0866_c18

Vista previa del material en texto

18
 
This chapter emp
and simulation o
integrated circuit
that may not ma
should be perfor
ulous considerat
Furthermore, ba
micromachines (
proof-of-concept
and solve a spec
prototyping of n
(devised) before 
conversion, oper
control, optimiz
electromagnetic 
 
* 
 
Parts of this ch
 
CRC Press, Boca Ra
 
of Micro- and Nan
 
Sergey Edward
 
Rochester Institute 
 
0866_book.fm  Page 1  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
Nanotechnology*
18.1 Introduction
18.2 Applications of Engineering Biomimetics 
in Nanomachines Prototyping
18.3 Nanomachines Synthesis and Classification
18.4 Synthesis, Design and Analysis of Nanomachines
18.5 Synchronous Reluctance Nanomachines
Prototyping and Synthesis of Synchronous Reluctance 
Nanomachines • Modeling, Analysis, and Design of 
Synchronous Reluctance Nanomachines
18.6 Permanent-Magnet Synchronous Nanomachines.
Prototyping and Synthesis of Permanent-Magnet Synchronous 
Nanomachines • Modeling of Permanent-Magnet 
Synchronous Nanomachines • Optimization of Permanent-
Magnet Synchronous Nanomachines
18.7 Induction Nanomachines
Prototyping and Synthesis of Induction Nanomachines • 
Modeling of Induction Nanomachines • Simulation of 
Induction Nanomachines
18.8 Conclusions
hasizes the far-reaching problems in synthesis, design, analysis, modeling, simulation,
f nanomachines. Rotational and translational nanomachines, controlled by nanoscale
s, can be widely used as nanoscale actuators and sensors. Although this is still a vision
terialize in near future, say within 20 to 30 years, fundamental and applied research
med. The implications of nanotechnology to motion nanodevices have received metic-
ion as technologies to fabricate these nanomachines have been studied and developed.
sic fundamentals and applied researched have been performed. Organic and inorganic
fabricated using micromachining technologies) serve as nanomachine prototypes and
 paradigm. These micromachines have been tested and characterized. One must address
trum of problems in synthesis, analysis, modeling, optimization, biomimicking, and
anomachines. These nanomachines and motion nanodevices must be synthesized
attempts to analyze, optimize, and fabricate them, because basic physical features, energy
ating principles, and other issues significantly contribute to sequential tasks in analysis,
ation, and design. This is of particular significance for electromagnetic and chemo-
motion nanomachines. This chapter reports and successfully applies distinct concepts
apter were published in Lyshevski, S.E., 2002. NEMS and NEMS: Systems, Devices, and Structures,
ton, FL and Lyshevski, S.E. 1999, 2004. Nano- and Micro-Electromechanical Systems: Fundamentals
o-Engineering, 1st and 2nd editions, CRC Press, Boca Raton, FL.
 Lyshevski
of Technology
ss LLC
 
18
 
-2
 
Chapter 18
 
and methods. In particular, the field of engineering biomimetics is applied to prototype nanomachines,
and the synthesis and classification solver that 
 
 
 
allows one to synthesize novel nanomachines, as well as
classify and refine
results are docum
validity, and effe
 
18.1 Intro
 
The benchmarkin
of time. All synth
biomachines. Du
operate. The basi
nanobiomachine
netic nanomachi
Nanomachine
the questions of 
 
magnetotactic ba
horizon by devisi
simulation, analy
models are deve
programs have b
data-intensive an
overall performa
illustrate the effic
 
18.2 Appl
 
in N
 
One of the mos
physics understa
design nanomach
tionary developed
 
Although promis
hended and virtu
 
different electrom
 
chines is based o
the 
 
E. coli
 
 and 
 
Sa
 
voltages supplied
the proteins that
nanomachines.
Consider the n
 
propulsion. The 
 
filament is drive
membrane form
of to the axial 
 
pro
 
were found to be
 
• Angular v
• Torque is 
 
• Efficiency
 
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© 2005 by CRC Pre
 various motion nanodevices, is discussed. The fundamental, applied, and experimental
ented in order to accomplish the analysis and design illustrating their significance,
ctiveness. 
duction
g problems in the synthesis of nanomachines have challenged scientists for a long period
esized nano- and microscale machines and motion devices benefit from mimicking of
e to nanobiomachines complexity, it is yet unknown how these motion nanobiodevices
c physics of different electromagnetic-based nanomachines must be examined because
s operate based on chemo-electromagnetic phenomena. Distinct feasible electromag-
nes are reported in this chapter.
s and motion nanodevices should be modeled, simulated, and analyzed. We examine
viability of the devised nanomachines studying Escherichia coli (E. coli) nanobiomotor,
cteria, and so forth. The goal is to further expand nanotechnology and nanosystems
ng new nanomachines and motion nanodevices solving sequential synthesis, modeling,
sis, and optimization problems. To attain the highest degree of integrity, high-fidelity
loped and examined. A wide spectrum of interactive software tools, algorithms, and
een developed to solve these long-standing problems in heterogeneous simulation and
alysis. The optimization and control problems should be solved to guarantee the superior
nce of nanomachines. Using the developed mathematical models, the simulation results
iency of the modeling, analysis, and optimization methods. 
ications of Engineering Biomimetics 
anomachines Prototyping
t challenging problems in nanomachine synthesis and prototyping involves the basic
nding, analysis, synthesis, and optimization. The synergetic attempts to prototype and
ines have been pursued through analysis of complex patterns and paradigms of evolu-
 nanobiomachines, for example, Escherichia coli, Salmonella typhimurium, and others.1–4
ing results have been reported, the basic physics of nanobiomachines is barely compre-
ally unknown.2 At the same time, distinct nanomachines have been devised postulating
agnetic fundamentals.3,4 For example, it is possible that the physics of some nanoma-
n magnetic media, variable reluctance, or induction electromagnetics. The analysis of
lmonella typhimurium rotor structures indicates that nanobiowindings can exist. The
 to these nanowindings can be controlled (regulated) by the nanobiocircuits formed by
 may form nanobioprocessors. As a result, we study different electromagnetic-based
anobiomotor of E. coli bacteria. The flagella (rotated by nanobiomotors) are used for
bacterium is propelled with a maximum speed of 20 µm/sec by flagellar filaments. This
n by a 45 nm rotor of the nanobiomotor embedded in the cell wall. The cytoplasmic
s a stator. This nanobiomotor integrates more than 20 proteins and operates as a result
tonomotive force resulting due to the proton flux. The rated nanobiomotor parameters
 as follows:2 
elocity is 20 rad/sec. 
1 × 10–16 N-m. 
 is 50% (estimated).
ss LLC
 
Nanotechnology
 
18
 
-3
 
It was commo
 
FliN) that contro
 
involved in the fl
18.2.1.
 
