Precision Engine for Nanobiomedical Research

Abstract

The transfer function and the transfer coefficient of a precision electromagnetoelastic engine for nanobiomedical research are obtained. The structural diagram of an electromagnetoelastic engine has a difference in the visibility of energy conversion from Cady and Mason electrical equivalent circuits of a piezo vibrator. The structural diagram of an electromagnetoelastic engine is founded. The structural diagram of the piezo engine for nanobiomedical research is written. The transfer functions of the piezo engine or are obtained.

Full text

J. Biomedical Research and Clinical Reviews Copy rights@ Afonin SM
Auctores Publishing – Volume 3(4)-051 www.auctoresonline.org
ISSN: 2692-9406 Page 1 of 5
Precision Engine for Nanobiomedical Research
Afonin SM
National Research University of Electronic Technology, MIET, Moscow, Russia.
Corresponding Author: Afonin Sergey Mikhailovich, National Research University of Electronic Technology, MIET, 124498, Moscow,
Russia.
Received Date: February 08, 2021; Accepted Date: March 01, 2021; Published Date: March 12, 2021
Citation:Afonin SM. (2021) Precision engine for nanobiomedical research. Biomedical Research and Clinical Reviews. 3(4); DOI: 10.31579/2692-
9406/051
Copyright:© 2021 Afonin SM, This is an open-access article distributed under the terms of the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract:
The transfer function and the transfer coefficient of a precision electromagnetoelastic engine for
nanobiomedical research are obtained. The structural diagram of an electromagnetoelastic engine has a
difference in the visibility of energy conversion from Cady and Mason electrical equivalent cir cuits of a
piezo vibrator. The structural diagram of an electromagnetoelastic engine is founded. The structural
diagram of the piezo engine for nanobiomedical research is written. The transfer functions of the piezo
engine or are obtained.
Keywords: precision engine; electromagnetoelastic engine; transfer function; structural model and
diagram; nanobiomedical research; piezo engine; deformation; transfer coefficient
Introduction
A precision electromagnetoelastic engines in the form of piezo engines or
magnetostriction engines are applied in nanomanipulators, nanopumps,
scanning microscopes for nanobiomedical research [1-6]. The piezo
engine is used for nanodisplacements in photolithography, medical
equipment of microsurgical operations, adaptive optics systems and fiber-
optic systems for transmitting and receiving information [4-12].
The electromagnetoelasticity equation and the differential equation are
solved to construct the structural diagram of an electromagnetoelastic
engine. The structural diagram of the engine has a difference in the
visibility of energy conversion for from Cady and Mason electrical
equivalent circuits of a piezo vibrator [4-8].
Transfer function
The structural diagram of a precision engine for nanobiomedical research
is changed from Cady and Mason electrical equivalent circuits [4-8]. For
a precision engine the equation of electromagnetoelasticity [2-14] has the
form of the equation of the reverse effect
jijmmiiTsdS 

where
i
S
,
mi
d
,
m

,

ij
s
and
j
T
are the relative deformation, the
module, the control parameter or the intensity of field, the elastic
compliance, the mechanical intensity;
621 ,...,,i 
;
321 ,,m 
; and
621 ,...,,j 
are the indexes.
The equation of the force on the face of a precision engine has the form
[10-19]
 
TSFtdt,xdM 0
22 
Where
M
,
F
,

,
x
,
t
,
0
S
are the mass and force of load, the
displacemen, the coordinate, the time, the area of engine.
The differential equation of a precision engine has the form [4-32]
   
0
222  p,xdxp,xd
 
cp
Where
 
p,x
is the transform of Laplace for displacement;
p
,

,

c
,

are the operator of transform, the coefficient of wave
propagation, the speed of sound, the coefficien of attenuation. The
system of the equations for the forces on faces of a precision engine is
written [10-40]
     
p,TSpFppM j0
011
2
1
     
p,lTSpFppM j022
2
2
Where
 
p
1

,
 
p
1

are transforms displacement of faces 1 and 2 for
a precision engine.
The system of equations for the structural diagram and model of a
precision engine for the distributed parameters in nanobiomedical
research on Figure 1 has the form
Open Access
Review Article
Biomedical Research and Clinical Reviews
Afonin SM*
AUCTORES
Globalize your Research

J. Biomedical Research and Clinical Reviews Copy rights@ Afonin SM
Auctores Publishing – Volume 3(4)-051 www.auctoresonline.org
ISSN: 2692-9406 Page 2 of 5
 
 
 
 
   
 
     
 























plp
lpd
pF
pMp mmi
ij
12
1
1
2
11
ch
sh
1
 
 
 
 
   
 
     
