Department of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mechanical Engineering

ME 2082

Piezoelectric Resonators

Department of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringDepartment of Mechanical Engineering

Introduction

KT: relative dielectric constant of the materialεo: relative permittivity of free space (8.854*10-

12F/m) h: distance between electrodes (m - material thickness) A: area of the electrodes (m2) C0: measured capacitance at 1kHz (F)

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Topics of Discussion� Equivalent Circuit of a Ceramic Element

(Non-resonant operation)

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Mechanical Q

� Mechanical Q EquationFr: resonance frequency (Hz) Fa: anti-resonance frequency (Hz) Zm: resistance at Fr (ohm) C0 :static capacitance (Farad)

� Alternatively, QM can also be determined using the equation:

where F1, F2 are -3dB points on the frequency/impendance curve from the resonance frequency Fr.

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Piezoelectric Modes of Vibration

� The frequency constant, N, is the product of the resonance frequency and the linear dimension governing the resonance. The various modes of resonance are shown schematically for:

� N1=FrD (Hz.m) Radial Mode Disc

� N2=Frl (Hz.m) Length Mode Plate

� N3=Frl (Hz.m) Length Mode Cylinder

� N4=Frh (Hz.m) Thickness Mode Disc, Plate

� N5=Frh (Hz.m) Shear Mode Plate

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Variation of Coupling Coefficients as a Function of Relative Frequency Interval between Series and Parallel Resonant Frequencies

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Equivalent Circuit of a Piezoelectric Resonator

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Measurement of Resonant Frequencies - Circuits

� Constant Voltage Circuit: � Constant Current Circuit:

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Measurement of Resonant Frequencies - Variations

� Variation of Impedance with Frequency:

� Variation of Admittance with Frequency:

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� Variation of Phase Angle with Frequency:

Measurement of Resonant Frequencies - Variations

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� 1-3 Composites

Piezoelectric Composite Transducers

Property 1-3 Composites Monolithic CeramicDielectric Constant K33T 890 ± 20% 3250

Dissipation factor 0.03 0.025

Frequency Constant N3 1475 ± 5% 1850

Kε 0.62

Q (unloaded) 5 70

Ceramic Volume 25-30% 100

Frequency 150 KHz-1.5MHz 150 KHz-5 MHz

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Piezoelectric Flexure Elements

� Bimorph: Flexure elements have two layers of PZT material bonded together, with electrodes in series or parallel configuration. These elements offer large displacements for positioning devices or actuators.

� Series configuration:

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Piezoelectric Flexure Elements

� Parallel configuration:

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� An actuator is a device that produces a displacement (movement) when voltage is applied. Actuators are used for many functions, including canceling vibration, tool adjustment and control, micro-pumps, mirror positioning, wave generation, structural deformation, inspection systems and scanning microscopes. When a voltage is applied to the assembly, it produces small displacements with a high force capability. These actuators can be built from wide rangingpiezoelectric materials offered by Sensor, depending on the various end uses.

Piezoelectric Actuators

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� Bending mode actuators

Piezoelectric Actuators

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� Multilayer piezoelectric actuator is a device consisting of a number of piezoelectric elements in a stack. The elements are generally connected in parallel either through the electrode structure or the insertion of brass electrodes between the elements

Piezoelectric Actuators

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� Diaphragm actuators:Diaphragm actuators consist of a piezoelectric washer bonded to a metal diaphragm. This configuration provide a low cost but good displacement actuator. In applications, the diaphragm must be clamped on its edges to produce the deflection.

Piezoelectric Actuators

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� Tube actuators: A piezoelectric tube element with electrodes on its curved surfaces can be used as an actuator element. The elements offer good structural rigidity, but are more difficult to manufacture. They are often used in such applications as scanning tunnelling microscopes (STMs).

� A tube actuator is generally poled through the wall, but other configurations involving split electrodes and segments are also used as actuator elements.

� The extension of the piezoelectric tube element under a DC voltage V applied in the direction of polarization is given by the formula:Displacement = [L/W]d31V

Where: � L is the length of the tube � W is the thickness of the wall � d31 is the piezoelectric coefficient � V is the applied voltage

Piezoelectric Actuators

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� Electrode Configurations for Tube Elements:

Piezoelectric Actuators

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Igniter Elements

� Operating Principle:� High voltages are generated when piezoelectric

materials are impacted. When this voltage is applied across an air gap, an arc is generated whenever the voltage exceeds the breakdown voltage of the air gap.

� The voltage V generated during the impact can be expressed as:

� V=L x g33 x S� Where L is the length of the element, g33 is the

piezoelectric voltage coefficient and S is the mechanical load in the axial direction.

� A spring-loaded mechanism is generally used to produce the mechanical load on the ceramic element. The energy E is then determined by the equation:

� E= 1/2 CV2