2-4
 
 The na
 
(connected to th
Consider nano
MotA and MotB
so-called MS and
bearing is built f
rings each conta
there are eight st
torque is develop
the sodium ions 
and/or pH gradi
 
MotA and Mo
location may cau
on FliG. The mo
command signals
and the cell body
biomotor rotates
forward (bacteri
evaluated, the ba
 
Some bacteria
magnetite (Fe
 
3
 
O
 
able to precipita
bacteria. It was f
particles) enclose
chain or chains fi
are ether 30 to 10
 
FIGURE 18.2.1 
 
E
 
and rings, rotor im
ω
Filament with
hollow core
O
Mem
I
 Me
FliC(Pep
 
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© 2005 by CRC Pre
nly reported that the E. coli nanobiomotor has three switch proteins (FliG, FliM, and
l the torque, angular velocity, and direction of rotation, respectively.2 These proteins are
agellar assembly. The flagellum, flexible joint, and nanobiomotor are shown in Figure
nobiomotor has two major parts: a stator (connected to the cell wall) and a rotor
e flagellar filament through a flexible joint).
biomotor assembly using common terminology. The stator is built using the so-called
 complexes, while the rotor is built by FliF, FliG, FliM, and FliN proteins forming the
 C rings. The shaft is made from the proteins FlgB, FlgC, FlgF, and FlgG, whereas the
rom the proteins FlgH and FlgI forming the so-called L and P rings. The MS, P, and L
in many copies of FliF, FlgI, and FlgH proteins, respectively. Reference 2 reports that
ator elements (MotA and MotB complexes), each of which exerts the same force. The
ed due to axial flux of protons (in marine bacteria and bacteria that live at high pH,
establish the axial flux). The source of energy is a transmembrane electrical potential
ent. Thus, the E. coli nanobiomotor is a chemo-electromagnetic nanobiomachine.
tB complexes form a transmembrane channel. According to reference 2, proton trans-
se the cytoplasmic part of MotA to move or change the geometry, producing the force
tor rotates clockwise and counterclockwise, changing the direction as a result of the
. When the nanobiomotor rotates clockwise, the flagellar filaments work independently,
 moves erratically with little net displacement (bacterium tumbles). When the nano-
 counterclockwise, the filaments rotate in parallel in a bundle that propels the cell body
um runs). Although the direction of rotation and some nanobiomotor data can be
sic physics of nanobiomachines and their components (proteins) is virtually unknown.2
 have organic and inorganic magnetic media. In 1962 Professor Lowenstam discovered
4) biomineralization in the teeth of chitons, demonstrating that living organisms were
te the mineral magnetite. In 1975 Richard Blakemore discovered the magnetotactic
ound that distinct magnetotactic bacteria contain magnetosomes (magnetic mineral
d in the protein-based membranes. In most cases the magnetosomes are arranged in a
xed within the cell. In many magnetotactic bacteria, the magnetosome mineral particles
0 nm magnetite (Fe3O4) or, in marine and sulfidic environments, greigite (Fe3S4). These
. coli nanobiomotor: integrated nanobiomotor-coupling-flagella complex with different proteins
age, and possible protein-based bionanocircuitry geometry.
ft
L Ring, FlgH
ω
Basal Disk
Mot B
Mot A
Hook FlgE
C Ring FliM, FliN
M Ring
uter
brane
Cell wall
H+ H+
nner
mbrane
45 nm
Rotor of the E.coli
bionanomotor
P Ring, FlgI
S RingMS Ring
FliF, FliG
FlgK
FlgL
FlgB, FlgC, FlgF
Transport Apparatus
FliH,I,O,P,Q,R
Possible Stator
Nanobiowindings Topology
FlgG
Flh A,B
tidoglycan Layer)
ss LLC
 
18
 
-4
 
Chapter 18
 
nanoscale perma
field lines. Wheth
particles constitu
totactic bacteria 
the cell. The pol
chain of particle
permanent magn
graphic magnetic
chain assembly is
occur in at least
 
crystal symmetry
elongated hexago
observed in som
shaped, teardrop
Examining na
important that th
manner. The iron
 
from 15 to 30 nm
 
magnets can be m
size, and 8 g/cm
 
3
 
 
 
assemblies that ca
These Fe and Co
 
18.3 Nan
 
The field of eng
nanomachines an
motion devices. U
 
have shown that n
 
system, interacti
electromagnetics
 
FIGURE 18.2.2 
 
M
mineral magnetic p
 
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© 2005 by CRC Pre
nent magnets sense the magnetic field, and bacteria swim (migrate) along the magnetic
er the magnetic mineral particles are magnetite or greigite, the chain of magnetosome
tes a permanent magnetic dipole fixed within the bacterium. Correspondingly, magne-
have two magnetic poles depending on the orientation of the magnetic dipole within
es can remagnetized by a magnetic pulse that is greater than the coercive force of the
s. The magnetosome particles that are almost perfectly uniformly magnetized form
etic domains. All particles are arranged along the chain axis such that the crystallo-
 easy axes are also aligned. The size specificity and crystallographic orientation of the
 optimally designed for magnetotaxis in the geomagnetic field. Magnetosome particles
 three different crystal forms. In M. magnetotacticum, cubo-octahedral forms (cubic
 of magnetite) is observed. A second type, found in coccoid and vibrioid strains, is an
nal prism with the axis of elongation parallel to the 111 crystal direction. A third type,
e uncultured cells, is an elongated cubo-octahedral form producing cylindrical, bullet-
 and arrowhead particles, as Figure 18.2.2 shows.
nomachines and motion nanodevices that can be fabricated using nanotechnology, it is
ese magnetic materials and magnetic nanoassemblies can be created in a straightforward
 oxide (Fe3O4) can be affordably fabricated with 99% purity, and the size of particles is
 (the morphology is spherical and the density is 5 g/cm3). High-energy density nano-
ade. Figure 18.2.2 illustrates the nanotechnology-based fabricated Fe (99% purity, 25 nm
density) and Co (99.8% purity, 27 nm size, and 9 g/cm3 density) nanoparticles and their
n be used in electromagnetic (and electrostatic) nanomachines and motion nanodevices.
 nanoparticles can be magnetized, making the nanomagnet arrays for nanomachines.
omachines Synthesis and Classification
ineering biomimetics addresses fundamental design issues that are common to all
d provides valuable insight in prototyping, synthesis, and design of nanomachines and
sing recently developed basic results and performing fundamental research,3,4 researchers
anobiomachines can operate due to the reluctance difference in the closed protonomotive
on of magnetic fields established by nanowindings and magnetic media, induction
, and so forth. Nanomachine performance depends on nanomachine operating principle,
agnetotactic bacterium and image of a chain of 60–100 nm diameter cylindrical magnetosome
articles. Nanobabricated Fe and Co nanoparticles and their nanoassemblies.
Fe
 100 nm
Co
ss LLC
 