 























plp
lpd
pF
pMp mmi
ij
21
2
1
2
22
ch
sh
1
Where
0
Ssijij  
,




153133
153133
d,d,d
d,d,d
dmi
,




13
13
H,H
E,E
m
,





HHH
EEE
ij s,s,s
s,s,s
s
551133
551133
,





 H
E
,
E
is the intensity of electric field,
H
is
the intensity of magnetic field.
Figure 1: Structural diagram of precision engine for distributed parameters.
The matrix equation of a precision engine for nanobiomedical research
has the form
 
       
     
 
 
 





























pF
pF
p
pWpWpW
pWpWpW
p
pm
2
1
232221
131211
2
1
The equation of the direct piezoelectric effect for the piezo engine in
nanobiomedical research [10-14] has the form
k
E
mkimimETdD 
Where
m
D
,
E
mk

are the electric induction and the permittivity;
321 ,,k 
is the index.
The equation for the coefficient of the direct piezoelectric effect
d
k
for
the piezo engine at
constE
has the form
 
 
E
ij
mi
n
n
ds
Sd
p
pI
k



0

,
21,n 
Where
 
pI n


,
 
p
n


are transforms of current and velocity;
n
is
number of the face engine.
After conversion the structural diagram on Figure 1 the structural diagram
of the piezo engine for nanobiomedical research has form Figure 2. The
equation for negative feedback for structural diagram of piezo engine on
Figure 2 has the form
   
p
s
RSd
pU n
E
ij
mi
n



0

,
21,n 
The equation for
r
k
the coefficient of the reverse piezoelectric effect for
the piezo engine in nanobiomedical research is obtained in the form
E
ij
mi
dr s
Sd
kk 
 0

J. Biomedical Research and Clinical Reviews Copy rights@ Afonin SM
Auctores Publishing – Volume 3(4)-051 www.auctoresonline.org
ISSN: 2692-9406 Page 3 of 5
Figure 2: Structural diagram of piezo engine for nanobiomedical research.
The structural diagram of the piezo engine with one fixed face for the lumped parameters is received on Figure 3.
Figure 3: Structural diagram of piezo engine for lumped parameters.
The transfer function of the piezo engine for the lumped parameters in
nanobiomedical research on Figure 3 at
0R
has the form
   
 
e
E
ijv
r
CCpkpM
k
pU
p
pW 




2
2
2
Where
 
pU
is transformations of the voltage. Therefore, the transfer
function of the piezo engine has the follow form
   
 
12
22
2



pTpT
k
pU
p
pW
ttt
U
mi
 
 
E
ijemi
U
mi CCldk  1
,
 
e
E
ijtCCMT  2
Where
U
mi
k
,
t
T
,
t

are the transfer coefficient, the time constant, the
coefficient attenuation;
   
llsSC E
ij
E
ij
E
ij  1
0
is the stiffness of the
piezo engine at E= const. The transfer function of the transverse piezo
engine has the form
   
 
12
22 31
2



pTpT
k
pU
p
pW
ttt
U
 
 
E
e
UCChdk 113131 1
,
 
E
et CCMT 112

J. Biomedical Research and Clinical Reviews Copy rights@ Afonin SM
Auctores Publishing – Volume 3(4)-051 www.auctoresonline.org
ISSN: 2692-9406 Page 4 of 5
Where
h
,

are the height and the thickness;
   
hhsSC EEE 1111011 1
is the stiffness of the transverse piezo engine
at
constE
.
The transient process of the piezo engine at the transverse piezoelectric
effect at the step input voltage has the form
   




















 tt
t
t
t
Ut
T
t
e
Ukt sin
1
12
312
t
t
tT
2
1

,











t
t
t
2
1
arctg
For the piezo engine with the transverse piezoelectric effect made from
ceramic PZT at
31
d
= 2∙10-10 m/V,
h
=16,
2
M
= 2 kg,
E
C11
=
2.8∙107 N/m,
e
C
= 0.4∙107 N/m,
U
= 25 V, its parameters are obtained
t
T
= 0.25∙10-3 s and steady-state displacement
ht t 











22
= 70 nm.
The characteristics of an electromagnetoelastic engine for
nanobiomedical research are obtained. The mechanical characteristic of
the engine is received as





ji TS
or
 
Fl
[10-15]
jijmmiiTsdS 
  constconst
The regulation characteristics of an electromagnetoelastic engine for
nanobiomedical research is obtained as





mi
S
or
 
Ul
[10-15]
const
const 

 T
jijmmi
T
iTsdS
The mechanical characteristic of a precision engine has the following
form
 
maxmax 1FFll 
The maximum of the parameters
max
l
and
max
F
of the mechanical
characteristic of a precision engine have the form
ldl mmi  max

 ijmmijsSdSTF 00max max
Where index max is used for the maximum value of parameter of a
precision engine.
The maximum values of parameters of the piezo engine for the
transverse piezoelectric effect have the form
hEdh 331max 
E
sSEdF 110331max 
For the transverse piezo engine at
31
d
= 2∙10-10 m/V,
3
E
= 0.5∙105
V/m,
h
= 2.5∙10-2 m,
0
S
= 1.5∙10-5 m2,
E
s11
= 15∙10-12 m2/N its
parameters on are found
max
h
= 250 nm and
max
F
= 10 N. Theoretical
and practical parameters of the piezo engines are coincidences with an
error of 10%.
The regulation characteristic of an electromagnetoelastic engine for
nanobiomedical research at elastic load
lCF e
is obtained in the form
l
S
Cs
d
l
leij
mmi 

