Optimization Computational Model for Piezoelectric Energy Harvesters Considering Material Piezoelectric Microstructure

Transcription

1 Optimization Computational Model for Piezoelectric Energy Harvesters Considering Material Piezoelectric Microstructure Agostinho Matos, José Guedes, K. Jayachandran, Hélder Rodrigues Contact: 11/09/2014 Instituto Superior Técnico

2 Motivation Nowadays there are many sources of free energy: a) Natural Energy wind, waves, solar, etc b) Human Technology engines, industrial machines, etc Many of the energy sources cause mechanical vibrations. A piezoelectric material can convert vibrations to power Real world applications can have various types of loadings

3 Motivation Applications & More...

4 Motivation To deliver power it is not enough... It is necessary to deliver the required power... A piezofiber composite plate of 2.2 cm 3 produces 120 mw Now in 2014 it can be done 1.73e10 computations per mwh.

5 Piezoelectric Constitutive Equations & Others S = S E T + d T E k D = d T + ε T E k The electric current goint out the electrode (S φ ) is: I = Q e Q e = S φ n i D i ds For a Resistor, the harvested power: P a = 1 2 R I 2

6 Piezoelectric Problem Equations Constitutive Equations T ji,j = ρu i D i,i = 0 S ij = u i,j+u j,i ; E 2 i = φ,i Electric Machine Equations, for a Resistor V=RI Boundary Conditions: φ = φ on S φ (electroded part) D j n j = 0 on S D (not electrodes) T ij n i = t j on S T u i = u i on S u S = S φ S D = S u S T

7 Piezoelectric Harvester Setup Longitudinal Generator Unimorph Cantilever Transverse Generator Bimorph Cantilever i) Yellow and Vi surfaces are electrodes; ii) Dark blue is substrate and light blue is a piezoelectric iii) Orange vector P indicates polarization or z-direction

8 Non-Ressonance Results The electrical power of one resistance is P a Harvester P a Loading Longitudinal Generator Transverse Generator Cantilever Unimorph 1 2 R wd 3,3 σ lpa 2 Pressure 1 2 R wd 3,2 σ tpa 2 Pressure 1 2 R wd 3,2 σ apa 2 Tip Bending Moment For the bimorph similar expressions to unimorph;

9 Piezo Materials Piezo Materials : PZT-5H and BaTiO3 - are transversely isotropic (IEEE format) S E in 1e- 12 m^2/n S11 S12 S13 S33 S44 S66 ε T in 8.85e- 12 F/m ε 11 ε 33 PZT-5H BaTiO PZT-5H BaTiO d in 1e-12 C/N d31 d33 d15 For substrate it is used Brass PZT-5H BaTiO

10 FEM Validation It is compared the power results of the developed equations and ANSYS FEM results; power relative error is inferior to 8.5% Configuration P a 0 (pw) P a Theory_0 (pw) RE (%) L.G. 3.92e e T.G. 5.05e e Unimorph 3.23e e Bimorph Series 4.79e e Bimorph Parallel 1.92e e

11 Optimization Algorithm The objective function : Max P a The design variables : (φ, θ, ψ) [313] for each piezoelectric material layer Constraints: (φ, θ, ψ) ε [ 180, 180] degrees Optimization method: simulated annealing

12 Setup Loadings L.G. And T.G All the loadings are harmonic 1Hz Load Cases for Longitudinal & Transverse Generators: Load Cases P: 10 MPa 10 MPa Load Cases PS: 10 or 40 MPa Shear Maximizing P a is the same as maximizing piezoelectric constants Max d in 1e-12 C/N d31 d33 d34 d35 BaTio PZT 5H

13 Configura tion Plus Shear Load (MPa) Results L.G. And T.G Piezo Mat P a 0 Time (min) N eval φ max θ max ψ max P a max P a max P a 0 Loading Condition (pw) (deg) (deg) (deg) (pw) P.1 L.G BaTiO e e P.2 L.G PZT-5H 1.56e e P.3 T.G BaTiO e e P.4 T.G PZT-5H 3.33e e Configura tion Plus Shear Load (MPa) Piezo Mat P a 0 Time (min) N eval φ max θ max ψ max P a max P a max P a 0 Loading Condition (pw) (deg) (deg) (deg) (pw) PS.1 L.G. 10 BaTiO e e PS.2 L.G. 10 PZT-5H 1.56e e PS.3 T.G. 10 BaTiO e e PS.4 T.G. 10 PZT-5H 3.33e e PS.5 L.G. 40 BaTiO e e PS.6 L.G. 40 PZT-5H 1.56e e PS.7 T.G. 40 BaTiO e e PS.8 T.G. 40 PZT-5H 3.33e e-2 1.6

14 Conclusion & Future Work Non-ressonance with a resistance connected what is desired to increase in the case of a constant stress loading is the piezoelectric constants d ij ; It is necessary to investigate if in ressonance the power will increase too as for out of ressonance When choosing a piezoelectric material for a specific application the loading type must be accounted The piezo material can be modelled as a polycrystallyne one

15 Homogenization & Future Work A piezoelectric material has a crystalline microstructure. Each crystal or grain has its own orientation with its grain boundaries; the 3D orientation of each single crystal can be knowed using X-ray diffraction contrast tomography; Homogenization theory allows to calculate overall material properties based in the microstructure 3D grains reconstruction

16 Homogenization & Future Work The homogenization calculates overall material properties of a composite microstructure Optimizing overall material d33 varying material orientation increases d33 114%

17 Acknowledgements: This work is supported by the Project FCT PT DC/EME-PME /120630/2010? Questions?

18 Bimorph Series and Parallel Connections