Nanotechnology
 
18
 
-5
 
topology, materi
synthesis paradig
applied as the ba
were developed i
A 
 
nanomachin
 
solver, which allo
tioned into 3 hor
of characters, for
 
and, in general, w
The electroma
 
Here, the first 
 
I
 
 are the 
 
endless
 
, 
 
TABLE 18.3.1 
 
Nanomachines Synthesis and Classifier
M
G
P
El
ec
tro
m
ag
ne
tic
 S
ys
te
m
In
te
gr
at
ed
, I
O
pe
n 
En
de
d 
 
(O
pe
n),
 O
En
dl
es
s 
(C
los
ed
), E
Geometry
 M G× = {
 
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© 2005 by CRC Pre
als, and other factors. Novel nanomachines should be synthesized, and cornerstone
ms must be derived. It is evident that electromagnetic systems and geometry can be
sic variables of particular importance. Different synthesis and classification paradigms
n References 3–5.
e synthesis and classification solver is described and demonstrated in Table 18.3.1.3,4 This
ws one to synthesize and classify electromagnetic-based motion nanodevices, is parti-
izontal and 6 vertical strips, and contains 18 sections, each identified by ordered pairs
 example, (E, P) or (O, C). Hence, the electromagnetic system–geometric set is given as
,
e have .
gnetic synthesis and classification solver represents nanomachines and nanodevicesas
entry is a letter chosen from the bounded electromagnetic system set, where E, O, and
open-ended, and integrated electromagnetic systems, respectively; hence, M = {E, O, I}.
late, P Spherical, S Torroidal, T Conical, N Cylindrical, C Asymmetrical, A
Σ
Σ
ΣΣΣΣ Σ
M G E F E S E T I N I C I A× = ( ) ( ) ( ) ( ) ( ) ( ){ }, , , , , , , , , , , ,�
M G m g m M g G× = ( ) ∈ ∈{ }, : and
m g m M g G( ) ∈ ∈ }, : ,and M G E F E S E T I N I C I A× = ( ) ( ) ( ) ( ) ( ) ( ){ }, , , , , , , , , , , ,�
ss LLC
 
18
 
-6
 
Chapter 18
 
The second entry is a letter from the geometric set, where the geometries are denoted as plate (
 
P
 
),
spherical (
 
S
 
), torroidal (
 
T
 
), conical (
 
N
 
), cylindrical (
 
C
 
), and asymmetrical (
 
A
 
) geometry, that is, 
 
G
 
 =
{
 
P
 
, 
 
S
 
, 
 
T
 
, 
 
N
 
, 
 
C
 
, 
 
A
 
}.
It must be em
synthesis. For exa
electromagnetic 
 
integrated
 
), nove
features (inductio
netization charac
 
modeling, simula
critical problems
intensive analysis
The analysis o
 
There are some p
sponding operati
1. Synchrono
netic field
by the rot
2. Induction
varying st
due to the
3. Variable r
minimize 
the magne
time-vary
 
18.4 Synt
 
Different nano- a
3 and 4. In gener
induction. A step
1. Devise (sy
ciples, top
2. Study elec
(phenome
3. Define ap
4. Perform e
(stator, ro
5. Define (af
(stator, ro
6. Perform c
performan
7. Modify, re
Thus, in addi
examined. It is i
electromechanica
For example, the
 
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© 2005 by CRC Pre
phasized that the synthesis and classification solver allows one to attain the topological
mple, radial and axial topology nanomachines result. Using the possible geometry and
(chemo-electromagnetic or opto-electromagnetic) systems (endless, open-ended, and
l organic, inorganic, and hybrid nanoactuators can be synthesized. Different distinct
n and synchronous electromagnetics, magnets and ferromagnetic core geometry, mag-
teristics, emf distribution, power, torque, size, packaging, etc.) result. Then, performing
tion, and analysis, the designer optimizes nanomachine performance. One of the most
 is to develop accurate mathematical models that allow the designer to perform data-
 and heterogeneous simulations in order to guarantee accurate performance predictions.
f nanobiomachines is far from complete, and there is a significant lack of reliable data.1–4
ossible torque production and energy conversion mechanisms that lead to the corre-
on of electromagnetic-based nanomachines and motion nanodevices:
us electromagnetics: The torque results due to the interaction of a time-varying mag-
 established by the stator (rotor) windings and a stationary magnetic field established
or (stator) permanent nanomagnets or nanomagnet arrays.
 electromagnetics: The rotor currents are induced in the rotor windings due to the time-
ator magnetic field and motion of the rotor with respect to the stator; the torque results
 interaction of time-varying electromagnetic fields.
eluctance electromagnetics (synchronous nanomachine): The torque is produced to
the reluctance of the electromagnetic system; for example, the torque is developed by
tic system in an attempt to align the minimum-reluctance path of the rotor with the
ing rotating air gap mmf.
hesis, Design and Analysis of Nanomachines
nd microscale machines and motion devices have been devised and studied in References
al, the rotational and translational nanomachines can be classified as synchronous and
-by-step procedure in the nanomachine synthesis and design is as follows:
nthesis, prototyping and classification tasks) nanomachine researching operational prin-
ologies, configurations, geometry, electromagnetic systems, and other features.
tro-chemo-mechanical energy conversion and sensing-feedback-control mechanisms
na).
plication and environmental requirements with performance specifications.
lectromagnetic, energy conversion, mechanical, vibroacoustic, and sizing/dimension
tor, nanomagnets, air gap, winding, etc.) estimates.
fordable and high-yield) technologies, processes, and materials to fabricate structures
tor, bearing, post, shaft, etc.) and assembly of nanomachines.
oherent electromagnetic, mechanical, vibroacoustic, and thermodynamic design with
ce analysis synergetically assessing synthesis, design, and optimization.
fine, and optimize the design.
tion to devising nanomachines and motion nanodevices, they should be coherently
mportant to accurately model, simulate, and analyze very complex electromagnetic,
l, and vibroacoustic phenomena in motion nanodevices in order to optimize the design.
 ultimate goals can be 
ss LLC
 
Nanotechnology
 
18
 
-7
 
• Increase efficiency, reliability, robustness, ruggedness, and survivability.
• Maximize the power, torque, and force densities. 
• Minimize 
• Minimize 
In this way, af
cantly influence 
addressed and so
optimization with
 
power density, et
concepts. We intr
1. Engineerin
2. The synth
3. Electroma
To attain our 
order to ensure s
 
tromagnetic load
and high-frequen
must be examine
of robust and affo
robustness, reliab
 