0
The equation of the displacement of an electromagnetoelastic engine at
elastic load has the form




ije
mmi
CC
ld
l1
The equation of the displacement of the transverse piezo engine at elastic
load has the form
 
Uk
CC
Uhd
hU
E
e
31
11
31
1



For the transverse piezo actuator at
31
d
= 2∙10-10 m/V,
h
= 20,
E
C11
= 2∙107 N/m,
e
C
= 0.2∙107 N/m,
U
= 55 V, its parameters are found
U
k31
= 3.64 nm/V and steady-state displacement
ht t 











22
= 200 nm.
For calculations the mechatronics control systems for nanobiomedical
research with a precision engine its characteristics are found.
Conclusions
The transfer function and the transfer coefficient of a precision
electromagnetoelastic engine are received. The structural diagram of a
precision engine for nanobiomedical research is obtained. The structural
diagram of an electromagnetoelastic engine for nanobiomedical research
is distinguished by the clarity of energy conversion from Cady and Mason
electrical equivalent circuits of a piezo vibrator.
The electromagnetoelasticity equation and the differential equation are
used to construct the structural diagram of an electromagnetoelastic
engine. The structural diagram of an electromagnetoelastic engine is
found from its electromagnetoelasticity and differential equations. The
structural diagram of the piezo engine is received using the reverse and
direct piezoelectric effects. The back electromotive force for the piezo
engine is founded from the direct piezoelectric effect. The characteristics
of a precision engine for nanobiomedical research are obtained.
References
1. Schultz J, Ueda J, Asada H. (2017) Cellular Actuators.
Butterworth-Heinemann Publisher, Oxford, 382.
2. Afonin SM. (2006) Absolute stability conditions for a system
controlling the deformation of an elecromagnetoelastic
transduser. Doklady Mathematics 74(3): 943-948.
3. Uchino K (1997) Piezoelectric actuator and ultrasonic motors.

