5 PASSIVE INTERFACES FOR RESONANT CANTILEVER-BASED
5.2 Description of the interfaces
Since RL conducts the same current as the resistors R and s R , then the add energy dissipated by the load per half cycle will be divided in proportion to the resistors‟ magnitude as:
2 OC s add L L 2 L s L L 8 2 1 V C Q R R R V C R R R W loss . (5-3)
From Equation (5-3) it can be observed that W is maximised when R L Rloss, for which: s add loss 2 1 C L R Q . (5-4)
This, in turn, corresponds to a maximum load power equal to:
s 2 s 2 OC 2 max ω π 2 π R C V Q W P . (5-5)
Magnetically and mechanically activated interfaces are here proposed to passively achieve the SSHI and so to enhance the performance of resonant cantilever-based piezoelectric energy harvesters.
5.2 Description of the interfaces
5.2.1 Magnetically activated SSHI
Figure 5-2 depicts the design of a novel developed passive interface with magnetically activated SSHI for resonant cantilever-based piezoelectric energy harvesters at low frequency.
Figure 5-2 A schematic of the passive interface circuit with two reed switches for magnetically activated SSHI
This circuit configuration is like the one seen in Figure 3-7 for the implemented cantilever-based piezoelectric energy harvester but, in this case, the inductor
add
L is added in series to the piezoelectric harvester and the connected resistive load RL; in addition, two reed switches determine the flow of the generated current into the circuit. The reed switch is an electrical switch made of two contacts on ferrous metal reeds, which are magnetisable, flexible, and hermetically sealed at the opposite ends of a glass envelope. In the circuit configuration of Figure 5-2 the contacts are separated by a small gap as the reed switches are in a normal open condition, thus drawing zero power, but can be operated (i.e., closed contacts) by an applied magnetic field of the right intensity. The reed switches, in fact, are characterised by a specific pull-in distance, which is defined as the distance from the permanent magnet used for its activation. Such a distance depends both on the switch‟s design and the intensity of the generated magnetic field. The harvester‟s permanent magnets on the top and bottom of the proof masses are essential for the correct working order of such a passive interface design. Due to the displacement of the beam under vibrations, the magnetic tip mass gets closer to the respective reed switches. As a general rule, a 50% overlap region ensures 100% activation of the switch. The majority of the manufacturers also specify 20% hold region and 80% close region [226]. Therefore, the switch has to deflect on either side for a
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particular, known the tip displacement of the piezoelectric beam at resonance and within the acceleration region of interest, the position of the reed switches can be set so as to be closed when the beam deflection has reached an extremum. The same behavior is desired for both the top and the bottom set of the switches. By reaching the desired deflection, the piezoelectric element is not in an open circuit anymore but connected to the inductor L , which causes the add inversion of the piezoelectric voltage , for an enhanced power transfer to the resistive load RL. The resistive load is then connected when V is maximal in either polarity (i.e., at the zero crossing of the current source), which coincides with the extremum displacements of the cantilever beam. As the beam tip bends back away from the switches and the magnets move along, the switches return to their normally open state. Such an operation repeats at every half cycle of the sinusoidal input but could be adopted for any kind of input whose waveform reaches the same peak levels in terms of amplitude rather than time. Being hermetically sealed, hence protected from the outside environment, the contacts of the reed switches are not susceptible to wear and can typically perform billions of reliable operations.
5.2.2 Compression springs for force amplification through fixed strips Figure 5-3 depicts the piezoelectric harvester implemented as in Paragraph 3.2.3 with, in addition, two compression springs on the free end of the proof masses.
Figure 5-3 A schematic of the passive interface circuit with two compression springs on the free end of the proof masses and two strips for the amplification of the applied force
On both sides of the harvester‟s cantilever beam, close to the compression springs, there are also two conductive strips that are spatially fixed. The strips are on each side separated by an air gap and not connected to the rest of the circuit so that, from an electrical point of view, they represent an open circuit and do not contribute to the overall working functioning of the circuit. From a mechanical point of view, however, the strips form a fixed frame that counteracts the deflection of the piezoelectric beam tip under vibration. The presence of the compression springs generates an enhancement of the mechanical force acting on the tip of the piezoelectric beam depending on the design of the harvester and on the characteristics of the input vibration (i.e., the magnitude of the acceleration in the case of resonant applications). The diameter of the springs is bigger than the air gap between the strips and they are reciprocally aligned in a way that, at each deflection of the beam tip, the ends of the springs impact against the strips leaving their air gap in between. As the springs offer resistance to the compressing force, they push back the beam tip trying to restore their original length. Because of the compression springs, such an interface is more flexible to small variations of the vibration input, especially in the case of resonant applications or applications where the frequency of the excitation is always within a narrow bandwidth. The distance of the strips from the springs can be set in a way that the deflection of the piezoelectric cantilever beam is not damped but magnified as the constrained swing of the beam, between the two frames, generates a mechanical resonance through the reciprocal compression of the springs. The compression of the springs required to trigger the mechanical enhancement on the acting force is tiny for low resonant frequency applications under small acceleration magnitudes. This increases the service life of the springs as contact stress is reduced; additionally, side deflections or loading problems related to the maximum speed of shifts of the moving end of the spring are also reduced. 5.2.3 Mechanically activated SSHI
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activation is here operated by the mechanical contact between the compression springs and the conductive strips.
Figure 5-4 A schematic of the passive interface circuit with compression springs and conductive strips for mechanically activated SSHI
One end of both the conductive strips at the top side and bottom side of the piezoelectric cantilever beam is connected to the series made by the harvester and the inductor L whilst the opposite ends are connected across the resistive add load RL in a reciprocal way. The electrical circuit is left open in correspondence of the air gap between the two ends of the conductive strips and closed by the contact onto the compression springs at every positive or negative beam deflection that reaches the pre-tuned distance between the springs and the strips. Thus the flow of the current from the harvester to the resistive load can be ensured through the inductance L at every half cycle of the input add excitation. Known the displacement of the cantilever beam in correspondence to a certain excitation frequency (e.g., resonance) and acceleration magnitude, the position of the strips can be experimentally determined to achieve the synchronisation of the switching process at every extremum displacement of the piezoelectric cantilever beam. In such a way, the SSHI technique is passively enabled in a mechanical way. The inversion process, started from the contact between the compression springs and the conductive strips, is naturally blocked with the release of that contact in correspondence to a change of direction in the beam‟s displacement. Figure 5-5(a) illustrates the trend of the voltage developed across the piezoelectric cantilever-beam as a consequence of the
switching process, whose main steps are show in Figure 5-5(b) for the duration of a whole cycle of the beam‟s oscillation.
(a) (b)
Figure 5-5 An illustration of the mechanically activated SSHI process: (a) a trend of the voltage developed across the piezoelectric cantilever-beam and (b) the correspondent beam’s oscillation for the duration of a whole cycle
It has to be noticed that the compression springs act like a mechanical energy storage under the acting force of the piezoelectric cantilever beam. The energy stored by the contact between the compression springs and the conductive strips is released immediately after that contact, thus yielding an increase of the inversion quality towards a more effective PEH process where the voltage onto which the piezoelectric current source drives its charge is further augmented.