18.5 Sync
 
Prototyping 
 
The protein foldi
the 
 
E. coli
 
 rotor (
the 
 
E. coli
 
 nanobi
 
FIGURE 18.5.1 
 
E
  
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© 2005 by CRC Pre
and attenuate vibrations and noise. 
losses and torque ripple.
fordable high-yield fabrication can be achieved. The nanomachine topologies signifi-
nanodevice performance and fabrication. Many of the problems listed have not been
lved yet. To meet our objectives, one must study complex phenomena and perform
 ultimate objectives to guarantee superior achievable performance (efficiency, robustness,
c.). To attain the desired nanomachines integrity, we must depart from the conventional
oduce entirely new paradigms that are based on 
g biomimetics (to prototype nanomachines) 
esis and classification solver (to synthesize and classify nanomachines) 
gnetic-mechanical optimal design (to maximize efficiency, robustness, power density, etc.) 
objectives, mathematical models are developed as nanomachines are synthesized. In
uperior achievable performance, these nanomachines must be designed for high elec-
s, electromagnetic field and flux (current) densities integrating saturation, hysteresis,
cy harmonics effects. Therefore, the electromagnetic and electromechanical mechanisms
d. Hence, the major emphases should be focused on the development and validation
rdable concepts that guarantee significant advantages, for example, increase of efficiency,
ility, torque density, and expanded operating envelope.
hronous Reluctance Nanomachines
and Synthesis of Synchronous Reluctance Nanomachines
ng changes the permeability of the media. This can result in the variable reluctance of
the MS ring that consists of FliF and FliG proteins) as rotor rotates. At the same time,
omotor can operate as a synchronous reluctance nanomachine, as shown in Figure 18.5.1.
. coli nanobiomotor with a possible rotor protein assembly.
ss LLC
 
18
 
-8
 
Chapter 18
 
One can hypo
 
in the E. coli nan
rotor rotates. To
dimensional mol
truncated octahe
18.5.1 results in 
media (protein) 
as a function of th
nanomachines. In
design a nanoma
the rotor rotates
Figure 18.5.2. Th
Modeling, A
Having performe
model, simulate,
mathematical mo
1. circuitry e
2. tensional-m
Here, the nan
and ψas; the ang
and load torques
The synchrono
inertia J, and the
As illustratedi
rotates with angu
ment θr. Using th
This magnetizing
mum values. In 
The inductance c
18.5.3. Hence, on
tance; L∆m is the 
The analytic ex
analysis with ava
One can approxi
FIGURE 18.5.2 S
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© 2005 by CRC Pre
thesize that there is a possible reluctance difference in the closed protonomotive system
obiomotor. Correspondingly, the torque is developed due to change of reluctances as
 illustrate the concept, consider the nanoactuator prototype synthesized using three-
ecular assemblies. For example, the engineered6 triangle, square, pentagon, heptagon,
dron, cross, star N5,6,7,…, and other geometry of protein assemblies shown in Figure
different reluctances due to the distinct length of the protonomotive flux through the
as rotor rotates. Hence, the reluctance of the magnetic path varies as the rotor rotates
e rotor angular displacement θr. This leads one to synthesis of the synchronous reluctance
 particular, instead of in the closed protonomotive system in the E. coli nanobiomotor, we
chine with the endless (closed) electromagnetic system that has a different reluctances as
. To illustrate the paradigm, a single-phase reluctance nanoactuator is documented in
is nanomachine can be fabricated as a nanoactuator, shown in Figure 18.5.2.
nalysis, and Design of Synchronous Reluctance Nanomachines
d synthesis (and classification) of synchronous reluctance nanomachines, we must now
 analyze, and optimize those nanomachines. To fulfill our objectives, the augmented
del for the studied single-phase nanomotor is developed as3
quation (Kirchhoff ’s law) is .
echanical equation (Newton’s law) is .
omachine variables are the phase voltage, current and flux linkages denoted as uas, ias
ular velocity and angular displacement denoted as ωr and θr; and the electromagnetic
 denoted as Te and TL.
us reluctance nanomachine parameters are the armature resistance rs, the moment of
 friction coefficient Bm.
n Figure 18.5.2, the quadrature and direct magnetic axes are fixed with the rotor. The rotor
lar velocity ωr. The magnetizing reluctance is a function of the rotor angular displace-
e number of turns Ns, the magnetizing inductance is found to be Lm(θr) = .
 inductance varies twice per one revolution of the rotor and has minimum and maxi-
particular, one has and Lmmax =
hanges as a sinusoidal function of the rotor angular displacement as reported in Figure
e has , where is the average value of the magnetizing induc-
half of amplitude of the sinusoidal variation of the magnetizing inductance.
pression for the Lm(θr) is needed. In general, this can be performed using the finite-element
ilable high-performance software, for example, MATLAB, ANSYS, or MATHEMATICA.
mate these variations of Lm(θr) as , n= 1, 3, 5, …
ingle-phase reluctance nanomachine and the proposed nanomotor with variable reluctance rotor.
u r i
d
dt
as s as
as
= +
ψ
T B T J
d
dt
e m r L
r
− − =ω
θ2
2
ℜm
Ns m r
2 1ℜ− ( )θ
L Nm s m r
r
min max , , ,...
( )= ℜ−
=
2 1
0 2
θ θ π π Ns m r r
2 1
1
2
3
2
5
2
ℜ−
=min , , ,...( )θ θ π π π
L L L fm r m m r( ) ( )θ θ= − ∆ Lm
L L Lm r m m
n
rθ θ( ) = − ∆ cos 2
ss LLC
Nanotechnology 18-9
The electroma
expression for th
finds
Thus, the sync
The average v
angular displacem
Making use of
and taking note 
nonlinear differe
The lamped-p
particular, the 10
FIGURE 18.5.3 M
L
Lm
i ias M= (Re sin2
T L ie m as= ∆
2
 
di
dt L
as
= −
dωrr
r
r
dt J
L
d
dt
= (
=
1
θ
ω
0866_book.fm  Page 9  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
gnetic torque, developed by single-phase reluctance nanomotors, is found using the
e co-energy as given by . Letting , one
hronous reluctance nanomotor electromagnetic torque is given as
alue of Te is not equal to zero if the current (magnetic field) is a function of the rotor
ent θr. As an illustration, let the following current be fed to the motor nanowinding
. Then, the electromagnetic torque is
 and 
 Kirchhoff ’s and Newton’s second laws
, 
of the flux linkage equation , one obtains a set of three
ntial equations that models single-phase synchronous reluctance nanomotors as
 
