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Angular poling effect on cymbal piezoelectric structure using rhombohedral and tetragonal PMN-0.33PT for energy harvesting applications

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Abstract

Cymbal transducers have been discovered as a viable design for piezoelectric energy harvesting under heavy impact loads. However, low-output voltage remains a source of concern; therefore, many promising approaches for enhancing performance efficiency are crucial in the field of piezoelectricity. This study presents a viable angular poling approach for flex tensional based cymbal structures solely for energy harvesting applications. Elementary and Euler angular poling are two types of angular poling introduced for cymbal piezoelectric transducers. Using the energy method, theoretical modelling is performed on a cymbal structure exposed to a 1000 N impact force. Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-0.33 PT) is utilised as a piezoelectric material because of its strong piezoelectric properties in both tetragonal and rhombohedral symmetry. The findings show that Euler angular poling outperforms elementary angular poling due to its reliance on two angles. When elementary angular poling is used, the voltage and energy reach 108.9 V and 380.1 μJ, respectively, resulting in a 198.02% and 2800% enhancement over the original PMN-0.33PT material. Similarly, in Euler angular poling, voltage and energy reached 123.59 V and 450 μJ, respectively, resulting in increase of 238.1% and 3340%. Finally, potential applications include powering light-emitting diodes and charging small portable electronic devices such as digital cameras and cell phones. A large-scale system can be built using cymbal piezoelectric tiles, making it suitable for use in industrial applications such as ultrasonic welding, diesel fuel injectors, and robotic systems.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\(a_{0}\) :

Distance from that apex to the top of the cavity [mm]

\(a\) :

Radial distance from the imaginary apex of the cone to the outer edge [mm]

\(\lambda\) :

Cavity angle [degree]

\(C_{s}\) :

In-plane force per unit circumference [mm]

\(\delta\) :

Angle between the vertical load axis and the slope of the end cap cavity [degree]

\(d_{ij}\) :

Piezoelectric strain coefficient, i varies from 1 to 3 and j varies from 1 to 6 [C/N]

\(\varepsilon_{c}\) :

Strain developed in laminar composite due to compression

\(\varepsilon_{t}\) :

Strain developed in laminar composite due to tension

\(E_{3}\) :

Electric field along third direction [V/m]

\(F_{u}\) :

Edge load per unit length [N/m]

\(h_{e}\) :

Thickness of metal end cap [mm]

\(h_{c}\) :

Height of cavity [mm]

\(h_{p}\) :

Thickness of piezoelectric material [mm]

\(h_{s}\) :

Thickness of substrate material [mm]

\(P\) :

Electric polarisation [Q/m2]

\(R_{a}\) :

Radius of apex [mm]

\(R_{c}\) :

Radius of cavity [mm]

\(R\) :

Radius of end cap [mm]

\(s_{ij}\) :

Compliance coefficients i and j ranges from 1 to 6 [m2/N]

\(Y_{s}\) :

Elastic modulus of substrate material [Pa]

\(Y_{p}\) :

Elastic modulus of piezoelectric material [Pa]

\(Y_{c}\) :

Elastic modulus of laminar composite [Pa]

\(\in_{ij}\) :

Electrical permittivity coefficient, i and j varies from 1 to 3 [C/Vm]

\(\psi\),\(\chi\) :

Transformation matrices

\(\sigma_{t}\),\(\sigma_{c}\) :

Tensile and compressive stresses generated in cymbal [Pa]

\(\sigma_{tp}\) :

Tensile stress generated in piezoelectric material [Pa]

\(\sigma_{ts}\) :

Tensile stress generated in substrate material [Pa]

\(\sigma_{x}\) :

Stress generated in x direction [Pa]

\(\sigma_{y}\) :

Stress generated in y direction [Pa]

\(dU_{tp}\) :

Energy generated by tension for piezoelectric in a small volume of the inner cavity region [J]

\(dU_{ts}\) :

Energy generated by tension for substrate in a small volume of the inner cavity region [J]

\(dU_{cp}\) :

Energy developed for piezoelectric due to compression for small volume at outer region [J]

\(dU_{cs}\) :

Energy developed for substrate due to compression for small volume at outer region [J]

\(\eta\),\(\kappa\),\(\varphi\) :

Angular poling angles [degree]

\(Q\) :

Total electrical charge [C]

\(Q_{gen}\) :

Charge generated with no applied external electric field or voltage [C]

\(C\) :

Capacitance of cymbal structure [F]

\(V\) :

Voltage generated in cymbal structure [V]

\(U\) :

