Saturday, August 13, 2022

Effect of Temperature and Pressure on the Thickness Mode Resonant Spectra of Piezoelectric Ceramic

 HELLOOO……. all my fellow interested readers, Wondering what the topic means and if will you be able to understand this topic, which I agree sounds kind of complicated but worry not this blog will help you understand what the research paper is all about.
It will help people interested in it to get an in-site in this topic and understand it with ease
 So, before we start with the topic
Let’s first understand some important terms in this paper


IMPORTANT TERMINOLOGIES

Let’s understand Piezoelectric ceramic materials

Lead zirconate titanate (PZT), barium titanate (BT), and strontium titanate (ST) are the most widely used piezoelectric ceramic materials. where ε is the relative permittivity or dielectric constant of piezoelectric ceramic materials and is defined as the dielectric displacement per unit electric field.

What is an Acoustic Transducer?

An acoustic transducer is an electrical device that converts sound wave vibrations into mechanical or electrical energy.

As many of you must’ve guessed Piezoelectric ceramics are used to make modern acoustic transducers.

Here we discuss the Effect of Temperature and Pressure on the Thickness Mode Resonant Spectra of Piezoelectric Ceramic

Thickness mode : the standing wave patterns produced are called "modes". When a piezoelectric material is excited by an ac signal two series of resonance are observed. One is in radial mode and other is in thickness mode. The frequency in thickness mode(axial) has high resonance because piezoelectric material is designed to be driven in that direction.

Resonant spectra are emission spectrums resulting from the illumination of a substance by radiation of a definite frequency or definite frequencies.

(And of course, resonance is a phenomenon when the matching vibrations of another object increase the amplitude of an object's oscillations)

The most commonly used piezoelectric material is PZT (Lead zirconate titanate)


This is the structure of PZT for reference

Now that some of the important terms used in a research paper are discussed with an understanding of what the paper discusses



THEORY

Here we use the Van Dyke circuit model that’s recommended by the IEEE standard on piezoelectricity.

Now let’s understand The van Dyke first

Van Dyke model, four real circuit parameters Co, C1, L1 and R1 represent the impedance of the piezoelectric resonator at resonance




The branch L1 , R1 , C1 represents the mechanical behaviour of the piezoelectric disc while C0 represents the electric nature.

For the above equivalent circuit

 The resonant frequency (fr)      

                   

The anti-resonant frequency(fa)

And the C1 is represented by


The characterization of piezoelectric ceramics is done using the resonance method as mentioned in the IEEE standard on piezoelectricity. A small ac electrical signal is used to excite an elastic wave in the piezoelectric via an electromechanical coupling. Depending on the sample dimensions, the frequency at which resonance occurs is observed by measuring the impedance of the sample at various frequencies.



EXPERIMENTAL ARRANGEMENTS

The discs used here had dimensions of, a diameter of 25 mm, a thickness of 2 mm, and a diameter to thickness ratio of 12.5.

And as we know scientific experiments are a little extravagant, the flat surfaces used in the sample are coated with silver electrodes to facilitate an ohmic contact for measuring electric properties

What is ohmic contact?  just think about this for a little while the answer is in the name itself Ohmic contact is a low resistance junction (non-rectifying) that provides current conduction from metal to semiconductor and vice versa. The current here increases /decreases linearly Theoretically!!!

Let’s have a look at the experiment and understand the context of the paper through the experiment conducted for the paper

As can be seen, below given fig A temperature-controlled water bath is used here for studying the effect of change in temperature on the resonant and anti-resonant frequencies. The temperature preferred is in the range of 5 C to 40⁰C.

First Resonant and anti-resonant frequencies are observed at different temperatures with sufficient soaking, this process is repeated 10 times and then average values are computed, and average values are calculated to eliminate errors.

For open channel flow metering, the transducer is located at a maximum of 10m below the water surface. The head pressure acting on the transducer affects its resonant frequency. A height of 10 m of water creates a head pressure of approximate 1 kg.cm^2.

Weights calibrated in terms of pressure were used for simulating the head pressure acting on the transducers, and the weight to be applied on the disc was calibrated using the maximum pressure and the area of the disc.

The pre-calibrated weights are applied to the piezoelectric disc and the values of resonant and anti-resonant frequencies are observed using the circuit shown in the fig above.



RESULTS





Based on these practically obtained model parameters, mathematical modelling using an equivalent circuit approach was implemented in Simulink.

Check what’s Simulink after reading this blog

Below fig is what Simulink does i.e., make a relevant equivalent circuit of the piezoelectric element.

Check the below graphs to understand the results that were obtained.

The resonant frequency is inversely proportional to the thickness of the piezoelectric disc. As pressure is applied to the piezoelectric element, the thickness decreases and so there is an increase in the resonant frequency. As the pressure acting on the piezoelectric disc increases, the stiffness increases and so the resonant frequency increases. The values of resonant and anti-resonance frequencies obtained from the model response match with those obtained experimentally.



CONCLUSION

In this paper, a process condition-based equivalent circuit model of the piezoelectric disk is developed. The process conditions and their ranges considered are suitable for underwater applications. Here the required data is experimentally obtained and the model parameters were computed and a more realistic model was obtained.

 The values of resonant and anti-resonant frequencies of the model response match with the experimentally obtained values for given temperature and pressure conditions. This shows that the model parameters computed are accurate. This work can be further extended to compute other material constants which can be used to develop Finite element analysis-based models of piezoelectric discs.


Credit:
Pratik Nagre (TY Mechanical)
(Team R&D)

References:

https://www.researchgate.net/publication/319599612_Effect_of_Temperature_and_Pressure_on_the_Thickness_Mode_Resonant_Spectra_of_Piezoelectric_Ceramic



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