arameters mathematical model developed is verified through nonlinear simulations. In
0 nm (length) × 100 nm (height) × 25 nm (width) synchronous nanomotor with 65 nm
agnetizing inductance Lm(θr) =
–
Lm – L∆m f(θr).
Lm min
m max
Lm
L∆m
L∆m
0 1
2 π
3
2 π
π 2π θr
W i L ic as r m r as( , ) ( )θ θ= 12
2 L L Lm r m m rθ θ( ) = − ∆ cos2
W i L L L ic as r ls m m r as, cosθ θ( ) = + −( )12 22∆
T
W i i L L L
e
c as r
r
as ls m m r
=
∂ ( )
∂ =
∂ + −( ), cosθ
θ
θ1
2
2 2∆(( )
∂ =θ θr m as r
L i∆
2 2sin
r )θ
L ir m M r r= ( ) ≠∆ 2 22 2 2 0sin Re sin sinθ θ θ T L i d L ieav m as r r m M= =∫1 22
0
1
4
2
π
θ θ
π
∆ ∆sin
u r i
d
dt
as s as
as
= +
ψ
T B T J
d
dt
e m r L
r
− − =ω
θ2
2
ψ θas ls m m r asL L L i= + −( )∆ cos2
r
L L
i
L
L L L
s
ls m m r
as
m
ls m+ −
−
+ −∆
∆
∆cos2
2
θ mm r
as r r
ls m m r
asi
L L L
u
cos
sin
cos
,
2
2
1
2θ
ω θ
θ
+
+ − ∆
m as r m r Li B T− − )22∆ sin θ ω
ss LLC
18-10 Chapter 18
(length) × 25 nm
nanowindings ca
magnetic materi
assigned to be 4. 
Lmd /Lmq ratio (to
represented in Fi
Maxwell’s equ
application of th
of synchronous r
where Az is the z
and σ and µ are 
In general, thr
ity tensors. These
magnetic torque,
model synchrono
magnetic loads a
losses, and other 
and numerical d
The synchron
guarantee high p
18.6 Perm
Prototyping a
Despite the limite
machines can be 
performance axia
FIGURE 18.5.4 A
Synchronous Reluctance
Nanomotor Angular Velocity, ωrm
rad
sec( )
0866_book.fm  Page 10  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
 (width) rotor is examined (see Figure 18.5.2). This nanomotor can be fabricated and
n be deposited using available nanotechnologies. The relative permeability of the ferro-
al was assumed to be 30000µ0, and the friction was neglected. The ratio Lmd /Lmq was
This ratio significantly influences the electromagnetic torque developed. However, high
 attain higher torque) results in torque ripple and vibrations. The simulation results are
gure 18.5.4.
ations are used to attain high-fidelity modeling of nanomachines.3 For example, the
e magnetic potential as the variable gives the following equation to model the dynamics
eluctance nanomachines: 
-component of the magnetic potential; v is the velocity vector; J is the current density;
the conductivity and permeability.
ee-dimensional Maxwell’s equations must be applied using conductivity and permeabil-
 three-dimensional Maxwell’s equations, integrated with the relationships for electro-
 torsional-mechanical dynamics, and virboacoustic transient behavior, must be used to
us reluctance nanomachines. Utilizing this high-fidelity modeling concept, high electro-
nd flux densities, saturation, hysteresis, high-frequency harmonics effects, eddy current
phenomena can be integrated and examined. Although this leads to formidable analytical
ifficulties, they can be resolved using high-performance software such as MATLAB. 
ous reluctance motors, though quite simple from the fabrication viewpoints, cannot
erformance. As a result, other nanomachines are considered.
anent-Magnet Synchronous Nanomachines
nd Synthesis of Permanent-Magnet Synchronous Nanomachines
d research, availability, and inconsistency, efficient permanent-magnet synchronous nano-
synthesized utilizing the axial topology and endless electromagnetic system. In fact, high-
l topology micromachines have been synthesized, designed, testedand characterized.3
cceleration of a synchronous reluctance nanomotor.
0 0.002 0.004 0.006 0.008 0.01
0
20,000
40,000
60,000
80,000
100,000
Time, (µsec)
σ
µ
σ
∂
∂ =
∇
− ∇( )+AA AA vv AA JJz z z
t
2
ss LLC
Nanotechnology 18-11
Although these n
have permanent 
defined and well
nology. The adva
plicity, affordabil
1. Nanomagn
2. There are 
3. Rotor bac
4. It is easy t
Utilizing the a
synchronous nan
machine has we
emphasized that 
machine with 40
evident from Fig
Modeling of 
The prototyping
the sequential an
electromagnetic-
hensively assess a
machines. Our g
simulation, guara
of equations of m
simulation, data-
The nanomac
examined. In nan
ical-vibroacousti
Maxwell’s equati
fields in motion 
where E and H a
permittivity, perm
FIGURE 18.6.1 A
Stator
Stator Rotor
N
N
S
S
N
S
S
N
N
S
S
N
S
S
Rotor
0866_book.fm  Page 11  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
anomachines are different compared with the E. coli nanobiomotor, which may not
magnets, a similar topology is utilized. Furthermore, we progressed to the same well-
-understood inorganic motion nanodevices that can be fabricated utilizing nanotech-
ntages of axial topology nanomachines are efficiency and reliability. Fabrication sim-
ity, and high-yield result because 
ets are flat (planar) without strict requirements on the surface roughness and uniformity. 
no strict shape and magnetic properties requirements imposed on nanomagnets. 
k ferromagnetic material is not required. 
o deposit planar nanowires on the flat stator forming nanowindings. 
xial topology and endless electromagnetic system, we synthesize permanent-magnet
omachines. The synthesized nanomachine is reported in Figure 18.6.1. This nano-
ll-defined topological analogy compared with the E. coli nanobiomotor. It must be
the documented motion nanodevice can be fabricated, and a prototype of the micro-
 µm rotor was tested and characterized. The planar segmented nanomagnet array, as
ure 18.6.1, can be deposited as thin films nanomagnets.
Permanent-Magnet Synchronous Nanomachines
 and synthesis tasks have been reported and performed. As nanomachines are devised,
alysis and design problems must be researched. In this section we develop an integrated
mechanical-vibroacoustic modeling, analysis, and optimization paradigm to compre-
nd control electromagnetic, electromechanical, and vibroacoustic phenomena in nano-
oal is to perform high-fidelity modeling to achieve the highest degree of confidence in
nteeing accuracy. In particular, the problems to be researched are modeling (deviations
otion to model complex phenomena and effects in the time domain), heterogeneous
intensive analysis, and robust design. 
hine electromagnetics, electromagnetic torque production, and energy conversion are
omachines, vibration and noise result due to complex electromagnetic-electromechan-
c phenomena that are studied. Electromagnetic fields modeling is performed applying
ons.3 The following partial differential equations describe time-varying electromagnetic
nanodevices that are not based on quantum effects:
, , , 
re the electric and magnetic field intensities; J is the current density; ε, µ, and σ are the
eability, and conductivity tensors, respectively; and ρv is the volume charge density.
xial permanent-magnet synchronous nanomachine.
Stator
Windings
N
N
S
S
S
N S
S
S
N
N
N
ωr
∇ × = −EE HHµ ∂∂t ∇ × = +HH EE JJσ ∇⋅ =EE
ρ
ε
v ∇⋅ =HH 0
ss LLC
18-12 Chapter 18
The Lorenz force, which relates the electromagnetic and mechanical phenomena, is given as
The electroma
volume integral t
where the electro
For two region
flux densities as
where M is the r
recoil permeabili
The negative g
The scalar ma
zero current den
used. We have th
Solving the pa
the three-dimens
0866_book.fm  Page 12  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
gnetic force is found by applying the Maxwell stress tensor. This concept employs a
o obtain the stored energy, and
magnetic stress energy tensor is 
s (air gap ag and permanent magnets pm), we have the air gap and permanent magnet
 and 
esidual magnetization vector, M = Br /µ0µr; Br is the remanence; and µr is the relative
ty.
radient of the scalar magnetic potential V gives the magnetic field intensity, for example, 
gnetic potential satisfies the Laplace equation in free and homogeneous media (with
sity and J = 0). For axial topology nanomachines, the cylindrical coordinate system is
e equation
rtial differential equation3,7 
ional air-gap flux density is found as
FF EE vv BB EE JJ BB= + × = + ×ρ ρv v( )
FF EE JJ BB ss= + × = ⋅∫ ∫( )ρ µv
v
s
s
dv T d
1 ��
T T T
E D E D E D E D
E D E D Es s
E
s
M
j j
j= + =
−
−
1 1
1
2 1 2 1 3
2 1 2 2
1
2 DD E D
E D E D E D E D
B H
j
j j
2 3
3 1 3 2 3 3
1
2
1 1
1
−






