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A2 Exam – 22/23 LSA
(a) A sample has a rectangular shape as indicated in Figure 1(a). When this sample is compressed in one direction, it elongates in a perpendicular direction as indicated in Figure 1 (b) below.
Figure 1
(i)For the shape given in Figure 1 (a), taking into consideration the nature of the deformation in Figure 1 (b), discuss in 100 words, possible directions in which the poling of this piezoelectric element should be carried out. The direction should be indicated in a schematic.
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(ii)Draw a schematic indicating the poling process as required in (a) (i) above and discuss the strategy used to ensure homogenous heating of the element being subjected to poling.
[20%]
(b) Figure 2 shows two designs for piezoelectric energy harvesting devices. Each of these designs are realised by combining multiple units of the piezoelectric element discussed in (a). Adjacent piezoelectric elements through a flexible conductor. A1 and A2 indicate electrodes while Fy indicates loads acting on the devices .
Figure 2
(i)Taking into consideration the direction in which the load is applied, and the placement of the electrodes, discuss in which direction poling direction for this design.
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(ii)Based on your knowledge on the operation of piezoelectric energy harvesting devices and the deformation of materials under applied loads, discuss why Design 2 can potentially lead to better energy harvesting in comparison to Design 1.
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(c)You have been given the following expression which indicates the improvement ratio ( when a design is modified from a single piezoelectric element , to 3 piezoelectric elements .
Here is a constant, is the piezoelectric coupling coefficient for elements while is the piezoelectric coupling coefficient for elements & .
Using the above relationship, discuss which of the following conditions leads to the best improvement ratio. Your discussion must be supported by calculations.
Condition 1: when
Condition 2: when
Condition 3: when
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Model Answers
(a)
(i)For the shape given in Figure 1 (a), taking into consideration the nature of the deformation in Figure 1 (b), discuss in 100 words, possible directions in which the poling of this piezoelectric element should be carried out. The direction should be indicated in a schematic.
In the shown schematic, the load is applied on the material in the schematic, the load is applied on the material in the y direction while the deformation happens in the z direction. Based on the direction of the load application and the shown schematic, the deformation of the material proceeds in both the y and z direction. Therefore, poling can be carried out in either of these directions and should be chosen based on the targeted application. These directions are shown by the red arrows in (b).
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(ii)
We will assume that the element is to be operated such that the deformation is significant in the z direction as drawn in the previous schematic.
In order to ensure that the sample is kept at a uniform temperature and not overheated at any localised point, the sample is immersed in an oil bath. This is to avoid any changes in the structure or performance as a result of localised hotspots when the material is subjected to high voltages (usually in kV range).
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(b)
(iii) In both devices demonstrated, the piezoelectric elements are connected such that the overall units elongate in a direction perpendicular to the applied loading. The electrodes for the given device architectures are also placed in a direction perpendicular to which the load is applied to. Therefore, the energy harvesting is anticipated to be carried out based on the polarisation of the material in the direction perpendicular to which the load is applied. Based on the above, the polarisation of the material should be carried out in the direction perpendicular to the load application direction.
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(iv)
In design 1, the deformation of the material is limited by the total deformation that can be achieved as a result of the applied load in the Fy direction. In Design 2, A, C due to its curved nature, these are subjected to additional extension as a result of the applied load Fy,. This leads to an enhanced extension also for section B in comparison to the design 1. If the materials are judiciously selected and the poling is done is the direction for all elements used in the direction to which the load is expected to add, Design 2 will lead to a higher power output.
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(c)
For condition 1:
For condition 2, as
or
For condition 4, as
or
Therefore
Therefore based on the given conditions, the best efficiency enhancements are realised when followed by when while the least efficiency enahcmenet is achieved when
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