J. Biomedical Research and Clinical Reviews Copy rights@ Afonin SM
Auctores Publishing – Volume 3(4)-051 www.auctoresonline.org
ISSN: 2692-9406 Page 5 of 5
Boston, MA: Kluwer Academic Publisher. 347.
4. Afonin SM. (2005) Generalized parametric structural model of a
compound elecromagnetoelastic transduser. Doklady Physics
50(2): 77-82.
5. Afonin SM. (2008) Structural parametric model of a piezoelectric
nanodisplacement transducer. Doklady Physics 53(3): 137-143.
6. Afonin SM. (2006) Solution of the wave equation for the control
of an elecromagnetoelastic transduser. Doklady Mathematics
73(2): 307-313.
7. Cady WG. (1946) Piezoelectricity: An introduction to the theory
and applications of electro mechancial phenomena in crystals.
McGraw-Hill Book Company, New York, London, 806.
8. Physical Acoustics: Principles and Methods. Vol.1. Part A.
Methods and Devices. Ed.: Mason W (1964). Academic Press,
New York, 515.
9. Zwillinger D. (1989) Handbook of Differential Equations.
Academic Press, Boston, 673.
10. Afonin SM. (2006) A generalized structural-parametric model of
an elecromagnetoelastic converter for nano- and micrometric
movement control systems: III. Transformation parametric
structural circuits of an elecromagnetoelastic converter for nano-
and micrometric movement control systems, Journal of Computer
and Systems Sciences International 45(2): 317-325.
11. Afonin SM. (2016) Decision wave equation and block diagram of
electromagnetoelastic actuator nano- and microdisplacement for
communications systems. International Journal of Information
and Communication Sciences 1(2): 22-29.
12. Afonin SM. (2015) Structural-parametric model and transfer
functions of electroelastic actuator for nano- and
microdisplacement. Chapter 9 in Piezoelectrics and
Nanomaterials: Fundamentals, Developments and Applications.
Ed. Parinov IA. Nova Science, New York, pp. 225-242.
13. Afonin SM. (2017) A structural-parametric model of
electroelastic actuator for nano- and microdisplacement of
mechatronic system. Chapter 8 in Advances in Nanotechnology.
Volume 19. Eds. Bartul Z, Trenor J, Nova Science, New York, pp.
259-284.
14. Afonin SM. (2018) Electromagnetoelastic nano- and
microactuators for mechatronic systems. Russian Engineering
Research 38(12): 938-944.
15. Afonin SM. (2012) Nano- and micro-scale piezomotors. Russian
Engineering Research 32(7-8): 519-522.
16. Afonin SM. (2007) Elastic compliances and mechanical and
adjusting characteristics of composite piezoelectric transducers,
Mechanics of Solids 42(1): 43-49.
17. Afonin SM. (2014) Stability of strain control systems of nano-and
microdisplacement piezotransducers. Mechanics of Solids 49(2):
196-207.
18. Afonin SM. (2017) Structural-parametric model
electromagnetoelastic actuator nanodisplacement for
mechatronics. International Journal of Physics 5(1): 9-15.
19. Afonin SM. (2019) Structural-parametric model multilayer
electromagnetoelastic actuator for nanomechatronics.
International Journal of Physics 7(2): 50-57.
20. Afonin SM. (2017) Structural-parametric model of piezoactuator
nano- and microdisplacement for nanoscience. AASCIT Journal
of Nanoscience 3(3): 12-18.
21. Afonin SM. (2016) Solution wave equation and parametric
structural schematic diagrams of electromagnetoelastic actuators
nano- and microdisplacement. International Journal of
Mathematical Analysis and Applications 3(4): 31-38.
22. Afonin SM (2018) Structural-parametric model of
electromagnetoelastic actuator for nanomechanics. Actuators
7(1): 1-9.
23. Afonin SM. (2019) Structural-parametric model and diagram of a
multilayer electromagnetoelastic actuator for nanomechanics.
Actuators 8(3): 1-14.
24. Afonin SM. (2016) Structural-parametric models and transfer
functions of electromagnetoelastic actuators nano- and
microdisplacement for mechatronic systems. International
Journal of Theoretical and Applied Mathematics 2(2): 52-59.
25. Afonin SM. (2018) Structural-parametric model of electro elastic
actuator for nanotechnology and biotechnology. Journal of
Pharmacy and Pharmaceutics 5(1): 8-12.
26. Afonin SM. (2010) Design static and dynamic characteristics of
a piezoelectric nanomicrotransducers. Mechanics of Solids 45(1):
123-132.
27. Afonin SM (2018) Electromagnetoelastic Actuator for
Nanomechanics. Global Journal of Research in Engineering: A
Mechanical and Mechanics Engineering 18(2): 19-23.
28. Afonin SM. (2018) Multilayer electromagnetoelastic actuator for
robotics systems of nanotechnology, Proceedings of the 2018
IEEE Conference EIConRus, 1698-1701.
29. Afonin SM. (2018) A block diagram of electromagnetoelastic
actuator nanodisplacement for communications systems.
Transactions on Networks and Communications 6(3): 1-9.
30. Afonin SM. (2019) Decision matrix equation and block diagram
of multilayer electromagnetoelastic actuator micro and
nanodisplacement for communications systems, Transactions on
Nnetworks and Communications 7(3): 11-21.
31. Afonin SM. (2020) Condition absolute stability control system of
electromagnetoelastic actuator for communication equipment.
Transactions on Networks and Communications 8(1): 8-15.
32. Afonin SM. (2020) A Block diagram of electromagnetoelastic
actuator for control systems in nanoscience and nanotechnology,
Transactions on Machine Learning and Artificial Intelligence
8(4): 23-33.
33. Afonin SM. (2020) Optimal control of a multilayer electroelastic
engine with a longitudinal piezoeffect for nanomechatronics
systems. Applied System Innovation 3(4): 1-7.
34. Afonin SM. (2020) Structural scheme actuator for nano research.
COJ Reviews and Research 2(5): 1-3.
35. Afonin SM. (2018) Structural–parametric model electroelastic
actuator nano- and microdisplacement of mechatronics systems
for nanotechnology and ecology research. MOJ Ecology and
Environmental Sciences 3(5): 306‒309.
36. Afonin SM. (2019) Condition absolute stability of control system
with electro elastic actuator for nano bioengineering and
microsurgery. Surgery & Case Studies Open Access Jjournal 3(3):
307–309.
37. Afonin SM. (2019) Electro elastic actuator for micro and nano
surgical repairs. Open Access Journal of Biomedical Engineering
and Biosciences 3(2): 270-272.
38. Afonin SM (2020) Multilayer engine for microsurgery and nano
biomedicine. Surgery & Case Studies Open Access Jjournal 4(4):
423-425.
39. Afonin SM. (2020) Structural-parametric model actuator of
adaptive optics for composite telescope and astrophysics
equipment. Physics & Astronomy International Journal 4(1): 18-
21.
40. Nalwa HS. (2004) Encyclopedia of Nanoscience and
Nanotechnology. Los Angeles: American Scientific Publishers.
10 Volumes.