Piezoelectric Materials: Solutions to Questions

This document provides solutions to questions related to piezoelectric materials. It covers topics such as open loop control, recommendations for piezoelectric actuators, material selection based on properties, and the elimination process for choosing the most suitable material. The document also discusses the operating temperature range and other factors to consider when selecting an actuator material.

First Name Last Name
Instructor
Mechanical Engineering
23 March 2019
Piezoelectric Materials
Solutions to questions:
a. Part:
i. An open loop control refers to a kind of unremitting control system whereby
the output produces no effect on the input signal control mechanism. It is also
known as a non-feedback system. Therefore, in an open loop control there is
no measurement of the output or feedback for purposes of assessment with the
input. The input command remains activated regardless the set point or the
input command of the final outcome. An open loop control system has no
mechanisms for error corrections from instances such as preset value drifts
and deviations from the readings. Any variations in conditions as well as
disturbances are hardly mitigated by such a system as it is poorly equipped to
manage in such situations. This has a negative bearing on its ability to sustain
active tasks whenever such variations or disturbances occur. In fact, the
timing controller remains operative for as long as thirty minutes with internal
functioning already disconnected. This is due to the fact that it lacks feedback
mechanism to adjust accordingly.
ii. I would recommend piezoelectric actuators. Piezoelectric actuators have been
established to have been established to achieve optimum working blend of
moderate to high strain, little to moderate hysteresis, and resistance to stress
depoling (Damjanovic & Newnham 2012). Electro strictive actuators on the
other hand normally used in high frequency transducers have been found to
show some stress induced domain orientation properties that relied on the
operating temperature and the dive conditions. Electro strictive actuators
comprising of high lead titanate compositions are worse as these effects are
more amplified. In respects of all these, piezoelectric actuators would make a
more suitable choice compared to Electro strictive actuators.

iii. Yes, there is a criterion specified by the manufacturer (table 2a) have an
impact on the recommendation in (ii) above.
 Operating temperature range: Electro strictive actuators show less
hysteresis than Piezo actuators, in a restricted temperature go.
Notwithstanding of the diminished hysteresis, they give very nonlinear
movement as a result of the quadratic connection among voltage and
displacement. Additionally, they can't be utilized in a bipolar mode with
decreased electric field quality (switching the electric field does not result
in withdrawal).
 Drive voltage range: Piezoelectric actuators demonstrate an electrical
capacitance four to multiple times as high as piezo actuators requiring
altogether higher driving flows for dynamic applications.
b. For current application I would use series connection. Based on this, which
actuator configurations such as C1p, C2p, C3p, and C4p should be eliminated from
further consideration. Parallel connection will in general keep running at the
equivalent no-heap speed, which will tumble off to some degree with connected
torque; series wiring connection will create a uniform torque, which will tumble off
for all actuators in the arrangement dependent on the aggregate speed of the actuators.
At any minute in time, the rotational speed of the engine will be straightforwardly
relative to the voltage over the "perfect" some portion of the actuator motors, and the
torque on the engine will correspond to the current ("The selection of mechanical
actuators based on performance ..." 2017). These are both bidirectional connections,
so changing the speed will change the voltage and vice versa.
When the actuators are physically connected to such an extent that they will keep
running at a similar speed, wiring them in series will adjust the torque on them. In the
event that they are not associated that way physically but rather should keep running
close to a similar speed, wiring them in parallel will make them do as such, however
in the event that they exposed to contrasting measures of torque that may make the
rotational velocities vary to some degree (Cho, Yang, & Kwon 2010).
c. Based on technique for order preference by similarity to ideal solution (TOPSIS), I
would eliminate piezoelectric 1 designated M1. Young’s modulus identifies materials
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ability to accommodate linear changes when under compression, and/ or tension.
Based on this consideration, M2 is preferable to M1. M2 has a Young’s modulus of
62GPa while M1 has a Young’s modulus of 83 GPa making M2 more suited as it has
more capacity to accommodate changes in length. Changes in length under loading
shares a direct relation with stress buildup within the material hence when not
properly considered, a material can get ton or deformed hindering its performance.
The ability of the material to accommodate changes in length hence means less strain
resulting and hence the impacts on the material ("Design choices: MEMS actuators -
Free Online Course Materials" 2018).
Based on respective relative permittivity property of the two materials, M1 and M2,
M2 is again a more ideal option. M2 has a relative permittivity value of 3800 with
M2 only having 12. Relative permittivity also known as dielectric constant is a ratio
of absolute permittivity to the permittivity in free space.