Electrical energy generated in cymbal structure [J

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Authors and Affiliations

  1. School of Engineering, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, 175005, India

    Jitendra Adhikari, Rajeev Kumar & Satish Chandra Jain

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  1. Jitendra Adhikari
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Appendix

Appendix

\(\psi_{Z} ,\psi_{X} ,\psi_{Z}\) are the rotation matrices about Z, X and Z respectively

$$\psi_{Z} = \left[ {\begin{array}{*{20}c} {\cos \eta } & {\sin \eta } & 0 \\ { - \sin \eta } & {\cos \eta } & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]$$
(A1)
$$\psi_{X} = \left[ {\begin{array}{*{20}c} 1 & 0 & 0 \\ 0 & {\cos \kappa } & {\sin \kappa } \\ 0 & { - \sin \kappa } & {\cos \kappa } \\ \end{array} } \right]$$
(A2)
$$\psi_{Z} = \left[ {\begin{array}{*{20}c} {\cos \varphi } & {\sin \varphi } & 0 \\ { - \sin \varphi } & {\cos \varphi } & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]$$
(A3)

Substituting equations (A1–A3) in Eq. (46) to get

$$\psi = \left[ {\begin{array}{*{20}c} {\cos \eta \cos \varphi - \sin \eta \cos \kappa \sin \varphi } & {\cos \eta \sin \varphi + \sin \eta \cos \kappa \cos \varphi } & {\sin \eta \sin \kappa } \\ { - \sin \eta \cos \varphi - \cos \eta \cos \kappa \sin \varphi } & { - \sin \eta \sin \varphi + \cos \eta \cos \kappa \cos \varphi } & { - \cos \eta \sin \kappa } \\ {\sin \kappa \sin \varphi } & { - \cos \varphi \sin \kappa } & {\cos \kappa } \\ \end{array} } \right]$$
(A4)

\(\chi_{Z} ,\chi_{X} ,\chi_{Z}\) are the transformation matrices for Z, X and Z respectively, given as follows:

$$\chi_{Z} = \left[ {\begin{array}{*{20}c} {\cos^{2} \eta } & {\sin^{2} \eta } & 0 & 0 & 0 & { - 2\cos \eta \sin \eta } \\ {\sin^{2} \eta } & {\cos^{2} \eta } & 0 & 0 & 0 & {2\cos \eta \sin \eta } \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & {\cos \eta } & {\sin \eta } & 0 \\ 0 & 0 & 0 & { - \sin \eta } & {\cos \eta } & 0 \\ {\cos \eta \sin \eta } & { - \cos \eta \sin \eta } & 0 & 0 & 0 & {\cos^{2} \eta - \sin^{2} \eta } \\ \end{array} } \right]$$
(A5)
$$\chi_{X} = \left[ {\begin{array}{*{20}c} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & {\cos^{2} \kappa } & {\sin^{2} \kappa } & {2\cos \kappa \sin \kappa } & 0 & 0 \\ 0 & {\sin^{2} \kappa } & {\cos^{2} \kappa } & { - 2\cos \kappa \sin \kappa } & 0 & 0 \\ 0 & { - \cos \kappa \sin \kappa } & {\cos \kappa \sin \kappa } & {\cos^{2} \kappa - \sin^{2} \kappa } & 0 & 0 \\ 0 & 0 & 0 & 0 & {\cos \kappa } & { - \sin \eta } \\ 0 & 0 & 0 & 0 & {\sin \eta } & {\cos \kappa } \\ \end{array} } \right]$$
(A6)
$$\chi_{Z} = \left[ {\begin{array}{*{20}c} {\cos^{2} \varphi } & {\sin^{2} \varphi } & 0 & 0 & 0 & { - 2\cos \varphi \sin \varphi } \\ {\sin^{2} \varphi } & {\cos^{2} \varphi } & 0 & 0 & 0 & {2\cos \varphi \sin \varphi } \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & {\cos \varphi } & {\sin \varphi } & 0 \\ 0 & 0 & 0 & { - \sin \varphi } & {\cos \varphi } & 0 \\ {\cos \varphi \sin \varphi } & { - \cos \varphi \sin \varphi } & 0 & 0 & 0 & {\cos^{2} \varphi - \sin^{2} \varphi } \\ \end{array} } \right]$$
(A7)

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Adhikari, J., Kumar, R. & Jain, S.C. Angular poling effect on cymbal piezoelectric structure using rhombohedral and tetragonal PMN-0.33PT for energy harvesting applications. Appl. Phys. A 128, 384 (2022). https://doi.org/10.1007/s00339-022-05512-1

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