Cylindric Single Coil VCA VCAs generally consist of a cylindric permanent magnet and an ambiant cylindric coil. An optional ferrite ring, which is directly coupled to the magnet, encases the coil to concentrate the magnetic field lines for achieving higher Lorentz forces. 23

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