Skip to main content

Advertisement

SpringerLink
Log in

Modeling the performance of a micromachined piezoelectric energy harvester

  • Technical Paper
  • Published:
Microsystem Technologies Aims and scope Submit manuscript

Abstract

Piezoelectric energy microgenerators are devices that generate continuously electricity when they are subjected to varying mechanical strain due to e.g. ambient vibrations. This paper presents the mathematical analysis, modelling and validation of a miniaturized piezoelectric energy harvester based on ambient random vibrations. Aluminium nitride as piezoelectric material is arranged between two electrodes. The device design includes a silicon cantilever on which AlN film is deposited and which features a seismic mass at the end of the cantilever. Euler–Bernoulli energy approach and Hamilton’s principle are applied for device modeling and analysis of the operation of the device at various acceleration values. The model shows good agreement with the experimental findings, thus giving confidence into model. Both mechanical and electrical characteristics are considered and compared with the experimental data, and good agreement is obtained. The developed analytical model can be applied for the design of piezoelectric microgenerators with enhanced performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

L:

Length of cantilever beam (m)

B:

Width of cantilever beam (m)

H:

Thickness of structural layer (m)

T:

Thickness of piezoelectric layer (m)

V:

Voltage across piezoelectric element (m)

Z:

Coordinate parallel to beam thickness (m)

X:

Coordinate parallel to beam length or axial coordinate (m)

Tk :

Kinetic energy (J)

U:

Internal energy (J)

We :

Electrical work (J)

W:

External work (J)

ρs :

Density of structural layer (kg m−3)

ρp :

Density of piezoelectric layer (kg m−3)

U:

Displacement (M)

S:

Applied strain (None)

T:

Developed stress (Pa)

E:

Electric field (V m−1)

D:

Electric displacement (C m−2)

dVs :

Differential volume of structural layer (m3)

dVp :

Differential volume of piezoelectric layer (m3)

E:

Effective piezoelectric coupling coefficient C (m2)

Cs:

Elastic modulus of structural layer (Pa)

cp :

Elastic modulus of structural layer (Pa)

εS :

Clamped permittivity (F/m)

εT :

Free permittivity (F/m)

ε0 :

Permittivity of free space (F/m)

R:

Generalized mechanical coordinate (M)

Ψ:

Bending mode function

Φ :

Voltage distribution function

F:

Discretized force (N)

Q:

Discretized charge (C)

z t :

Coordinate with origin at the neutral axis and direction pointing parallel to the thickness of the beam (M)

B f :

Forcing vector (Kg)

A:

Applied acceleration (m s−2)

M:

Effective mass (Kg)

K:

Effective spring constant (N m−1)

Θ:

Alternative coupling coefficient (F V−1)

Η:

Viscous drag coefficient (N s m−1)

Cp :

Capacitance of piezoelectric element (F)

Q:

Charge stored (C)

L0 :

Length of tip mass (M)

h0 :

Thickness of tip mass (M)

M0 :

Mass of tip mass (Kg)

J0 :

Moment of inertia of tip mass (kg m2)

S0 :

Static moment of tip mass (kg m)

M:

Mass per length of beam (kg m−1)

EI:

The sum of the moments of area of each layer multiplied by their respective elastic moduli (N m2)

Ω:

Angular frequency (s−1)

ωn :

Resonant angular frequency (s−1)

c, d, e, f:

Constants in the bending mode function

Aij :

Matrix elements

λN :

Mode number (m−1)

Ap :

Differential cross sectional area of piezoelectric layer (m2)

As :

Differential cross sectional area of structural layer (m2)

zp :

Distance between neutral axis of beam and neutral axis of piezoelectric layer (M)

zs :

Distance between neutral axis of beam and neutral axis of structural layer (M)

D:

Piezoelectric coupling coefficient (M V−1)

S:

Compliance (GPa−1)

ut, u0 :

Tip displacement, tip displacement amplitude (M)

ΨL :

Bending mode function evaluated at x = L

Ce :

Filtering Capacitance (F)

I:

Current through device (A)

F, F0 :

Force, force amplitude (N)

Θ:

Phase between force and displacement

Vc :

Rectified voltage across load (V)

