#+TITLE: Piezo

Use the below to create your own sonotrode
https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=14002

No, like seriously, if you combine this with a frequency generator and a waveform aplifier capacable to handling high frequency loads, you'd have a academic weapon.




Music acoustics
https://www.phys.unsw.edu.au/jw/basics.html

https://www.animations.physics.unsw.edu.au/jw/dB.htm

https://sengpielaudio.com/calculator-leveladding.htm

The ‘piezoelectric effect’ describes a phenomenon exhibited by a few crystalline materials in which they produce an electrical charge when subjected to mechanical stress, i.e. squeezed. The sign of the resulting voltage changes if compression crosses over to tension. For historical reasons this is referred to as ‘the direct piezoelectric effect’.   The phenomenon is reversible. For these same materials, forcing a charge onto their surface via applied voltage will cause them to mechanically expand or contract. This is referred to as ‘the converse piezoelectric effect’.   As with the direct effect, the direction of crystal distortion (i.e. expansion or contraction) will follow the plus or minus sign of the applied voltage.

The converse piezoelectric effect is what makes power ultrasonic devices possible.   While natural crystals exhibit piezoelectricy, quartz being the prime example, artificial crystals can exhibit much higher electromechanical conversion effectiveness and are exclusively used for the power ultrasonics we will discuss. Lead zirconate titanate compounds in ceramic form are by far the most commonly use for devices currently in use.

An AC voltage applied to a piezoelectric crystal will cause it to expand and contract in response. The expansion and contraction can create sound pressure waves or otherwise act on adjacent media. For practical use, piezoelectric crystals are bolted, bonded, soldered, or otherwise incorporated into composite ultrasonic transducers with the right geometry to convert the applied AC voltage into useful vibrational energy.

Piezo-driven ultrasonics have low power and high-power applications. Examples of low power applications include medical devices for imaging internal organs or structures such as heart valves and fetuses and clock signal generators in electronic instrumentation. We will focus on the high-power application including sonar, flow metering, underwater communications, ultrasonic drills, ultrasonic cleaners, friction welding, cutting blades, dental scalers, and fluid atomization.


* Langevin transducer

An ultrasonic transducer where one or more piezoelectric elements are mechanically compressed (prestressed) between end masses (i.e., a front driver and a back driver).


The term “ Langevin transducer” now describes any piezoelectric-driven longitudinal resonator based on sandwiching piezoelectric materials between two plates secured by a center bolt. Figure 3 shows a modern Langevin ultrasonic transducer. The components of the transducer perform the following functions:

    The transducer has two layers of piezoelectric discs. Use of two piezoelectric discs allows the outer metal cylinders to be at ground potential which protects personnel from shock hazards and minimizes the risk of a short circuit. The discs are placed such that their polarities are opposite to each other; and that allows applying high voltage only to a single location, a center conductor that is sandwiched between the two piezoelectric discs.
    The bolt provides precompression on the piezoelectric discs. Piezoelectric materials can fracture easily from tensile stresses of around 2,000 psi, but their compression strength can withstand a five times greater pressure of 10,000 psi. The bolt bias the discs into their compression region. Thus, when the discs vibrate, their motion is from full compression to a small amount of compression and they never see destructive tension. The Animation in Figure 4 illustrates the motion of the transducer.
    The end plates distribute the point force of the bolt over the entire piezo surface so that the both the static and dynamic compressions in the piezo material are uniform through its volume.



#+CAPTION: Example of simple Langevin transducer (Berlincourt (3), p. 249)
[[attachment:_20240323_194235screenshot.png]]


* Horn design

Horn Designs

Because the only real rule for horn design is conservation of momentum, there are a huge variety of horn shapes and horn tips. Examples of the myriad styles of horn shapes with different tips are shown in Figure 6. The far-right horn, for example, is an assembly of multiple horns attached to one transducer. Each shape has a unique purpose. Each design converts the vibration at the face of the Langevin engine to a vibration on the face of the tip of the horn. The geometrical design of the horn tip provides a cross sectional shape and motion designed to accomplish a specific task.



* Tornplitz

By itself, the Langevin transducer creates mechanical motion. The transducer has plenty of power, but by itself does not lend itself to producing useful work. In Part 2, I introduced a transmission mechanism, the horn, which attaches to the Langevin piezoelectric transducer, the acoustic engine. The horn directs and amplifies the mechanical motion generated by the Langevin transducer allowing its energy to be delivered to the tip of the horn in a high velocity regime suitable for friction welding, cutting, and scaling among other applications. You could think of the horn as an acoustic lever.

In this final part, I will present a second transmission method, Tonpilz transmission technology. In contrast to the horn that leverages the Langevin’s energy into a high vibrational velocity tip for mechanical work, the Tonpilz transmission scheme is aimed at getting 100% of the Langevin’s output into broadcasting acoustic waves from one end and 0% off the other. This makes the Tonpilz type transducer ideal for energy efficient high intensity ultrasound sources.
Applications Using the Tonpilz Transmission

One application in which the Tonpilz transducer-transmission assembly excels is its use in an ultrasonic cleaner. Some ultrasonic cleaners have piezoelectric discs glued permanently to the bottom of the tank. That construct works fine until a piezoelectric disc breaks. Replacement involves a time-consuming effort to chip off the broken disc, cleaning down to the metal, and bonding a new disc into place. Installing a new disc involves faith that another disc may not break soon so the whole process would have to be repeated. Fortunately, there is a better solution. The solution is the construction of ultrasonic cleaners with modular, replaceable piezoelectric elements which can be bolted and unbolted from the assembly. Figure 5 shows an ultrasonic cleaner module and a cross-sectional view of an assembly having two piezoelectric discs, the bolt, the heavy metal back end and the lighter metal, most likely aluminum, head. This is bolted to the bottom of the cleaner tank.