Piezoelectric coefficient is an indicator of change in volume when a piezoelectric
material is placed in an electric field (Davim 2017). The lower the value of the
piezoelectric coefficient, the better the piezoelectric material. In that regard, M2 has a
piezoelectric coefficient of 630×10^-12 m/V while M1’s piezoelectric coefficient is
43×10^-12 m/V hence M2 is a better alternative.
The materials dielectric strength relates to the maximum electric field which a given
material can endure under ideal conditions without failure. Materials with higher
dielectric strength properties are better insulating material. M1 has a dielectric
strength of 2×10^8 V/m compared to M2’s of 1×10^8 V/m. this means M1 is not
suited as it records the highest insulating properties, twice as much as M2.
Considering the last property, that is curie point, M1 is a favorable alternative over
M2. Curie point is the temperature beyond which certain materials lose their
permanent magnetic properties, to be substituted by induced magnetism. For M1 this
value is at 110 degree Celsius while for M2 the value s at 250 degree Celsius. This
simply means that M2 takes longer to lose its magnetism than M1 hence takes longer
to fit in the electric field and limit resistance from magnetic properties. This makes it
less ideal but stable.
(Going by the above considerations, M1 is hence eliminated, M2 chosen)
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d. The three remaining material are Piezoelectric 2(M2), Electro strictive ceramic 1
(relaxor ferroelectric) (M3), and Electro strictive ceramic 2 (relaxer ferroelectric)
(M4). Based on the operating temperature range of the respective materials, their
compatibility is assessed as follows:
Piezoelectric materials that can work at high temperatures without distress are wanted
for auxiliary wellbeing observing or potentially nondestructive assessment of the
cutting-edge turbines, progressively proficient fly motors, steam, and
atomic/electrical power plants. The operational temperature scope of keen transducers
is restricted by the detecting ability of the piezoelectric material at raised
temperatures, expanded conductivity and mechanical lessening, variety of the
piezoelectric properties with temperature (Dotson 2013). Contrasted with ferroelectric
polycrystalline materials, piezoelectric single crystal maintains a strategic aging from
domain‐related aging conduct, while having high electrical resistivities and low
failures, with magnificent thermal stability. Specifically, piezoelectric type oxyborate
[ReCa4O (BO3)3] single gems for ultrahigh temperature applications has an
operational temperature range exceeding 1000 degree Celsius. These gems offer
piezoelectric coefficients, and electromechanical coupling factors, on the request of
3– 16 pC/N and 6%– 31%, individually, fundamentally higher than those estimations
of α‐quartz piezo crystals (~2 pC/N and 8%). Moreover, the nonappearance of stage
changes before their dissolving focuses ~1500°C, together with ultrahigh electrical
resistivities (>106 Ω·cm at 1000°C) and thermal strength of piezoelectric properties
(< 20% varieties in the scope of room temperature ~1000°C), permit potential task at
outrageous temperature and unforgiving conditions ("Types of Actuators and Their
Applications and Uses - A Thomas Net Buying Guide" 2018).
Relaxor-PbTiO3 (PT) based ferroelectric precious stones with the perovskite structure
have been examined in the course of the most recent couple of decades due to their
ultrahigh piezoelectric coefficients (d33 > 1500 pC/N) and electromechanical
coupling factors (k33 > 90%), far outflanking best in class ferroelectric
polycrystalline Pb(Zr,Ti)O3 pottery, and are at the cutting edge of cutting edge
electroacoustic applications. In this survey, the execution benefits of relaxor-PT gems
in different electroacoustic gadgets are exhibited from a piezoelectric material
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perspective. Openings originate from not just the ultrahigh properties, explicitly
coupling and piezoelectric coefficients, however through novel vibration modes and
crystallographic/space building.
Electrocaloric nanocomposites at the same time get high electrocaloric quality from
inorganic considerations and high dielectric quality from the polymer framework to
show an articulated electrocaloric effect (ECE). By planning the inorganic filler and
polymer lattice, which are both relaxor ferroelectrics with the encompassing
temperature stage progress and limited hysteresis, an expansive ECE winds up
available with high cooling proficiency over a wide temperature run at and close
room temperature. Relaxor ferroelectric polymer poly (vinylidene fluoride–
trifluoroethylene– chlorofluoroethylene) (P(VDF-TrFE-CFE)) and its mixes have
been appeared to show an immense electrocaloric impact over a wide temperature
range from -15 to 50 °C. This temperature is far beneath the dielectric crest
temperature of the relaxor mix and the outcomes uncover the guarantee of the relaxor
polymers for an expansive scope of electrocaloric cooling applications.
