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Presentation Layout
- Project description
- Historical Background
- Piezoelectricity & Piezoelectric transducers
- Coupled field analysis
- Piezoelectric analysis
- Material properties
- Acoustic analysis
- Harmonic analysis
- Results of Single and multiple layers
- Results of Cantilever bimorph beam
- Conclusion
- Future Work
Project Description
- The project deals with the modeling of ultrasonic
(piezoelectric) transducer in ANSYS.
- Piezoelectric transducer used in different application areas,
this thesis contains result for sonar (sound navigation and
ranging) application and some introduction to bimorph beam.
- Modeling is done only for the sonar transmitter application
and for bimorph both actuation and sensing mode results are
obtained.
- Material used is piezoceremic (PZT 5H, PZT 5R, PZT 5A), in
single and multilayer configurations.
Piezoelectricity
- “Piezo” is a Greek word which means “to press”.
- Piezoelectricity means the pressing of material by the
application of electricity (voltage).
- Piezoelectricity is the property of materials possessing
piezoelectric effect.
- Material produce an electric field when the material
dimensions are changed as a result of an imposed mechanical force and vice verse.
Piezoelectric Transducer
- A vital part of the ultrasonic instrumentation system to be used for the generation and detection of the ultrasound.
- Piezoelectric transducer are linear and low cost transducers.
- Piezoelectric transducer are reversible in nature.
- Piezoelectric sensors react on compression. It converts electrical pulses to pressure waves (Transmitter) and the conversion of returned pressure waves back into electrical energy (Receiver).
- Piezoelectric sensors are used in many systems for actuation sensing, detection and energy harvesting.
- used to measure force, torque, pressure, motion, surface roughness and sound.
Ultrasonic Transducer Applications
- Ultrasonic Transducer main Application areas are
- Biomedical imaging and therapy
- Electronic devices
- Industrial processing
- Non-destructive testing (NDT)
- Remote sensing
- Micro electromechanical systems (MEMS)
- Sound Navigation and Ranging (SONAR)
Why using ANSYS?
- There are specialized software available for the modeling of
piezoelectric transducers like PZ flex is tailored for Piezo
analysis using FEM.
- At PIEAS we do not have this software therefore ANSYS is
used to simulate the piezoelectric transducer.
- Modeling in ANSYS is a tedious job, involves the coupled field
piezoelectric and coupled field acoustic analyses combined
even for a simplest working model.
Piezoelectric Analysis
- Piezoelectric is the coupling of structural and electrical
fields which is a natural property of materials such as quartz and piezoceramic.
- Possible piezoelectric analysis types are static, modal
harmonic, and transient.
- Harmonic analysis is used to observe the characteristic
behaviour of transducer.
- Transient analysis is performed to observe the travelling
wave in the medium.
Piezoelectric Analysis (Contd.)
- The electric and mechanical behaviour of any piezoelectric
material can be described by following equations.
- Where
- {T} is the stress tensor
- [c] is the material stiffness matrix under a constant electric field
- {S} is the strain tensor
- {D} is the electrical flux density vector
- [] is the dielectric tensor at constant mechanical strain
- {E} is the electric field vector
- [e] is piezoelectric matrix
T c S e E
D e T S E
Material Properties
- Relative Permittivity [ε]
- Ratio of the amount of stored electrical energy when a
voltage is applied, relative to the permittivity of a vacuum.
- The permittivity values represent the diagonal components
ε 11 , ε 22 , and ε 33 respectively of the permittivity matrix.
Material Properties (Contd.)
- Piezoelectric matrix
- It relates the electric field to the stress or strain
- One can define the piezoelectric matrix in [e] form
(piezoelectric stress matrix) or in [d] form (piezoelectric
strain matrix).
Acoustic Analysis
- Acoustics is the study of the generation, propagation
absorption, and reflection of sound pressure waves in a fluid medium.
- Involves modeling the fluid medium and the surrounding
structure.
- A coupled acoustic analysis takes the fluid-structure
interaction into account.
- Acoustic elements required density and speed of sound
as material properties.
Acoustic Analysis (Contd.)
- Acoustic wave equations is:
- Assumptions are:
- pressure and density changes are small compared to their starting values
- no mean fluid flow
- fluid is inviscid
- one-dimensional form of wave equation is:
2
2 2 2
2 x
P C t
P
P t
P v
2 2 2 2
1
Harmonic Analysis
- The equation of motion governing the harmonic behavior of a structure is given by:
- Where
- F 0 is the maximum forcing amplitude
- i denotes a complex operator
- denotes a phase angle, in radians.
- After simplification we get the following equation
- Where
- U 1 & F 1 are real
- U 2 & F 2 are imaginary
M u C u^ K u F 0 e i ^ t^
2 M i C K u 1 i u 2 F 1 i F 2
Transducer Modeling
- 3D model, interested only in thickness direction of the
model, therefore model known as 1D model.
- Model lateral dimensions must be greater then thickness
to prominent thickness mode.
- Results are taken for single and multiple active layers.
- Voltage is applied at front, back and interacting faces
- Acoustic fluid loading at front and back face