R:

Load resistance (Ω)

R:

Normalized resistance

k e :

Electromechanical coupling coefficient

Ζ:

Mechanical damping ratio

Ω:

Frequency ratio

P:

Power (W)

References

  • Anton SR, Sodano HA (2007) A review of power harvesting using piezoelectric materials. Smart Mater Struct 16:R1–R21

    Article  Google Scholar 

  • Cook-Chennault KA, Thambi N, Sastry AM (2008) Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Mater Struct 17:043001

    Article  Google Scholar 

  • du Toit NE, Wardle BL, Kim SG (2005) Design considerations for MEMS-scale piezoelectric mechanical vibration energy harvesters. Integrated Ferroelectronics 71:121–160

    Article  Google Scholar 

  • Erturk A, Inman DJ (2009) An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater Struct 18(2):025009

    Article  Google Scholar 

  • Inman DJ (1996) Engineering Vibration. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Kamel TM, Elfrink R, Hohlfeld D, Goedbloed M, van Andel Y, de Nooijer C, Jambunathan M, van Schaijk R (2009) MEMS-based aluminum nitride piezoelectric energy harvesting module. Smart Syst Integr, Brussels, 10–11 March

  • Law HH, Rossiter PL, Simon GP, Koss LL (1996) Characterization of mechanical vibration damping by piezoelectric materials. J Sound Vibr 197(4):378–402

    Article  Google Scholar 

  • Lesieutre GA, Hofmann HF, Ottman GK (2002) Structural damping due to piezoelectric energy harvesting the 13th international conference on adaptive structures and technologies

  • Meninger S, Mur-Miranda JO, Amirtharajah R, Chandrakasan AP, Lang J H (2001) Vibration-to-electric energy conversion. IEEE Trans Very Large Scale Integr (VLSI) Syst 9:64–76

    Google Scholar 

  • Oguamanam D (2003) Free vibration of beams with finite mass rigid tip load and flexural-torsional coupling. Int J Mech Sci 45(6–7):963–979

    Article  MATH  Google Scholar 

  • Rama Bhat B, Wagner H (1976) Natural frequencies of a uniform cantilever with a tip mass slender in the axial direction. J Sound Vib 45(2):304–307

    Article  Google Scholar 

  • Renaud M, Karakaya K, Sterken T, Fiorini P, van Hoof C, Puers R (2008) Fabrication, modelling and characterization of MEMS piezoelectric vibration harvesters. Sensors Actuators A 145–146:380

  • Renno JM, Daqaq MF, Inman DJ (2009) On the optimal energy harvesting for a vibration source. J Sound Vibr 320:386–405

    Article  Google Scholar 

  • Roundy S, Wright PK, Rabaey J (2003) A study of low level vibrations as a power source for wireless sensor nodes. Comput Commun 26:1131–1144

    Article  Google Scholar 

  • Shu YC, Lien IC (2006) Analysis of power output for piezoelectric energy harvesting systems. Smart Mater Struct 15:1499–1512

    Article  Google Scholar 

  • Sodano HA, Park G, Leo DJ, Inman DJ (2003) “Model of piezoelectric power harvesting beam”. In: ASME International mechanical engineering congress and exposition (IMECE2003). ASME, Washington DC, pp 345–354

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Toronto, 10 King’s College Road, Toronto, ON, M5S 3G4, Canada

    Ali B. Alamin Dow, David Koo, Hasan A. Al-Rubaye & Nazir Kherani

  2. Department for Microsystems Technology, Institute of Sensors and Actuator Systems, Vienna University of Technology, Floragasse 7, 1040, Vienna, Austria

    M. Schneider, A. Bittner & U. Schmid

Authors
  1. Ali B. Alamin Dow
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Schneider
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David Koo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hasan A. Al-Rubaye
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Bittner
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. U. Schmid
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Nazir Kherani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali B. Alamin Dow.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alamin Dow, A.B., Schneider, M., Koo, D. et al. Modeling the performance of a micromachined piezoelectric energy harvester. Microsyst Technol 18, 1035–1043 (2012). https://doi.org/10.1007/s00542-012-1436-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00542-012-1436-x

Keywords

Search

Navigation