Coil Topology Optimization for Transducers Based on Cylindrical Magnets
The previous chapters have been concerned with the optimization and comparison of eight different coupling architectures in electromagnetic vibration transducers. In summary, geometrical dimensions were found which yield to a maximum output power and outp
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Coil Topology Optimization for Transducers Based on Cylindrical Magnets
6.1 Introduction The previous chapters have been concerned with the optimization and comparison of eight different coupling architectures in electromagnetic vibration transducers. In summary, geometrical dimensions were found which yield to a maximum output power and output voltage, respectively. The comparison of the maximum performance limits yield the most efficient architectures which should consequently be favoured in the application whenever possible. However a basic characteristic of all the architectures (independent of the architecture class) is that the topology of the coil has always been predefined to be cylindrical. Hence the underlying optimization approach is strictly speaking a sizing optimization. Obviously this makes sense because cylindrical coils, especially made of enamelled copper wire, are state of the art and easy to fabricate. Moreover the optimized dimensions (especially for the “Magnet across coil” architecture class) show that the resulting coils are rather thin. Consequently there is not much space left for an optimization of the coil topology. But for all that an interesting question arises from this: Is there an axially symmetrical coil topology for an arbitrary cylindrical magnet, which results in a higher output power than a cylindrical coil, and how does it look like? To answer this question a coil topology optimization procedure was developed which is the topic of this chapter. The chapter is divided into four sections. Section 6.2 introduces the basic idea behind the topology optimization formulation strategy. Section 6.3 presents results of the output power topology optimization based on a predefined cylindrical magnet. To evaluate the performance of the topology optimized coil, architecture A II was chosen as benchmark because it performs best within the architectures based on cylindrical magnets without back iron (refer to Sect. 4.4.1). The chapter concludes with a summary and a discussion of the benefit and the applicability of topology optimized coils. Note that in spite of the previously presented sizing optimization, where the output power and the output voltage are considered separately the topology optimization focuses only on D. Spreemann and Y. Manoli, Electromagnetic Vibration Energy Harvesting Devices, Springer Series in Advanced Microelectronics 35, DOI 10.1007/978-94-007-2944-5 6, © Springer ScienceCBusiness Media B.V. 2012
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6 Coil Topology Optimization for Transducers Based on Cylindrical Magnets
the output power. This is because the limited construction volume condition is no more valid. However, the magnet dimensions must be predefined which results in a variable construction volume. Hence, even coil windings that are very far from a given cylindrical magnet will contribute to the overall output voltage, since the transduction factor is still greater than zero, regardless of the resistance or volume. Consequently a voltage topology optimization would result in huge coils which p
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