+
− 22 1 2 1 3
2 1 2 2
1
2 2 3
3 1 3 2 3
B H B H B H
B H B H B H B H
B H B H B
j j
j j−
HH B Hj j3
1
2−






.
BB HHag ag= µ0 BB HH JJ HH MMpm pm r pm= + = +µ µ µ0 0( )
HH = −∇V
∇⋅ = ∂ ∂ +
∂
∂ +
∂
∂MM
1 1
r
rM
r r
M
r
M
z
r z( ) φ
1 1
1
2
2
2
2+ ∂
∂
∂
∂



 +
+ ∂
∂
+ +
∂χ χ
φ χ
t t ag
r r
r
V
r r
V V
( )
∂∂
= ∇⋅
z 2
MM,
 
B r z
M
a
v h
r
v h gag z i
i r
i r
( , , )
sinh
sinh
(
φ µ
χ
ε
ε
=
+ +
0 0
1 aag
i
i
i
r
v z
r
v
)
cosh sin
=
∞∑
1
ε φ
ss LLC
Nanotechnology 18-13
where χ and χt are the reversible susceptibility along the easy and transverse magnetization axes; ai is the
harmonic amplitude coefficient, and for the trapezoidal-wave magnetization,
hr ≤ z ≤ gag + hr, 
One-dimensio
Thus, the maxim
Using the deri
one finds three-d
vibration. It shou
The radiated p
the developed eq
chronous electro
Optimization
One must attain 
including perma
design is based o
complex electrom
system, compon
efficiency (η) an
ripple (Ter), unde
In addition to t
examined to ensu
may want to atta
due to the physic
0866_book.fm  Page 13  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
;
hr is the rotor thickness.
nal air-gap flux density is found to be
.
um flux density in the air gap is
.
ved equations for the air-gap flux and emf 
imensional electromagnetic model for nanomachines dynamics, torque production, and
ld be emphasized that the electromagnetic torque is given as
ressure p(r, θ, φ, t) is found using the Green function G. We have
uations of motion model electromagnetic-mechanical-vibroacoustic behavior of syn-
magnetic nanomachines. 
 of Permanent-Magnet Synchronous Nanomachines
optimal electromagnetic, mechanical, and vibroacoustic behavior of all nanomachines,
nent-magnet synchronous motion nanodevices. The electromagnetic and mechanical
n the application of Maxwell’s equations and tensor calculus in order to optimize the
echanical behavior in nanomachines. For example, the nanomachine electromagnetic
ents (magnets, windings, air gap, etc.) and geometry can be optimized to maximize
d robustness, maximizing the electromagnetic torque (Te), as well as minimize torque
sirable torque components (Tx and Ty), vibroacoustic signature (p), losses, and so forth.
he passive optimization, the active optimization control problem can formulated and
re optimal achievable performance. It should be emphasized that although the designer
in the ideal characteristics and performance, usually they cannot be achieved simply
al limits imposed (power and torque densities, current density, angular velocity, etc.).
a
i
i
i =
−−
4 2 1
2 1 2
sin( )
( )π
B
M h
h g
a vag z
r
r ag
i
i
i( )
( )( )
sinφ µ
χ
φ=
+ +
=
∞∑0 0
1
1
B
M h
h g
az
r
r ag
i
i
i
max
( )( )
( )=
+ +
−
+
=
∞∑µχ0 0 1
1
1
1
emf d
t
d
s
= = −
∂
∂ ⋅∫ ∫EE ll BB ss�
TT mm BB= ×
p r t z t G r d dz
R
R
( , , , ) ( , , ) ( , , )θ φ ρ ω φ θ φ φ
π
=
−
+∫∫ ��
0
2
ss LLC
18-14 Chapter 18
The mathema
nonlinear optimi
where u is the co
Different cont
electro-magnetic
18.7 Indu
Prototyping 
Complex three-d
bacteria were stu
ring that consists
assume that shor
complex three-di
the AAA (ATPase
protein superfam
including an ATP
are found in all o
on the geometry 
biomotor and syn
Modeling of 
By making use th
Figure 18.7.1. Th
mathematical mo
the variables, the
as the stator and 
equations are fou
FIGURE 18.7.1 E
tion nanomachine.
Mot B
Mot A
Hook F
Filament with
hollow core
Outer
Membrane
Cell wall
(Peptidoglycan Layer)
Inner
 Membrane
FliC
Tr
M
rs
−
as′
Nanostator
FliH
ω
0866_book.fm  Page 14  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
tical formulation of the active optimization control problem is given as the mini-max
zation formulation, for example,
ntrol vector.
rol variables can be used. For axial and radial topology synchronous nanomachines, the
 field is controlled by varying applied phase voltages.
ction Nanomachines
and Synthesis of Induction Nanomachines
imensional organic complexes and assemblies in E. coli and Salmonella typhimurium
died in this chapter. For example, the 45 nm E. coli nanorotor is built as the so-called MS
 of FliF and FliG proteins. These proteins’ geometry and folding are unknown. One can
t-circuited nanowindings can be formed by these proteins. It should be emphasized that
mensional organic circuits (windings) can be engineered.6 As another example, consider
s Associated with various cellular Activities) interacting protein superfamily. This AAA
ily is characterized by a highly conserved module of more than 230 amino acid residues,
 binding consensus, present in one or two copies in the AAA proteins. The AAA proteins
rganisms and are essential for their functionality. The specific attention should be focused
and folding of different protein complexes and assemblies. In addition, the E. coli nano-
thesized nanomachines can operate as induction nanomachines; see Figure 18.7.1.
Induction Nanomachines
e documented results, the studied two-phase induction nanomachine is illustrated in
e control variables are the phase voltages uas and ubs. To develop lumped-parameter
dels of induction nanomachines, we model the stator and rotor circuitry dynamics. As
 voltages applied to the stator and rotor windings (as, bs and ar, br, respectively) as well
rotor currents and flux linkages are used. Using Kirchhoff ’s voltage law, four differential
nd to be
. coli nanobiomotor with assumed short-circuited rotor nanobiowindings and two-phase induc-
L Ring, FlgH Basal Disk
lgE
C Ring FliM, FliN
45 nm
Rotor of the E. coli
bionanomotor
P Ring, FlgI
FlgK
FlgL
FlgB, FlgC, FlgF
ansport Apparatus
FlgG
S Ring FliF, FliG
+
+−
Lss
rs
Lss
ibs
ubs
uas ias
Ns bs
as
bs′
br
br′
ar
ar′
rr
+ +
−
−
Lrr
rr
Lrr
ibr
ubr
uar
iar
Nr
Electromagnetic Coupling
Nanorotor
Flh A,B,I,O,P,Q,R
ωr
ωr ,Te
max min , , , , , ( , , , )
uu
TT
∈
 
