PIEZOELECTRIC ACTUATORS

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PIEZOELECTRIC ACTUATORS

• Ellad Tadmor and Gabor Kosa
• Department of Mechanical Engineering, Technion

Special Thanks Yogev Or
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Introduction (1)

• Piezo-Electric Microphone

• Piezo-Electric Cantilevers

(b)
EPFL, Dep. Micro-Systems Engineering
Akedo (2000)
Kanno (1997)
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Introduction (2)

• Piezo-Electric Constitutive Relation.

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Introduction (3)

• Gibbs Free energy

• Coupling coefficient

• Uchino(1997)

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Polar Actuator (1)

• Radial Actuator

• Important Variables

• Axi-Symmetry

• Constitutive Equations

• The Important Mechanical and Electric Variables

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Polar Actuator (2)

• Coupling coefficient

• Radial Actuator

• Energies

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Introduction (4)

• Centroid of the beam

- z Coordinate when the origin is at the centroid
- Coordinates from an arbitrary origin
- zeta of the centroid of the i-th layer when
the origin is at the centroid
- z of the centroid of the i-th layer from an
arbitrary origin
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Introduction (4)

• 1D form of the constitutive relation for a beam

• Purpose Solving the Equations Above by
  Decoupling the Mechanical and Electric Domains.

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Layered piezoelectric beam model (1)

• The potential along i-th layer is

• By defining the average stress in the layer one
  can describe D(x) as follows

• Thus the electric field of the i-th layer is

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Layered Piezoelectric Beam Model (2)

• By substituting the stress-strain relation

• The electric field of the i-th layer (with EMC)

• The electric field within the i-th layer (with
  EMC)

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Layered Piezoelectric Beam Model (3)

• Axial Force equilibrium and Moment equilibrium

• The curvature and the neutral axis of the beam is

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Layered Piezoelectric Beam Model (4)

• Moment along the beam

• Field Equation

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Illustrative Example (1)

• Asymmetric Bimorph

• Dimensions

• Material properties

• Curvature

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Illustrative Example (2)

• Asymmetric Bimorph

• Maximal difference between the regular
  formulation and the application of our correction