In summary, M2 is more applicable in high temperatures ranges of up to 1000 degree
Celsius. This is far much above the specified values of between -10 to 40 degree
Celsius. M3 and M4 materials (relaxor ferroelectric) is more suited for temperature
ranges of between -15 degree Celsius to 50 degree Celsius. M2 is therefore eliminated
from further assessment.
e. To choose between M3 and M4 relaxor ferroelectric materials, I will consider an
analysis of their respective properties in table 2(b). considering young’s modulus, M4
appear a better alternative to M3 since it has a higher Young’s modulus property
value. M4 young’s modulus is 105GPa compared to 98 GPa in M3. Remember that
Young’s modulus identifies materials ability to accommodate linear changes when
under compression, and/ or tension.
Based on relative permittivity of the two materials, M4 is well placed than M3.
Relative permittivity is a ratio of absolute permittivity to the permittivity in free
space. M4 has a relative permittivity value of 20000 while M3 has a permittivity
value of 17700, 2300 less.
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Considering Electro strictive coefficient, M4 has a value of 1.5×10^-16 m2/V2
compared to Electro strictive coefficient of M3 which is 1.7×10-16 m2/V2. In this
scenario, M3 is a better alternative. The lesser the value of Electro strictive
coefficient, the more suitable a material is for use as an actuator material.
Another point of analysis entails comparison of the dielectric strength of the two
materials. The dielectric strength of a material relates to the maximum electric field
which a given material can endure under ideal conditions without failure. M4 has a
dielectric strength of 2.5×10^8 V/m while the dielectric strength of M3 is1.9×10^8
V/m. this makes M4 more durable under extreme electric fields than M3 hence a
better alternative.
Lastly, we consider curie point and how it compares between the two. Curie point is
the temperature beyond which certain materials lose their permanent magnetic
properties, to be substituted by induced magnetism. This indicates the level of
material’s susceptibility to external magnetic and electric fields and influences the
operational temperature range as well (Engdahl 2010). M3 has a curie point of
47degree Celsius while M4 has a curie point of -21degree Celsius. 47-degree Celsius
is within the required operating temperature range of -10 to 40-degree Celsius
exposing M3 to interference or failure as a result of magnetic field. However, -21 is
way much below the operational temperature range hence M4 would unlikely fail or
loose its magnetic properties within operation temperature range.
From the analysis, M3 stands eliminated leaving M4 as the only suitable material
from which an actuator conforming to the key criteria adopted and desirable material
properties can be made.
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References
Cho, Y.-J., Yang, T.-H., and Kwon, D.-S., 2010. A New Miniature Smart Actuator
based on Piezoelectric material and Solenoid for Mobile Devices. The Abstracts of
the international conference on advanced mechatronics : toward evolutionary fusion
of IT and mechatronics : ICAM, 2010.5, 615–620.
Damjanovic, D. and Newnham, R., 2012. Electrostrictive and Piezoelectric Materials
for Actuator Applications. Journal of Intelligent Material Systems and Structures, 3
(2), 190–208.
Davim, J.P., 2017. Computational methods and production engineering: research and
development. Duxford, United Kingdom: Woodhead Publishing.
Design choices: MEMS actuators - Free Online Course Materials [online], 2018.
[online]. Available from: https://ocw.mit.edu/courses/electrical-engineering-and-
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spring-2007/lecture-notes/07lecture21.pdf [Accessed 23 Mar 2019].
Dotson, Z.S., 2013. Material selection for the actuator design for a biomimetic rolling
robot conducive to miniaturization.
Engdahl, G., 2010. Magnetostrictive Material and Actuator Characterization.
Handbook of Giant Magnetostrictive Materials, 265–286.
The selection of mechanical actuators based on performance ... [online], 2017.
[online]. Available from:
http://www-mech.eng.cam.ac.uk/profiles/fleck/papers/85.pdf [Accessed 23 Mar
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Types of Actuators and Their Applications and Uses - A ThomasNet Buying Guide
[online], 2018. [online]. ThomasNet® - Product Sourcing and Supplier Discovery
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Available from: https://www.thomasnet.com/articles/pumps-valves-accessories/types-
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