U
e er x yT T T p t rη θ φ
ss LLC
Nanotechnology 18-15
• Stator circuitry and 
• Rotor circ
Here, the nano
ibs, iar, ibr, ψas, ψbs
The nanomach
The flux linka
angular displacem
where is the a
Lms is the stator m
The number o
Taking note of
One obtains th
rotor circuitry dy
u r i
d
dt
as s as
as
= +
ψ
u r i
d
dt
bs s bs
bs
= +
ψ
 θr
′ =iar
 
di
dt
as
 
di
dt
bs
0866_book.fm  Page 15  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
uitry and 
machine variables are the phase voltage, current, and flux linkages uas, ubs, uar, ubr, ias,
, ψar and ψbr. 
ine parameters are the resistances of the stator and rotor windings rs and rr.
ges are expressed using the phase currents and inductances that are functions of rotor
ent. We have
ngular displacement; Lss and Lrr are the self-inductances of the stator and rotor windings;
agnetizing inductance; and Lls and Llr are the stator and rotor leakage inductances.
f turns in the stator and rotor windings are used. We have the expressions
, , 
 the turn ratio, we have the following expressions for inductances and rotor resistance:
 and 
e following set of nonlinear differential equations in Cauchy’s form to model the stator-
namics of induction nanomachines:
u r i
d
dt
ar r ar
ar
= +
ψ
u r i
d
dt
br r br
br
= +
ψ
 
ψ
ψ
ψ
ψ
θas
bs
ar
br
ss ms rL L L
'
'
cos





=
−0 mms r
ss ms r ms r
ms r ms
L L L
L L
sin
sin cos
cos sin
θ
θ θ
θ θ
0
rr rr
ms r ms r rr
L
L L L
'
'sin cos
0
0−





θ θ
ii
i
i
i
as
bs
ar
br
'
'






′ =
N
N
i i
N
N
ir
s
ar br
r
s
br, ′ = ′ =u
N
N
u u
N
N
uar
r
s
ar br
r
s
br, ′ = ′ =ψ ψ ψ ψar r
s
ar br
r
s
br
N
N
N
N
,
′ = = ′ = ′ +L L
N
N
L L L Lmr ms
s
r
sr rr lr ms, ′=r
N
N
rr
s
r
r
2
2
L r
L L L
i
L
L L L
rr s
ss rr ms
as
ms
ss rr
= −
′
′ −
+
′ −
2
2
mms
bs r
ms rr
ss rr ms
ar r ri
L L
L L L
i
r
2 2
ω ω θ+ ′
′ −
′ +
′
sin rr
rr
r
ms rr
ss rr ms
br
L
L L
L L L
i
′




+
′
′ −
cos
'
θ
ω
2 rr r
r
rr
r
rr
ss rr ms
r
L
L
L L L
cos sinθ θ− ′
′



 +
′
′ −
2
uu
L
L L L
u
L
L L L
as
ms
ss rr ms
r ar
ms
ss rr
−
′ −
′
+
′ −
2
cosθ
mms
r bru2 sin ,θ ′
L r
L L L
i
L
L L L
rr s
ss rr ms
bs
ms
ss rr
= −
′
′ −
−
′ −
2
2
mms
as r
ms rr
ss rr ms
ar r ri
L L
L L L
i
r
2 2
ω ω θ− ′
′ −
′ −
′
cos rr
rr
r
ms rr
ss rr ms
br
L
L L
L L L
i
′




+
′
′ −
′
sinθ
ω
2 rr r
r
rr
r
rr
ss rr ms
r
L
L
L L L
sin cosθ θ+ ′
′



 +
′
′ −
2
uu
L
L L L
u
L
L L L
bs
ms
ss rr ms
r ar
ms
ss rr
−
′ −
′
−
′ −
2
sinθ
mms
r bru2 cos ,θ ′
ss LLC
18-16 Chapter 18
In these differ
variables. Theref
evolution of ind
motion, we have
The electroma
Wc,3 one has the
where P is the nu
Thus, the torsi
It should be em
is high. In partic
the number of po
the output torqu
Two torsional-
set of nonlinear 
Simulation o
The mathematica
and steady-state 
 
di
dt
L r
L L
i
L Lar ss r
ss
ar
ms ss′
= −
′
′ +2 as r r
s
r
ms ssi
r L L
+



 −2 ω θ θsin cos bs r r s ri r
L
−




−
2
ω θ θcos sin
ss rL L′
 
di
dt
L
L L
br
ss
′
= −
+
ssL L
 
T
P
e =
2
∂
P
= −
2
0866_book.fm  Page 16  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
 
ential equations, the angular velocity ωr and displacement θr are used as the state
ore, the torsional-mechanical equation of motion must be incorporated to describe the
uction nanomachines in the time domain. From Newton’s second law for rotational
 the following differential equations:gnetic torque developed by induction nanomotors must be found. Using the co-energy
 following relationship for the electromagnetic torque:
mber of poles.
onal-mechanical equations of motion are found to be 
phasized that the angular velocity of nanobiomotors is low whereas the output torque
ular, the angular velocity of the E. coli nanobiomotor is 20 rad/sec. This suggests that
les may be high. In fact, the output angular velocity of nanomachine is , and
e is given as .
mechanical differential equations are integrated with the circuitry dynamics to derive a
differential equations to model two-phase induction nanomotors. 
f Induction Nanomachines
l model developed is verified performing analysis and examining the transient dynamics
operation. We study an induction nanomotor with 100 nm stator outer diameter. The
L L Lrr ms ss′ − ′rrr ms ssL L L−   sss rr ms ss
m
L L L′ −  
ss
r ms
br r
ms
ss rr ms
r
L
i
L
L L L
u
2
2 2
−
′ −
′ −
ω θcos aas ms
ss rr ms
r bs
ss
ss rr ms
L
L L L
u
L
L L L
−
′ −
+
′ −
2 2
sinθ ′′uar ,
r
L
i
L L
L L
ss r
rr ms
br
ms ss
ss
′
′ −
′ +
′
2
rrr ms
as r r
s
ss
r
ms ss
L
i
r
L
L L
L−
−



