Scaling of electromagnetic transducers for shunt damping and energy harvesting

Abstract

In order for an electromagnetic transducer to operate well as either a mechanical shunt damper or as a vibration energy harvester, it must have good electromechanical coupling. A simple two-port analysis is used to derive a non-dimensional measure of electromechanical coupling, which must be large compared with unity for efficient operation in both of these applications. The two-port parameters for an inertial electromagnetic transducer are derived, from which this non-dimensional coupling parameter can be evaluated. The largest value that this parameter takes is approximately equal to the square of the magnetic flux density times the length of wire in the field, divided by the mechanical damping times the electrical resistance. This parameter is found to be only of order of one for laboratory devices that weigh about 1 kg, and so such devices are generally not efficient, within the definition used here, in either of these applications. The non-dimensional coupling parameter is found to scale in approximate proportion to the device's characteristic length, however, and so although miniaturised devices are less efficient, much greater efficiency can be obtained with large devices, such as those used to control civil engineering structures.

Output power and efficiency of electromagnetic energy harvesting systems with constrained range of motion

“…In this article, the maximum power condition and the corresponding efficiency for constrained vibration based linear and rotational energy harvesting devices were presented. For convenience, and for enabling the comparison of different systems, the definition for the coupling coefficient of an energy harvesting device given by (32) is employed [27]. In a linear system, electromechanical coupling coefficient ( It is shown that in a system with linear motion and constrained throw, even with the assumption of negligible mechanical losses, the maximum harvestable power (at optimum condition, i.e., max ,, l linear P i RR  ) is half of the mechanical power that can be absorbed by the transducer.…”

“…A question that arises here is "how do the output power and efficiency of a system change by increasing the size of the generator?". Elliott and Zilletti [27] . Hence, an option in increasing the coupling coefficient of a transducer is to increase its overall size.…”

“…differentiation of (26), which results in By comparing the optimum load resistance for maximum output power ( max ,, l linear P i RR  ), and the load resistance corresponding to the maximum achievable system efficiency derived in (27), it is realized that the latter is always greater than the former. Therefore, in a practical linear system it is not possible to achieve maximum efficiency at the maximum output power point.…”

“…By replacing (7) in (9)  is a non-dimensional electromechanical coupling coefficient of an energy harvesting system and is defined as [27] for linear systems and for rotational systems. By increasing this coefficient (i.e., em    ) the maximum output power, given by (31), approaches the following expression This shows that the maximum theoretical power is determined by the environmental vibration characteristics ( n  , Y ) and also the system mass and the maximum allowable displacement.…”

“…Note that n  is a characteristic of the transducer, but here the system is designed such that the undamped natural frequency of the device is equal to the frequency of excitation. Considering (26), the efficiency of a constrained linear system for the load resistance corresponding to the maximum output power ( max ,, l linear P i RR  ), can readily be shown to be [27] For weak linear coupled systems, the efficiency is low. By increasing em  the efficiency increases until it reaches a maximum value of 50%, i.e.…”