* Practical stuff

https://blog.piezo.com/how-to-safely-solder-joints-onto-piezo-transducers




* Thorlabs

Introduction

In this tutorial we will look at some of the basics of piezoelectronic device structure and operation. These devices utilize piezoelectricity, a phenomenon in which electricity is created from pressure on the device. Piezoelectrics either produce a voltage in response to mechanical stress (known as direct mode) or a physical displacement as a result of an applied electrical field (known as indirect mode). Due to these modes, piezoelectric materials have found considerable use in both sensors and actuators and are often called “smart” or “intelligent” materials. One material in particular, lead-zirconate-titanate (PZT), has found prolific use for piezoelectric devices. Consequently, PZT is the ceramic material that makes up the bulk of piezoelectric actuator devices available on the market. It is not only piezoelectric but also pyroelectric and ferroelectric. PZT devices are capable of driving precision articulation of mechanical devices (such as a mirror mount or translating stage) due to the piezoelectric effect, which can be described through a set of coupled equations known as strain-charge (essentially coupling the electric field equations with the strain tensor of Hooke’s law):



$$ D_i = e^{\sigma}_{ij} d^{d}_{im}\sigma_m $$

$$ \epsilon_k = d^{c}_{jk} + s^{E}_{km} \sigma_m $$

Here D is the electric displacement vector, ε is the strain vector, E is the applied electric field vector, σm is the stress vector, eσij is the dielectric permittivity, ddim & dcjk are the piezoelectric coefficients, and sEkm is the elastic compliance (the inverse of stiffness). The specific matrix elements are used to calculate the useful measures of PZT functionality, though the full derivation of these equations is beyond the scope of this tutorial.



* Piezo Symbol Definitions

|--------+-------------+-------+-----------------+-------------------------------------------------------------|
| Symbol | Object Type | Size  | Units           | Meaning                                                     |
|--------+-------------+-------+-----------------+-------------------------------------------------------------|
| T      | vector      | 6 x 1 | $\frac{N}{m^2}$ | stress components (e.g. s1)                                 |
| S      | vector      | 6 x 1 | $\frac{m}{m}$   | strain components (e.g. e3)                                 |
| E      | vector      | 3 x 1 | $\frac{N}{C}$   | electric field components                                   |
| D      | vector      | 3 x 1 | $\frac{C}{m^2}$ | electric charge density displacement components             |
| s      | matrix      | 6 x 6 | $\frac{m^2}{N}$ | compliance coefficients                                     |
| c      | matrix      | 6 x 6 | $\frac{N}{m^2}$ | stiffness coefficients                                      |
| \epsilon      | matrix      | 3 x 3 | $\frac{F}{m}$   | electric permittivity                                       |
| d      | matrix      | 3 x 6 | $\frac{C}{N}$   | piezoelectric coupling coefficients for Strain-Charge form  |
| e      | matrix      | 3 x 6 | $\frac{C}{m^2}$ | piezoelectric coupling coefficients for Stress-Charge form  |
| g      | matrix      | 3 x 6 | $\frac{m^2}{C}$ | piezoelectric coupling coefficients for Strain-Voltage form |
| q      | matrix      | 3 x 6 | $\frac{N}{C}$   | piezoelectric coupling coefficients for Stress-Voltage form |
|--------+-------------+-------+-----------------+-------------------------------------------------------------|


* Hooke's Law and Dielectrics
What is a constitutive equation? For mechanical problems, a constitutive equation describes how a material strains when it is stressed, or vice-versa. Constitutive equations exist also for electrical problems; they describe how charge moves in a (dielectric) material when it is subjected to a voltage, or vice-versa.

Engineers are already familiar with the most common mechanical constitutive equation that applies for everyday metals and plastics. This equation is known as Hooke's Law and is written as:

$$ S = s . T $$

In words, this equation states: Strain = Compliance × Stress.

However, since piezoelectric materials are concerned with electrical properties too, we must also consider the constitutive equation for common dielectrics:
$$ D = \epsilon . E $$
In words, this equation states: ChargeDensity = Permittivity × ElectricField.


* Coupled Equation
Piezoelectric materials combine these two seemingly dissimilar constitutive equations into one coupled equation, written as:
$$ S = s_E . T + d^t . E $$
$$ D = d . T + \epsilon_T . E $$
The piezoelectric coupling terms are in the matrix d.

In order to describe or model piezoelectric materials, one must have knowledge about the material's mechanical properties (compliance or stiffness), its electrical properties (permittivity), and its piezoelectric coupling properties.
The subscripts in piezoelectric constitutive equations have very important meanings. They describe the conditions under which the material property data was measured. For example, the subscript E on the compliance matrix sE means that the compliance data was measured under at least a constant, and preferably a zero, electric field. Likewise, the subscript T on the permittivity matrix eT means that the permittivity data was measured under at least a constant, and preferably a zero, stress field.



* Material Selection
Select from the following list of piezoelectric materials to view their constitutive property data. The data is presented in constitutive matrix form.
Insulators
Ammonium Dihydrogen Phosphate
Potassium Dihydrogen Phosphate
Barium Sodium Niobate
Barium Titanate
Barium Titanate (poled)
Lithium Niobate
Lithium Tantalate 	Lead Zirconate Titanate:
PZT-2, PZT-4, PZT-4D, PZT-5A, PZT-5H, PZT-5J, PZT-7A, PZT-8

Quartz
Rochelle Salt
Bismuth Germanate
Semiconductors
Cadmium Sulfide
Gallium Arsenide
Tellurium Dioxide 	Zinc Oxide
Zinc Sulfide