 +2 ω θ θcos sin sss rr ms bs r r
s
ss
r
L L
i
r
L
L
′ −
+



2 ω θ θsin cos
mms
rr ms
ar r
ms
ss rr ms
r
L
i
L
L L L
2
2 2
′ −
′ +
′ −
ω θsin uu L
L L L
u
L
L L L
as
ms
ss rr ms
r bs
ss
ss rr ms
−
′ −
+
′ −
2
cosθ
22 ′
ubr .
d
dt J
T B T
d
dt
r
e m r L
r
r
ω
ω
θ
ω
= − −( )
=
1
W Pc abs abr r
r
abs
T sr r′( )
=
′
2
θ
∂θ
∂ θii ii
ii
LL, , ( )
∂∂θ
θ θ
θr
abr ms as bs
r r
r
P
L i i′ =  
− −
−
ii
2
sin cos
cos ssinθr
ar
br
ms as ar b
i
i
L i i i




′
′




′ + ss br r as br bs ar ri i i i i′( ) + ′ − ′( ) sin cos ,θ θ
d
dt
P
J
L i i i i i ir ms as ar bs br r as b
ω θ= − ′ + ′( ) + ′2
4
sin rr bs ar r
m
r L
r
r
i i
B
J
P
J
T
d
dt
− ′( )  − −
=
cos ,θ ω
θ
ω
2
ω ωrm P r=
2
T Tem
P
e= 2
ss LLC
Nanotechnology 18-17
nanomotor para
and materials th
rotor resistances 
is Lms = 0.000035
10–6 H. The fricti
to be 3 × 10–3 V 
The correspon
The angular velo
that the angular 
are performed fo
are integrated. T
nanomotor reach
effects should be
hysteresis, vibrat
18.8 Con
This chapter rese
tromagnetic-base
many ways. In p
society for 50 ye
have analogies an
The synthesis an
nanomachines. A
used in design an
oped. These elec
derived equation
nanomachines. T
unsolved basic p
high-performanc
nanomachines ca
and viability of t
FIGURE 18.7.2 A
Induction Nanomotor Angular Velocity, ωrm
2000
rad
sec( )
0866_book.fm  Page 17  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
meters are obtained using the dimension estimates, as well as technologies, processes,
at can be potentially used to fabricate this nanomachine. In particular, the stator and
are found to be rs = 3125 ohm and rr = 1890 ohm. The stator magnetizing inductance
 H, whereas the stator and rotor leakage inductances are estimated to be Lls = Llr = 3 ×
on is neglected (Bm = 0), and P = 2. The rated phase voltages and currents are estimated
and 1 µA, respectively.
ding files to simulate and analyze this induction nanomachine are developed in MATLAB.
city response (transient dynamics) is illustrated in Figure 18.7.2. It must be emphasized
velocity is controlled by changing the frequency of the phase voltages. The simulations
r an open-loop induction nanomotor without a controller, and the limits on the variables
he peak phase currents are 3 µA. The simulation results illustrate that the induction
es the rated angular velocity within 0.22 µsec. Although, in general additional nonlinear
 integrated in the modeling and analysis of nanomachines (nonlinear magnetization,
ion, friction, etc.), the realistic results are obtained.
clusions
arches benchmarking engineering problems in synthesis, design, and analysis of elec-
d nanomachines and motion nanodevices. This complements the nanotechnology in
articular, high-performance motion nano- and microdevices have been challenged the
ars, and very limited progress has been achieved to date. Different nanomachines that
d equivalence in nanobiomotors were proposed, prototyped, classified, and examined.
d classification solver can be applied to devise, refine (modify), and classify novel
ccurate assessment of nanomachine performance depends on mathematical models
d analysis. Therefore, high-fidelity mathematical models of nanomachines were devel-
tromechanical models were found in the form of nonlinear differential equations. The
s of motion allow the designer to study the dynamic and steady-state behavior of
his chapter performs fundamental and applied research in response to long-standing
roblems, engineering enterprise, and emerging evolutionary demands in synthesis of
e affordable nanomachines and motion nanodevices. It is important that the reported
n be fabricated achieving affordable high-yield fabrications due to simplicity, feasibility,
he motion nanodevices documented.
cceleration of a 100 nm induction nanomotor.
0 0.1 0.2 0.3 0.4 0.5
0
500
1000
1500
Time, (µsec)
ss LLC
18-18 Chapter 18
References
1. Drexler, E.
Interscienc
2. Berg, H. C
3. Lyshevski, S
4. Lyshevski, 
Microengin
5. Seeman, N
437–443, 1
6. Sinkarenko
trodynamic
7. Zilichev, Y
micromoto
0866_book.fm  Page 18  Thursday, August 5, 2004  3:37 PM
© 2005 by CRC Pre
K. 2002. Nanosystems: Molecular Machinery, Manufacturing, and Computations, Wiley
e, New York.
., The rotary motor of bacterial flagella. J. Annual Rev. Biochemistry, 72, 19–54, 2003.
.E., 2002. MEMS and NEMS: Systems, Devices, and Structures, CRC Press, Boca Raton, FL.
S.E. 1999, 2004. Nano- and Microelectromechanical Systems: Fundamentals of Nano- and
eering, 1st and 2nd editions, CRC Press, Boca Raton, FL.
.C., DNA engineering and its application to nanotechnology. Nanotechnology, 17,
999.
, V., Multiobjective classification of electromechanical energy conversion devices. Elec-
s, 1, 31–35, 1994.
.N., Numerically-analytical 3D model for calculations of disk type permanent magnet
rs. Proc. Conf. Power Electronics and Motion Control, Warsaw, Poland, 1994.
ss LLC
	Table of Contents
	Chapter 18
	Nanotechnology
	18.1 Introduction
	18.2 Applications of Engineering Biomimetics in Nanomachines Prototyping
	18.3 Nanomachines Synthesis and Classification
	18.4 Synthesis, Design and Analysis of Nanomachines
	18.5 Synchronous Reluctance Nanomachines
	Prototyping and Synthesis of Synchronous Reluctance Nanomachines
	Modeling, Analysis, and Design of Synchronous Reluctance Nanomachines
	18.6 Permanent-Magnet Synchronous Nanomachines
	Prototyping and Synthesis of Permanent-Magnet Synchronous Nanomachines
	Modeling of Permanent-Magnet Synchronous Nanomachines
	Optimization of Permanent-Magnet Synchronous Nanomachines
	18.7 Induction Nanomachines
	Prototyping and Synthesis of Induction Nanomachines
	Modeling of Induction Nanomachines
	Simulation of Induction Nanomachines
	18.8 Conclusions
	References